diff --git a/books/bookvol10.3.pamphlet b/books/bookvol10.3.pamphlet index 0799fb8..41005c6 100644 --- a/books/bookvol10.3.pamphlet +++ b/books/bookvol10.3.pamphlet @@ -311,6 +311,7 @@ in the bootstrap set. Thus, \chapter{Chapter A} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain AFFPL AffinePlane} + <>= )set break resume )sys rm -f AffinePlane.output @@ -388,6 +389,7 @@ AffinePlane(K):Exports == Implementation where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain AFFPLPS AffinePlaneOverPseudoAlgebraicClosureOfFiniteField} + <>= )set break resume )sys rm -f AffinePlaneOverPseudoAlgebraicClosureOfFiniteField.output @@ -487,6 +489,7 @@ AffinePlaneOverPseudoAlgebraicClosureOfFiniteField(K):Exports == Impl where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain AFFSP AffineSpace} + <>= )set break resume )sys rm -f AffineSpace.output @@ -668,6 +671,102 @@ AffineSpace(dim,K):Exports == Implementation where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain ALGSC AlgebraGivenByStructuralConstants} + +<>= +)set break resume +)sys rm -f AlgebraGivenByStructuralConstants.output +)spool AlgebraGivenByStructuralConstants.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show AlgebraGivenByStructuralConstants +--R AlgebraGivenByStructuralConstants(R: Field,n: PositiveInteger,ls: List Symbol,gamma: Vector Matrix R) is a domain constructor +--R Abbreviation for AlgebraGivenByStructuralConstants is ALGSC +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for ALGSC +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (SquareMatrix(n,R),%) -> % ?*? : (R,%) -> % +--R ?*? : (%,R) -> % ?*? : (%,%) -> % +--R ?*? : (Integer,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,PositiveInteger) -> % ?+? : (%,%) -> % +--R ?-? : (%,%) -> % -? : % -> % +--R ?=? : (%,%) -> Boolean 0 : () -> % +--R alternative? : () -> Boolean antiAssociative? : () -> Boolean +--R antiCommutative? : () -> Boolean antiCommutator : (%,%) -> % +--R apply : (Matrix R,%) -> % associative? : () -> Boolean +--R associator : (%,%,%) -> % basis : () -> Vector % +--R coerce : Vector R -> % coerce : % -> OutputForm +--R commutative? : () -> Boolean commutator : (%,%) -> % +--R convert : Vector R -> % convert : % -> Vector R +--R coordinates : % -> Vector R ?.? : (%,Integer) -> R +--R flexible? : () -> Boolean hash : % -> SingleInteger +--R jacobiIdentity? : () -> Boolean jordanAdmissible? : () -> Boolean +--R jordanAlgebra? : () -> Boolean latex : % -> String +--R leftAlternative? : () -> Boolean leftDiscriminant : () -> R +--R leftDiscriminant : Vector % -> R leftNorm : % -> R +--R leftTrace : % -> R leftTraceMatrix : () -> Matrix R +--R lieAdmissible? : () -> Boolean lieAlgebra? : () -> Boolean +--R powerAssociative? : () -> Boolean rank : () -> PositiveInteger +--R represents : Vector R -> % rightAlternative? : () -> Boolean +--R rightDiscriminant : () -> R rightDiscriminant : Vector % -> R +--R rightNorm : % -> R rightTrace : % -> R +--R rightTraceMatrix : () -> Matrix R sample : () -> % +--R someBasis : () -> Vector % zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean +--R ?*? : (NonNegativeInteger,%) -> % +--R associatorDependence : () -> List Vector R if R has INTDOM +--R conditionsForIdempotents : () -> List Polynomial R +--R conditionsForIdempotents : Vector % -> List Polynomial R +--R coordinates : Vector % -> Matrix R +--R coordinates : (Vector %,Vector %) -> Matrix R +--R coordinates : (%,Vector %) -> Vector R +--R leftCharacteristicPolynomial : % -> SparseUnivariatePolynomial R +--R leftMinimalPolynomial : % -> SparseUnivariatePolynomial R if R has INTDOM +--R leftPower : (%,PositiveInteger) -> % +--R leftRankPolynomial : () -> SparseUnivariatePolynomial Polynomial R if R has FIELD +--R leftRecip : % -> Union(%,"failed") if R has INTDOM +--R leftRegularRepresentation : % -> Matrix R +--R leftRegularRepresentation : (%,Vector %) -> Matrix R +--R leftTraceMatrix : Vector % -> Matrix R +--R leftUnit : () -> Union(%,"failed") if R has INTDOM +--R leftUnits : () -> Union(Record(particular: %,basis: List %),"failed") if R has INTDOM +--R noncommutativeJordanAlgebra? : () -> Boolean +--R plenaryPower : (%,PositiveInteger) -> % +--R recip : % -> Union(%,"failed") if R has INTDOM +--R represents : (Vector R,Vector %) -> % +--R rightCharacteristicPolynomial : % -> SparseUnivariatePolynomial R +--R rightMinimalPolynomial : % -> SparseUnivariatePolynomial R if R has INTDOM +--R rightPower : (%,PositiveInteger) -> % +--R rightRankPolynomial : () -> SparseUnivariatePolynomial Polynomial R if R has FIELD +--R rightRecip : % -> Union(%,"failed") if R has INTDOM +--R rightRegularRepresentation : % -> Matrix R +--R rightRegularRepresentation : (%,Vector %) -> Matrix R +--R rightTraceMatrix : Vector % -> Matrix R +--R rightUnit : () -> Union(%,"failed") if R has INTDOM +--R rightUnits : () -> Union(Record(particular: %,basis: List %),"failed") if R has INTDOM +--R structuralConstants : () -> Vector Matrix R +--R structuralConstants : Vector % -> Vector Matrix R +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R unit : () -> Union(%,"failed") if R has INTDOM +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +AlgebraGivenByStructuralConstants examples +==================================================================== + +See Also: +o )show AlgebraGivenByStructuralConstants + +@ + \pagehead{AlgebraGivenByStructuralConstants}{ALGSC} \pagepic{ps/v103algebragivenbystructuralconstants.ps}{ALGSC}{1.00} @@ -1144,6 +1243,188 @@ AlgebraGivenByStructuralConstants(R:Field, n : PositiveInteger,_ @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain ALGFF AlgebraicFunctionField} + +<>= +)set break resume +)sys rm -f AlgebraicFunctionField.output +)spool AlgebraicFunctionField.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show AlgebraicFunctionField +--R AlgebraicFunctionField(F: Field,UP: UnivariatePolynomialCategory F,UPUP: UnivariatePolynomialCategory Fraction UP,modulus: UPUP) is a domain constructor +--R Abbreviation for AlgebraicFunctionField is ALGFF +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for ALGFF +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (Fraction UP,%) -> % ?*? : (%,Fraction UP) -> % +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ?=? : (%,%) -> Boolean +--R 1 : () -> % 0 : () -> % +--R ?^? : (%,PositiveInteger) -> % basis : () -> Vector % +--R branchPoint? : UP -> Boolean branchPoint? : F -> Boolean +--R coerce : Fraction UP -> % coerce : Integer -> % +--R coerce : % -> OutputForm convert : UPUP -> % +--R convert : % -> UPUP convert : Vector Fraction UP -> % +--R convert : % -> Vector Fraction UP definingPolynomial : () -> UPUP +--R discriminant : () -> Fraction UP elt : (%,F,F) -> F +--R generator : () -> % genus : () -> NonNegativeInteger +--R hash : % -> SingleInteger integral? : (%,UP) -> Boolean +--R integral? : (%,F) -> Boolean integral? : % -> Boolean +--R integralBasis : () -> Vector % latex : % -> String +--R lift : % -> UPUP norm : % -> Fraction UP +--R one? : % -> Boolean primitivePart : % -> % +--R ramified? : UP -> Boolean ramified? : F -> Boolean +--R rank : () -> PositiveInteger rationalPoint? : (F,F) -> Boolean +--R recip : % -> Union(%,"failed") reduce : UPUP -> % +--R represents : (Vector UP,UP) -> % retract : % -> Fraction UP +--R sample : () -> % singular? : UP -> Boolean +--R singular? : F -> Boolean trace : % -> Fraction UP +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean +--R ?*? : (%,Fraction Integer) -> % if Fraction UP has FIELD +--R ?*? : (Fraction Integer,%) -> % if Fraction UP has FIELD +--R ?*? : (NonNegativeInteger,%) -> % +--R ?**? : (%,Integer) -> % if Fraction UP has FIELD +--R ?**? : (%,NonNegativeInteger) -> % +--R ?/? : (%,%) -> % if Fraction UP has FIELD +--R D : % -> % if Fraction UP has DIFRING and Fraction UP has FIELD or Fraction UP has FFIELDC +--R D : (%,NonNegativeInteger) -> % if Fraction UP has DIFRING and Fraction UP has FIELD or Fraction UP has FFIELDC +--R D : (%,Symbol) -> % if Fraction UP has FIELD and Fraction UP has PDRING SYMBOL +--R D : (%,List Symbol) -> % if Fraction UP has FIELD and Fraction UP has PDRING SYMBOL +--R D : (%,Symbol,NonNegativeInteger) -> % if Fraction UP has FIELD and Fraction UP has PDRING SYMBOL +--R D : (%,List Symbol,List NonNegativeInteger) -> % if Fraction UP has FIELD and Fraction UP has PDRING SYMBOL +--R D : (%,(Fraction UP -> Fraction UP)) -> % if Fraction UP has FIELD +--R D : (%,(Fraction UP -> Fraction UP),NonNegativeInteger) -> % if Fraction UP has FIELD +--R ?^? : (%,Integer) -> % if Fraction UP has FIELD +--R ?^? : (%,NonNegativeInteger) -> % +--R absolutelyIrreducible? : () -> Boolean +--R algSplitSimple : (%,(UP -> UP)) -> Record(num: %,den: UP,derivden: UP,gd: UP) +--R associates? : (%,%) -> Boolean if Fraction UP has FIELD +--R branchPointAtInfinity? : () -> Boolean +--R characteristic : () -> NonNegativeInteger +--R characteristicPolynomial : % -> UPUP +--R charthRoot : % -> Union(%,"failed") if Fraction UP has CHARNZ +--R charthRoot : % -> % if Fraction UP has FFIELDC +--R coerce : % -> % if Fraction UP has FIELD +--R coerce : Fraction Integer -> % if Fraction UP has FIELD or Fraction UP has RETRACT FRAC INT +--R complementaryBasis : Vector % -> Vector % +--R conditionP : Matrix % -> Union(Vector %,"failed") if Fraction UP has FFIELDC +--R coordinates : Vector % -> Matrix Fraction UP +--R coordinates : % -> Vector Fraction UP +--R coordinates : (Vector %,Vector %) -> Matrix Fraction UP +--R coordinates : (%,Vector %) -> Vector Fraction UP +--R createPrimitiveElement : () -> % if Fraction UP has FFIELDC +--R derivationCoordinates : (Vector %,(Fraction UP -> Fraction UP)) -> Matrix Fraction UP if Fraction UP has FIELD +--R differentiate : % -> % if Fraction UP has DIFRING and Fraction UP has FIELD or Fraction UP has FFIELDC +--R differentiate : (%,NonNegativeInteger) -> % if Fraction UP has DIFRING and Fraction UP has FIELD or Fraction UP has FFIELDC +--R differentiate : (%,Symbol) -> % if Fraction UP has FIELD and Fraction UP has PDRING SYMBOL +--R differentiate : (%,List Symbol) -> % if Fraction UP has FIELD and Fraction UP has PDRING SYMBOL +--R differentiate : (%,Symbol,NonNegativeInteger) -> % if Fraction UP has FIELD and Fraction UP has PDRING SYMBOL +--R differentiate : (%,List Symbol,List NonNegativeInteger) -> % if Fraction UP has FIELD and Fraction UP has PDRING SYMBOL +--R differentiate : (%,(UP -> UP)) -> % +--R differentiate : (%,(Fraction UP -> Fraction UP)) -> % if Fraction UP has FIELD +--R differentiate : (%,(Fraction UP -> Fraction UP),NonNegativeInteger) -> % if Fraction UP has FIELD +--R discreteLog : (%,%) -> Union(NonNegativeInteger,"failed") if Fraction UP has FFIELDC +--R discreteLog : % -> NonNegativeInteger if Fraction UP has FFIELDC +--R discriminant : Vector % -> Fraction UP +--R divide : (%,%) -> Record(quotient: %,remainder: %) if Fraction UP has FIELD +--R elliptic : () -> Union(UP,"failed") +--R euclideanSize : % -> NonNegativeInteger if Fraction UP has FIELD +--R expressIdealMember : (List %,%) -> Union(List %,"failed") if Fraction UP has FIELD +--R exquo : (%,%) -> Union(%,"failed") if Fraction UP has FIELD +--R extendedEuclidean : (%,%) -> Record(coef1: %,coef2: %,generator: %) if Fraction UP has FIELD +--R extendedEuclidean : (%,%,%) -> Union(Record(coef1: %,coef2: %),"failed") if Fraction UP has FIELD +--R factor : % -> Factored % if Fraction UP has FIELD +--R factorsOfCyclicGroupSize : () -> List Record(factor: Integer,exponent: Integer) if Fraction UP has FFIELDC +--R gcd : (%,%) -> % if Fraction UP has FIELD +--R gcd : List % -> % if Fraction UP has FIELD +--R gcdPolynomial : (SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial % if Fraction UP has FIELD +--R hyperelliptic : () -> Union(UP,"failed") +--R index : PositiveInteger -> % if Fraction UP has FINITE +--R init : () -> % if Fraction UP has FFIELDC +--R integralAtInfinity? : % -> Boolean +--R integralBasisAtInfinity : () -> Vector % +--R integralCoordinates : % -> Record(num: Vector UP,den: UP) +--R integralDerivationMatrix : (UP -> UP) -> Record(num: Matrix UP,den: UP) +--R integralMatrix : () -> Matrix Fraction UP +--R integralMatrixAtInfinity : () -> Matrix Fraction UP +--R integralRepresents : (Vector UP,UP) -> % +--R inv : % -> % if Fraction UP has FIELD +--R inverseIntegralMatrix : () -> Matrix Fraction UP +--R inverseIntegralMatrixAtInfinity : () -> Matrix Fraction UP +--R knownInfBasis : NonNegativeInteger -> Void +--R lcm : (%,%) -> % if Fraction UP has FIELD +--R lcm : List % -> % if Fraction UP has FIELD +--R lookup : % -> PositiveInteger if Fraction UP has FINITE +--R minimalPolynomial : % -> UPUP if Fraction UP has FIELD +--R multiEuclidean : (List %,%) -> Union(List %,"failed") if Fraction UP has FIELD +--R nextItem : % -> Union(%,"failed") if Fraction UP has FFIELDC +--R nonSingularModel : Symbol -> List Polynomial F if F has FIELD +--R normalizeAtInfinity : Vector % -> Vector % +--R numberOfComponents : () -> NonNegativeInteger +--R order : % -> OnePointCompletion PositiveInteger if Fraction UP has FFIELDC +--R order : % -> PositiveInteger if Fraction UP has FFIELDC +--R prime? : % -> Boolean if Fraction UP has FIELD +--R primeFrobenius : % -> % if Fraction UP has FFIELDC +--R primeFrobenius : (%,NonNegativeInteger) -> % if Fraction UP has FFIELDC +--R primitive? : % -> Boolean if Fraction UP has FFIELDC +--R primitiveElement : () -> % if Fraction UP has FFIELDC +--R principalIdeal : List % -> Record(coef: List %,generator: %) if Fraction UP has FIELD +--R ?quo? : (%,%) -> % if Fraction UP has FIELD +--R ramifiedAtInfinity? : () -> Boolean +--R random : () -> % if Fraction UP has FINITE +--R rationalPoints : () -> List List F if F has FINITE +--R reduce : Fraction UPUP -> Union(%,"failed") if Fraction UP has FIELD +--R reduceBasisAtInfinity : Vector % -> Vector % +--R reducedSystem : Matrix % -> Matrix Fraction UP +--R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix Fraction UP,vec: Vector Fraction UP) +--R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix Integer,vec: Vector Integer) if Fraction UP has LINEXP INT +--R reducedSystem : Matrix % -> Matrix Integer if Fraction UP has LINEXP INT +--R regularRepresentation : % -> Matrix Fraction UP +--R regularRepresentation : (%,Vector %) -> Matrix Fraction UP +--R ?rem? : (%,%) -> % if Fraction UP has FIELD +--R representationType : () -> Union("prime",polynomial,normal,cyclic) if Fraction UP has FFIELDC +--R represents : Vector Fraction UP -> % +--R represents : (Vector Fraction UP,Vector %) -> % +--R retract : % -> Fraction Integer if Fraction UP has RETRACT FRAC INT +--R retract : % -> Integer if Fraction UP has RETRACT INT +--R retractIfCan : % -> Union(Fraction UP,"failed") +--R retractIfCan : % -> Union(Fraction Integer,"failed") if Fraction UP has RETRACT FRAC INT +--R retractIfCan : % -> Union(Integer,"failed") if Fraction UP has RETRACT INT +--R singularAtInfinity? : () -> Boolean +--R size : () -> NonNegativeInteger if Fraction UP has FINITE +--R sizeLess? : (%,%) -> Boolean if Fraction UP has FIELD +--R squareFree : % -> Factored % if Fraction UP has FIELD +--R squareFreePart : % -> % if Fraction UP has FIELD +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R tableForDiscreteLogarithm : Integer -> Table(PositiveInteger,NonNegativeInteger) if Fraction UP has FFIELDC +--R traceMatrix : () -> Matrix Fraction UP +--R traceMatrix : Vector % -> Matrix Fraction UP +--R unit? : % -> Boolean if Fraction UP has FIELD +--R unitCanonical : % -> % if Fraction UP has FIELD +--R unitNormal : % -> Record(unit: %,canonical: %,associate: %) if Fraction UP has FIELD +--R yCoordinates : % -> Record(num: Vector UP,den: UP) +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +AlgebraicFunctionField examples +==================================================================== + +See Also: +o )show AlgebraicFunctionField + +@ + \pagehead{AlgebraicFunctionField}{ALGFF} \pagepic{ps/v103algebraicfunctionfield.ps}{ALGFF}{1.00} {\bf See}\\ @@ -1414,6 +1695,144 @@ AlgebraicFunctionField(F, UP, UPUP, modulus): Exports == Impl where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain AN AlgebraicNumber} + +<>= +)set break resume +)sys rm -f AlgebraicNumber.output +)spool AlgebraicNumber.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show AlgebraicNumber +--R AlgebraicNumber is a domain constructor +--R Abbreviation for AlgebraicNumber is AN +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for AN +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (PositiveInteger,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (%,%) -> % ?*? : (%,Fraction Integer) -> % +--R ?*? : (Fraction Integer,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?**? : (%,Integer) -> % ?**? : (%,Fraction Integer) -> % +--R ?+? : (%,%) -> % -? : % -> % +--R ?-? : (%,%) -> % ?/? : (%,%) -> % +--R ? Boolean ?<=? : (%,%) -> Boolean +--R ?=? : (%,%) -> Boolean ?>? : (%,%) -> Boolean +--R ?>=? : (%,%) -> Boolean D : % -> % +--R D : (%,NonNegativeInteger) -> % 1 : () -> % +--R 0 : () -> % ?^? : (%,PositiveInteger) -> % +--R ?^? : (%,Integer) -> % associates? : (%,%) -> Boolean +--R belong? : BasicOperator -> Boolean box : List % -> % +--R box : % -> % coerce : Integer -> % +--R coerce : % -> % coerce : Fraction Integer -> % +--R coerce : Kernel % -> % coerce : % -> OutputForm +--R convert : % -> Complex Float convert : % -> DoubleFloat +--R convert : % -> Float differentiate : % -> % +--R distribute : (%,%) -> % distribute : % -> % +--R elt : (BasicOperator,%,%) -> % elt : (BasicOperator,%) -> % +--R eval : (%,List %,List %) -> % eval : (%,%,%) -> % +--R eval : (%,Equation %) -> % eval : (%,List Equation %) -> % +--R eval : (%,Kernel %,%) -> % factor : % -> Factored % +--R freeOf? : (%,Symbol) -> Boolean freeOf? : (%,%) -> Boolean +--R gcd : (%,%) -> % gcd : List % -> % +--R hash : % -> SingleInteger height : % -> NonNegativeInteger +--R inv : % -> % is? : (%,Symbol) -> Boolean +--R kernel : (BasicOperator,%) -> % kernels : % -> List Kernel % +--R latex : % -> String lcm : (%,%) -> % +--R lcm : List % -> % map : ((% -> %),Kernel %) -> % +--R max : (%,%) -> % min : (%,%) -> % +--R norm : (%,List Kernel %) -> % norm : (%,Kernel %) -> % +--R nthRoot : (%,Integer) -> % one? : % -> Boolean +--R paren : List % -> % paren : % -> % +--R prime? : % -> Boolean ?quo? : (%,%) -> % +--R recip : % -> Union(%,"failed") reduce : % -> % +--R ?rem? : (%,%) -> % retract : % -> Fraction Integer +--R retract : % -> Integer retract : % -> Kernel % +--R rootOf : Polynomial % -> % rootsOf : Polynomial % -> List % +--R sample : () -> % sizeLess? : (%,%) -> Boolean +--R sqrt : % -> % squareFree : % -> Factored % +--R squareFreePart : % -> % subst : (%,Equation %) -> % +--R tower : % -> List Kernel % unit? : % -> Boolean +--R unitCanonical : % -> % zero? : % -> Boolean +--R zeroOf : Polynomial % -> % zerosOf : Polynomial % -> List % +--R ?~=? : (%,%) -> Boolean +--R ?*? : (NonNegativeInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % +--R ?^? : (%,NonNegativeInteger) -> % +--R characteristic : () -> NonNegativeInteger +--R coerce : SparseMultivariatePolynomial(Integer,Kernel %) -> % +--R definingPolynomial : % -> % if $ has RING +--R denom : % -> SparseMultivariatePolynomial(Integer,Kernel %) +--R differentiate : (%,NonNegativeInteger) -> % +--R divide : (%,%) -> Record(quotient: %,remainder: %) +--R elt : (BasicOperator,List %) -> % +--R elt : (BasicOperator,%,%,%,%) -> % +--R elt : (BasicOperator,%,%,%) -> % +--R euclideanSize : % -> NonNegativeInteger +--R eval : (%,BasicOperator,(% -> %)) -> % +--R eval : (%,BasicOperator,(List % -> %)) -> % +--R eval : (%,List BasicOperator,List (List % -> %)) -> % +--R eval : (%,List BasicOperator,List (% -> %)) -> % +--R eval : (%,Symbol,(% -> %)) -> % +--R eval : (%,Symbol,(List % -> %)) -> % +--R eval : (%,List Symbol,List (List % -> %)) -> % +--R eval : (%,List Symbol,List (% -> %)) -> % +--R eval : (%,List Kernel %,List %) -> % +--R even? : % -> Boolean if $ has RETRACT INT +--R expressIdealMember : (List %,%) -> Union(List %,"failed") +--R exquo : (%,%) -> Union(%,"failed") +--R extendedEuclidean : (%,%) -> Record(coef1: %,coef2: %,generator: %) +--R extendedEuclidean : (%,%,%) -> Union(Record(coef1: %,coef2: %),"failed") +--R gcdPolynomial : (SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial % +--R is? : (%,BasicOperator) -> Boolean +--R kernel : (BasicOperator,List %) -> % +--R mainKernel : % -> Union(Kernel %,"failed") +--R minPoly : Kernel % -> SparseUnivariatePolynomial % if $ has RING +--R multiEuclidean : (List %,%) -> Union(List %,"failed") +--R norm : (SparseUnivariatePolynomial %,List Kernel %) -> SparseUnivariatePolynomial % +--R norm : (SparseUnivariatePolynomial %,Kernel %) -> SparseUnivariatePolynomial % +--R numer : % -> SparseMultivariatePolynomial(Integer,Kernel %) +--R odd? : % -> Boolean if $ has RETRACT INT +--R operator : BasicOperator -> BasicOperator +--R operators : % -> List BasicOperator +--R principalIdeal : List % -> Record(coef: List %,generator: %) +--R reducedSystem : Matrix % -> Matrix Fraction Integer +--R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix Fraction Integer,vec: Vector Fraction Integer) +--R reducedSystem : Matrix % -> Matrix Integer +--R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix Integer,vec: Vector Integer) +--R retractIfCan : % -> Union(Fraction Integer,"failed") +--R retractIfCan : % -> Union(Integer,"failed") +--R retractIfCan : % -> Union(Kernel %,"failed") +--R rootOf : SparseUnivariatePolynomial % -> % +--R rootOf : (SparseUnivariatePolynomial %,Symbol) -> % +--R rootsOf : SparseUnivariatePolynomial % -> List % +--R rootsOf : (SparseUnivariatePolynomial %,Symbol) -> List % +--R subst : (%,List Kernel %,List %) -> % +--R subst : (%,List Equation %) -> % +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R unitNormal : % -> Record(unit: %,canonical: %,associate: %) +--R zeroOf : SparseUnivariatePolynomial % -> % +--R zeroOf : (SparseUnivariatePolynomial %,Symbol) -> % +--R zerosOf : SparseUnivariatePolynomial % -> List % +--R zerosOf : (SparseUnivariatePolynomial %,Symbol) -> List % +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +AlgebraicNumber examples +==================================================================== + +See Also: +o )show AlgebraicNumber + +@ + \pagehead{AlgebraicNumber}{AN} \pagepic{ps/v103algebraicnumber.ps}{AN}{1.00} {\bf See}\\ @@ -1567,6 +1986,42 @@ AlgebraicNumber(): Exports == Implementation where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain ANON AnonymousFunction} + +<>= +)set break resume +)sys rm -f AnonymousFunction.output +)spool AnonymousFunction.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show AnonymousFunction +--R AnonymousFunction is a domain constructor +--R Abbreviation for AnonymousFunction is ANON +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for ANON +--R +--R------------------------------- Operations -------------------------------- +--R ?=? : (%,%) -> Boolean coerce : % -> OutputForm +--R hash : % -> SingleInteger latex : % -> String +--R ?~=? : (%,%) -> Boolean +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +AnonymousFunction examples +==================================================================== + +See Also: +o )show AnonymousFunction + +@ + \pagehead{AnonymousFunction}{ANON} \pagepic{ps/v103anonymousfunction.ps}{ANON}{1.00} @@ -1599,6 +2054,62 @@ AnonymousFunction():SetCategory == add @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain ANTISYM AntiSymm} + +<>= +)set break resume +)sys rm -f AntiSymm.output +)spool AntiSymm.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show AntiSymm +--R AntiSymm(R: Ring,lVar: List Symbol) is a domain constructor +--R Abbreviation for AntiSymm is ANTISYM +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for ANTISYM +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (R,%) -> % ?*? : (%,%) -> % +--R ?*? : (Integer,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,PositiveInteger) -> % ?+? : (%,%) -> % +--R ?-? : (%,%) -> % -? : % -> % +--R ?=? : (%,%) -> Boolean 1 : () -> % +--R 0 : () -> % ?^? : (%,PositiveInteger) -> % +--R coefficient : (%,%) -> R coerce : R -> % +--R coerce : Integer -> % coerce : % -> OutputForm +--R degree : % -> NonNegativeInteger exp : List Integer -> % +--R hash : % -> SingleInteger homogeneous? : % -> Boolean +--R latex : % -> String leadingBasisTerm : % -> % +--R leadingCoefficient : % -> R map : ((R -> R),%) -> % +--R one? : % -> Boolean recip : % -> Union(%,"failed") +--R reductum : % -> % retract : % -> R +--R retractable? : % -> Boolean sample : () -> % +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean +--R ?*? : (NonNegativeInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % +--R ?^? : (%,NonNegativeInteger) -> % +--R characteristic : () -> NonNegativeInteger +--R generator : NonNegativeInteger -> % +--R retractIfCan : % -> Union(R,"failed") +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +AntiSymm examples +==================================================================== + +See Also: +o )show AntiSymm + +@ + \pagehead{AntiSymm}{ANTISYM} \pagepic{ps/v103antisymm.ps}{ANTISYM}{1.00} {\bf See}\\ @@ -1843,6 +2354,7 @@ AntiSymm(R:Ring, lVar:List Symbol): Export == Implement where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain ANY Any} + <>= )set break resume )sys rm -f Any.output @@ -2197,6 +2709,7 @@ Any(): SetCategory with @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain ASTACK ArrayStack} + <>= )set break resume )sys rm -f ArrayStack.output @@ -3068,6 +3581,53 @@ ArrayStack(S:SetCategory): StackAggregate(S) with @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain ASP1 Asp1} + +<>= +)set break resume +)sys rm -f Asp1.output +)spool Asp1.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show Asp1 +--R Asp1 name: Symbol is a domain constructor +--R Abbreviation for Asp1 is ASP1 +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for ASP1 +--R +--R------------------------------- Operations -------------------------------- +--R coerce : FortranCode -> % coerce : List FortranCode -> % +--R coerce : % -> OutputForm outputAsFortran : % -> Void +--R retract : Polynomial Integer -> % retract : Polynomial Float -> % +--R retract : Expression Integer -> % retract : Expression Float -> % +--R coerce : FortranExpression([construct,QUOTEX],[construct],MachineFloat) -> % +--R coerce : Record(localSymbols: SymbolTable,code: List FortranCode) -> % +--R retract : Fraction Polynomial Integer -> % +--R retract : Fraction Polynomial Float -> % +--R retractIfCan : Fraction Polynomial Integer -> Union(%,"failed") +--R retractIfCan : Fraction Polynomial Float -> Union(%,"failed") +--R retractIfCan : Polynomial Integer -> Union(%,"failed") +--R retractIfCan : Polynomial Float -> Union(%,"failed") +--R retractIfCan : Expression Integer -> Union(%,"failed") +--R retractIfCan : Expression Float -> Union(%,"failed") +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +Asp1 examples +==================================================================== + +See Also: +o )show Asp1 + +@ + \pagehead{Asp1}{ASP1} \pagepic{ps/v103asp1.ps}{ASP1}{1.00} @@ -3191,6 +3751,55 @@ Asp1(name): Exports == Implementation where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain ASP10 Asp10} + +<>= +)set break resume +)sys rm -f Asp10.output +)spool Asp10.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show Asp10 +--R Asp10 name: Symbol is a domain constructor +--R Abbreviation for Asp10 is ASP10 +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for ASP10 +--R +--R------------------------------- Operations -------------------------------- +--R coerce : FortranCode -> % coerce : List FortranCode -> % +--R coerce : % -> OutputForm outputAsFortran : % -> Void +--R coerce : Vector FortranExpression([construct,QUOTEJINT,QUOTEX,QUOTEELAM],[construct],MachineFloat) -> % +--R coerce : Record(localSymbols: SymbolTable,code: List FortranCode) -> % +--R retract : Vector Fraction Polynomial Integer -> % +--R retract : Vector Fraction Polynomial Float -> % +--R retract : Vector Polynomial Integer -> % +--R retract : Vector Polynomial Float -> % +--R retract : Vector Expression Integer -> % +--R retract : Vector Expression Float -> % +--R retractIfCan : Vector Fraction Polynomial Integer -> Union(%,"failed") +--R retractIfCan : Vector Fraction Polynomial Float -> Union(%,"failed") +--R retractIfCan : Vector Polynomial Integer -> Union(%,"failed") +--R retractIfCan : Vector Polynomial Float -> Union(%,"failed") +--R retractIfCan : Vector Expression Integer -> Union(%,"failed") +--R retractIfCan : Vector Expression Float -> Union(%,"failed") +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +Asp10 examples +==================================================================== + +See Also: +o )show Asp10 + +@ + \pagehead{Asp10}{ASP10} \pagepic{ps/v103asp10.ps}{ASP10}{1.00} @@ -3346,6 +3955,41 @@ Asp10(name): Exports == Implementation where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain ASP12 Asp12} + +<>= +)set break resume +)sys rm -f Asp12.output +)spool Asp12.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show Asp12 +--R Asp12 name: Symbol is a domain constructor +--R Abbreviation for Asp12 is ASP12 +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for ASP12 +--R +--R------------------------------- Operations -------------------------------- +--R coerce : % -> OutputForm outputAsFortran : () -> Void +--R outputAsFortran : % -> Void +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +Asp12 examples +==================================================================== + +See Also: +o )show Asp12 + +@ + \pagehead{Asp12}{ASP12} \pagepic{ps/v103asp12.ps}{ASP12}{1.00} @@ -3429,6 +4073,55 @@ Asp12(name): Exports == Implementation where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain ASP19 Asp19} + +<>= +)set break resume +)sys rm -f Asp19.output +)spool Asp19.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show Asp19 +--R Asp19 name: Symbol is a domain constructor +--R Abbreviation for Asp19 is ASP19 +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for ASP19 +--R +--R------------------------------- Operations -------------------------------- +--R coerce : FortranCode -> % coerce : List FortranCode -> % +--R coerce : % -> OutputForm outputAsFortran : % -> Void +--R coerce : Vector FortranExpression([construct],[construct,QUOTEXC],MachineFloat) -> % +--R coerce : Record(localSymbols: SymbolTable,code: List FortranCode) -> % +--R retract : Vector Fraction Polynomial Integer -> % +--R retract : Vector Fraction Polynomial Float -> % +--R retract : Vector Polynomial Integer -> % +--R retract : Vector Polynomial Float -> % +--R retract : Vector Expression Integer -> % +--R retract : Vector Expression Float -> % +--R retractIfCan : Vector Fraction Polynomial Integer -> Union(%,"failed") +--R retractIfCan : Vector Fraction Polynomial Float -> Union(%,"failed") +--R retractIfCan : Vector Polynomial Integer -> Union(%,"failed") +--R retractIfCan : Vector Polynomial Float -> Union(%,"failed") +--R retractIfCan : Vector Expression Integer -> Union(%,"failed") +--R retractIfCan : Vector Expression Float -> Union(%,"failed") +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +Asp19 examples +==================================================================== + +See Also: +o )show Asp19 + +@ + \pagehead{Asp19}{ASP19} \pagepic{ps/v103asp19.ps}{ASP19}{1.00} @@ -3718,6 +4411,55 @@ Asp19(name): Exports == Implementation where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain ASP20 Asp20} + +<>= +)set break resume +)sys rm -f Asp20.output +)spool Asp20.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show Asp20 +--R Asp20 name: Symbol is a domain constructor +--R Abbreviation for Asp20 is ASP20 +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for ASP20 +--R +--R------------------------------- Operations -------------------------------- +--R coerce : FortranCode -> % coerce : List FortranCode -> % +--R coerce : % -> OutputForm outputAsFortran : % -> Void +--R coerce : Matrix FortranExpression([construct],[construct,QUOTEX,QUOTEHESS],MachineFloat) -> % +--R coerce : Record(localSymbols: SymbolTable,code: List FortranCode) -> % +--R retract : Matrix Fraction Polynomial Integer -> % +--R retract : Matrix Fraction Polynomial Float -> % +--R retract : Matrix Polynomial Integer -> % +--R retract : Matrix Polynomial Float -> % +--R retract : Matrix Expression Integer -> % +--R retract : Matrix Expression Float -> % +--R retractIfCan : Matrix Fraction Polynomial Integer -> Union(%,"failed") +--R retractIfCan : Matrix Fraction Polynomial Float -> Union(%,"failed") +--R retractIfCan : Matrix Polynomial Integer -> Union(%,"failed") +--R retractIfCan : Matrix Polynomial Float -> Union(%,"failed") +--R retractIfCan : Matrix Expression Integer -> Union(%,"failed") +--R retractIfCan : Matrix Expression Float -> Union(%,"failed") +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +Asp20 examples +==================================================================== + +See Also: +o )show Asp20 + +@ + \pagehead{Asp20}{ASP20} \pagepic{ps/v103asp20.ps}{ASP20}{1.00} @@ -3899,6 +4641,53 @@ Asp20(name): Exports == Implementation where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain ASP24 Asp24} + +<>= +)set break resume +)sys rm -f Asp24.output +)spool Asp24.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show Asp24 +--R Asp24 name: Symbol is a domain constructor +--R Abbreviation for Asp24 is ASP24 +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for ASP24 +--R +--R------------------------------- Operations -------------------------------- +--R coerce : FortranCode -> % coerce : List FortranCode -> % +--R coerce : % -> OutputForm outputAsFortran : % -> Void +--R retract : Polynomial Integer -> % retract : Polynomial Float -> % +--R retract : Expression Integer -> % retract : Expression Float -> % +--R coerce : FortranExpression([construct],[construct,QUOTEXC],MachineFloat) -> % +--R coerce : Record(localSymbols: SymbolTable,code: List FortranCode) -> % +--R retract : Fraction Polynomial Integer -> % +--R retract : Fraction Polynomial Float -> % +--R retractIfCan : Fraction Polynomial Integer -> Union(%,"failed") +--R retractIfCan : Fraction Polynomial Float -> Union(%,"failed") +--R retractIfCan : Polynomial Integer -> Union(%,"failed") +--R retractIfCan : Polynomial Float -> Union(%,"failed") +--R retractIfCan : Expression Integer -> Union(%,"failed") +--R retractIfCan : Expression Float -> Union(%,"failed") +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +Asp24 examples +==================================================================== + +See Also: +o )show Asp24 + +@ + \pagehead{Asp24}{ASP24} \pagepic{ps/v103asp24.ps}{ASP24}{1.00} @@ -4032,6 +4821,43 @@ Asp24(name): Exports == Implementation where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain ASP27 Asp27} + +<>= +)set break resume +)sys rm -f Asp27.output +)spool Asp27.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show Asp27 +--R Asp27 name: Symbol is a domain constructor +--R Abbreviation for Asp27 is ASP27 +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for ASP27 +--R +--R------------------------------- Operations -------------------------------- +--R coerce : FortranCode -> % coerce : List FortranCode -> % +--R coerce : Matrix MachineFloat -> % coerce : % -> OutputForm +--R outputAsFortran : % -> Void +--R coerce : Record(localSymbols: SymbolTable,code: List FortranCode) -> % +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +Asp27 examples +==================================================================== + +See Also: +o )show Asp27 + +@ + \pagehead{Asp27}{ASP27} \pagepic{ps/v103asp27.ps}{ASP27}{1.00} @@ -4144,6 +4970,43 @@ Asp27(name): Exports == Implementation where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain ASP28 Asp28} + +<>= +)set break resume +)sys rm -f Asp28.output +)spool Asp28.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show Asp28 +--R Asp28 name: Symbol is a domain constructor +--R Abbreviation for Asp28 is ASP28 +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for ASP28 +--R +--R------------------------------- Operations -------------------------------- +--R coerce : FortranCode -> % coerce : List FortranCode -> % +--R coerce : Matrix MachineFloat -> % coerce : % -> OutputForm +--R outputAsFortran : % -> Void +--R coerce : Record(localSymbols: SymbolTable,code: List FortranCode) -> % +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +Asp28 examples +==================================================================== + +See Also: +o )show Asp28 + +@ + \pagehead{Asp28}{ASP28} \pagepic{ps/v103asp28.ps}{ASP28}{1.00} @@ -4367,6 +5230,41 @@ Asp28(name): Exports == Implementation where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain ASP29 Asp29} + +<>= +)set break resume +)sys rm -f Asp29.output +)spool Asp29.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show Asp29 +--R Asp29 name: Symbol is a domain constructor +--R Abbreviation for Asp29 is ASP29 +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for ASP29 +--R +--R------------------------------- Operations -------------------------------- +--R coerce : % -> OutputForm outputAsFortran : () -> Void +--R outputAsFortran : % -> Void +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +Asp29 examples +==================================================================== + +See Also: +o )show Asp29 + +@ + \pagehead{Asp29}{ASP29} \pagepic{ps/v103asp29.ps}{ASP29}{1.00} @@ -4453,6 +5351,43 @@ Asp29(name): Exports == Implementation where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain ASP30 Asp30} + +<>= +)set break resume +)sys rm -f Asp30.output +)spool Asp30.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show Asp30 +--R Asp30 name: Symbol is a domain constructor +--R Abbreviation for Asp30 is ASP30 +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for ASP30 +--R +--R------------------------------- Operations -------------------------------- +--R coerce : FortranCode -> % coerce : List FortranCode -> % +--R coerce : Matrix MachineFloat -> % coerce : % -> OutputForm +--R outputAsFortran : % -> Void +--R coerce : Record(localSymbols: SymbolTable,code: List FortranCode) -> % +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +Asp30 examples +==================================================================== + +See Also: +o )show Asp30 + +@ + \pagehead{Asp30}{ASP30} \pagepic{ps/v103asp30.ps}{ASP30}{1.00} @@ -4595,6 +5530,55 @@ Asp30(name): Exports == Implementation where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain ASP31 Asp31} + +<>= +)set break resume +)sys rm -f Asp31.output +)spool Asp31.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show Asp31 +--R Asp31 name: Symbol is a domain constructor +--R Abbreviation for Asp31 is ASP31 +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for ASP31 +--R +--R------------------------------- Operations -------------------------------- +--R coerce : FortranCode -> % coerce : List FortranCode -> % +--R coerce : % -> OutputForm outputAsFortran : % -> Void +--R coerce : Vector FortranExpression([construct,QUOTEX],[construct,QUOTEY],MachineFloat) -> % +--R coerce : Record(localSymbols: SymbolTable,code: List FortranCode) -> % +--R retract : Vector Fraction Polynomial Integer -> % +--R retract : Vector Fraction Polynomial Float -> % +--R retract : Vector Polynomial Integer -> % +--R retract : Vector Polynomial Float -> % +--R retract : Vector Expression Integer -> % +--R retract : Vector Expression Float -> % +--R retractIfCan : Vector Fraction Polynomial Integer -> Union(%,"failed") +--R retractIfCan : Vector Fraction Polynomial Float -> Union(%,"failed") +--R retractIfCan : Vector Polynomial Integer -> Union(%,"failed") +--R retractIfCan : Vector Polynomial Float -> Union(%,"failed") +--R retractIfCan : Vector Expression Integer -> Union(%,"failed") +--R retractIfCan : Vector Expression Float -> Union(%,"failed") +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +Asp31 examples +==================================================================== + +See Also: +o )show Asp31 + +@ + \pagehead{Asp31}{ASP31} \pagepic{ps/v103asp31.ps}{ASP31}{1.00} @@ -4773,6 +5757,41 @@ Asp31(name): Exports == Implementation where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain ASP33 Asp33} + +<>= +)set break resume +)sys rm -f Asp33.output +)spool Asp33.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show Asp33 +--R Asp33 name: Symbol is a domain constructor +--R Abbreviation for Asp33 is ASP33 +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for ASP33 +--R +--R------------------------------- Operations -------------------------------- +--R coerce : % -> OutputForm outputAsFortran : () -> Void +--R outputAsFortran : % -> Void +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +Asp33 examples +==================================================================== + +See Also: +o )show Asp33 + +@ + \pagehead{Asp33}{ASP33} \pagepic{ps/v103asp33.ps}{ASP33}{1.00} @@ -4839,6 +5858,43 @@ Asp33(name): Exports == Implementation where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain ASP34 Asp34} + +<>= +)set break resume +)sys rm -f Asp34.output +)spool Asp34.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show Asp34 +--R Asp34 name: Symbol is a domain constructor +--R Abbreviation for Asp34 is ASP34 +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for ASP34 +--R +--R------------------------------- Operations -------------------------------- +--R coerce : FortranCode -> % coerce : List FortranCode -> % +--R coerce : Matrix MachineFloat -> % coerce : % -> OutputForm +--R outputAsFortran : % -> Void +--R coerce : Record(localSymbols: SymbolTable,code: List FortranCode) -> % +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +Asp34 examples +==================================================================== + +See Also: +o )show Asp34 + +@ + \pagehead{Asp34}{ASP34} \pagepic{ps/v103asp34.ps}{ASP34}{1.00} @@ -4953,6 +6009,55 @@ Asp34(name): Exports == Implementation where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain ASP35 Asp35} + +<>= +)set break resume +)sys rm -f Asp35.output +)spool Asp35.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show Asp35 +--R Asp35 name: Symbol is a domain constructor +--R Abbreviation for Asp35 is ASP35 +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for ASP35 +--R +--R------------------------------- Operations -------------------------------- +--R coerce : FortranCode -> % coerce : List FortranCode -> % +--R coerce : % -> OutputForm outputAsFortran : % -> Void +--R coerce : Vector FortranExpression([construct],[construct,QUOTEX],MachineFloat) -> % +--R coerce : Record(localSymbols: SymbolTable,code: List FortranCode) -> % +--R retract : Vector Fraction Polynomial Integer -> % +--R retract : Vector Fraction Polynomial Float -> % +--R retract : Vector Polynomial Integer -> % +--R retract : Vector Polynomial Float -> % +--R retract : Vector Expression Integer -> % +--R retract : Vector Expression Float -> % +--R retractIfCan : Vector Fraction Polynomial Integer -> Union(%,"failed") +--R retractIfCan : Vector Fraction Polynomial Float -> Union(%,"failed") +--R retractIfCan : Vector Polynomial Integer -> Union(%,"failed") +--R retractIfCan : Vector Polynomial Float -> Union(%,"failed") +--R retractIfCan : Vector Expression Integer -> Union(%,"failed") +--R retractIfCan : Vector Expression Float -> Union(%,"failed") +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +Asp35 examples +==================================================================== + +See Also: +o )show Asp35 + +@ + \pagehead{Asp35}{ASP35} \pagepic{ps/v103asp35.ps}{ASP35}{1.00} @@ -5141,6 +6246,53 @@ Asp35(name): Exports == Implementation where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain ASP4 Asp4} + +<>= +)set break resume +)sys rm -f Asp4.output +)spool Asp4.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show Asp4 +--R Asp4 name: Symbol is a domain constructor +--R Abbreviation for Asp4 is ASP4 +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for ASP4 +--R +--R------------------------------- Operations -------------------------------- +--R coerce : FortranCode -> % coerce : List FortranCode -> % +--R coerce : % -> OutputForm outputAsFortran : % -> Void +--R retract : Polynomial Integer -> % retract : Polynomial Float -> % +--R retract : Expression Integer -> % retract : Expression Float -> % +--R coerce : FortranExpression([construct],[construct,QUOTEX],MachineFloat) -> % +--R coerce : Record(localSymbols: SymbolTable,code: List FortranCode) -> % +--R retract : Fraction Polynomial Integer -> % +--R retract : Fraction Polynomial Float -> % +--R retractIfCan : Fraction Polynomial Integer -> Union(%,"failed") +--R retractIfCan : Fraction Polynomial Float -> Union(%,"failed") +--R retractIfCan : Polynomial Integer -> Union(%,"failed") +--R retractIfCan : Polynomial Float -> Union(%,"failed") +--R retractIfCan : Expression Integer -> Union(%,"failed") +--R retractIfCan : Expression Float -> Union(%,"failed") +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +Asp4 examples +==================================================================== + +See Also: +o )show Asp4 + +@ + \pagehead{Asp4}{ASP4} \pagepic{ps/v103asp4.ps}{ASP4}{1.00} @@ -5267,6 +6419,55 @@ Asp4(name): Exports == Implementation where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain ASP41 Asp41} + +<>= +)set break resume +)sys rm -f Asp41.output +)spool Asp41.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show Asp41 +--R Asp41(nameOne: Symbol,nameTwo: Symbol,nameThree: Symbol) is a domain constructor +--R Abbreviation for Asp41 is ASP41 +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for ASP41 +--R +--R------------------------------- Operations -------------------------------- +--R coerce : FortranCode -> % coerce : List FortranCode -> % +--R coerce : % -> OutputForm outputAsFortran : % -> Void +--R coerce : Vector FortranExpression([construct,QUOTEX,QUOTEEPS],[construct,QUOTEY],MachineFloat) -> % +--R coerce : Record(localSymbols: SymbolTable,code: List FortranCode) -> % +--R retract : Vector Fraction Polynomial Integer -> % +--R retract : Vector Fraction Polynomial Float -> % +--R retract : Vector Polynomial Integer -> % +--R retract : Vector Polynomial Float -> % +--R retract : Vector Expression Integer -> % +--R retract : Vector Expression Float -> % +--R retractIfCan : Vector Fraction Polynomial Integer -> Union(%,"failed") +--R retractIfCan : Vector Fraction Polynomial Float -> Union(%,"failed") +--R retractIfCan : Vector Polynomial Integer -> Union(%,"failed") +--R retractIfCan : Vector Polynomial Float -> Union(%,"failed") +--R retractIfCan : Vector Expression Integer -> Union(%,"failed") +--R retractIfCan : Vector Expression Float -> Union(%,"failed") +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +Asp41 examples +==================================================================== + +See Also: +o )show Asp41 + +@ + \pagehead{Asp41}{ASP41} \pagepic{ps/v103asp41.ps}{ASP41}{1.00} @@ -5501,6 +6702,55 @@ Asp41(nameOne,nameTwo,nameThree): Exports == Implementation where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain ASP42 Asp42} + +<>= +)set break resume +)sys rm -f Asp42.output +)spool Asp42.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show Asp42 +--R Asp42(nameOne: Symbol,nameTwo: Symbol,nameThree: Symbol) is a domain constructor +--R Abbreviation for Asp42 is ASP42 +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for ASP42 +--R +--R------------------------------- Operations -------------------------------- +--R coerce : FortranCode -> % coerce : List FortranCode -> % +--R coerce : % -> OutputForm outputAsFortran : % -> Void +--R coerce : Vector FortranExpression([construct,QUOTEEPS],[construct,QUOTEYA,QUOTEYB],MachineFloat) -> % +--R coerce : Record(localSymbols: SymbolTable,code: List FortranCode) -> % +--R retract : Vector Fraction Polynomial Integer -> % +--R retract : Vector Fraction Polynomial Float -> % +--R retract : Vector Polynomial Integer -> % +--R retract : Vector Polynomial Float -> % +--R retract : Vector Expression Integer -> % +--R retract : Vector Expression Float -> % +--R retractIfCan : Vector Fraction Polynomial Integer -> Union(%,"failed") +--R retractIfCan : Vector Fraction Polynomial Float -> Union(%,"failed") +--R retractIfCan : Vector Polynomial Integer -> Union(%,"failed") +--R retractIfCan : Vector Polynomial Float -> Union(%,"failed") +--R retractIfCan : Vector Expression Integer -> Union(%,"failed") +--R retractIfCan : Vector Expression Float -> Union(%,"failed") +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +Asp42 examples +==================================================================== + +See Also: +o )show Asp42 + +@ + \pagehead{Asp42}{ASP42} \pagepic{ps/v103asp42.ps}{ASP42}{1.00} @@ -5757,6 +7007,53 @@ Asp42(nameOne,nameTwo,nameThree): Exports == Implementation where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain ASP49 Asp49} + +<>= +)set break resume +)sys rm -f Asp49.output +)spool Asp49.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show Asp49 +--R Asp49 name: Symbol is a domain constructor +--R Abbreviation for Asp49 is ASP49 +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for ASP49 +--R +--R------------------------------- Operations -------------------------------- +--R coerce : FortranCode -> % coerce : List FortranCode -> % +--R coerce : % -> OutputForm outputAsFortran : % -> Void +--R retract : Polynomial Integer -> % retract : Polynomial Float -> % +--R retract : Expression Integer -> % retract : Expression Float -> % +--R coerce : FortranExpression([construct],[construct,QUOTEX],MachineFloat) -> % +--R coerce : Record(localSymbols: SymbolTable,code: List FortranCode) -> % +--R retract : Fraction Polynomial Integer -> % +--R retract : Fraction Polynomial Float -> % +--R retractIfCan : Fraction Polynomial Integer -> Union(%,"failed") +--R retractIfCan : Fraction Polynomial Float -> Union(%,"failed") +--R retractIfCan : Polynomial Integer -> Union(%,"failed") +--R retractIfCan : Polynomial Float -> Union(%,"failed") +--R retractIfCan : Expression Integer -> Union(%,"failed") +--R retractIfCan : Expression Float -> Union(%,"failed") +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +Asp49 examples +==================================================================== + +See Also: +o )show Asp49 + +@ + \pagehead{Asp49}{ASP49} \pagepic{ps/v103asp49.ps}{ASP49}{1.00} @@ -5919,6 +7216,55 @@ Asp49(name): Exports == Implementation where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain ASP50 Asp50} + +<>= +)set break resume +)sys rm -f Asp50.output +)spool Asp50.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show Asp50 +--R Asp50 name: Symbol is a domain constructor +--R Abbreviation for Asp50 is ASP50 +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for ASP50 +--R +--R------------------------------- Operations -------------------------------- +--R coerce : FortranCode -> % coerce : List FortranCode -> % +--R coerce : % -> OutputForm outputAsFortran : % -> Void +--R coerce : Vector FortranExpression([construct],[construct,QUOTEXC],MachineFloat) -> % +--R coerce : Record(localSymbols: SymbolTable,code: List FortranCode) -> % +--R retract : Vector Fraction Polynomial Integer -> % +--R retract : Vector Fraction Polynomial Float -> % +--R retract : Vector Polynomial Integer -> % +--R retract : Vector Polynomial Float -> % +--R retract : Vector Expression Integer -> % +--R retract : Vector Expression Float -> % +--R retractIfCan : Vector Fraction Polynomial Integer -> Union(%,"failed") +--R retractIfCan : Vector Fraction Polynomial Float -> Union(%,"failed") +--R retractIfCan : Vector Polynomial Integer -> Union(%,"failed") +--R retractIfCan : Vector Polynomial Float -> Union(%,"failed") +--R retractIfCan : Vector Expression Integer -> Union(%,"failed") +--R retractIfCan : Vector Expression Float -> Union(%,"failed") +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +Asp50 examples +==================================================================== + +See Also: +o )show Asp50 + +@ + \pagehead{Asp50}{ASP50} \pagepic{ps/v103asp50.ps}{ASP50}{1.00} @@ -6097,6 +7443,55 @@ Asp50(name): Exports == Implementation where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain ASP55 Asp55} + +<>= +)set break resume +)sys rm -f Asp55.output +)spool Asp55.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show Asp55 +--R Asp55 name: Symbol is a domain constructor +--R Abbreviation for Asp55 is ASP55 +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for ASP55 +--R +--R------------------------------- Operations -------------------------------- +--R coerce : FortranCode -> % coerce : List FortranCode -> % +--R coerce : % -> OutputForm outputAsFortran : % -> Void +--R coerce : Vector FortranExpression([construct],[construct,QUOTEX],MachineFloat) -> % +--R coerce : Record(localSymbols: SymbolTable,code: List FortranCode) -> % +--R retract : Vector Fraction Polynomial Integer -> % +--R retract : Vector Fraction Polynomial Float -> % +--R retract : Vector Polynomial Integer -> % +--R retract : Vector Polynomial Float -> % +--R retract : Vector Expression Integer -> % +--R retract : Vector Expression Float -> % +--R retractIfCan : Vector Fraction Polynomial Integer -> Union(%,"failed") +--R retractIfCan : Vector Fraction Polynomial Float -> Union(%,"failed") +--R retractIfCan : Vector Polynomial Integer -> Union(%,"failed") +--R retractIfCan : Vector Polynomial Float -> Union(%,"failed") +--R retractIfCan : Vector Expression Integer -> Union(%,"failed") +--R retractIfCan : Vector Expression Float -> Union(%,"failed") +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +Asp55 examples +==================================================================== + +See Also: +o )show Asp55 + +@ + \pagehead{Asp55}{ASP55} \pagepic{ps/v103asp55.ps}{ASP55}{1.00} @@ -6318,6 +7713,55 @@ Asp55(name): Exports == Implementation where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain ASP6 Asp6} + +<>= +)set break resume +)sys rm -f Asp6.output +)spool Asp6.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show Asp6 +--R Asp6 name: Symbol is a domain constructor +--R Abbreviation for Asp6 is ASP6 +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for ASP6 +--R +--R------------------------------- Operations -------------------------------- +--R coerce : FortranCode -> % coerce : List FortranCode -> % +--R coerce : % -> OutputForm outputAsFortran : % -> Void +--R coerce : Vector FortranExpression([construct],[construct,QUOTEX],MachineFloat) -> % +--R coerce : Record(localSymbols: SymbolTable,code: List FortranCode) -> % +--R retract : Vector Fraction Polynomial Integer -> % +--R retract : Vector Fraction Polynomial Float -> % +--R retract : Vector Polynomial Integer -> % +--R retract : Vector Polynomial Float -> % +--R retract : Vector Expression Integer -> % +--R retract : Vector Expression Float -> % +--R retractIfCan : Vector Fraction Polynomial Integer -> Union(%,"failed") +--R retractIfCan : Vector Fraction Polynomial Float -> Union(%,"failed") +--R retractIfCan : Vector Polynomial Integer -> Union(%,"failed") +--R retractIfCan : Vector Polynomial Float -> Union(%,"failed") +--R retractIfCan : Vector Expression Integer -> Union(%,"failed") +--R retractIfCan : Vector Expression Float -> Union(%,"failed") +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +Asp6 examples +==================================================================== + +See Also: +o )show Asp6 + +@ + \pagehead{Asp6}{ASP6} \pagepic{ps/v103asp6.ps}{ASP6}{1.00} @@ -6482,6 +7926,55 @@ Asp6(name): Exports == Implementation where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain ASP7 Asp7} + +<>= +)set break resume +)sys rm -f Asp7.output +)spool Asp7.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show Asp7 +--R Asp7 name: Symbol is a domain constructor +--R Abbreviation for Asp7 is ASP7 +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for ASP7 +--R +--R------------------------------- Operations -------------------------------- +--R coerce : FortranCode -> % coerce : List FortranCode -> % +--R coerce : % -> OutputForm outputAsFortran : % -> Void +--R coerce : Vector FortranExpression([construct,QUOTEX],[construct,QUOTEY],MachineFloat) -> % +--R coerce : Record(localSymbols: SymbolTable,code: List FortranCode) -> % +--R retract : Vector Fraction Polynomial Integer -> % +--R retract : Vector Fraction Polynomial Float -> % +--R retract : Vector Polynomial Integer -> % +--R retract : Vector Polynomial Float -> % +--R retract : Vector Expression Integer -> % +--R retract : Vector Expression Float -> % +--R retractIfCan : Vector Fraction Polynomial Integer -> Union(%,"failed") +--R retractIfCan : Vector Fraction Polynomial Float -> Union(%,"failed") +--R retractIfCan : Vector Polynomial Integer -> Union(%,"failed") +--R retractIfCan : Vector Polynomial Float -> Union(%,"failed") +--R retractIfCan : Vector Expression Integer -> Union(%,"failed") +--R retractIfCan : Vector Expression Float -> Union(%,"failed") +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +Asp7 examples +==================================================================== + +See Also: +o )show Asp7 + +@ + \pagehead{Asp7}{ASP7} \pagepic{ps/v103asp7.ps}{ASP7}{1.00} @@ -6631,6 +8124,55 @@ Asp7(name): Exports == Implementation where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain ASP73 Asp73} + +<>= +)set break resume +)sys rm -f Asp73.output +)spool Asp73.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show Asp73 +--R Asp73 name: Symbol is a domain constructor +--R Abbreviation for Asp73 is ASP73 +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for ASP73 +--R +--R------------------------------- Operations -------------------------------- +--R coerce : FortranCode -> % coerce : List FortranCode -> % +--R coerce : % -> OutputForm outputAsFortran : % -> Void +--R coerce : Vector FortranExpression([construct,QUOTEX,QUOTEY],[construct],MachineFloat) -> % +--R coerce : Record(localSymbols: SymbolTable,code: List FortranCode) -> % +--R retract : Vector Fraction Polynomial Integer -> % +--R retract : Vector Fraction Polynomial Float -> % +--R retract : Vector Polynomial Integer -> % +--R retract : Vector Polynomial Float -> % +--R retract : Vector Expression Integer -> % +--R retract : Vector Expression Float -> % +--R retractIfCan : Vector Fraction Polynomial Integer -> Union(%,"failed") +--R retractIfCan : Vector Fraction Polynomial Float -> Union(%,"failed") +--R retractIfCan : Vector Polynomial Integer -> Union(%,"failed") +--R retractIfCan : Vector Polynomial Float -> Union(%,"failed") +--R retractIfCan : Vector Expression Integer -> Union(%,"failed") +--R retractIfCan : Vector Expression Float -> Union(%,"failed") +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +Asp73 examples +==================================================================== + +See Also: +o )show Asp73 + +@ + \pagehead{Asp73}{ASP73} \pagepic{ps/v103asp73.ps}{ASP73}{1.00} @@ -6792,6 +8334,55 @@ Asp73(name): Exports == Implementation where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain ASP74 Asp74} + +<>= +)set break resume +)sys rm -f Asp74.output +)spool Asp74.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show Asp74 +--R Asp74 name: Symbol is a domain constructor +--R Abbreviation for Asp74 is ASP74 +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for ASP74 +--R +--R------------------------------- Operations -------------------------------- +--R coerce : FortranCode -> % coerce : List FortranCode -> % +--R coerce : % -> OutputForm outputAsFortran : % -> Void +--R coerce : Matrix FortranExpression([construct,QUOTEX,QUOTEY],[construct],MachineFloat) -> % +--R coerce : Record(localSymbols: SymbolTable,code: List FortranCode) -> % +--R retract : Matrix Fraction Polynomial Integer -> % +--R retract : Matrix Fraction Polynomial Float -> % +--R retract : Matrix Polynomial Integer -> % +--R retract : Matrix Polynomial Float -> % +--R retract : Matrix Expression Integer -> % +--R retract : Matrix Expression Float -> % +--R retractIfCan : Matrix Fraction Polynomial Integer -> Union(%,"failed") +--R retractIfCan : Matrix Fraction Polynomial Float -> Union(%,"failed") +--R retractIfCan : Matrix Polynomial Integer -> Union(%,"failed") +--R retractIfCan : Matrix Polynomial Float -> Union(%,"failed") +--R retractIfCan : Matrix Expression Integer -> Union(%,"failed") +--R retractIfCan : Matrix Expression Float -> Union(%,"failed") +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +Asp74 examples +==================================================================== + +See Also: +o )show Asp74 + +@ + \pagehead{Asp74}{ASP74} \pagepic{ps/v103asp74.ps}{ASP74}{1.00} @@ -6995,6 +8586,55 @@ Asp74(name): Exports == Implementation where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain ASP77 Asp77} + +<>= +)set break resume +)sys rm -f Asp77.output +)spool Asp77.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show Asp77 +--R Asp77 name: Symbol is a domain constructor +--R Abbreviation for Asp77 is ASP77 +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for ASP77 +--R +--R------------------------------- Operations -------------------------------- +--R coerce : FortranCode -> % coerce : List FortranCode -> % +--R coerce : % -> OutputForm outputAsFortran : % -> Void +--R coerce : Matrix FortranExpression([construct,QUOTEX],[construct],MachineFloat) -> % +--R coerce : Record(localSymbols: SymbolTable,code: List FortranCode) -> % +--R retract : Matrix Fraction Polynomial Integer -> % +--R retract : Matrix Fraction Polynomial Float -> % +--R retract : Matrix Polynomial Integer -> % +--R retract : Matrix Polynomial Float -> % +--R retract : Matrix Expression Integer -> % +--R retract : Matrix Expression Float -> % +--R retractIfCan : Matrix Fraction Polynomial Integer -> Union(%,"failed") +--R retractIfCan : Matrix Fraction Polynomial Float -> Union(%,"failed") +--R retractIfCan : Matrix Polynomial Integer -> Union(%,"failed") +--R retractIfCan : Matrix Polynomial Float -> Union(%,"failed") +--R retractIfCan : Matrix Expression Integer -> Union(%,"failed") +--R retractIfCan : Matrix Expression Float -> Union(%,"failed") +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +Asp77 examples +==================================================================== + +See Also: +o )show Asp77 + +@ + \pagehead{Asp77}{ASP77} \pagepic{ps/v103asp77.ps}{ASP77}{1.00} @@ -7163,6 +8803,55 @@ Asp77(name): Exports == Implementation where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain ASP78 Asp78} + +<>= +)set break resume +)sys rm -f Asp78.output +)spool Asp78.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show Asp78 +--R Asp78 name: Symbol is a domain constructor +--R Abbreviation for Asp78 is ASP78 +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for ASP78 +--R +--R------------------------------- Operations -------------------------------- +--R coerce : FortranCode -> % coerce : List FortranCode -> % +--R coerce : % -> OutputForm outputAsFortran : % -> Void +--R coerce : Vector FortranExpression([construct,QUOTEX],[construct],MachineFloat) -> % +--R coerce : Record(localSymbols: SymbolTable,code: List FortranCode) -> % +--R retract : Vector Fraction Polynomial Integer -> % +--R retract : Vector Fraction Polynomial Float -> % +--R retract : Vector Polynomial Integer -> % +--R retract : Vector Polynomial Float -> % +--R retract : Vector Expression Integer -> % +--R retract : Vector Expression Float -> % +--R retractIfCan : Vector Fraction Polynomial Integer -> Union(%,"failed") +--R retractIfCan : Vector Fraction Polynomial Float -> Union(%,"failed") +--R retractIfCan : Vector Polynomial Integer -> Union(%,"failed") +--R retractIfCan : Vector Polynomial Float -> Union(%,"failed") +--R retractIfCan : Vector Expression Integer -> Union(%,"failed") +--R retractIfCan : Vector Expression Float -> Union(%,"failed") +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +Asp78 examples +==================================================================== + +See Also: +o )show Asp78 + +@ + \pagehead{Asp78}{ASP78} \pagepic{ps/v103asp78.ps}{ASP78}{1.00} @@ -7306,6 +8995,43 @@ Asp78(name): Exports == Implementation where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain ASP8 Asp8} + +<>= +)set break resume +)sys rm -f Asp8.output +)spool Asp8.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show Asp8 +--R Asp8 name: Symbol is a domain constructor +--R Abbreviation for Asp8 is ASP8 +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for ASP8 +--R +--R------------------------------- Operations -------------------------------- +--R coerce : FortranCode -> % coerce : List FortranCode -> % +--R coerce : Vector MachineFloat -> % coerce : % -> OutputForm +--R outputAsFortran : % -> Void +--R coerce : Record(localSymbols: SymbolTable,code: List FortranCode) -> % +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +Asp8 examples +==================================================================== + +See Also: +o )show Asp8 + +@ + \pagehead{Asp8}{ASP8} \pagepic{ps/v103asp8.ps}{ASP8}{1.00} @@ -7449,6 +9175,55 @@ Asp8(name): Exports == Implementation where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain ASP80 Asp80} + +<>= +)set break resume +)sys rm -f Asp80.output +)spool Asp80.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show Asp80 +--R Asp80 name: Symbol is a domain constructor +--R Abbreviation for Asp80 is ASP80 +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for ASP80 +--R +--R------------------------------- Operations -------------------------------- +--R coerce : FortranCode -> % coerce : List FortranCode -> % +--R coerce : % -> OutputForm outputAsFortran : % -> Void +--R coerce : Matrix FortranExpression([construct,QUOTEXL,QUOTEXR,QUOTEELAM],[construct],MachineFloat) -> % +--R coerce : Record(localSymbols: SymbolTable,code: List FortranCode) -> % +--R retract : Matrix Fraction Polynomial Integer -> % +--R retract : Matrix Fraction Polynomial Float -> % +--R retract : Matrix Polynomial Integer -> % +--R retract : Matrix Polynomial Float -> % +--R retract : Matrix Expression Integer -> % +--R retract : Matrix Expression Float -> % +--R retractIfCan : Matrix Fraction Polynomial Integer -> Union(%,"failed") +--R retractIfCan : Matrix Fraction Polynomial Float -> Union(%,"failed") +--R retractIfCan : Matrix Polynomial Integer -> Union(%,"failed") +--R retractIfCan : Matrix Polynomial Float -> Union(%,"failed") +--R retractIfCan : Matrix Expression Integer -> Union(%,"failed") +--R retractIfCan : Matrix Expression Float -> Union(%,"failed") +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +Asp80 examples +==================================================================== + +See Also: +o )show Asp80 + +@ + \pagehead{Asp80}{ASP80} \pagepic{ps/v103asp80.ps}{ASP80}{1.00} @@ -7615,6 +9390,53 @@ Asp80(name): Exports == Implementation where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain ASP9 Asp9} + +<>= +)set break resume +)sys rm -f Asp9.output +)spool Asp9.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show Asp9 +--R Asp9 name: Symbol is a domain constructor +--R Abbreviation for Asp9 is ASP9 +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for ASP9 +--R +--R------------------------------- Operations -------------------------------- +--R coerce : FortranCode -> % coerce : List FortranCode -> % +--R coerce : % -> OutputForm outputAsFortran : % -> Void +--R retract : Polynomial Integer -> % retract : Polynomial Float -> % +--R retract : Expression Integer -> % retract : Expression Float -> % +--R coerce : FortranExpression([construct,QUOTEX],[construct,QUOTEY],MachineFloat) -> % +--R coerce : Record(localSymbols: SymbolTable,code: List FortranCode) -> % +--R retract : Fraction Polynomial Integer -> % +--R retract : Fraction Polynomial Float -> % +--R retractIfCan : Fraction Polynomial Integer -> Union(%,"failed") +--R retractIfCan : Fraction Polynomial Float -> Union(%,"failed") +--R retractIfCan : Polynomial Integer -> Union(%,"failed") +--R retractIfCan : Polynomial Float -> Union(%,"failed") +--R retractIfCan : Expression Integer -> Union(%,"failed") +--R retractIfCan : Expression Float -> Union(%,"failed") +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +Asp9 examples +==================================================================== + +See Also: +o )show Asp9 + +@ + \pagehead{Asp9}{ASP9} \pagepic{ps/v103asp9.ps}{ASP9}{1.00} @@ -7759,6 +9581,118 @@ Asp9(name): Exports == Implementation where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain JORDAN AssociatedJordanAlgebra} + +<>= +)set break resume +)sys rm -f AssociatedJordanAlgebra.output +)spool AssociatedJordanAlgebra.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show AssociatedJordanAlgebra +--R AssociatedJordanAlgebra(R: CommutativeRing,A: NonAssociativeAlgebra R) is a domain constructor +--R Abbreviation for AssociatedJordanAlgebra is JORDAN +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for JORDAN +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (R,%) -> % ?*? : (%,R) -> % +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ?=? : (%,%) -> Boolean +--R 0 : () -> % antiCommutator : (%,%) -> % +--R associator : (%,%,%) -> % coerce : A -> % +--R coerce : % -> A coerce : % -> OutputForm +--R commutator : (%,%) -> % hash : % -> SingleInteger +--R latex : % -> String sample : () -> % +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean +--R ?*? : (NonNegativeInteger,%) -> % +--R alternative? : () -> Boolean if A has FINAALG R +--R antiAssociative? : () -> Boolean if A has FINAALG R +--R antiCommutative? : () -> Boolean if A has FINAALG R +--R apply : (Matrix R,%) -> % if A has FRNAALG R +--R associative? : () -> Boolean if A has FINAALG R +--R associatorDependence : () -> List Vector R if A has FINAALG R and R has INTDOM or A has FRNAALG R and R has INTDOM +--R basis : () -> Vector % if A has FRNAALG R +--R commutative? : () -> Boolean if A has FINAALG R +--R conditionsForIdempotents : Vector % -> List Polynomial R if A has FINAALG R +--R conditionsForIdempotents : () -> List Polynomial R if A has FRNAALG R +--R convert : % -> Vector R if A has FRNAALG R +--R convert : Vector R -> % if A has FRNAALG R +--R coordinates : (%,Vector %) -> Vector R if A has FINAALG R +--R coordinates : (Vector %,Vector %) -> Matrix R if A has FINAALG R +--R coordinates : % -> Vector R if A has FRNAALG R +--R coordinates : Vector % -> Matrix R if A has FRNAALG R +--R ?.? : (%,Integer) -> R if A has FRNAALG R +--R flexible? : () -> Boolean if A has FINAALG R +--R jacobiIdentity? : () -> Boolean if A has FINAALG R +--R jordanAdmissible? : () -> Boolean if A has FINAALG R +--R jordanAlgebra? : () -> Boolean if A has FINAALG R +--R leftAlternative? : () -> Boolean if A has FINAALG R +--R leftCharacteristicPolynomial : % -> SparseUnivariatePolynomial R if A has FINAALG R +--R leftDiscriminant : Vector % -> R if A has FINAALG R +--R leftDiscriminant : () -> R if A has FRNAALG R +--R leftMinimalPolynomial : % -> SparseUnivariatePolynomial R if A has FINAALG R and R has INTDOM or A has FRNAALG R and R has INTDOM +--R leftNorm : % -> R if A has FINAALG R +--R leftPower : (%,PositiveInteger) -> % +--R leftRankPolynomial : () -> SparseUnivariatePolynomial Polynomial R if A has FRNAALG R and R has FIELD +--R leftRecip : % -> Union(%,"failed") if A has FINAALG R and R has INTDOM or A has FRNAALG R and R has INTDOM +--R leftRegularRepresentation : (%,Vector %) -> Matrix R if A has FINAALG R +--R leftRegularRepresentation : % -> Matrix R if A has FRNAALG R +--R leftTrace : % -> R if A has FINAALG R +--R leftTraceMatrix : Vector % -> Matrix R if A has FINAALG R +--R leftTraceMatrix : () -> Matrix R if A has FRNAALG R +--R leftUnit : () -> Union(%,"failed") if A has FINAALG R and R has INTDOM or A has FRNAALG R and R has INTDOM +--R leftUnits : () -> Union(Record(particular: %,basis: List %),"failed") if A has FINAALG R and R has INTDOM or A has FRNAALG R and R has INTDOM +--R lieAdmissible? : () -> Boolean if A has FINAALG R +--R lieAlgebra? : () -> Boolean if A has FINAALG R +--R noncommutativeJordanAlgebra? : () -> Boolean if A has FINAALG R +--R plenaryPower : (%,PositiveInteger) -> % +--R powerAssociative? : () -> Boolean if A has FINAALG R +--R rank : () -> PositiveInteger if A has FINAALG R +--R recip : % -> Union(%,"failed") if A has FINAALG R and R has INTDOM or A has FRNAALG R and R has INTDOM +--R represents : (Vector R,Vector %) -> % if A has FINAALG R +--R represents : Vector R -> % if A has FRNAALG R +--R rightAlternative? : () -> Boolean if A has FINAALG R +--R rightCharacteristicPolynomial : % -> SparseUnivariatePolynomial R if A has FINAALG R +--R rightDiscriminant : Vector % -> R if A has FINAALG R +--R rightDiscriminant : () -> R if A has FRNAALG R +--R rightMinimalPolynomial : % -> SparseUnivariatePolynomial R if A has FINAALG R and R has INTDOM or A has FRNAALG R and R has INTDOM +--R rightNorm : % -> R if A has FINAALG R +--R rightPower : (%,PositiveInteger) -> % +--R rightRankPolynomial : () -> SparseUnivariatePolynomial Polynomial R if A has FRNAALG R and R has FIELD +--R rightRecip : % -> Union(%,"failed") if A has FINAALG R and R has INTDOM or A has FRNAALG R and R has INTDOM +--R rightRegularRepresentation : (%,Vector %) -> Matrix R if A has FINAALG R +--R rightRegularRepresentation : % -> Matrix R if A has FRNAALG R +--R rightTrace : % -> R if A has FINAALG R +--R rightTraceMatrix : Vector % -> Matrix R if A has FINAALG R +--R rightTraceMatrix : () -> Matrix R if A has FRNAALG R +--R rightUnit : () -> Union(%,"failed") if A has FINAALG R and R has INTDOM or A has FRNAALG R and R has INTDOM +--R rightUnits : () -> Union(Record(particular: %,basis: List %),"failed") if A has FINAALG R and R has INTDOM or A has FRNAALG R and R has INTDOM +--R someBasis : () -> Vector % if A has FINAALG R +--R structuralConstants : Vector % -> Vector Matrix R if A has FINAALG R +--R structuralConstants : () -> Vector Matrix R if A has FRNAALG R +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R unit : () -> Union(%,"failed") if A has FINAALG R and R has INTDOM or A has FRNAALG R and R has INTDOM +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +AssociatedJordanAlgebra examples +==================================================================== + +See Also: +o )show AssociatedJordanAlgebra + +@ + \pagehead{AssociatedJordanAlgebra}{JORDAN} \pagepic{ps/v103associatedjordanalgebra.ps}{JORDAN}{1.00} {\bf See}\\ @@ -7906,6 +9840,118 @@ AssociatedJordanAlgebra(R:CommutativeRing,A:NonAssociativeAlgebra R): @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain LIE AssociatedLieAlgebra} + +<>= +)set break resume +)sys rm -f AssociatedLieAlgebra.output +)spool AssociatedLieAlgebra.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show AssociatedLieAlgebra +--R AssociatedLieAlgebra(R: CommutativeRing,A: NonAssociativeAlgebra R) is a domain constructor +--R Abbreviation for AssociatedLieAlgebra is LIE +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for LIE +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (R,%) -> % ?*? : (%,R) -> % +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ?=? : (%,%) -> Boolean +--R 0 : () -> % antiCommutator : (%,%) -> % +--R associator : (%,%,%) -> % coerce : A -> % +--R coerce : % -> A coerce : % -> OutputForm +--R commutator : (%,%) -> % hash : % -> SingleInteger +--R latex : % -> String sample : () -> % +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean +--R ?*? : (NonNegativeInteger,%) -> % +--R alternative? : () -> Boolean if A has FINAALG R +--R antiAssociative? : () -> Boolean if A has FINAALG R +--R antiCommutative? : () -> Boolean if A has FINAALG R +--R apply : (Matrix R,%) -> % if A has FRNAALG R +--R associative? : () -> Boolean if A has FINAALG R +--R associatorDependence : () -> List Vector R if A has FINAALG R and R has INTDOM or A has FRNAALG R and R has INTDOM +--R basis : () -> Vector % if A has FRNAALG R +--R commutative? : () -> Boolean if A has FINAALG R +--R conditionsForIdempotents : Vector % -> List Polynomial R if A has FINAALG R +--R conditionsForIdempotents : () -> List Polynomial R if A has FRNAALG R +--R convert : % -> Vector R if A has FRNAALG R +--R convert : Vector R -> % if A has FRNAALG R +--R coordinates : (%,Vector %) -> Vector R if A has FINAALG R +--R coordinates : (Vector %,Vector %) -> Matrix R if A has FINAALG R +--R coordinates : % -> Vector R if A has FRNAALG R +--R coordinates : Vector % -> Matrix R if A has FRNAALG R +--R ?.? : (%,Integer) -> R if A has FRNAALG R +--R flexible? : () -> Boolean if A has FINAALG R +--R jacobiIdentity? : () -> Boolean if A has FINAALG R +--R jordanAdmissible? : () -> Boolean if A has FINAALG R +--R jordanAlgebra? : () -> Boolean if A has FINAALG R +--R leftAlternative? : () -> Boolean if A has FINAALG R +--R leftCharacteristicPolynomial : % -> SparseUnivariatePolynomial R if A has FINAALG R +--R leftDiscriminant : Vector % -> R if A has FINAALG R +--R leftDiscriminant : () -> R if A has FRNAALG R +--R leftMinimalPolynomial : % -> SparseUnivariatePolynomial R if A has FINAALG R and R has INTDOM or A has FRNAALG R and R has INTDOM +--R leftNorm : % -> R if A has FINAALG R +--R leftPower : (%,PositiveInteger) -> % +--R leftRankPolynomial : () -> SparseUnivariatePolynomial Polynomial R if A has FRNAALG R and R has FIELD +--R leftRecip : % -> Union(%,"failed") if A has FINAALG R and R has INTDOM or A has FRNAALG R and R has INTDOM +--R leftRegularRepresentation : (%,Vector %) -> Matrix R if A has FINAALG R +--R leftRegularRepresentation : % -> Matrix R if A has FRNAALG R +--R leftTrace : % -> R if A has FINAALG R +--R leftTraceMatrix : Vector % -> Matrix R if A has FINAALG R +--R leftTraceMatrix : () -> Matrix R if A has FRNAALG R +--R leftUnit : () -> Union(%,"failed") if A has FINAALG R and R has INTDOM or A has FRNAALG R and R has INTDOM +--R leftUnits : () -> Union(Record(particular: %,basis: List %),"failed") if A has FINAALG R and R has INTDOM or A has FRNAALG R and R has INTDOM +--R lieAdmissible? : () -> Boolean if A has FINAALG R +--R lieAlgebra? : () -> Boolean if A has FINAALG R +--R noncommutativeJordanAlgebra? : () -> Boolean if A has FINAALG R +--R plenaryPower : (%,PositiveInteger) -> % +--R powerAssociative? : () -> Boolean if A has FINAALG R +--R rank : () -> PositiveInteger if A has FINAALG R +--R recip : % -> Union(%,"failed") if A has FINAALG R and R has INTDOM or A has FRNAALG R and R has INTDOM +--R represents : (Vector R,Vector %) -> % if A has FINAALG R +--R represents : Vector R -> % if A has FRNAALG R +--R rightAlternative? : () -> Boolean if A has FINAALG R +--R rightCharacteristicPolynomial : % -> SparseUnivariatePolynomial R if A has FINAALG R +--R rightDiscriminant : Vector % -> R if A has FINAALG R +--R rightDiscriminant : () -> R if A has FRNAALG R +--R rightMinimalPolynomial : % -> SparseUnivariatePolynomial R if A has FINAALG R and R has INTDOM or A has FRNAALG R and R has INTDOM +--R rightNorm : % -> R if A has FINAALG R +--R rightPower : (%,PositiveInteger) -> % +--R rightRankPolynomial : () -> SparseUnivariatePolynomial Polynomial R if A has FRNAALG R and R has FIELD +--R rightRecip : % -> Union(%,"failed") if A has FINAALG R and R has INTDOM or A has FRNAALG R and R has INTDOM +--R rightRegularRepresentation : (%,Vector %) -> Matrix R if A has FINAALG R +--R rightRegularRepresentation : % -> Matrix R if A has FRNAALG R +--R rightTrace : % -> R if A has FINAALG R +--R rightTraceMatrix : Vector % -> Matrix R if A has FINAALG R +--R rightTraceMatrix : () -> Matrix R if A has FRNAALG R +--R rightUnit : () -> Union(%,"failed") if A has FINAALG R and R has INTDOM or A has FRNAALG R and R has INTDOM +--R rightUnits : () -> Union(Record(particular: %,basis: List %),"failed") if A has FINAALG R and R has INTDOM or A has FRNAALG R and R has INTDOM +--R someBasis : () -> Vector % if A has FINAALG R +--R structuralConstants : Vector % -> Vector Matrix R if A has FINAALG R +--R structuralConstants : () -> Vector Matrix R if A has FRNAALG R +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R unit : () -> Union(%,"failed") if A has FINAALG R and R has INTDOM or A has FRNAALG R and R has INTDOM +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +AssociatedLieAlgebra examples +==================================================================== + +See Also: +o )show AssociatedLieAlgebra + +@ + \pagehead{AssociatedLieAlgebra}{LIE} \pagepic{ps/v103associatedliealgebra.ps}{LIE}{1.00} {\bf See}\\ @@ -8051,6 +10097,7 @@ AssociatedLieAlgebra(R:CommutativeRing,A:NonAssociativeAlgebra R): @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain ALIST AssociationList} + <>= )set break resume )sys rm -f AssociationList.output @@ -8448,6 +10495,49 @@ AssociationList(Key:SetCategory, Entry:SetCategory): @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain ATTRBUT AttributeButtons} + +<>= +)set break resume +)sys rm -f AttributeButtons.output +)spool AttributeButtons.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show AttributeButtons +--R AttributeButtons is a domain constructor +--R Abbreviation for AttributeButtons is ATTRBUT +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for ATTRBUT +--R +--R------------------------------- Operations -------------------------------- +--R ?=? : (%,%) -> Boolean coerce : % -> OutputForm +--R decrease : String -> Float hash : % -> SingleInteger +--R increase : String -> Float latex : % -> String +--R resetAttributeButtons : () -> Void ?~=? : (%,%) -> Boolean +--R decrease : (String,String) -> Float +--R getButtonValue : (String,String) -> Float +--R increase : (String,String) -> Float +--R setAttributeButtonStep : Float -> Float +--R setButtonValue : (String,String,Float) -> Float +--R setButtonValue : (String,Float) -> Float +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +AttributeButtons examples +==================================================================== + +See Also: +o )show AttributeButtons + +@ + \pagehead{AttributeButtons}{ATTRBUT} \pagepic{ps/v103attributebuttons.ps}{ATTRBUT}{1.00} @@ -8686,6 +10776,53 @@ AttributeButtons(): E == I where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain AUTOMOR Automorphism} + +<>= +)set break resume +)sys rm -f Automorphism.output +)spool Automorphism.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show Automorphism +--R Automorphism R: Ring is a domain constructor +--R Abbreviation for Automorphism is AUTOMOR +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for AUTOMOR +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (%,%) -> % ?**? : (%,Integer) -> % +--R ?**? : (%,PositiveInteger) -> % ?/? : (%,%) -> % +--R ?=? : (%,%) -> Boolean 1 : () -> % +--R ?^? : (%,Integer) -> % ?^? : (%,PositiveInteger) -> % +--R coerce : % -> OutputForm commutator : (%,%) -> % +--R conjugate : (%,%) -> % ?.? : (%,R) -> R +--R hash : % -> SingleInteger inv : % -> % +--R latex : % -> String morphism : (R -> R) -> % +--R one? : % -> Boolean recip : % -> Union(%,"failed") +--R sample : () -> % ?~=? : (%,%) -> Boolean +--R ?**? : (%,NonNegativeInteger) -> % +--R ?^? : (%,NonNegativeInteger) -> % +--R morphism : ((R,Integer) -> R) -> % +--R morphism : ((R -> R),(R -> R)) -> % +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +Automorphism examples +==================================================================== + +See Also: +o )show Automorphism + +@ + \pagehead{Automorphism}{AUTOMOR} \pagepic{ps/v103automorphism.ps}{AUTOMOR}{1.00} {\bf See}\\ @@ -8782,6 +10919,7 @@ Automorphism(R:Ring): Join(Group, Eltable(R, R)) with \chapter{Chapter B} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain BBTREE BalancedBinaryTree} + <>= )set break resume )sys rm -f BalancedBinaryTree.output @@ -9146,6 +11284,76 @@ BalancedBinaryTree(S: SetCategory): Exports == Implementation where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain BPADIC BalancedPAdicInteger} + +<>= +)set break resume +)sys rm -f BalancedPAdicInteger.output +)spool BalancedPAdicInteger.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show BalancedPAdicInteger +--R BalancedPAdicInteger p: Integer is a domain constructor +--R Abbreviation for BalancedPAdicInteger is BPADIC +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for BPADIC +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ?=? : (%,%) -> Boolean +--R 1 : () -> % 0 : () -> % +--R ?^? : (%,PositiveInteger) -> % associates? : (%,%) -> Boolean +--R coerce : % -> % coerce : Integer -> % +--R coerce : % -> OutputForm complete : % -> % +--R digits : % -> Stream Integer extend : (%,Integer) -> % +--R gcd : List % -> % gcd : (%,%) -> % +--R hash : % -> SingleInteger latex : % -> String +--R lcm : List % -> % lcm : (%,%) -> % +--R moduloP : % -> Integer modulus : () -> Integer +--R one? : % -> Boolean order : % -> NonNegativeInteger +--R ?quo? : (%,%) -> % quotientByP : % -> % +--R recip : % -> Union(%,"failed") ?rem? : (%,%) -> % +--R sample : () -> % sizeLess? : (%,%) -> Boolean +--R sqrt : (%,Integer) -> % unit? : % -> Boolean +--R unitCanonical : % -> % zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean +--R ?*? : (NonNegativeInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % +--R ?^? : (%,NonNegativeInteger) -> % +--R approximate : (%,Integer) -> Integer +--R characteristic : () -> NonNegativeInteger +--R divide : (%,%) -> Record(quotient: %,remainder: %) +--R euclideanSize : % -> NonNegativeInteger +--R expressIdealMember : (List %,%) -> Union(List %,"failed") +--R exquo : (%,%) -> Union(%,"failed") +--R extendedEuclidean : (%,%,%) -> Union(Record(coef1: %,coef2: %),"failed") +--R extendedEuclidean : (%,%) -> Record(coef1: %,coef2: %,generator: %) +--R gcdPolynomial : (SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial % +--R multiEuclidean : (List %,%) -> Union(List %,"failed") +--R principalIdeal : List % -> Record(coef: List %,generator: %) +--R root : (SparseUnivariatePolynomial Integer,Integer) -> % +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R unitNormal : % -> Record(unit: %,canonical: %,associate: %) +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +BalancedPAdicInteger examples +==================================================================== + +See Also: +o )show BalancedPAdicInteger + +@ + \pagehead{BalancedPAdicInteger}{BPADIC} \pagepic{ps/v103balancedpadicinteger.ps}{BPADIC}{1.00} {\bf See}\\ @@ -9232,6 +11440,152 @@ BalancedPAdicInteger(p:Integer) == InnerPAdicInteger(p,false$Boolean) @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain BPADICRT BalancedPAdicRational} + +<>= +)set break resume +)sys rm -f BalancedPAdicRational.output +)spool BalancedPAdicRational.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show BalancedPAdicRational +--R BalancedPAdicRational p: Integer is a domain constructor +--R Abbreviation for BalancedPAdicRational is BPADICRT +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for BPADICRT +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (Fraction Integer,%) -> % ?*? : (%,Fraction Integer) -> % +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?**? : (%,Integer) -> % +--R ?**? : (%,PositiveInteger) -> % ?+? : (%,%) -> % +--R ?-? : (%,%) -> % -? : % -> % +--R ?/? : (%,%) -> % ?=? : (%,%) -> Boolean +--R 1 : () -> % 0 : () -> % +--R ?^? : (%,Integer) -> % ?^? : (%,PositiveInteger) -> % +--R associates? : (%,%) -> Boolean coerce : Fraction Integer -> % +--R coerce : % -> % coerce : Integer -> % +--R coerce : % -> OutputForm denominator : % -> % +--R factor : % -> Factored % gcd : List % -> % +--R gcd : (%,%) -> % hash : % -> SingleInteger +--R inv : % -> % latex : % -> String +--R lcm : List % -> % lcm : (%,%) -> % +--R numerator : % -> % one? : % -> Boolean +--R prime? : % -> Boolean ?quo? : (%,%) -> % +--R recip : % -> Union(%,"failed") ?rem? : (%,%) -> % +--R removeZeroes : (Integer,%) -> % removeZeroes : % -> % +--R sample : () -> % sizeLess? : (%,%) -> Boolean +--R squareFree : % -> Factored % squareFreePart : % -> % +--R unit? : % -> Boolean unitCanonical : % -> % +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean +--R ?*? : (%,BalancedPAdicInteger p) -> % +--R ?*? : (BalancedPAdicInteger p,%) -> % +--R ?*? : (NonNegativeInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % +--R ?/? : (BalancedPAdicInteger p,BalancedPAdicInteger p) -> % +--R ? Boolean if BalancedPAdicInteger p has ORDSET +--R ?<=? : (%,%) -> Boolean if BalancedPAdicInteger p has ORDSET +--R ?>? : (%,%) -> Boolean if BalancedPAdicInteger p has ORDSET +--R ?>=? : (%,%) -> Boolean if BalancedPAdicInteger p has ORDSET +--R D : (%,(BalancedPAdicInteger p -> BalancedPAdicInteger p)) -> % +--R D : (%,(BalancedPAdicInteger p -> BalancedPAdicInteger p),NonNegativeInteger) -> % +--R D : (%,List Symbol,List NonNegativeInteger) -> % if BalancedPAdicInteger p has PDRING SYMBOL +--R D : (%,Symbol,NonNegativeInteger) -> % if BalancedPAdicInteger p has PDRING SYMBOL +--R D : (%,List Symbol) -> % if BalancedPAdicInteger p has PDRING SYMBOL +--R D : (%,Symbol) -> % if BalancedPAdicInteger p has PDRING SYMBOL +--R D : (%,NonNegativeInteger) -> % if BalancedPAdicInteger p has DIFRING +--R D : % -> % if BalancedPAdicInteger p has DIFRING +--R ?^? : (%,NonNegativeInteger) -> % +--R abs : % -> % if BalancedPAdicInteger p has OINTDOM +--R approximate : (%,Integer) -> Fraction Integer +--R ceiling : % -> BalancedPAdicInteger p if BalancedPAdicInteger p has INS +--R characteristic : () -> NonNegativeInteger +--R charthRoot : % -> Union(%,"failed") if $ has CHARNZ and BalancedPAdicInteger p has PFECAT or BalancedPAdicInteger p has CHARNZ +--R coerce : Symbol -> % if BalancedPAdicInteger p has RETRACT SYMBOL +--R coerce : BalancedPAdicInteger p -> % +--R conditionP : Matrix % -> Union(Vector %,"failed") if $ has CHARNZ and BalancedPAdicInteger p has PFECAT +--R continuedFraction : % -> ContinuedFraction Fraction Integer +--R convert : % -> DoubleFloat if BalancedPAdicInteger p has REAL +--R convert : % -> Float if BalancedPAdicInteger p has REAL +--R convert : % -> InputForm if BalancedPAdicInteger p has KONVERT INFORM +--R convert : % -> Pattern Float if BalancedPAdicInteger p has KONVERT PATTERN FLOAT +--R convert : % -> Pattern Integer if BalancedPAdicInteger p has KONVERT PATTERN INT +--R denom : % -> BalancedPAdicInteger p +--R differentiate : (%,(BalancedPAdicInteger p -> BalancedPAdicInteger p)) -> % +--R differentiate : (%,(BalancedPAdicInteger p -> BalancedPAdicInteger p),NonNegativeInteger) -> % +--R differentiate : (%,List Symbol,List NonNegativeInteger) -> % if BalancedPAdicInteger p has PDRING SYMBOL +--R differentiate : (%,Symbol,NonNegativeInteger) -> % if BalancedPAdicInteger p has PDRING SYMBOL +--R differentiate : (%,List Symbol) -> % if BalancedPAdicInteger p has PDRING SYMBOL +--R differentiate : (%,Symbol) -> % if BalancedPAdicInteger p has PDRING SYMBOL +--R differentiate : (%,NonNegativeInteger) -> % if BalancedPAdicInteger p has DIFRING +--R differentiate : % -> % if BalancedPAdicInteger p has DIFRING +--R divide : (%,%) -> Record(quotient: %,remainder: %) +--R ?.? : (%,BalancedPAdicInteger p) -> % if BalancedPAdicInteger p has ELTAB(BPADIC p,BPADIC p) +--R euclideanSize : % -> NonNegativeInteger +--R eval : (%,Symbol,BalancedPAdicInteger p) -> % if BalancedPAdicInteger p has IEVALAB(SYMBOL,BPADIC p) +--R eval : (%,List Symbol,List BalancedPAdicInteger p) -> % if BalancedPAdicInteger p has IEVALAB(SYMBOL,BPADIC p) +--R eval : (%,List Equation BalancedPAdicInteger p) -> % if BalancedPAdicInteger p has EVALAB BPADIC p +--R eval : (%,Equation BalancedPAdicInteger p) -> % if BalancedPAdicInteger p has EVALAB BPADIC p +--R eval : (%,BalancedPAdicInteger p,BalancedPAdicInteger p) -> % if BalancedPAdicInteger p has EVALAB BPADIC p +--R eval : (%,List BalancedPAdicInteger p,List BalancedPAdicInteger p) -> % if BalancedPAdicInteger p has EVALAB BPADIC p +--R expressIdealMember : (List %,%) -> Union(List %,"failed") +--R exquo : (%,%) -> Union(%,"failed") +--R extendedEuclidean : (%,%,%) -> Union(Record(coef1: %,coef2: %),"failed") +--R extendedEuclidean : (%,%) -> Record(coef1: %,coef2: %,generator: %) +--R factorPolynomial : SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if BalancedPAdicInteger p has PFECAT +--R factorSquareFreePolynomial : SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if BalancedPAdicInteger p has PFECAT +--R floor : % -> BalancedPAdicInteger p if BalancedPAdicInteger p has INS +--R fractionPart : % -> % if BalancedPAdicInteger p has EUCDOM +--R gcdPolynomial : (SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial % +--R init : () -> % if BalancedPAdicInteger p has STEP +--R map : ((BalancedPAdicInteger p -> BalancedPAdicInteger p),%) -> % +--R max : (%,%) -> % if BalancedPAdicInteger p has ORDSET +--R min : (%,%) -> % if BalancedPAdicInteger p has ORDSET +--R multiEuclidean : (List %,%) -> Union(List %,"failed") +--R negative? : % -> Boolean if BalancedPAdicInteger p has OINTDOM +--R nextItem : % -> Union(%,"failed") if BalancedPAdicInteger p has STEP +--R numer : % -> BalancedPAdicInteger p +--R patternMatch : (%,Pattern Float,PatternMatchResult(Float,%)) -> PatternMatchResult(Float,%) if BalancedPAdicInteger p has PATMAB FLOAT +--R patternMatch : (%,Pattern Integer,PatternMatchResult(Integer,%)) -> PatternMatchResult(Integer,%) if BalancedPAdicInteger p has PATMAB INT +--R positive? : % -> Boolean if BalancedPAdicInteger p has OINTDOM +--R principalIdeal : List % -> Record(coef: List %,generator: %) +--R random : () -> % if BalancedPAdicInteger p has INS +--R reducedSystem : Matrix % -> Matrix BalancedPAdicInteger p +--R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix BalancedPAdicInteger p,vec: Vector BalancedPAdicInteger p) +--R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix Integer,vec: Vector Integer) if BalancedPAdicInteger p has LINEXP INT +--R reducedSystem : Matrix % -> Matrix Integer if BalancedPAdicInteger p has LINEXP INT +--R retract : % -> Integer if BalancedPAdicInteger p has RETRACT INT +--R retract : % -> Fraction Integer if BalancedPAdicInteger p has RETRACT INT +--R retract : % -> Symbol if BalancedPAdicInteger p has RETRACT SYMBOL +--R retract : % -> BalancedPAdicInteger p +--R retractIfCan : % -> Union(Integer,"failed") if BalancedPAdicInteger p has RETRACT INT +--R retractIfCan : % -> Union(Fraction Integer,"failed") if BalancedPAdicInteger p has RETRACT INT +--R retractIfCan : % -> Union(Symbol,"failed") if BalancedPAdicInteger p has RETRACT SYMBOL +--R retractIfCan : % -> Union(BalancedPAdicInteger p,"failed") +--R sign : % -> Integer if BalancedPAdicInteger p has OINTDOM +--R solveLinearPolynomialEquation : (List SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> Union(List SparseUnivariatePolynomial %,"failed") if BalancedPAdicInteger p has PFECAT +--R squareFreePolynomial : SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if BalancedPAdicInteger p has PFECAT +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R unitNormal : % -> Record(unit: %,canonical: %,associate: %) +--R wholePart : % -> BalancedPAdicInteger p if BalancedPAdicInteger p has EUCDOM +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +BalancedPAdicRational examples +==================================================================== + +See Also: +o )show BalancedPAdicRational + +@ + \pagehead{BalancedPAdicRational}{BPADICRT} \pagepic{ps/v103balancedpadicrational.ps}{BPADICRT}{1.00} {\bf See}\\ @@ -9356,6 +11710,43 @@ BalancedPAdicRational(p:Integer) == @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain BFUNCT BasicFunctions} + +<>= +)set break resume +)sys rm -f BasicFunctions.output +)spool BasicFunctions.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show BasicFunctions +--R BasicFunctions is a domain constructor +--R Abbreviation for BasicFunctions is BFUNCT +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for BFUNCT +--R +--R------------------------------- Operations -------------------------------- +--R ?=? : (%,%) -> Boolean bfKeys : () -> List Symbol +--R coerce : % -> OutputForm hash : % -> SingleInteger +--R latex : % -> String ?~=? : (%,%) -> Boolean +--R bfEntry : Symbol -> Record(zeros: Stream DoubleFloat,ones: Stream DoubleFloat,singularities: Stream DoubleFloat) +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +BasicFunctions examples +==================================================================== + +See Also: +o )show BasicFunctions + +@ + \pagehead{BasicFunctions}{BFUNCT} \pagepic{ps/v103basicfunctions.ps}{BFUNCT}{1.00} @@ -9445,6 +11836,7 @@ BasicFunctions(): E == I where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain BOP BasicOperator} + <>= )set break resume )sys rm -f BasicOperator.output @@ -9981,6 +12373,7 @@ BasicOperator(): Exports == Implementation where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain BINARY BinaryExpansion} + <>= )set break resume )sys rm -f BinaryExpansion.output @@ -10276,6 +12669,49 @@ BinaryExpansion(): Exports == Implementation where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain BINFILE BinaryFile} + +<>= +)set break resume +)sys rm -f BinaryFile.output +)spool BinaryFile.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show BinaryFile +--R BinaryFile is a domain constructor +--R Abbreviation for BinaryFile is BINFILE +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for BINFILE +--R +--R------------------------------- Operations -------------------------------- +--R ?=? : (%,%) -> Boolean close! : % -> % +--R coerce : % -> OutputForm flush : % -> Void +--R hash : % -> SingleInteger iomode : % -> String +--R latex : % -> String name : % -> FileName +--R open : (FileName,String) -> % open : FileName -> % +--R position : % -> SingleInteger read! : % -> SingleInteger +--R reopen! : (%,String) -> % ?~=? : (%,%) -> Boolean +--R position! : (%,SingleInteger) -> SingleInteger +--R readIfCan! : % -> Union(SingleInteger,"failed") +--R write! : (%,SingleInteger) -> SingleInteger +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +BinaryFile examples +==================================================================== + +See Also: +o )show BinaryFile + +@ + \pagehead{BinaryFile}{BINFILE} \pagepic{ps/v103binaryfile.ps}{BINFILE}{1.00} {\bf See}\\ @@ -10416,6 +12852,7 @@ BinaryFile: Cat == Def where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain BSTREE BinarySearchTree} + <>= )set break resume )sys rm -f BinarySearchTree.output @@ -10759,10 +13196,85 @@ BinarySearchTree(S: OrderedSet): Exports == Implementation where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain BTOURN BinaryTournament} + A BinaryTournament(S) is the domain of binary trees where elements are ordered down the tree. A binary search tree is either empty or is a node containing a value of type S, and a right and a left which are both BinaryTree(S) + +<>= +)set break resume +)sys rm -f BinaryTournament.output +)spool BinaryTournament.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show BinaryTournament +--R BinaryTournament S: OrderedSet is a domain constructor +--R Abbreviation for BinaryTournament is BTOURN +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for BTOURN +--R +--R------------------------------- Operations -------------------------------- +--R binaryTournament : List S -> % children : % -> List % +--R copy : % -> % cyclic? : % -> Boolean +--R distance : (%,%) -> Integer ?.right : (%,right) -> % +--R ?.left : (%,left) -> % ?.value : (%,value) -> S +--R empty : () -> % empty? : % -> Boolean +--R eq? : (%,%) -> Boolean insert! : (S,%) -> % +--R leaf? : % -> Boolean leaves : % -> List S +--R left : % -> % map : ((S -> S),%) -> % +--R node : (%,S,%) -> % nodes : % -> List % +--R right : % -> % sample : () -> % +--R value : % -> S +--R #? : % -> NonNegativeInteger if $ has finiteAggregate +--R ?=? : (%,%) -> Boolean if S has SETCAT +--R any? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate +--R child? : (%,%) -> Boolean if S has SETCAT +--R coerce : % -> OutputForm if S has SETCAT +--R count : (S,%) -> NonNegativeInteger if $ has finiteAggregate and S has SETCAT +--R count : ((S -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate +--R eval : (%,List S,List S) -> % if S has EVALAB S and S has SETCAT +--R eval : (%,S,S) -> % if S has EVALAB S and S has SETCAT +--R eval : (%,Equation S) -> % if S has EVALAB S and S has SETCAT +--R eval : (%,List Equation S) -> % if S has EVALAB S and S has SETCAT +--R every? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate +--R hash : % -> SingleInteger if S has SETCAT +--R latex : % -> String if S has SETCAT +--R less? : (%,NonNegativeInteger) -> Boolean +--R map! : ((S -> S),%) -> % if $ has shallowlyMutable +--R member? : (S,%) -> Boolean if $ has finiteAggregate and S has SETCAT +--R members : % -> List S if $ has finiteAggregate +--R more? : (%,NonNegativeInteger) -> Boolean +--R node? : (%,%) -> Boolean if S has SETCAT +--R parts : % -> List S if $ has finiteAggregate +--R setchildren! : (%,List %) -> % if $ has shallowlyMutable +--R setelt : (%,right,%) -> % if $ has shallowlyMutable +--R setelt : (%,left,%) -> % if $ has shallowlyMutable +--R setelt : (%,value,S) -> S if $ has shallowlyMutable +--R setleft! : (%,%) -> % if $ has shallowlyMutable +--R setright! : (%,%) -> % if $ has shallowlyMutable +--R setvalue! : (%,S) -> S if $ has shallowlyMutable +--R size? : (%,NonNegativeInteger) -> Boolean +--R ?~=? : (%,%) -> Boolean if S has SETCAT +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +BinaryTournament examples +==================================================================== + +See Also: +o )show BinaryTournament + +@ + \pagehead{BinaryTournament}{BTOURN} \pagepic{ps/v103binarytournament.ps}{BTOURN}{1.00} {\bf See}\\ @@ -10869,6 +13381,80 @@ BinaryTournament(S: OrderedSet): Exports == Implementation where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain BTREE BinaryTree} + +<>= +)set break resume +)sys rm -f BinaryTree.output +)spool BinaryTree.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show BinaryTree +--R BinaryTree S: SetCategory is a domain constructor +--R Abbreviation for BinaryTree is BTREE +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for BTREE +--R +--R------------------------------- Operations -------------------------------- +--R binaryTree : (%,S,%) -> % binaryTree : S -> % +--R children : % -> List % copy : % -> % +--R cyclic? : % -> Boolean distance : (%,%) -> Integer +--R ?.right : (%,right) -> % ?.left : (%,left) -> % +--R ?.value : (%,value) -> S empty : () -> % +--R empty? : % -> Boolean eq? : (%,%) -> Boolean +--R leaf? : % -> Boolean leaves : % -> List S +--R left : % -> % map : ((S -> S),%) -> % +--R node : (%,S,%) -> % nodes : % -> List % +--R right : % -> % sample : () -> % +--R value : % -> S +--R #? : % -> NonNegativeInteger if $ has finiteAggregate +--R ?=? : (%,%) -> Boolean if S has SETCAT +--R any? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate +--R child? : (%,%) -> Boolean if S has SETCAT +--R coerce : % -> OutputForm if S has SETCAT +--R count : (S,%) -> NonNegativeInteger if $ has finiteAggregate and S has SETCAT +--R count : ((S -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate +--R eval : (%,List S,List S) -> % if S has EVALAB S and S has SETCAT +--R eval : (%,S,S) -> % if S has EVALAB S and S has SETCAT +--R eval : (%,Equation S) -> % if S has EVALAB S and S has SETCAT +--R eval : (%,List Equation S) -> % if S has EVALAB S and S has SETCAT +--R every? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate +--R hash : % -> SingleInteger if S has SETCAT +--R latex : % -> String if S has SETCAT +--R less? : (%,NonNegativeInteger) -> Boolean +--R map! : ((S -> S),%) -> % if $ has shallowlyMutable +--R member? : (S,%) -> Boolean if $ has finiteAggregate and S has SETCAT +--R members : % -> List S if $ has finiteAggregate +--R more? : (%,NonNegativeInteger) -> Boolean +--R node? : (%,%) -> Boolean if S has SETCAT +--R parts : % -> List S if $ has finiteAggregate +--R setchildren! : (%,List %) -> % if $ has shallowlyMutable +--R setelt : (%,right,%) -> % if $ has shallowlyMutable +--R setelt : (%,left,%) -> % if $ has shallowlyMutable +--R setelt : (%,value,S) -> S if $ has shallowlyMutable +--R setleft! : (%,%) -> % if $ has shallowlyMutable +--R setright! : (%,%) -> % if $ has shallowlyMutable +--R setvalue! : (%,S) -> S if $ has shallowlyMutable +--R size? : (%,NonNegativeInteger) -> Boolean +--R ?~=? : (%,%) -> Boolean if S has SETCAT +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +BinaryTree examples +==================================================================== + +See Also: +o )show BinaryTree + +@ + \pagehead{BinaryTree}{BTREE} \pagepic{ps/v103binarytree.ps}{BTREE}{1.00} {\bf See}\\ @@ -10991,6 +13577,114 @@ BinaryTree(S: SetCategory): Exports == Implementation where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain BITS Bits} + +<>= +)set break resume +)sys rm -f Bits.output +)spool Bits.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show Bits +--R Bits is a domain constructor +--R Abbreviation for Bits is BITS +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for BITS +--R +--R------------------------------- Operations -------------------------------- +--R ?/\? : (%,%) -> % ? Boolean +--R ?<=? : (%,%) -> Boolean ?=? : (%,%) -> Boolean +--R ?>? : (%,%) -> Boolean ?>=? : (%,%) -> Boolean +--R ?\/? : (%,%) -> % ^? : % -> % +--R ?and? : (%,%) -> % coerce : % -> OutputForm +--R concat : (%,Boolean) -> % concat : (Boolean,%) -> % +--R concat : (%,%) -> % concat : List % -> % +--R construct : List Boolean -> % copy : % -> % +--R delete : (%,Integer) -> % ?.? : (%,Integer) -> Boolean +--R empty : () -> % empty? : % -> Boolean +--R entries : % -> List Boolean eq? : (%,%) -> Boolean +--R hash : % -> SingleInteger index? : (Integer,%) -> Boolean +--R indices : % -> List Integer insert : (%,%,Integer) -> % +--R latex : % -> String max : (%,%) -> % +--R min : (%,%) -> % nand : (%,%) -> % +--R nor : (%,%) -> % not? : % -> % +--R ?or? : (%,%) -> % qelt : (%,Integer) -> Boolean +--R reverse : % -> % sample : () -> % +--R xor : (%,%) -> % ~? : % -> % +--R ?~=? : (%,%) -> Boolean +--R #? : % -> NonNegativeInteger if $ has finiteAggregate +--R any? : ((Boolean -> Boolean),%) -> Boolean if $ has finiteAggregate +--R bits : (NonNegativeInteger,Boolean) -> % +--R convert : % -> InputForm if Boolean has KONVERT INFORM +--R copyInto! : (%,%,Integer) -> % if $ has shallowlyMutable +--R count : ((Boolean -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate +--R count : (Boolean,%) -> NonNegativeInteger if $ has finiteAggregate and Boolean has SETCAT +--R delete : (%,UniversalSegment Integer) -> % +--R elt : (%,Integer,Boolean) -> Boolean +--R ?.? : (%,UniversalSegment Integer) -> % +--R entry? : (Boolean,%) -> Boolean if $ has finiteAggregate and Boolean has SETCAT +--R eval : (%,List Equation Boolean) -> % if Boolean has EVALAB BOOLEAN and Boolean has SETCAT +--R eval : (%,Equation Boolean) -> % if Boolean has EVALAB BOOLEAN and Boolean has SETCAT +--R eval : (%,Boolean,Boolean) -> % if Boolean has EVALAB BOOLEAN and Boolean has SETCAT +--R eval : (%,List Boolean,List Boolean) -> % if Boolean has EVALAB BOOLEAN and Boolean has SETCAT +--R every? : ((Boolean -> Boolean),%) -> Boolean if $ has finiteAggregate +--R fill! : (%,Boolean) -> % if $ has shallowlyMutable +--R find : ((Boolean -> Boolean),%) -> Union(Boolean,"failed") +--R first : % -> Boolean if Integer has ORDSET +--R insert : (Boolean,%,Integer) -> % +--R less? : (%,NonNegativeInteger) -> Boolean +--R map : ((Boolean -> Boolean),%) -> % +--R map : (((Boolean,Boolean) -> Boolean),%,%) -> % +--R map! : ((Boolean -> Boolean),%) -> % if $ has shallowlyMutable +--R maxIndex : % -> Integer if Integer has ORDSET +--R member? : (Boolean,%) -> Boolean if $ has finiteAggregate and Boolean has SETCAT +--R members : % -> List Boolean if $ has finiteAggregate +--R merge : (((Boolean,Boolean) -> Boolean),%,%) -> % +--R merge : (%,%) -> % if Boolean has ORDSET +--R minIndex : % -> Integer if Integer has ORDSET +--R more? : (%,NonNegativeInteger) -> Boolean +--R new : (NonNegativeInteger,Boolean) -> % +--R parts : % -> List Boolean if $ has finiteAggregate +--R position : ((Boolean -> Boolean),%) -> Integer +--R position : (Boolean,%) -> Integer if Boolean has SETCAT +--R position : (Boolean,%,Integer) -> Integer if Boolean has SETCAT +--R qsetelt! : (%,Integer,Boolean) -> Boolean if $ has shallowlyMutable +--R reduce : (((Boolean,Boolean) -> Boolean),%,Boolean,Boolean) -> Boolean if $ has finiteAggregate and Boolean has SETCAT +--R reduce : (((Boolean,Boolean) -> Boolean),%,Boolean) -> Boolean if $ has finiteAggregate +--R reduce : (((Boolean,Boolean) -> Boolean),%) -> Boolean if $ has finiteAggregate +--R remove : (Boolean,%) -> % if $ has finiteAggregate and Boolean has SETCAT +--R remove : ((Boolean -> Boolean),%) -> % if $ has finiteAggregate +--R removeDuplicates : % -> % if $ has finiteAggregate and Boolean has SETCAT +--R reverse! : % -> % if $ has shallowlyMutable +--R select : ((Boolean -> Boolean),%) -> % if $ has finiteAggregate +--R setelt : (%,Integer,Boolean) -> Boolean if $ has shallowlyMutable +--R setelt : (%,UniversalSegment Integer,Boolean) -> Boolean if $ has shallowlyMutable +--R size? : (%,NonNegativeInteger) -> Boolean +--R sort : (((Boolean,Boolean) -> Boolean),%) -> % +--R sort : % -> % if Boolean has ORDSET +--R sort! : (((Boolean,Boolean) -> Boolean),%) -> % if $ has shallowlyMutable +--R sort! : % -> % if $ has shallowlyMutable and Boolean has ORDSET +--R sorted? : (((Boolean,Boolean) -> Boolean),%) -> Boolean +--R sorted? : % -> Boolean if Boolean has ORDSET +--R swap! : (%,Integer,Integer) -> Void if $ has shallowlyMutable +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +Bits examples +==================================================================== + +See Also: +o )show Bits + +@ + \pagehead{Bits}{BITS} \pagepic{ps/v103bits.ps}{BITS}{1.00} {\bf See}\\ @@ -11102,6 +13796,7 @@ Bits(): Exports == Implementation where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain BLHN BlowUpWithHamburgerNoether} + <>= )set break resume )sys rm -f BlowUpWithHamburgerNoether.output @@ -11207,6 +13902,7 @@ BlowUpWithHamburgerNoether: Exports == Implementation where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain BLQT BlowUpWithQuadTrans} + <>= )set break resume )sys rm -f BlowUpWithQuadTrans.output @@ -11313,6 +14009,54 @@ BlowUpWithQuadTrans: Exports == Implementation where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain BOOLEAN Boolean} + +<>= +)set break resume +)sys rm -f Boolean.output +)spool Boolean.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show Boolean +--R Boolean is a domain constructor +--R Abbreviation for Boolean is BOOLEAN +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for BOOLEAN +--R +--R------------------------------- Operations -------------------------------- +--R ?/\? : (%,%) -> % ? Boolean +--R ?<=? : (%,%) -> Boolean ?=? : (%,%) -> Boolean +--R ?>? : (%,%) -> Boolean ?>=? : (%,%) -> Boolean +--R ?\/? : (%,%) -> % ^? : % -> % +--R ?and? : (%,%) -> % coerce : % -> OutputForm +--R convert : % -> InputForm false : () -> % +--R hash : % -> SingleInteger implies : (%,%) -> % +--R index : PositiveInteger -> % latex : % -> String +--R lookup : % -> PositiveInteger max : (%,%) -> % +--R min : (%,%) -> % nand : (%,%) -> % +--R nor : (%,%) -> % not? : % -> % +--R ?or? : (%,%) -> % random : () -> % +--R size : () -> NonNegativeInteger test : % -> Boolean +--R true : () -> % xor : (%,%) -> % +--R ~? : % -> % ?~=? : (%,%) -> Boolean +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +Boolean examples +==================================================================== + +See Also: +o )show Boolean + +@ + \pagehead{Boolean}{BOOLEAN} \pagepic{ps/v103boolean.ps}{BOOLEAN}{1.00} {\bf See}\\ @@ -11447,6 +14191,7 @@ Boolean(): Join(OrderedSet, Finite, Logic, ConvertibleTo InputForm) with \chapter{Chapter C} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain CARD CardinalNumber} + <>= )set break resume )sys rm -f CardinalNumber.output @@ -11995,6 +14740,7 @@ CardinalNumber: Join(OrderedSet, AbelianMonoid, Monoid, @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain CARTEN CartesianTensor} + <>= )set break resume )sys rm -f CartesianTensor.output @@ -13590,6 +16336,7 @@ CartesianTensor(minix, dim, R): Exports == Implementation where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain CHAR Character} + <>= )set break resume )sys rm -f Character.output @@ -13981,6 +16728,7 @@ Character: OrderedFinite() with @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain CCLASS CharacterClass} + <>= )set break resume )sys rm -f CharacterClass.output @@ -15457,6 +18205,47 @@ CliffordAlgebra(n, K, Q): T == Impl where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain COLOR Color} + +<>= +)set break resume +)sys rm -f Color.output +)spool Color.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show Color +--R Color is a domain constructor +--R Abbreviation for Color is COLOR +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for COLOR +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (DoubleFloat,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?+? : (%,%) -> % ?=? : (%,%) -> Boolean +--R blue : () -> % coerce : % -> OutputForm +--R color : Integer -> % green : () -> % +--R hash : % -> SingleInteger hue : % -> Integer +--R latex : % -> String red : () -> % +--R yellow : () -> % ?~=? : (%,%) -> Boolean +--R numberOfHues : () -> PositiveInteger +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +Color examples +==================================================================== + +See Also: +o )show Color + +@ + \pagehead{Color}{COLOR} \pagepic{ps/v103color.ps}{COLOR}{1.00} {\bf See}\\ @@ -15582,6 +18371,43 @@ Color(): Exports == Implementation where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain COMM Commutator} + +<>= +)set break resume +)sys rm -f Commutator.output +)spool Commutator.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show Commutator +--R Commutator is a domain constructor +--R Abbreviation for Commutator is COMM +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for COMM +--R +--R------------------------------- Operations -------------------------------- +--R ?=? : (%,%) -> Boolean coerce : % -> OutputForm +--R hash : % -> SingleInteger latex : % -> String +--R mkcomm : (%,%) -> % mkcomm : Integer -> % +--R ?~=? : (%,%) -> Boolean +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +Commutator examples +==================================================================== + +See Also: +o )show Commutator + +@ + \pagehead{Commutator}{COMM} \pagepic{ps/v103commutator.ps}{COMM}{1.00} {\bf See}\\ @@ -15650,6 +18476,7 @@ Commutator: Export == Implement where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain COMPLEX Complex} + <>= )set break resume )sys rm -f Complex.output @@ -16168,6 +18995,7 @@ Complex(R:CommutativeRing): ComplexCategory(R) with @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain CONTFRAC ContinuedFraction} + <>= )set break resume )sys rm -f ContinuedFraction.output @@ -17115,6 +19943,51 @@ ContinuedFraction(R): Exports == Implementation where \chapter{Chapter D} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain DBASE Database} + +<>= +)set break resume +)sys rm -f Database.output +)spool Database.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show Database +--R Database S where +--R S: OrderedSet with +--R ?.? : (%,Symbol) -> String +--R display : % -> Void +--R fullDisplay : % -> Void is a domain constructor +--R Abbreviation for Database is DBASE +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for DBASE +--R +--R------------------------------- Operations -------------------------------- +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R ?=? : (%,%) -> Boolean coerce : List S -> % +--R coerce : % -> OutputForm display : % -> Void +--R ?.? : (%,QueryEquation) -> % fullDisplay : % -> Void +--R hash : % -> SingleInteger latex : % -> String +--R ?~=? : (%,%) -> Boolean +--R ?.? : (%,Symbol) -> DataList String +--R fullDisplay : (%,PositiveInteger,PositiveInteger) -> Void +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +Database examples +==================================================================== + +See Also: +o )show Database + +@ + \pagehead{Database}{DBASE} \pagepic{ps/v103database.ps}{DBASE}{1.00} {\bf See}\\ @@ -17196,6 +20069,151 @@ Database(S): Exports == Implementation where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain DLIST DataList} + +<>= +)set break resume +)sys rm -f DataList.output +)spool DataList.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show DataList +--R DataList S: OrderedSet is a domain constructor +--R Abbreviation for DataList is DLIST +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for DLIST +--R +--R------------------------------- Operations -------------------------------- +--R children : % -> List % coerce : % -> List S +--R coerce : List S -> % concat : (%,S) -> % +--R concat : List % -> % concat : (S,%) -> % +--R concat : (%,%) -> % concat! : (%,S) -> % +--R concat! : (%,%) -> % construct : List S -> % +--R copy : % -> % cycleEntry : % -> % +--R cycleTail : % -> % cyclic? : % -> Boolean +--R datalist : List S -> % delete : (%,Integer) -> % +--R delete! : (%,Integer) -> % distance : (%,%) -> Integer +--R ?.sort : (%,sort) -> % ?.unique : (%,unique) -> % +--R elt : (%,Integer,S) -> S ?.? : (%,Integer) -> S +--R ?.last : (%,last) -> S ?.rest : (%,rest) -> % +--R ?.first : (%,first) -> S ?.value : (%,value) -> S +--R empty : () -> % empty? : % -> Boolean +--R entries : % -> List S eq? : (%,%) -> Boolean +--R explicitlyFinite? : % -> Boolean first : % -> S +--R index? : (Integer,%) -> Boolean indices : % -> List Integer +--R insert : (S,%,Integer) -> % insert : (%,%,Integer) -> % +--R insert! : (S,%,Integer) -> % insert! : (%,%,Integer) -> % +--R last : % -> S leaf? : % -> Boolean +--R leaves : % -> List S list : S -> % +--R map : (((S,S) -> S),%,%) -> % map : ((S -> S),%) -> % +--R new : (NonNegativeInteger,S) -> % nodes : % -> List % +--R possiblyInfinite? : % -> Boolean qelt : (%,Integer) -> S +--R rest : % -> % reverse : % -> % +--R sample : () -> % second : % -> S +--R tail : % -> % third : % -> S +--R value : % -> S +--R #? : % -> NonNegativeInteger if $ has finiteAggregate +--R ? Boolean if S has ORDSET +--R ?<=? : (%,%) -> Boolean if S has ORDSET +--R ?=? : (%,%) -> Boolean if S has SETCAT +--R ?>? : (%,%) -> Boolean if S has ORDSET +--R ?>=? : (%,%) -> Boolean if S has ORDSET +--R any? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate +--R child? : (%,%) -> Boolean if S has SETCAT +--R coerce : % -> OutputForm if S has SETCAT +--R convert : % -> InputForm if S has KONVERT INFORM +--R copyInto! : (%,%,Integer) -> % if $ has shallowlyMutable +--R count : (S,%) -> NonNegativeInteger if $ has finiteAggregate and S has SETCAT +--R count : ((S -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate +--R cycleLength : % -> NonNegativeInteger +--R cycleSplit! : % -> % if $ has shallowlyMutable +--R delete : (%,UniversalSegment Integer) -> % +--R delete! : (%,UniversalSegment Integer) -> % +--R ?.count : (%,count) -> NonNegativeInteger +--R ?.? : (%,UniversalSegment Integer) -> % +--R entry? : (S,%) -> Boolean if $ has finiteAggregate and S has SETCAT +--R eval : (%,List S,List S) -> % if S has EVALAB S and S has SETCAT +--R eval : (%,S,S) -> % if S has EVALAB S and S has SETCAT +--R eval : (%,Equation S) -> % if S has EVALAB S and S has SETCAT +--R eval : (%,List Equation S) -> % if S has EVALAB S and S has SETCAT +--R every? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate +--R fill! : (%,S) -> % if $ has shallowlyMutable +--R find : ((S -> Boolean),%) -> Union(S,"failed") +--R first : (%,NonNegativeInteger) -> % +--R hash : % -> SingleInteger if S has SETCAT +--R last : (%,NonNegativeInteger) -> % +--R latex : % -> String if S has SETCAT +--R less? : (%,NonNegativeInteger) -> Boolean +--R map! : ((S -> S),%) -> % if $ has shallowlyMutable +--R max : (%,%) -> % if S has ORDSET +--R maxIndex : % -> Integer if Integer has ORDSET +--R member? : (S,%) -> Boolean if $ has finiteAggregate and S has SETCAT +--R members : % -> List S if $ has finiteAggregate +--R merge : (((S,S) -> Boolean),%,%) -> % +--R merge : (%,%) -> % if S has ORDSET +--R merge! : (((S,S) -> Boolean),%,%) -> % +--R merge! : (%,%) -> % if S has ORDSET +--R min : (%,%) -> % if S has ORDSET +--R minIndex : % -> Integer if Integer has ORDSET +--R more? : (%,NonNegativeInteger) -> Boolean +--R node? : (%,%) -> Boolean if S has SETCAT +--R parts : % -> List S if $ has finiteAggregate +--R position : ((S -> Boolean),%) -> Integer +--R position : (S,%) -> Integer if S has SETCAT +--R position : (S,%,Integer) -> Integer if S has SETCAT +--R qsetelt! : (%,Integer,S) -> S if $ has shallowlyMutable +--R reduce : (((S,S) -> S),%,S,S) -> S if $ has finiteAggregate and S has SETCAT +--R reduce : (((S,S) -> S),%,S) -> S if $ has finiteAggregate +--R reduce : (((S,S) -> S),%) -> S if $ has finiteAggregate +--R remove : (S,%) -> % if $ has finiteAggregate and S has SETCAT +--R remove : ((S -> Boolean),%) -> % if $ has finiteAggregate +--R remove! : ((S -> Boolean),%) -> % +--R remove! : (S,%) -> % if S has SETCAT +--R removeDuplicates : % -> % if $ has finiteAggregate and S has SETCAT +--R removeDuplicates! : % -> % if S has SETCAT +--R rest : (%,NonNegativeInteger) -> % +--R reverse! : % -> % if $ has shallowlyMutable +--R select : ((S -> Boolean),%) -> % if $ has finiteAggregate +--R select! : ((S -> Boolean),%) -> % +--R setchildren! : (%,List %) -> % if $ has shallowlyMutable +--R setelt : (%,Integer,S) -> S if $ has shallowlyMutable +--R setelt : (%,UniversalSegment Integer,S) -> S if $ has shallowlyMutable +--R setelt : (%,last,S) -> S if $ has shallowlyMutable +--R setelt : (%,rest,%) -> % if $ has shallowlyMutable +--R setelt : (%,first,S) -> S if $ has shallowlyMutable +--R setelt : (%,value,S) -> S if $ has shallowlyMutable +--R setfirst! : (%,S) -> S if $ has shallowlyMutable +--R setlast! : (%,S) -> S if $ has shallowlyMutable +--R setrest! : (%,%) -> % if $ has shallowlyMutable +--R setvalue! : (%,S) -> S if $ has shallowlyMutable +--R size? : (%,NonNegativeInteger) -> Boolean +--R sort : (((S,S) -> Boolean),%) -> % +--R sort : % -> % if S has ORDSET +--R sort! : (((S,S) -> Boolean),%) -> % if $ has shallowlyMutable +--R sort! : % -> % if $ has shallowlyMutable and S has ORDSET +--R sorted? : (((S,S) -> Boolean),%) -> Boolean +--R sorted? : % -> Boolean if S has ORDSET +--R split! : (%,Integer) -> % if $ has shallowlyMutable +--R swap! : (%,Integer,Integer) -> Void if $ has shallowlyMutable +--R ?~=? : (%,%) -> Boolean if S has SETCAT +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +DataList examples +==================================================================== + +See Also: +o )show DataList + +@ + \pagehead{DataList}{DLIST} \pagepic{ps/v103datalist.ps}{DLIST}{1.00} {\bf See}\\ @@ -17351,6 +20369,7 @@ DataList(S:OrderedSet) : Exports == Implementation where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain DECIMAL DecimalExpansion} + <>= )set break resume )sys rm -f DecimalExpansion.output @@ -17634,6 +20653,7 @@ DecimalExpansion(): Exports == Implementation where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{Denavit-Hartenberg Matrices} + \subsection{Homogeneous Transformations} The study of robot manipulation is concerned with the relationship between objects, and between objects and manipulators. In this chapter we will @@ -19402,6 +22422,7 @@ DenavitHartenbergMatrix(R): Exports == Implementation where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain DEQUEUE Dequeue} + <>= )set break resume )sys rm -f Dequeue.output @@ -20611,6 +23632,7 @@ Dequeue(S:SetCategory): DequeueAggregate S with @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain DERHAM DeRhamComplex} + <>= )set break resume )sys rm -f DeRhamComplex.output @@ -21352,8 +24374,8 @@ DeRhamComplex(CoefRing,listIndVar:List Symbol): Export == Implement where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -DSTREE DesingTree \section{domain DSTREE DesingTree} + <>= )set break resume )sys rm -f DesingTree.output @@ -21551,6 +24573,187 @@ DesingTree(S: SetCategory): T==C where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain DSMP DifferentialSparseMultivariatePolynomial} + +<>= +)set break resume +)sys rm -f DifferentialSparseMultivariatePolynomial.output +)spool DifferentialSparseMultivariatePolynomial.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show DifferentialSparseMultivariatePolynomial +--R DifferentialSparseMultivariatePolynomial(R: Ring,S: OrderedSet,V: DifferentialVariableCategory S) is a domain constructor +--R Abbreviation for DifferentialSparseMultivariatePolynomial is DSMP +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for DSMP +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (%,R) -> % ?*? : (R,%) -> % +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ?=? : (%,%) -> Boolean +--R D : (%,(R -> R)) -> % D : % -> % if R has DIFRING +--R D : (%,List V) -> % D : (%,V) -> % +--R 1 : () -> % 0 : () -> % +--R ?^? : (%,PositiveInteger) -> % coefficients : % -> List R +--R coerce : S -> % coerce : V -> % +--R coerce : R -> % coerce : Integer -> % +--R coerce : % -> OutputForm degree : % -> IndexedExponents V +--R differentiate : (%,List V) -> % differentiate : (%,V) -> % +--R eval : (%,List V,List %) -> % eval : (%,V,%) -> % +--R eval : (%,List V,List R) -> % eval : (%,V,R) -> % +--R eval : (%,List %,List %) -> % eval : (%,%,%) -> % +--R eval : (%,Equation %) -> % eval : (%,List Equation %) -> % +--R ground : % -> R ground? : % -> Boolean +--R hash : % -> SingleInteger initial : % -> % +--R isobaric? : % -> Boolean latex : % -> String +--R leader : % -> V leadingCoefficient : % -> R +--R leadingMonomial : % -> % map : ((R -> R),%) -> % +--R monomial? : % -> Boolean monomials : % -> List % +--R one? : % -> Boolean order : % -> NonNegativeInteger +--R primitiveMonomials : % -> List % recip : % -> Union(%,"failed") +--R reductum : % -> % retract : % -> S +--R retract : % -> V retract : % -> R +--R sample : () -> % separant : % -> % +--R variables : % -> List V weight : % -> NonNegativeInteger +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean +--R ?*? : (Fraction Integer,%) -> % if R has ALGEBRA FRAC INT +--R ?*? : (%,Fraction Integer) -> % if R has ALGEBRA FRAC INT +--R ?*? : (NonNegativeInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % +--R ?/? : (%,R) -> % if R has FIELD +--R ? Boolean if R has ORDSET +--R ?<=? : (%,%) -> Boolean if R has ORDSET +--R ?>? : (%,%) -> Boolean if R has ORDSET +--R ?>=? : (%,%) -> Boolean if R has ORDSET +--R D : (%,(R -> R),NonNegativeInteger) -> % +--R D : (%,List Symbol,List NonNegativeInteger) -> % if R has PDRING SYMBOL +--R D : (%,Symbol,NonNegativeInteger) -> % if R has PDRING SYMBOL +--R D : (%,List Symbol) -> % if R has PDRING SYMBOL +--R D : (%,Symbol) -> % if R has PDRING SYMBOL +--R D : (%,NonNegativeInteger) -> % if R has DIFRING +--R D : (%,List V,List NonNegativeInteger) -> % +--R D : (%,V,NonNegativeInteger) -> % +--R ?^? : (%,NonNegativeInteger) -> % +--R associates? : (%,%) -> Boolean if R has INTDOM +--R binomThmExpt : (%,%,NonNegativeInteger) -> % if R has COMRING +--R characteristic : () -> NonNegativeInteger +--R charthRoot : % -> Union(%,"failed") if $ has CHARNZ and R has PFECAT or R has CHARNZ +--R coefficient : (%,List V,List NonNegativeInteger) -> % +--R coefficient : (%,V,NonNegativeInteger) -> % +--R coefficient : (%,IndexedExponents V) -> R +--R coerce : % -> % if R has INTDOM +--R coerce : Fraction Integer -> % if R has ALGEBRA FRAC INT or R has RETRACT FRAC INT +--R coerce : SparseMultivariatePolynomial(R,S) -> % +--R conditionP : Matrix % -> Union(Vector %,"failed") if $ has CHARNZ and R has PFECAT +--R content : (%,V) -> % if R has GCDDOM +--R content : % -> R if R has GCDDOM +--R convert : % -> InputForm if R has KONVERT INFORM and V has KONVERT INFORM +--R convert : % -> Pattern Integer if R has KONVERT PATTERN INT and V has KONVERT PATTERN INT +--R convert : % -> Pattern Float if R has KONVERT PATTERN FLOAT and V has KONVERT PATTERN FLOAT +--R degree : (%,S) -> NonNegativeInteger +--R degree : (%,List V) -> List NonNegativeInteger +--R degree : (%,V) -> NonNegativeInteger +--R differentialVariables : % -> List S +--R differentiate : (%,(R -> R)) -> % +--R differentiate : (%,(R -> R),NonNegativeInteger) -> % +--R differentiate : (%,List Symbol,List NonNegativeInteger) -> % if R has PDRING SYMBOL +--R differentiate : (%,Symbol,NonNegativeInteger) -> % if R has PDRING SYMBOL +--R differentiate : (%,List Symbol) -> % if R has PDRING SYMBOL +--R differentiate : (%,Symbol) -> % if R has PDRING SYMBOL +--R differentiate : (%,NonNegativeInteger) -> % if R has DIFRING +--R differentiate : % -> % if R has DIFRING +--R differentiate : (%,List V,List NonNegativeInteger) -> % +--R differentiate : (%,V,NonNegativeInteger) -> % +--R discriminant : (%,V) -> % if R has COMRING +--R eval : (%,List S,List R) -> % if R has DIFRING +--R eval : (%,S,R) -> % if R has DIFRING +--R eval : (%,List S,List %) -> % if R has DIFRING +--R eval : (%,S,%) -> % if R has DIFRING +--R exquo : (%,%) -> Union(%,"failed") if R has INTDOM +--R exquo : (%,R) -> Union(%,"failed") if R has INTDOM +--R factor : % -> Factored % if R has PFECAT +--R factorPolynomial : SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if R has PFECAT +--R factorSquareFreePolynomial : SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if R has PFECAT +--R gcd : (%,%) -> % if R has GCDDOM +--R gcd : List % -> % if R has GCDDOM +--R gcdPolynomial : (SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial % if R has GCDDOM +--R isExpt : % -> Union(Record(var: V,exponent: NonNegativeInteger),"failed") +--R isPlus : % -> Union(List %,"failed") +--R isTimes : % -> Union(List %,"failed") +--R lcm : (%,%) -> % if R has GCDDOM +--R lcm : List % -> % if R has GCDDOM +--R mainVariable : % -> Union(V,"failed") +--R makeVariable : % -> (NonNegativeInteger -> %) if R has DIFRING +--R makeVariable : S -> (NonNegativeInteger -> %) +--R mapExponents : ((IndexedExponents V -> IndexedExponents V),%) -> % +--R max : (%,%) -> % if R has ORDSET +--R min : (%,%) -> % if R has ORDSET +--R minimumDegree : (%,List V) -> List NonNegativeInteger +--R minimumDegree : (%,V) -> NonNegativeInteger +--R minimumDegree : % -> IndexedExponents V +--R monicDivide : (%,%,V) -> Record(quotient: %,remainder: %) +--R monomial : (%,List V,List NonNegativeInteger) -> % +--R monomial : (%,V,NonNegativeInteger) -> % +--R monomial : (R,IndexedExponents V) -> % +--R multivariate : (SparseUnivariatePolynomial %,V) -> % +--R multivariate : (SparseUnivariatePolynomial R,V) -> % +--R numberOfMonomials : % -> NonNegativeInteger +--R order : (%,S) -> NonNegativeInteger +--R patternMatch : (%,Pattern Integer,PatternMatchResult(Integer,%)) -> PatternMatchResult(Integer,%) if R has PATMAB INT and V has PATMAB INT +--R patternMatch : (%,Pattern Float,PatternMatchResult(Float,%)) -> PatternMatchResult(Float,%) if R has PATMAB FLOAT and V has PATMAB FLOAT +--R pomopo! : (%,R,IndexedExponents V,%) -> % +--R prime? : % -> Boolean if R has PFECAT +--R primitivePart : (%,V) -> % if R has GCDDOM +--R primitivePart : % -> % if R has GCDDOM +--R reducedSystem : Matrix % -> Matrix R +--R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix R,vec: Vector R) +--R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix Integer,vec: Vector Integer) if R has LINEXP INT +--R reducedSystem : Matrix % -> Matrix Integer if R has LINEXP INT +--R resultant : (%,%,V) -> % if R has COMRING +--R retract : % -> SparseMultivariatePolynomial(R,S) +--R retract : % -> Integer if R has RETRACT INT +--R retract : % -> Fraction Integer if R has RETRACT FRAC INT +--R retractIfCan : % -> Union(SparseMultivariatePolynomial(R,S),"failed") +--R retractIfCan : % -> Union(S,"failed") +--R retractIfCan : % -> Union(V,"failed") +--R retractIfCan : % -> Union(Integer,"failed") if R has RETRACT INT +--R retractIfCan : % -> Union(Fraction Integer,"failed") if R has RETRACT FRAC INT +--R retractIfCan : % -> Union(R,"failed") +--R solveLinearPolynomialEquation : (List SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> Union(List SparseUnivariatePolynomial %,"failed") if R has PFECAT +--R squareFree : % -> Factored % if R has GCDDOM +--R squareFreePart : % -> % if R has GCDDOM +--R squareFreePolynomial : SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if R has PFECAT +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R totalDegree : (%,List V) -> NonNegativeInteger +--R totalDegree : % -> NonNegativeInteger +--R unit? : % -> Boolean if R has INTDOM +--R unitCanonical : % -> % if R has INTDOM +--R unitNormal : % -> Record(unit: %,canonical: %,associate: %) if R has INTDOM +--R univariate : % -> SparseUnivariatePolynomial R +--R univariate : (%,V) -> SparseUnivariatePolynomial % +--R weight : (%,S) -> NonNegativeInteger +--R weights : (%,S) -> List NonNegativeInteger +--R weights : % -> List NonNegativeInteger +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +DifferentialSparseMultivariatePolynomial examples +==================================================================== + +See Also: +o )show DifferentialSparseMultivariatePolynomial + +@ + \pagehead{DifferentialSparseMultivariatePolynomial}{DSMP} \pagepic{ps/v103differentialsparsemultivariatepolynomial.ps}{DSMP}{1.00} {\bf See}\\ @@ -21707,6 +24910,142 @@ DifferentialSparseMultivariatePolynomial(R, S, V): @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain DIRPROD DirectProduct} + +<>= +)set break resume +)sys rm -f DirectProduct.output +)spool DirectProduct.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show DirectProduct +--R DirectProduct(dim: NonNegativeInteger,R: Type) is a domain constructor +--R Abbreviation for DirectProduct is DIRPROD +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for DIRPROD +--R +--R------------------------------- Operations -------------------------------- +--R -? : % -> % if R has RING 1 : () -> % if R has MONOID +--R 0 : () -> % if R has CABMON coerce : % -> Vector R +--R copy : % -> % directProduct : Vector R -> % +--R ?.? : (%,Integer) -> R elt : (%,Integer,R) -> R +--R empty : () -> % empty? : % -> Boolean +--R entries : % -> List R eq? : (%,%) -> Boolean +--R index? : (Integer,%) -> Boolean indices : % -> List Integer +--R map : ((R -> R),%) -> % qelt : (%,Integer) -> R +--R sample : () -> % +--R #? : % -> NonNegativeInteger if $ has finiteAggregate +--R ?*? : (PositiveInteger,%) -> % if R has ABELSG +--R ?*? : (NonNegativeInteger,%) -> % if R has CABMON +--R ?*? : (R,%) -> % if R has RING +--R ?*? : (%,R) -> % if R has RING +--R ?*? : (%,%) -> % if R has MONOID +--R ?*? : (Integer,%) -> % if R has RING +--R ?**? : (%,PositiveInteger) -> % if R has MONOID +--R ?**? : (%,NonNegativeInteger) -> % if R has MONOID +--R ?+? : (%,%) -> % if R has ABELSG +--R ?-? : (%,%) -> % if R has RING +--R ?/? : (%,R) -> % if R has FIELD +--R ? Boolean if R has OAMONS or R has ORDRING +--R ?<=? : (%,%) -> Boolean if R has OAMONS or R has ORDRING +--R ?=? : (%,%) -> Boolean if R has SETCAT +--R ?>? : (%,%) -> Boolean if R has OAMONS or R has ORDRING +--R ?>=? : (%,%) -> Boolean if R has OAMONS or R has ORDRING +--R D : (%,(R -> R)) -> % if R has RING +--R D : (%,(R -> R),NonNegativeInteger) -> % if R has RING +--R D : (%,List Symbol,List NonNegativeInteger) -> % if R has PDRING SYMBOL and R has RING +--R D : (%,Symbol,NonNegativeInteger) -> % if R has PDRING SYMBOL and R has RING +--R D : (%,List Symbol) -> % if R has PDRING SYMBOL and R has RING +--R D : (%,Symbol) -> % if R has PDRING SYMBOL and R has RING +--R D : (%,NonNegativeInteger) -> % if R has DIFRING and R has RING +--R D : % -> % if R has DIFRING and R has RING +--R ?^? : (%,PositiveInteger) -> % if R has MONOID +--R ?^? : (%,NonNegativeInteger) -> % if R has MONOID +--R abs : % -> % if R has ORDRING +--R any? : ((R -> Boolean),%) -> Boolean if $ has finiteAggregate +--R characteristic : () -> NonNegativeInteger if R has RING +--R coerce : R -> % if R has SETCAT +--R coerce : Fraction Integer -> % if R has RETRACT FRAC INT and R has SETCAT +--R coerce : Integer -> % if R has RETRACT INT and R has SETCAT or R has RING +--R coerce : % -> OutputForm if R has SETCAT +--R count : (R,%) -> NonNegativeInteger if $ has finiteAggregate and R has SETCAT +--R count : ((R -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate +--R differentiate : (%,(R -> R)) -> % if R has RING +--R differentiate : (%,(R -> R),NonNegativeInteger) -> % if R has RING +--R differentiate : (%,List Symbol,List NonNegativeInteger) -> % if R has PDRING SYMBOL and R has RING +--R differentiate : (%,Symbol,NonNegativeInteger) -> % if R has PDRING SYMBOL and R has RING +--R differentiate : (%,List Symbol) -> % if R has PDRING SYMBOL and R has RING +--R differentiate : (%,Symbol) -> % if R has PDRING SYMBOL and R has RING +--R differentiate : (%,NonNegativeInteger) -> % if R has DIFRING and R has RING +--R differentiate : % -> % if R has DIFRING and R has RING +--R dimension : () -> CardinalNumber if R has FIELD +--R dot : (%,%) -> R if R has RING +--R entry? : (R,%) -> Boolean if $ has finiteAggregate and R has SETCAT +--R eval : (%,List R,List R) -> % if R has EVALAB R and R has SETCAT +--R eval : (%,R,R) -> % if R has EVALAB R and R has SETCAT +--R eval : (%,Equation R) -> % if R has EVALAB R and R has SETCAT +--R eval : (%,List Equation R) -> % if R has EVALAB R and R has SETCAT +--R every? : ((R -> Boolean),%) -> Boolean if $ has finiteAggregate +--R fill! : (%,R) -> % if $ has shallowlyMutable +--R first : % -> R if Integer has ORDSET +--R hash : % -> SingleInteger if R has SETCAT +--R index : PositiveInteger -> % if R has FINITE +--R latex : % -> String if R has SETCAT +--R less? : (%,NonNegativeInteger) -> Boolean +--R lookup : % -> PositiveInteger if R has FINITE +--R map! : ((R -> R),%) -> % if $ has shallowlyMutable +--R max : (%,%) -> % if R has OAMONS or R has ORDRING +--R maxIndex : % -> Integer if Integer has ORDSET +--R member? : (R,%) -> Boolean if $ has finiteAggregate and R has SETCAT +--R members : % -> List R if $ has finiteAggregate +--R min : (%,%) -> % if R has OAMONS or R has ORDRING +--R minIndex : % -> Integer if Integer has ORDSET +--R more? : (%,NonNegativeInteger) -> Boolean +--R negative? : % -> Boolean if R has ORDRING +--R one? : % -> Boolean if R has MONOID +--R parts : % -> List R if $ has finiteAggregate +--R positive? : % -> Boolean if R has ORDRING +--R qsetelt! : (%,Integer,R) -> R if $ has shallowlyMutable +--R random : () -> % if R has FINITE +--R recip : % -> Union(%,"failed") if R has MONOID +--R reducedSystem : Matrix % -> Matrix R if R has RING +--R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix R,vec: Vector R) if R has RING +--R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix Integer,vec: Vector Integer) if R has LINEXP INT and R has RING +--R reducedSystem : Matrix % -> Matrix Integer if R has LINEXP INT and R has RING +--R retract : % -> R if R has SETCAT +--R retract : % -> Fraction Integer if R has RETRACT FRAC INT and R has SETCAT +--R retract : % -> Integer if R has RETRACT INT and R has SETCAT +--R retractIfCan : % -> Union(R,"failed") if R has SETCAT +--R retractIfCan : % -> Union(Fraction Integer,"failed") if R has RETRACT FRAC INT and R has SETCAT +--R retractIfCan : % -> Union(Integer,"failed") if R has RETRACT INT and R has SETCAT +--R setelt : (%,Integer,R) -> R if $ has shallowlyMutable +--R sign : % -> Integer if R has ORDRING +--R size : () -> NonNegativeInteger if R has FINITE +--R size? : (%,NonNegativeInteger) -> Boolean +--R subtractIfCan : (%,%) -> Union(%,"failed") if R has CABMON +--R sup : (%,%) -> % if R has OAMONS +--R swap! : (%,Integer,Integer) -> Void if $ has shallowlyMutable +--R unitVector : PositiveInteger -> % if R has RING +--R zero? : % -> Boolean if R has CABMON +--R ?~=? : (%,%) -> Boolean if R has SETCAT +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +DirectProduct examples +==================================================================== + +See Also: +o )show DirectProduct + +@ + \pagehead{DirectProduct}{DIRPROD} \pagepic{ps/v103directproduct.ps}{DIRPROD}{1.00} @@ -21898,6 +25237,138 @@ DirectProduct(dim:NonNegativeInteger, R:Type): @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain DPMM DirectProductMatrixModule} + +<>= +)set break resume +)sys rm -f DirectProductMatrixModule.output +)spool DirectProductMatrixModule.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show DirectProductMatrixModule +--R DirectProductMatrixModule(n: PositiveInteger,R: Ring,M: SquareMatrixCategory(n,R,DirectProduct(n,R),DirectProduct(n,R)),S: LeftModule R) is a domain constructor +--R Abbreviation for DirectProductMatrixModule is DPMM +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for DPMM +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (M,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?*? : (Integer,%) -> % ?*? : (R,%) -> % +--R ?+? : (%,%) -> % -? : % -> % +--R ?-? : (%,%) -> % ?=? : (%,%) -> Boolean +--R 0 : () -> % coerce : % -> OutputForm +--R coerce : % -> Vector S copy : % -> % +--R directProduct : Vector S -> % ?.? : (%,Integer) -> S +--R elt : (%,Integer,S) -> S empty : () -> % +--R empty? : % -> Boolean entries : % -> List S +--R eq? : (%,%) -> Boolean hash : % -> SingleInteger +--R index? : (Integer,%) -> Boolean indices : % -> List Integer +--R latex : % -> String map : ((S -> S),%) -> % +--R qelt : (%,Integer) -> S sample : () -> % +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean +--R #? : % -> NonNegativeInteger if $ has finiteAggregate +--R ?*? : (%,%) -> % if S has DIFRING and S has RING or S has LINEXP INT and S has RING or S has MONOID or S has PDRING SYMBOL and S has RING +--R ?*? : (S,%) -> % if S has RING +--R ?*? : (%,S) -> % if S has RING +--R ?*? : (NonNegativeInteger,%) -> % +--R ?**? : (%,PositiveInteger) -> % if S has DIFRING and S has RING or S has LINEXP INT and S has RING or S has MONOID or S has PDRING SYMBOL and S has RING +--R ?**? : (%,NonNegativeInteger) -> % if S has DIFRING and S has RING or S has LINEXP INT and S has RING or S has MONOID or S has PDRING SYMBOL and S has RING +--R ?/? : (%,S) -> % if S has FIELD +--R ? Boolean if S has OAMONS or S has ORDRING +--R ?<=? : (%,%) -> Boolean if S has OAMONS or S has ORDRING +--R ?>? : (%,%) -> Boolean if S has OAMONS or S has ORDRING +--R ?>=? : (%,%) -> Boolean if S has OAMONS or S has ORDRING +--R D : % -> % if S has DIFRING and S has RING +--R D : (%,NonNegativeInteger) -> % if S has DIFRING and S has RING +--R D : (%,Symbol) -> % if S has PDRING SYMBOL and S has RING +--R D : (%,List Symbol) -> % if S has PDRING SYMBOL and S has RING +--R D : (%,Symbol,NonNegativeInteger) -> % if S has PDRING SYMBOL and S has RING +--R D : (%,List Symbol,List NonNegativeInteger) -> % if S has PDRING SYMBOL and S has RING +--R D : (%,(S -> S)) -> % if S has RING +--R D : (%,(S -> S),NonNegativeInteger) -> % if S has RING +--R 1 : () -> % if S has DIFRING and S has RING or S has LINEXP INT and S has RING or S has MONOID or S has PDRING SYMBOL and S has RING +--R ?^? : (%,PositiveInteger) -> % if S has DIFRING and S has RING or S has LINEXP INT and S has RING or S has MONOID or S has PDRING SYMBOL and S has RING +--R ?^? : (%,NonNegativeInteger) -> % if S has DIFRING and S has RING or S has LINEXP INT and S has RING or S has MONOID or S has PDRING SYMBOL and S has RING +--R abs : % -> % if S has ORDRING +--R any? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate +--R characteristic : () -> NonNegativeInteger if S has RING +--R coerce : Fraction Integer -> % if S has RETRACT FRAC INT and S has SETCAT +--R coerce : Integer -> % if S has RETRACT INT and S has SETCAT or S has RING +--R coerce : S -> % if S has SETCAT +--R count : (S,%) -> NonNegativeInteger if $ has finiteAggregate and S has SETCAT +--R count : ((S -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate +--R differentiate : % -> % if S has DIFRING and S has RING +--R differentiate : (%,NonNegativeInteger) -> % if S has DIFRING and S has RING +--R differentiate : (%,Symbol) -> % if S has PDRING SYMBOL and S has RING +--R differentiate : (%,List Symbol) -> % if S has PDRING SYMBOL and S has RING +--R differentiate : (%,Symbol,NonNegativeInteger) -> % if S has PDRING SYMBOL and S has RING +--R differentiate : (%,List Symbol,List NonNegativeInteger) -> % if S has PDRING SYMBOL and S has RING +--R differentiate : (%,(S -> S)) -> % if S has RING +--R differentiate : (%,(S -> S),NonNegativeInteger) -> % if S has RING +--R dimension : () -> CardinalNumber if S has FIELD +--R dot : (%,%) -> S if S has RING +--R entry? : (S,%) -> Boolean if $ has finiteAggregate and S has SETCAT +--R eval : (%,List S,List S) -> % if S has EVALAB S and S has SETCAT +--R eval : (%,S,S) -> % if S has EVALAB S and S has SETCAT +--R eval : (%,Equation S) -> % if S has EVALAB S and S has SETCAT +--R eval : (%,List Equation S) -> % if S has EVALAB S and S has SETCAT +--R every? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate +--R fill! : (%,S) -> % if $ has shallowlyMutable +--R first : % -> S if Integer has ORDSET +--R index : PositiveInteger -> % if S has FINITE +--R less? : (%,NonNegativeInteger) -> Boolean +--R lookup : % -> PositiveInteger if S has FINITE +--R map! : ((S -> S),%) -> % if $ has shallowlyMutable +--R max : (%,%) -> % if S has OAMONS or S has ORDRING +--R maxIndex : % -> Integer if Integer has ORDSET +--R member? : (S,%) -> Boolean if $ has finiteAggregate and S has SETCAT +--R members : % -> List S if $ has finiteAggregate +--R min : (%,%) -> % if S has OAMONS or S has ORDRING +--R minIndex : % -> Integer if Integer has ORDSET +--R more? : (%,NonNegativeInteger) -> Boolean +--R negative? : % -> Boolean if S has ORDRING +--R one? : % -> Boolean if S has DIFRING and S has RING or S has LINEXP INT and S has RING or S has MONOID or S has PDRING SYMBOL and S has RING +--R parts : % -> List S if $ has finiteAggregate +--R positive? : % -> Boolean if S has ORDRING +--R qsetelt! : (%,Integer,S) -> S if $ has shallowlyMutable +--R random : () -> % if S has FINITE +--R recip : % -> Union(%,"failed") if S has DIFRING and S has RING or S has LINEXP INT and S has RING or S has MONOID or S has PDRING SYMBOL and S has RING +--R reducedSystem : Matrix % -> Matrix Integer if S has LINEXP INT and S has RING +--R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix Integer,vec: Vector Integer) if S has LINEXP INT and S has RING +--R reducedSystem : Matrix % -> Matrix S if S has RING +--R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix S,vec: Vector S) if S has RING +--R retract : % -> Fraction Integer if S has RETRACT FRAC INT and S has SETCAT +--R retract : % -> Integer if S has RETRACT INT and S has SETCAT +--R retract : % -> S if S has SETCAT +--R retractIfCan : % -> Union(Fraction Integer,"failed") if S has RETRACT FRAC INT and S has SETCAT +--R retractIfCan : % -> Union(Integer,"failed") if S has RETRACT INT and S has SETCAT +--R retractIfCan : % -> Union(S,"failed") if S has SETCAT +--R setelt : (%,Integer,S) -> S if $ has shallowlyMutable +--R sign : % -> Integer if S has ORDRING +--R size : () -> NonNegativeInteger if S has FINITE +--R size? : (%,NonNegativeInteger) -> Boolean +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R sup : (%,%) -> % if S has OAMONS +--R swap! : (%,Integer,Integer) -> Void if $ has shallowlyMutable +--R unitVector : PositiveInteger -> % if S has RING +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +DirectProductMatrixModule examples +==================================================================== + +See Also: +o )show DirectProductMatrixModule + +@ + \pagehead{DirectProductMatrixModule}{DPMM} \pagepic{ps/v103directproductmatrixmodule.ps}{DPMM}{1.00} {\bf See}\\ @@ -22024,6 +25495,138 @@ DirectProductMatrixModule(n, R, M, S): DPcategory == DPcapsule where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain DPMO DirectProductModule} + +<>= +)set break resume +)sys rm -f DirectProductModule.output +)spool DirectProductModule.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show DirectProductModule +--R DirectProductModule(n: NonNegativeInteger,R: Ring,S: LeftModule R) is a domain constructor +--R Abbreviation for DirectProductModule is DPMO +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for DPMO +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (PositiveInteger,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (R,%) -> % ?+? : (%,%) -> % +--R -? : % -> % ?-? : (%,%) -> % +--R ?=? : (%,%) -> Boolean 0 : () -> % +--R coerce : % -> OutputForm coerce : % -> Vector S +--R copy : % -> % directProduct : Vector S -> % +--R ?.? : (%,Integer) -> S elt : (%,Integer,S) -> S +--R empty : () -> % empty? : % -> Boolean +--R entries : % -> List S eq? : (%,%) -> Boolean +--R hash : % -> SingleInteger index? : (Integer,%) -> Boolean +--R indices : % -> List Integer latex : % -> String +--R map : ((S -> S),%) -> % qelt : (%,Integer) -> S +--R sample : () -> % zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean +--R #? : % -> NonNegativeInteger if $ has finiteAggregate +--R ?*? : (%,%) -> % if S has DIFRING and S has RING or S has LINEXP INT and S has RING or S has MONOID or S has PDRING SYMBOL and S has RING +--R ?*? : (S,%) -> % if S has RING +--R ?*? : (%,S) -> % if S has RING +--R ?*? : (NonNegativeInteger,%) -> % +--R ?**? : (%,PositiveInteger) -> % if S has DIFRING and S has RING or S has LINEXP INT and S has RING or S has MONOID or S has PDRING SYMBOL and S has RING +--R ?**? : (%,NonNegativeInteger) -> % if S has DIFRING and S has RING or S has LINEXP INT and S has RING or S has MONOID or S has PDRING SYMBOL and S has RING +--R ?/? : (%,S) -> % if S has FIELD +--R ? Boolean if S has OAMONS or S has ORDRING +--R ?<=? : (%,%) -> Boolean if S has OAMONS or S has ORDRING +--R ?>? : (%,%) -> Boolean if S has OAMONS or S has ORDRING +--R ?>=? : (%,%) -> Boolean if S has OAMONS or S has ORDRING +--R D : % -> % if S has DIFRING and S has RING +--R D : (%,NonNegativeInteger) -> % if S has DIFRING and S has RING +--R D : (%,Symbol) -> % if S has PDRING SYMBOL and S has RING +--R D : (%,List Symbol) -> % if S has PDRING SYMBOL and S has RING +--R D : (%,Symbol,NonNegativeInteger) -> % if S has PDRING SYMBOL and S has RING +--R D : (%,List Symbol,List NonNegativeInteger) -> % if S has PDRING SYMBOL and S has RING +--R D : (%,(S -> S)) -> % if S has RING +--R D : (%,(S -> S),NonNegativeInteger) -> % if S has RING +--R 1 : () -> % if S has DIFRING and S has RING or S has LINEXP INT and S has RING or S has MONOID or S has PDRING SYMBOL and S has RING +--R ?^? : (%,PositiveInteger) -> % if S has DIFRING and S has RING or S has LINEXP INT and S has RING or S has MONOID or S has PDRING SYMBOL and S has RING +--R ?^? : (%,NonNegativeInteger) -> % if S has DIFRING and S has RING or S has LINEXP INT and S has RING or S has MONOID or S has PDRING SYMBOL and S has RING +--R abs : % -> % if S has ORDRING +--R any? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate +--R characteristic : () -> NonNegativeInteger if S has RING +--R coerce : Fraction Integer -> % if S has RETRACT FRAC INT and S has SETCAT +--R coerce : Integer -> % if S has RETRACT INT and S has SETCAT or S has RING +--R coerce : S -> % if S has SETCAT +--R count : (S,%) -> NonNegativeInteger if $ has finiteAggregate and S has SETCAT +--R count : ((S -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate +--R differentiate : % -> % if S has DIFRING and S has RING +--R differentiate : (%,NonNegativeInteger) -> % if S has DIFRING and S has RING +--R differentiate : (%,Symbol) -> % if S has PDRING SYMBOL and S has RING +--R differentiate : (%,List Symbol) -> % if S has PDRING SYMBOL and S has RING +--R differentiate : (%,Symbol,NonNegativeInteger) -> % if S has PDRING SYMBOL and S has RING +--R differentiate : (%,List Symbol,List NonNegativeInteger) -> % if S has PDRING SYMBOL and S has RING +--R differentiate : (%,(S -> S)) -> % if S has RING +--R differentiate : (%,(S -> S),NonNegativeInteger) -> % if S has RING +--R dimension : () -> CardinalNumber if S has FIELD +--R dot : (%,%) -> S if S has RING +--R entry? : (S,%) -> Boolean if $ has finiteAggregate and S has SETCAT +--R eval : (%,List S,List S) -> % if S has EVALAB S and S has SETCAT +--R eval : (%,S,S) -> % if S has EVALAB S and S has SETCAT +--R eval : (%,Equation S) -> % if S has EVALAB S and S has SETCAT +--R eval : (%,List Equation S) -> % if S has EVALAB S and S has SETCAT +--R every? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate +--R fill! : (%,S) -> % if $ has shallowlyMutable +--R first : % -> S if Integer has ORDSET +--R index : PositiveInteger -> % if S has FINITE +--R less? : (%,NonNegativeInteger) -> Boolean +--R lookup : % -> PositiveInteger if S has FINITE +--R map! : ((S -> S),%) -> % if $ has shallowlyMutable +--R max : (%,%) -> % if S has OAMONS or S has ORDRING +--R maxIndex : % -> Integer if Integer has ORDSET +--R member? : (S,%) -> Boolean if $ has finiteAggregate and S has SETCAT +--R members : % -> List S if $ has finiteAggregate +--R min : (%,%) -> % if S has OAMONS or S has ORDRING +--R minIndex : % -> Integer if Integer has ORDSET +--R more? : (%,NonNegativeInteger) -> Boolean +--R negative? : % -> Boolean if S has ORDRING +--R one? : % -> Boolean if S has DIFRING and S has RING or S has LINEXP INT and S has RING or S has MONOID or S has PDRING SYMBOL and S has RING +--R parts : % -> List S if $ has finiteAggregate +--R positive? : % -> Boolean if S has ORDRING +--R qsetelt! : (%,Integer,S) -> S if $ has shallowlyMutable +--R random : () -> % if S has FINITE +--R recip : % -> Union(%,"failed") if S has DIFRING and S has RING or S has LINEXP INT and S has RING or S has MONOID or S has PDRING SYMBOL and S has RING +--R reducedSystem : Matrix % -> Matrix Integer if S has LINEXP INT and S has RING +--R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix Integer,vec: Vector Integer) if S has LINEXP INT and S has RING +--R reducedSystem : Matrix % -> Matrix S if S has RING +--R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix S,vec: Vector S) if S has RING +--R retract : % -> Fraction Integer if S has RETRACT FRAC INT and S has SETCAT +--R retract : % -> Integer if S has RETRACT INT and S has SETCAT +--R retract : % -> S if S has SETCAT +--R retractIfCan : % -> Union(Fraction Integer,"failed") if S has RETRACT FRAC INT and S has SETCAT +--R retractIfCan : % -> Union(Integer,"failed") if S has RETRACT INT and S has SETCAT +--R retractIfCan : % -> Union(S,"failed") if S has SETCAT +--R setelt : (%,Integer,S) -> S if $ has shallowlyMutable +--R sign : % -> Integer if S has ORDRING +--R size : () -> NonNegativeInteger if S has FINITE +--R size? : (%,NonNegativeInteger) -> Boolean +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R sup : (%,%) -> % if S has OAMONS +--R swap! : (%,Integer,Integer) -> Void if $ has shallowlyMutable +--R unitVector : PositiveInteger -> % if S has RING +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +DirectProductModule examples +==================================================================== + +See Also: +o )show DirectProductModule + +@ + \pagehead{DirectProductModule}{DPMO} \pagepic{ps/v103directproductmodule.ps}{DPMO}{1.00} {\bf See}\\ @@ -22148,6 +25751,7 @@ DirectProductModule(n, R, S): DPcategory == DPcapsule where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain DMP DistributedMultivariatePolynomial} + <>= )set break resume )sys rm -f DistributedMultivariatePolynomial.output @@ -22497,6 +26101,7 @@ DistributedMultivariatePolynomial(vl,R): public == private where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain DIV Divisor} + <>= )set break resume )sys rm -f Divisor.output @@ -23613,6 +27218,60 @@ DoubleFloat(): Join(FloatingPointSystem, DifferentialRing, OpenMath, @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain DROPT DrawOption} + +<>= +)set break resume +)sys rm -f DrawOption.output +)spool DrawOption.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show DrawOption +--R DrawOption is a domain constructor +--R Abbreviation for DrawOption is DROPT +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for DROPT +--R +--R------------------------------- Operations -------------------------------- +--R ?=? : (%,%) -> Boolean adaptive : Boolean -> % +--R clip : List Segment Float -> % clip : Boolean -> % +--R coerce : % -> OutputForm curveColor : Palette -> % +--R curveColor : Float -> % hash : % -> SingleInteger +--R latex : % -> String pointColor : Palette -> % +--R pointColor : Float -> % range : List Segment Float -> % +--R ranges : List Segment Float -> % style : String -> % +--R title : String -> % toScale : Boolean -> % +--R tubePoints : PositiveInteger -> % tubeRadius : Float -> % +--R unit : List Float -> % var1Steps : PositiveInteger -> % +--R var2Steps : PositiveInteger -> % ?~=? : (%,%) -> Boolean +--R colorFunction : ((DoubleFloat,DoubleFloat,DoubleFloat) -> DoubleFloat) -> % +--R colorFunction : ((DoubleFloat,DoubleFloat) -> DoubleFloat) -> % +--R colorFunction : (DoubleFloat -> DoubleFloat) -> % +--R coord : (Point DoubleFloat -> Point DoubleFloat) -> % +--R coordinates : (Point DoubleFloat -> Point DoubleFloat) -> % +--R option : (List %,Symbol) -> Union(Any,"failed") +--R option? : (List %,Symbol) -> Boolean +--R range : List Segment Fraction Integer -> % +--R space : ThreeSpace DoubleFloat -> % +--R viewpoint : Record(theta: DoubleFloat,phi: DoubleFloat,scale: DoubleFloat,scaleX: DoubleFloat,scaleY: DoubleFloat,scaleZ: DoubleFloat,deltaX: DoubleFloat,deltaY: DoubleFloat) -> % +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +DrawOption examples +==================================================================== + +See Also: +o )show DrawOption + +@ + \pagehead{DrawOption}{DROPT} \pagepic{ps/v103drawoption.ps}{DROPT}{1.00} @@ -23867,6 +27526,46 @@ DrawOption(): Exports == Implementation where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain D01AJFA d01ajfAnnaType} + +<>= +)set break resume +)sys rm -f d01ajfAnnaType.output +)spool d01ajfAnnaType.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show d01ajfAnnaType +--R d01ajfAnnaType is a domain constructor +--R Abbreviation for d01ajfAnnaType is D01AJFA +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for D01AJFA +--R +--R------------------------------- Operations -------------------------------- +--R ?=? : (%,%) -> Boolean coerce : % -> OutputForm +--R hash : % -> SingleInteger latex : % -> String +--R ?~=? : (%,%) -> Boolean +--R measure : (RoutinesTable,Record(fn: Expression DoubleFloat,range: List Segment OrderedCompletion DoubleFloat,abserr: DoubleFloat,relerr: DoubleFloat)) -> Record(measure: Float,explanations: String,extra: Result) +--R measure : (RoutinesTable,Record(var: Symbol,fn: Expression DoubleFloat,range: Segment OrderedCompletion DoubleFloat,abserr: DoubleFloat,relerr: DoubleFloat)) -> Record(measure: Float,explanations: String,extra: Result) +--R numericalIntegration : (Record(fn: Expression DoubleFloat,range: List Segment OrderedCompletion DoubleFloat,abserr: DoubleFloat,relerr: DoubleFloat),Result) -> Result +--R numericalIntegration : (Record(var: Symbol,fn: Expression DoubleFloat,range: Segment OrderedCompletion DoubleFloat,abserr: DoubleFloat,relerr: DoubleFloat),Result) -> Result +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +d01ajfAnnaType examples +==================================================================== + +See Also: +o )show d01ajfAnnaType + +@ + \pagehead{d01ajfAnnaType}{D01AJFA} \pagepic{ps/v103d01ajfannatype.ps}{D01AJFA}{1.00} @@ -23944,6 +27643,46 @@ d01ajfAnnaType(): NumericalIntegrationCategory == Result add @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain D01AKFA d01akfAnnaType} + +<>= +)set break resume +)sys rm -f d01akfAnnaType.output +)spool d01akfAnnaType.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show d01akfAnnaType +--R d01akfAnnaType is a domain constructor +--R Abbreviation for d01akfAnnaType is D01AKFA +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for D01AKFA +--R +--R------------------------------- Operations -------------------------------- +--R ?=? : (%,%) -> Boolean coerce : % -> OutputForm +--R hash : % -> SingleInteger latex : % -> String +--R ?~=? : (%,%) -> Boolean +--R measure : (RoutinesTable,Record(fn: Expression DoubleFloat,range: List Segment OrderedCompletion DoubleFloat,abserr: DoubleFloat,relerr: DoubleFloat)) -> Record(measure: Float,explanations: String,extra: Result) +--R measure : (RoutinesTable,Record(var: Symbol,fn: Expression DoubleFloat,range: Segment OrderedCompletion DoubleFloat,abserr: DoubleFloat,relerr: DoubleFloat)) -> Record(measure: Float,explanations: String,extra: Result) +--R numericalIntegration : (Record(fn: Expression DoubleFloat,range: List Segment OrderedCompletion DoubleFloat,abserr: DoubleFloat,relerr: DoubleFloat),Result) -> Result +--R numericalIntegration : (Record(var: Symbol,fn: Expression DoubleFloat,range: Segment OrderedCompletion DoubleFloat,abserr: DoubleFloat,relerr: DoubleFloat),Result) -> Result +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +d01akfAnnaType examples +==================================================================== + +See Also: +o )show d01akfAnnaType + +@ + \pagehead{d01akfAnnaType}{D01AKFA} \pagepic{ps/v103d01akfannatype.ps}{D01AKFA}{1.00} @@ -24026,6 +27765,46 @@ d01akfAnnaType(): NumericalIntegrationCategory == Result add @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain D01ALFA d01alfAnnaType} + +<>= +)set break resume +)sys rm -f d01alfAnnaType.output +)spool d01alfAnnaType.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show d01alfAnnaType +--R d01alfAnnaType is a domain constructor +--R Abbreviation for d01alfAnnaType is D01ALFA +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for D01ALFA +--R +--R------------------------------- Operations -------------------------------- +--R ?=? : (%,%) -> Boolean coerce : % -> OutputForm +--R hash : % -> SingleInteger latex : % -> String +--R ?~=? : (%,%) -> Boolean +--R measure : (RoutinesTable,Record(fn: Expression DoubleFloat,range: List Segment OrderedCompletion DoubleFloat,abserr: DoubleFloat,relerr: DoubleFloat)) -> Record(measure: Float,explanations: String,extra: Result) +--R measure : (RoutinesTable,Record(var: Symbol,fn: Expression DoubleFloat,range: Segment OrderedCompletion DoubleFloat,abserr: DoubleFloat,relerr: DoubleFloat)) -> Record(measure: Float,explanations: String,extra: Result) +--R numericalIntegration : (Record(fn: Expression DoubleFloat,range: List Segment OrderedCompletion DoubleFloat,abserr: DoubleFloat,relerr: DoubleFloat),Result) -> Result +--R numericalIntegration : (Record(var: Symbol,fn: Expression DoubleFloat,range: Segment OrderedCompletion DoubleFloat,abserr: DoubleFloat,relerr: DoubleFloat),Result) -> Result +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +d01alfAnnaType examples +==================================================================== + +See Also: +o )show d01alfAnnaType + +@ + \pagehead{d01alfAnnaType}{D01ALFA} \pagepic{ps/v103d01alfannatype.ps}{D01ALFA}{1.00} @@ -24120,6 +27899,46 @@ d01alfAnnaType(): NumericalIntegrationCategory == Result add @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain D01AMFA d01amfAnnaType} + +<>= +)set break resume +)sys rm -f d01amfAnnaType.output +)spool d01amfAnnaType.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show d01amfAnnaType +--R d01amfAnnaType is a domain constructor +--R Abbreviation for d01amfAnnaType is D01AMFA +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for D01AMFA +--R +--R------------------------------- Operations -------------------------------- +--R ?=? : (%,%) -> Boolean coerce : % -> OutputForm +--R hash : % -> SingleInteger latex : % -> String +--R ?~=? : (%,%) -> Boolean +--R measure : (RoutinesTable,Record(fn: Expression DoubleFloat,range: List Segment OrderedCompletion DoubleFloat,abserr: DoubleFloat,relerr: DoubleFloat)) -> Record(measure: Float,explanations: String,extra: Result) +--R measure : (RoutinesTable,Record(var: Symbol,fn: Expression DoubleFloat,range: Segment OrderedCompletion DoubleFloat,abserr: DoubleFloat,relerr: DoubleFloat)) -> Record(measure: Float,explanations: String,extra: Result) +--R numericalIntegration : (Record(fn: Expression DoubleFloat,range: List Segment OrderedCompletion DoubleFloat,abserr: DoubleFloat,relerr: DoubleFloat),Result) -> Result +--R numericalIntegration : (Record(var: Symbol,fn: Expression DoubleFloat,range: Segment OrderedCompletion DoubleFloat,abserr: DoubleFloat,relerr: DoubleFloat),Result) -> Result +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +d01amfAnnaType examples +==================================================================== + +See Also: +o )show d01amfAnnaType + +@ + \pagehead{d01amfAnnaType}{D01AMFA} \pagepic{ps/v103d01amfannatype.ps}{D01AMFA}{1.00} @@ -24210,6 +28029,46 @@ d01amfAnnaType(): NumericalIntegrationCategory == Result add @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain D01ANFA d01anfAnnaType} + +<>= +)set break resume +)sys rm -f d01anfAnnaType.output +)spool d01anfAnnaType.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show d01anfAnnaType +--R d01anfAnnaType is a domain constructor +--R Abbreviation for d01anfAnnaType is D01ANFA +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for D01ANFA +--R +--R------------------------------- Operations -------------------------------- +--R ?=? : (%,%) -> Boolean coerce : % -> OutputForm +--R hash : % -> SingleInteger latex : % -> String +--R ?~=? : (%,%) -> Boolean +--R measure : (RoutinesTable,Record(fn: Expression DoubleFloat,range: List Segment OrderedCompletion DoubleFloat,abserr: DoubleFloat,relerr: DoubleFloat)) -> Record(measure: Float,explanations: String,extra: Result) +--R measure : (RoutinesTable,Record(var: Symbol,fn: Expression DoubleFloat,range: Segment OrderedCompletion DoubleFloat,abserr: DoubleFloat,relerr: DoubleFloat)) -> Record(measure: Float,explanations: String,extra: Result) +--R numericalIntegration : (Record(fn: Expression DoubleFloat,range: List Segment OrderedCompletion DoubleFloat,abserr: DoubleFloat,relerr: DoubleFloat),Result) -> Result +--R numericalIntegration : (Record(var: Symbol,fn: Expression DoubleFloat,range: Segment OrderedCompletion DoubleFloat,abserr: DoubleFloat,relerr: DoubleFloat),Result) -> Result +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +d01anfAnnaType examples +==================================================================== + +See Also: +o )show d01anfAnnaType + +@ + \pagehead{d01anfAnnaType}{D01ANFA} \pagepic{ps/v103d01anfannatype.ps}{D01ANFA}{1.00} @@ -24302,6 +28161,46 @@ d01anfAnnaType(): NumericalIntegrationCategory == Result add @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain D01APFA d01apfAnnaType} + +<>= +)set break resume +)sys rm -f d01apfAnnaType.output +)spool d01apfAnnaType.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show d01apfAnnaType +--R d01apfAnnaType is a domain constructor +--R Abbreviation for d01apfAnnaType is D01APFA +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for D01APFA +--R +--R------------------------------- Operations -------------------------------- +--R ?=? : (%,%) -> Boolean coerce : % -> OutputForm +--R hash : % -> SingleInteger latex : % -> String +--R ?~=? : (%,%) -> Boolean +--R measure : (RoutinesTable,Record(fn: Expression DoubleFloat,range: List Segment OrderedCompletion DoubleFloat,abserr: DoubleFloat,relerr: DoubleFloat)) -> Record(measure: Float,explanations: String,extra: Result) +--R measure : (RoutinesTable,Record(var: Symbol,fn: Expression DoubleFloat,range: Segment OrderedCompletion DoubleFloat,abserr: DoubleFloat,relerr: DoubleFloat)) -> Record(measure: Float,explanations: String,extra: Result) +--R numericalIntegration : (Record(fn: Expression DoubleFloat,range: List Segment OrderedCompletion DoubleFloat,abserr: DoubleFloat,relerr: DoubleFloat),Result) -> Result +--R numericalIntegration : (Record(var: Symbol,fn: Expression DoubleFloat,range: Segment OrderedCompletion DoubleFloat,abserr: DoubleFloat,relerr: DoubleFloat),Result) -> Result +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +d01apfAnnaType examples +==================================================================== + +See Also: +o )show d01apfAnnaType + +@ + \pagehead{d01apfAnnaType}{D01APFA} \pagepic{ps/v103d01apfannatype.ps}{D01APFA}{1.00} @@ -24407,6 +28306,46 @@ d01apfAnnaType(): NumericalIntegrationCategory == Result add @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain D01AQFA d01aqfAnnaType} + +<>= +)set break resume +)sys rm -f d01aqfAnnaType.output +)spool d01aqfAnnaType.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show d01aqfAnnaType +--R d01aqfAnnaType is a domain constructor +--R Abbreviation for d01aqfAnnaType is D01AQFA +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for D01AQFA +--R +--R------------------------------- Operations -------------------------------- +--R ?=? : (%,%) -> Boolean coerce : % -> OutputForm +--R hash : % -> SingleInteger latex : % -> String +--R ?~=? : (%,%) -> Boolean +--R measure : (RoutinesTable,Record(fn: Expression DoubleFloat,range: List Segment OrderedCompletion DoubleFloat,abserr: DoubleFloat,relerr: DoubleFloat)) -> Record(measure: Float,explanations: String,extra: Result) +--R measure : (RoutinesTable,Record(var: Symbol,fn: Expression DoubleFloat,range: Segment OrderedCompletion DoubleFloat,abserr: DoubleFloat,relerr: DoubleFloat)) -> Record(measure: Float,explanations: String,extra: Result) +--R numericalIntegration : (Record(fn: Expression DoubleFloat,range: List Segment OrderedCompletion DoubleFloat,abserr: DoubleFloat,relerr: DoubleFloat),Result) -> Result +--R numericalIntegration : (Record(var: Symbol,fn: Expression DoubleFloat,range: Segment OrderedCompletion DoubleFloat,abserr: DoubleFloat,relerr: DoubleFloat),Result) -> Result +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +d01aqfAnnaType examples +==================================================================== + +See Also: +o )show d01aqfAnnaType + +@ + \pagehead{d01aqfAnnaType}{D01AQFA} \pagepic{ps/v103d01aqfannatype.ps}{D01AQFA}{1.00} @@ -24508,6 +28447,46 @@ d01aqfAnnaType(): NumericalIntegrationCategory == Result add @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain D01ASFA d01asfAnnaType} + +<>= +)set break resume +)sys rm -f d01asfAnnaType.output +)spool d01asfAnnaType.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show d01asfAnnaType +--R d01asfAnnaType is a domain constructor +--R Abbreviation for d01asfAnnaType is D01ASFA +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for D01ASFA +--R +--R------------------------------- Operations -------------------------------- +--R ?=? : (%,%) -> Boolean coerce : % -> OutputForm +--R hash : % -> SingleInteger latex : % -> String +--R ?~=? : (%,%) -> Boolean +--R measure : (RoutinesTable,Record(fn: Expression DoubleFloat,range: List Segment OrderedCompletion DoubleFloat,abserr: DoubleFloat,relerr: DoubleFloat)) -> Record(measure: Float,explanations: String,extra: Result) +--R measure : (RoutinesTable,Record(var: Symbol,fn: Expression DoubleFloat,range: Segment OrderedCompletion DoubleFloat,abserr: DoubleFloat,relerr: DoubleFloat)) -> Record(measure: Float,explanations: String,extra: Result) +--R numericalIntegration : (Record(fn: Expression DoubleFloat,range: List Segment OrderedCompletion DoubleFloat,abserr: DoubleFloat,relerr: DoubleFloat),Result) -> Result +--R numericalIntegration : (Record(var: Symbol,fn: Expression DoubleFloat,range: Segment OrderedCompletion DoubleFloat,abserr: DoubleFloat,relerr: DoubleFloat),Result) -> Result +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +d01asfAnnaType examples +==================================================================== + +See Also: +o )show d01asfAnnaType + +@ + \pagehead{d01asfAnnaType}{D01ASFA} \pagepic{ps/v103d01asfannatype.ps}{D01ASFA}{1.00} @@ -24606,6 +28585,46 @@ d01asfAnnaType(): NumericalIntegrationCategory == Result add @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain D01FCFA d01fcfAnnaType} + +<>= +)set break resume +)sys rm -f d01fcfAnnaType.output +)spool d01fcfAnnaType.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show d01fcfAnnaType +--R d01fcfAnnaType is a domain constructor +--R Abbreviation for d01fcfAnnaType is D01FCFA +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for D01FCFA +--R +--R------------------------------- Operations -------------------------------- +--R ?=? : (%,%) -> Boolean coerce : % -> OutputForm +--R hash : % -> SingleInteger latex : % -> String +--R ?~=? : (%,%) -> Boolean +--R measure : (RoutinesTable,Record(fn: Expression DoubleFloat,range: List Segment OrderedCompletion DoubleFloat,abserr: DoubleFloat,relerr: DoubleFloat)) -> Record(measure: Float,explanations: String,extra: Result) +--R measure : (RoutinesTable,Record(var: Symbol,fn: Expression DoubleFloat,range: Segment OrderedCompletion DoubleFloat,abserr: DoubleFloat,relerr: DoubleFloat)) -> Record(measure: Float,explanations: String,extra: Result) +--R numericalIntegration : (Record(fn: Expression DoubleFloat,range: List Segment OrderedCompletion DoubleFloat,abserr: DoubleFloat,relerr: DoubleFloat),Result) -> Result +--R numericalIntegration : (Record(var: Symbol,fn: Expression DoubleFloat,range: Segment OrderedCompletion DoubleFloat,abserr: DoubleFloat,relerr: DoubleFloat),Result) -> Result +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +d01fcfAnnaType examples +==================================================================== + +See Also: +o )show d01fcfAnnaType + +@ + \pagehead{d01fcfAnnaType}{D01FCFA} \pagepic{ps/v103d01fcfannatype.ps}{D01FCFA}{1.00} @@ -24694,6 +28713,46 @@ d01fcfAnnaType(): NumericalIntegrationCategory == Result add @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain D01GBFA d01gbfAnnaType} + +<>= +)set break resume +)sys rm -f d01gbfAnnaType.output +)spool d01gbfAnnaType.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show d01gbfAnnaType +--R d01gbfAnnaType is a domain constructor +--R Abbreviation for d01gbfAnnaType is D01GBFA +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for D01GBFA +--R +--R------------------------------- Operations -------------------------------- +--R ?=? : (%,%) -> Boolean coerce : % -> OutputForm +--R hash : % -> SingleInteger latex : % -> String +--R ?~=? : (%,%) -> Boolean +--R measure : (RoutinesTable,Record(fn: Expression DoubleFloat,range: List Segment OrderedCompletion DoubleFloat,abserr: DoubleFloat,relerr: DoubleFloat)) -> Record(measure: Float,explanations: String,extra: Result) +--R measure : (RoutinesTable,Record(var: Symbol,fn: Expression DoubleFloat,range: Segment OrderedCompletion DoubleFloat,abserr: DoubleFloat,relerr: DoubleFloat)) -> Record(measure: Float,explanations: String,extra: Result) +--R numericalIntegration : (Record(fn: Expression DoubleFloat,range: List Segment OrderedCompletion DoubleFloat,abserr: DoubleFloat,relerr: DoubleFloat),Result) -> Result +--R numericalIntegration : (Record(var: Symbol,fn: Expression DoubleFloat,range: Segment OrderedCompletion DoubleFloat,abserr: DoubleFloat,relerr: DoubleFloat),Result) -> Result +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +d01gbfAnnaType examples +==================================================================== + +See Also: +o )show d01gbfAnnaType + +@ + \pagehead{d01gbfAnnaType}{D01GBFA} \pagepic{ps/v103d01gbfannatype.ps}{D01GBFA}{1.00} @@ -24788,6 +28847,46 @@ d01gbfAnnaType(): NumericalIntegrationCategory == Result add @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain D01TRNS d01TransformFunctionType} + +<>= +)set break resume +)sys rm -f d01TransformFunctionType.output +)spool d01TransformFunctionType.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show d01TransformFunctionType +--R d01TransformFunctionType is a domain constructor +--R Abbreviation for d01TransformFunctionType is D01TRNS +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for D01TRNS +--R +--R------------------------------- Operations -------------------------------- +--R ?=? : (%,%) -> Boolean coerce : % -> OutputForm +--R hash : % -> SingleInteger latex : % -> String +--R ?~=? : (%,%) -> Boolean +--R measure : (RoutinesTable,Record(fn: Expression DoubleFloat,range: List Segment OrderedCompletion DoubleFloat,abserr: DoubleFloat,relerr: DoubleFloat)) -> Record(measure: Float,explanations: String,extra: Result) +--R measure : (RoutinesTable,Record(var: Symbol,fn: Expression DoubleFloat,range: Segment OrderedCompletion DoubleFloat,abserr: DoubleFloat,relerr: DoubleFloat)) -> Record(measure: Float,explanations: String,extra: Result) +--R numericalIntegration : (Record(fn: Expression DoubleFloat,range: List Segment OrderedCompletion DoubleFloat,abserr: DoubleFloat,relerr: DoubleFloat),Result) -> Result +--R numericalIntegration : (Record(var: Symbol,fn: Expression DoubleFloat,range: Segment OrderedCompletion DoubleFloat,abserr: DoubleFloat,relerr: DoubleFloat),Result) -> Result +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +d01TransformFunctionType examples +==================================================================== + +See Also: +o )show d01TransformFunctionType + +@ + \pagehead{d01TransformFunctionType}{D01TRNS} \pagepic{ps/v103d01transformfunctiontype.ps}{D01TRNS}{1.00} @@ -24968,6 +29067,44 @@ d01TransformFunctionType():NumericalIntegrationCategory == Result add @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain D02BBFA d02bbfAnnaType} + +<>= +)set break resume +)sys rm -f d02bbfAnnaType.output +)spool d02bbfAnnaType.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show d02bbfAnnaType +--R d02bbfAnnaType is a domain constructor +--R Abbreviation for d02bbfAnnaType is D02BBFA +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for D02BBFA +--R +--R------------------------------- Operations -------------------------------- +--R ?=? : (%,%) -> Boolean coerce : % -> OutputForm +--R hash : % -> SingleInteger latex : % -> String +--R ?~=? : (%,%) -> Boolean +--R ODESolve : Record(xinit: DoubleFloat,xend: DoubleFloat,fn: Vector Expression DoubleFloat,yinit: List DoubleFloat,intvals: List DoubleFloat,g: Expression DoubleFloat,abserr: DoubleFloat,relerr: DoubleFloat) -> Result +--R measure : (RoutinesTable,Record(xinit: DoubleFloat,xend: DoubleFloat,fn: Vector Expression DoubleFloat,yinit: List DoubleFloat,intvals: List DoubleFloat,g: Expression DoubleFloat,abserr: DoubleFloat,relerr: DoubleFloat)) -> Record(measure: Float,explanations: String) +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +d02bbfAnnaType examples +==================================================================== + +See Also: +o )show d02bbfAnnaType + +@ + \pagehead{d02bbfAnnaType}{D02BBFA} \pagepic{ps/v103d02bbfannatype.ps}{D02BBFA}{1.00} @@ -25081,6 +29218,44 @@ d02bbfAnnaType():OrdinaryDifferentialEquationsSolverCategory == Result add @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain D02BHFA d02bhfAnnaType} + +<>= +)set break resume +)sys rm -f d02bhfAnnaType.output +)spool d02bhfAnnaType.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show d02bhfAnnaType +--R d02bhfAnnaType is a domain constructor +--R Abbreviation for d02bhfAnnaType is D02BHFA +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for D02BHFA +--R +--R------------------------------- Operations -------------------------------- +--R ?=? : (%,%) -> Boolean coerce : % -> OutputForm +--R hash : % -> SingleInteger latex : % -> String +--R ?~=? : (%,%) -> Boolean +--R ODESolve : Record(xinit: DoubleFloat,xend: DoubleFloat,fn: Vector Expression DoubleFloat,yinit: List DoubleFloat,intvals: List DoubleFloat,g: Expression DoubleFloat,abserr: DoubleFloat,relerr: DoubleFloat) -> Result +--R measure : (RoutinesTable,Record(xinit: DoubleFloat,xend: DoubleFloat,fn: Vector Expression DoubleFloat,yinit: List DoubleFloat,intvals: List DoubleFloat,g: Expression DoubleFloat,abserr: DoubleFloat,relerr: DoubleFloat)) -> Record(measure: Float,explanations: String) +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +d02bhfAnnaType examples +==================================================================== + +See Also: +o )show d02bhfAnnaType + +@ + \pagehead{d02bhfAnnaType}{D02BHFA} \pagepic{ps/v103d02bhfannatype.ps}{D02BHFA}{1.00} @@ -25191,6 +29366,44 @@ d02bhfAnnaType():OrdinaryDifferentialEquationsSolverCategory == Result add @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain D02CJFA d02cjfAnnaType} + +<>= +)set break resume +)sys rm -f d02cjfAnnaType.output +)spool d02cjfAnnaType.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show d02cjfAnnaType +--R d02cjfAnnaType is a domain constructor +--R Abbreviation for d02cjfAnnaType is D02CJFA +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for D02CJFA +--R +--R------------------------------- Operations -------------------------------- +--R ?=? : (%,%) -> Boolean coerce : % -> OutputForm +--R hash : % -> SingleInteger latex : % -> String +--R ?~=? : (%,%) -> Boolean +--R ODESolve : Record(xinit: DoubleFloat,xend: DoubleFloat,fn: Vector Expression DoubleFloat,yinit: List DoubleFloat,intvals: List DoubleFloat,g: Expression DoubleFloat,abserr: DoubleFloat,relerr: DoubleFloat) -> Result +--R measure : (RoutinesTable,Record(xinit: DoubleFloat,xend: DoubleFloat,fn: Vector Expression DoubleFloat,yinit: List DoubleFloat,intvals: List DoubleFloat,g: Expression DoubleFloat,abserr: DoubleFloat,relerr: DoubleFloat)) -> Record(measure: Float,explanations: String) +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +d02cjfAnnaType examples +==================================================================== + +See Also: +o )show d02cjfAnnaType + +@ + \pagehead{d02cjfAnnaType}{D02CJFA} \pagepic{ps/v103d02cjfannatype.ps}{D02CJFA}{1.00} @@ -25294,6 +29507,44 @@ d02cjfAnnaType():OrdinaryDifferentialEquationsSolverCategory == Result add @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain D02EJFA d02ejfAnnaType} + +<>= +)set break resume +)sys rm -f d02ejfAnnaType.output +)spool d02ejfAnnaType.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show d02ejfAnnaType +--R d02ejfAnnaType is a domain constructor +--R Abbreviation for d02ejfAnnaType is D02EJFA +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for D02EJFA +--R +--R------------------------------- Operations -------------------------------- +--R ?=? : (%,%) -> Boolean coerce : % -> OutputForm +--R hash : % -> SingleInteger latex : % -> String +--R ?~=? : (%,%) -> Boolean +--R ODESolve : Record(xinit: DoubleFloat,xend: DoubleFloat,fn: Vector Expression DoubleFloat,yinit: List DoubleFloat,intvals: List DoubleFloat,g: Expression DoubleFloat,abserr: DoubleFloat,relerr: DoubleFloat) -> Result +--R measure : (RoutinesTable,Record(xinit: DoubleFloat,xend: DoubleFloat,fn: Vector Expression DoubleFloat,yinit: List DoubleFloat,intvals: List DoubleFloat,g: Expression DoubleFloat,abserr: DoubleFloat,relerr: DoubleFloat)) -> Record(measure: Float,explanations: String) +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +d02ejfAnnaType examples +==================================================================== + +See Also: +o )show d02ejfAnnaType + +@ + \pagehead{d02ejfAnnaType}{D02EJFA} \pagepic{ps/v103d02ejfannatype.ps}{D02EJFA}{1.00} @@ -25428,6 +29679,44 @@ d02ejfAnnaType():OrdinaryDifferentialEquationsSolverCategory == Result add @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain D03EEFA d03eefAnnaType} + +<>= +)set break resume +)sys rm -f d03eefAnnaType.output +)spool d03eefAnnaType.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show d03eefAnnaType +--R d03eefAnnaType is a domain constructor +--R Abbreviation for d03eefAnnaType is D03EEFA +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for D03EEFA +--R +--R------------------------------- Operations -------------------------------- +--R ?=? : (%,%) -> Boolean coerce : % -> OutputForm +--R hash : % -> SingleInteger latex : % -> String +--R ?~=? : (%,%) -> Boolean +--R PDESolve : Record(pde: List Expression DoubleFloat,constraints: List Record(start: DoubleFloat,finish: DoubleFloat,grid: NonNegativeInteger,boundaryType: Integer,dStart: Matrix DoubleFloat,dFinish: Matrix DoubleFloat),f: List List Expression DoubleFloat,st: String,tol: DoubleFloat) -> Result +--R measure : (RoutinesTable,Record(pde: List Expression DoubleFloat,constraints: List Record(start: DoubleFloat,finish: DoubleFloat,grid: NonNegativeInteger,boundaryType: Integer,dStart: Matrix DoubleFloat,dFinish: Matrix DoubleFloat),f: List List Expression DoubleFloat,st: String,tol: DoubleFloat)) -> Record(measure: Float,explanations: String) +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +d03eefAnnaType examples +==================================================================== + +See Also: +o )show d03eefAnnaType + +@ + \pagehead{d03eefAnnaType}{D03EEFA} \pagepic{ps/v103d03eefannatype.ps}{D03EEFA}{1.00} @@ -25522,6 +29811,44 @@ d03eefAnnaType():PartialDifferentialEquationsSolverCategory == Result add @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain D03FAFA d03fafAnnaType} + +<>= +)set break resume +)sys rm -f d03fafAnnaType.output +)spool d03fafAnnaType.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show d03fafAnnaType +--R d03fafAnnaType is a domain constructor +--R Abbreviation for d03fafAnnaType is D03FAFA +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for D03FAFA +--R +--R------------------------------- Operations -------------------------------- +--R ?=? : (%,%) -> Boolean coerce : % -> OutputForm +--R hash : % -> SingleInteger latex : % -> String +--R ?~=? : (%,%) -> Boolean +--R PDESolve : Record(pde: List Expression DoubleFloat,constraints: List Record(start: DoubleFloat,finish: DoubleFloat,grid: NonNegativeInteger,boundaryType: Integer,dStart: Matrix DoubleFloat,dFinish: Matrix DoubleFloat),f: List List Expression DoubleFloat,st: String,tol: DoubleFloat) -> Result +--R measure : (RoutinesTable,Record(pde: List Expression DoubleFloat,constraints: List Record(start: DoubleFloat,finish: DoubleFloat,grid: NonNegativeInteger,boundaryType: Integer,dStart: Matrix DoubleFloat,dFinish: Matrix DoubleFloat),f: List List Expression DoubleFloat,st: String,tol: DoubleFloat)) -> Record(measure: Float,explanations: String) +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +d03fafAnnaType examples +==================================================================== + +See Also: +o )show d03fafAnnaType + +@ + \pagehead{d03fafAnnaType}{D03FAFA} \pagepic{ps/v103d03fafannatype.ps}{D03FAFA}{1.00} @@ -25585,6 +29912,7 @@ d03fafAnnaType():PartialDifferentialEquationsSolverCategory == Result add \chapter{Chapter E} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain EQ Equation} + <>= )set break resume )sys rm -f Equation.output @@ -26042,6 +30370,7 @@ Equation(S: Type): public == private where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain EQTBL EqTable} + <>= )set break resume )sys rm -f EqTable.output @@ -26244,6 +30573,73 @@ EqTable(Key: SetCategory, Entry: SetCategory) == @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain EMR EuclideanModularRing} + +<>= +)set break resume +)sys rm -f EuclideanModularRing.output +)spool EuclideanModularRing.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show EuclideanModularRing +--R EuclideanModularRing(S: CommutativeRing,R: UnivariatePolynomialCategory S,Mod: AbelianMonoid,reduction: ((R,Mod) -> R),merge: ((Mod,Mod) -> Union(Mod,"failed")),exactQuo: ((R,R,Mod) -> Union(R,"failed"))) is a domain constructor +--R Abbreviation for EuclideanModularRing is EMR +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for EMR +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ?=? : (%,%) -> Boolean +--R 1 : () -> % 0 : () -> % +--R ?^? : (%,PositiveInteger) -> % associates? : (%,%) -> Boolean +--R coerce : % -> R coerce : % -> % +--R coerce : Integer -> % coerce : % -> OutputForm +--R ?.? : (%,R) -> R gcd : List % -> % +--R gcd : (%,%) -> % hash : % -> SingleInteger +--R inv : % -> % latex : % -> String +--R lcm : List % -> % lcm : (%,%) -> % +--R modulus : % -> Mod one? : % -> Boolean +--R ?quo? : (%,%) -> % recip : % -> Union(%,"failed") +--R reduce : (R,Mod) -> % ?rem? : (%,%) -> % +--R sample : () -> % sizeLess? : (%,%) -> Boolean +--R unit? : % -> Boolean unitCanonical : % -> % +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean +--R ?*? : (NonNegativeInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % +--R ?^? : (%,NonNegativeInteger) -> % +--R characteristic : () -> NonNegativeInteger +--R divide : (%,%) -> Record(quotient: %,remainder: %) +--R euclideanSize : % -> NonNegativeInteger +--R exQuo : (%,%) -> Union(%,"failed") +--R expressIdealMember : (List %,%) -> Union(List %,"failed") +--R exquo : (%,%) -> Union(%,"failed") +--R extendedEuclidean : (%,%,%) -> Union(Record(coef1: %,coef2: %),"failed") +--R extendedEuclidean : (%,%) -> Record(coef1: %,coef2: %,generator: %) +--R gcdPolynomial : (SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial % +--R multiEuclidean : (List %,%) -> Union(List %,"failed") +--R principalIdeal : List % -> Record(coef: List %,generator: %) +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R unitNormal : % -> Record(unit: %,canonical: %,associate: %) +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +EuclideanModularRing examples +==================================================================== + +See Also: +o )show EuclideanModularRing + +@ + \pagehead{EuclideanModularRing}{EMR} \pagepic{ps/v103euclideanmodularring.ps}{EMR}{1.00} {\bf See}\\ @@ -26409,6 +30805,7 @@ EuclideanModularRing(S,R,Mod,reduction:(R,Mod) -> R, @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain EXIT Exit} + <>= )set break resume )sys rm -f Exit.output @@ -26557,6 +30954,153 @@ Exit: SetCategory == add @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain EXPEXPAN ExponentialExpansion} + +<>= +)set break resume +)sys rm -f ExponentialExpansion.output +)spool ExponentialExpansion.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show ExponentialExpansion +--R ExponentialExpansion(R: Join(OrderedSet,RetractableTo Integer,LinearlyExplicitRingOver Integer,GcdDomain),FE: Join(AlgebraicallyClosedField,TranscendentalFunctionCategory,FunctionSpace R),var: Symbol,cen: FE) is a domain constructor +--R Abbreviation for ExponentialExpansion is EXPEXPAN +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for EXPEXPAN +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (Fraction Integer,%) -> % ?*? : (%,Fraction Integer) -> % +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?**? : (%,Integer) -> % +--R ?**? : (%,PositiveInteger) -> % ?+? : (%,%) -> % +--R ?-? : (%,%) -> % -? : % -> % +--R ?/? : (%,%) -> % ?=? : (%,%) -> Boolean +--R 1 : () -> % 0 : () -> % +--R ?^? : (%,Integer) -> % ?^? : (%,PositiveInteger) -> % +--R associates? : (%,%) -> Boolean coerce : Fraction Integer -> % +--R coerce : % -> % coerce : Integer -> % +--R coerce : % -> OutputForm denominator : % -> % +--R factor : % -> Factored % gcd : List % -> % +--R gcd : (%,%) -> % hash : % -> SingleInteger +--R inv : % -> % latex : % -> String +--R lcm : List % -> % lcm : (%,%) -> % +--R numerator : % -> % one? : % -> Boolean +--R prime? : % -> Boolean ?quo? : (%,%) -> % +--R recip : % -> Union(%,"failed") ?rem? : (%,%) -> % +--R sample : () -> % sizeLess? : (%,%) -> Boolean +--R squareFree : % -> Factored % squareFreePart : % -> % +--R unit? : % -> Boolean unitCanonical : % -> % +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean +--R ?*? : (%,UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen)) -> % +--R ?*? : (UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen),%) -> % +--R ?*? : (NonNegativeInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % +--R ?/? : (UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen),UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen)) -> % +--R ? Boolean if UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) has ORDSET +--R ?<=? : (%,%) -> Boolean if UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) has ORDSET +--R ?>? : (%,%) -> Boolean if UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) has ORDSET +--R ?>=? : (%,%) -> Boolean if UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) has ORDSET +--R D : (%,(UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) -> UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen))) -> % +--R D : (%,(UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) -> UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen)),NonNegativeInteger) -> % +--R D : (%,List Symbol,List NonNegativeInteger) -> % if UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) has PDRING SYMBOL +--R D : (%,Symbol,NonNegativeInteger) -> % if UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) has PDRING SYMBOL +--R D : (%,List Symbol) -> % if UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) has PDRING SYMBOL +--R D : (%,Symbol) -> % if UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) has PDRING SYMBOL +--R D : (%,NonNegativeInteger) -> % if UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) has DIFRING +--R D : % -> % if UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) has DIFRING +--R ?^? : (%,NonNegativeInteger) -> % +--R abs : % -> % if UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) has OINTDOM +--R ceiling : % -> UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) if UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) has INS +--R characteristic : () -> NonNegativeInteger +--R charthRoot : % -> Union(%,"failed") if $ has CHARNZ and UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) has PFECAT or UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) has CHARNZ +--R coerce : UnivariatePuiseuxSeries(FE,var,cen) -> % +--R coerce : Symbol -> % if UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) has RETRACT SYMBOL +--R coerce : UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) -> % +--R conditionP : Matrix % -> Union(Vector %,"failed") if $ has CHARNZ and UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) has PFECAT +--R convert : % -> DoubleFloat if UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) has REAL +--R convert : % -> Float if UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) has REAL +--R convert : % -> InputForm if UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) has KONVERT INFORM +--R convert : % -> Pattern Float if UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) has KONVERT PATTERN FLOAT +--R convert : % -> Pattern Integer if UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) has KONVERT PATTERN INT +--R denom : % -> UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) +--R differentiate : (%,(UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) -> UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen))) -> % +--R differentiate : (%,(UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) -> UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen)),NonNegativeInteger) -> % +--R differentiate : (%,List Symbol,List NonNegativeInteger) -> % if UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) has PDRING SYMBOL +--R differentiate : (%,Symbol,NonNegativeInteger) -> % if UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) has PDRING SYMBOL +--R differentiate : (%,List Symbol) -> % if UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) has PDRING SYMBOL +--R differentiate : (%,Symbol) -> % if UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) has PDRING SYMBOL +--R differentiate : (%,NonNegativeInteger) -> % if UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) has DIFRING +--R differentiate : % -> % if UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) has DIFRING +--R divide : (%,%) -> Record(quotient: %,remainder: %) +--R ?.? : (%,UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen)) -> % if UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) has ELTAB(UPXSSING(R,FE,var,cen),UPXSSING(R,FE,var,cen)) +--R euclideanSize : % -> NonNegativeInteger +--R eval : (%,Symbol,UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen)) -> % if UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) has IEVALAB(SYMBOL,UPXSSING(R,FE,var,cen)) +--R eval : (%,List Symbol,List UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen)) -> % if UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) has IEVALAB(SYMBOL,UPXSSING(R,FE,var,cen)) +--R eval : (%,List Equation UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen)) -> % if UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) has EVALAB UPXSSING(R,FE,var,cen) +--R eval : (%,Equation UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen)) -> % if UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) has EVALAB UPXSSING(R,FE,var,cen) +--R eval : (%,UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen),UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen)) -> % if UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) has EVALAB UPXSSING(R,FE,var,cen) +--R eval : (%,List UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen),List UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen)) -> % if UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) has EVALAB UPXSSING(R,FE,var,cen) +--R expressIdealMember : (List %,%) -> Union(List %,"failed") +--R exquo : (%,%) -> Union(%,"failed") +--R extendedEuclidean : (%,%,%) -> Union(Record(coef1: %,coef2: %),"failed") +--R extendedEuclidean : (%,%) -> Record(coef1: %,coef2: %,generator: %) +--R factorPolynomial : SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) has PFECAT +--R factorSquareFreePolynomial : SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) has PFECAT +--R floor : % -> UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) if UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) has INS +--R fractionPart : % -> % if UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) has EUCDOM +--R gcdPolynomial : (SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial % +--R init : () -> % if UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) has STEP +--R limitPlus : % -> Union(OrderedCompletion FE,"failed") +--R map : ((UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) -> UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen)),%) -> % +--R max : (%,%) -> % if UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) has ORDSET +--R min : (%,%) -> % if UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) has ORDSET +--R multiEuclidean : (List %,%) -> Union(List %,"failed") +--R negative? : % -> Boolean if UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) has OINTDOM +--R nextItem : % -> Union(%,"failed") if UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) has STEP +--R numer : % -> UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) +--R patternMatch : (%,Pattern Float,PatternMatchResult(Float,%)) -> PatternMatchResult(Float,%) if UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) has PATMAB FLOAT +--R patternMatch : (%,Pattern Integer,PatternMatchResult(Integer,%)) -> PatternMatchResult(Integer,%) if UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) has PATMAB INT +--R positive? : % -> Boolean if UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) has OINTDOM +--R principalIdeal : List % -> Record(coef: List %,generator: %) +--R random : () -> % if UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) has INS +--R reducedSystem : Matrix % -> Matrix UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) +--R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen),vec: Vector UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen)) +--R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix Integer,vec: Vector Integer) if UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) has LINEXP INT +--R reducedSystem : Matrix % -> Matrix Integer if UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) has LINEXP INT +--R retract : % -> UnivariatePuiseuxSeries(FE,var,cen) +--R retract : % -> Integer if UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) has RETRACT INT +--R retract : % -> Fraction Integer if UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) has RETRACT INT +--R retract : % -> Symbol if UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) has RETRACT SYMBOL +--R retract : % -> UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) +--R retractIfCan : % -> Union(UnivariatePuiseuxSeries(FE,var,cen),"failed") +--R retractIfCan : % -> Union(Integer,"failed") if UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) has RETRACT INT +--R retractIfCan : % -> Union(Fraction Integer,"failed") if UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) has RETRACT INT +--R retractIfCan : % -> Union(Symbol,"failed") if UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) has RETRACT SYMBOL +--R retractIfCan : % -> Union(UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen),"failed") +--R sign : % -> Integer if UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) has OINTDOM +--R solveLinearPolynomialEquation : (List SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> Union(List SparseUnivariatePolynomial %,"failed") if UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) has PFECAT +--R squareFreePolynomial : SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) has PFECAT +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R unitNormal : % -> Record(unit: %,canonical: %,associate: %) +--R wholePart : % -> UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) if UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen) has EUCDOM +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +ExponentialExpansion examples +==================================================================== + +See Also: +o )show ExponentialExpansion + +@ + \pagehead{ExponentialExpansion}{EXPEXPAN} \pagepic{ps/v103exponentialexpansion.ps}{EXPEXPAN}{1.00} {\bf See}\\ @@ -26804,6 +31348,7 @@ ExponentialExpansion(R,FE,var,cen): Exports == Implementation where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain EXPR Expression} + <>= )set break resume )sys rm -f Expression.output @@ -27880,6 +32425,163 @@ Expression(R:OrderedSet): Exports == Implementation where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain EXPUPXS ExponentialOfUnivariatePuiseuxSeries} + +<>= +)set break resume +)sys rm -f ExponentialOfUnivariatePuiseuxSeries.output +)spool ExponentialOfUnivariatePuiseuxSeries.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show ExponentialOfUnivariatePuiseuxSeries +--R ExponentialOfUnivariatePuiseuxSeries(FE: Join(Field,OrderedSet),var: Symbol,cen: FE) is a domain constructor +--R Abbreviation for ExponentialOfUnivariatePuiseuxSeries is EXPUPXS +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for EXPUPXS +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (FE,%) -> % ?*? : (%,FE) -> % +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ? Boolean +--R ?<=? : (%,%) -> Boolean ?=? : (%,%) -> Boolean +--R ?>? : (%,%) -> Boolean ?>=? : (%,%) -> Boolean +--R 1 : () -> % 0 : () -> % +--R ?^? : (%,PositiveInteger) -> % center : % -> FE +--R coerce : Integer -> % coerce : % -> OutputForm +--R complete : % -> % degree : % -> Fraction Integer +--R ?.? : (%,Fraction Integer) -> FE hash : % -> SingleInteger +--R inv : % -> % if FE has FIELD latex : % -> String +--R leadingCoefficient : % -> FE leadingMonomial : % -> % +--R map : ((FE -> FE),%) -> % max : (%,%) -> % +--R min : (%,%) -> % monomial? : % -> Boolean +--R one? : % -> Boolean order : % -> Fraction Integer +--R pole? : % -> Boolean recip : % -> Union(%,"failed") +--R reductum : % -> % sample : () -> % +--R variable : % -> Symbol zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean +--R ?*? : (%,Fraction Integer) -> % if FE has ALGEBRA FRAC INT +--R ?*? : (Fraction Integer,%) -> % if FE has ALGEBRA FRAC INT +--R ?*? : (NonNegativeInteger,%) -> % +--R ?**? : (%,Fraction Integer) -> % if FE has ALGEBRA FRAC INT +--R ?**? : (%,%) -> % if FE has ALGEBRA FRAC INT +--R ?**? : (%,Integer) -> % if FE has FIELD +--R ?**? : (%,NonNegativeInteger) -> % +--R ?/? : (%,%) -> % if FE has FIELD +--R ?/? : (%,FE) -> % if FE has FIELD +--R D : % -> % if FE has *: (Fraction Integer,FE) -> FE +--R D : (%,NonNegativeInteger) -> % if FE has *: (Fraction Integer,FE) -> FE +--R D : (%,Symbol) -> % if FE has *: (Fraction Integer,FE) -> FE and FE has PDRING SYMBOL +--R D : (%,List Symbol) -> % if FE has *: (Fraction Integer,FE) -> FE and FE has PDRING SYMBOL +--R D : (%,Symbol,NonNegativeInteger) -> % if FE has *: (Fraction Integer,FE) -> FE and FE has PDRING SYMBOL +--R D : (%,List Symbol,List NonNegativeInteger) -> % if FE has *: (Fraction Integer,FE) -> FE and FE has PDRING SYMBOL +--R ?^? : (%,Integer) -> % if FE has FIELD +--R ?^? : (%,NonNegativeInteger) -> % +--R acos : % -> % if FE has ALGEBRA FRAC INT +--R acosh : % -> % if FE has ALGEBRA FRAC INT +--R acot : % -> % if FE has ALGEBRA FRAC INT +--R acoth : % -> % if FE has ALGEBRA FRAC INT +--R acsc : % -> % if FE has ALGEBRA FRAC INT +--R acsch : % -> % if FE has ALGEBRA FRAC INT +--R approximate : (%,Fraction Integer) -> FE if FE has **: (FE,Fraction Integer) -> FE and FE has coerce: Symbol -> FE +--R asec : % -> % if FE has ALGEBRA FRAC INT +--R asech : % -> % if FE has ALGEBRA FRAC INT +--R asin : % -> % if FE has ALGEBRA FRAC INT +--R asinh : % -> % if FE has ALGEBRA FRAC INT +--R associates? : (%,%) -> Boolean if FE has INTDOM +--R atan : % -> % if FE has ALGEBRA FRAC INT +--R atanh : % -> % if FE has ALGEBRA FRAC INT +--R characteristic : () -> NonNegativeInteger +--R charthRoot : % -> Union(%,"failed") if FE has CHARNZ +--R coefficient : (%,Fraction Integer) -> FE +--R coerce : % -> % if FE has INTDOM +--R coerce : Fraction Integer -> % if FE has ALGEBRA FRAC INT +--R coerce : FE -> % if FE has COMRING +--R cos : % -> % if FE has ALGEBRA FRAC INT +--R cosh : % -> % if FE has ALGEBRA FRAC INT +--R cot : % -> % if FE has ALGEBRA FRAC INT +--R coth : % -> % if FE has ALGEBRA FRAC INT +--R csc : % -> % if FE has ALGEBRA FRAC INT +--R csch : % -> % if FE has ALGEBRA FRAC INT +--R differentiate : % -> % if FE has *: (Fraction Integer,FE) -> FE +--R differentiate : (%,NonNegativeInteger) -> % if FE has *: (Fraction Integer,FE) -> FE +--R differentiate : (%,Symbol) -> % if FE has *: (Fraction Integer,FE) -> FE and FE has PDRING SYMBOL +--R differentiate : (%,List Symbol) -> % if FE has *: (Fraction Integer,FE) -> FE and FE has PDRING SYMBOL +--R differentiate : (%,Symbol,NonNegativeInteger) -> % if FE has *: (Fraction Integer,FE) -> FE and FE has PDRING SYMBOL +--R differentiate : (%,List Symbol,List NonNegativeInteger) -> % if FE has *: (Fraction Integer,FE) -> FE and FE has PDRING SYMBOL +--R divide : (%,%) -> Record(quotient: %,remainder: %) if FE has FIELD +--R ?.? : (%,%) -> % if Fraction Integer has SGROUP +--R euclideanSize : % -> NonNegativeInteger if FE has FIELD +--R eval : (%,FE) -> Stream FE if FE has **: (FE,Fraction Integer) -> FE +--R exp : % -> % if FE has ALGEBRA FRAC INT +--R exponent : % -> UnivariatePuiseuxSeries(FE,var,cen) +--R exponential : UnivariatePuiseuxSeries(FE,var,cen) -> % +--R exponentialOrder : % -> Fraction Integer +--R expressIdealMember : (List %,%) -> Union(List %,"failed") if FE has FIELD +--R exquo : (%,%) -> Union(%,"failed") if FE has INTDOM +--R extend : (%,Fraction Integer) -> % +--R extendedEuclidean : (%,%) -> Record(coef1: %,coef2: %,generator: %) if FE has FIELD +--R extendedEuclidean : (%,%,%) -> Union(Record(coef1: %,coef2: %),"failed") if FE has FIELD +--R factor : % -> Factored % if FE has FIELD +--R gcd : (%,%) -> % if FE has FIELD +--R gcd : List % -> % if FE has FIELD +--R gcdPolynomial : (SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial % if FE has FIELD +--R integrate : (%,Symbol) -> % if FE has integrate: (FE,Symbol) -> FE and FE has variables: FE -> List Symbol and FE has ALGEBRA FRAC INT or FE has ACFS INT and FE has ALGEBRA FRAC INT and FE has PRIMCAT and FE has TRANFUN +--R integrate : % -> % if FE has ALGEBRA FRAC INT +--R lcm : (%,%) -> % if FE has FIELD +--R lcm : List % -> % if FE has FIELD +--R log : % -> % if FE has ALGEBRA FRAC INT +--R monomial : (%,List SingletonAsOrderedSet,List Fraction Integer) -> % +--R monomial : (%,SingletonAsOrderedSet,Fraction Integer) -> % +--R monomial : (FE,Fraction Integer) -> % +--R multiEuclidean : (List %,%) -> Union(List %,"failed") if FE has FIELD +--R multiplyExponents : (%,Fraction Integer) -> % +--R multiplyExponents : (%,PositiveInteger) -> % +--R nthRoot : (%,Integer) -> % if FE has ALGEBRA FRAC INT +--R order : (%,Fraction Integer) -> Fraction Integer +--R pi : () -> % if FE has ALGEBRA FRAC INT +--R prime? : % -> Boolean if FE has FIELD +--R principalIdeal : List % -> Record(coef: List %,generator: %) if FE has FIELD +--R ?quo? : (%,%) -> % if FE has FIELD +--R ?rem? : (%,%) -> % if FE has FIELD +--R sec : % -> % if FE has ALGEBRA FRAC INT +--R sech : % -> % if FE has ALGEBRA FRAC INT +--R series : (NonNegativeInteger,Stream Record(k: Fraction Integer,c: FE)) -> % +--R sin : % -> % if FE has ALGEBRA FRAC INT +--R sinh : % -> % if FE has ALGEBRA FRAC INT +--R sizeLess? : (%,%) -> Boolean if FE has FIELD +--R sqrt : % -> % if FE has ALGEBRA FRAC INT +--R squareFree : % -> Factored % if FE has FIELD +--R squareFreePart : % -> % if FE has FIELD +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R tan : % -> % if FE has ALGEBRA FRAC INT +--R tanh : % -> % if FE has ALGEBRA FRAC INT +--R terms : % -> Stream Record(k: Fraction Integer,c: FE) +--R truncate : (%,Fraction Integer,Fraction Integer) -> % +--R truncate : (%,Fraction Integer) -> % +--R unit? : % -> Boolean if FE has INTDOM +--R unitCanonical : % -> % if FE has INTDOM +--R unitNormal : % -> Record(unit: %,canonical: %,associate: %) if FE has INTDOM +--R variables : % -> List SingletonAsOrderedSet +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +ExponentialOfUnivariatePuiseuxSeries examples +==================================================================== + +See Also: +o )show ExponentialOfUnivariatePuiseuxSeries + +@ + \pagehead{ExponentialOfUnivariatePuiseuxSeries}{EXPUPXS} \pagepic{ps/v103exponentialofunivariatepuiseuxseries.ps}{EXPUPXS}{1.00} {\bf See}\\ @@ -28077,6 +32779,47 @@ ExponentialOfUnivariatePuiseuxSeries(FE,var,cen):_ @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain EAB ExtAlgBasis} + +<>= +)set break resume +)sys rm -f ExtAlgBasis.output +)spool ExtAlgBasis.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show ExtAlgBasis +--R ExtAlgBasis is a domain constructor +--R Abbreviation for ExtAlgBasis is EAB +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for EAB +--R +--R------------------------------- Operations -------------------------------- +--R ? Boolean ?<=? : (%,%) -> Boolean +--R ?=? : (%,%) -> Boolean ?>? : (%,%) -> Boolean +--R ?>=? : (%,%) -> Boolean Nul : NonNegativeInteger -> % +--R coerce : List Integer -> % coerce : % -> OutputForm +--R degree : % -> NonNegativeInteger exponents : % -> List Integer +--R hash : % -> SingleInteger latex : % -> String +--R max : (%,%) -> % min : (%,%) -> % +--R ?~=? : (%,%) -> Boolean +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +ExtAlgBasis examples +==================================================================== + +See Also: +o )show ExtAlgBasis + +@ + \pagehead{ExtAlgBasis}{EAB} \pagepic{ps/v103extalgbasis.ps}{EAB}{1.00} {\bf See}\\ @@ -28191,6 +32934,46 @@ ExtAlgBasis(): Export == Implement where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain E04DGFA e04dgfAnnaType} + +<>= +)set break resume +)sys rm -f e04dgfAnnaType.output +)spool e04dgfAnnaType.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show e04dgfAnnaType +--R e04dgfAnnaType is a domain constructor +--R Abbreviation for e04dgfAnnaType is E04DGFA +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for E04DGFA +--R +--R------------------------------- Operations -------------------------------- +--R ?=? : (%,%) -> Boolean coerce : % -> OutputForm +--R hash : % -> SingleInteger latex : % -> String +--R ?~=? : (%,%) -> Boolean +--R measure : (RoutinesTable,Record(lfn: List Expression DoubleFloat,init: List DoubleFloat)) -> Record(measure: Float,explanations: String) +--R measure : (RoutinesTable,Record(fn: Expression DoubleFloat,init: List DoubleFloat,lb: List OrderedCompletion DoubleFloat,cf: List Expression DoubleFloat,ub: List OrderedCompletion DoubleFloat)) -> Record(measure: Float,explanations: String) +--R numericalOptimization : Record(fn: Expression DoubleFloat,init: List DoubleFloat,lb: List OrderedCompletion DoubleFloat,cf: List Expression DoubleFloat,ub: List OrderedCompletion DoubleFloat) -> Result +--R numericalOptimization : Record(lfn: List Expression DoubleFloat,init: List DoubleFloat) -> Result +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +e04dgfAnnaType examples +==================================================================== + +See Also: +o )show e04dgfAnnaType + +@ + \pagehead{e04dgfAnnaType}{E04DGFA} \pagepic{ps/v103e04dgfannatype.ps}{E04DGFA}{1.00} {\bf See}\\ @@ -28290,6 +33073,46 @@ e04dgfAnnaType(): NumericalOptimizationCategory == Result add @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain E04FDFA e04fdfAnnaType} + +<>= +)set break resume +)sys rm -f e04fdfAnnaType.output +)spool e04fdfAnnaType.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show e04fdfAnnaType +--R e04fdfAnnaType is a domain constructor +--R Abbreviation for e04fdfAnnaType is E04FDFA +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for E04FDFA +--R +--R------------------------------- Operations -------------------------------- +--R ?=? : (%,%) -> Boolean coerce : % -> OutputForm +--R hash : % -> SingleInteger latex : % -> String +--R ?~=? : (%,%) -> Boolean +--R measure : (RoutinesTable,Record(lfn: List Expression DoubleFloat,init: List DoubleFloat)) -> Record(measure: Float,explanations: String) +--R measure : (RoutinesTable,Record(fn: Expression DoubleFloat,init: List DoubleFloat,lb: List OrderedCompletion DoubleFloat,cf: List Expression DoubleFloat,ub: List OrderedCompletion DoubleFloat)) -> Record(measure: Float,explanations: String) +--R numericalOptimization : Record(fn: Expression DoubleFloat,init: List DoubleFloat,lb: List OrderedCompletion DoubleFloat,cf: List Expression DoubleFloat,ub: List OrderedCompletion DoubleFloat) -> Result +--R numericalOptimization : Record(lfn: List Expression DoubleFloat,init: List DoubleFloat) -> Result +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +e04fdfAnnaType examples +==================================================================== + +See Also: +o )show e04fdfAnnaType + +@ + \pagehead{e04fdfAnnaType}{E04FDFA} \pagepic{ps/v103e04fdfannatype.ps}{E04FDFA}{1.00} {\bf See}\\ @@ -28415,6 +33238,46 @@ e04fdfAnnaType(): NumericalOptimizationCategory == Result add @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain E04GCFA e04gcfAnnaType} + +<>= +)set break resume +)sys rm -f e04gcfAnnaType.output +)spool e04gcfAnnaType.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show e04gcfAnnaType +--R e04gcfAnnaType is a domain constructor +--R Abbreviation for e04gcfAnnaType is E04GCFA +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for E04GCFA +--R +--R------------------------------- Operations -------------------------------- +--R ?=? : (%,%) -> Boolean coerce : % -> OutputForm +--R hash : % -> SingleInteger latex : % -> String +--R ?~=? : (%,%) -> Boolean +--R measure : (RoutinesTable,Record(lfn: List Expression DoubleFloat,init: List DoubleFloat)) -> Record(measure: Float,explanations: String) +--R measure : (RoutinesTable,Record(fn: Expression DoubleFloat,init: List DoubleFloat,lb: List OrderedCompletion DoubleFloat,cf: List Expression DoubleFloat,ub: List OrderedCompletion DoubleFloat)) -> Record(measure: Float,explanations: String) +--R numericalOptimization : Record(fn: Expression DoubleFloat,init: List DoubleFloat,lb: List OrderedCompletion DoubleFloat,cf: List Expression DoubleFloat,ub: List OrderedCompletion DoubleFloat) -> Result +--R numericalOptimization : Record(lfn: List Expression DoubleFloat,init: List DoubleFloat) -> Result +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +e04gcfAnnaType examples +==================================================================== + +See Also: +o )show e04gcfAnnaType + +@ + \pagehead{e04gcfAnnaType}{E04GCFA} \pagepic{ps/v103e04gcfannatype.ps}{E04GCFA}{1.00} {\bf See}\\ @@ -28556,6 +33419,46 @@ e04gcfAnnaType(): NumericalOptimizationCategory == Result add @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain E04JAFA e04jafAnnaType} + +<>= +)set break resume +)sys rm -f e04jafAnnaType.output +)spool e04jafAnnaType.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show e04jafAnnaType +--R e04jafAnnaType is a domain constructor +--R Abbreviation for e04jafAnnaType is E04JAFA +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for E04JAFA +--R +--R------------------------------- Operations -------------------------------- +--R ?=? : (%,%) -> Boolean coerce : % -> OutputForm +--R hash : % -> SingleInteger latex : % -> String +--R ?~=? : (%,%) -> Boolean +--R measure : (RoutinesTable,Record(lfn: List Expression DoubleFloat,init: List DoubleFloat)) -> Record(measure: Float,explanations: String) +--R measure : (RoutinesTable,Record(fn: Expression DoubleFloat,init: List DoubleFloat,lb: List OrderedCompletion DoubleFloat,cf: List Expression DoubleFloat,ub: List OrderedCompletion DoubleFloat)) -> Record(measure: Float,explanations: String) +--R numericalOptimization : Record(fn: Expression DoubleFloat,init: List DoubleFloat,lb: List OrderedCompletion DoubleFloat,cf: List Expression DoubleFloat,ub: List OrderedCompletion DoubleFloat) -> Result +--R numericalOptimization : Record(lfn: List Expression DoubleFloat,init: List DoubleFloat) -> Result +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +e04jafAnnaType examples +==================================================================== + +See Also: +o )show e04jafAnnaType + +@ + \pagehead{e04jafAnnaType}{E04JAFA} \pagepic{ps/v103e04jafannatype.ps}{E04JAFA}{1.00} {\bf See}\\ @@ -28672,6 +33575,46 @@ e04jafAnnaType(): NumericalOptimizationCategory == Result add @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain E04MBFA e04mbfAnnaType} + +<>= +)set break resume +)sys rm -f e04mbfAnnaType.output +)spool e04mbfAnnaType.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show e04mbfAnnaType +--R e04mbfAnnaType is a domain constructor +--R Abbreviation for e04mbfAnnaType is E04MBFA +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for E04MBFA +--R +--R------------------------------- Operations -------------------------------- +--R ?=? : (%,%) -> Boolean coerce : % -> OutputForm +--R hash : % -> SingleInteger latex : % -> String +--R ?~=? : (%,%) -> Boolean +--R measure : (RoutinesTable,Record(lfn: List Expression DoubleFloat,init: List DoubleFloat)) -> Record(measure: Float,explanations: String) +--R measure : (RoutinesTable,Record(fn: Expression DoubleFloat,init: List DoubleFloat,lb: List OrderedCompletion DoubleFloat,cf: List Expression DoubleFloat,ub: List OrderedCompletion DoubleFloat)) -> Record(measure: Float,explanations: String) +--R numericalOptimization : Record(fn: Expression DoubleFloat,init: List DoubleFloat,lb: List OrderedCompletion DoubleFloat,cf: List Expression DoubleFloat,ub: List OrderedCompletion DoubleFloat) -> Result +--R numericalOptimization : Record(lfn: List Expression DoubleFloat,init: List DoubleFloat) -> Result +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +e04mbfAnnaType examples +==================================================================== + +See Also: +o )show e04mbfAnnaType + +@ + \pagehead{e04mbfAnnaType}{E04MBFA} \pagepic{ps/v103e04mbfannatype.ps}{E04MBFA}{1.00} {\bf See}\\ @@ -28774,6 +33717,46 @@ e04mbfAnnaType(): NumericalOptimizationCategory == Result add @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain E04NAFA e04nafAnnaType} + +<>= +)set break resume +)sys rm -f e04nafAnnaType.output +)spool e04nafAnnaType.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show e04nafAnnaType +--R e04nafAnnaType is a domain constructor +--R Abbreviation for e04nafAnnaType is E04NAFA +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for E04NAFA +--R +--R------------------------------- Operations -------------------------------- +--R ?=? : (%,%) -> Boolean coerce : % -> OutputForm +--R hash : % -> SingleInteger latex : % -> String +--R ?~=? : (%,%) -> Boolean +--R measure : (RoutinesTable,Record(lfn: List Expression DoubleFloat,init: List DoubleFloat)) -> Record(measure: Float,explanations: String) +--R measure : (RoutinesTable,Record(fn: Expression DoubleFloat,init: List DoubleFloat,lb: List OrderedCompletion DoubleFloat,cf: List Expression DoubleFloat,ub: List OrderedCompletion DoubleFloat)) -> Record(measure: Float,explanations: String) +--R numericalOptimization : Record(fn: Expression DoubleFloat,init: List DoubleFloat,lb: List OrderedCompletion DoubleFloat,cf: List Expression DoubleFloat,ub: List OrderedCompletion DoubleFloat) -> Result +--R numericalOptimization : Record(lfn: List Expression DoubleFloat,init: List DoubleFloat) -> Result +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +e04nafAnnaType examples +==================================================================== + +See Also: +o )show e04nafAnnaType + +@ + \pagehead{e04nafAnnaType}{E04NAFA} \pagepic{ps/v103e04nafannatype.ps}{E04NAFA}{1.00} {\bf See}\\ @@ -28891,6 +33874,46 @@ e04nafAnnaType(): NumericalOptimizationCategory == Result add @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain E04UCFA e04ucfAnnaType} + +<>= +)set break resume +)sys rm -f e04ucfAnnaType.output +)spool e04ucfAnnaType.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show e04ucfAnnaType +--R e04ucfAnnaType is a domain constructor +--R Abbreviation for e04ucfAnnaType is E04UCFA +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for E04UCFA +--R +--R------------------------------- Operations -------------------------------- +--R ?=? : (%,%) -> Boolean coerce : % -> OutputForm +--R hash : % -> SingleInteger latex : % -> String +--R ?~=? : (%,%) -> Boolean +--R measure : (RoutinesTable,Record(lfn: List Expression DoubleFloat,init: List DoubleFloat)) -> Record(measure: Float,explanations: String) +--R measure : (RoutinesTable,Record(fn: Expression DoubleFloat,init: List DoubleFloat,lb: List OrderedCompletion DoubleFloat,cf: List Expression DoubleFloat,ub: List OrderedCompletion DoubleFloat)) -> Record(measure: Float,explanations: String) +--R numericalOptimization : Record(fn: Expression DoubleFloat,init: List DoubleFloat,lb: List OrderedCompletion DoubleFloat,cf: List Expression DoubleFloat,ub: List OrderedCompletion DoubleFloat) -> Result +--R numericalOptimization : Record(lfn: List Expression DoubleFloat,init: List DoubleFloat) -> Result +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +e04ucfAnnaType examples +==================================================================== + +See Also: +o )show e04ucfAnnaType + +@ + \pagehead{e04ucfAnnaType}{E04UCFA} \pagepic{ps/v103e04ucfannatype.ps}{E04UCFA}{1.00} {\bf See}\\ @@ -29026,6 +34049,7 @@ e04ucfAnnaType(): NumericalOptimizationCategory == Result add \chapter{Chapter F} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain FR Factored} + <>= )set break resume )sys rm -f Factored.output @@ -30267,6 +35291,7 @@ Factored(R: IntegralDomain): Exports == Implementation where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain FILE File} + <>= )set break resume )sys rm -f File.output @@ -30584,6 +35609,7 @@ File(S:SetCategory): FileCategory(FileName, S) with @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain FNAME FileName} + <>= )set break resume )sys rm -f FileName.output @@ -30927,6 +35953,56 @@ FileName(): FileNameCategory == add @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain FDIV FiniteDivisor} + +<>= +)set break resume +)sys rm -f FiniteDivisor.output +)spool FiniteDivisor.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show FiniteDivisor +--R FiniteDivisor(F: Field,UP: UnivariatePolynomialCategory F,UPUP: UnivariatePolynomialCategory Fraction UP,R: FunctionFieldCategory(F,UP,UPUP)) is a domain constructor +--R Abbreviation for FiniteDivisor is FDIV +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for FDIV +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (Integer,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ?=? : (%,%) -> Boolean +--R 0 : () -> % coerce : % -> OutputForm +--R divisor : (R,UP,UP,UP,F) -> % divisor : (F,F,Integer) -> % +--R divisor : (F,F) -> % divisor : R -> % +--R finiteBasis : % -> Vector R hash : % -> SingleInteger +--R lSpaceBasis : % -> Vector R latex : % -> String +--R principal? : % -> Boolean reduce : % -> % +--R sample : () -> % zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean +--R ?*? : (NonNegativeInteger,%) -> % +--R decompose : % -> Record(id: FractionalIdeal(UP,Fraction UP,UPUP,R),principalPart: R) +--R divisor : FractionalIdeal(UP,Fraction UP,UPUP,R) -> % +--R generator : % -> Union(R,"failed") +--R ideal : % -> FractionalIdeal(UP,Fraction UP,UPUP,R) +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +FiniteDivisor examples +==================================================================== + +See Also: +o )show FiniteDivisor + +@ + \pagehead{FiniteDivisor}{FDIV} \pagepic{ps/v103finitedivisor.ps}{FDIV}{1.00} {\bf See}\\ @@ -31096,6 +36172,131 @@ FiniteDivisor(F, UP, UPUP, R): Exports == Implementation where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain FF FiniteField} + +<>= +)set break resume +)sys rm -f FiniteField.output +)spool FiniteField.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show FiniteField +--R FiniteField(p: PositiveInteger,n: PositiveInteger) is a domain constructor +--R Abbreviation for FiniteField is FF +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for FF +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (PrimeField p,%) -> % ?*? : (%,PrimeField p) -> % +--R ?*? : (Fraction Integer,%) -> % ?*? : (%,Fraction Integer) -> % +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?**? : (%,Integer) -> % +--R ?**? : (%,PositiveInteger) -> % ?+? : (%,%) -> % +--R ?-? : (%,%) -> % -? : % -> % +--R ?/? : (%,PrimeField p) -> % ?/? : (%,%) -> % +--R ?=? : (%,%) -> Boolean 1 : () -> % +--R 0 : () -> % ?^? : (%,Integer) -> % +--R ?^? : (%,PositiveInteger) -> % algebraic? : % -> Boolean +--R associates? : (%,%) -> Boolean basis : () -> Vector % +--R coerce : PrimeField p -> % coerce : Fraction Integer -> % +--R coerce : % -> % coerce : Integer -> % +--R coerce : % -> OutputForm degree : % -> PositiveInteger +--R dimension : () -> CardinalNumber factor : % -> Factored % +--R gcd : List % -> % gcd : (%,%) -> % +--R hash : % -> SingleInteger inGroundField? : % -> Boolean +--R inv : % -> % latex : % -> String +--R lcm : List % -> % lcm : (%,%) -> % +--R norm : % -> PrimeField p one? : % -> Boolean +--R prime? : % -> Boolean ?quo? : (%,%) -> % +--R recip : % -> Union(%,"failed") ?rem? : (%,%) -> % +--R retract : % -> PrimeField p sample : () -> % +--R sizeLess? : (%,%) -> Boolean squareFree : % -> Factored % +--R squareFreePart : % -> % trace : % -> PrimeField p +--R transcendent? : % -> Boolean unit? : % -> Boolean +--R unitCanonical : % -> % zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean +--R ?*? : (NonNegativeInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % +--R D : (%,NonNegativeInteger) -> % if PrimeField p has FINITE +--R D : % -> % if PrimeField p has FINITE +--R Frobenius : (%,NonNegativeInteger) -> % if PrimeField p has FINITE +--R Frobenius : % -> % if PrimeField p has FINITE +--R ?^? : (%,NonNegativeInteger) -> % +--R basis : PositiveInteger -> Vector % +--R characteristic : () -> NonNegativeInteger +--R charthRoot : % -> Union(%,"failed") if PrimeField p has CHARNZ or PrimeField p has FINITE +--R charthRoot : % -> % if PrimeField p has FINITE +--R conditionP : Matrix % -> Union(Vector %,"failed") if PrimeField p has FINITE +--R coordinates : Vector % -> Matrix PrimeField p +--R coordinates : % -> Vector PrimeField p +--R createNormalElement : () -> % if PrimeField p has FINITE +--R createPrimitiveElement : () -> % if PrimeField p has FINITE +--R definingPolynomial : () -> SparseUnivariatePolynomial PrimeField p +--R degree : % -> OnePointCompletion PositiveInteger +--R differentiate : (%,NonNegativeInteger) -> % if PrimeField p has FINITE +--R differentiate : % -> % if PrimeField p has FINITE +--R discreteLog : (%,%) -> Union(NonNegativeInteger,"failed") if PrimeField p has CHARNZ or PrimeField p has FINITE +--R discreteLog : % -> NonNegativeInteger if PrimeField p has FINITE +--R divide : (%,%) -> Record(quotient: %,remainder: %) +--R euclideanSize : % -> NonNegativeInteger +--R expressIdealMember : (List %,%) -> Union(List %,"failed") +--R exquo : (%,%) -> Union(%,"failed") +--R extendedEuclidean : (%,%,%) -> Union(Record(coef1: %,coef2: %),"failed") +--R extendedEuclidean : (%,%) -> Record(coef1: %,coef2: %,generator: %) +--R extensionDegree : () -> PositiveInteger +--R extensionDegree : () -> OnePointCompletion PositiveInteger +--R factorsOfCyclicGroupSize : () -> List Record(factor: Integer,exponent: Integer) if PrimeField p has FINITE +--R gcdPolynomial : (SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial % +--R generator : () -> % if PrimeField p has FINITE +--R index : PositiveInteger -> % if PrimeField p has FINITE +--R init : () -> % if PrimeField p has FINITE +--R linearAssociatedExp : (%,SparseUnivariatePolynomial PrimeField p) -> % if PrimeField p has FINITE +--R linearAssociatedLog : (%,%) -> Union(SparseUnivariatePolynomial PrimeField p,"failed") if PrimeField p has FINITE +--R linearAssociatedLog : % -> SparseUnivariatePolynomial PrimeField p if PrimeField p has FINITE +--R linearAssociatedOrder : % -> SparseUnivariatePolynomial PrimeField p if PrimeField p has FINITE +--R lookup : % -> PositiveInteger if PrimeField p has FINITE +--R minimalPolynomial : (%,PositiveInteger) -> SparseUnivariatePolynomial % if PrimeField p has FINITE +--R minimalPolynomial : % -> SparseUnivariatePolynomial PrimeField p +--R multiEuclidean : (List %,%) -> Union(List %,"failed") +--R nextItem : % -> Union(%,"failed") if PrimeField p has FINITE +--R norm : (%,PositiveInteger) -> % if PrimeField p has FINITE +--R normal? : % -> Boolean if PrimeField p has FINITE +--R normalElement : () -> % if PrimeField p has FINITE +--R order : % -> OnePointCompletion PositiveInteger if PrimeField p has CHARNZ or PrimeField p has FINITE +--R order : % -> PositiveInteger if PrimeField p has FINITE +--R primeFrobenius : % -> % if PrimeField p has CHARNZ or PrimeField p has FINITE +--R primeFrobenius : (%,NonNegativeInteger) -> % if PrimeField p has CHARNZ or PrimeField p has FINITE +--R primitive? : % -> Boolean if PrimeField p has FINITE +--R primitiveElement : () -> % if PrimeField p has FINITE +--R principalIdeal : List % -> Record(coef: List %,generator: %) +--R random : () -> % if PrimeField p has FINITE +--R representationType : () -> Union("prime",polynomial,normal,cyclic) if PrimeField p has FINITE +--R represents : Vector PrimeField p -> % +--R retractIfCan : % -> Union(PrimeField p,"failed") +--R size : () -> NonNegativeInteger if PrimeField p has FINITE +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R tableForDiscreteLogarithm : Integer -> Table(PositiveInteger,NonNegativeInteger) if PrimeField p has FINITE +--R trace : (%,PositiveInteger) -> % if PrimeField p has FINITE +--R transcendenceDegree : () -> NonNegativeInteger +--R unitNormal : % -> Record(unit: %,canonical: %,associate: %) +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +FiniteField examples +==================================================================== + +See Also: +o )show FiniteField + +@ + \pagehead{FiniteField}{FF} \pagepic{ps/v103finitefield.ps}{FF}{1.00} {\bf See}\\ @@ -31230,6 +36431,132 @@ FiniteField(p:PositiveInteger, n:PositiveInteger): _ @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain FFCG FiniteFieldCyclicGroup} + +<>= +)set break resume +)sys rm -f FiniteFieldCyclicGroup.output +)spool FiniteFieldCyclicGroup.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show FiniteFieldCyclicGroup +--R FiniteFieldCyclicGroup(p: PositiveInteger,extdeg: PositiveInteger) is a domain constructor +--R Abbreviation for FiniteFieldCyclicGroup is FFCG +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for FFCG +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (PrimeField p,%) -> % ?*? : (%,PrimeField p) -> % +--R ?*? : (Fraction Integer,%) -> % ?*? : (%,Fraction Integer) -> % +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?**? : (%,Integer) -> % +--R ?**? : (%,PositiveInteger) -> % ?+? : (%,%) -> % +--R ?-? : (%,%) -> % -? : % -> % +--R ?/? : (%,PrimeField p) -> % ?/? : (%,%) -> % +--R ?=? : (%,%) -> Boolean 1 : () -> % +--R 0 : () -> % ?^? : (%,Integer) -> % +--R ?^? : (%,PositiveInteger) -> % algebraic? : % -> Boolean +--R associates? : (%,%) -> Boolean basis : () -> Vector % +--R coerce : PrimeField p -> % coerce : Fraction Integer -> % +--R coerce : % -> % coerce : Integer -> % +--R coerce : % -> OutputForm degree : % -> PositiveInteger +--R dimension : () -> CardinalNumber factor : % -> Factored % +--R gcd : List % -> % gcd : (%,%) -> % +--R hash : % -> SingleInteger inGroundField? : % -> Boolean +--R inv : % -> % latex : % -> String +--R lcm : List % -> % lcm : (%,%) -> % +--R norm : % -> PrimeField p one? : % -> Boolean +--R prime? : % -> Boolean ?quo? : (%,%) -> % +--R recip : % -> Union(%,"failed") ?rem? : (%,%) -> % +--R retract : % -> PrimeField p sample : () -> % +--R sizeLess? : (%,%) -> Boolean squareFree : % -> Factored % +--R squareFreePart : % -> % trace : % -> PrimeField p +--R transcendent? : % -> Boolean unit? : % -> Boolean +--R unitCanonical : % -> % zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean +--R ?*? : (NonNegativeInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % +--R D : (%,NonNegativeInteger) -> % if PrimeField p has FINITE +--R D : % -> % if PrimeField p has FINITE +--R Frobenius : (%,NonNegativeInteger) -> % if PrimeField p has FINITE +--R Frobenius : % -> % if PrimeField p has FINITE +--R ?^? : (%,NonNegativeInteger) -> % +--R basis : PositiveInteger -> Vector % +--R characteristic : () -> NonNegativeInteger +--R charthRoot : % -> Union(%,"failed") if PrimeField p has CHARNZ or PrimeField p has FINITE +--R charthRoot : % -> % if PrimeField p has FINITE +--R conditionP : Matrix % -> Union(Vector %,"failed") if PrimeField p has FINITE +--R coordinates : Vector % -> Matrix PrimeField p +--R coordinates : % -> Vector PrimeField p +--R createNormalElement : () -> % if PrimeField p has FINITE +--R createPrimitiveElement : () -> % if PrimeField p has FINITE +--R definingPolynomial : () -> SparseUnivariatePolynomial PrimeField p +--R degree : % -> OnePointCompletion PositiveInteger +--R differentiate : (%,NonNegativeInteger) -> % if PrimeField p has FINITE +--R differentiate : % -> % if PrimeField p has FINITE +--R discreteLog : (%,%) -> Union(NonNegativeInteger,"failed") if PrimeField p has CHARNZ or PrimeField p has FINITE +--R discreteLog : % -> NonNegativeInteger if PrimeField p has FINITE +--R divide : (%,%) -> Record(quotient: %,remainder: %) +--R euclideanSize : % -> NonNegativeInteger +--R expressIdealMember : (List %,%) -> Union(List %,"failed") +--R exquo : (%,%) -> Union(%,"failed") +--R extendedEuclidean : (%,%,%) -> Union(Record(coef1: %,coef2: %),"failed") +--R extendedEuclidean : (%,%) -> Record(coef1: %,coef2: %,generator: %) +--R extensionDegree : () -> PositiveInteger +--R extensionDegree : () -> OnePointCompletion PositiveInteger +--R factorsOfCyclicGroupSize : () -> List Record(factor: Integer,exponent: Integer) if PrimeField p has FINITE +--R gcdPolynomial : (SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial % +--R generator : () -> % if PrimeField p has FINITE +--R getZechTable : () -> PrimitiveArray SingleInteger +--R index : PositiveInteger -> % if PrimeField p has FINITE +--R init : () -> % if PrimeField p has FINITE +--R linearAssociatedExp : (%,SparseUnivariatePolynomial PrimeField p) -> % if PrimeField p has FINITE +--R linearAssociatedLog : (%,%) -> Union(SparseUnivariatePolynomial PrimeField p,"failed") if PrimeField p has FINITE +--R linearAssociatedLog : % -> SparseUnivariatePolynomial PrimeField p if PrimeField p has FINITE +--R linearAssociatedOrder : % -> SparseUnivariatePolynomial PrimeField p if PrimeField p has FINITE +--R lookup : % -> PositiveInteger if PrimeField p has FINITE +--R minimalPolynomial : (%,PositiveInteger) -> SparseUnivariatePolynomial % if PrimeField p has FINITE +--R minimalPolynomial : % -> SparseUnivariatePolynomial PrimeField p +--R multiEuclidean : (List %,%) -> Union(List %,"failed") +--R nextItem : % -> Union(%,"failed") if PrimeField p has FINITE +--R norm : (%,PositiveInteger) -> % if PrimeField p has FINITE +--R normal? : % -> Boolean if PrimeField p has FINITE +--R normalElement : () -> % if PrimeField p has FINITE +--R order : % -> OnePointCompletion PositiveInteger if PrimeField p has CHARNZ or PrimeField p has FINITE +--R order : % -> PositiveInteger if PrimeField p has FINITE +--R primeFrobenius : % -> % if PrimeField p has CHARNZ or PrimeField p has FINITE +--R primeFrobenius : (%,NonNegativeInteger) -> % if PrimeField p has CHARNZ or PrimeField p has FINITE +--R primitive? : % -> Boolean if PrimeField p has FINITE +--R primitiveElement : () -> % if PrimeField p has FINITE +--R principalIdeal : List % -> Record(coef: List %,generator: %) +--R random : () -> % if PrimeField p has FINITE +--R representationType : () -> Union("prime",polynomial,normal,cyclic) if PrimeField p has FINITE +--R represents : Vector PrimeField p -> % +--R retractIfCan : % -> Union(PrimeField p,"failed") +--R size : () -> NonNegativeInteger if PrimeField p has FINITE +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R tableForDiscreteLogarithm : Integer -> Table(PositiveInteger,NonNegativeInteger) if PrimeField p has FINITE +--R trace : (%,PositiveInteger) -> % if PrimeField p has FINITE +--R transcendenceDegree : () -> NonNegativeInteger +--R unitNormal : % -> Record(unit: %,canonical: %,associate: %) +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +FiniteFieldCyclicGroup examples +==================================================================== + +See Also: +o )show FiniteFieldCyclicGroup + +@ + \pagehead{FiniteFieldCyclicGroup}{FFCG} \pagepic{ps/v103finitefieldcyclicgroup.ps}{FFCG}{1.00} {\bf See}\\ @@ -31374,6 +36701,130 @@ FiniteFieldCyclicGroup(p,extdeg):_ @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain FFCGX FiniteFieldCyclicGroupExtension} + +<>= +)set break resume +)sys rm -f FiniteFieldCyclicGroupExtension.output +)spool FiniteFieldCyclicGroupExtension.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show FiniteFieldCyclicGroupExtension +--R FiniteFieldCyclicGroupExtension(GF: FiniteFieldCategory,extdeg: PositiveInteger) is a domain constructor +--R Abbreviation for FiniteFieldCyclicGroupExtension is FFCGX +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for FFCGX +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (GF,%) -> % ?*? : (%,GF) -> % +--R ?*? : (Fraction Integer,%) -> % ?*? : (%,Fraction Integer) -> % +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?**? : (%,Integer) -> % +--R ?**? : (%,PositiveInteger) -> % ?+? : (%,%) -> % +--R ?-? : (%,%) -> % -? : % -> % +--R ?/? : (%,GF) -> % ?/? : (%,%) -> % +--R ?=? : (%,%) -> Boolean D : % -> % if GF has FINITE +--R 1 : () -> % 0 : () -> % +--R ?^? : (%,Integer) -> % ?^? : (%,PositiveInteger) -> % +--R algebraic? : % -> Boolean associates? : (%,%) -> Boolean +--R basis : () -> Vector % coerce : GF -> % +--R coerce : Fraction Integer -> % coerce : % -> % +--R coerce : Integer -> % coerce : % -> OutputForm +--R coordinates : % -> Vector GF degree : % -> PositiveInteger +--R dimension : () -> CardinalNumber factor : % -> Factored % +--R gcd : List % -> % gcd : (%,%) -> % +--R hash : % -> SingleInteger inGroundField? : % -> Boolean +--R inv : % -> % latex : % -> String +--R lcm : List % -> % lcm : (%,%) -> % +--R norm : % -> GF one? : % -> Boolean +--R prime? : % -> Boolean ?quo? : (%,%) -> % +--R recip : % -> Union(%,"failed") ?rem? : (%,%) -> % +--R represents : Vector GF -> % retract : % -> GF +--R sample : () -> % sizeLess? : (%,%) -> Boolean +--R squareFree : % -> Factored % squareFreePart : % -> % +--R trace : % -> GF transcendent? : % -> Boolean +--R unit? : % -> Boolean unitCanonical : % -> % +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean +--R ?*? : (NonNegativeInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % +--R D : (%,NonNegativeInteger) -> % if GF has FINITE +--R Frobenius : (%,NonNegativeInteger) -> % if GF has FINITE +--R Frobenius : % -> % if GF has FINITE +--R ?^? : (%,NonNegativeInteger) -> % +--R basis : PositiveInteger -> Vector % +--R characteristic : () -> NonNegativeInteger +--R charthRoot : % -> Union(%,"failed") if GF has CHARNZ or GF has FINITE +--R charthRoot : % -> % if GF has FINITE +--R conditionP : Matrix % -> Union(Vector %,"failed") if GF has FINITE +--R coordinates : Vector % -> Matrix GF +--R createNormalElement : () -> % if GF has FINITE +--R createPrimitiveElement : () -> % if GF has FINITE +--R definingPolynomial : () -> SparseUnivariatePolynomial GF +--R degree : % -> OnePointCompletion PositiveInteger +--R differentiate : (%,NonNegativeInteger) -> % if GF has FINITE +--R differentiate : % -> % if GF has FINITE +--R discreteLog : (%,%) -> Union(NonNegativeInteger,"failed") if GF has CHARNZ or GF has FINITE +--R discreteLog : % -> NonNegativeInteger if GF has FINITE +--R divide : (%,%) -> Record(quotient: %,remainder: %) +--R euclideanSize : % -> NonNegativeInteger +--R expressIdealMember : (List %,%) -> Union(List %,"failed") +--R exquo : (%,%) -> Union(%,"failed") +--R extendedEuclidean : (%,%,%) -> Union(Record(coef1: %,coef2: %),"failed") +--R extendedEuclidean : (%,%) -> Record(coef1: %,coef2: %,generator: %) +--R extensionDegree : () -> PositiveInteger +--R extensionDegree : () -> OnePointCompletion PositiveInteger +--R factorsOfCyclicGroupSize : () -> List Record(factor: Integer,exponent: Integer) if GF has FINITE +--R gcdPolynomial : (SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial % +--R generator : () -> % if GF has FINITE +--R getZechTable : () -> PrimitiveArray SingleInteger +--R index : PositiveInteger -> % if GF has FINITE +--R init : () -> % if GF has FINITE +--R linearAssociatedExp : (%,SparseUnivariatePolynomial GF) -> % if GF has FINITE +--R linearAssociatedLog : (%,%) -> Union(SparseUnivariatePolynomial GF,"failed") if GF has FINITE +--R linearAssociatedLog : % -> SparseUnivariatePolynomial GF if GF has FINITE +--R linearAssociatedOrder : % -> SparseUnivariatePolynomial GF if GF has FINITE +--R lookup : % -> PositiveInteger if GF has FINITE +--R minimalPolynomial : (%,PositiveInteger) -> SparseUnivariatePolynomial % if GF has FINITE +--R minimalPolynomial : % -> SparseUnivariatePolynomial GF +--R multiEuclidean : (List %,%) -> Union(List %,"failed") +--R nextItem : % -> Union(%,"failed") if GF has FINITE +--R norm : (%,PositiveInteger) -> % if GF has FINITE +--R normal? : % -> Boolean if GF has FINITE +--R normalElement : () -> % if GF has FINITE +--R order : % -> OnePointCompletion PositiveInteger if GF has CHARNZ or GF has FINITE +--R order : % -> PositiveInteger if GF has FINITE +--R primeFrobenius : % -> % if GF has CHARNZ or GF has FINITE +--R primeFrobenius : (%,NonNegativeInteger) -> % if GF has CHARNZ or GF has FINITE +--R primitive? : % -> Boolean if GF has FINITE +--R primitiveElement : () -> % if GF has FINITE +--R principalIdeal : List % -> Record(coef: List %,generator: %) +--R random : () -> % if GF has FINITE +--R representationType : () -> Union("prime",polynomial,normal,cyclic) if GF has FINITE +--R retractIfCan : % -> Union(GF,"failed") +--R size : () -> NonNegativeInteger if GF has FINITE +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R tableForDiscreteLogarithm : Integer -> Table(PositiveInteger,NonNegativeInteger) if GF has FINITE +--R trace : (%,PositiveInteger) -> % if GF has FINITE +--R transcendenceDegree : () -> NonNegativeInteger +--R unitNormal : % -> Record(unit: %,canonical: %,associate: %) +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +FiniteFieldCyclicGroupExtension examples +==================================================================== + +See Also: +o )show FiniteFieldCyclicGroupExtension + +@ + \pagehead{FiniteFieldCyclicGroupExtension}{FFCGX} \pagepic{ps/v103finitefieldcyclicgroupextension.ps}{FFCGX}{1.00} {\bf See}\\ @@ -31520,6 +36971,130 @@ FiniteFieldCyclicGroupExtension(GF,extdeg):_ @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain FFCGP FiniteFieldCyclicGroupExtensionByPolynomial} + +<>= +)set break resume +)sys rm -f FiniteFieldCyclicGroupExtensionByPolynomial.output +)spool FiniteFieldCyclicGroupExtensionByPolynomial.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show FiniteFieldCyclicGroupExtensionByPolynomial +--R FiniteFieldCyclicGroupExtensionByPolynomial(GF: FiniteFieldCategory,defpol: SparseUnivariatePolynomial GF) is a domain constructor +--R Abbreviation for FiniteFieldCyclicGroupExtensionByPolynomial is FFCGP +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for FFCGP +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (GF,%) -> % ?*? : (%,GF) -> % +--R ?*? : (Fraction Integer,%) -> % ?*? : (%,Fraction Integer) -> % +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?**? : (%,Integer) -> % +--R ?**? : (%,PositiveInteger) -> % ?+? : (%,%) -> % +--R ?-? : (%,%) -> % -? : % -> % +--R ?/? : (%,GF) -> % ?/? : (%,%) -> % +--R ?=? : (%,%) -> Boolean D : % -> % if GF has FINITE +--R 1 : () -> % 0 : () -> % +--R ?^? : (%,Integer) -> % ?^? : (%,PositiveInteger) -> % +--R algebraic? : % -> Boolean associates? : (%,%) -> Boolean +--R basis : () -> Vector % coerce : GF -> % +--R coerce : Fraction Integer -> % coerce : % -> % +--R coerce : Integer -> % coerce : % -> OutputForm +--R coordinates : % -> Vector GF degree : % -> PositiveInteger +--R dimension : () -> CardinalNumber factor : % -> Factored % +--R gcd : List % -> % gcd : (%,%) -> % +--R hash : % -> SingleInteger inGroundField? : % -> Boolean +--R inv : % -> % latex : % -> String +--R lcm : List % -> % lcm : (%,%) -> % +--R norm : % -> GF one? : % -> Boolean +--R prime? : % -> Boolean ?quo? : (%,%) -> % +--R recip : % -> Union(%,"failed") ?rem? : (%,%) -> % +--R represents : Vector GF -> % retract : % -> GF +--R sample : () -> % sizeLess? : (%,%) -> Boolean +--R squareFree : % -> Factored % squareFreePart : % -> % +--R trace : % -> GF transcendent? : % -> Boolean +--R unit? : % -> Boolean unitCanonical : % -> % +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean +--R ?*? : (NonNegativeInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % +--R D : (%,NonNegativeInteger) -> % if GF has FINITE +--R Frobenius : (%,NonNegativeInteger) -> % if GF has FINITE +--R Frobenius : % -> % if GF has FINITE +--R ?^? : (%,NonNegativeInteger) -> % +--R basis : PositiveInteger -> Vector % +--R characteristic : () -> NonNegativeInteger +--R charthRoot : % -> Union(%,"failed") if GF has CHARNZ or GF has FINITE +--R charthRoot : % -> % if GF has FINITE +--R conditionP : Matrix % -> Union(Vector %,"failed") if GF has FINITE +--R coordinates : Vector % -> Matrix GF +--R createNormalElement : () -> % if GF has FINITE +--R createPrimitiveElement : () -> % if GF has FINITE +--R definingPolynomial : () -> SparseUnivariatePolynomial GF +--R degree : % -> OnePointCompletion PositiveInteger +--R differentiate : (%,NonNegativeInteger) -> % if GF has FINITE +--R differentiate : % -> % if GF has FINITE +--R discreteLog : (%,%) -> Union(NonNegativeInteger,"failed") if GF has CHARNZ or GF has FINITE +--R discreteLog : % -> NonNegativeInteger if GF has FINITE +--R divide : (%,%) -> Record(quotient: %,remainder: %) +--R euclideanSize : % -> NonNegativeInteger +--R expressIdealMember : (List %,%) -> Union(List %,"failed") +--R exquo : (%,%) -> Union(%,"failed") +--R extendedEuclidean : (%,%,%) -> Union(Record(coef1: %,coef2: %),"failed") +--R extendedEuclidean : (%,%) -> Record(coef1: %,coef2: %,generator: %) +--R extensionDegree : () -> PositiveInteger +--R extensionDegree : () -> OnePointCompletion PositiveInteger +--R factorsOfCyclicGroupSize : () -> List Record(factor: Integer,exponent: Integer) if GF has FINITE +--R gcdPolynomial : (SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial % +--R generator : () -> % if GF has FINITE +--R getZechTable : () -> PrimitiveArray SingleInteger +--R index : PositiveInteger -> % if GF has FINITE +--R init : () -> % if GF has FINITE +--R linearAssociatedExp : (%,SparseUnivariatePolynomial GF) -> % if GF has FINITE +--R linearAssociatedLog : (%,%) -> Union(SparseUnivariatePolynomial GF,"failed") if GF has FINITE +--R linearAssociatedLog : % -> SparseUnivariatePolynomial GF if GF has FINITE +--R linearAssociatedOrder : % -> SparseUnivariatePolynomial GF if GF has FINITE +--R lookup : % -> PositiveInteger if GF has FINITE +--R minimalPolynomial : (%,PositiveInteger) -> SparseUnivariatePolynomial % if GF has FINITE +--R minimalPolynomial : % -> SparseUnivariatePolynomial GF +--R multiEuclidean : (List %,%) -> Union(List %,"failed") +--R nextItem : % -> Union(%,"failed") if GF has FINITE +--R norm : (%,PositiveInteger) -> % if GF has FINITE +--R normal? : % -> Boolean if GF has FINITE +--R normalElement : () -> % if GF has FINITE +--R order : % -> OnePointCompletion PositiveInteger if GF has CHARNZ or GF has FINITE +--R order : % -> PositiveInteger if GF has FINITE +--R primeFrobenius : % -> % if GF has CHARNZ or GF has FINITE +--R primeFrobenius : (%,NonNegativeInteger) -> % if GF has CHARNZ or GF has FINITE +--R primitive? : % -> Boolean if GF has FINITE +--R primitiveElement : () -> % if GF has FINITE +--R principalIdeal : List % -> Record(coef: List %,generator: %) +--R random : () -> % if GF has FINITE +--R representationType : () -> Union("prime",polynomial,normal,cyclic) if GF has FINITE +--R retractIfCan : % -> Union(GF,"failed") +--R size : () -> NonNegativeInteger if GF has FINITE +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R tableForDiscreteLogarithm : Integer -> Table(PositiveInteger,NonNegativeInteger) if GF has FINITE +--R trace : (%,PositiveInteger) -> % if GF has FINITE +--R transcendenceDegree : () -> NonNegativeInteger +--R unitNormal : % -> Record(unit: %,canonical: %,associate: %) +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +FiniteFieldCyclicGroupExtensionByPolynomial examples +==================================================================== + +See Also: +o )show FiniteFieldCyclicGroupExtensionByPolynomial + +@ + \pagehead{FiniteFieldCyclicGroupExtensionByPolynomial}{FFCGP} \pagepic{ps/v103finitefieldcyclicgroupextensionbypolynomial.ps}{FFCGP}{1.00} {\bf See}\\ @@ -31932,6 +37507,129 @@ FiniteFieldCyclicGroupExtensionByPolynomial(GF,defpol):_ @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain FFX FiniteFieldExtension} + +<>= +)set break resume +)sys rm -f FiniteFieldExtension.output +)spool FiniteFieldExtension.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show FiniteFieldExtension +--R FiniteFieldExtension(GF: FiniteFieldCategory,n: PositiveInteger) is a domain constructor +--R Abbreviation for FiniteFieldExtension is FFX +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for FFX +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (GF,%) -> % ?*? : (%,GF) -> % +--R ?*? : (Fraction Integer,%) -> % ?*? : (%,Fraction Integer) -> % +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?**? : (%,Integer) -> % +--R ?**? : (%,PositiveInteger) -> % ?+? : (%,%) -> % +--R ?-? : (%,%) -> % -? : % -> % +--R ?/? : (%,GF) -> % ?/? : (%,%) -> % +--R ?=? : (%,%) -> Boolean D : % -> % if GF has FINITE +--R 1 : () -> % 0 : () -> % +--R ?^? : (%,Integer) -> % ?^? : (%,PositiveInteger) -> % +--R algebraic? : % -> Boolean associates? : (%,%) -> Boolean +--R basis : () -> Vector % coerce : GF -> % +--R coerce : Fraction Integer -> % coerce : % -> % +--R coerce : Integer -> % coerce : % -> OutputForm +--R coordinates : % -> Vector GF degree : % -> PositiveInteger +--R dimension : () -> CardinalNumber factor : % -> Factored % +--R gcd : List % -> % gcd : (%,%) -> % +--R hash : % -> SingleInteger inGroundField? : % -> Boolean +--R inv : % -> % latex : % -> String +--R lcm : List % -> % lcm : (%,%) -> % +--R norm : % -> GF one? : % -> Boolean +--R prime? : % -> Boolean ?quo? : (%,%) -> % +--R recip : % -> Union(%,"failed") ?rem? : (%,%) -> % +--R represents : Vector GF -> % retract : % -> GF +--R sample : () -> % sizeLess? : (%,%) -> Boolean +--R squareFree : % -> Factored % squareFreePart : % -> % +--R trace : % -> GF transcendent? : % -> Boolean +--R unit? : % -> Boolean unitCanonical : % -> % +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean +--R ?*? : (NonNegativeInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % +--R D : (%,NonNegativeInteger) -> % if GF has FINITE +--R Frobenius : (%,NonNegativeInteger) -> % if GF has FINITE +--R Frobenius : % -> % if GF has FINITE +--R ?^? : (%,NonNegativeInteger) -> % +--R basis : PositiveInteger -> Vector % +--R characteristic : () -> NonNegativeInteger +--R charthRoot : % -> Union(%,"failed") if GF has CHARNZ or GF has FINITE +--R charthRoot : % -> % if GF has FINITE +--R conditionP : Matrix % -> Union(Vector %,"failed") if GF has FINITE +--R coordinates : Vector % -> Matrix GF +--R createNormalElement : () -> % if GF has FINITE +--R createPrimitiveElement : () -> % if GF has FINITE +--R definingPolynomial : () -> SparseUnivariatePolynomial GF +--R degree : % -> OnePointCompletion PositiveInteger +--R differentiate : (%,NonNegativeInteger) -> % if GF has FINITE +--R differentiate : % -> % if GF has FINITE +--R discreteLog : (%,%) -> Union(NonNegativeInteger,"failed") if GF has CHARNZ or GF has FINITE +--R discreteLog : % -> NonNegativeInteger if GF has FINITE +--R divide : (%,%) -> Record(quotient: %,remainder: %) +--R euclideanSize : % -> NonNegativeInteger +--R expressIdealMember : (List %,%) -> Union(List %,"failed") +--R exquo : (%,%) -> Union(%,"failed") +--R extendedEuclidean : (%,%,%) -> Union(Record(coef1: %,coef2: %),"failed") +--R extendedEuclidean : (%,%) -> Record(coef1: %,coef2: %,generator: %) +--R extensionDegree : () -> PositiveInteger +--R extensionDegree : () -> OnePointCompletion PositiveInteger +--R factorsOfCyclicGroupSize : () -> List Record(factor: Integer,exponent: Integer) if GF has FINITE +--R gcdPolynomial : (SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial % +--R generator : () -> % if GF has FINITE +--R index : PositiveInteger -> % if GF has FINITE +--R init : () -> % if GF has FINITE +--R linearAssociatedExp : (%,SparseUnivariatePolynomial GF) -> % if GF has FINITE +--R linearAssociatedLog : (%,%) -> Union(SparseUnivariatePolynomial GF,"failed") if GF has FINITE +--R linearAssociatedLog : % -> SparseUnivariatePolynomial GF if GF has FINITE +--R linearAssociatedOrder : % -> SparseUnivariatePolynomial GF if GF has FINITE +--R lookup : % -> PositiveInteger if GF has FINITE +--R minimalPolynomial : (%,PositiveInteger) -> SparseUnivariatePolynomial % if GF has FINITE +--R minimalPolynomial : % -> SparseUnivariatePolynomial GF +--R multiEuclidean : (List %,%) -> Union(List %,"failed") +--R nextItem : % -> Union(%,"failed") if GF has FINITE +--R norm : (%,PositiveInteger) -> % if GF has FINITE +--R normal? : % -> Boolean if GF has FINITE +--R normalElement : () -> % if GF has FINITE +--R order : % -> OnePointCompletion PositiveInteger if GF has CHARNZ or GF has FINITE +--R order : % -> PositiveInteger if GF has FINITE +--R primeFrobenius : % -> % if GF has CHARNZ or GF has FINITE +--R primeFrobenius : (%,NonNegativeInteger) -> % if GF has CHARNZ or GF has FINITE +--R primitive? : % -> Boolean if GF has FINITE +--R primitiveElement : () -> % if GF has FINITE +--R principalIdeal : List % -> Record(coef: List %,generator: %) +--R random : () -> % if GF has FINITE +--R representationType : () -> Union("prime",polynomial,normal,cyclic) if GF has FINITE +--R retractIfCan : % -> Union(GF,"failed") +--R size : () -> NonNegativeInteger if GF has FINITE +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R tableForDiscreteLogarithm : Integer -> Table(PositiveInteger,NonNegativeInteger) if GF has FINITE +--R trace : (%,PositiveInteger) -> % if GF has FINITE +--R transcendenceDegree : () -> NonNegativeInteger +--R unitNormal : % -> Record(unit: %,canonical: %,associate: %) +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +FiniteFieldExtension examples +==================================================================== + +See Also: +o )show FiniteFieldExtension + +@ + \pagehead{FiniteFieldExtension}{FFX} \pagepic{ps/v103finitefieldextension.ps}{FFX}{1.00} {\bf See}\\ @@ -32072,6 +37770,129 @@ FiniteFieldExtension(GF, n): Exports == Implementation where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain FFP FiniteFieldExtensionByPolynomial} + +<>= +)set break resume +)sys rm -f FiniteFieldExtensionByPolynomial.output +)spool FiniteFieldExtensionByPolynomial.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show FiniteFieldExtensionByPolynomial +--R FiniteFieldExtensionByPolynomial(GF: FiniteFieldCategory,defpol: SparseUnivariatePolynomial GF) is a domain constructor +--R Abbreviation for FiniteFieldExtensionByPolynomial is FFP +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for FFP +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (GF,%) -> % ?*? : (%,GF) -> % +--R ?*? : (Fraction Integer,%) -> % ?*? : (%,Fraction Integer) -> % +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?**? : (%,Integer) -> % +--R ?**? : (%,PositiveInteger) -> % ?+? : (%,%) -> % +--R ?-? : (%,%) -> % -? : % -> % +--R ?/? : (%,GF) -> % ?/? : (%,%) -> % +--R ?=? : (%,%) -> Boolean D : % -> % if GF has FINITE +--R 1 : () -> % 0 : () -> % +--R ?^? : (%,Integer) -> % ?^? : (%,PositiveInteger) -> % +--R algebraic? : % -> Boolean associates? : (%,%) -> Boolean +--R basis : () -> Vector % coerce : GF -> % +--R coerce : Fraction Integer -> % coerce : % -> % +--R coerce : Integer -> % coerce : % -> OutputForm +--R coordinates : % -> Vector GF degree : % -> PositiveInteger +--R dimension : () -> CardinalNumber factor : % -> Factored % +--R gcd : List % -> % gcd : (%,%) -> % +--R hash : % -> SingleInteger inGroundField? : % -> Boolean +--R inv : % -> % latex : % -> String +--R lcm : List % -> % lcm : (%,%) -> % +--R norm : % -> GF one? : % -> Boolean +--R prime? : % -> Boolean ?quo? : (%,%) -> % +--R recip : % -> Union(%,"failed") ?rem? : (%,%) -> % +--R represents : Vector GF -> % retract : % -> GF +--R sample : () -> % sizeLess? : (%,%) -> Boolean +--R squareFree : % -> Factored % squareFreePart : % -> % +--R trace : % -> GF transcendent? : % -> Boolean +--R unit? : % -> Boolean unitCanonical : % -> % +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean +--R ?*? : (NonNegativeInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % +--R D : (%,NonNegativeInteger) -> % if GF has FINITE +--R Frobenius : (%,NonNegativeInteger) -> % if GF has FINITE +--R Frobenius : % -> % if GF has FINITE +--R ?^? : (%,NonNegativeInteger) -> % +--R basis : PositiveInteger -> Vector % +--R characteristic : () -> NonNegativeInteger +--R charthRoot : % -> Union(%,"failed") if GF has CHARNZ or GF has FINITE +--R charthRoot : % -> % if GF has FINITE +--R conditionP : Matrix % -> Union(Vector %,"failed") if GF has FINITE +--R coordinates : Vector % -> Matrix GF +--R createNormalElement : () -> % if GF has FINITE +--R createPrimitiveElement : () -> % if GF has FINITE +--R definingPolynomial : () -> SparseUnivariatePolynomial GF +--R degree : % -> OnePointCompletion PositiveInteger +--R differentiate : (%,NonNegativeInteger) -> % if GF has FINITE +--R differentiate : % -> % if GF has FINITE +--R discreteLog : (%,%) -> Union(NonNegativeInteger,"failed") if GF has CHARNZ or GF has FINITE +--R discreteLog : % -> NonNegativeInteger if GF has FINITE +--R divide : (%,%) -> Record(quotient: %,remainder: %) +--R euclideanSize : % -> NonNegativeInteger +--R expressIdealMember : (List %,%) -> Union(List %,"failed") +--R exquo : (%,%) -> Union(%,"failed") +--R extendedEuclidean : (%,%,%) -> Union(Record(coef1: %,coef2: %),"failed") +--R extendedEuclidean : (%,%) -> Record(coef1: %,coef2: %,generator: %) +--R extensionDegree : () -> PositiveInteger +--R extensionDegree : () -> OnePointCompletion PositiveInteger +--R factorsOfCyclicGroupSize : () -> List Record(factor: Integer,exponent: Integer) if GF has FINITE +--R gcdPolynomial : (SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial % +--R generator : () -> % if GF has FINITE +--R index : PositiveInteger -> % if GF has FINITE +--R init : () -> % if GF has FINITE +--R linearAssociatedExp : (%,SparseUnivariatePolynomial GF) -> % if GF has FINITE +--R linearAssociatedLog : (%,%) -> Union(SparseUnivariatePolynomial GF,"failed") if GF has FINITE +--R linearAssociatedLog : % -> SparseUnivariatePolynomial GF if GF has FINITE +--R linearAssociatedOrder : % -> SparseUnivariatePolynomial GF if GF has FINITE +--R lookup : % -> PositiveInteger if GF has FINITE +--R minimalPolynomial : (%,PositiveInteger) -> SparseUnivariatePolynomial % if GF has FINITE +--R minimalPolynomial : % -> SparseUnivariatePolynomial GF +--R multiEuclidean : (List %,%) -> Union(List %,"failed") +--R nextItem : % -> Union(%,"failed") if GF has FINITE +--R norm : (%,PositiveInteger) -> % if GF has FINITE +--R normal? : % -> Boolean if GF has FINITE +--R normalElement : () -> % if GF has FINITE +--R order : % -> OnePointCompletion PositiveInteger if GF has CHARNZ or GF has FINITE +--R order : % -> PositiveInteger if GF has FINITE +--R primeFrobenius : % -> % if GF has CHARNZ or GF has FINITE +--R primeFrobenius : (%,NonNegativeInteger) -> % if GF has CHARNZ or GF has FINITE +--R primitive? : % -> Boolean if GF has FINITE +--R primitiveElement : () -> % if GF has FINITE +--R principalIdeal : List % -> Record(coef: List %,generator: %) +--R random : () -> % if GF has FINITE +--R representationType : () -> Union("prime",polynomial,normal,cyclic) if GF has FINITE +--R retractIfCan : % -> Union(GF,"failed") +--R size : () -> NonNegativeInteger if GF has FINITE +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R tableForDiscreteLogarithm : Integer -> Table(PositiveInteger,NonNegativeInteger) if GF has FINITE +--R trace : (%,PositiveInteger) -> % if GF has FINITE +--R transcendenceDegree : () -> NonNegativeInteger +--R unitNormal : % -> Record(unit: %,canonical: %,associate: %) +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +FiniteFieldExtensionByPolynomial examples +==================================================================== + +See Also: +o )show FiniteFieldExtensionByPolynomial + +@ + \pagehead{FiniteFieldExtensionByPolynomial}{FFP} \pagepic{ps/v103finitefieldextensionbypolynomial.ps}{FFP}{1.00} {\bf See}\\ @@ -32410,6 +38231,134 @@ FiniteFieldExtensionByPolynomial(GF:FiniteFieldCategory,_ @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain FFNB FiniteFieldNormalBasis} + +<>= +)set break resume +)sys rm -f FiniteFieldNormalBasis.output +)spool FiniteFieldNormalBasis.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show FiniteFieldNormalBasis +--R FiniteFieldNormalBasis(p: PositiveInteger,extdeg: PositiveInteger) is a domain constructor +--R Abbreviation for FiniteFieldNormalBasis is FFNB +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for FFNB +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (PrimeField p,%) -> % ?*? : (%,PrimeField p) -> % +--R ?*? : (Fraction Integer,%) -> % ?*? : (%,Fraction Integer) -> % +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?**? : (%,Integer) -> % +--R ?**? : (%,PositiveInteger) -> % ?+? : (%,%) -> % +--R ?-? : (%,%) -> % -? : % -> % +--R ?/? : (%,PrimeField p) -> % ?/? : (%,%) -> % +--R ?=? : (%,%) -> Boolean 1 : () -> % +--R 0 : () -> % ?^? : (%,Integer) -> % +--R ?^? : (%,PositiveInteger) -> % algebraic? : % -> Boolean +--R associates? : (%,%) -> Boolean basis : () -> Vector % +--R coerce : PrimeField p -> % coerce : Fraction Integer -> % +--R coerce : % -> % coerce : Integer -> % +--R coerce : % -> OutputForm degree : % -> PositiveInteger +--R dimension : () -> CardinalNumber factor : % -> Factored % +--R gcd : List % -> % gcd : (%,%) -> % +--R hash : % -> SingleInteger inGroundField? : % -> Boolean +--R inv : % -> % latex : % -> String +--R lcm : List % -> % lcm : (%,%) -> % +--R norm : % -> PrimeField p one? : % -> Boolean +--R prime? : % -> Boolean ?quo? : (%,%) -> % +--R recip : % -> Union(%,"failed") ?rem? : (%,%) -> % +--R retract : % -> PrimeField p sample : () -> % +--R sizeLess? : (%,%) -> Boolean squareFree : % -> Factored % +--R squareFreePart : % -> % trace : % -> PrimeField p +--R transcendent? : % -> Boolean unit? : % -> Boolean +--R unitCanonical : % -> % zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean +--R ?*? : (NonNegativeInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % +--R D : (%,NonNegativeInteger) -> % if PrimeField p has FINITE +--R D : % -> % if PrimeField p has FINITE +--R Frobenius : (%,NonNegativeInteger) -> % if PrimeField p has FINITE +--R Frobenius : % -> % if PrimeField p has FINITE +--R ?^? : (%,NonNegativeInteger) -> % +--R basis : PositiveInteger -> Vector % +--R characteristic : () -> NonNegativeInteger +--R charthRoot : % -> Union(%,"failed") if PrimeField p has CHARNZ or PrimeField p has FINITE +--R charthRoot : % -> % if PrimeField p has FINITE +--R conditionP : Matrix % -> Union(Vector %,"failed") if PrimeField p has FINITE +--R coordinates : Vector % -> Matrix PrimeField p +--R coordinates : % -> Vector PrimeField p +--R createNormalElement : () -> % if PrimeField p has FINITE +--R createPrimitiveElement : () -> % if PrimeField p has FINITE +--R definingPolynomial : () -> SparseUnivariatePolynomial PrimeField p +--R degree : % -> OnePointCompletion PositiveInteger +--R differentiate : (%,NonNegativeInteger) -> % if PrimeField p has FINITE +--R differentiate : % -> % if PrimeField p has FINITE +--R discreteLog : (%,%) -> Union(NonNegativeInteger,"failed") if PrimeField p has CHARNZ or PrimeField p has FINITE +--R discreteLog : % -> NonNegativeInteger if PrimeField p has FINITE +--R divide : (%,%) -> Record(quotient: %,remainder: %) +--R euclideanSize : % -> NonNegativeInteger +--R expressIdealMember : (List %,%) -> Union(List %,"failed") +--R exquo : (%,%) -> Union(%,"failed") +--R extendedEuclidean : (%,%,%) -> Union(Record(coef1: %,coef2: %),"failed") +--R extendedEuclidean : (%,%) -> Record(coef1: %,coef2: %,generator: %) +--R extensionDegree : () -> PositiveInteger +--R extensionDegree : () -> OnePointCompletion PositiveInteger +--R factorsOfCyclicGroupSize : () -> List Record(factor: Integer,exponent: Integer) if PrimeField p has FINITE +--R gcdPolynomial : (SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial % +--R generator : () -> % if PrimeField p has FINITE +--R getMultiplicationMatrix : () -> Matrix PrimeField p +--R getMultiplicationTable : () -> Vector List Record(value: PrimeField p,index: SingleInteger) +--R index : PositiveInteger -> % if PrimeField p has FINITE +--R init : () -> % if PrimeField p has FINITE +--R linearAssociatedExp : (%,SparseUnivariatePolynomial PrimeField p) -> % if PrimeField p has FINITE +--R linearAssociatedLog : (%,%) -> Union(SparseUnivariatePolynomial PrimeField p,"failed") if PrimeField p has FINITE +--R linearAssociatedLog : % -> SparseUnivariatePolynomial PrimeField p if PrimeField p has FINITE +--R linearAssociatedOrder : % -> SparseUnivariatePolynomial PrimeField p if PrimeField p has FINITE +--R lookup : % -> PositiveInteger if PrimeField p has FINITE +--R minimalPolynomial : (%,PositiveInteger) -> SparseUnivariatePolynomial % if PrimeField p has FINITE +--R minimalPolynomial : % -> SparseUnivariatePolynomial PrimeField p +--R multiEuclidean : (List %,%) -> Union(List %,"failed") +--R nextItem : % -> Union(%,"failed") if PrimeField p has FINITE +--R norm : (%,PositiveInteger) -> % if PrimeField p has FINITE +--R normal? : % -> Boolean if PrimeField p has FINITE +--R normalElement : () -> % if PrimeField p has FINITE +--R order : % -> OnePointCompletion PositiveInteger if PrimeField p has CHARNZ or PrimeField p has FINITE +--R order : % -> PositiveInteger if PrimeField p has FINITE +--R primeFrobenius : % -> % if PrimeField p has CHARNZ or PrimeField p has FINITE +--R primeFrobenius : (%,NonNegativeInteger) -> % if PrimeField p has CHARNZ or PrimeField p has FINITE +--R primitive? : % -> Boolean if PrimeField p has FINITE +--R primitiveElement : () -> % if PrimeField p has FINITE +--R principalIdeal : List % -> Record(coef: List %,generator: %) +--R random : () -> % if PrimeField p has FINITE +--R representationType : () -> Union("prime",polynomial,normal,cyclic) if PrimeField p has FINITE +--R represents : Vector PrimeField p -> % +--R retractIfCan : % -> Union(PrimeField p,"failed") +--R size : () -> NonNegativeInteger if PrimeField p has FINITE +--R sizeMultiplication : () -> NonNegativeInteger +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R tableForDiscreteLogarithm : Integer -> Table(PositiveInteger,NonNegativeInteger) if PrimeField p has FINITE +--R trace : (%,PositiveInteger) -> % if PrimeField p has FINITE +--R transcendenceDegree : () -> NonNegativeInteger +--R unitNormal : % -> Record(unit: %,canonical: %,associate: %) +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +FiniteFieldNormalBasis examples +==================================================================== + +See Also: +o )show FiniteFieldNormalBasis + +@ + \pagehead{FiniteFieldNormalBasis}{FFNB} \pagepic{ps/v103finitefieldnormalbasis.ps}{FFNB}{1.00} {\bf See}\\ @@ -32566,6 +38515,132 @@ FiniteFieldNormalBasis(p,extdeg):_ @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain FFNBX FiniteFieldNormalBasisExtension} + +<>= +)set break resume +)sys rm -f FiniteFieldNormalBasisExtension.output +)spool FiniteFieldNormalBasisExtension.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show FiniteFieldNormalBasisExtension +--R FiniteFieldNormalBasisExtension(GF: FiniteFieldCategory,extdeg: PositiveInteger) is a domain constructor +--R Abbreviation for FiniteFieldNormalBasisExtension is FFNBX +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for FFNBX +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (GF,%) -> % ?*? : (%,GF) -> % +--R ?*? : (Fraction Integer,%) -> % ?*? : (%,Fraction Integer) -> % +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?**? : (%,Integer) -> % +--R ?**? : (%,PositiveInteger) -> % ?+? : (%,%) -> % +--R ?-? : (%,%) -> % -? : % -> % +--R ?/? : (%,GF) -> % ?/? : (%,%) -> % +--R ?=? : (%,%) -> Boolean D : % -> % if GF has FINITE +--R 1 : () -> % 0 : () -> % +--R ?^? : (%,Integer) -> % ?^? : (%,PositiveInteger) -> % +--R algebraic? : % -> Boolean associates? : (%,%) -> Boolean +--R basis : () -> Vector % coerce : GF -> % +--R coerce : Fraction Integer -> % coerce : % -> % +--R coerce : Integer -> % coerce : % -> OutputForm +--R coordinates : % -> Vector GF degree : % -> PositiveInteger +--R dimension : () -> CardinalNumber factor : % -> Factored % +--R gcd : List % -> % gcd : (%,%) -> % +--R hash : % -> SingleInteger inGroundField? : % -> Boolean +--R inv : % -> % latex : % -> String +--R lcm : List % -> % lcm : (%,%) -> % +--R norm : % -> GF one? : % -> Boolean +--R prime? : % -> Boolean ?quo? : (%,%) -> % +--R recip : % -> Union(%,"failed") ?rem? : (%,%) -> % +--R represents : Vector GF -> % retract : % -> GF +--R sample : () -> % sizeLess? : (%,%) -> Boolean +--R squareFree : % -> Factored % squareFreePart : % -> % +--R trace : % -> GF transcendent? : % -> Boolean +--R unit? : % -> Boolean unitCanonical : % -> % +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean +--R ?*? : (NonNegativeInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % +--R D : (%,NonNegativeInteger) -> % if GF has FINITE +--R Frobenius : (%,NonNegativeInteger) -> % if GF has FINITE +--R Frobenius : % -> % if GF has FINITE +--R ?^? : (%,NonNegativeInteger) -> % +--R basis : PositiveInteger -> Vector % +--R characteristic : () -> NonNegativeInteger +--R charthRoot : % -> Union(%,"failed") if GF has CHARNZ or GF has FINITE +--R charthRoot : % -> % if GF has FINITE +--R conditionP : Matrix % -> Union(Vector %,"failed") if GF has FINITE +--R coordinates : Vector % -> Matrix GF +--R createNormalElement : () -> % if GF has FINITE +--R createPrimitiveElement : () -> % if GF has FINITE +--R definingPolynomial : () -> SparseUnivariatePolynomial GF +--R degree : % -> OnePointCompletion PositiveInteger +--R differentiate : (%,NonNegativeInteger) -> % if GF has FINITE +--R differentiate : % -> % if GF has FINITE +--R discreteLog : (%,%) -> Union(NonNegativeInteger,"failed") if GF has CHARNZ or GF has FINITE +--R discreteLog : % -> NonNegativeInteger if GF has FINITE +--R divide : (%,%) -> Record(quotient: %,remainder: %) +--R euclideanSize : % -> NonNegativeInteger +--R expressIdealMember : (List %,%) -> Union(List %,"failed") +--R exquo : (%,%) -> Union(%,"failed") +--R extendedEuclidean : (%,%,%) -> Union(Record(coef1: %,coef2: %),"failed") +--R extendedEuclidean : (%,%) -> Record(coef1: %,coef2: %,generator: %) +--R extensionDegree : () -> PositiveInteger +--R extensionDegree : () -> OnePointCompletion PositiveInteger +--R factorsOfCyclicGroupSize : () -> List Record(factor: Integer,exponent: Integer) if GF has FINITE +--R gcdPolynomial : (SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial % +--R generator : () -> % if GF has FINITE +--R getMultiplicationMatrix : () -> Matrix GF +--R getMultiplicationTable : () -> Vector List Record(value: GF,index: SingleInteger) +--R index : PositiveInteger -> % if GF has FINITE +--R init : () -> % if GF has FINITE +--R linearAssociatedExp : (%,SparseUnivariatePolynomial GF) -> % if GF has FINITE +--R linearAssociatedLog : (%,%) -> Union(SparseUnivariatePolynomial GF,"failed") if GF has FINITE +--R linearAssociatedLog : % -> SparseUnivariatePolynomial GF if GF has FINITE +--R linearAssociatedOrder : % -> SparseUnivariatePolynomial GF if GF has FINITE +--R lookup : % -> PositiveInteger if GF has FINITE +--R minimalPolynomial : (%,PositiveInteger) -> SparseUnivariatePolynomial % if GF has FINITE +--R minimalPolynomial : % -> SparseUnivariatePolynomial GF +--R multiEuclidean : (List %,%) -> Union(List %,"failed") +--R nextItem : % -> Union(%,"failed") if GF has FINITE +--R norm : (%,PositiveInteger) -> % if GF has FINITE +--R normal? : % -> Boolean if GF has FINITE +--R normalElement : () -> % if GF has FINITE +--R order : % -> OnePointCompletion PositiveInteger if GF has CHARNZ or GF has FINITE +--R order : % -> PositiveInteger if GF has FINITE +--R primeFrobenius : % -> % if GF has CHARNZ or GF has FINITE +--R primeFrobenius : (%,NonNegativeInteger) -> % if GF has CHARNZ or GF has FINITE +--R primitive? : % -> Boolean if GF has FINITE +--R primitiveElement : () -> % if GF has FINITE +--R principalIdeal : List % -> Record(coef: List %,generator: %) +--R random : () -> % if GF has FINITE +--R representationType : () -> Union("prime",polynomial,normal,cyclic) if GF has FINITE +--R retractIfCan : % -> Union(GF,"failed") +--R size : () -> NonNegativeInteger if GF has FINITE +--R sizeMultiplication : () -> NonNegativeInteger +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R tableForDiscreteLogarithm : Integer -> Table(PositiveInteger,NonNegativeInteger) if GF has FINITE +--R trace : (%,PositiveInteger) -> % if GF has FINITE +--R transcendenceDegree : () -> NonNegativeInteger +--R unitNormal : % -> Record(unit: %,canonical: %,associate: %) +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +FiniteFieldNormalBasisExtension examples +==================================================================== + +See Also: +o )show FiniteFieldNormalBasisExtension + +@ + \pagehead{FiniteFieldNormalBasisExtension}{FFNBX} \pagepic{ps/v103finitefieldnormalbasisextension.ps}{FFNBX}{1.00} {\bf See}\\ @@ -32722,6 +38797,132 @@ FiniteFieldNormalBasisExtension(GF,extdeg):_ @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain FFNBP FiniteFieldNormalBasisExtensionByPolynomial} + +<>= +)set break resume +)sys rm -f FiniteFieldNormalBasisExtensionByPolynomial.output +)spool FiniteFieldNormalBasisExtensionByPolynomial.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show FiniteFieldNormalBasisExtensionByPolynomial +--R FiniteFieldNormalBasisExtensionByPolynomial(GF: FiniteFieldCategory,uni: Union(SparseUnivariatePolynomial GF,Vector List Record(value: GF,index: SingleInteger))) is a domain constructor +--R Abbreviation for FiniteFieldNormalBasisExtensionByPolynomial is FFNBP +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for FFNBP +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (GF,%) -> % ?*? : (%,GF) -> % +--R ?*? : (Fraction Integer,%) -> % ?*? : (%,Fraction Integer) -> % +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?**? : (%,Integer) -> % +--R ?**? : (%,PositiveInteger) -> % ?+? : (%,%) -> % +--R ?-? : (%,%) -> % -? : % -> % +--R ?/? : (%,GF) -> % ?/? : (%,%) -> % +--R ?=? : (%,%) -> Boolean D : % -> % if GF has FINITE +--R 1 : () -> % 0 : () -> % +--R ?^? : (%,Integer) -> % ?^? : (%,PositiveInteger) -> % +--R algebraic? : % -> Boolean associates? : (%,%) -> Boolean +--R basis : () -> Vector % coerce : GF -> % +--R coerce : Fraction Integer -> % coerce : % -> % +--R coerce : Integer -> % coerce : % -> OutputForm +--R coordinates : % -> Vector GF degree : % -> PositiveInteger +--R dimension : () -> CardinalNumber factor : % -> Factored % +--R gcd : List % -> % gcd : (%,%) -> % +--R hash : % -> SingleInteger inGroundField? : % -> Boolean +--R inv : % -> % latex : % -> String +--R lcm : List % -> % lcm : (%,%) -> % +--R norm : % -> GF one? : % -> Boolean +--R prime? : % -> Boolean ?quo? : (%,%) -> % +--R recip : % -> Union(%,"failed") ?rem? : (%,%) -> % +--R represents : Vector GF -> % retract : % -> GF +--R sample : () -> % sizeLess? : (%,%) -> Boolean +--R squareFree : % -> Factored % squareFreePart : % -> % +--R trace : % -> GF transcendent? : % -> Boolean +--R unit? : % -> Boolean unitCanonical : % -> % +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean +--R ?*? : (NonNegativeInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % +--R D : (%,NonNegativeInteger) -> % if GF has FINITE +--R Frobenius : (%,NonNegativeInteger) -> % if GF has FINITE +--R Frobenius : % -> % if GF has FINITE +--R ?^? : (%,NonNegativeInteger) -> % +--R basis : PositiveInteger -> Vector % +--R characteristic : () -> NonNegativeInteger +--R charthRoot : % -> Union(%,"failed") if GF has CHARNZ or GF has FINITE +--R charthRoot : % -> % if GF has FINITE +--R conditionP : Matrix % -> Union(Vector %,"failed") if GF has FINITE +--R coordinates : Vector % -> Matrix GF +--R createNormalElement : () -> % if GF has FINITE +--R createPrimitiveElement : () -> % if GF has FINITE +--R definingPolynomial : () -> SparseUnivariatePolynomial GF +--R degree : % -> OnePointCompletion PositiveInteger +--R differentiate : (%,NonNegativeInteger) -> % if GF has FINITE +--R differentiate : % -> % if GF has FINITE +--R discreteLog : (%,%) -> Union(NonNegativeInteger,"failed") if GF has CHARNZ or GF has FINITE +--R discreteLog : % -> NonNegativeInteger if GF has FINITE +--R divide : (%,%) -> Record(quotient: %,remainder: %) +--R euclideanSize : % -> NonNegativeInteger +--R expressIdealMember : (List %,%) -> Union(List %,"failed") +--R exquo : (%,%) -> Union(%,"failed") +--R extendedEuclidean : (%,%,%) -> Union(Record(coef1: %,coef2: %),"failed") +--R extendedEuclidean : (%,%) -> Record(coef1: %,coef2: %,generator: %) +--R extensionDegree : () -> PositiveInteger +--R extensionDegree : () -> OnePointCompletion PositiveInteger +--R factorsOfCyclicGroupSize : () -> List Record(factor: Integer,exponent: Integer) if GF has FINITE +--R gcdPolynomial : (SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial % +--R generator : () -> % if GF has FINITE +--R getMultiplicationMatrix : () -> Matrix GF +--R getMultiplicationTable : () -> Vector List Record(value: GF,index: SingleInteger) +--R index : PositiveInteger -> % if GF has FINITE +--R init : () -> % if GF has FINITE +--R linearAssociatedExp : (%,SparseUnivariatePolynomial GF) -> % if GF has FINITE +--R linearAssociatedLog : (%,%) -> Union(SparseUnivariatePolynomial GF,"failed") if GF has FINITE +--R linearAssociatedLog : % -> SparseUnivariatePolynomial GF if GF has FINITE +--R linearAssociatedOrder : % -> SparseUnivariatePolynomial GF if GF has FINITE +--R lookup : % -> PositiveInteger if GF has FINITE +--R minimalPolynomial : (%,PositiveInteger) -> SparseUnivariatePolynomial % if GF has FINITE +--R minimalPolynomial : % -> SparseUnivariatePolynomial GF +--R multiEuclidean : (List %,%) -> Union(List %,"failed") +--R nextItem : % -> Union(%,"failed") if GF has FINITE +--R norm : (%,PositiveInteger) -> % if GF has FINITE +--R normal? : % -> Boolean if GF has FINITE +--R normalElement : () -> % if GF has FINITE +--R order : % -> OnePointCompletion PositiveInteger if GF has CHARNZ or GF has FINITE +--R order : % -> PositiveInteger if GF has FINITE +--R primeFrobenius : % -> % if GF has CHARNZ or GF has FINITE +--R primeFrobenius : (%,NonNegativeInteger) -> % if GF has CHARNZ or GF has FINITE +--R primitive? : % -> Boolean if GF has FINITE +--R primitiveElement : () -> % if GF has FINITE +--R principalIdeal : List % -> Record(coef: List %,generator: %) +--R random : () -> % if GF has FINITE +--R representationType : () -> Union("prime",polynomial,normal,cyclic) if GF has FINITE +--R retractIfCan : % -> Union(GF,"failed") +--R size : () -> NonNegativeInteger if GF has FINITE +--R sizeMultiplication : () -> NonNegativeInteger +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R tableForDiscreteLogarithm : Integer -> Table(PositiveInteger,NonNegativeInteger) if GF has FINITE +--R trace : (%,PositiveInteger) -> % if GF has FINITE +--R transcendenceDegree : () -> NonNegativeInteger +--R unitNormal : % -> Record(unit: %,canonical: %,associate: %) +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +FiniteFieldNormalBasisExtensionByPolynomial examples +==================================================================== + +See Also: +o )show FiniteFieldNormalBasisExtensionByPolynomial + +@ + \pagehead{FiniteFieldNormalBasisExtensionByPolynomial}{FFNBP} \pagepic{ps/v103finitefieldnormalbasisextensionbypolynomial.ps}{FFNBP}{1.00} {\bf See}\\ @@ -33188,6 +39389,7 @@ divisor of the order of the multiplicative group" @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain FARRAY FlexibleArray} + <>= )set break resume )sys rm -f FlexibleArray.output @@ -35725,6 +41927,92 @@ Float(): @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain FC FortranCode} + +<>= +)set break resume +)sys rm -f FortranCode.output +)spool FortranCode.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show FortranCode +--R FortranCode is a domain constructor +--R Abbreviation for FortranCode is FC +--R This constructor is exposed in this frame. +--R Issue )edit NIL to see algebra source code for FC +--R +--R------------------------------- Operations -------------------------------- +--R ?=? : (%,%) -> Boolean assign : (Symbol,String) -> % +--R block : List % -> % call : String -> % +--R coerce : % -> OutputForm comment : List String -> % +--R comment : String -> % cond : (Switch,%,%) -> % +--R cond : (Switch,%) -> % continue : SingleInteger -> % +--R getCode : % -> SExpression goto : SingleInteger -> % +--R hash : % -> SingleInteger latex : % -> String +--R printCode : % -> Void returns : Expression Integer -> % +--R returns : Expression Float -> % returns : () -> % +--R save : () -> % stop : () -> % +--R whileLoop : (Switch,%) -> % ?~=? : (%,%) -> Boolean +--R assign : (Symbol,List Polynomial Integer,Expression Complex Float) -> % +--R assign : (Symbol,List Polynomial Integer,Expression Float) -> % +--R assign : (Symbol,List Polynomial Integer,Expression Integer) -> % +--R assign : (Symbol,Vector Expression Complex Float) -> % +--R assign : (Symbol,Vector Expression Float) -> % +--R assign : (Symbol,Vector Expression Integer) -> % +--R assign : (Symbol,Matrix Expression Complex Float) -> % +--R assign : (Symbol,Matrix Expression Float) -> % +--R assign : (Symbol,Matrix Expression Integer) -> % +--R assign : (Symbol,Expression Complex Float) -> % +--R assign : (Symbol,Expression Float) -> % +--R assign : (Symbol,Expression Integer) -> % +--R assign : (Symbol,List Polynomial Integer,Expression MachineComplex) -> % +--R assign : (Symbol,List Polynomial Integer,Expression MachineFloat) -> % +--R assign : (Symbol,List Polynomial Integer,Expression MachineInteger) -> % +--R assign : (Symbol,Vector Expression MachineComplex) -> % +--R assign : (Symbol,Vector Expression MachineFloat) -> % +--R assign : (Symbol,Vector Expression MachineInteger) -> % +--R assign : (Symbol,Matrix Expression MachineComplex) -> % +--R assign : (Symbol,Matrix Expression MachineFloat) -> % +--R assign : (Symbol,Matrix Expression MachineInteger) -> % +--R assign : (Symbol,Vector MachineComplex) -> % +--R assign : (Symbol,Vector MachineFloat) -> % +--R assign : (Symbol,Vector MachineInteger) -> % +--R assign : (Symbol,Matrix MachineComplex) -> % +--R assign : (Symbol,Matrix MachineFloat) -> % +--R assign : (Symbol,Matrix MachineInteger) -> % +--R assign : (Symbol,Expression MachineComplex) -> % +--R assign : (Symbol,Expression MachineFloat) -> % +--R assign : (Symbol,Expression MachineInteger) -> % +--R code : % -> Union(nullBranch: null,assignmentBranch: Record(var: Symbol,arrayIndex: List Polynomial Integer,rand: Record(ints2Floats?: Boolean,expr: OutputForm)),arrayAssignmentBranch: Record(var: Symbol,rand: OutputForm,ints2Floats?: Boolean),conditionalBranch: Record(switch: Switch,thenClause: %,elseClause: %),returnBranch: Record(empty?: Boolean,value: Record(ints2Floats?: Boolean,expr: OutputForm)),blockBranch: List %,commentBranch: List String,callBranch: String,forBranch: Record(range: SegmentBinding Polynomial Integer,span: Polynomial Integer,body: %),labelBranch: SingleInteger,loopBranch: Record(switch: Switch,body: %),commonBranch: Record(name: Symbol,contents: List Symbol),printBranch: List OutputForm) +--R common : (Symbol,List Symbol) -> % +--R forLoop : (SegmentBinding Polynomial Integer,Polynomial Integer,%) -> % +--R forLoop : (SegmentBinding Polynomial Integer,%) -> % +--R operation : % -> Union(Null: null,Assignment: assignment,Conditional: conditional,Return: return,Block: block,Comment: comment,Call: call,For: for,While: while,Repeat: repeat,Goto: goto,Continue: continue,ArrayAssignment: arrayAssignment,Save: save,Stop: stop,Common: common,Print: print) +--R printStatement : List OutputForm -> % +--R repeatUntilLoop : (Switch,%) -> % +--R returns : Expression Complex Float -> % +--R returns : Expression MachineComplex -> % +--R returns : Expression MachineInteger -> % +--R returns : Expression MachineFloat -> % +--R setLabelValue : SingleInteger -> SingleInteger +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +FortranCode examples +==================================================================== + +See Also: +o )show FortranCode + +@ + \pagehead{FortranCode}{FC} \pagepic{ps/v103fortrancode.ps}{FC}{1.00} {\bf See}\\ @@ -36365,6 +42653,128 @@ FortranCode(): public == private where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain FEXPR FortranExpression} + +<>= +)set break resume +)sys rm -f FortranExpression.output +)spool FortranExpression.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show FortranExpression +--R FortranExpression(basicSymbols: List Symbol,subscriptedSymbols: List Symbol,R: FortranMachineTypeCategory) is a domain constructor +--R Abbreviation for FortranExpression is FEXPR +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for FEXPR +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (PositiveInteger,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (%,%) -> % ?*? : (%,R) -> % +--R ?*? : (R,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?+? : (%,%) -> % -? : % -> % +--R ?-? : (%,%) -> % ? Boolean +--R ?<=? : (%,%) -> Boolean ?=? : (%,%) -> Boolean +--R ?>? : (%,%) -> Boolean ?>=? : (%,%) -> Boolean +--R D : (%,Symbol) -> % D : (%,List Symbol) -> % +--R 1 : () -> % 0 : () -> % +--R ?^? : (%,PositiveInteger) -> % abs : % -> % +--R acos : % -> % asin : % -> % +--R atan : % -> % belong? : BasicOperator -> Boolean +--R box : List % -> % box : % -> % +--R coerce : % -> Expression R coerce : Integer -> % +--R coerce : R -> % coerce : Kernel % -> % +--R coerce : % -> OutputForm cos : % -> % +--R cosh : % -> % differentiate : (%,Symbol) -> % +--R distribute : (%,%) -> % distribute : % -> % +--R elt : (BasicOperator,%,%) -> % elt : (BasicOperator,%) -> % +--R eval : (%,List %,List %) -> % eval : (%,%,%) -> % +--R eval : (%,Equation %) -> % eval : (%,List Equation %) -> % +--R eval : (%,Kernel %,%) -> % exp : % -> % +--R freeOf? : (%,Symbol) -> Boolean freeOf? : (%,%) -> Boolean +--R hash : % -> SingleInteger height : % -> NonNegativeInteger +--R is? : (%,Symbol) -> Boolean kernel : (BasicOperator,%) -> % +--R kernels : % -> List Kernel % latex : % -> String +--R log : % -> % log10 : % -> % +--R map : ((% -> %),Kernel %) -> % max : (%,%) -> % +--R min : (%,%) -> % one? : % -> Boolean +--R paren : List % -> % paren : % -> % +--R pi : () -> % recip : % -> Union(%,"failed") +--R retract : Symbol -> % retract : Expression R -> % +--R retract : % -> R retract : % -> Kernel % +--R sample : () -> % sin : % -> % +--R sinh : % -> % sqrt : % -> % +--R subst : (%,Equation %) -> % tan : % -> % +--R tanh : % -> % tower : % -> List Kernel % +--R useNagFunctions : () -> Boolean variables : % -> List Symbol +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean +--R ?*? : (NonNegativeInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % +--R D : (%,Symbol,NonNegativeInteger) -> % +--R D : (%,List Symbol,List NonNegativeInteger) -> % +--R ?^? : (%,NonNegativeInteger) -> % +--R characteristic : () -> NonNegativeInteger +--R definingPolynomial : % -> % if $ has RING +--R differentiate : (%,List Symbol) -> % +--R differentiate : (%,Symbol,NonNegativeInteger) -> % +--R differentiate : (%,List Symbol,List NonNegativeInteger) -> % +--R elt : (BasicOperator,List %) -> % +--R elt : (BasicOperator,%,%,%,%) -> % +--R elt : (BasicOperator,%,%,%) -> % +--R eval : (%,BasicOperator,(% -> %)) -> % +--R eval : (%,BasicOperator,(List % -> %)) -> % +--R eval : (%,List BasicOperator,List (List % -> %)) -> % +--R eval : (%,List BasicOperator,List (% -> %)) -> % +--R eval : (%,Symbol,(% -> %)) -> % +--R eval : (%,Symbol,(List % -> %)) -> % +--R eval : (%,List Symbol,List (List % -> %)) -> % +--R eval : (%,List Symbol,List (% -> %)) -> % +--R eval : (%,List Kernel %,List %) -> % +--R even? : % -> Boolean if $ has RETRACT INT +--R is? : (%,BasicOperator) -> Boolean +--R kernel : (BasicOperator,List %) -> % +--R mainKernel : % -> Union(Kernel %,"failed") +--R minPoly : Kernel % -> SparseUnivariatePolynomial % if $ has RING +--R odd? : % -> Boolean if $ has RETRACT INT +--R operator : BasicOperator -> BasicOperator +--R operators : % -> List BasicOperator +--R retract : Polynomial Float -> % if R has RETRACT FLOAT +--R retract : Fraction Polynomial Float -> % if R has RETRACT FLOAT +--R retract : Expression Float -> % if R has RETRACT FLOAT +--R retract : Polynomial Integer -> % if R has RETRACT INT +--R retract : Fraction Polynomial Integer -> % if R has RETRACT INT +--R retract : Expression Integer -> % if R has RETRACT INT +--R retractIfCan : Polynomial Float -> Union(%,"failed") if R has RETRACT FLOAT +--R retractIfCan : Fraction Polynomial Float -> Union(%,"failed") if R has RETRACT FLOAT +--R retractIfCan : Expression Float -> Union(%,"failed") if R has RETRACT FLOAT +--R retractIfCan : Polynomial Integer -> Union(%,"failed") if R has RETRACT INT +--R retractIfCan : Fraction Polynomial Integer -> Union(%,"failed") if R has RETRACT INT +--R retractIfCan : Expression Integer -> Union(%,"failed") if R has RETRACT INT +--R retractIfCan : Symbol -> Union(%,"failed") +--R retractIfCan : Expression R -> Union(%,"failed") +--R retractIfCan : % -> Union(R,"failed") +--R retractIfCan : % -> Union(Kernel %,"failed") +--R subst : (%,List Kernel %,List %) -> % +--R subst : (%,List Equation %) -> % +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R useNagFunctions : Boolean -> Boolean +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +FortranExpression examples +==================================================================== + +See Also: +o )show FortranExpression + +@ + \pagehead{FortranExpression}{FEXPR} \pagepic{ps/v103fortranexpression.ps}{FEXPR}{1.00} {\bf See}\\ @@ -36801,6 +43211,53 @@ FortranExpression(basicSymbols,subscriptedSymbols,R): @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain FORTRAN FortranProgram} + +<>= +)set break resume +)sys rm -f FortranProgram.output +)spool FortranProgram.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show FortranProgram +--R FortranProgram(name: Symbol,returnType: Union(fst: FortranScalarType,void: void),arguments: List Symbol,symbols: SymbolTable) is a domain constructor +--R Abbreviation for FortranProgram is FORTRAN +--R This constructor is exposed in this frame. +--R Issue )edit NIL to see algebra source code for FORTRAN +--R +--R------------------------------- Operations -------------------------------- +--R coerce : Expression Float -> % coerce : Expression Integer -> % +--R coerce : List FortranCode -> % coerce : FortranCode -> % +--R coerce : % -> OutputForm outputAsFortran : % -> Void +--R coerce : Equation Expression Complex Float -> % +--R coerce : Equation Expression Float -> % +--R coerce : Equation Expression Integer -> % +--R coerce : Expression Complex Float -> % +--R coerce : Equation Expression MachineComplex -> % +--R coerce : Equation Expression MachineFloat -> % +--R coerce : Equation Expression MachineInteger -> % +--R coerce : Expression MachineComplex -> % +--R coerce : Expression MachineFloat -> % +--R coerce : Expression MachineInteger -> % +--R coerce : Record(localSymbols: SymbolTable,code: List FortranCode) -> % +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +FortranProgram examples +==================================================================== + +See Also: +o )show FortranProgram + +@ + \pagehead{FortranProgram}{FORTRAN} \pagepic{ps/v103fortranprogram.ps}{FORTRAN}{1.00} {\bf See}\\ @@ -37052,6 +43509,46 @@ FortranProgram(name,returnType,arguments,symbols): Exports == Implement where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain FST FortranScalarType} + +<>= +)set break resume +)sys rm -f FortranScalarType.output +)spool FortranScalarType.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show FortranScalarType +--R FortranScalarType is a domain constructor +--R Abbreviation for FortranScalarType is FST +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for FST +--R +--R------------------------------- Operations -------------------------------- +--R ?=? : (%,%) -> Boolean character? : % -> Boolean +--R coerce : % -> SExpression coerce : % -> Symbol +--R coerce : Symbol -> % coerce : String -> % +--R coerce : % -> OutputForm complex? : % -> Boolean +--R double? : % -> Boolean doubleComplex? : % -> Boolean +--R integer? : % -> Boolean logical? : % -> Boolean +--R real? : % -> Boolean +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +FortranScalarType examples +==================================================================== + +See Also: +o )show FortranScalarType + +@ + \pagehead{FortranScalarType}{FST} \pagepic{ps/v103fortranscalartype.ps}{FST}{1.00} {\bf See}\\ @@ -37235,6 +43732,50 @@ FortranScalarType() : exports == implementation where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain FTEM FortranTemplate} + +<>= +)set break resume +)sys rm -f FortranTemplate.output +)spool FortranTemplate.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show FortranTemplate +--R FortranTemplate is a domain constructor +--R Abbreviation for FortranTemplate is FTEM +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for FTEM +--R +--R------------------------------- Operations -------------------------------- +--R ?=? : (%,%) -> Boolean close! : % -> % +--R coerce : % -> OutputForm flush : % -> Void +--R fortranCarriageReturn : () -> Void fortranLiteral : String -> Void +--R hash : % -> SingleInteger iomode : % -> String +--R latex : % -> String name : % -> FileName +--R open : (FileName,String) -> % open : FileName -> % +--R read! : % -> String reopen! : (%,String) -> % +--R write! : (%,String) -> String ?~=? : (%,%) -> Boolean +--R fortranLiteralLine : String -> Void +--R processTemplate : FileName -> FileName +--R processTemplate : (FileName,FileName) -> FileName +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +FortranTemplate examples +==================================================================== + +See Also: +o )show FortranTemplate + +@ + \pagehead{FortranTemplate}{FTEM} \pagepic{ps/v103fortrantemplate.ps}{FTEM}{1.00} {\bf See}\\ @@ -37367,6 +43908,50 @@ FortranTemplate() : specification == implementation where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain FT FortranType} + +<>= +)set break resume +)sys rm -f FortranType.output +)spool FortranType.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show FortranType +--R FortranType is a domain constructor +--R Abbreviation for FortranType is FT +--R This constructor is exposed in this frame. +--R Issue )edit NIL to see algebra source code for FT +--R +--R------------------------------- Operations -------------------------------- +--R ?=? : (%,%) -> Boolean coerce : FortranScalarType -> % +--R coerce : % -> OutputForm external? : % -> Boolean +--R fortranCharacter : () -> % fortranComplex : () -> % +--R fortranDouble : () -> % fortranDoubleComplex : () -> % +--R fortranInteger : () -> % fortranLogical : () -> % +--R fortranReal : () -> % hash : % -> SingleInteger +--R latex : % -> String ?~=? : (%,%) -> Boolean +--R construct : (Union(fst: FortranScalarType,void: void),List Polynomial Integer,Boolean) -> % +--R construct : (Union(fst: FortranScalarType,void: void),List Symbol,Boolean) -> % +--R dimensionsOf : % -> List Polynomial Integer +--R scalarTypeOf : % -> Union(fst: FortranScalarType,void: void) +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +FortranType examples +==================================================================== + +See Also: +o )show FortranType + +@ + \pagehead{FortranType}{FT} \pagepic{ps/v103fortrantype.ps}{FT}{1.00} {\bf See}\\ @@ -37512,6 +44097,47 @@ FortranType() : exports == implementation where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain FCOMP FourierComponent} + +<>= +)set break resume +)sys rm -f FourierComponent.output +)spool FourierComponent.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show FourierComponent +--R FourierComponent E: OrderedSet is a domain constructor +--R Abbreviation for FourierComponent is FCOMP +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for FCOMP +--R +--R------------------------------- Operations -------------------------------- +--R ? Boolean ?<=? : (%,%) -> Boolean +--R ?=? : (%,%) -> Boolean ?>? : (%,%) -> Boolean +--R ?>=? : (%,%) -> Boolean argument : % -> E +--R coerce : % -> OutputForm cos : E -> % +--R hash : % -> SingleInteger latex : % -> String +--R max : (%,%) -> % min : (%,%) -> % +--R sin : E -> % sin? : % -> Boolean +--R ?~=? : (%,%) -> Boolean +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +FourierComponent examples +==================================================================== + +See Also: +o )show FourierComponent + +@ + \pagehead{FourierComponent}{FCOMP} \pagepic{ps/v103fouriercomponent.ps}{FCOMP}{1.00} {\bf See}\\ @@ -37588,6 +44214,57 @@ FourierComponent(E:OrderedSet): @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain FSERIES FourierSeries} + +<>= +)set break resume +)sys rm -f FourierSeries.output +)spool FourierSeries.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show FourierSeries +--R FourierSeries(R: Join(CommutativeRing,Algebra Fraction Integer),E: Join(OrderedSet,AbelianGroup)) is a domain constructor +--R Abbreviation for FourierSeries is FSERIES +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for FSERIES +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (R,%) -> % ?*? : (%,R) -> % +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ?=? : (%,%) -> Boolean +--R 1 : () -> % 0 : () -> % +--R ?^? : (%,PositiveInteger) -> % coerce : FourierComponent E -> % +--R coerce : R -> % coerce : Integer -> % +--R coerce : % -> OutputForm hash : % -> SingleInteger +--R latex : % -> String makeCos : (E,R) -> % +--R makeSin : (E,R) -> % one? : % -> Boolean +--R recip : % -> Union(%,"failed") sample : () -> % +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean +--R ?*? : (NonNegativeInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % +--R ?^? : (%,NonNegativeInteger) -> % +--R characteristic : () -> NonNegativeInteger +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +FourierSeries examples +==================================================================== + +See Also: +o )show FourierSeries + +@ + \pagehead{FourierSeries}{FSERIES} \pagepic{ps/v103fourierseries.ps}{FSERIES}{1.00} {\bf See}\\ @@ -37702,6 +44379,7 @@ FourierSeries(R:Join(CommutativeRing,Algebra(Fraction Integer)), @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain FRAC Fraction} + <>= )set break resume )sys rm -f Fraction.output @@ -38384,6 +45062,54 @@ Fraction(S: IntegralDomain): QuotientFieldCategory S with @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain FRIDEAL FractionalIdeal} + +<>= +)set break resume +)sys rm -f FractionalIdeal.output +)spool FractionalIdeal.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show FractionalIdeal +--R FractionalIdeal(R: EuclideanDomain,F: QuotientFieldCategory R,UP: UnivariatePolynomialCategory F,A: Join(FramedAlgebra(F,UP),RetractableTo F)) is a domain constructor +--R Abbreviation for FractionalIdeal is FRIDEAL +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for FRIDEAL +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (%,%) -> % ?**? : (%,Integer) -> % +--R ?**? : (%,PositiveInteger) -> % ?/? : (%,%) -> % +--R ?=? : (%,%) -> Boolean 1 : () -> % +--R ?^? : (%,Integer) -> % ?^? : (%,PositiveInteger) -> % +--R basis : % -> Vector A coerce : % -> OutputForm +--R commutator : (%,%) -> % conjugate : (%,%) -> % +--R denom : % -> R hash : % -> SingleInteger +--R ideal : Vector A -> % inv : % -> % +--R latex : % -> String minimize : % -> % +--R norm : % -> F numer : % -> Vector A +--R one? : % -> Boolean recip : % -> Union(%,"failed") +--R sample : () -> % ?~=? : (%,%) -> Boolean +--R ?**? : (%,NonNegativeInteger) -> % +--R ?^? : (%,NonNegativeInteger) -> % +--R randomLC : (NonNegativeInteger,Vector A) -> A +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +FractionalIdeal examples +==================================================================== + +See Also: +o )show FractionalIdeal + +@ + \pagehead{FractionalIdeal}{FRIDEAL} \pagepic{ps/v103fractionalideal.ps}{FRIDEAL}{1.00} {\bf See}\\ @@ -38598,6 +45324,50 @@ FractionalIdeal(R, F, UP, A): Exports == Implementation where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain FRMOD FramedModule} + +<>= +)set break resume +)sys rm -f FramedModule.output +)spool FramedModule.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show FramedModule +--R FramedModule(R: EuclideanDomain,F: QuotientFieldCategory R,UP: UnivariatePolynomialCategory F,A: FramedAlgebra(F,UP),ibasis: Vector A) is a domain constructor +--R Abbreviation for FramedModule is FRMOD +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for FRMOD +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (%,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?=? : (%,%) -> Boolean 1 : () -> % +--R ?^? : (%,PositiveInteger) -> % basis : % -> Vector A +--R coerce : % -> OutputForm hash : % -> SingleInteger +--R latex : % -> String module : Vector A -> % +--R norm : % -> F one? : % -> Boolean +--R recip : % -> Union(%,"failed") sample : () -> % +--R ?~=? : (%,%) -> Boolean +--R ?**? : (%,NonNegativeInteger) -> % +--R ?^? : (%,NonNegativeInteger) -> % +--R module : FractionalIdeal(R,F,UP,A) -> % if A has RETRACT F +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +FramedModule examples +==================================================================== + +See Also: +o )show FramedModule + +@ + \pagehead{FramedModule}{FRMOD} \pagepic{ps/v103framedmodule.ps}{FRMOD}{1.00} {\bf See}\\ @@ -38739,6 +45509,63 @@ FramedModule(R, F, UP, A, ibasis): Exports == Implementation where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain FAGROUP FreeAbelianGroup} + +<>= +)set break resume +)sys rm -f FreeAbelianGroup.output +)spool FreeAbelianGroup.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show FreeAbelianGroup +--R FreeAbelianGroup S: SetCategory is a domain constructor +--R Abbreviation for FreeAbelianGroup is FAGROUP +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for FAGROUP +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (Integer,S) -> % ?*? : (%,Integer) -> % +--R ?*? : (Integer,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?+? : (S,%) -> % ?+? : (%,%) -> % +--R ?-? : (%,%) -> % -? : % -> % +--R ?=? : (%,%) -> Boolean 0 : () -> % +--R coefficient : (S,%) -> Integer coerce : S -> % +--R coerce : % -> OutputForm hash : % -> SingleInteger +--R latex : % -> String mapGen : ((S -> S),%) -> % +--R nthCoef : (%,Integer) -> Integer nthFactor : (%,Integer) -> S +--R retract : % -> S sample : () -> % +--R size : % -> NonNegativeInteger zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean +--R ?*? : (NonNegativeInteger,%) -> % +--R ? Boolean if S has ORDSET +--R ?<=? : (%,%) -> Boolean if S has ORDSET +--R ?>? : (%,%) -> Boolean if S has ORDSET +--R ?>=? : (%,%) -> Boolean if S has ORDSET +--R highCommonTerms : (%,%) -> % if Integer has OAMON +--R mapCoef : ((Integer -> Integer),%) -> % +--R max : (%,%) -> % if S has ORDSET +--R min : (%,%) -> % if S has ORDSET +--R retractIfCan : % -> Union(S,"failed") +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R terms : % -> List Record(gen: S,exp: Integer) +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +FreeAbelianGroup examples +==================================================================== + +See Also: +o )show FreeAbelianGroup + +@ + \pagehead{FreeAbelianGroup}{FAGROUP} \pagepic{ps/v103freeabeliangroup.ps}{FAGROUP}{1.00} {\bf See}\\ @@ -38835,6 +45662,56 @@ FreeAbelianGroup(S:SetCategory): Exports == Implementation where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain FAMONOID FreeAbelianMonoid} + +<>= +)set break resume +)sys rm -f FreeAbelianMonoid.output +)spool FreeAbelianMonoid.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show FreeAbelianMonoid +--R FreeAbelianMonoid S: SetCategory is a domain constructor +--R Abbreviation for FreeAbelianMonoid is FAMONOID +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for FAMONOID +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (NonNegativeInteger,S) -> % ?*? : (PositiveInteger,%) -> % +--R ?+? : (S,%) -> % ?+? : (%,%) -> % +--R ?=? : (%,%) -> Boolean 0 : () -> % +--R coerce : S -> % coerce : % -> OutputForm +--R hash : % -> SingleInteger latex : % -> String +--R mapGen : ((S -> S),%) -> % nthFactor : (%,Integer) -> S +--R retract : % -> S sample : () -> % +--R size : % -> NonNegativeInteger zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean +--R ?*? : (NonNegativeInteger,%) -> % +--R coefficient : (S,%) -> NonNegativeInteger +--R highCommonTerms : (%,%) -> % if NonNegativeInteger has OAMON +--R mapCoef : ((NonNegativeInteger -> NonNegativeInteger),%) -> % +--R nthCoef : (%,Integer) -> NonNegativeInteger +--R retractIfCan : % -> Union(S,"failed") +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R terms : % -> List Record(gen: S,exp: NonNegativeInteger) +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +FreeAbelianMonoid examples +==================================================================== + +See Also: +o )show FreeAbelianMonoid + +@ + \pagehead{FreeAbelianMonoid}{FAMONOID} \pagepic{ps/v103freeabelianmonoid.ps}{FAMONOID}{1.00} {\bf See}\\ @@ -38893,6 +45770,58 @@ FreeAbelianMonoid(S: SetCategory): @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain FGROUP FreeGroup} + +<>= +)set break resume +)sys rm -f FreeGroup.output +)spool FreeGroup.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show FreeGroup +--R FreeGroup S: SetCategory is a domain constructor +--R Abbreviation for FreeGroup is FGROUP +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for FGROUP +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (%,S) -> % ?*? : (S,%) -> % +--R ?*? : (%,%) -> % ?**? : (S,Integer) -> % +--R ?**? : (%,Integer) -> % ?**? : (%,PositiveInteger) -> % +--R ?/? : (%,%) -> % ?=? : (%,%) -> Boolean +--R 1 : () -> % ?^? : (%,Integer) -> % +--R ?^? : (%,PositiveInteger) -> % coerce : S -> % +--R coerce : % -> OutputForm commutator : (%,%) -> % +--R conjugate : (%,%) -> % hash : % -> SingleInteger +--R inv : % -> % latex : % -> String +--R mapGen : ((S -> S),%) -> % nthExpon : (%,Integer) -> Integer +--R nthFactor : (%,Integer) -> S one? : % -> Boolean +--R recip : % -> Union(%,"failed") retract : % -> S +--R sample : () -> % size : % -> NonNegativeInteger +--R ?~=? : (%,%) -> Boolean +--R ?**? : (%,NonNegativeInteger) -> % +--R ?^? : (%,NonNegativeInteger) -> % +--R factors : % -> List Record(gen: S,exp: Integer) +--R mapExpon : ((Integer -> Integer),%) -> % +--R retractIfCan : % -> Union(S,"failed") +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +FreeGroup examples +==================================================================== + +See Also: +o )show FreeGroup + +@ + \pagehead{FreeGroup}{FGROUP} \pagepic{ps/v103freegroup.ps}{FGROUP}{1.00} {\bf See}\\ @@ -39004,6 +45933,51 @@ FreeGroup(S: SetCategory): Join(Group, RetractableTo S) with @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain FM FreeModule} + +<>= +)set break resume +)sys rm -f FreeModule.output +)spool FreeModule.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show FreeModule +--R FreeModule(R: Ring,S: OrderedSet) is a domain constructor +--R Abbreviation for FreeModule is FM +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for FM +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (%,R) -> % ?*? : (R,%) -> % +--R ?*? : (Integer,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ?=? : (%,%) -> Boolean +--R 0 : () -> % coerce : % -> OutputForm +--R hash : % -> SingleInteger latex : % -> String +--R leadingCoefficient : % -> R leadingSupport : % -> S +--R map : ((R -> R),%) -> % monomial : (R,S) -> % +--R reductum : % -> % sample : () -> % +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean +--R ?*? : (NonNegativeInteger,%) -> % +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +FreeModule examples +==================================================================== + +See Also: +o )show FreeModule + +@ + \pagehead{FreeModule}{FM} \pagepic{ps/v103freemodule.ps}{FM}{1.00} {\bf See}\\ @@ -39110,6 +46084,59 @@ FreeModule(R:Ring,S:OrderedSet): @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain FM1 FreeModule1} + +<>= +)set break resume +)sys rm -f FreeModule1.output +)spool FreeModule1.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show FreeModule1 +--R FreeModule1(R: Ring,S: OrderedSet) is a domain constructor +--R Abbreviation for FreeModule1 is FM1 +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for FM1 +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (S,R) -> % ?*? : (R,S) -> % +--R ?*? : (%,R) -> % ?*? : (R,%) -> % +--R ?*? : (Integer,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ?=? : (%,%) -> Boolean +--R 0 : () -> % coefficient : (%,S) -> R +--R coefficients : % -> List R coerce : S -> % +--R coerce : % -> OutputForm hash : % -> SingleInteger +--R latex : % -> String leadingCoefficient : % -> R +--R leadingMonomial : % -> S map : ((R -> R),%) -> % +--R monom : (S,R) -> % monomial? : % -> Boolean +--R monomials : % -> List % reductum : % -> % +--R retract : % -> S sample : () -> % +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean +--R ?*? : (NonNegativeInteger,%) -> % +--R leadingTerm : % -> Record(k: S,c: R) +--R listOfTerms : % -> List Record(k: S,c: R) +--R numberOfMonomials : % -> NonNegativeInteger +--R retractIfCan : % -> Union(S,"failed") +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +FreeModule1 examples +==================================================================== + +See Also: +o )show FreeModule1 + +@ + \pagehead{FreeModule1}{FM1} \pagepic{ps/v103freemodule1.ps}{FM1}{1.00} @@ -39251,6 +46278,67 @@ FreeModule1(R:Ring,S:OrderedSet): FMcat == FMdef where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain FMONOID FreeMonoid} + +<>= +)set break resume +)sys rm -f FreeMonoid.output +)spool FreeMonoid.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show FreeMonoid +--R FreeMonoid S: SetCategory is a domain constructor +--R Abbreviation for FreeMonoid is FMONOID +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for FMONOID +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (%,S) -> % ?*? : (S,%) -> % +--R ?*? : (%,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?=? : (%,%) -> Boolean 1 : () -> % +--R ?^? : (%,PositiveInteger) -> % coerce : S -> % +--R coerce : % -> OutputForm hash : % -> SingleInteger +--R hclf : (%,%) -> % hcrf : (%,%) -> % +--R latex : % -> String mapGen : ((S -> S),%) -> % +--R nthFactor : (%,Integer) -> S one? : % -> Boolean +--R recip : % -> Union(%,"failed") retract : % -> S +--R sample : () -> % size : % -> NonNegativeInteger +--R ?~=? : (%,%) -> Boolean +--R ?**? : (S,NonNegativeInteger) -> % +--R ?**? : (%,NonNegativeInteger) -> % +--R ? Boolean if S has ORDSET +--R ?<=? : (%,%) -> Boolean if S has ORDSET +--R ?>? : (%,%) -> Boolean if S has ORDSET +--R ?>=? : (%,%) -> Boolean if S has ORDSET +--R ?^? : (%,NonNegativeInteger) -> % +--R divide : (%,%) -> Union(Record(lm: %,rm: %),"failed") +--R factors : % -> List Record(gen: S,exp: NonNegativeInteger) +--R lquo : (%,%) -> Union(%,"failed") +--R mapExpon : ((NonNegativeInteger -> NonNegativeInteger),%) -> % +--R max : (%,%) -> % if S has ORDSET +--R min : (%,%) -> % if S has ORDSET +--R nthExpon : (%,Integer) -> NonNegativeInteger +--R overlap : (%,%) -> Record(lm: %,mm: %,rm: %) +--R retractIfCan : % -> Union(S,"failed") +--R rquo : (%,%) -> Union(%,"failed") +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +FreeMonoid examples +==================================================================== + +See Also: +o )show FreeMonoid + +@ + \pagehead{FreeMonoid}{FMONOID} \pagepic{ps/v103freemonoid.ps}{FMONOID}{1.00} {\bf See}\\ @@ -39489,6 +46577,57 @@ FreeMonoid(S: SetCategory): FMcategory == FMdefinition where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain FNLA FreeNilpotentLie} + +<>= +)set break resume +)sys rm -f FreeNilpotentLie.output +)spool FreeNilpotentLie.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show FreeNilpotentLie +--R FreeNilpotentLie(n: NonNegativeInteger,class: NonNegativeInteger,R: CommutativeRing) is a domain constructor +--R Abbreviation for FreeNilpotentLie is FNLA +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for FNLA +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (R,%) -> % ?*? : (%,R) -> % +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ?=? : (%,%) -> Boolean +--R 0 : () -> % antiCommutator : (%,%) -> % +--R associator : (%,%,%) -> % coerce : % -> OutputForm +--R commutator : (%,%) -> % deepExpand : % -> OutputForm +--R hash : % -> SingleInteger latex : % -> String +--R sample : () -> % shallowExpand : % -> OutputForm +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean +--R ?*? : (NonNegativeInteger,%) -> % +--R dimension : () -> NonNegativeInteger +--R generator : NonNegativeInteger -> % +--R leftPower : (%,PositiveInteger) -> % +--R plenaryPower : (%,PositiveInteger) -> % +--R rightPower : (%,PositiveInteger) -> % +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +FreeNilpotentLie examples +==================================================================== + +See Also: +o )show FreeNilpotentLie + +@ + \pagehead{FreeNilpotentLie}{FNLA} \pagepic{ps/v103freenilpotentlie.ps}{FNLA}{1.00} {\bf See}\\ @@ -39649,6 +46788,7 @@ FreeNilpotentLie(n:NNI,class:NNI,R: CommutativeRing): Export == Implement where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain FPARFRAC FullPartialFractionExpansion} + <>= )set break resume )sys rm -f FullPartialFractionExpansion.output @@ -40330,6 +47470,42 @@ FullPartialFractionExpansion(F, UP): Exports == Implementation where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain FUNCTION FunctionCalled} + +<>= +)set break resume +)sys rm -f FunctionCalled.output +)spool FunctionCalled.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show FunctionCalled +--R FunctionCalled f: Symbol is a domain constructor +--R Abbreviation for FunctionCalled is FUNCTION +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for FUNCTION +--R +--R------------------------------- Operations -------------------------------- +--R ?=? : (%,%) -> Boolean coerce : % -> OutputForm +--R hash : % -> SingleInteger latex : % -> String +--R name : % -> Symbol ?~=? : (%,%) -> Boolean +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +FunctionCalled examples +==================================================================== + +See Also: +o )show FunctionCalled + +@ + \pagehead{FunctionCalled}{FUNCTION} \pagepic{ps/v103functioncalled.ps}{FUNCTION}{1.00} @@ -40369,6 +47545,7 @@ FunctionCalled(f:Symbol): SetCategory with \chapter{Chapter G} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain GDMP GeneralDistributedMultivariatePolynomial} + <>= )set break resume )sys rm -f GeneralDistributedMultivariatePolynomial.output @@ -40931,6 +48108,55 @@ GeneralDistributedMultivariatePolynomial(vl,R,E): public == private where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain GMODPOL GeneralModulePolynomial} + +<>= +)set break resume +)sys rm -f GeneralModulePolynomial.output +)spool GeneralModulePolynomial.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show GeneralModulePolynomial +--R GeneralModulePolynomial(vl: List Symbol,R: CommutativeRing,IS: OrderedSet,E: DirectProductCategory(# vl,NonNegativeInteger),ff: ((Record(index: IS,exponent: E),Record(index: IS,exponent: E)) -> Boolean),P: PolynomialCategory(R,E,OrderedVariableList vl)) is a domain constructor +--R Abbreviation for GeneralModulePolynomial is GMODPOL +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for GMODPOL +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (R,%) -> % ?*? : (%,R) -> % +--R ?*? : (%,P) -> % ?*? : (P,%) -> % +--R ?*? : (Integer,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ?=? : (%,%) -> Boolean +--R 0 : () -> % build : (R,IS,E) -> % +--R coerce : % -> OutputForm hash : % -> SingleInteger +--R latex : % -> String leadingCoefficient : % -> R +--R leadingExponent : % -> E leadingIndex : % -> IS +--R multMonom : (R,E,%) -> % reductum : % -> % +--R sample : () -> % unitVector : IS -> % +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean +--R ?*? : (NonNegativeInteger,%) -> % +--R leadingMonomial : % -> ModuleMonomial(IS,E,ff) +--R monomial : (R,ModuleMonomial(IS,E,ff)) -> % +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +GeneralModulePolynomial examples +==================================================================== + +See Also: +o )show GeneralModulePolynomial + +@ + \pagehead{GeneralModulePolynomial}{GMODPOL} \pagepic{ps/v103generalmodulepolynomial.ps}{GMODPOL}{1.00} {\bf See}\\ @@ -41044,6 +48270,129 @@ GeneralModulePolynomial(vl, R, IS, E, ff, P): public == private where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain GCNAALG GenericNonAssociativeAlgebra} + +<>= +)set break resume +)sys rm -f GenericNonAssociativeAlgebra.output +)spool GenericNonAssociativeAlgebra.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show GenericNonAssociativeAlgebra +--R GenericNonAssociativeAlgebra(R: CommutativeRing,n: PositiveInteger,ls: List Symbol,gamma: Vector Matrix R) is a domain constructor +--R Abbreviation for GenericNonAssociativeAlgebra is GCNAALG +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for GCNAALG +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ?=? : (%,%) -> Boolean +--R 0 : () -> % alternative? : () -> Boolean +--R antiAssociative? : () -> Boolean antiCommutative? : () -> Boolean +--R antiCommutator : (%,%) -> % associative? : () -> Boolean +--R associator : (%,%,%) -> % basis : () -> Vector % +--R coerce : % -> OutputForm commutative? : () -> Boolean +--R commutator : (%,%) -> % flexible? : () -> Boolean +--R generic : (Symbol,Vector %) -> % generic : Vector % -> % +--R generic : Vector Symbol -> % generic : Symbol -> % +--R generic : () -> % hash : % -> SingleInteger +--R jacobiIdentity? : () -> Boolean jordanAdmissible? : () -> Boolean +--R jordanAlgebra? : () -> Boolean latex : % -> String +--R leftAlternative? : () -> Boolean lieAdmissible? : () -> Boolean +--R lieAlgebra? : () -> Boolean powerAssociative? : () -> Boolean +--R rank : () -> PositiveInteger rightAlternative? : () -> Boolean +--R sample : () -> % someBasis : () -> Vector % +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean +--R ?*? : (SquareMatrix(n,Fraction Polynomial R),%) -> % +--R ?*? : (Fraction Polynomial R,%) -> % +--R ?*? : (%,Fraction Polynomial R) -> % +--R ?*? : (NonNegativeInteger,%) -> % +--R apply : (Matrix Fraction Polynomial R,%) -> % +--R associatorDependence : () -> List Vector Fraction Polynomial R if Fraction Polynomial R has INTDOM +--R coerce : Vector Fraction Polynomial R -> % +--R conditionsForIdempotents : () -> List Polynomial R if R has INTDOM +--R conditionsForIdempotents : Vector % -> List Polynomial R if R has INTDOM +--R conditionsForIdempotents : () -> List Polynomial Fraction Polynomial R +--R conditionsForIdempotents : Vector % -> List Polynomial Fraction Polynomial R +--R convert : Vector Fraction Polynomial R -> % +--R convert : % -> Vector Fraction Polynomial R +--R coordinates : Vector % -> Matrix Fraction Polynomial R +--R coordinates : % -> Vector Fraction Polynomial R +--R coordinates : (Vector %,Vector %) -> Matrix Fraction Polynomial R +--R coordinates : (%,Vector %) -> Vector Fraction Polynomial R +--R ?.? : (%,Integer) -> Fraction Polynomial R +--R generic : (Vector Symbol,Vector %) -> % +--R genericLeftDiscriminant : () -> Fraction Polynomial R if R has INTDOM +--R genericLeftMinimalPolynomial : % -> SparseUnivariatePolynomial Fraction Polynomial R if R has INTDOM +--R genericLeftNorm : % -> Fraction Polynomial R if R has INTDOM +--R genericLeftTrace : % -> Fraction Polynomial R if R has INTDOM +--R genericLeftTraceForm : (%,%) -> Fraction Polynomial R if R has INTDOM +--R genericRightDiscriminant : () -> Fraction Polynomial R if R has INTDOM +--R genericRightMinimalPolynomial : % -> SparseUnivariatePolynomial Fraction Polynomial R if R has INTDOM +--R genericRightNorm : % -> Fraction Polynomial R if R has INTDOM +--R genericRightTrace : % -> Fraction Polynomial R if R has INTDOM +--R genericRightTraceForm : (%,%) -> Fraction Polynomial R if R has INTDOM +--R leftCharacteristicPolynomial : % -> SparseUnivariatePolynomial Fraction Polynomial R +--R leftDiscriminant : () -> Fraction Polynomial R +--R leftDiscriminant : Vector % -> Fraction Polynomial R +--R leftMinimalPolynomial : % -> SparseUnivariatePolynomial Fraction Polynomial R if Fraction Polynomial R has INTDOM +--R leftNorm : % -> Fraction Polynomial R +--R leftPower : (%,PositiveInteger) -> % +--R leftRankPolynomial : () -> SparseUnivariatePolynomial Fraction Polynomial R if R has INTDOM +--R leftRankPolynomial : () -> SparseUnivariatePolynomial Polynomial Fraction Polynomial R if Fraction Polynomial R has FIELD +--R leftRecip : % -> Union(%,"failed") if Fraction Polynomial R has INTDOM +--R leftRegularRepresentation : % -> Matrix Fraction Polynomial R +--R leftRegularRepresentation : (%,Vector %) -> Matrix Fraction Polynomial R +--R leftTrace : % -> Fraction Polynomial R +--R leftTraceMatrix : () -> Matrix Fraction Polynomial R +--R leftTraceMatrix : Vector % -> Matrix Fraction Polynomial R +--R leftUnit : () -> Union(%,"failed") if Fraction Polynomial R has INTDOM +--R leftUnits : () -> Union(Record(particular: %,basis: List %),"failed") +--R noncommutativeJordanAlgebra? : () -> Boolean +--R plenaryPower : (%,PositiveInteger) -> % +--R recip : % -> Union(%,"failed") if Fraction Polynomial R has INTDOM +--R represents : Vector Fraction Polynomial R -> % +--R represents : (Vector Fraction Polynomial R,Vector %) -> % +--R rightCharacteristicPolynomial : % -> SparseUnivariatePolynomial Fraction Polynomial R +--R rightDiscriminant : () -> Fraction Polynomial R +--R rightDiscriminant : Vector % -> Fraction Polynomial R +--R rightMinimalPolynomial : % -> SparseUnivariatePolynomial Fraction Polynomial R if Fraction Polynomial R has INTDOM +--R rightNorm : % -> Fraction Polynomial R +--R rightPower : (%,PositiveInteger) -> % +--R rightRankPolynomial : () -> SparseUnivariatePolynomial Fraction Polynomial R if R has INTDOM +--R rightRankPolynomial : () -> SparseUnivariatePolynomial Polynomial Fraction Polynomial R if Fraction Polynomial R has FIELD +--R rightRecip : % -> Union(%,"failed") if Fraction Polynomial R has INTDOM +--R rightRegularRepresentation : % -> Matrix Fraction Polynomial R +--R rightRegularRepresentation : (%,Vector %) -> Matrix Fraction Polynomial R +--R rightTrace : % -> Fraction Polynomial R +--R rightTraceMatrix : () -> Matrix Fraction Polynomial R +--R rightTraceMatrix : Vector % -> Matrix Fraction Polynomial R +--R rightUnit : () -> Union(%,"failed") if Fraction Polynomial R has INTDOM +--R rightUnits : () -> Union(Record(particular: %,basis: List %),"failed") +--R structuralConstants : () -> Vector Matrix Fraction Polynomial R +--R structuralConstants : Vector % -> Vector Matrix Fraction Polynomial R +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R unit : () -> Union(%,"failed") if Fraction Polynomial R has INTDOM +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +GenericNonAssociativeAlgebra examples +==================================================================== + +See Also: +o )show GenericNonAssociativeAlgebra + +@ + \pagehead{GenericNonAssociativeAlgebra}{GCNAALG} \pagepic{ps/v103genericnonassociativealgebra.ps}{GCNAALG}{1.00} @@ -41448,6 +48797,87 @@ GenericNonAssociativeAlgebra(R : CommutativeRing, n : PositiveInteger,_ @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain GPOLSET GeneralPolynomialSet} + +<>= +)set break resume +)sys rm -f GeneralPolynomialSet.output +)spool GeneralPolynomialSet.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show GeneralPolynomialSet +--R GeneralPolynomialSet(R: Ring,E: OrderedAbelianMonoidSup,VarSet: OrderedSet,P: RecursivePolynomialCategory(R,E,VarSet)) is a domain constructor +--R Abbreviation for GeneralPolynomialSet is GPOLSET +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for GPOLSET +--R +--R------------------------------- Operations -------------------------------- +--R ?=? : (%,%) -> Boolean coerce : % -> List P +--R coerce : % -> OutputForm collect : (%,VarSet) -> % +--R collectUnder : (%,VarSet) -> % collectUpper : (%,VarSet) -> % +--R construct : List P -> % convert : List P -> % +--R copy : % -> % empty : () -> % +--R empty? : % -> Boolean eq? : (%,%) -> Boolean +--R hash : % -> SingleInteger latex : % -> String +--R mainVariables : % -> List VarSet map : ((P -> P),%) -> % +--R mvar : % -> VarSet retract : List P -> % +--R sample : () -> % trivialIdeal? : % -> Boolean +--R variables : % -> List VarSet ?~=? : (%,%) -> Boolean +--R #? : % -> NonNegativeInteger if $ has finiteAggregate +--R any? : ((P -> Boolean),%) -> Boolean if $ has finiteAggregate +--R convert : % -> InputForm if P has KONVERT INFORM +--R count : ((P -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate +--R count : (P,%) -> NonNegativeInteger if $ has finiteAggregate and P has SETCAT +--R eval : (%,List Equation P) -> % if P has EVALAB P and P has SETCAT +--R eval : (%,Equation P) -> % if P has EVALAB P and P has SETCAT +--R eval : (%,P,P) -> % if P has EVALAB P and P has SETCAT +--R eval : (%,List P,List P) -> % if P has EVALAB P and P has SETCAT +--R every? : ((P -> Boolean),%) -> Boolean if $ has finiteAggregate +--R find : ((P -> Boolean),%) -> Union(P,"failed") +--R headRemainder : (P,%) -> Record(num: P,den: R) if R has INTDOM +--R less? : (%,NonNegativeInteger) -> Boolean +--R mainVariable? : (VarSet,%) -> Boolean +--R map! : ((P -> P),%) -> % if $ has shallowlyMutable +--R member? : (P,%) -> Boolean if $ has finiteAggregate and P has SETCAT +--R members : % -> List P if $ has finiteAggregate +--R more? : (%,NonNegativeInteger) -> Boolean +--R parts : % -> List P if $ has finiteAggregate +--R reduce : (((P,P) -> P),%) -> P if $ has finiteAggregate +--R reduce : (((P,P) -> P),%,P) -> P if $ has finiteAggregate +--R reduce : (((P,P) -> P),%,P,P) -> P if $ has finiteAggregate and P has SETCAT +--R remainder : (P,%) -> Record(rnum: R,polnum: P,den: R) if R has INTDOM +--R remove : ((P -> Boolean),%) -> % if $ has finiteAggregate +--R remove : (P,%) -> % if $ has finiteAggregate and P has SETCAT +--R removeDuplicates : % -> % if $ has finiteAggregate and P has SETCAT +--R retractIfCan : List P -> Union(%,"failed") +--R rewriteIdealWithHeadRemainder : (List P,%) -> List P if R has INTDOM +--R rewriteIdealWithRemainder : (List P,%) -> List P if R has INTDOM +--R roughBase? : % -> Boolean if R has INTDOM +--R roughEqualIdeals? : (%,%) -> Boolean if R has INTDOM +--R roughSubIdeal? : (%,%) -> Boolean if R has INTDOM +--R roughUnitIdeal? : % -> Boolean if R has INTDOM +--R select : ((P -> Boolean),%) -> % if $ has finiteAggregate +--R size? : (%,NonNegativeInteger) -> Boolean +--R sort : (%,VarSet) -> Record(under: %,floor: %,upper: %) +--R triangular? : % -> Boolean if R has INTDOM +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +GeneralPolynomialSet examples +==================================================================== + +See Also: +o )show GeneralPolynomialSet + +@ + \pagehead{GeneralPolynomialSet}{GPOLSET} \pagepic{ps/v103generalpolynomialset.ps}{GPOLSET}{1.00} @@ -41594,6 +49024,7 @@ GeneralPolynomialSet(R,E,VarSet,P) : Exports == Implementation where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain GSTBL GeneralSparseTable} + <>= )set break resume )sys rm -f GeneralSparseTable.output @@ -41792,6 +49223,110 @@ GeneralSparseTable(Key, Entry, Tbl, dent): TableAggregate(Key, Entry) == Impl @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain GTSET GeneralTriangularSet} + +<>= +)set break resume +)sys rm -f GeneralTriangularSet.output +)spool GeneralTriangularSet.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show GeneralTriangularSet +--R GeneralTriangularSet(R: IntegralDomain,E: OrderedAbelianMonoidSup,V: OrderedSet,P: RecursivePolynomialCategory(R,E,V)) is a domain constructor +--R Abbreviation for GeneralTriangularSet is GTSET +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for GTSET +--R +--R------------------------------- Operations -------------------------------- +--R ?=? : (%,%) -> Boolean algebraic? : (V,%) -> Boolean +--R algebraicVariables : % -> List V coerce : % -> List P +--R coerce : % -> OutputForm collect : (%,V) -> % +--R collectQuasiMonic : % -> % collectUnder : (%,V) -> % +--R collectUpper : (%,V) -> % construct : List P -> % +--R copy : % -> % degree : % -> NonNegativeInteger +--R empty : () -> % empty? : % -> Boolean +--R eq? : (%,%) -> Boolean extend : (%,P) -> % +--R first : % -> Union(P,"failed") hash : % -> SingleInteger +--R headReduce : (P,%) -> P headReduced? : % -> Boolean +--R headReduced? : (P,%) -> Boolean infRittWu? : (%,%) -> Boolean +--R initiallyReduce : (P,%) -> P initiallyReduced? : % -> Boolean +--R initials : % -> List P last : % -> Union(P,"failed") +--R latex : % -> String mainVariable? : (V,%) -> Boolean +--R mainVariables : % -> List V map : ((P -> P),%) -> % +--R mvar : % -> V normalized? : % -> Boolean +--R normalized? : (P,%) -> Boolean reduceByQuasiMonic : (P,%) -> P +--R removeZero : (P,%) -> P rest : % -> Union(%,"failed") +--R retract : List P -> % sample : () -> % +--R stronglyReduce : (P,%) -> P stronglyReduced? : % -> Boolean +--R trivialIdeal? : % -> Boolean variables : % -> List V +--R zeroSetSplit : List P -> List % ?~=? : (%,%) -> Boolean +--R #? : % -> NonNegativeInteger if $ has finiteAggregate +--R any? : ((P -> Boolean),%) -> Boolean if $ has finiteAggregate +--R autoReduced? : (%,((P,List P) -> Boolean)) -> Boolean +--R basicSet : (List P,(P -> Boolean),((P,P) -> Boolean)) -> Union(Record(bas: %,top: List P),"failed") +--R basicSet : (List P,((P,P) -> Boolean)) -> Union(Record(bas: %,top: List P),"failed") +--R coHeight : % -> NonNegativeInteger if V has FINITE +--R convert : % -> InputForm if P has KONVERT INFORM +--R count : ((P -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate +--R count : (P,%) -> NonNegativeInteger if $ has finiteAggregate and P has SETCAT +--R eval : (%,List Equation P) -> % if P has EVALAB P and P has SETCAT +--R eval : (%,Equation P) -> % if P has EVALAB P and P has SETCAT +--R eval : (%,P,P) -> % if P has EVALAB P and P has SETCAT +--R eval : (%,List P,List P) -> % if P has EVALAB P and P has SETCAT +--R every? : ((P -> Boolean),%) -> Boolean if $ has finiteAggregate +--R extendIfCan : (%,P) -> Union(%,"failed") +--R find : ((P -> Boolean),%) -> Union(P,"failed") +--R headRemainder : (P,%) -> Record(num: P,den: R) if R has INTDOM +--R initiallyReduced? : (P,%) -> Boolean +--R less? : (%,NonNegativeInteger) -> Boolean +--R map! : ((P -> P),%) -> % if $ has shallowlyMutable +--R member? : (P,%) -> Boolean if $ has finiteAggregate and P has SETCAT +--R members : % -> List P if $ has finiteAggregate +--R more? : (%,NonNegativeInteger) -> Boolean +--R parts : % -> List P if $ has finiteAggregate +--R quasiComponent : % -> Record(close: List P,open: List P) +--R reduce : (P,%,((P,P) -> P),((P,P) -> Boolean)) -> P +--R reduce : (((P,P) -> P),%) -> P if $ has finiteAggregate +--R reduce : (((P,P) -> P),%,P) -> P if $ has finiteAggregate +--R reduce : (((P,P) -> P),%,P,P) -> P if $ has finiteAggregate and P has SETCAT +--R reduced? : (P,%,((P,P) -> Boolean)) -> Boolean +--R remainder : (P,%) -> Record(rnum: R,polnum: P,den: R) if R has INTDOM +--R remove : ((P -> Boolean),%) -> % if $ has finiteAggregate +--R remove : (P,%) -> % if $ has finiteAggregate and P has SETCAT +--R removeDuplicates : % -> % if $ has finiteAggregate and P has SETCAT +--R retractIfCan : List P -> Union(%,"failed") +--R rewriteIdealWithHeadRemainder : (List P,%) -> List P if R has INTDOM +--R rewriteIdealWithRemainder : (List P,%) -> List P if R has INTDOM +--R rewriteSetWithReduction : (List P,%,((P,P) -> P),((P,P) -> Boolean)) -> List P +--R roughBase? : % -> Boolean if R has INTDOM +--R roughEqualIdeals? : (%,%) -> Boolean if R has INTDOM +--R roughSubIdeal? : (%,%) -> Boolean if R has INTDOM +--R roughUnitIdeal? : % -> Boolean if R has INTDOM +--R select : (%,V) -> Union(P,"failed") +--R select : ((P -> Boolean),%) -> % if $ has finiteAggregate +--R size? : (%,NonNegativeInteger) -> Boolean +--R sort : (%,V) -> Record(under: %,floor: %,upper: %) +--R stronglyReduced? : (P,%) -> Boolean +--R triangular? : % -> Boolean if R has INTDOM +--R zeroSetSplitIntoTriangularSystems : List P -> List Record(close: %,open: List P) +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +GeneralTriangularSet examples +==================================================================== + +See Also: +o )show GeneralTriangularSet + +@ + \pagehead{GeneralTriangularSet}{GTSET} \pagepic{ps/v103generaltriangularset.ps}{GTSET}{1.00} {\bf See}\\ @@ -41997,6 +49532,161 @@ GeneralTriangularSet(R,E,V,P) : Exports == Implementation where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain GSERIES GeneralUnivariatePowerSeries} + +<>= +)set break resume +)sys rm -f GeneralUnivariatePowerSeries.output +)spool GeneralUnivariatePowerSeries.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show GeneralUnivariatePowerSeries +--R GeneralUnivariatePowerSeries(Coef: Ring,var: Symbol,cen: Coef) is a domain constructor +--R Abbreviation for GeneralUnivariatePowerSeries is GSERIES +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for GSERIES +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (Coef,%) -> % ?*? : (%,Coef) -> % +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ?=? : (%,%) -> Boolean +--R 1 : () -> % 0 : () -> % +--R ?^? : (%,PositiveInteger) -> % center : % -> Coef +--R coerce : Variable var -> % coerce : Integer -> % +--R coerce : % -> OutputForm complete : % -> % +--R degree : % -> Fraction Integer hash : % -> SingleInteger +--R latex : % -> String leadingCoefficient : % -> Coef +--R leadingMonomial : % -> % map : ((Coef -> Coef),%) -> % +--R monomial? : % -> Boolean one? : % -> Boolean +--R order : % -> Fraction Integer pole? : % -> Boolean +--R recip : % -> Union(%,"failed") reductum : % -> % +--R sample : () -> % variable : % -> Symbol +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean +--R ?*? : (%,Fraction Integer) -> % if Coef has ALGEBRA FRAC INT +--R ?*? : (Fraction Integer,%) -> % if Coef has ALGEBRA FRAC INT +--R ?*? : (NonNegativeInteger,%) -> % +--R ?**? : (%,Fraction Integer) -> % if Coef has ALGEBRA FRAC INT +--R ?**? : (%,%) -> % if Coef has ALGEBRA FRAC INT +--R ?**? : (%,Integer) -> % if Coef has FIELD +--R ?**? : (%,NonNegativeInteger) -> % +--R ?/? : (%,%) -> % if Coef has FIELD +--R ?/? : (%,Coef) -> % if Coef has FIELD +--R D : % -> % if Coef has *: (Fraction Integer,Coef) -> Coef +--R D : (%,NonNegativeInteger) -> % if Coef has *: (Fraction Integer,Coef) -> Coef +--R D : (%,Symbol) -> % if Coef has *: (Fraction Integer,Coef) -> Coef and Coef has PDRING SYMBOL +--R D : (%,List Symbol) -> % if Coef has *: (Fraction Integer,Coef) -> Coef and Coef has PDRING SYMBOL +--R D : (%,Symbol,NonNegativeInteger) -> % if Coef has *: (Fraction Integer,Coef) -> Coef and Coef has PDRING SYMBOL +--R D : (%,List Symbol,List NonNegativeInteger) -> % if Coef has *: (Fraction Integer,Coef) -> Coef and Coef has PDRING SYMBOL +--R ?^? : (%,Integer) -> % if Coef has FIELD +--R ?^? : (%,NonNegativeInteger) -> % +--R acos : % -> % if Coef has ALGEBRA FRAC INT +--R acosh : % -> % if Coef has ALGEBRA FRAC INT +--R acot : % -> % if Coef has ALGEBRA FRAC INT +--R acoth : % -> % if Coef has ALGEBRA FRAC INT +--R acsc : % -> % if Coef has ALGEBRA FRAC INT +--R acsch : % -> % if Coef has ALGEBRA FRAC INT +--R approximate : (%,Fraction Integer) -> Coef if Coef has **: (Coef,Fraction Integer) -> Coef and Coef has coerce: Symbol -> Coef +--R asec : % -> % if Coef has ALGEBRA FRAC INT +--R asech : % -> % if Coef has ALGEBRA FRAC INT +--R asin : % -> % if Coef has ALGEBRA FRAC INT +--R asinh : % -> % if Coef has ALGEBRA FRAC INT +--R associates? : (%,%) -> Boolean if Coef has INTDOM +--R atan : % -> % if Coef has ALGEBRA FRAC INT +--R atanh : % -> % if Coef has ALGEBRA FRAC INT +--R characteristic : () -> NonNegativeInteger +--R charthRoot : % -> Union(%,"failed") if Coef has CHARNZ +--R coefficient : (%,Fraction Integer) -> Coef +--R coerce : % -> % if Coef has INTDOM +--R coerce : Fraction Integer -> % if Coef has ALGEBRA FRAC INT +--R coerce : UnivariatePuiseuxSeries(Coef,var,cen) -> % +--R coerce : Coef -> % if Coef has COMRING +--R cos : % -> % if Coef has ALGEBRA FRAC INT +--R cosh : % -> % if Coef has ALGEBRA FRAC INT +--R cot : % -> % if Coef has ALGEBRA FRAC INT +--R coth : % -> % if Coef has ALGEBRA FRAC INT +--R csc : % -> % if Coef has ALGEBRA FRAC INT +--R csch : % -> % if Coef has ALGEBRA FRAC INT +--R differentiate : (%,Variable var) -> % +--R differentiate : % -> % if Coef has *: (Fraction Integer,Coef) -> Coef +--R differentiate : (%,NonNegativeInteger) -> % if Coef has *: (Fraction Integer,Coef) -> Coef +--R differentiate : (%,Symbol) -> % if Coef has *: (Fraction Integer,Coef) -> Coef and Coef has PDRING SYMBOL +--R differentiate : (%,List Symbol) -> % if Coef has *: (Fraction Integer,Coef) -> Coef and Coef has PDRING SYMBOL +--R differentiate : (%,Symbol,NonNegativeInteger) -> % if Coef has *: (Fraction Integer,Coef) -> Coef and Coef has PDRING SYMBOL +--R differentiate : (%,List Symbol,List NonNegativeInteger) -> % if Coef has *: (Fraction Integer,Coef) -> Coef and Coef has PDRING SYMBOL +--R divide : (%,%) -> Record(quotient: %,remainder: %) if Coef has FIELD +--R ?.? : (%,%) -> % if Fraction Integer has SGROUP +--R ?.? : (%,Fraction Integer) -> Coef +--R euclideanSize : % -> NonNegativeInteger if Coef has FIELD +--R eval : (%,Coef) -> Stream Coef if Coef has **: (Coef,Fraction Integer) -> Coef +--R exp : % -> % if Coef has ALGEBRA FRAC INT +--R expressIdealMember : (List %,%) -> Union(List %,"failed") if Coef has FIELD +--R exquo : (%,%) -> Union(%,"failed") if Coef has INTDOM +--R extend : (%,Fraction Integer) -> % +--R extendedEuclidean : (%,%) -> Record(coef1: %,coef2: %,generator: %) if Coef has FIELD +--R extendedEuclidean : (%,%,%) -> Union(Record(coef1: %,coef2: %),"failed") if Coef has FIELD +--R factor : % -> Factored % if Coef has FIELD +--R gcd : (%,%) -> % if Coef has FIELD +--R gcd : List % -> % if Coef has FIELD +--R gcdPolynomial : (SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial % if Coef has FIELD +--R integrate : (%,Variable var) -> % if Coef has ALGEBRA FRAC INT +--R integrate : (%,Symbol) -> % if Coef has integrate: (Coef,Symbol) -> Coef and Coef has variables: Coef -> List Symbol and Coef has ALGEBRA FRAC INT or Coef has ACFS INT and Coef has ALGEBRA FRAC INT and Coef has PRIMCAT and Coef has TRANFUN +--R integrate : % -> % if Coef has ALGEBRA FRAC INT +--R inv : % -> % if Coef has FIELD +--R lcm : (%,%) -> % if Coef has FIELD +--R lcm : List % -> % if Coef has FIELD +--R log : % -> % if Coef has ALGEBRA FRAC INT +--R monomial : (%,List SingletonAsOrderedSet,List Fraction Integer) -> % +--R monomial : (%,SingletonAsOrderedSet,Fraction Integer) -> % +--R monomial : (Coef,Fraction Integer) -> % +--R multiEuclidean : (List %,%) -> Union(List %,"failed") if Coef has FIELD +--R multiplyExponents : (%,Fraction Integer) -> % +--R multiplyExponents : (%,PositiveInteger) -> % +--R nthRoot : (%,Integer) -> % if Coef has ALGEBRA FRAC INT +--R order : (%,Fraction Integer) -> Fraction Integer +--R pi : () -> % if Coef has ALGEBRA FRAC INT +--R prime? : % -> Boolean if Coef has FIELD +--R principalIdeal : List % -> Record(coef: List %,generator: %) if Coef has FIELD +--R ?quo? : (%,%) -> % if Coef has FIELD +--R ?rem? : (%,%) -> % if Coef has FIELD +--R sec : % -> % if Coef has ALGEBRA FRAC INT +--R sech : % -> % if Coef has ALGEBRA FRAC INT +--R series : (NonNegativeInteger,Stream Record(k: Fraction Integer,c: Coef)) -> % +--R sin : % -> % if Coef has ALGEBRA FRAC INT +--R sinh : % -> % if Coef has ALGEBRA FRAC INT +--R sizeLess? : (%,%) -> Boolean if Coef has FIELD +--R sqrt : % -> % if Coef has ALGEBRA FRAC INT +--R squareFree : % -> Factored % if Coef has FIELD +--R squareFreePart : % -> % if Coef has FIELD +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R tan : % -> % if Coef has ALGEBRA FRAC INT +--R tanh : % -> % if Coef has ALGEBRA FRAC INT +--R terms : % -> Stream Record(k: Fraction Integer,c: Coef) +--R truncate : (%,Fraction Integer,Fraction Integer) -> % +--R truncate : (%,Fraction Integer) -> % +--R unit? : % -> Boolean if Coef has INTDOM +--R unitCanonical : % -> % if Coef has INTDOM +--R unitNormal : % -> Record(unit: %,canonical: %,associate: %) if Coef has INTDOM +--R variables : % -> List SingletonAsOrderedSet +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +GeneralUnivariatePowerSeries examples +==================================================================== + +See Also: +o )show GeneralUnivariatePowerSeries + +@ + \pagehead{GeneralUnivariatePowerSeries}{GSERIES} \pagepic{ps/v103generalunivariatepowerseries.ps}{GSERIES}{1.00} @@ -42220,6 +49910,58 @@ GeneralUnivariatePowerSeries(Coef,var,cen): Exports == Implementation where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain GRIMAGE GraphImage} + +<>= +)set break resume +)sys rm -f GraphImage.output +)spool GraphImage.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show GraphImage +--R GraphImage is a domain constructor +--R Abbreviation for GraphImage is GRIMAGE +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for GRIMAGE +--R +--R------------------------------- Operations -------------------------------- +--R ?=? : (%,%) -> Boolean coerce : % -> OutputForm +--R graphImage : () -> % hash : % -> SingleInteger +--R key : % -> Integer latex : % -> String +--R makeGraphImage : % -> % ranges : % -> List Segment Float +--R units : % -> List Float ?~=? : (%,%) -> Boolean +--R appendPoint : (%,Point DoubleFloat) -> Void +--R coerce : List List Point DoubleFloat -> % +--R component : (%,Point DoubleFloat,Palette,Palette,PositiveInteger) -> Void +--R component : (%,Point DoubleFloat) -> Void +--R component : (%,List Point DoubleFloat,Palette,Palette,PositiveInteger) -> Void +--R figureUnits : List List Point DoubleFloat -> List DoubleFloat +--R makeGraphImage : (List List Point DoubleFloat,List Palette,List Palette,List PositiveInteger,List DrawOption) -> % +--R makeGraphImage : (List List Point DoubleFloat,List Palette,List Palette,List PositiveInteger) -> % +--R makeGraphImage : List List Point DoubleFloat -> % +--R point : (%,Point DoubleFloat,Palette) -> Void +--R pointLists : % -> List List Point DoubleFloat +--R putColorInfo : (List List Point DoubleFloat,List Palette) -> List List Point DoubleFloat +--R ranges : (%,List Segment Float) -> List Segment Float +--R units : (%,List Float) -> List Float +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +GraphImage examples +==================================================================== + +See Also: +o )show GraphImage + +@ + \pagehead{GraphImage}{GRIMAGE} \pagepic{ps/v103graphimage.ps}{GRIMAGE}{1.00} @@ -42659,6 +50401,51 @@ GraphImage (): Exports == Implementation where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain GOPT GuessOption} + +<>= +)set break resume +)sys rm -f GuessOption.output +)spool GuessOption.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show GuessOption +--R GuessOption is a domain constructor +--R Abbreviation for GuessOption is GOPT +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for GOPT +--R +--R------------------------------- Operations -------------------------------- +--R ?=? : (%,%) -> Boolean allDegrees : Boolean -> % +--R checkOptions : List % -> Void coerce : % -> OutputForm +--R debug : Boolean -> % displayAsGF : Boolean -> % +--R functionName : Symbol -> % hash : % -> SingleInteger +--R homogeneous : Boolean -> % indexName : Symbol -> % +--R latex : % -> String maxDegree : Integer -> % +--R maxDerivative : Integer -> % maxLevel : Integer -> % +--R maxPower : Integer -> % maxShift : Integer -> % +--R one : Boolean -> % safety : NonNegativeInteger -> % +--R variableName : Symbol -> % ?~=? : (%,%) -> Boolean +--R option : (List %,Symbol) -> Union(Any,"failed") +--R option? : (List %,Symbol) -> Boolean +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +GuessOption examples +==================================================================== + +See Also: +o )show GuessOption + +@ + \pagehead{GuessOption}{GOPT} \pagepic{ps/v103guessoption.ps}{GOPT}{1.00} @@ -42842,6 +50629,111 @@ GuessOption(): Exports == Implementation where \chapter{Chapter H} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain HASHTBL HashTable} + +<>= +)set break resume +)sys rm -f HashTable.output +)spool HashTable.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show HashTable +--R HashTable(Key: SetCategory,Entry: SetCategory,hashfn: String) is a domain constructor +--R Abbreviation for HashTable is HASHTBL +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for HASHTBL +--R +--R------------------------------- Operations -------------------------------- +--R copy : % -> % dictionary : () -> % +--R elt : (%,Key,Entry) -> Entry ?.? : (%,Key) -> Entry +--R empty : () -> % empty? : % -> Boolean +--R entries : % -> List Entry eq? : (%,%) -> Boolean +--R index? : (Key,%) -> Boolean indices : % -> List Key +--R key? : (Key,%) -> Boolean keys : % -> List Key +--R map : ((Entry -> Entry),%) -> % qelt : (%,Key) -> Entry +--R sample : () -> % setelt : (%,Key,Entry) -> Entry +--R table : () -> % +--R #? : % -> NonNegativeInteger if $ has finiteAggregate +--R ?=? : (%,%) -> Boolean if Record(key: Key,entry: Entry) has SETCAT or Entry has SETCAT +--R any? : ((Entry -> Boolean),%) -> Boolean if $ has finiteAggregate +--R any? : ((Record(key: Key,entry: Entry) -> Boolean),%) -> Boolean if $ has finiteAggregate +--R bag : List Record(key: Key,entry: Entry) -> % +--R coerce : % -> OutputForm if Record(key: Key,entry: Entry) has SETCAT or Entry has SETCAT +--R construct : List Record(key: Key,entry: Entry) -> % +--R convert : % -> InputForm if Record(key: Key,entry: Entry) has KONVERT INFORM +--R count : ((Entry -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate +--R count : (Entry,%) -> NonNegativeInteger if $ has finiteAggregate and Entry has SETCAT +--R count : (Record(key: Key,entry: Entry),%) -> NonNegativeInteger if $ has finiteAggregate and Record(key: Key,entry: Entry) has SETCAT +--R count : ((Record(key: Key,entry: Entry) -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate +--R dictionary : List Record(key: Key,entry: Entry) -> % +--R entry? : (Entry,%) -> Boolean if $ has finiteAggregate and Entry has SETCAT +--R eval : (%,List Equation Entry) -> % if Entry has EVALAB Entry and Entry has SETCAT +--R eval : (%,Equation Entry) -> % if Entry has EVALAB Entry and Entry has SETCAT +--R eval : (%,Entry,Entry) -> % if Entry has EVALAB Entry and Entry has SETCAT +--R eval : (%,List Entry,List Entry) -> % if Entry has EVALAB Entry and Entry has SETCAT +--R eval : (%,List Record(key: Key,entry: Entry),List Record(key: Key,entry: Entry)) -> % if Record(key: Key,entry: Entry) has EVALAB Record(key: Key,entry: Entry) and Record(key: Key,entry: Entry) has SETCAT +--R eval : (%,Record(key: Key,entry: Entry),Record(key: Key,entry: Entry)) -> % if Record(key: Key,entry: Entry) has EVALAB Record(key: Key,entry: Entry) and Record(key: Key,entry: Entry) has SETCAT +--R eval : (%,Equation Record(key: Key,entry: Entry)) -> % if Record(key: Key,entry: Entry) has EVALAB Record(key: Key,entry: Entry) and Record(key: Key,entry: Entry) has SETCAT +--R eval : (%,List Equation Record(key: Key,entry: Entry)) -> % if Record(key: Key,entry: Entry) has EVALAB Record(key: Key,entry: Entry) and Record(key: Key,entry: Entry) has SETCAT +--R every? : ((Entry -> Boolean),%) -> Boolean if $ has finiteAggregate +--R every? : ((Record(key: Key,entry: Entry) -> Boolean),%) -> Boolean if $ has finiteAggregate +--R extract! : % -> Record(key: Key,entry: Entry) +--R fill! : (%,Entry) -> % if $ has shallowlyMutable +--R find : ((Record(key: Key,entry: Entry) -> Boolean),%) -> Union(Record(key: Key,entry: Entry),"failed") +--R first : % -> Entry if Key has ORDSET +--R hash : % -> SingleInteger if Record(key: Key,entry: Entry) has SETCAT or Entry has SETCAT +--R insert! : (Record(key: Key,entry: Entry),%) -> % +--R inspect : % -> Record(key: Key,entry: Entry) +--R latex : % -> String if Record(key: Key,entry: Entry) has SETCAT or Entry has SETCAT +--R less? : (%,NonNegativeInteger) -> Boolean +--R map : (((Entry,Entry) -> Entry),%,%) -> % +--R map : ((Record(key: Key,entry: Entry) -> Record(key: Key,entry: Entry)),%) -> % +--R map! : ((Entry -> Entry),%) -> % if $ has shallowlyMutable +--R map! : ((Record(key: Key,entry: Entry) -> Record(key: Key,entry: Entry)),%) -> % if $ has shallowlyMutable +--R maxIndex : % -> Key if Key has ORDSET +--R member? : (Entry,%) -> Boolean if $ has finiteAggregate and Entry has SETCAT +--R member? : (Record(key: Key,entry: Entry),%) -> Boolean if $ has finiteAggregate and Record(key: Key,entry: Entry) has SETCAT +--R members : % -> List Entry if $ has finiteAggregate +--R members : % -> List Record(key: Key,entry: Entry) if $ has finiteAggregate +--R minIndex : % -> Key if Key has ORDSET +--R more? : (%,NonNegativeInteger) -> Boolean +--R parts : % -> List Entry if $ has finiteAggregate +--R parts : % -> List Record(key: Key,entry: Entry) if $ has finiteAggregate +--R qsetelt! : (%,Key,Entry) -> Entry if $ has shallowlyMutable +--R reduce : (((Record(key: Key,entry: Entry),Record(key: Key,entry: Entry)) -> Record(key: Key,entry: Entry)),%) -> Record(key: Key,entry: Entry) if $ has finiteAggregate +--R reduce : (((Record(key: Key,entry: Entry),Record(key: Key,entry: Entry)) -> Record(key: Key,entry: Entry)),%,Record(key: Key,entry: Entry)) -> Record(key: Key,entry: Entry) if $ has finiteAggregate +--R reduce : (((Record(key: Key,entry: Entry),Record(key: Key,entry: Entry)) -> Record(key: Key,entry: Entry)),%,Record(key: Key,entry: Entry),Record(key: Key,entry: Entry)) -> Record(key: Key,entry: Entry) if $ has finiteAggregate and Record(key: Key,entry: Entry) has SETCAT +--R remove : ((Record(key: Key,entry: Entry) -> Boolean),%) -> % if $ has finiteAggregate +--R remove : (Record(key: Key,entry: Entry),%) -> % if $ has finiteAggregate and Record(key: Key,entry: Entry) has SETCAT +--R remove! : (Key,%) -> Union(Entry,"failed") +--R remove! : ((Record(key: Key,entry: Entry) -> Boolean),%) -> % if $ has finiteAggregate +--R remove! : (Record(key: Key,entry: Entry),%) -> % if $ has finiteAggregate +--R removeDuplicates : % -> % if $ has finiteAggregate and Record(key: Key,entry: Entry) has SETCAT +--R search : (Key,%) -> Union(Entry,"failed") +--R select : ((Record(key: Key,entry: Entry) -> Boolean),%) -> % if $ has finiteAggregate +--R select! : ((Record(key: Key,entry: Entry) -> Boolean),%) -> % if $ has finiteAggregate +--R size? : (%,NonNegativeInteger) -> Boolean +--R swap! : (%,Key,Key) -> Void if $ has shallowlyMutable +--R table : List Record(key: Key,entry: Entry) -> % +--R ?~=? : (%,%) -> Boolean if Record(key: Key,entry: Entry) has SETCAT or Entry has SETCAT +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +HashTable examples +==================================================================== + +See Also: +o )show HashTable + +@ + \pagehead{HashTable}{HASHTBL} \pagepic{ps/v103hashtable.ps}{HASHTBL}{1.00} {\bf See}\\ @@ -42969,6 +50861,7 @@ HashTable(Key, Entry, hashfn): Exports == Implementation where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain HEAP Heap} + <>= )set break resume )sys rm -f Heap.output @@ -43841,6 +51734,7 @@ Heap(S:OrderedSet): Exports == Implementation where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain HEXADEC HexadecimalExpansion} + <>= )set break resume )sys rm -f HexadecimalExpansion.output @@ -44117,6 +52011,142 @@ HexadecimalExpansion(): Exports == Implementation where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain HDP HomogeneousDirectProduct} + +<>= +)set break resume +)sys rm -f HomogeneousDirectProduct.output +)spool HomogeneousDirectProduct.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show HomogeneousDirectProduct +--R HomogeneousDirectProduct(dim: NonNegativeInteger,S: OrderedAbelianMonoidSup) is a domain constructor +--R Abbreviation for HomogeneousDirectProduct is HDP +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for HDP +--R +--R------------------------------- Operations -------------------------------- +--R -? : % -> % if S has RING 1 : () -> % if S has MONOID +--R 0 : () -> % if S has CABMON coerce : % -> Vector S +--R copy : % -> % directProduct : Vector S -> % +--R ?.? : (%,Integer) -> S elt : (%,Integer,S) -> S +--R empty : () -> % empty? : % -> Boolean +--R entries : % -> List S eq? : (%,%) -> Boolean +--R index? : (Integer,%) -> Boolean indices : % -> List Integer +--R map : ((S -> S),%) -> % qelt : (%,Integer) -> S +--R sample : () -> % +--R #? : % -> NonNegativeInteger if $ has finiteAggregate +--R ?*? : (PositiveInteger,%) -> % if S has ABELSG +--R ?*? : (NonNegativeInteger,%) -> % if S has CABMON +--R ?*? : (S,%) -> % if S has RING +--R ?*? : (%,S) -> % if S has RING +--R ?*? : (%,%) -> % if S has MONOID +--R ?*? : (Integer,%) -> % if S has RING +--R ?**? : (%,PositiveInteger) -> % if S has MONOID +--R ?**? : (%,NonNegativeInteger) -> % if S has MONOID +--R ?+? : (%,%) -> % if S has ABELSG +--R ?-? : (%,%) -> % if S has RING +--R ?/? : (%,S) -> % if S has FIELD +--R ? Boolean if S has OAMONS or S has ORDRING +--R ?<=? : (%,%) -> Boolean if S has OAMONS or S has ORDRING +--R ?=? : (%,%) -> Boolean if S has SETCAT +--R ?>? : (%,%) -> Boolean if S has OAMONS or S has ORDRING +--R ?>=? : (%,%) -> Boolean if S has OAMONS or S has ORDRING +--R D : (%,(S -> S)) -> % if S has RING +--R D : (%,(S -> S),NonNegativeInteger) -> % if S has RING +--R D : (%,List Symbol,List NonNegativeInteger) -> % if S has PDRING SYMBOL and S has RING +--R D : (%,Symbol,NonNegativeInteger) -> % if S has PDRING SYMBOL and S has RING +--R D : (%,List Symbol) -> % if S has PDRING SYMBOL and S has RING +--R D : (%,Symbol) -> % if S has PDRING SYMBOL and S has RING +--R D : (%,NonNegativeInteger) -> % if S has DIFRING and S has RING +--R D : % -> % if S has DIFRING and S has RING +--R ?^? : (%,PositiveInteger) -> % if S has MONOID +--R ?^? : (%,NonNegativeInteger) -> % if S has MONOID +--R abs : % -> % if S has ORDRING +--R any? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate +--R characteristic : () -> NonNegativeInteger if S has RING +--R coerce : S -> % if S has SETCAT +--R coerce : Fraction Integer -> % if S has RETRACT FRAC INT and S has SETCAT +--R coerce : Integer -> % if S has RETRACT INT and S has SETCAT or S has RING +--R coerce : % -> OutputForm if S has SETCAT +--R count : (S,%) -> NonNegativeInteger if $ has finiteAggregate and S has SETCAT +--R count : ((S -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate +--R differentiate : (%,(S -> S)) -> % if S has RING +--R differentiate : (%,(S -> S),NonNegativeInteger) -> % if S has RING +--R differentiate : (%,List Symbol,List NonNegativeInteger) -> % if S has PDRING SYMBOL and S has RING +--R differentiate : (%,Symbol,NonNegativeInteger) -> % if S has PDRING SYMBOL and S has RING +--R differentiate : (%,List Symbol) -> % if S has PDRING SYMBOL and S has RING +--R differentiate : (%,Symbol) -> % if S has PDRING SYMBOL and S has RING +--R differentiate : (%,NonNegativeInteger) -> % if S has DIFRING and S has RING +--R differentiate : % -> % if S has DIFRING and S has RING +--R dimension : () -> CardinalNumber if S has FIELD +--R dot : (%,%) -> S if S has RING +--R entry? : (S,%) -> Boolean if $ has finiteAggregate and S has SETCAT +--R eval : (%,List S,List S) -> % if S has EVALAB S and S has SETCAT +--R eval : (%,S,S) -> % if S has EVALAB S and S has SETCAT +--R eval : (%,Equation S) -> % if S has EVALAB S and S has SETCAT +--R eval : (%,List Equation S) -> % if S has EVALAB S and S has SETCAT +--R every? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate +--R fill! : (%,S) -> % if $ has shallowlyMutable +--R first : % -> S if Integer has ORDSET +--R hash : % -> SingleInteger if S has SETCAT +--R index : PositiveInteger -> % if S has FINITE +--R latex : % -> String if S has SETCAT +--R less? : (%,NonNegativeInteger) -> Boolean +--R lookup : % -> PositiveInteger if S has FINITE +--R map! : ((S -> S),%) -> % if $ has shallowlyMutable +--R max : (%,%) -> % if S has OAMONS or S has ORDRING +--R maxIndex : % -> Integer if Integer has ORDSET +--R member? : (S,%) -> Boolean if $ has finiteAggregate and S has SETCAT +--R members : % -> List S if $ has finiteAggregate +--R min : (%,%) -> % if S has OAMONS or S has ORDRING +--R minIndex : % -> Integer if Integer has ORDSET +--R more? : (%,NonNegativeInteger) -> Boolean +--R negative? : % -> Boolean if S has ORDRING +--R one? : % -> Boolean if S has MONOID +--R parts : % -> List S if $ has finiteAggregate +--R positive? : % -> Boolean if S has ORDRING +--R qsetelt! : (%,Integer,S) -> S if $ has shallowlyMutable +--R random : () -> % if S has FINITE +--R recip : % -> Union(%,"failed") if S has MONOID +--R reducedSystem : Matrix % -> Matrix S if S has RING +--R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix S,vec: Vector S) if S has RING +--R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix Integer,vec: Vector Integer) if S has LINEXP INT and S has RING +--R reducedSystem : Matrix % -> Matrix Integer if S has LINEXP INT and S has RING +--R retract : % -> S if S has SETCAT +--R retract : % -> Fraction Integer if S has RETRACT FRAC INT and S has SETCAT +--R retract : % -> Integer if S has RETRACT INT and S has SETCAT +--R retractIfCan : % -> Union(S,"failed") if S has SETCAT +--R retractIfCan : % -> Union(Fraction Integer,"failed") if S has RETRACT FRAC INT and S has SETCAT +--R retractIfCan : % -> Union(Integer,"failed") if S has RETRACT INT and S has SETCAT +--R setelt : (%,Integer,S) -> S if $ has shallowlyMutable +--R sign : % -> Integer if S has ORDRING +--R size : () -> NonNegativeInteger if S has FINITE +--R size? : (%,NonNegativeInteger) -> Boolean +--R subtractIfCan : (%,%) -> Union(%,"failed") if S has CABMON +--R sup : (%,%) -> % if S has OAMONS +--R swap! : (%,Integer,Integer) -> Void if $ has shallowlyMutable +--R unitVector : PositiveInteger -> % if S has RING +--R zero? : % -> Boolean if S has CABMON +--R ?~=? : (%,%) -> Boolean if S has SETCAT +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +HomogeneousDirectProduct examples +==================================================================== + +See Also: +o )show HomogeneousDirectProduct + +@ + \pagehead{HomogeneousDirectProduct}{HDP} \pagepic{ps/v103homogeneousdirectproduct.ps}{HDP}{1.00} {\bf See}\\ @@ -44250,6 +52280,7 @@ HomogeneousDirectProduct(dim,S) : T == C where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain HDMP HomogeneousDistributedMultivariatePolynomial} + <>= )set break resume )sys rm -f HomogeneousDistributedMultivariatePolynomial.output @@ -44600,6 +52631,55 @@ HomogeneousDistributedMultivariatePolynomial(vl,R): public == private where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain HELLFDIV HyperellipticFiniteDivisor} + +<>= +)set break resume +)sys rm -f HyperellipticFiniteDivisor.output +)spool HyperellipticFiniteDivisor.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show HyperellipticFiniteDivisor +--R HyperellipticFiniteDivisor(F: Field,UP: UnivariatePolynomialCategory F,UPUP: UnivariatePolynomialCategory Fraction UP,R: FunctionFieldCategory(F,UP,UPUP)) is a domain constructor +--R Abbreviation for HyperellipticFiniteDivisor is HELLFDIV +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for HELLFDIV +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (Integer,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ?=? : (%,%) -> Boolean +--R 0 : () -> % coerce : % -> OutputForm +--R divisor : (R,UP,UP,UP,F) -> % divisor : (F,F,Integer) -> % +--R divisor : (F,F) -> % divisor : R -> % +--R hash : % -> SingleInteger latex : % -> String +--R principal? : % -> Boolean reduce : % -> % +--R sample : () -> % zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean +--R ?*? : (NonNegativeInteger,%) -> % +--R decompose : % -> Record(id: FractionalIdeal(UP,Fraction UP,UPUP,R),principalPart: R) +--R divisor : FractionalIdeal(UP,Fraction UP,UPUP,R) -> % +--R generator : % -> Union(R,"failed") +--R ideal : % -> FractionalIdeal(UP,Fraction UP,UPUP,R) +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +HyperellipticFiniteDivisor examples +==================================================================== + +See Also: +o )show HyperellipticFiniteDivisor + +@ + \pagehead{HyperellipticFiniteDivisor}{HELLFDIV} \pagepic{ps/v103hyperellipticfinitedivisor.ps}{HELLFDIV}{1.00} {\bf See}\\ @@ -44807,6 +52887,7 @@ HyperellipticFiniteDivisor(F, UP, UPUP, R): Exports == Implementation where \chapter{Chapter I} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain ICP InfClsPt} + <>= )set break resume )sys rm -f InfClsPt.output @@ -44943,6 +53024,47 @@ InfClsPt(K,symb,BLMET):Exports == Implementation where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain ICARD IndexCard} + +<>= +)set break resume +)sys rm -f IndexCard.output +)spool IndexCard.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show IndexCard +--R IndexCard is a domain constructor +--R Abbreviation for IndexCard is ICARD +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for ICARD +--R +--R------------------------------- Operations -------------------------------- +--R ? Boolean ?<=? : (%,%) -> Boolean +--R ?=? : (%,%) -> Boolean ?>? : (%,%) -> Boolean +--R ?>=? : (%,%) -> Boolean coerce : String -> % +--R coerce : % -> OutputForm display : % -> Void +--R ?.? : (%,Symbol) -> String fullDisplay : % -> Void +--R hash : % -> SingleInteger latex : % -> String +--R max : (%,%) -> % min : (%,%) -> % +--R ?~=? : (%,%) -> Boolean +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +IndexCard examples +==================================================================== + +See Also: +o )show IndexCard + +@ + \pagehead{IndexCard}{ICARD} \pagepic{ps/v103indexcard.ps}{ICARD}{1.00} {\bf See}\\ @@ -45036,6 +53158,7 @@ IndexCard() : Exports == Implementation where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain IBITS IndexedBits} + <>= )set break resume )sys rm -f IndexedBits.output @@ -45352,6 +53475,50 @@ IndexedBits(mn:Integer): BitAggregate() with @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain IDPAG IndexedDirectProductAbelianGroup} + +<>= +)set break resume +)sys rm -f IndexedDirectProductAbelianGroup.output +)spool IndexedDirectProductAbelianGroup.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show IndexedDirectProductAbelianGroup +--R IndexedDirectProductAbelianGroup(A: AbelianGroup,S: OrderedSet) is a domain constructor +--R Abbreviation for IndexedDirectProductAbelianGroup is IDPAG +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for IDPAG +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (Integer,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ?=? : (%,%) -> Boolean +--R 0 : () -> % coerce : % -> OutputForm +--R hash : % -> SingleInteger latex : % -> String +--R leadingCoefficient : % -> A leadingSupport : % -> S +--R map : ((A -> A),%) -> % monomial : (A,S) -> % +--R reductum : % -> % sample : () -> % +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean +--R ?*? : (NonNegativeInteger,%) -> % +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +IndexedDirectProductAbelianGroup examples +==================================================================== + +See Also: +o )show IndexedDirectProductAbelianGroup + +@ + \pagehead{IndexedDirectProductAbelianGroup}{IDPAG} \pagepic{ps/v103indexeddirectproductabeliangroup.ps}{IDPAG}{1.00} {\bf See}\\ @@ -45462,6 +53629,48 @@ IndexedDirectProductAbelianGroup(A:AbelianGroup,S:OrderedSet): @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain IDPAM IndexedDirectProductAbelianMonoid} + +<>= +)set break resume +)sys rm -f IndexedDirectProductAbelianMonoid.output +)spool IndexedDirectProductAbelianMonoid.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show IndexedDirectProductAbelianMonoid +--R IndexedDirectProductAbelianMonoid(A: AbelianMonoid,S: OrderedSet) is a domain constructor +--R Abbreviation for IndexedDirectProductAbelianMonoid is IDPAM +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for IDPAM +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (PositiveInteger,%) -> % ?+? : (%,%) -> % +--R ?=? : (%,%) -> Boolean 0 : () -> % +--R coerce : % -> OutputForm hash : % -> SingleInteger +--R latex : % -> String leadingCoefficient : % -> A +--R leadingSupport : % -> S map : ((A -> A),%) -> % +--R monomial : (A,S) -> % reductum : % -> % +--R sample : () -> % zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean +--R ?*? : (NonNegativeInteger,%) -> % +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +IndexedDirectProductAbelianMonoid examples +==================================================================== + +See Also: +o )show IndexedDirectProductAbelianMonoid + +@ + \pagehead{IndexedDirectProductAbelianMonoid}{IDPAM} \pagepic{ps/v103indexeddirectproductabelianmonoid.ps}{IDPAM}{1.00} {\bf See}\\ @@ -45580,6 +53789,44 @@ IndexedDirectProductAbelianMonoid(A:AbelianMonoid,S:OrderedSet): @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain IDPO IndexedDirectProductObject} + +<>= +)set break resume +)sys rm -f IndexedDirectProductObject.output +)spool IndexedDirectProductObject.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show IndexedDirectProductObject +--R IndexedDirectProductObject(A: SetCategory,S: OrderedSet) is a domain constructor +--R Abbreviation for IndexedDirectProductObject is IDPO +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for IDPO +--R +--R------------------------------- Operations -------------------------------- +--R ?=? : (%,%) -> Boolean coerce : % -> OutputForm +--R hash : % -> SingleInteger latex : % -> String +--R leadingCoefficient : % -> A leadingSupport : % -> S +--R map : ((A -> A),%) -> % monomial : (A,S) -> % +--R reductum : % -> % ?~=? : (%,%) -> Boolean +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +IndexedDirectProductObject examples +==================================================================== + +See Also: +o )show IndexedDirectProductObject + +@ + \pagehead{IndexedDirectProductObject}{IDPO} \pagepic{ps/v103indexeddirectproductobject.ps}{IDPO}{1.00} {\bf See}\\ @@ -45656,6 +53903,51 @@ IndexedDirectProductObject(A:SetCategory,S:OrderedSet): _ @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain IDPOAM IndexedDirectProductOrderedAbelianMonoid} + +<>= +)set break resume +)sys rm -f IndexedDirectProductOrderedAbelianMonoid.output +)spool IndexedDirectProductOrderedAbelianMonoid.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show IndexedDirectProductOrderedAbelianMonoid +--R IndexedDirectProductOrderedAbelianMonoid(A: OrderedAbelianMonoid,S: OrderedSet) is a domain constructor +--R Abbreviation for IndexedDirectProductOrderedAbelianMonoid is IDPOAM +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for IDPOAM +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (PositiveInteger,%) -> % ?+? : (%,%) -> % +--R ? Boolean ?<=? : (%,%) -> Boolean +--R ?=? : (%,%) -> Boolean ?>? : (%,%) -> Boolean +--R ?>=? : (%,%) -> Boolean 0 : () -> % +--R coerce : % -> OutputForm hash : % -> SingleInteger +--R latex : % -> String leadingCoefficient : % -> A +--R leadingSupport : % -> S map : ((A -> A),%) -> % +--R max : (%,%) -> % min : (%,%) -> % +--R monomial : (A,S) -> % reductum : % -> % +--R sample : () -> % zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean +--R ?*? : (NonNegativeInteger,%) -> % +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +IndexedDirectProductOrderedAbelianMonoid examples +==================================================================== + +See Also: +o )show IndexedDirectProductOrderedAbelianMonoid + +@ + \pagehead{IndexedDirectProductOrderedAbelianMonoid}{IDPOAM} \pagepic{ps/v103indexeddirectproductorderedabelianmonoid.ps}{IDPOAM}{1.00} {\bf See}\\ @@ -45723,6 +54015,52 @@ IndexedDirectProductOrderedAbelianMonoid(A:OrderedAbelianMonoid,S:OrderedSet): @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain IDPOAMS IndexedDirectProductOrderedAbelianMonoidSup} + +<>= +)set break resume +)sys rm -f IndexedDirectProductOrderedAbelianMonoidSup.output +)spool IndexedDirectProductOrderedAbelianMonoidSup.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show IndexedDirectProductOrderedAbelianMonoidSup +--R IndexedDirectProductOrderedAbelianMonoidSup(A: OrderedAbelianMonoidSup,S: OrderedSet) is a domain constructor +--R Abbreviation for IndexedDirectProductOrderedAbelianMonoidSup is IDPOAMS +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for IDPOAMS +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (PositiveInteger,%) -> % ?+? : (%,%) -> % +--R ? Boolean ?<=? : (%,%) -> Boolean +--R ?=? : (%,%) -> Boolean ?>? : (%,%) -> Boolean +--R ?>=? : (%,%) -> Boolean 0 : () -> % +--R coerce : % -> OutputForm hash : % -> SingleInteger +--R latex : % -> String leadingCoefficient : % -> A +--R leadingSupport : % -> S map : ((A -> A),%) -> % +--R max : (%,%) -> % min : (%,%) -> % +--R monomial : (A,S) -> % reductum : % -> % +--R sample : () -> % sup : (%,%) -> % +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean +--R ?*? : (NonNegativeInteger,%) -> % +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +IndexedDirectProductOrderedAbelianMonoidSup examples +==================================================================== + +See Also: +o )show IndexedDirectProductOrderedAbelianMonoidSup + +@ + \pagehead{IndexedDirectProductOrderedAbelianMonoidSup}{IDPOAMS} \pagepic{ps/v103indexeddirectproductorderedabelianmonoidsup.ps}{IDPOAMS}{1.00} {\bf See}\\ @@ -45808,6 +54146,54 @@ IndexedDirectProductOrderedAbelianMonoidSup(A:OrderedAbelianMonoidSup,S:OrderedS @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain INDE IndexedExponents} + +<>= +)set break resume +)sys rm -f IndexedExponents.output +)spool IndexedExponents.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show IndexedExponents +--R IndexedExponents Varset: OrderedSet is a domain constructor +--R Abbreviation for IndexedExponents is INDE +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for INDE +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (PositiveInteger,%) -> % ?+? : (%,%) -> % +--R ? Boolean ?<=? : (%,%) -> Boolean +--R ?=? : (%,%) -> Boolean ?>? : (%,%) -> Boolean +--R ?>=? : (%,%) -> Boolean 0 : () -> % +--R coerce : % -> OutputForm hash : % -> SingleInteger +--R latex : % -> String leadingSupport : % -> Varset +--R max : (%,%) -> % min : (%,%) -> % +--R reductum : % -> % sample : () -> % +--R sup : (%,%) -> % zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean +--R ?*? : (NonNegativeInteger,%) -> % +--R leadingCoefficient : % -> NonNegativeInteger +--R map : ((NonNegativeInteger -> NonNegativeInteger),%) -> % +--R monomial : (NonNegativeInteger,Varset) -> % +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +IndexedExponents examples +==================================================================== + +See Also: +o )show IndexedExponents + +@ + \pagehead{IndexedExponents}{INDE} \pagepic{ps/v103indexedexponents.ps}{INDE}{1.00} {\bf See}\\ @@ -45883,6 +54269,123 @@ IndexedExponents(Varset:OrderedSet): C == T where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain IFARRAY IndexedFlexibleArray} + +<>= +)set break resume +)sys rm -f IndexedFlexibleArray.output +)spool IndexedFlexibleArray.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show IndexedFlexibleArray +--R IndexedFlexibleArray(S: Type,mn: Integer) is a domain constructor +--R Abbreviation for IndexedFlexibleArray is IFARRAY +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for IFARRAY +--R +--R------------------------------- Operations -------------------------------- +--R concat : List % -> % concat : (%,%) -> % +--R concat : (S,%) -> % concat : (%,S) -> % +--R concat! : (%,S) -> % concat! : (%,%) -> % +--R construct : List S -> % copy : % -> % +--R delete : (%,Integer) -> % delete! : (%,Integer) -> % +--R ?.? : (%,Integer) -> S elt : (%,Integer,S) -> S +--R empty : () -> % empty? : % -> Boolean +--R entries : % -> List S eq? : (%,%) -> Boolean +--R flexibleArray : List S -> % index? : (Integer,%) -> Boolean +--R indices : % -> List Integer insert : (%,%,Integer) -> % +--R insert : (S,%,Integer) -> % insert! : (S,%,Integer) -> % +--R insert! : (%,%,Integer) -> % map : (((S,S) -> S),%,%) -> % +--R map : ((S -> S),%) -> % new : (NonNegativeInteger,S) -> % +--R qelt : (%,Integer) -> S reverse : % -> % +--R sample : () -> % shrinkable : Boolean -> Boolean +--R #? : % -> NonNegativeInteger if $ has finiteAggregate +--R ? Boolean if S has ORDSET +--R ?<=? : (%,%) -> Boolean if S has ORDSET +--R ?=? : (%,%) -> Boolean if S has SETCAT +--R ?>? : (%,%) -> Boolean if S has ORDSET +--R ?>=? : (%,%) -> Boolean if S has ORDSET +--R any? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate +--R coerce : % -> OutputForm if S has SETCAT +--R convert : % -> InputForm if S has KONVERT INFORM +--R copyInto! : (%,%,Integer) -> % if $ has shallowlyMutable +--R count : (S,%) -> NonNegativeInteger if $ has finiteAggregate and S has SETCAT +--R count : ((S -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate +--R delete : (%,UniversalSegment Integer) -> % +--R delete! : (%,UniversalSegment Integer) -> % +--R ?.? : (%,UniversalSegment Integer) -> % +--R entry? : (S,%) -> Boolean if $ has finiteAggregate and S has SETCAT +--R eval : (%,List S,List S) -> % if S has EVALAB S and S has SETCAT +--R eval : (%,S,S) -> % if S has EVALAB S and S has SETCAT +--R eval : (%,Equation S) -> % if S has EVALAB S and S has SETCAT +--R eval : (%,List Equation S) -> % if S has EVALAB S and S has SETCAT +--R every? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate +--R fill! : (%,S) -> % if $ has shallowlyMutable +--R find : ((S -> Boolean),%) -> Union(S,"failed") +--R first : % -> S if Integer has ORDSET +--R hash : % -> SingleInteger if S has SETCAT +--R latex : % -> String if S has SETCAT +--R less? : (%,NonNegativeInteger) -> Boolean +--R map! : ((S -> S),%) -> % if $ has shallowlyMutable +--R max : (%,%) -> % if S has ORDSET +--R maxIndex : % -> Integer if Integer has ORDSET +--R member? : (S,%) -> Boolean if $ has finiteAggregate and S has SETCAT +--R members : % -> List S if $ has finiteAggregate +--R merge : (%,%) -> % if S has ORDSET +--R merge : (((S,S) -> Boolean),%,%) -> % +--R merge! : (((S,S) -> Boolean),%,%) -> % +--R merge! : (%,%) -> % if S has ORDSET +--R min : (%,%) -> % if S has ORDSET +--R minIndex : % -> Integer if Integer has ORDSET +--R more? : (%,NonNegativeInteger) -> Boolean +--R parts : % -> List S if $ has finiteAggregate +--R physicalLength : % -> NonNegativeInteger +--R physicalLength! : (%,Integer) -> % +--R position : (S,%,Integer) -> Integer if S has SETCAT +--R position : (S,%) -> Integer if S has SETCAT +--R position : ((S -> Boolean),%) -> Integer +--R qsetelt! : (%,Integer,S) -> S if $ has shallowlyMutable +--R reduce : (((S,S) -> S),%) -> S if $ has finiteAggregate +--R reduce : (((S,S) -> S),%,S) -> S if $ has finiteAggregate +--R reduce : (((S,S) -> S),%,S,S) -> S if $ has finiteAggregate and S has SETCAT +--R remove : ((S -> Boolean),%) -> % if $ has finiteAggregate +--R remove : (S,%) -> % if $ has finiteAggregate and S has SETCAT +--R remove! : ((S -> Boolean),%) -> % +--R remove! : (S,%) -> % if S has SETCAT +--R removeDuplicates : % -> % if $ has finiteAggregate and S has SETCAT +--R removeDuplicates! : % -> % if S has SETCAT +--R reverse! : % -> % if $ has shallowlyMutable +--R select : ((S -> Boolean),%) -> % if $ has finiteAggregate +--R select! : ((S -> Boolean),%) -> % +--R setelt : (%,UniversalSegment Integer,S) -> S if $ has shallowlyMutable +--R setelt : (%,Integer,S) -> S if $ has shallowlyMutable +--R size? : (%,NonNegativeInteger) -> Boolean +--R sort : % -> % if S has ORDSET +--R sort : (((S,S) -> Boolean),%) -> % +--R sort! : % -> % if $ has shallowlyMutable and S has ORDSET +--R sort! : (((S,S) -> Boolean),%) -> % if $ has shallowlyMutable +--R sorted? : % -> Boolean if S has ORDSET +--R sorted? : (((S,S) -> Boolean),%) -> Boolean +--R swap! : (%,Integer,Integer) -> Void if $ has shallowlyMutable +--R ?~=? : (%,%) -> Boolean if S has SETCAT +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +IndexedFlexibleArray examples +==================================================================== + +See Also: +o )show IndexedFlexibleArray + +@ + \pagehead{IndexedFlexibleArray}{IFARRAY} \pagepic{ps/v103indexedflexiblearray.ps}{IFARRAY}{1.00} {\bf See}\\ @@ -46214,6 +54717,147 @@ IndexedFlexibleArray(S:Type, mn: Integer): Exports == Implementation where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain ILIST IndexedList} + +<>= +)set break resume +)sys rm -f IndexedList.output +)spool IndexedList.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show IndexedList +--R IndexedList(S: Type,mn: Integer) is a domain constructor +--R Abbreviation for IndexedList is ILIST +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for ILIST +--R +--R------------------------------- Operations -------------------------------- +--R children : % -> List % concat : (%,S) -> % +--R concat : List % -> % concat : (S,%) -> % +--R concat : (%,%) -> % concat! : (%,S) -> % +--R concat! : (%,%) -> % construct : List S -> % +--R copy : % -> % cycleEntry : % -> % +--R cycleTail : % -> % cyclic? : % -> Boolean +--R delete : (%,Integer) -> % delete! : (%,Integer) -> % +--R distance : (%,%) -> Integer elt : (%,Integer,S) -> S +--R ?.? : (%,Integer) -> S ?.last : (%,last) -> S +--R ?.rest : (%,rest) -> % ?.first : (%,first) -> S +--R ?.value : (%,value) -> S empty : () -> % +--R empty? : % -> Boolean entries : % -> List S +--R eq? : (%,%) -> Boolean explicitlyFinite? : % -> Boolean +--R first : % -> S index? : (Integer,%) -> Boolean +--R indices : % -> List Integer insert : (S,%,Integer) -> % +--R insert : (%,%,Integer) -> % insert! : (S,%,Integer) -> % +--R insert! : (%,%,Integer) -> % last : % -> S +--R leaf? : % -> Boolean leaves : % -> List S +--R list : S -> % map : (((S,S) -> S),%,%) -> % +--R map : ((S -> S),%) -> % new : (NonNegativeInteger,S) -> % +--R nodes : % -> List % possiblyInfinite? : % -> Boolean +--R qelt : (%,Integer) -> S rest : % -> % +--R reverse : % -> % sample : () -> % +--R second : % -> S tail : % -> % +--R third : % -> S value : % -> S +--R #? : % -> NonNegativeInteger if $ has finiteAggregate +--R ? Boolean if S has ORDSET +--R ?<=? : (%,%) -> Boolean if S has ORDSET +--R ?=? : (%,%) -> Boolean if S has SETCAT +--R ?>? : (%,%) -> Boolean if S has ORDSET +--R ?>=? : (%,%) -> Boolean if S has ORDSET +--R any? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate +--R child? : (%,%) -> Boolean if S has SETCAT +--R coerce : % -> OutputForm if S has SETCAT +--R convert : % -> InputForm if S has KONVERT INFORM +--R copyInto! : (%,%,Integer) -> % if $ has shallowlyMutable +--R count : (S,%) -> NonNegativeInteger if $ has finiteAggregate and S has SETCAT +--R count : ((S -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate +--R cycleLength : % -> NonNegativeInteger +--R cycleSplit! : % -> % if $ has shallowlyMutable +--R delete : (%,UniversalSegment Integer) -> % +--R delete! : (%,UniversalSegment Integer) -> % +--R ?.? : (%,UniversalSegment Integer) -> % +--R entry? : (S,%) -> Boolean if $ has finiteAggregate and S has SETCAT +--R eval : (%,List S,List S) -> % if S has EVALAB S and S has SETCAT +--R eval : (%,S,S) -> % if S has EVALAB S and S has SETCAT +--R eval : (%,Equation S) -> % if S has EVALAB S and S has SETCAT +--R eval : (%,List Equation S) -> % if S has EVALAB S and S has SETCAT +--R every? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate +--R fill! : (%,S) -> % if $ has shallowlyMutable +--R find : ((S -> Boolean),%) -> Union(S,"failed") +--R first : (%,NonNegativeInteger) -> % +--R hash : % -> SingleInteger if S has SETCAT +--R last : (%,NonNegativeInteger) -> % +--R latex : % -> String if S has SETCAT +--R less? : (%,NonNegativeInteger) -> Boolean +--R map! : ((S -> S),%) -> % if $ has shallowlyMutable +--R max : (%,%) -> % if S has ORDSET +--R maxIndex : % -> Integer if Integer has ORDSET +--R member? : (S,%) -> Boolean if $ has finiteAggregate and S has SETCAT +--R members : % -> List S if $ has finiteAggregate +--R merge : (((S,S) -> Boolean),%,%) -> % +--R merge : (%,%) -> % if S has ORDSET +--R merge! : (((S,S) -> Boolean),%,%) -> % +--R merge! : (%,%) -> % if S has ORDSET +--R min : (%,%) -> % if S has ORDSET +--R minIndex : % -> Integer if Integer has ORDSET +--R more? : (%,NonNegativeInteger) -> Boolean +--R node? : (%,%) -> Boolean if S has SETCAT +--R parts : % -> List S if $ has finiteAggregate +--R position : ((S -> Boolean),%) -> Integer +--R position : (S,%) -> Integer if S has SETCAT +--R position : (S,%,Integer) -> Integer if S has SETCAT +--R qsetelt! : (%,Integer,S) -> S if $ has shallowlyMutable +--R reduce : (((S,S) -> S),%,S,S) -> S if $ has finiteAggregate and S has SETCAT +--R reduce : (((S,S) -> S),%,S) -> S if $ has finiteAggregate +--R reduce : (((S,S) -> S),%) -> S if $ has finiteAggregate +--R remove : (S,%) -> % if $ has finiteAggregate and S has SETCAT +--R remove : ((S -> Boolean),%) -> % if $ has finiteAggregate +--R remove! : ((S -> Boolean),%) -> % +--R remove! : (S,%) -> % if S has SETCAT +--R removeDuplicates : % -> % if $ has finiteAggregate and S has SETCAT +--R removeDuplicates! : % -> % if S has SETCAT +--R rest : (%,NonNegativeInteger) -> % +--R reverse! : % -> % if $ has shallowlyMutable +--R select : ((S -> Boolean),%) -> % if $ has finiteAggregate +--R select! : ((S -> Boolean),%) -> % +--R setchildren! : (%,List %) -> % if $ has shallowlyMutable +--R setelt : (%,Integer,S) -> S if $ has shallowlyMutable +--R setelt : (%,UniversalSegment Integer,S) -> S if $ has shallowlyMutable +--R setelt : (%,last,S) -> S if $ has shallowlyMutable +--R setelt : (%,rest,%) -> % if $ has shallowlyMutable +--R setelt : (%,first,S) -> S if $ has shallowlyMutable +--R setelt : (%,value,S) -> S if $ has shallowlyMutable +--R setfirst! : (%,S) -> S if $ has shallowlyMutable +--R setlast! : (%,S) -> S if $ has shallowlyMutable +--R setrest! : (%,%) -> % if $ has shallowlyMutable +--R setvalue! : (%,S) -> S if $ has shallowlyMutable +--R size? : (%,NonNegativeInteger) -> Boolean +--R sort : (((S,S) -> Boolean),%) -> % +--R sort : % -> % if S has ORDSET +--R sort! : (((S,S) -> Boolean),%) -> % if $ has shallowlyMutable +--R sort! : % -> % if $ has shallowlyMutable and S has ORDSET +--R sorted? : (((S,S) -> Boolean),%) -> Boolean +--R sorted? : % -> Boolean if S has ORDSET +--R split! : (%,Integer) -> % if $ has shallowlyMutable +--R swap! : (%,Integer,Integer) -> Void if $ has shallowlyMutable +--R ?~=? : (%,%) -> Boolean if S has SETCAT +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +IndexedList examples +==================================================================== + +See Also: +o )show IndexedList + +@ + \pagehead{IndexedList}{ILIST} \pagepic{ps/v103indexedlist.ps}{ILIST}{1.00} {\bf See}\\ @@ -46524,6 +55168,110 @@ IndexedList(S:Type, mn:Integer): Exports == Implementation where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain IMATRIX IndexedMatrix} + +<>= +)set break resume +)sys rm -f IndexedMatrix.output +)spool IndexedMatrix.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show IndexedMatrix +--R IndexedMatrix(R: Ring,mnRow: Integer,mnCol: Integer) is a domain constructor +--R Abbreviation for IndexedMatrix is IMATRIX +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for IMATRIX +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (Integer,%) -> % ?*? : (%,R) -> % +--R ?*? : (R,%) -> % ?*? : (%,%) -> % +--R ?+? : (%,%) -> % -? : % -> % +--R ?-? : (%,%) -> % antisymmetric? : % -> Boolean +--R copy : % -> % diagonal? : % -> Boolean +--R diagonalMatrix : List % -> % diagonalMatrix : List R -> % +--R elt : (%,Integer,Integer,R) -> R elt : (%,Integer,Integer) -> R +--R empty : () -> % empty? : % -> Boolean +--R eq? : (%,%) -> Boolean fill! : (%,R) -> % +--R horizConcat : (%,%) -> % listOfLists : % -> List List R +--R map : (((R,R) -> R),%,%,R) -> % map : (((R,R) -> R),%,%) -> % +--R map : ((R -> R),%) -> % map! : ((R -> R),%) -> % +--R matrix : List List R -> % maxColIndex : % -> Integer +--R maxRowIndex : % -> Integer minColIndex : % -> Integer +--R minRowIndex : % -> Integer ncols : % -> NonNegativeInteger +--R nrows : % -> NonNegativeInteger parts : % -> List R +--R qelt : (%,Integer,Integer) -> R sample : () -> % +--R square? : % -> Boolean squareTop : % -> % +--R symmetric? : % -> Boolean transpose : % -> % +--R vertConcat : (%,%) -> % +--R #? : % -> NonNegativeInteger if $ has finiteAggregate +--R ?*? : (IndexedVector(R,mnCol),%) -> IndexedVector(R,mnCol) +--R ?*? : (%,IndexedVector(R,mnRow)) -> IndexedVector(R,mnRow) +--R ?**? : (%,Integer) -> % if R has FIELD +--R ?**? : (%,NonNegativeInteger) -> % +--R ?/? : (%,R) -> % if R has FIELD +--R ?=? : (%,%) -> Boolean if R has SETCAT +--R any? : ((R -> Boolean),%) -> Boolean if $ has finiteAggregate +--R coerce : IndexedVector(R,mnRow) -> % +--R coerce : % -> OutputForm if R has SETCAT +--R column : (%,Integer) -> IndexedVector(R,mnRow) +--R columnSpace : % -> List IndexedVector(R,mnRow) if R has EUCDOM +--R count : (R,%) -> NonNegativeInteger if $ has finiteAggregate and R has SETCAT +--R count : ((R -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate +--R determinant : % -> R if R has commutative * +--R elt : (%,List Integer,List Integer) -> % +--R eval : (%,List R,List R) -> % if R has EVALAB R and R has SETCAT +--R eval : (%,R,R) -> % if R has EVALAB R and R has SETCAT +--R eval : (%,Equation R) -> % if R has EVALAB R and R has SETCAT +--R eval : (%,List Equation R) -> % if R has EVALAB R and R has SETCAT +--R every? : ((R -> Boolean),%) -> Boolean if $ has finiteAggregate +--R exquo : (%,R) -> Union(%,"failed") if R has INTDOM +--R hash : % -> SingleInteger if R has SETCAT +--R inverse : % -> Union(%,"failed") if R has FIELD +--R latex : % -> String if R has SETCAT +--R less? : (%,NonNegativeInteger) -> Boolean +--R member? : (R,%) -> Boolean if $ has finiteAggregate and R has SETCAT +--R members : % -> List R if $ has finiteAggregate +--R minordet : % -> R if R has commutative * +--R more? : (%,NonNegativeInteger) -> Boolean +--R new : (NonNegativeInteger,NonNegativeInteger,R) -> % +--R nullSpace : % -> List IndexedVector(R,mnRow) if R has INTDOM +--R nullity : % -> NonNegativeInteger if R has INTDOM +--R pfaffian : % -> R if R has COMRING +--R qsetelt! : (%,Integer,Integer,R) -> R +--R rank : % -> NonNegativeInteger if R has INTDOM +--R row : (%,Integer) -> IndexedVector(R,mnCol) +--R rowEchelon : % -> % if R has EUCDOM +--R scalarMatrix : (NonNegativeInteger,R) -> % +--R setColumn! : (%,Integer,IndexedVector(R,mnRow)) -> % +--R setRow! : (%,Integer,IndexedVector(R,mnCol)) -> % +--R setelt : (%,List Integer,List Integer,%) -> % +--R setelt : (%,Integer,Integer,R) -> R +--R setsubMatrix! : (%,Integer,Integer,%) -> % +--R size? : (%,NonNegativeInteger) -> Boolean +--R subMatrix : (%,Integer,Integer,Integer,Integer) -> % +--R swapColumns! : (%,Integer,Integer) -> % +--R swapRows! : (%,Integer,Integer) -> % +--R transpose : IndexedVector(R,mnCol) -> % +--R zero : (NonNegativeInteger,NonNegativeInteger) -> % +--R ?~=? : (%,%) -> Boolean if R has SETCAT +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +IndexedMatrix examples +==================================================================== + +See Also: +o )show IndexedMatrix + +@ + \pagehead{IndexedMatrix}{IMATRIX} \pagepic{ps/v103indexedmatrix.ps}{IMATRIX}{1.00} {\bf See}\\ @@ -46683,6 +55431,111 @@ IndexedMatrix(R,mnRow,mnCol): Exports == Implementation where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain IARRAY1 IndexedOneDimensionalArray} + +<>= +)set break resume +)sys rm -f IndexedOneDimensionalArray.output +)spool IndexedOneDimensionalArray.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show IndexedOneDimensionalArray +--R IndexedOneDimensionalArray(S: Type,mn: Integer) is a domain constructor +--R Abbreviation for IndexedOneDimensionalArray is IARRAY1 +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for IARRAY1 +--R +--R------------------------------- Operations -------------------------------- +--R concat : List % -> % concat : (%,%) -> % +--R concat : (S,%) -> % concat : (%,S) -> % +--R construct : List S -> % copy : % -> % +--R delete : (%,Integer) -> % ?.? : (%,Integer) -> S +--R elt : (%,Integer,S) -> S empty : () -> % +--R empty? : % -> Boolean entries : % -> List S +--R eq? : (%,%) -> Boolean index? : (Integer,%) -> Boolean +--R indices : % -> List Integer insert : (%,%,Integer) -> % +--R insert : (S,%,Integer) -> % map : (((S,S) -> S),%,%) -> % +--R map : ((S -> S),%) -> % new : (NonNegativeInteger,S) -> % +--R qelt : (%,Integer) -> S reverse : % -> % +--R sample : () -> % +--R #? : % -> NonNegativeInteger if $ has finiteAggregate +--R ? Boolean if S has ORDSET +--R ?<=? : (%,%) -> Boolean if S has ORDSET +--R ?=? : (%,%) -> Boolean if S has SETCAT +--R ?>? : (%,%) -> Boolean if S has ORDSET +--R ?>=? : (%,%) -> Boolean if S has ORDSET +--R any? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate +--R coerce : % -> OutputForm if S has SETCAT +--R convert : % -> InputForm if S has KONVERT INFORM +--R copyInto! : (%,%,Integer) -> % if $ has shallowlyMutable +--R count : (S,%) -> NonNegativeInteger if $ has finiteAggregate and S has SETCAT +--R count : ((S -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate +--R delete : (%,UniversalSegment Integer) -> % +--R ?.? : (%,UniversalSegment Integer) -> % +--R entry? : (S,%) -> Boolean if $ has finiteAggregate and S has SETCAT +--R eval : (%,List S,List S) -> % if S has EVALAB S and S has SETCAT +--R eval : (%,S,S) -> % if S has EVALAB S and S has SETCAT +--R eval : (%,Equation S) -> % if S has EVALAB S and S has SETCAT +--R eval : (%,List Equation S) -> % if S has EVALAB S and S has SETCAT +--R every? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate +--R fill! : (%,S) -> % if $ has shallowlyMutable +--R find : ((S -> Boolean),%) -> Union(S,"failed") +--R first : % -> S if Integer has ORDSET +--R hash : % -> SingleInteger if S has SETCAT +--R latex : % -> String if S has SETCAT +--R less? : (%,NonNegativeInteger) -> Boolean +--R map! : ((S -> S),%) -> % if $ has shallowlyMutable +--R max : (%,%) -> % if S has ORDSET +--R maxIndex : % -> Integer if Integer has ORDSET +--R member? : (S,%) -> Boolean if $ has finiteAggregate and S has SETCAT +--R members : % -> List S if $ has finiteAggregate +--R merge : (%,%) -> % if S has ORDSET +--R merge : (((S,S) -> Boolean),%,%) -> % +--R min : (%,%) -> % if S has ORDSET +--R minIndex : % -> Integer if Integer has ORDSET +--R more? : (%,NonNegativeInteger) -> Boolean +--R parts : % -> List S if $ has finiteAggregate +--R position : (S,%,Integer) -> Integer if S has SETCAT +--R position : (S,%) -> Integer if S has SETCAT +--R position : ((S -> Boolean),%) -> Integer +--R qsetelt! : (%,Integer,S) -> S if $ has shallowlyMutable +--R reduce : (((S,S) -> S),%) -> S if $ has finiteAggregate +--R reduce : (((S,S) -> S),%,S) -> S if $ has finiteAggregate +--R reduce : (((S,S) -> S),%,S,S) -> S if $ has finiteAggregate and S has SETCAT +--R remove : ((S -> Boolean),%) -> % if $ has finiteAggregate +--R remove : (S,%) -> % if $ has finiteAggregate and S has SETCAT +--R removeDuplicates : % -> % if $ has finiteAggregate and S has SETCAT +--R reverse! : % -> % if $ has shallowlyMutable +--R select : ((S -> Boolean),%) -> % if $ has finiteAggregate +--R setelt : (%,UniversalSegment Integer,S) -> S if $ has shallowlyMutable +--R setelt : (%,Integer,S) -> S if $ has shallowlyMutable +--R size? : (%,NonNegativeInteger) -> Boolean +--R sort : % -> % if S has ORDSET +--R sort : (((S,S) -> Boolean),%) -> % +--R sort! : % -> % if $ has shallowlyMutable and S has ORDSET +--R sort! : (((S,S) -> Boolean),%) -> % if $ has shallowlyMutable +--R sorted? : % -> Boolean if S has ORDSET +--R sorted? : (((S,S) -> Boolean),%) -> Boolean +--R swap! : (%,Integer,Integer) -> Void if $ has shallowlyMutable +--R ?~=? : (%,%) -> Boolean if S has SETCAT +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +IndexedOneDimensionalArray examples +==================================================================== + +See Also: +o )show IndexedOneDimensionalArray + +@ + \pagehead{IndexedOneDimensionalArray}{IARRAY1} \pagepic{ps/v103indexedonedimensionalarray.ps}{IARRAY1}{1.00} {\bf See}\\ @@ -46871,6 +55724,129 @@ IndexedOneDimensionalArray(S:Type, mn:Integer): @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain ISTRING IndexedString} + +<>= +)set break resume +)sys rm -f IndexedString.output +)spool IndexedString.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show IndexedString +--R IndexedString mn: Integer is a domain constructor +--R Abbreviation for IndexedString is ISTRING +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for ISTRING +--R +--R------------------------------- Operations -------------------------------- +--R coerce : Character -> % concat : List % -> % +--R concat : (%,%) -> % concat : (Character,%) -> % +--R concat : (%,Character) -> % construct : List Character -> % +--R copy : % -> % delete : (%,Integer) -> % +--R ?.? : (%,%) -> % ?.? : (%,Integer) -> Character +--R empty : () -> % empty? : % -> Boolean +--R entries : % -> List Character eq? : (%,%) -> Boolean +--R hash : % -> Integer index? : (Integer,%) -> Boolean +--R indices : % -> List Integer insert : (%,%,Integer) -> % +--R leftTrim : (%,Character) -> % lowerCase : % -> % +--R lowerCase! : % -> % prefix? : (%,%) -> Boolean +--R qelt : (%,Integer) -> Character reverse : % -> % +--R rightTrim : (%,Character) -> % sample : () -> % +--R split : (%,Character) -> List % suffix? : (%,%) -> Boolean +--R trim : (%,CharacterClass) -> % trim : (%,Character) -> % +--R upperCase : % -> % upperCase! : % -> % +--R #? : % -> NonNegativeInteger if $ has finiteAggregate +--R ? Boolean if Character has ORDSET +--R ?<=? : (%,%) -> Boolean if Character has ORDSET +--R ?=? : (%,%) -> Boolean if Character has SETCAT +--R ?>? : (%,%) -> Boolean if Character has ORDSET +--R ?>=? : (%,%) -> Boolean if Character has ORDSET +--R any? : ((Character -> Boolean),%) -> Boolean if $ has finiteAggregate +--R coerce : % -> OutputForm if Character has SETCAT +--R convert : % -> InputForm if Character has KONVERT INFORM +--R copyInto! : (%,%,Integer) -> % if $ has shallowlyMutable +--R count : (Character,%) -> NonNegativeInteger if $ has finiteAggregate and Character has SETCAT +--R count : ((Character -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate +--R delete : (%,UniversalSegment Integer) -> % +--R ?.? : (%,UniversalSegment Integer) -> % +--R elt : (%,Integer,Character) -> Character +--R entry? : (Character,%) -> Boolean if $ has finiteAggregate and Character has SETCAT +--R eval : (%,List Character,List Character) -> % if Character has EVALAB CHAR and Character has SETCAT +--R eval : (%,Character,Character) -> % if Character has EVALAB CHAR and Character has SETCAT +--R eval : (%,Equation Character) -> % if Character has EVALAB CHAR and Character has SETCAT +--R eval : (%,List Equation Character) -> % if Character has EVALAB CHAR and Character has SETCAT +--R every? : ((Character -> Boolean),%) -> Boolean if $ has finiteAggregate +--R fill! : (%,Character) -> % if $ has shallowlyMutable +--R find : ((Character -> Boolean),%) -> Union(Character,"failed") +--R first : % -> Character if Integer has ORDSET +--R hash : % -> SingleInteger if Character has SETCAT +--R insert : (Character,%,Integer) -> % +--R latex : % -> String if Character has SETCAT +--R leftTrim : (%,CharacterClass) -> % +--R less? : (%,NonNegativeInteger) -> Boolean +--R map : (((Character,Character) -> Character),%,%) -> % +--R map : ((Character -> Character),%) -> % +--R map! : ((Character -> Character),%) -> % if $ has shallowlyMutable +--R match : (%,%,Character) -> NonNegativeInteger +--R match? : (%,%,Character) -> Boolean +--R max : (%,%) -> % if Character has ORDSET +--R maxIndex : % -> Integer if Integer has ORDSET +--R member? : (Character,%) -> Boolean if $ has finiteAggregate and Character has SETCAT +--R members : % -> List Character if $ has finiteAggregate +--R merge : (%,%) -> % if Character has ORDSET +--R merge : (((Character,Character) -> Boolean),%,%) -> % +--R min : (%,%) -> % if Character has ORDSET +--R minIndex : % -> Integer if Integer has ORDSET +--R more? : (%,NonNegativeInteger) -> Boolean +--R new : (NonNegativeInteger,Character) -> % +--R parts : % -> List Character if $ has finiteAggregate +--R position : (CharacterClass,%,Integer) -> Integer +--R position : (%,%,Integer) -> Integer +--R position : (Character,%,Integer) -> Integer if Character has SETCAT +--R position : (Character,%) -> Integer if Character has SETCAT +--R position : ((Character -> Boolean),%) -> Integer +--R qsetelt! : (%,Integer,Character) -> Character if $ has shallowlyMutable +--R reduce : (((Character,Character) -> Character),%) -> Character if $ has finiteAggregate +--R reduce : (((Character,Character) -> Character),%,Character) -> Character if $ has finiteAggregate +--R reduce : (((Character,Character) -> Character),%,Character,Character) -> Character if $ has finiteAggregate and Character has SETCAT +--R remove : ((Character -> Boolean),%) -> % if $ has finiteAggregate +--R remove : (Character,%) -> % if $ has finiteAggregate and Character has SETCAT +--R removeDuplicates : % -> % if $ has finiteAggregate and Character has SETCAT +--R replace : (%,UniversalSegment Integer,%) -> % +--R reverse! : % -> % if $ has shallowlyMutable +--R rightTrim : (%,CharacterClass) -> % +--R select : ((Character -> Boolean),%) -> % if $ has finiteAggregate +--R setelt : (%,UniversalSegment Integer,Character) -> Character if $ has shallowlyMutable +--R setelt : (%,Integer,Character) -> Character if $ has shallowlyMutable +--R size? : (%,NonNegativeInteger) -> Boolean +--R sort : % -> % if Character has ORDSET +--R sort : (((Character,Character) -> Boolean),%) -> % +--R sort! : % -> % if $ has shallowlyMutable and Character has ORDSET +--R sort! : (((Character,Character) -> Boolean),%) -> % if $ has shallowlyMutable +--R sorted? : % -> Boolean if Character has ORDSET +--R sorted? : (((Character,Character) -> Boolean),%) -> Boolean +--R split : (%,CharacterClass) -> List % +--R substring? : (%,%,Integer) -> Boolean +--R swap! : (%,Integer,Integer) -> Void if $ has shallowlyMutable +--R ?~=? : (%,%) -> Boolean if Character has SETCAT +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +IndexedString examples +==================================================================== + +See Also: +o )show IndexedString + +@ + \pagehead{IndexedString}{ISTRING} \pagepic{ps/v103indexedstring.ps}{ISTRING}{1.00} {\bf See}\\ @@ -47164,6 +56140,7 @@ IndexedString(mn:Integer): Export == Implementation where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain IARRAY2 IndexedTwoDimensionalArray} + An IndexedTwoDimensionalArray is a 2-dimensional array where the minimal row and column indices are parameters of the type. Rows and columns are returned as IndexedOneDimensionalArray's with @@ -47173,6 +56150,75 @@ function 'minRowIndex'. The index of the 'first' column may be obtained by calling the function 'minColIndex'. The index of the first element of a 'Row' is the same as the index of the first column in an array and vice versa. + +<>= +)set break resume +)sys rm -f IndexedTwoDimensionalArray.output +)spool IndexedTwoDimensionalArray.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show IndexedTwoDimensionalArray +--R IndexedTwoDimensionalArray(R: Type,mnRow: Integer,mnCol: Integer) is a domain constructor +--R Abbreviation for IndexedTwoDimensionalArray is IARRAY2 +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for IARRAY2 +--R +--R------------------------------- Operations -------------------------------- +--R copy : % -> % elt : (%,Integer,Integer,R) -> R +--R elt : (%,Integer,Integer) -> R empty : () -> % +--R empty? : % -> Boolean eq? : (%,%) -> Boolean +--R fill! : (%,R) -> % map : (((R,R) -> R),%,%,R) -> % +--R map : (((R,R) -> R),%,%) -> % map : ((R -> R),%) -> % +--R map! : ((R -> R),%) -> % maxColIndex : % -> Integer +--R maxRowIndex : % -> Integer minColIndex : % -> Integer +--R minRowIndex : % -> Integer ncols : % -> NonNegativeInteger +--R nrows : % -> NonNegativeInteger parts : % -> List R +--R qelt : (%,Integer,Integer) -> R sample : () -> % +--R #? : % -> NonNegativeInteger if $ has finiteAggregate +--R ?=? : (%,%) -> Boolean if R has SETCAT +--R any? : ((R -> Boolean),%) -> Boolean if $ has finiteAggregate +--R coerce : % -> OutputForm if R has SETCAT +--R column : (%,Integer) -> IndexedOneDimensionalArray(R,mnRow) +--R count : (R,%) -> NonNegativeInteger if $ has finiteAggregate and R has SETCAT +--R count : ((R -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate +--R eval : (%,List R,List R) -> % if R has EVALAB R and R has SETCAT +--R eval : (%,R,R) -> % if R has EVALAB R and R has SETCAT +--R eval : (%,Equation R) -> % if R has EVALAB R and R has SETCAT +--R eval : (%,List Equation R) -> % if R has EVALAB R and R has SETCAT +--R every? : ((R -> Boolean),%) -> Boolean if $ has finiteAggregate +--R hash : % -> SingleInteger if R has SETCAT +--R latex : % -> String if R has SETCAT +--R less? : (%,NonNegativeInteger) -> Boolean +--R member? : (R,%) -> Boolean if $ has finiteAggregate and R has SETCAT +--R members : % -> List R if $ has finiteAggregate +--R more? : (%,NonNegativeInteger) -> Boolean +--R new : (NonNegativeInteger,NonNegativeInteger,R) -> % +--R qsetelt! : (%,Integer,Integer,R) -> R +--R row : (%,Integer) -> IndexedOneDimensionalArray(R,mnCol) +--R setColumn! : (%,Integer,IndexedOneDimensionalArray(R,mnRow)) -> % +--R setRow! : (%,Integer,IndexedOneDimensionalArray(R,mnCol)) -> % +--R setelt : (%,Integer,Integer,R) -> R +--R size? : (%,NonNegativeInteger) -> Boolean +--R ?~=? : (%,%) -> Boolean if R has SETCAT +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +IndexedTwoDimensionalArray examples +==================================================================== + +See Also: +o )show IndexedTwoDimensionalArray + +@ + \pagehead{IndexedTwoDimensionalArray}{IARRAY2} \pagepic{ps/v103indexedtwodimensionalarray.ps}{IARRAY2}{1.00} {\bf See}\\ @@ -47251,6 +56297,122 @@ IndexedTwoDimensionalArray(R,mnRow,mnCol):Exports == Implementation where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain IVECTOR IndexedVector} + +<>= +)set break resume +)sys rm -f IndexedVector.output +)spool IndexedVector.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show IndexedVector +--R IndexedVector(R: Type,mn: Integer) is a domain constructor +--R Abbreviation for IndexedVector is IVECTOR +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for IVECTOR +--R +--R------------------------------- Operations -------------------------------- +--R -? : % -> % if R has ABELGRP concat : List % -> % +--R concat : (%,%) -> % concat : (R,%) -> % +--R concat : (%,R) -> % construct : List R -> % +--R copy : % -> % delete : (%,Integer) -> % +--R ?.? : (%,Integer) -> R elt : (%,Integer,R) -> R +--R empty : () -> % empty? : % -> Boolean +--R entries : % -> List R eq? : (%,%) -> Boolean +--R index? : (Integer,%) -> Boolean indices : % -> List Integer +--R insert : (%,%,Integer) -> % insert : (R,%,Integer) -> % +--R map : (((R,R) -> R),%,%) -> % map : ((R -> R),%) -> % +--R new : (NonNegativeInteger,R) -> % qelt : (%,Integer) -> R +--R reverse : % -> % sample : () -> % +--R #? : % -> NonNegativeInteger if $ has finiteAggregate +--R ?*? : (%,R) -> % if R has MONOID +--R ?*? : (R,%) -> % if R has MONOID +--R ?*? : (Integer,%) -> % if R has ABELGRP +--R ?+? : (%,%) -> % if R has ABELSG +--R ?-? : (%,%) -> % if R has ABELGRP +--R ? Boolean if R has ORDSET +--R ?<=? : (%,%) -> Boolean if R has ORDSET +--R ?=? : (%,%) -> Boolean if R has SETCAT +--R ?>? : (%,%) -> Boolean if R has ORDSET +--R ?>=? : (%,%) -> Boolean if R has ORDSET +--R any? : ((R -> Boolean),%) -> Boolean if $ has finiteAggregate +--R coerce : % -> OutputForm if R has SETCAT +--R convert : % -> InputForm if R has KONVERT INFORM +--R copyInto! : (%,%,Integer) -> % if $ has shallowlyMutable +--R count : (R,%) -> NonNegativeInteger if $ has finiteAggregate and R has SETCAT +--R count : ((R -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate +--R cross : (%,%) -> % if R has RING +--R delete : (%,UniversalSegment Integer) -> % +--R dot : (%,%) -> R if R has RING +--R ?.? : (%,UniversalSegment Integer) -> % +--R entry? : (R,%) -> Boolean if $ has finiteAggregate and R has SETCAT +--R eval : (%,List R,List R) -> % if R has EVALAB R and R has SETCAT +--R eval : (%,R,R) -> % if R has EVALAB R and R has SETCAT +--R eval : (%,Equation R) -> % if R has EVALAB R and R has SETCAT +--R eval : (%,List Equation R) -> % if R has EVALAB R and R has SETCAT +--R every? : ((R -> Boolean),%) -> Boolean if $ has finiteAggregate +--R fill! : (%,R) -> % if $ has shallowlyMutable +--R find : ((R -> Boolean),%) -> Union(R,"failed") +--R first : % -> R if Integer has ORDSET +--R hash : % -> SingleInteger if R has SETCAT +--R latex : % -> String if R has SETCAT +--R length : % -> R if R has RADCAT and R has RING +--R less? : (%,NonNegativeInteger) -> Boolean +--R magnitude : % -> R if R has RADCAT and R has RING +--R map! : ((R -> R),%) -> % if $ has shallowlyMutable +--R max : (%,%) -> % if R has ORDSET +--R maxIndex : % -> Integer if Integer has ORDSET +--R member? : (R,%) -> Boolean if $ has finiteAggregate and R has SETCAT +--R members : % -> List R if $ has finiteAggregate +--R merge : (%,%) -> % if R has ORDSET +--R merge : (((R,R) -> Boolean),%,%) -> % +--R min : (%,%) -> % if R has ORDSET +--R minIndex : % -> Integer if Integer has ORDSET +--R more? : (%,NonNegativeInteger) -> Boolean +--R outerProduct : (%,%) -> Matrix R if R has RING +--R parts : % -> List R if $ has finiteAggregate +--R position : (R,%,Integer) -> Integer if R has SETCAT +--R position : (R,%) -> Integer if R has SETCAT +--R position : ((R -> Boolean),%) -> Integer +--R qsetelt! : (%,Integer,R) -> R if $ has shallowlyMutable +--R reduce : (((R,R) -> R),%) -> R if $ has finiteAggregate +--R reduce : (((R,R) -> R),%,R) -> R if $ has finiteAggregate +--R reduce : (((R,R) -> R),%,R,R) -> R if $ has finiteAggregate and R has SETCAT +--R remove : ((R -> Boolean),%) -> % if $ has finiteAggregate +--R remove : (R,%) -> % if $ has finiteAggregate and R has SETCAT +--R removeDuplicates : % -> % if $ has finiteAggregate and R has SETCAT +--R reverse! : % -> % if $ has shallowlyMutable +--R select : ((R -> Boolean),%) -> % if $ has finiteAggregate +--R setelt : (%,UniversalSegment Integer,R) -> R if $ has shallowlyMutable +--R setelt : (%,Integer,R) -> R if $ has shallowlyMutable +--R size? : (%,NonNegativeInteger) -> Boolean +--R sort : % -> % if R has ORDSET +--R sort : (((R,R) -> Boolean),%) -> % +--R sort! : % -> % if $ has shallowlyMutable and R has ORDSET +--R sort! : (((R,R) -> Boolean),%) -> % if $ has shallowlyMutable +--R sorted? : % -> Boolean if R has ORDSET +--R sorted? : (((R,R) -> Boolean),%) -> Boolean +--R swap! : (%,Integer,Integer) -> Void if $ has shallowlyMutable +--R zero : NonNegativeInteger -> % if R has ABELMON +--R ?~=? : (%,%) -> Boolean if R has SETCAT +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +IndexedVector examples +==================================================================== + +See Also: +o )show IndexedVector + +@ + \pagehead{IndexedVector}{IVECTOR} \pagepic{ps/v103indexedvector.ps}{IVECTOR}{1.00} @@ -47356,6 +56518,44 @@ IndexedVector(R:Type, mn:Integer): @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain ITUPLE InfiniteTuple} + +<>= +)set break resume +)sys rm -f InfiniteTuple.output +)spool InfiniteTuple.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show InfiniteTuple +--R InfiniteTuple S: Type is a domain constructor +--R Abbreviation for InfiniteTuple is ITUPLE +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for ITUPLE +--R +--R------------------------------- Operations -------------------------------- +--R coerce : % -> OutputForm construct : % -> Stream S +--R generate : ((S -> S),S) -> % map : ((S -> S),%) -> % +--R select : ((S -> Boolean),%) -> % +--R filterUntil : ((S -> Boolean),%) -> % +--R filterWhile : ((S -> Boolean),%) -> % +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +InfiniteTuple examples +==================================================================== + +See Also: +o )show InfiniteTuple + +@ + \pagehead{InfiniteTuple}{ITUPLE} \pagepic{ps/v103infinitetuple.ps}{ITUPLE}{1.00} @@ -47417,6 +56617,7 @@ InfiniteTuple(S:Type): Exports == Implementation where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain INFCLSPT InfinitlyClosePoint} + <>= )set break resume )sys rm -f InfinitlyClosePoint.output @@ -47685,6 +56886,7 @@ InfinitlyClosePoint(K,symb,PolyRing,E,ProjPt,PCS,Plc,DIVISOR,BLMET):Exports == I @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain INFCLSPS InfinitlyClosePointOverPseudoAlgebraicClosureOfFiniteField} + <>= )set break resume )sys rm -f InfinitlyClosePointOverPseudoAlgebraicClosureOfFiniteField.output @@ -47824,6 +57026,144 @@ InfinitlyClosePointOverPseudoAlgebraicClosureOfFiniteField(K,symb,BLMET):_ @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain IAN InnerAlgebraicNumber} + +<>= +)set break resume +)sys rm -f InnerAlgebraicNumber.output +)spool InnerAlgebraicNumber.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show InnerAlgebraicNumber +--R InnerAlgebraicNumber is a domain constructor +--R Abbreviation for InnerAlgebraicNumber is IAN +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for IAN +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (PositiveInteger,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (%,%) -> % ?*? : (%,Fraction Integer) -> % +--R ?*? : (Fraction Integer,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?**? : (%,Integer) -> % ?**? : (%,Fraction Integer) -> % +--R ?+? : (%,%) -> % -? : % -> % +--R ?-? : (%,%) -> % ?/? : (%,%) -> % +--R ? Boolean ?<=? : (%,%) -> Boolean +--R ?=? : (%,%) -> Boolean ?>? : (%,%) -> Boolean +--R ?>=? : (%,%) -> Boolean D : % -> % +--R D : (%,NonNegativeInteger) -> % 1 : () -> % +--R 0 : () -> % ?^? : (%,PositiveInteger) -> % +--R ?^? : (%,Integer) -> % associates? : (%,%) -> Boolean +--R belong? : BasicOperator -> Boolean box : List % -> % +--R box : % -> % coerce : Integer -> % +--R coerce : % -> % coerce : Fraction Integer -> % +--R coerce : Kernel % -> % coerce : % -> OutputForm +--R convert : % -> Complex Float convert : % -> DoubleFloat +--R convert : % -> Float differentiate : % -> % +--R distribute : (%,%) -> % distribute : % -> % +--R elt : (BasicOperator,%,%) -> % elt : (BasicOperator,%) -> % +--R eval : (%,List %,List %) -> % eval : (%,%,%) -> % +--R eval : (%,Equation %) -> % eval : (%,List Equation %) -> % +--R eval : (%,Kernel %,%) -> % factor : % -> Factored % +--R freeOf? : (%,Symbol) -> Boolean freeOf? : (%,%) -> Boolean +--R gcd : (%,%) -> % gcd : List % -> % +--R hash : % -> SingleInteger height : % -> NonNegativeInteger +--R inv : % -> % is? : (%,Symbol) -> Boolean +--R kernel : (BasicOperator,%) -> % kernels : % -> List Kernel % +--R latex : % -> String lcm : (%,%) -> % +--R lcm : List % -> % map : ((% -> %),Kernel %) -> % +--R max : (%,%) -> % min : (%,%) -> % +--R norm : (%,List Kernel %) -> % norm : (%,Kernel %) -> % +--R nthRoot : (%,Integer) -> % one? : % -> Boolean +--R paren : List % -> % paren : % -> % +--R prime? : % -> Boolean ?quo? : (%,%) -> % +--R recip : % -> Union(%,"failed") reduce : % -> % +--R ?rem? : (%,%) -> % retract : % -> Fraction Integer +--R retract : % -> Integer retract : % -> Kernel % +--R rootOf : Polynomial % -> % rootsOf : Polynomial % -> List % +--R sample : () -> % sizeLess? : (%,%) -> Boolean +--R sqrt : % -> % squareFree : % -> Factored % +--R squareFreePart : % -> % subst : (%,Equation %) -> % +--R tower : % -> List Kernel % trueEqual : (%,%) -> Boolean +--R unit? : % -> Boolean unitCanonical : % -> % +--R zero? : % -> Boolean zeroOf : Polynomial % -> % +--R zerosOf : Polynomial % -> List % ?~=? : (%,%) -> Boolean +--R ?*? : (NonNegativeInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % +--R ?^? : (%,NonNegativeInteger) -> % +--R characteristic : () -> NonNegativeInteger +--R coerce : SparseMultivariatePolynomial(Integer,Kernel %) -> % +--R definingPolynomial : % -> % if $ has RING +--R denom : % -> SparseMultivariatePolynomial(Integer,Kernel %) +--R differentiate : (%,NonNegativeInteger) -> % +--R divide : (%,%) -> Record(quotient: %,remainder: %) +--R elt : (BasicOperator,List %) -> % +--R elt : (BasicOperator,%,%,%,%) -> % +--R elt : (BasicOperator,%,%,%) -> % +--R euclideanSize : % -> NonNegativeInteger +--R eval : (%,BasicOperator,(% -> %)) -> % +--R eval : (%,BasicOperator,(List % -> %)) -> % +--R eval : (%,List BasicOperator,List (List % -> %)) -> % +--R eval : (%,List BasicOperator,List (% -> %)) -> % +--R eval : (%,Symbol,(% -> %)) -> % +--R eval : (%,Symbol,(List % -> %)) -> % +--R eval : (%,List Symbol,List (List % -> %)) -> % +--R eval : (%,List Symbol,List (% -> %)) -> % +--R eval : (%,List Kernel %,List %) -> % +--R even? : % -> Boolean if $ has RETRACT INT +--R expressIdealMember : (List %,%) -> Union(List %,"failed") +--R exquo : (%,%) -> Union(%,"failed") +--R extendedEuclidean : (%,%) -> Record(coef1: %,coef2: %,generator: %) +--R extendedEuclidean : (%,%,%) -> Union(Record(coef1: %,coef2: %),"failed") +--R gcdPolynomial : (SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial % +--R is? : (%,BasicOperator) -> Boolean +--R kernel : (BasicOperator,List %) -> % +--R mainKernel : % -> Union(Kernel %,"failed") +--R minPoly : Kernel % -> SparseUnivariatePolynomial % if $ has RING +--R multiEuclidean : (List %,%) -> Union(List %,"failed") +--R norm : (SparseUnivariatePolynomial %,List Kernel %) -> SparseUnivariatePolynomial % +--R norm : (SparseUnivariatePolynomial %,Kernel %) -> SparseUnivariatePolynomial % +--R numer : % -> SparseMultivariatePolynomial(Integer,Kernel %) +--R odd? : % -> Boolean if $ has RETRACT INT +--R operator : BasicOperator -> BasicOperator +--R operators : % -> List BasicOperator +--R principalIdeal : List % -> Record(coef: List %,generator: %) +--R reducedSystem : Matrix % -> Matrix Fraction Integer +--R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix Fraction Integer,vec: Vector Fraction Integer) +--R reducedSystem : Matrix % -> Matrix Integer +--R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix Integer,vec: Vector Integer) +--R retractIfCan : % -> Union(Fraction Integer,"failed") +--R retractIfCan : % -> Union(Integer,"failed") +--R retractIfCan : % -> Union(Kernel %,"failed") +--R rootOf : SparseUnivariatePolynomial % -> % +--R rootOf : (SparseUnivariatePolynomial %,Symbol) -> % +--R rootsOf : SparseUnivariatePolynomial % -> List % +--R rootsOf : (SparseUnivariatePolynomial %,Symbol) -> List % +--R subst : (%,List Kernel %,List %) -> % +--R subst : (%,List Equation %) -> % +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R unitNormal : % -> Record(unit: %,canonical: %,associate: %) +--R zeroOf : SparseUnivariatePolynomial % -> % +--R zeroOf : (SparseUnivariatePolynomial %,Symbol) -> % +--R zerosOf : SparseUnivariatePolynomial % -> List % +--R zerosOf : (SparseUnivariatePolynomial %,Symbol) -> List % +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +InnerAlgebraicNumber examples +==================================================================== + +See Also: +o )show InnerAlgebraicNumber + +@ + \pagehead{InnerAlgebraicNumber}{IAN} \pagepic{ps/v103inneralgebraicnumber.ps}{IAN}{1.00} {\bf See}\\ @@ -48075,6 +57415,131 @@ InnerAlgebraicNumber(): Exports == Implementation where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain IFF InnerFiniteField} + +<>= +)set break resume +)sys rm -f InnerFiniteField.output +)spool InnerFiniteField.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show InnerFiniteField +--R InnerFiniteField(p: PositiveInteger,n: PositiveInteger) is a domain constructor +--R Abbreviation for InnerFiniteField is IFF +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for IFF +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (InnerPrimeField p,%) -> % ?*? : (%,InnerPrimeField p) -> % +--R ?*? : (Fraction Integer,%) -> % ?*? : (%,Fraction Integer) -> % +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?**? : (%,Integer) -> % +--R ?**? : (%,PositiveInteger) -> % ?+? : (%,%) -> % +--R ?-? : (%,%) -> % -? : % -> % +--R ?/? : (%,InnerPrimeField p) -> % ?/? : (%,%) -> % +--R ?=? : (%,%) -> Boolean 1 : () -> % +--R 0 : () -> % ?^? : (%,Integer) -> % +--R ?^? : (%,PositiveInteger) -> % algebraic? : % -> Boolean +--R associates? : (%,%) -> Boolean basis : () -> Vector % +--R coerce : InnerPrimeField p -> % coerce : Fraction Integer -> % +--R coerce : % -> % coerce : Integer -> % +--R coerce : % -> OutputForm degree : % -> PositiveInteger +--R dimension : () -> CardinalNumber factor : % -> Factored % +--R gcd : List % -> % gcd : (%,%) -> % +--R hash : % -> SingleInteger inGroundField? : % -> Boolean +--R inv : % -> % latex : % -> String +--R lcm : List % -> % lcm : (%,%) -> % +--R norm : % -> InnerPrimeField p one? : % -> Boolean +--R prime? : % -> Boolean ?quo? : (%,%) -> % +--R recip : % -> Union(%,"failed") ?rem? : (%,%) -> % +--R retract : % -> InnerPrimeField p sample : () -> % +--R sizeLess? : (%,%) -> Boolean squareFree : % -> Factored % +--R squareFreePart : % -> % trace : % -> InnerPrimeField p +--R transcendent? : % -> Boolean unit? : % -> Boolean +--R unitCanonical : % -> % zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean +--R ?*? : (NonNegativeInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % +--R D : (%,NonNegativeInteger) -> % if InnerPrimeField p has FINITE +--R D : % -> % if InnerPrimeField p has FINITE +--R Frobenius : (%,NonNegativeInteger) -> % if InnerPrimeField p has FINITE +--R Frobenius : % -> % if InnerPrimeField p has FINITE +--R ?^? : (%,NonNegativeInteger) -> % +--R basis : PositiveInteger -> Vector % +--R characteristic : () -> NonNegativeInteger +--R charthRoot : % -> Union(%,"failed") if InnerPrimeField p has CHARNZ or InnerPrimeField p has FINITE +--R charthRoot : % -> % if InnerPrimeField p has FINITE +--R conditionP : Matrix % -> Union(Vector %,"failed") if InnerPrimeField p has FINITE +--R coordinates : Vector % -> Matrix InnerPrimeField p +--R coordinates : % -> Vector InnerPrimeField p +--R createNormalElement : () -> % if InnerPrimeField p has FINITE +--R createPrimitiveElement : () -> % if InnerPrimeField p has FINITE +--R definingPolynomial : () -> SparseUnivariatePolynomial InnerPrimeField p +--R degree : % -> OnePointCompletion PositiveInteger +--R differentiate : (%,NonNegativeInteger) -> % if InnerPrimeField p has FINITE +--R differentiate : % -> % if InnerPrimeField p has FINITE +--R discreteLog : (%,%) -> Union(NonNegativeInteger,"failed") if InnerPrimeField p has CHARNZ or InnerPrimeField p has FINITE +--R discreteLog : % -> NonNegativeInteger if InnerPrimeField p has FINITE +--R divide : (%,%) -> Record(quotient: %,remainder: %) +--R euclideanSize : % -> NonNegativeInteger +--R expressIdealMember : (List %,%) -> Union(List %,"failed") +--R exquo : (%,%) -> Union(%,"failed") +--R extendedEuclidean : (%,%,%) -> Union(Record(coef1: %,coef2: %),"failed") +--R extendedEuclidean : (%,%) -> Record(coef1: %,coef2: %,generator: %) +--R extensionDegree : () -> PositiveInteger +--R extensionDegree : () -> OnePointCompletion PositiveInteger +--R factorsOfCyclicGroupSize : () -> List Record(factor: Integer,exponent: Integer) if InnerPrimeField p has FINITE +--R gcdPolynomial : (SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial % +--R generator : () -> % if InnerPrimeField p has FINITE +--R index : PositiveInteger -> % if InnerPrimeField p has FINITE +--R init : () -> % if InnerPrimeField p has FINITE +--R linearAssociatedExp : (%,SparseUnivariatePolynomial InnerPrimeField p) -> % if InnerPrimeField p has FINITE +--R linearAssociatedLog : (%,%) -> Union(SparseUnivariatePolynomial InnerPrimeField p,"failed") if InnerPrimeField p has FINITE +--R linearAssociatedLog : % -> SparseUnivariatePolynomial InnerPrimeField p if InnerPrimeField p has FINITE +--R linearAssociatedOrder : % -> SparseUnivariatePolynomial InnerPrimeField p if InnerPrimeField p has FINITE +--R lookup : % -> PositiveInteger if InnerPrimeField p has FINITE +--R minimalPolynomial : (%,PositiveInteger) -> SparseUnivariatePolynomial % if InnerPrimeField p has FINITE +--R minimalPolynomial : % -> SparseUnivariatePolynomial InnerPrimeField p +--R multiEuclidean : (List %,%) -> Union(List %,"failed") +--R nextItem : % -> Union(%,"failed") if InnerPrimeField p has FINITE +--R norm : (%,PositiveInteger) -> % if InnerPrimeField p has FINITE +--R normal? : % -> Boolean if InnerPrimeField p has FINITE +--R normalElement : () -> % if InnerPrimeField p has FINITE +--R order : % -> OnePointCompletion PositiveInteger if InnerPrimeField p has CHARNZ or InnerPrimeField p has FINITE +--R order : % -> PositiveInteger if InnerPrimeField p has FINITE +--R primeFrobenius : % -> % if InnerPrimeField p has CHARNZ or InnerPrimeField p has FINITE +--R primeFrobenius : (%,NonNegativeInteger) -> % if InnerPrimeField p has CHARNZ or InnerPrimeField p has FINITE +--R primitive? : % -> Boolean if InnerPrimeField p has FINITE +--R primitiveElement : () -> % if InnerPrimeField p has FINITE +--R principalIdeal : List % -> Record(coef: List %,generator: %) +--R random : () -> % if InnerPrimeField p has FINITE +--R representationType : () -> Union("prime",polynomial,normal,cyclic) if InnerPrimeField p has FINITE +--R represents : Vector InnerPrimeField p -> % +--R retractIfCan : % -> Union(InnerPrimeField p,"failed") +--R size : () -> NonNegativeInteger if InnerPrimeField p has FINITE +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R tableForDiscreteLogarithm : Integer -> Table(PositiveInteger,NonNegativeInteger) if InnerPrimeField p has FINITE +--R trace : (%,PositiveInteger) -> % if InnerPrimeField p has FINITE +--R transcendenceDegree : () -> NonNegativeInteger +--R unitNormal : % -> Record(unit: %,canonical: %,associate: %) +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +InnerFiniteField examples +==================================================================== + +See Also: +o )show InnerFiniteField + +@ + \pagehead{InnerFiniteField}{IFF} \pagepic{ps/v103innerfinitefield.ps}{IFF}{1.00} {\bf See}\\ @@ -48205,6 +57670,54 @@ InnerFiniteField(p:PositiveInteger, n:PositiveInteger) == @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain IFAMON InnerFreeAbelianMonoid} + +<>= +)set break resume +)sys rm -f InnerFreeAbelianMonoid.output +)spool InnerFreeAbelianMonoid.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show InnerFreeAbelianMonoid +--R InnerFreeAbelianMonoid(S: SetCategory,E: CancellationAbelianMonoid,un: E) is a domain constructor +--R Abbreviation for InnerFreeAbelianMonoid is IFAMON +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for IFAMON +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (E,S) -> % ?*? : (PositiveInteger,%) -> % +--R ?+? : (S,%) -> % ?+? : (%,%) -> % +--R ?=? : (%,%) -> Boolean 0 : () -> % +--R coefficient : (S,%) -> E coerce : S -> % +--R coerce : % -> OutputForm hash : % -> SingleInteger +--R latex : % -> String mapCoef : ((E -> E),%) -> % +--R mapGen : ((S -> S),%) -> % nthCoef : (%,Integer) -> E +--R nthFactor : (%,Integer) -> S retract : % -> S +--R sample : () -> % size : % -> NonNegativeInteger +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean +--R ?*? : (NonNegativeInteger,%) -> % +--R highCommonTerms : (%,%) -> % if E has OAMON +--R retractIfCan : % -> Union(S,"failed") +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R terms : % -> List Record(gen: S,exp: E) +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +InnerFreeAbelianMonoid examples +==================================================================== + +See Also: +o )show InnerFreeAbelianMonoid + +@ + \pagehead{InnerFreeAbelianMonoid}{IFAMON} \pagepic{ps/v103innerfreeabelianmonoid.ps}{IFAMON}{1.00} {\bf See}\\ @@ -48284,8 +57797,77 @@ InnerFreeAbelianMonoid(S: SetCategory, E:CancellationAbelianMonoid, un:E): @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain IIARRAY2 InnerIndexedTwoDimensionalArray} + This is an internal type which provides an implementation of 2-dimensional arrays as PrimitiveArray's of PrimitiveArray's. + +<>= +)set break resume +)sys rm -f InnerIndexedTwoDimensionalArray.output +)spool InnerIndexedTwoDimensionalArray.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show InnerIndexedTwoDimensionalArray +--R InnerIndexedTwoDimensionalArray(R: Type,mnRow: Integer,mnCol: Integer,Row: FiniteLinearAggregate R,Col: FiniteLinearAggregate R) is a domain constructor +--R Abbreviation for InnerIndexedTwoDimensionalArray is IIARRAY2 +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for IIARRAY2 +--R +--R------------------------------- Operations -------------------------------- +--R column : (%,Integer) -> Col copy : % -> % +--R elt : (%,Integer,Integer,R) -> R elt : (%,Integer,Integer) -> R +--R empty : () -> % empty? : % -> Boolean +--R eq? : (%,%) -> Boolean fill! : (%,R) -> % +--R map : (((R,R) -> R),%,%,R) -> % map : (((R,R) -> R),%,%) -> % +--R map : ((R -> R),%) -> % map! : ((R -> R),%) -> % +--R maxColIndex : % -> Integer maxRowIndex : % -> Integer +--R minColIndex : % -> Integer minRowIndex : % -> Integer +--R ncols : % -> NonNegativeInteger nrows : % -> NonNegativeInteger +--R parts : % -> List R qelt : (%,Integer,Integer) -> R +--R row : (%,Integer) -> Row sample : () -> % +--R setRow! : (%,Integer,Row) -> % +--R #? : % -> NonNegativeInteger if $ has finiteAggregate +--R ?=? : (%,%) -> Boolean if R has SETCAT +--R any? : ((R -> Boolean),%) -> Boolean if $ has finiteAggregate +--R coerce : % -> OutputForm if R has SETCAT +--R count : (R,%) -> NonNegativeInteger if $ has finiteAggregate and R has SETCAT +--R count : ((R -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate +--R eval : (%,List R,List R) -> % if R has EVALAB R and R has SETCAT +--R eval : (%,R,R) -> % if R has EVALAB R and R has SETCAT +--R eval : (%,Equation R) -> % if R has EVALAB R and R has SETCAT +--R eval : (%,List Equation R) -> % if R has EVALAB R and R has SETCAT +--R every? : ((R -> Boolean),%) -> Boolean if $ has finiteAggregate +--R hash : % -> SingleInteger if R has SETCAT +--R latex : % -> String if R has SETCAT +--R less? : (%,NonNegativeInteger) -> Boolean +--R member? : (R,%) -> Boolean if $ has finiteAggregate and R has SETCAT +--R members : % -> List R if $ has finiteAggregate +--R more? : (%,NonNegativeInteger) -> Boolean +--R new : (NonNegativeInteger,NonNegativeInteger,R) -> % +--R qsetelt! : (%,Integer,Integer,R) -> R +--R setColumn! : (%,Integer,Col) -> % +--R setelt : (%,Integer,Integer,R) -> R +--R size? : (%,NonNegativeInteger) -> Boolean +--R ?~=? : (%,%) -> Boolean if R has SETCAT +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +InnerIndexedTwoDimensionalArray examples +==================================================================== + +See Also: +o )show InnerIndexedTwoDimensionalArray + +@ + \pagehead{InnerIndexedTwoDimensionalArray}{IIARRAY2} \pagepic{ps/v103innerindexedtwodimensionalarray.ps}{IIARRAY2}{1.00} {\bf See}\\ @@ -48431,6 +58013,76 @@ InnerIndexedTwoDimensionalArray(R,mnRow,mnCol,Row,Col):_ @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain IPADIC InnerPAdicInteger} + +<>= +)set break resume +)sys rm -f InnerPAdicInteger.output +)spool InnerPAdicInteger.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show InnerPAdicInteger +--R InnerPAdicInteger(p: Integer,unBalanced?: Boolean) is a domain constructor +--R Abbreviation for InnerPAdicInteger is IPADIC +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for IPADIC +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ?=? : (%,%) -> Boolean +--R 1 : () -> % 0 : () -> % +--R ?^? : (%,PositiveInteger) -> % associates? : (%,%) -> Boolean +--R coerce : % -> % coerce : Integer -> % +--R coerce : % -> OutputForm complete : % -> % +--R digits : % -> Stream Integer extend : (%,Integer) -> % +--R gcd : List % -> % gcd : (%,%) -> % +--R hash : % -> SingleInteger latex : % -> String +--R lcm : List % -> % lcm : (%,%) -> % +--R moduloP : % -> Integer modulus : () -> Integer +--R one? : % -> Boolean order : % -> NonNegativeInteger +--R ?quo? : (%,%) -> % quotientByP : % -> % +--R recip : % -> Union(%,"failed") ?rem? : (%,%) -> % +--R sample : () -> % sizeLess? : (%,%) -> Boolean +--R sqrt : (%,Integer) -> % unit? : % -> Boolean +--R unitCanonical : % -> % zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean +--R ?*? : (NonNegativeInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % +--R ?^? : (%,NonNegativeInteger) -> % +--R approximate : (%,Integer) -> Integer +--R characteristic : () -> NonNegativeInteger +--R divide : (%,%) -> Record(quotient: %,remainder: %) +--R euclideanSize : % -> NonNegativeInteger +--R expressIdealMember : (List %,%) -> Union(List %,"failed") +--R exquo : (%,%) -> Union(%,"failed") +--R extendedEuclidean : (%,%,%) -> Union(Record(coef1: %,coef2: %),"failed") +--R extendedEuclidean : (%,%) -> Record(coef1: %,coef2: %,generator: %) +--R gcdPolynomial : (SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial % +--R multiEuclidean : (List %,%) -> Union(List %,"failed") +--R principalIdeal : List % -> Record(coef: List %,generator: %) +--R root : (SparseUnivariatePolynomial Integer,Integer) -> % +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R unitNormal : % -> Record(unit: %,canonical: %,associate: %) +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +InnerPAdicInteger examples +==================================================================== + +See Also: +o )show InnerPAdicInteger + +@ + \pagehead{InnerPAdicInteger}{IPADIC} \pagepic{ps/v103innerpadicinteger.ps}{IPADIC}{1.00} {\bf See}\\ @@ -48751,6 +58403,121 @@ InnerPAdicInteger(p,unBalanced?): Exports == Implementation where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain IPF InnerPrimeField} + +<>= +)set break resume +)sys rm -f InnerPrimeField.output +)spool InnerPrimeField.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show InnerPrimeField +--R InnerPrimeField p: PositiveInteger is a domain constructor +--R Abbreviation for InnerPrimeField is IPF +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for IPF +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (Fraction Integer,%) -> % ?*? : (%,Fraction Integer) -> % +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?**? : (%,Integer) -> % +--R ?**? : (%,PositiveInteger) -> % ?+? : (%,%) -> % +--R ?-? : (%,%) -> % -? : % -> % +--R ?/? : (%,%) -> % ?=? : (%,%) -> Boolean +--R D : % -> % D : (%,NonNegativeInteger) -> % +--R 1 : () -> % 0 : () -> % +--R ?^? : (%,Integer) -> % ?^? : (%,PositiveInteger) -> % +--R algebraic? : % -> Boolean associates? : (%,%) -> Boolean +--R basis : () -> Vector % charthRoot : % -> % +--R coerce : Fraction Integer -> % coerce : % -> % +--R coerce : Integer -> % coerce : % -> OutputForm +--R convert : % -> Integer coordinates : % -> Vector % +--R createPrimitiveElement : () -> % degree : % -> PositiveInteger +--R differentiate : % -> % dimension : () -> CardinalNumber +--R factor : % -> Factored % gcd : List % -> % +--R gcd : (%,%) -> % hash : % -> SingleInteger +--R inGroundField? : % -> Boolean index : PositiveInteger -> % +--R init : () -> % inv : % -> % +--R latex : % -> String lcm : List % -> % +--R lcm : (%,%) -> % lookup : % -> PositiveInteger +--R norm : % -> % one? : % -> Boolean +--R order : % -> PositiveInteger prime? : % -> Boolean +--R primeFrobenius : % -> % primitive? : % -> Boolean +--R primitiveElement : () -> % ?quo? : (%,%) -> % +--R random : () -> % recip : % -> Union(%,"failed") +--R ?rem? : (%,%) -> % represents : Vector % -> % +--R retract : % -> % sample : () -> % +--R size : () -> NonNegativeInteger sizeLess? : (%,%) -> Boolean +--R squareFree : % -> Factored % squareFreePart : % -> % +--R trace : % -> % transcendent? : % -> Boolean +--R unit? : % -> Boolean unitCanonical : % -> % +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean +--R ?*? : (NonNegativeInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % +--R Frobenius : % -> % if $ has FINITE +--R Frobenius : (%,NonNegativeInteger) -> % if $ has FINITE +--R ?^? : (%,NonNegativeInteger) -> % +--R basis : PositiveInteger -> Vector % +--R characteristic : () -> NonNegativeInteger +--R charthRoot : % -> Union(%,"failed") +--R conditionP : Matrix % -> Union(Vector %,"failed") +--R coordinates : Vector % -> Matrix % +--R createNormalElement : () -> % if $ has FINITE +--R definingPolynomial : () -> SparseUnivariatePolynomial % +--R degree : % -> OnePointCompletion PositiveInteger +--R differentiate : (%,NonNegativeInteger) -> % +--R discreteLog : % -> NonNegativeInteger +--R discreteLog : (%,%) -> Union(NonNegativeInteger,"failed") +--R divide : (%,%) -> Record(quotient: %,remainder: %) +--R euclideanSize : % -> NonNegativeInteger +--R expressIdealMember : (List %,%) -> Union(List %,"failed") +--R exquo : (%,%) -> Union(%,"failed") +--R extendedEuclidean : (%,%,%) -> Union(Record(coef1: %,coef2: %),"failed") +--R extendedEuclidean : (%,%) -> Record(coef1: %,coef2: %,generator: %) +--R extensionDegree : () -> OnePointCompletion PositiveInteger +--R extensionDegree : () -> PositiveInteger +--R factorsOfCyclicGroupSize : () -> List Record(factor: Integer,exponent: Integer) +--R gcdPolynomial : (SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial % +--R generator : () -> % if $ has FINITE +--R linearAssociatedExp : (%,SparseUnivariatePolynomial %) -> % if $ has FINITE +--R linearAssociatedLog : % -> SparseUnivariatePolynomial % if $ has FINITE +--R linearAssociatedLog : (%,%) -> Union(SparseUnivariatePolynomial %,"failed") if $ has FINITE +--R linearAssociatedOrder : % -> SparseUnivariatePolynomial % if $ has FINITE +--R minimalPolynomial : % -> SparseUnivariatePolynomial % +--R minimalPolynomial : (%,PositiveInteger) -> SparseUnivariatePolynomial % if $ has FINITE +--R multiEuclidean : (List %,%) -> Union(List %,"failed") +--R nextItem : % -> Union(%,"failed") +--R norm : (%,PositiveInteger) -> % if $ has FINITE +--R normal? : % -> Boolean if $ has FINITE +--R normalElement : () -> % if $ has FINITE +--R order : % -> OnePointCompletion PositiveInteger +--R primeFrobenius : (%,NonNegativeInteger) -> % +--R principalIdeal : List % -> Record(coef: List %,generator: %) +--R representationType : () -> Union("prime",polynomial,normal,cyclic) +--R retractIfCan : % -> Union(%,"failed") +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R tableForDiscreteLogarithm : Integer -> Table(PositiveInteger,NonNegativeInteger) +--R trace : (%,PositiveInteger) -> % if $ has FINITE +--R transcendenceDegree : () -> NonNegativeInteger +--R unitNormal : % -> Record(unit: %,canonical: %,associate: %) +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +InnerPrimeField examples +==================================================================== + +See Also: +o )show InnerPrimeField + +@ + \pagehead{InnerPrimeField}{IPF} \pagepic{ps/v103innerprimefield.ps}{IPF}{1.00} {\bf See}\\ @@ -49033,6 +58800,134 @@ InnerPrimeField(p:PositiveInteger): Exports == Implementation where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain ISUPS InnerSparseUnivariatePowerSeries} + +<>= +)set break resume +)sys rm -f InnerSparseUnivariatePowerSeries.output +)spool InnerSparseUnivariatePowerSeries.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show InnerSparseUnivariatePowerSeries +--R InnerSparseUnivariatePowerSeries Coef: Ring is a domain constructor +--R Abbreviation for InnerSparseUnivariatePowerSeries is ISUPS +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for ISUPS +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (Coef,%) -> % ?*? : (%,Coef) -> % +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ?=? : (%,%) -> Boolean +--R 1 : () -> % 0 : () -> % +--R ?^? : (%,PositiveInteger) -> % center : % -> Coef +--R coefficient : (%,Integer) -> Coef coerce : Integer -> % +--R coerce : % -> OutputForm complete : % -> % +--R degree : % -> Integer ?.? : (%,Integer) -> Coef +--R extend : (%,Integer) -> % hash : % -> SingleInteger +--R iCompose : (%,%) -> % latex : % -> String +--R leadingCoefficient : % -> Coef leadingMonomial : % -> % +--R map : ((Coef -> Coef),%) -> % monomial : (Coef,Integer) -> % +--R monomial? : % -> Boolean one? : % -> Boolean +--R order : (%,Integer) -> Integer order : % -> Integer +--R pole? : % -> Boolean recip : % -> Union(%,"failed") +--R reductum : % -> % sample : () -> % +--R taylorQuoByVar : % -> % truncate : (%,Integer) -> % +--R variable : % -> Symbol zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean +--R ?*? : (%,Fraction Integer) -> % if Coef has ALGEBRA FRAC INT +--R ?*? : (Fraction Integer,%) -> % if Coef has ALGEBRA FRAC INT +--R ?*? : (NonNegativeInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % +--R ?/? : (%,Coef) -> % if Coef has FIELD +--R D : % -> % if Coef has *: (Integer,Coef) -> Coef +--R D : (%,NonNegativeInteger) -> % if Coef has *: (Integer,Coef) -> Coef +--R D : (%,Symbol) -> % if Coef has *: (Integer,Coef) -> Coef and Coef has PDRING SYMBOL +--R D : (%,List Symbol) -> % if Coef has *: (Integer,Coef) -> Coef and Coef has PDRING SYMBOL +--R D : (%,Symbol,NonNegativeInteger) -> % if Coef has *: (Integer,Coef) -> Coef and Coef has PDRING SYMBOL +--R D : (%,List Symbol,List NonNegativeInteger) -> % if Coef has *: (Integer,Coef) -> Coef and Coef has PDRING SYMBOL +--R ?^? : (%,NonNegativeInteger) -> % +--R approximate : (%,Integer) -> Coef if Coef has **: (Coef,Integer) -> Coef and Coef has coerce: Symbol -> Coef +--R associates? : (%,%) -> Boolean if Coef has INTDOM +--R cAcos : % -> % if Coef has ALGEBRA FRAC INT +--R cAcosh : % -> % if Coef has ALGEBRA FRAC INT +--R cAcot : % -> % if Coef has ALGEBRA FRAC INT +--R cAcoth : % -> % if Coef has ALGEBRA FRAC INT +--R cAcsc : % -> % if Coef has ALGEBRA FRAC INT +--R cAcsch : % -> % if Coef has ALGEBRA FRAC INT +--R cAsec : % -> % if Coef has ALGEBRA FRAC INT +--R cAsech : % -> % if Coef has ALGEBRA FRAC INT +--R cAsin : % -> % if Coef has ALGEBRA FRAC INT +--R cAsinh : % -> % if Coef has ALGEBRA FRAC INT +--R cAtan : % -> % if Coef has ALGEBRA FRAC INT +--R cAtanh : % -> % if Coef has ALGEBRA FRAC INT +--R cCos : % -> % if Coef has ALGEBRA FRAC INT +--R cCosh : % -> % if Coef has ALGEBRA FRAC INT +--R cCot : % -> % if Coef has ALGEBRA FRAC INT +--R cCoth : % -> % if Coef has ALGEBRA FRAC INT +--R cCsc : % -> % if Coef has ALGEBRA FRAC INT +--R cCsch : % -> % if Coef has ALGEBRA FRAC INT +--R cExp : % -> % if Coef has ALGEBRA FRAC INT +--R cLog : % -> % if Coef has ALGEBRA FRAC INT +--R cPower : (%,Coef) -> % if Coef has ALGEBRA FRAC INT +--R cRationalPower : (%,Fraction Integer) -> % if Coef has ALGEBRA FRAC INT +--R cSec : % -> % if Coef has ALGEBRA FRAC INT +--R cSech : % -> % if Coef has ALGEBRA FRAC INT +--R cSin : % -> % if Coef has ALGEBRA FRAC INT +--R cSinh : % -> % if Coef has ALGEBRA FRAC INT +--R cTan : % -> % if Coef has ALGEBRA FRAC INT +--R cTanh : % -> % if Coef has ALGEBRA FRAC INT +--R characteristic : () -> NonNegativeInteger +--R charthRoot : % -> Union(%,"failed") if Coef has CHARNZ +--R coerce : Coef -> % if Coef has COMRING +--R coerce : % -> % if Coef has INTDOM +--R coerce : Fraction Integer -> % if Coef has ALGEBRA FRAC INT +--R differentiate : % -> % if Coef has *: (Integer,Coef) -> Coef +--R differentiate : (%,NonNegativeInteger) -> % if Coef has *: (Integer,Coef) -> Coef +--R differentiate : (%,Symbol) -> % if Coef has *: (Integer,Coef) -> Coef and Coef has PDRING SYMBOL +--R differentiate : (%,List Symbol) -> % if Coef has *: (Integer,Coef) -> Coef and Coef has PDRING SYMBOL +--R differentiate : (%,Symbol,NonNegativeInteger) -> % if Coef has *: (Integer,Coef) -> Coef and Coef has PDRING SYMBOL +--R differentiate : (%,List Symbol,List NonNegativeInteger) -> % if Coef has *: (Integer,Coef) -> Coef and Coef has PDRING SYMBOL +--R ?.? : (%,%) -> % if Integer has SGROUP +--R eval : (%,Coef) -> Stream Coef if Coef has **: (Coef,Integer) -> Coef +--R exquo : (%,%) -> Union(%,"failed") if Coef has INTDOM +--R getRef : % -> Reference OrderedCompletion Integer +--R getStream : % -> Stream Record(k: Integer,c: Coef) +--R iExquo : (%,%,Boolean) -> Union(%,"failed") +--R integrate : % -> % if Coef has ALGEBRA FRAC INT +--R makeSeries : (Reference OrderedCompletion Integer,Stream Record(k: Integer,c: Coef)) -> % +--R monomial : (%,List SingletonAsOrderedSet,List Integer) -> % +--R monomial : (%,SingletonAsOrderedSet,Integer) -> % +--R multiplyCoefficients : ((Integer -> Coef),%) -> % +--R multiplyExponents : (%,PositiveInteger) -> % +--R series : Stream Record(k: Integer,c: Coef) -> % +--R seriesToOutputForm : (Stream Record(k: Integer,c: Coef),Reference OrderedCompletion Integer,Symbol,Coef,Fraction Integer) -> OutputForm +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R terms : % -> Stream Record(k: Integer,c: Coef) +--R truncate : (%,Integer,Integer) -> % +--R unit? : % -> Boolean if Coef has INTDOM +--R unitCanonical : % -> % if Coef has INTDOM +--R unitNormal : % -> Record(unit: %,canonical: %,associate: %) if Coef has INTDOM +--R variables : % -> List SingletonAsOrderedSet +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +InnerSparseUnivariatePowerSeries examples +==================================================================== + +See Also: +o )show InnerSparseUnivariatePowerSeries + +@ + \pagehead{InnerSparseUnivariatePowerSeries}{ISUPS} \pagepic{ps/v103innersparseunivariatepowerseries.ps}{ISUPS}{1.00} @@ -50203,6 +60098,113 @@ InnerSparseUnivariatePowerSeries(Coef): Exports == Implementation where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain INTABL InnerTable} + +<>= +)set break resume +)sys rm -f InnerTable.output +)spool InnerTable.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show InnerTable +--R InnerTable(Key: SetCategory,Entry: SetCategory,addDom) where +--R addDom: TableAggregate(Key,Entry) with +--R finiteAggregate is a domain constructor +--R Abbreviation for InnerTable is INTABL +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for INTABL +--R +--R------------------------------- Operations -------------------------------- +--R copy : % -> % dictionary : () -> % +--R elt : (%,Key,Entry) -> Entry ?.? : (%,Key) -> Entry +--R empty : () -> % empty? : % -> Boolean +--R entries : % -> List Entry eq? : (%,%) -> Boolean +--R index? : (Key,%) -> Boolean indices : % -> List Key +--R key? : (Key,%) -> Boolean keys : % -> List Key +--R map : ((Entry -> Entry),%) -> % qelt : (%,Key) -> Entry +--R sample : () -> % setelt : (%,Key,Entry) -> Entry +--R table : () -> % +--R #? : % -> NonNegativeInteger if $ has finiteAggregate +--R ?=? : (%,%) -> Boolean if Record(key: Key,entry: Entry) has SETCAT or Entry has SETCAT +--R any? : ((Entry -> Boolean),%) -> Boolean if $ has finiteAggregate +--R any? : ((Record(key: Key,entry: Entry) -> Boolean),%) -> Boolean if $ has finiteAggregate +--R bag : List Record(key: Key,entry: Entry) -> % +--R coerce : % -> OutputForm if Record(key: Key,entry: Entry) has SETCAT or Entry has SETCAT +--R construct : List Record(key: Key,entry: Entry) -> % +--R convert : % -> InputForm if Record(key: Key,entry: Entry) has KONVERT INFORM +--R count : ((Entry -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate +--R count : (Entry,%) -> NonNegativeInteger if $ has finiteAggregate and Entry has SETCAT +--R count : (Record(key: Key,entry: Entry),%) -> NonNegativeInteger if $ has finiteAggregate and Record(key: Key,entry: Entry) has SETCAT +--R count : ((Record(key: Key,entry: Entry) -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate +--R dictionary : List Record(key: Key,entry: Entry) -> % +--R entry? : (Entry,%) -> Boolean if $ has finiteAggregate and Entry has SETCAT +--R eval : (%,List Equation Entry) -> % if Entry has EVALAB Entry and Entry has SETCAT +--R eval : (%,Equation Entry) -> % if Entry has EVALAB Entry and Entry has SETCAT +--R eval : (%,Entry,Entry) -> % if Entry has EVALAB Entry and Entry has SETCAT +--R eval : (%,List Entry,List Entry) -> % if Entry has EVALAB Entry and Entry has SETCAT +--R eval : (%,List Record(key: Key,entry: Entry),List Record(key: Key,entry: Entry)) -> % if Record(key: Key,entry: Entry) has EVALAB Record(key: Key,entry: Entry) and Record(key: Key,entry: Entry) has SETCAT +--R eval : (%,Record(key: Key,entry: Entry),Record(key: Key,entry: Entry)) -> % if Record(key: Key,entry: Entry) has EVALAB Record(key: Key,entry: Entry) and Record(key: Key,entry: Entry) has SETCAT +--R eval : (%,Equation Record(key: Key,entry: Entry)) -> % if Record(key: Key,entry: Entry) has EVALAB Record(key: Key,entry: Entry) and Record(key: Key,entry: Entry) has SETCAT +--R eval : (%,List Equation Record(key: Key,entry: Entry)) -> % if Record(key: Key,entry: Entry) has EVALAB Record(key: Key,entry: Entry) and Record(key: Key,entry: Entry) has SETCAT +--R every? : ((Entry -> Boolean),%) -> Boolean if $ has finiteAggregate +--R every? : ((Record(key: Key,entry: Entry) -> Boolean),%) -> Boolean if $ has finiteAggregate +--R extract! : % -> Record(key: Key,entry: Entry) +--R fill! : (%,Entry) -> % if $ has shallowlyMutable +--R find : ((Record(key: Key,entry: Entry) -> Boolean),%) -> Union(Record(key: Key,entry: Entry),"failed") +--R first : % -> Entry if Key has ORDSET +--R hash : % -> SingleInteger if Record(key: Key,entry: Entry) has SETCAT or Entry has SETCAT +--R insert! : (Record(key: Key,entry: Entry),%) -> % +--R inspect : % -> Record(key: Key,entry: Entry) +--R latex : % -> String if Record(key: Key,entry: Entry) has SETCAT or Entry has SETCAT +--R less? : (%,NonNegativeInteger) -> Boolean +--R map : (((Entry,Entry) -> Entry),%,%) -> % +--R map : ((Record(key: Key,entry: Entry) -> Record(key: Key,entry: Entry)),%) -> % +--R map! : ((Entry -> Entry),%) -> % if $ has shallowlyMutable +--R map! : ((Record(key: Key,entry: Entry) -> Record(key: Key,entry: Entry)),%) -> % if $ has shallowlyMutable +--R maxIndex : % -> Key if Key has ORDSET +--R member? : (Entry,%) -> Boolean if $ has finiteAggregate and Entry has SETCAT +--R member? : (Record(key: Key,entry: Entry),%) -> Boolean if $ has finiteAggregate and Record(key: Key,entry: Entry) has SETCAT +--R members : % -> List Entry if $ has finiteAggregate +--R members : % -> List Record(key: Key,entry: Entry) if $ has finiteAggregate +--R minIndex : % -> Key if Key has ORDSET +--R more? : (%,NonNegativeInteger) -> Boolean +--R parts : % -> List Entry if $ has finiteAggregate +--R parts : % -> List Record(key: Key,entry: Entry) if $ has finiteAggregate +--R qsetelt! : (%,Key,Entry) -> Entry if $ has shallowlyMutable +--R reduce : (((Record(key: Key,entry: Entry),Record(key: Key,entry: Entry)) -> Record(key: Key,entry: Entry)),%) -> Record(key: Key,entry: Entry) if $ has finiteAggregate +--R reduce : (((Record(key: Key,entry: Entry),Record(key: Key,entry: Entry)) -> Record(key: Key,entry: Entry)),%,Record(key: Key,entry: Entry)) -> Record(key: Key,entry: Entry) if $ has finiteAggregate +--R reduce : (((Record(key: Key,entry: Entry),Record(key: Key,entry: Entry)) -> Record(key: Key,entry: Entry)),%,Record(key: Key,entry: Entry),Record(key: Key,entry: Entry)) -> Record(key: Key,entry: Entry) if $ has finiteAggregate and Record(key: Key,entry: Entry) has SETCAT +--R remove : ((Record(key: Key,entry: Entry) -> Boolean),%) -> % if $ has finiteAggregate +--R remove : (Record(key: Key,entry: Entry),%) -> % if $ has finiteAggregate and Record(key: Key,entry: Entry) has SETCAT +--R remove! : (Key,%) -> Union(Entry,"failed") +--R remove! : ((Record(key: Key,entry: Entry) -> Boolean),%) -> % if $ has finiteAggregate +--R remove! : (Record(key: Key,entry: Entry),%) -> % if $ has finiteAggregate +--R removeDuplicates : % -> % if $ has finiteAggregate and Record(key: Key,entry: Entry) has SETCAT +--R search : (Key,%) -> Union(Entry,"failed") +--R select : ((Record(key: Key,entry: Entry) -> Boolean),%) -> % if $ has finiteAggregate +--R select! : ((Record(key: Key,entry: Entry) -> Boolean),%) -> % if $ has finiteAggregate +--R size? : (%,NonNegativeInteger) -> Boolean +--R swap! : (%,Key,Key) -> Void if $ has shallowlyMutable +--R table : List Record(key: Key,entry: Entry) -> % +--R ?~=? : (%,%) -> Boolean if Record(key: Key,entry: Entry) has SETCAT or Entry has SETCAT +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +InnerTable examples +==================================================================== + +See Also: +o )show InnerTable + +@ + \pagehead{InnerTable}{INTABL} \pagepic{ps/v103innertable.ps}{INTABL}{1.00} {\bf See}\\ @@ -50305,6 +60307,65 @@ InnerTable(Key: SetCategory, Entry: SetCategory, addDom):Exports == Implementati @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain ITAYLOR InnerTaylorSeries} + +<>= +)set break resume +)sys rm -f InnerTaylorSeries.output +)spool InnerTaylorSeries.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show InnerTaylorSeries +--R InnerTaylorSeries Coef: Ring is a domain constructor +--R Abbreviation for InnerTaylorSeries is ITAYLOR +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for ITAYLOR +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (%,Integer) -> % ?*? : (%,Coef) -> % +--R ?*? : (Coef,%) -> % ?*? : (%,%) -> % +--R ?*? : (Integer,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,PositiveInteger) -> % ?+? : (%,%) -> % +--R ?-? : (%,%) -> % -? : % -> % +--R ?=? : (%,%) -> Boolean 1 : () -> % +--R 0 : () -> % ?^? : (%,PositiveInteger) -> % +--R coefficients : % -> Stream Coef coerce : Integer -> % +--R coerce : % -> OutputForm hash : % -> SingleInteger +--R latex : % -> String one? : % -> Boolean +--R order : % -> NonNegativeInteger pole? : % -> Boolean +--R recip : % -> Union(%,"failed") sample : () -> % +--R series : Stream Coef -> % zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean +--R ?*? : (NonNegativeInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % +--R ?^? : (%,NonNegativeInteger) -> % +--R associates? : (%,%) -> Boolean if Coef has INTDOM +--R characteristic : () -> NonNegativeInteger +--R coerce : % -> % if Coef has INTDOM +--R exquo : (%,%) -> Union(%,"failed") if Coef has INTDOM +--R order : (%,NonNegativeInteger) -> NonNegativeInteger +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R unit? : % -> Boolean if Coef has INTDOM +--R unitCanonical : % -> % if Coef has INTDOM +--R unitNormal : % -> Record(unit: %,canonical: %,associate: %) if Coef has INTDOM +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +InnerTaylorSeries examples +==================================================================== + +See Also: +o )show InnerTaylorSeries + +@ + \pagehead{InnerTaylorSeries}{ITAYLOR} \pagepic{ps/v103innertaylorseries.ps}{ITAYLOR}{1.00} {\bf See}\\ @@ -50488,6 +60549,65 @@ InnerTaylorSeries(Coef): Exports == Implementation where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain INFORM InputForm} + +<>= +)set break resume +)sys rm -f InputForm.output +)spool InputForm.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show InputForm +--R InputForm is a domain constructor +--R Abbreviation for InputForm is INFORM +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for INFORM +--R +--R------------------------------- Operations -------------------------------- +--R #? : % -> Integer ?*? : (%,%) -> % +--R ?**? : (%,Integer) -> % ?+? : (%,%) -> % +--R ?/? : (%,%) -> % ?=? : (%,%) -> Boolean +--R 1 : () -> % 0 : () -> % +--R atom? : % -> Boolean binary : (%,List %) -> % +--R car : % -> % cdr : % -> % +--R coerce : % -> OutputForm convert : SExpression -> % +--R convert : % -> SExpression convert : OutputForm -> % +--R convert : DoubleFloat -> % convert : Integer -> % +--R convert : Symbol -> % convert : String -> % +--R convert : List % -> % declare : List % -> Symbol +--R destruct : % -> List % ?.? : (%,List Integer) -> % +--R ?.? : (%,Integer) -> % eq : (%,%) -> Boolean +--R expr : % -> OutputForm flatten : % -> % +--R float : % -> DoubleFloat float? : % -> Boolean +--R hash : % -> SingleInteger integer : % -> Integer +--R integer? : % -> Boolean interpret : % -> Any +--R lambda : (%,List Symbol) -> % latex : % -> String +--R list? : % -> Boolean null? : % -> Boolean +--R pair? : % -> Boolean parse : String -> % +--R string : % -> String string? : % -> Boolean +--R symbol : % -> Symbol symbol? : % -> Boolean +--R unparse : % -> String ?~=? : (%,%) -> Boolean +--R ?**? : (%,NonNegativeInteger) -> % +--R compile : (Symbol,List %) -> Symbol +--R function : (%,List Symbol,Symbol) -> % +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +InputForm examples +==================================================================== + +See Also: +o )show InputForm + +@ + \pagehead{InputForm}{INFORM} \pagepic{ps/v103inputform.ps}{INFORM}{1.00} @@ -50733,6 +60853,7 @@ InputForm(): The function {\bf one?} has been rewritten back to its original form. The NAG version called a lisp primitive that exists only in Codemist Common Lisp and is not defined in Common Lisp. + <>= )set break resume )sys rm -f Integer.output @@ -51680,6 +61801,58 @@ Integer: Join(IntegerNumberSystem, ConvertibleTo String, OpenMath) with @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain ZMOD IntegerMod} + +<>= +)set break resume +)sys rm -f IntegerMod.output +)spool IntegerMod.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show IntegerMod +--R IntegerMod p: PositiveInteger is a domain constructor +--R Abbreviation for IntegerMod is ZMOD +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for ZMOD +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ?=? : (%,%) -> Boolean +--R 1 : () -> % 0 : () -> % +--R ?^? : (%,PositiveInteger) -> % coerce : Integer -> % +--R coerce : % -> OutputForm convert : % -> Integer +--R hash : % -> SingleInteger index : PositiveInteger -> % +--R init : () -> % latex : % -> String +--R lookup : % -> PositiveInteger one? : % -> Boolean +--R random : () -> % recip : % -> Union(%,"failed") +--R sample : () -> % size : () -> NonNegativeInteger +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean +--R ?*? : (NonNegativeInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % +--R ?^? : (%,NonNegativeInteger) -> % +--R characteristic : () -> NonNegativeInteger +--R nextItem : % -> Union(%,"failed") +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +IntegerMod examples +==================================================================== + +See Also: +o )show IntegerMod + +@ + \pagehead{IntegerMod}{ZMOD} \pagepic{ps/v103integermod.ps}{ZMOD}{1.00} @@ -51808,6 +61981,46 @@ IntegerMod(p:PositiveInteger): @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain INTFTBL IntegrationFunctionsTable} + +<>= +)set break resume +)sys rm -f IntegrationFunctionsTable.output +)spool IntegrationFunctionsTable.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show IntegrationFunctionsTable +--R IntegrationFunctionsTable is a domain constructor +--R Abbreviation for IntegrationFunctionsTable is INTFTBL +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for INTFTBL +--R +--R------------------------------- Operations -------------------------------- +--R clearTheFTable : () -> Void showTheFTable : () -> % +--R entries : % -> List Record(key: Record(var: Symbol,fn: Expression DoubleFloat,range: Segment OrderedCompletion DoubleFloat,abserr: DoubleFloat,relerr: DoubleFloat),entry: Record(endPointContinuity: Union(continuous: Continuous at the end points,lowerSingular: There is a singularity at the lower end point,upperSingular: There is a singularity at the upper end point,bothSingular: There are singularities at both end points,notEvaluated: End point continuity not yet evaluated),singularitiesStream: Union(str: Stream DoubleFloat,notEvaluated: Internal singularities not yet evaluated),range: Union(finite: The range is finite,lowerInfinite: The bottom of range is infinite,upperInfinite: The top of range is infinite,bothInfinite: Both top and bottom points are infinite,notEvaluated: Range not yet evaluated))) +--R entry : Record(var: Symbol,fn: Expression DoubleFloat,range: Segment OrderedCompletion DoubleFloat,abserr: DoubleFloat,relerr: DoubleFloat) -> Record(endPointContinuity: Union(continuous: Continuous at the end points,lowerSingular: There is a singularity at the lower end point,upperSingular: There is a singularity at the upper end point,bothSingular: There are singularities at both end points,notEvaluated: End point continuity not yet evaluated),singularitiesStream: Union(str: Stream DoubleFloat,notEvaluated: Internal singularities not yet evaluated),range: Union(finite: The range is finite,lowerInfinite: The bottom of range is infinite,upperInfinite: The top of range is infinite,bothInfinite: Both top and bottom points are infinite,notEvaluated: Range not yet evaluated)) +--R fTable : List Record(key: Record(var: Symbol,fn: Expression DoubleFloat,range: Segment OrderedCompletion DoubleFloat,abserr: DoubleFloat,relerr: DoubleFloat),entry: Record(endPointContinuity: Union(continuous: Continuous at the end points,lowerSingular: There is a singularity at the lower end point,upperSingular: There is a singularity at the upper end point,bothSingular: There are singularities at both end points,notEvaluated: End point continuity not yet evaluated),singularitiesStream: Union(str: Stream DoubleFloat,notEvaluated: Internal singularities not yet evaluated),range: Union(finite: The range is finite,lowerInfinite: The bottom of range is infinite,upperInfinite: The top of range is infinite,bothInfinite: Both top and bottom points are infinite,notEvaluated: Range not yet evaluated))) -> % +--R insert! : Record(key: Record(var: Symbol,fn: Expression DoubleFloat,range: Segment OrderedCompletion DoubleFloat,abserr: DoubleFloat,relerr: DoubleFloat),entry: Record(endPointContinuity: Union(continuous: Continuous at the end points,lowerSingular: There is a singularity at the lower end point,upperSingular: There is a singularity at the upper end point,bothSingular: There are singularities at both end points,notEvaluated: End point continuity not yet evaluated),singularitiesStream: Union(str: Stream DoubleFloat,notEvaluated: Internal singularities not yet evaluated),range: Union(finite: The range is finite,lowerInfinite: The bottom of range is infinite,upperInfinite: The top of range is infinite,bothInfinite: Both top and bottom points are infinite,notEvaluated: Range not yet evaluated))) -> % +--R keys : % -> List Record(var: Symbol,fn: Expression DoubleFloat,range: Segment OrderedCompletion DoubleFloat,abserr: DoubleFloat,relerr: DoubleFloat) +--R showAttributes : Record(var: Symbol,fn: Expression DoubleFloat,range: Segment OrderedCompletion DoubleFloat,abserr: DoubleFloat,relerr: DoubleFloat) -> Union(Record(endPointContinuity: Union(continuous: Continuous at the end points,lowerSingular: There is a singularity at the lower end point,upperSingular: There is a singularity at the upper end point,bothSingular: There are singularities at both end points,notEvaluated: End point continuity not yet evaluated),singularitiesStream: Union(str: Stream DoubleFloat,notEvaluated: Internal singularities not yet evaluated),range: Union(finite: The range is finite,lowerInfinite: The bottom of range is infinite,upperInfinite: The top of range is infinite,bothInfinite: Both top and bottom points are infinite,notEvaluated: Range not yet evaluated)),"failed") +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +IntegrationFunctionsTable examples +==================================================================== + +See Also: +o )show IntegrationFunctionsTable + +@ + \pagehead{IntegrationFunctionsTable}{INTFTBL} \pagepic{ps/v103integrationfunctionstable.ps}{INTFTBL}{1.00} @@ -51930,6 +62143,58 @@ IntegrationFunctionsTable(): E == I where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain IR IntegrationResult} + +<>= +)set break resume +)sys rm -f IntegrationResult.output +)spool IntegrationResult.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show IntegrationResult +--R IntegrationResult F: Field is a domain constructor +--R Abbreviation for IntegrationResult is IR +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for IR +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (%,Fraction Integer) -> % ?*? : (Fraction Integer,%) -> % +--R ?*? : (Integer,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ?=? : (%,%) -> Boolean +--R 0 : () -> % coerce : F -> % +--R coerce : % -> OutputForm differentiate : (%,(F -> F)) -> F +--R elem? : % -> Boolean hash : % -> SingleInteger +--R integral : (F,F) -> % latex : % -> String +--R ratpart : % -> F retract : % -> F +--R sample : () -> % zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean +--R ?*? : (NonNegativeInteger,%) -> % +--R differentiate : (%,Symbol) -> F if F has PDRING SYMBOL +--R integral : (F,Symbol) -> % if F has RETRACT SYMBOL +--R logpart : % -> List Record(scalar: Fraction Integer,coeff: SparseUnivariatePolynomial F,logand: SparseUnivariatePolynomial F) +--R mkAnswer : (F,List Record(scalar: Fraction Integer,coeff: SparseUnivariatePolynomial F,logand: SparseUnivariatePolynomial F),List Record(integrand: F,intvar: F)) -> % +--R notelem : % -> List Record(integrand: F,intvar: F) +--R retractIfCan : % -> Union(F,"failed") +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +IntegrationResult examples +==================================================================== + +See Also: +o )show IntegrationResult + +@ + \pagehead{IntegrationResult}{IR} \pagepic{ps/v103integrationresult.ps}{IR}{1.00} @@ -52140,6 +62405,7 @@ IntegrationResult(F:Field): Exports == Implementation where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain INTRVL Interval} + <>= )set break resume )sys rm -f Interval.output @@ -52894,6 +63160,7 @@ Interval(R:Join(FloatingPointSystem,TranscendentalFunctionCategory)): IntervalCa \chapter{Chapter K} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain KERNEL Kernel} + <>= )set break resume )sys rm -f Kernel.output @@ -53383,6 +63650,7 @@ Kernel(S:OrderedSet): Exports == Implementation where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain KAFILE KeyedAccessFile} + <>= )set break resume )sys rm -f KeyedAccessFile.output @@ -53878,6 +64146,104 @@ KeyedAccessFile(Entry): KAFcategory == KAFcapsule where \chapter{Chapter L} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain LAUPOL LaurentPolynomial} + +<>= +)set break resume +)sys rm -f LaurentPolynomial.output +)spool LaurentPolynomial.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show LaurentPolynomial +--R LaurentPolynomial(R: IntegralDomain,UP: UnivariatePolynomialCategory R) is a domain constructor +--R Abbreviation for LaurentPolynomial is LAUPOL +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for LAUPOL +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ?=? : (%,%) -> Boolean +--R D : % -> % if UP has DIFRING D : (%,(UP -> UP)) -> % +--R 1 : () -> % 0 : () -> % +--R ?^? : (%,PositiveInteger) -> % associates? : (%,%) -> Boolean +--R coefficient : (%,Integer) -> R coerce : UP -> % +--R coerce : R -> % coerce : % -> % +--R coerce : Integer -> % coerce : % -> OutputForm +--R convert : % -> Fraction UP degree : % -> Integer +--R hash : % -> SingleInteger latex : % -> String +--R leadingCoefficient : % -> R monomial : (R,Integer) -> % +--R monomial? : % -> Boolean one? : % -> Boolean +--R order : % -> Integer recip : % -> Union(%,"failed") +--R reductum : % -> % retract : % -> UP +--R retract : % -> R sample : () -> % +--R trailingCoefficient : % -> R unit? : % -> Boolean +--R unitCanonical : % -> % zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean +--R ?*? : (NonNegativeInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % +--R D : (%,NonNegativeInteger) -> % if UP has DIFRING +--R D : (%,Symbol) -> % if UP has PDRING SYMBOL +--R D : (%,List Symbol) -> % if UP has PDRING SYMBOL +--R D : (%,Symbol,NonNegativeInteger) -> % if UP has PDRING SYMBOL +--R D : (%,List Symbol,List NonNegativeInteger) -> % if UP has PDRING SYMBOL +--R D : (%,(UP -> UP),NonNegativeInteger) -> % +--R ?^? : (%,NonNegativeInteger) -> % +--R characteristic : () -> NonNegativeInteger +--R charthRoot : % -> Union(%,"failed") if R has CHARNZ +--R coerce : Fraction Integer -> % if R has RETRACT FRAC INT +--R differentiate : % -> % if UP has DIFRING +--R differentiate : (%,NonNegativeInteger) -> % if UP has DIFRING +--R differentiate : (%,Symbol) -> % if UP has PDRING SYMBOL +--R differentiate : (%,List Symbol) -> % if UP has PDRING SYMBOL +--R differentiate : (%,Symbol,NonNegativeInteger) -> % if UP has PDRING SYMBOL +--R differentiate : (%,List Symbol,List NonNegativeInteger) -> % if UP has PDRING SYMBOL +--R differentiate : (%,(UP -> UP),NonNegativeInteger) -> % +--R differentiate : (%,(UP -> UP)) -> % +--R divide : (%,%) -> Record(quotient: %,remainder: %) if R has FIELD +--R euclideanSize : % -> NonNegativeInteger if R has FIELD +--R expressIdealMember : (List %,%) -> Union(List %,"failed") if R has FIELD +--R exquo : (%,%) -> Union(%,"failed") +--R extendedEuclidean : (%,%) -> Record(coef1: %,coef2: %,generator: %) if R has FIELD +--R extendedEuclidean : (%,%,%) -> Union(Record(coef1: %,coef2: %),"failed") if R has FIELD +--R gcd : (%,%) -> % if R has FIELD +--R gcd : List % -> % if R has FIELD +--R gcdPolynomial : (SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial % if R has FIELD +--R lcm : (%,%) -> % if R has FIELD +--R lcm : List % -> % if R has FIELD +--R multiEuclidean : (List %,%) -> Union(List %,"failed") if R has FIELD +--R principalIdeal : List % -> Record(coef: List %,generator: %) if R has FIELD +--R ?quo? : (%,%) -> % if R has FIELD +--R ?rem? : (%,%) -> % if R has FIELD +--R retract : % -> Fraction Integer if R has RETRACT FRAC INT +--R retract : % -> Integer if R has RETRACT INT +--R retractIfCan : % -> Union(UP,"failed") +--R retractIfCan : % -> Union(R,"failed") +--R retractIfCan : % -> Union(Fraction Integer,"failed") if R has RETRACT FRAC INT +--R retractIfCan : % -> Union(Integer,"failed") if R has RETRACT INT +--R separate : Fraction UP -> Record(polyPart: %,fracPart: Fraction UP) if R has FIELD +--R sizeLess? : (%,%) -> Boolean if R has FIELD +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R unitNormal : % -> Record(unit: %,canonical: %,associate: %) +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +LaurentPolynomial examples +==================================================================== + +See Also: +o )show LaurentPolynomial + +@ + \pagehead{LaurentPolynomial}{LAUPOL} \pagepic{ps/v103laurentpolynomial.ps}{LAUPOL}{1.00} @@ -54105,6 +64471,7 @@ LaurentPolynomial(R, UP): Exports == Implementation where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain LIB Library} + <>= )set break resume )sys rm -f Library.output @@ -54342,6 +64709,7 @@ Library(): TableAggregate(String, Any) with @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain LEXP LieExponentials} + <>= )set break resume )sys rm -f LieExponentials.output @@ -54735,6 +65103,7 @@ LieExponentials(VarSet, R, Order): XDPcat == XDPdef where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain LPOLY LiePolynomial} + <>= )set break resume )sys rm -f LiePolynomial.output @@ -55384,6 +65753,175 @@ LiePolynomial(VarSet:OrderedSet, R:CommutativeRing) : Public == Private where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain LSQM LieSquareMatrix} + +<>= +)set break resume +)sys rm -f LieSquareMatrix.output +)spool LieSquareMatrix.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show LieSquareMatrix +--R LieSquareMatrix(n: PositiveInteger,R: CommutativeRing) is a domain constructor +--R Abbreviation for LieSquareMatrix is LSQM +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for LSQM +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (R,%) -> % ?*? : (%,R) -> % +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ?=? : (%,%) -> Boolean +--R D : % -> % if R has DIFRING D : (%,(R -> R)) -> % +--R 1 : () -> % 0 : () -> % +--R ?^? : (%,PositiveInteger) -> % alternative? : () -> Boolean +--R antiAssociative? : () -> Boolean antiCommutative? : () -> Boolean +--R antiCommutator : (%,%) -> % antisymmetric? : % -> Boolean +--R apply : (Matrix R,%) -> % associative? : () -> Boolean +--R associator : (%,%,%) -> % basis : () -> Vector % +--R coerce : % -> Matrix R coerce : R -> % +--R coerce : Integer -> % coerce : % -> OutputForm +--R commutative? : () -> Boolean commutator : (%,%) -> % +--R convert : % -> Vector R convert : Vector R -> % +--R coordinates : % -> Vector R copy : % -> % +--R diagonal? : % -> Boolean diagonalMatrix : List R -> % +--R diagonalProduct : % -> R ?.? : (%,Integer) -> R +--R elt : (%,Integer,Integer) -> R elt : (%,Integer,Integer,R) -> R +--R empty : () -> % empty? : % -> Boolean +--R eq? : (%,%) -> Boolean flexible? : () -> Boolean +--R hash : % -> SingleInteger jacobiIdentity? : () -> Boolean +--R jordanAdmissible? : () -> Boolean jordanAlgebra? : () -> Boolean +--R latex : % -> String leftAlternative? : () -> Boolean +--R leftDiscriminant : Vector % -> R leftDiscriminant : () -> R +--R leftNorm : % -> R leftTrace : % -> R +--R leftTraceMatrix : () -> Matrix R lieAdmissible? : () -> Boolean +--R lieAlgebra? : () -> Boolean listOfLists : % -> List List R +--R map : ((R -> R),%) -> % map : (((R,R) -> R),%,%) -> % +--R matrix : List List R -> % maxColIndex : % -> Integer +--R maxRowIndex : % -> Integer minColIndex : % -> Integer +--R minRowIndex : % -> Integer ncols : % -> NonNegativeInteger +--R nrows : % -> NonNegativeInteger one? : % -> Boolean +--R powerAssociative? : () -> Boolean qelt : (%,Integer,Integer) -> R +--R rank : () -> PositiveInteger recip : % -> Union(%,"failed") +--R represents : Vector R -> % retract : % -> R +--R rightAlternative? : () -> Boolean rightDiscriminant : Vector % -> R +--R rightDiscriminant : () -> R rightNorm : % -> R +--R rightTrace : % -> R rightTraceMatrix : () -> Matrix R +--R sample : () -> % scalarMatrix : R -> % +--R someBasis : () -> Vector % square? : % -> Boolean +--R symmetric? : % -> Boolean trace : % -> R +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean +--R #? : % -> NonNegativeInteger if $ has finiteAggregate +--R ?*? : (DirectProduct(n,R),%) -> DirectProduct(n,R) +--R ?*? : (%,DirectProduct(n,R)) -> DirectProduct(n,R) +--R ?*? : (NonNegativeInteger,%) -> % +--R ?**? : (%,Integer) -> % if R has FIELD +--R ?**? : (%,NonNegativeInteger) -> % +--R ?/? : (%,R) -> % if R has FIELD +--R D : (%,NonNegativeInteger) -> % if R has DIFRING +--R D : (%,Symbol) -> % if R has PDRING SYMBOL +--R D : (%,List Symbol) -> % if R has PDRING SYMBOL +--R D : (%,Symbol,NonNegativeInteger) -> % if R has PDRING SYMBOL +--R D : (%,List Symbol,List NonNegativeInteger) -> % if R has PDRING SYMBOL +--R D : (%,(R -> R),NonNegativeInteger) -> % +--R ?^? : (%,NonNegativeInteger) -> % +--R any? : ((R -> Boolean),%) -> Boolean if $ has finiteAggregate +--R associatorDependence : () -> List Vector R if R has INTDOM +--R characteristic : () -> NonNegativeInteger +--R coerce : Fraction Integer -> % if R has RETRACT FRAC INT +--R column : (%,Integer) -> DirectProduct(n,R) +--R conditionsForIdempotents : Vector % -> List Polynomial R +--R conditionsForIdempotents : () -> List Polynomial R +--R coordinates : (%,Vector %) -> Vector R +--R coordinates : (Vector %,Vector %) -> Matrix R +--R coordinates : Vector % -> Matrix R +--R count : (R,%) -> NonNegativeInteger if $ has finiteAggregate and R has SETCAT +--R count : ((R -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate +--R determinant : % -> R if R has commutative * +--R diagonal : % -> DirectProduct(n,R) +--R differentiate : % -> % if R has DIFRING +--R differentiate : (%,NonNegativeInteger) -> % if R has DIFRING +--R differentiate : (%,Symbol) -> % if R has PDRING SYMBOL +--R differentiate : (%,List Symbol) -> % if R has PDRING SYMBOL +--R differentiate : (%,Symbol,NonNegativeInteger) -> % if R has PDRING SYMBOL +--R differentiate : (%,List Symbol,List NonNegativeInteger) -> % if R has PDRING SYMBOL +--R differentiate : (%,(R -> R),NonNegativeInteger) -> % +--R differentiate : (%,(R -> R)) -> % +--R eval : (%,List R,List R) -> % if R has EVALAB R and R has SETCAT +--R eval : (%,R,R) -> % if R has EVALAB R and R has SETCAT +--R eval : (%,Equation R) -> % if R has EVALAB R and R has SETCAT +--R eval : (%,List Equation R) -> % if R has EVALAB R and R has SETCAT +--R every? : ((R -> Boolean),%) -> Boolean if $ has finiteAggregate +--R exquo : (%,R) -> Union(%,"failed") if R has INTDOM +--R inverse : % -> Union(%,"failed") if R has FIELD +--R leftCharacteristicPolynomial : % -> SparseUnivariatePolynomial R +--R leftMinimalPolynomial : % -> SparseUnivariatePolynomial R if R has INTDOM +--R leftPower : (%,PositiveInteger) -> % +--R leftRankPolynomial : () -> SparseUnivariatePolynomial Polynomial R if R has FIELD +--R leftRecip : % -> Union(%,"failed") if R has INTDOM +--R leftRegularRepresentation : (%,Vector %) -> Matrix R +--R leftRegularRepresentation : % -> Matrix R +--R leftTraceMatrix : Vector % -> Matrix R +--R leftUnit : () -> Union(%,"failed") if R has INTDOM +--R leftUnits : () -> Union(Record(particular: %,basis: List %),"failed") if R has INTDOM +--R less? : (%,NonNegativeInteger) -> Boolean +--R map! : ((R -> R),%) -> % if $ has shallowlyMutable +--R member? : (R,%) -> Boolean if $ has finiteAggregate and R has SETCAT +--R members : % -> List R if $ has finiteAggregate +--R minordet : % -> R if R has commutative * +--R more? : (%,NonNegativeInteger) -> Boolean +--R noncommutativeJordanAlgebra? : () -> Boolean +--R nullSpace : % -> List DirectProduct(n,R) if R has INTDOM +--R nullity : % -> NonNegativeInteger if R has INTDOM +--R parts : % -> List R if $ has finiteAggregate +--R plenaryPower : (%,PositiveInteger) -> % +--R rank : % -> NonNegativeInteger if R has INTDOM +--R reducedSystem : Matrix % -> Matrix R +--R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix R,vec: Vector R) +--R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix Integer,vec: Vector Integer) if R has LINEXP INT +--R reducedSystem : Matrix % -> Matrix Integer if R has LINEXP INT +--R represents : (Vector R,Vector %) -> % +--R retract : % -> Fraction Integer if R has RETRACT FRAC INT +--R retract : % -> Integer if R has RETRACT INT +--R retractIfCan : % -> Union(R,"failed") +--R retractIfCan : % -> Union(Fraction Integer,"failed") if R has RETRACT FRAC INT +--R retractIfCan : % -> Union(Integer,"failed") if R has RETRACT INT +--R rightCharacteristicPolynomial : % -> SparseUnivariatePolynomial R +--R rightMinimalPolynomial : % -> SparseUnivariatePolynomial R if R has INTDOM +--R rightPower : (%,PositiveInteger) -> % +--R rightRankPolynomial : () -> SparseUnivariatePolynomial Polynomial R if R has FIELD +--R rightRecip : % -> Union(%,"failed") if R has INTDOM +--R rightRegularRepresentation : (%,Vector %) -> Matrix R +--R rightRegularRepresentation : % -> Matrix R +--R rightTraceMatrix : Vector % -> Matrix R +--R rightUnit : () -> Union(%,"failed") if R has INTDOM +--R rightUnits : () -> Union(Record(particular: %,basis: List %),"failed") if R has INTDOM +--R row : (%,Integer) -> DirectProduct(n,R) +--R rowEchelon : % -> % if R has EUCDOM +--R size? : (%,NonNegativeInteger) -> Boolean +--R structuralConstants : Vector % -> Vector Matrix R +--R structuralConstants : () -> Vector Matrix R +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R unit : () -> Union(%,"failed") if R has INTDOM +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +LieSquareMatrix examples +==================================================================== + +See Also: +o )show LieSquareMatrix + +@ + \pagehead{LieSquareMatrix}{LSQM} \pagepic{ps/v103liesquarematrix.ps}{LSQM}{1.00} {\bf See}\\ @@ -55616,6 +66154,7 @@ LieSquareMatrix(n,R): Exports == Implementation where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain LODO LinearOrdinaryDifferentialOperator} + <>= )set break resume )sys rm -f LinearOrdinaryDifferentialOperator.output @@ -56208,6 +66747,7 @@ LinearOrdinaryDifferentialOperator(A:Ring, diff: A -> A): @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain LODO1 LinearOrdinaryDifferentialOperator1} + <>= )set break resume )sys rm -f LinearOrdinaryDifferentialOperator1.output @@ -56689,6 +67229,7 @@ LinearOrdinaryDifferentialOperator1(A:DifferentialRing) == @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain LODO2 LinearOrdinaryDifferentialOperator2} + <>= )set break resume )sys rm -f LinearOrdinaryDifferentialOperator2.output @@ -57309,6 +67850,7 @@ LinearOrdinaryDifferentialOperator2(A, M): Exports == Implementation where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain LIST List} + <>= )set break resume )sys rm -f List.output @@ -58126,6 +68668,54 @@ List(S:Type): Exports == Implementation where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain LMOPS ListMonoidOps} + +<>= +)set break resume +)sys rm -f ListMonoidOps.output +)spool ListMonoidOps.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show ListMonoidOps +--R ListMonoidOps(S: SetCategory,E: AbelianMonoid,un: E) is a domain constructor +--R Abbreviation for ListMonoidOps is LMOPS +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for LMOPS +--R +--R------------------------------- Operations -------------------------------- +--R ?=? : (%,%) -> Boolean coerce : S -> % +--R coerce : % -> OutputForm hash : % -> SingleInteger +--R latex : % -> String leftMult : (S,%) -> % +--R makeTerm : (S,E) -> % makeUnit : () -> % +--R mapExpon : ((E -> E),%) -> % mapGen : ((S -> S),%) -> % +--R nthExpon : (%,Integer) -> E nthFactor : (%,Integer) -> S +--R plus : (%,%) -> % plus : (S,E,%) -> % +--R retract : % -> S reverse : % -> % +--R reverse! : % -> % rightMult : (%,S) -> % +--R size : % -> NonNegativeInteger ?~=? : (%,%) -> Boolean +--R commutativeEquality : (%,%) -> Boolean +--R listOfMonoms : % -> List Record(gen: S,exp: E) +--R makeMulti : List Record(gen: S,exp: E) -> % +--R outputForm : (%,((OutputForm,OutputForm) -> OutputForm),((OutputForm,OutputForm) -> OutputForm),Integer) -> OutputForm +--R retractIfCan : % -> Union(S,"failed") +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +ListMonoidOps examples +==================================================================== + +See Also: +o )show ListMonoidOps + +@ + \pagehead{ListMonoidOps}{LMOPS} \pagepic{ps/v103listmonoidops.ps}{LMOPS}{1.00} {\bf See}\\ @@ -58326,6 +68916,82 @@ ListMonoidOps(S, E, un): Exports == Implementation where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain LMDICT ListMultiDictionary} + +<>= +)set break resume +)sys rm -f ListMultiDictionary.output +)spool ListMultiDictionary.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show ListMultiDictionary +--R ListMultiDictionary S: SetCategory is a domain constructor +--R Abbreviation for ListMultiDictionary is LMDICT +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for LMDICT +--R +--R------------------------------- Operations -------------------------------- +--R bag : List S -> % construct : List S -> % +--R copy : % -> % dictionary : List S -> % +--R dictionary : () -> % duplicates? : % -> Boolean +--R empty : () -> % empty? : % -> Boolean +--R eq? : (%,%) -> Boolean extract! : % -> S +--R insert! : (S,%) -> % inspect : % -> S +--R map : ((S -> S),%) -> % removeDuplicates! : % -> % +--R sample : () -> % substitute : (S,S,%) -> % +--R #? : % -> NonNegativeInteger if $ has finiteAggregate +--R ?=? : (%,%) -> Boolean if S has SETCAT +--R any? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate +--R coerce : % -> OutputForm if S has SETCAT +--R convert : % -> InputForm if S has KONVERT INFORM +--R count : (S,%) -> NonNegativeInteger if $ has finiteAggregate and S has SETCAT +--R count : ((S -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate +--R duplicates : % -> List Record(entry: S,count: NonNegativeInteger) +--R eval : (%,List S,List S) -> % if S has EVALAB S and S has SETCAT +--R eval : (%,S,S) -> % if S has EVALAB S and S has SETCAT +--R eval : (%,Equation S) -> % if S has EVALAB S and S has SETCAT +--R eval : (%,List Equation S) -> % if S has EVALAB S and S has SETCAT +--R every? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate +--R find : ((S -> Boolean),%) -> Union(S,"failed") +--R hash : % -> SingleInteger if S has SETCAT +--R insert! : (S,%,NonNegativeInteger) -> % +--R latex : % -> String if S has SETCAT +--R less? : (%,NonNegativeInteger) -> Boolean +--R map! : ((S -> S),%) -> % if $ has shallowlyMutable +--R member? : (S,%) -> Boolean if $ has finiteAggregate and S has SETCAT +--R members : % -> List S if $ has finiteAggregate +--R more? : (%,NonNegativeInteger) -> Boolean +--R parts : % -> List S if $ has finiteAggregate +--R reduce : (((S,S) -> S),%) -> S if $ has finiteAggregate +--R reduce : (((S,S) -> S),%,S) -> S if $ has finiteAggregate +--R reduce : (((S,S) -> S),%,S,S) -> S if $ has finiteAggregate and S has SETCAT +--R remove : ((S -> Boolean),%) -> % if $ has finiteAggregate +--R remove : (S,%) -> % if $ has finiteAggregate and S has SETCAT +--R remove! : ((S -> Boolean),%) -> % if $ has finiteAggregate +--R remove! : (S,%) -> % if $ has finiteAggregate +--R removeDuplicates : % -> % if $ has finiteAggregate and S has SETCAT +--R select : ((S -> Boolean),%) -> % if $ has finiteAggregate +--R select! : ((S -> Boolean),%) -> % if $ has finiteAggregate +--R size? : (%,NonNegativeInteger) -> Boolean +--R ?~=? : (%,%) -> Boolean if S has SETCAT +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +ListMultiDictionary examples +==================================================================== + +See Also: +o )show ListMultiDictionary + +@ + \pagehead{ListMultiDictionary}{LMDICT} \pagepic{ps/v103listmultidictionary.ps}{LMDICT}{1.00} @@ -58527,6 +69193,68 @@ ListMultiDictionary(S:SetCategory): EE == II where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain LA LocalAlgebra} + +<>= +)set break resume +)sys rm -f LocalAlgebra.output +)spool LocalAlgebra.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show LocalAlgebra +--R LocalAlgebra(A: Algebra R,R: CommutativeRing,S: SubsetCategory(Monoid,R)) is a domain constructor +--R Abbreviation for LocalAlgebra is LA +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for LA +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (R,%) -> % ?*? : (%,R) -> % +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ?/? : (A,S) -> % +--R ?/? : (%,S) -> % ?=? : (%,%) -> Boolean +--R 1 : () -> % 0 : () -> % +--R ?^? : (%,PositiveInteger) -> % coerce : R -> % +--R coerce : Integer -> % coerce : % -> OutputForm +--R denom : % -> S hash : % -> SingleInteger +--R latex : % -> String numer : % -> A +--R one? : % -> Boolean recip : % -> Union(%,"failed") +--R sample : () -> % zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean +--R ?*? : (NonNegativeInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % +--R ? Boolean if A has ORDRING +--R ?<=? : (%,%) -> Boolean if A has ORDRING +--R ?>? : (%,%) -> Boolean if A has ORDRING +--R ?>=? : (%,%) -> Boolean if A has ORDRING +--R ?^? : (%,NonNegativeInteger) -> % +--R abs : % -> % if A has ORDRING +--R characteristic : () -> NonNegativeInteger +--R max : (%,%) -> % if A has ORDRING +--R min : (%,%) -> % if A has ORDRING +--R negative? : % -> Boolean if A has ORDRING +--R positive? : % -> Boolean if A has ORDRING +--R sign : % -> Integer if A has ORDRING +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +LocalAlgebra examples +==================================================================== + +See Also: +o )show LocalAlgebra + +@ + \pagehead{LocalAlgebra}{LA} \pagepic{ps/v103localalgebra.ps}{LA}{1.00} {\bf See}\\ @@ -58610,6 +69338,57 @@ LocalAlgebra(A: Algebra R, @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain LO Localize} + +<>= +)set break resume +)sys rm -f Localize.output +)spool Localize.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show Localize +--R Localize(M: Module R,R: CommutativeRing,S: SubsetCategory(Monoid,R)) is a domain constructor +--R Abbreviation for Localize is LO +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for LO +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (%,R) -> % ?*? : (R,%) -> % +--R ?*? : (Integer,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ?/? : (M,S) -> % +--R ?/? : (%,S) -> % ?=? : (%,%) -> Boolean +--R 0 : () -> % coerce : % -> OutputForm +--R denom : % -> S hash : % -> SingleInteger +--R latex : % -> String numer : % -> M +--R sample : () -> % zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean +--R ?*? : (NonNegativeInteger,%) -> % +--R ? Boolean if M has OAGROUP +--R ?<=? : (%,%) -> Boolean if M has OAGROUP +--R ?>? : (%,%) -> Boolean if M has OAGROUP +--R ?>=? : (%,%) -> Boolean if M has OAGROUP +--R max : (%,%) -> % if M has OAGROUP +--R min : (%,%) -> % if M has OAGROUP +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +Localize examples +==================================================================== + +See Also: +o )show Localize + +@ + \pagehead{Localize}{LO} \pagepic{ps/v103localize.ps}{LO}{1.00} {\bf See}\\ @@ -58718,6 +69497,7 @@ Localize(M:Module R, @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain LWORD LyndonWord} + <>= )set break resume )sys rm -f LyndonWord.output @@ -59262,6 +70042,224 @@ LyndonWord(VarSet:OrderedSet):Public == Private where \chapter{Chapter M} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain MCMPLX MachineComplex} + +<>= +)set break resume +)sys rm -f MachineComplex.output +)spool MachineComplex.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show MachineComplex +--R MachineComplex is a domain constructor +--R Abbreviation for MachineComplex is MCMPLX +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for MCMPLX +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (%,MachineFloat) -> % ?*? : (MachineFloat,%) -> % +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ? Boolean +--R ?<=? : (%,%) -> Boolean ?=? : (%,%) -> Boolean +--R ?>? : (%,%) -> Boolean ?>=? : (%,%) -> Boolean +--R 1 : () -> % 0 : () -> % +--R ?^? : (%,PositiveInteger) -> % associates? : (%,%) -> Boolean +--R basis : () -> Vector % coerce : % -> Complex Float +--R coerce : Complex Integer -> % coerce : Complex Float -> % +--R coerce : MachineFloat -> % coerce : Integer -> % +--R coerce : % -> % coerce : Integer -> % +--R coerce : % -> OutputForm conjugate : % -> % +--R discriminant : () -> MachineFloat generator : () -> % +--R hash : % -> SingleInteger imag : % -> MachineFloat +--R imaginary : () -> % latex : % -> String +--R max : (%,%) -> % min : (%,%) -> % +--R norm : % -> MachineFloat one? : % -> Boolean +--R rank : () -> PositiveInteger real : % -> MachineFloat +--R recip : % -> Union(%,"failed") retract : % -> MachineFloat +--R retract : % -> Integer sample : () -> % +--R trace : % -> MachineFloat unit? : % -> Boolean +--R unitCanonical : % -> % zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean +--R ?*? : (%,Fraction Integer) -> % if MachineFloat has FIELD +--R ?*? : (Fraction Integer,%) -> % if MachineFloat has FIELD +--R ?*? : (NonNegativeInteger,%) -> % +--R ?**? : (%,Integer) -> % if MachineFloat has FIELD +--R ?**? : (%,Fraction Integer) -> % if MachineFloat has RADCAT and MachineFloat has TRANFUN +--R ?**? : (%,%) -> % if MachineFloat has TRANFUN +--R ?**? : (%,NonNegativeInteger) -> % +--R ?/? : (%,%) -> % if MachineFloat has FIELD +--R D : % -> % if MachineFloat has DIFRING +--R D : (%,NonNegativeInteger) -> % if MachineFloat has DIFRING +--R D : (%,Symbol) -> % if MachineFloat has PDRING SYMBOL +--R D : (%,List Symbol) -> % if MachineFloat has PDRING SYMBOL +--R D : (%,Symbol,NonNegativeInteger) -> % if MachineFloat has PDRING SYMBOL +--R D : (%,List Symbol,List NonNegativeInteger) -> % if MachineFloat has PDRING SYMBOL +--R D : (%,(MachineFloat -> MachineFloat),NonNegativeInteger) -> % +--R D : (%,(MachineFloat -> MachineFloat)) -> % +--R ?^? : (%,Integer) -> % if MachineFloat has FIELD +--R ?^? : (%,NonNegativeInteger) -> % +--R abs : % -> % if MachineFloat has RNS +--R acos : % -> % if MachineFloat has TRANFUN +--R acosh : % -> % if MachineFloat has TRANFUN +--R acot : % -> % if MachineFloat has TRANFUN +--R acoth : % -> % if MachineFloat has TRANFUN +--R acsc : % -> % if MachineFloat has TRANFUN +--R acsch : % -> % if MachineFloat has TRANFUN +--R argument : % -> MachineFloat if MachineFloat has TRANFUN +--R asec : % -> % if MachineFloat has TRANFUN +--R asech : % -> % if MachineFloat has TRANFUN +--R asin : % -> % if MachineFloat has TRANFUN +--R asinh : % -> % if MachineFloat has TRANFUN +--R atan : % -> % if MachineFloat has TRANFUN +--R atanh : % -> % if MachineFloat has TRANFUN +--R characteristic : () -> NonNegativeInteger +--R characteristicPolynomial : % -> SparseUnivariatePolynomial MachineFloat +--R charthRoot : % -> Union(%,"failed") if $ has CHARNZ and MachineFloat has EUCDOM and MachineFloat has PFECAT or MachineFloat has CHARNZ +--R charthRoot : % -> % if MachineFloat has FFIELDC +--R coerce : Fraction Integer -> % if MachineFloat has FIELD or MachineFloat has RETRACT FRAC INT +--R coerce : Complex MachineInteger -> % +--R coerce : Complex MachineFloat -> % +--R complex : (MachineFloat,MachineFloat) -> % +--R conditionP : Matrix % -> Union(Vector %,"failed") if $ has CHARNZ and MachineFloat has EUCDOM and MachineFloat has PFECAT or MachineFloat has FFIELDC +--R convert : % -> Vector MachineFloat +--R convert : Vector MachineFloat -> % +--R convert : % -> SparseUnivariatePolynomial MachineFloat +--R convert : SparseUnivariatePolynomial MachineFloat -> % +--R convert : % -> Pattern Integer if MachineFloat has KONVERT PATTERN INT +--R convert : % -> Pattern Float if MachineFloat has KONVERT PATTERN FLOAT +--R convert : % -> Complex Float if MachineFloat has REAL +--R convert : % -> Complex DoubleFloat if MachineFloat has REAL +--R convert : % -> InputForm if MachineFloat has KONVERT INFORM +--R coordinates : (%,Vector %) -> Vector MachineFloat +--R coordinates : (Vector %,Vector %) -> Matrix MachineFloat +--R coordinates : % -> Vector MachineFloat +--R coordinates : Vector % -> Matrix MachineFloat +--R cos : % -> % if MachineFloat has TRANFUN +--R cosh : % -> % if MachineFloat has TRANFUN +--R cot : % -> % if MachineFloat has TRANFUN +--R coth : % -> % if MachineFloat has TRANFUN +--R createPrimitiveElement : () -> % if MachineFloat has FFIELDC +--R csc : % -> % if MachineFloat has TRANFUN +--R csch : % -> % if MachineFloat has TRANFUN +--R definingPolynomial : () -> SparseUnivariatePolynomial MachineFloat +--R derivationCoordinates : (Vector %,(MachineFloat -> MachineFloat)) -> Matrix MachineFloat if MachineFloat has FIELD +--R differentiate : % -> % if MachineFloat has DIFRING +--R differentiate : (%,NonNegativeInteger) -> % if MachineFloat has DIFRING +--R differentiate : (%,Symbol) -> % if MachineFloat has PDRING SYMBOL +--R differentiate : (%,List Symbol) -> % if MachineFloat has PDRING SYMBOL +--R differentiate : (%,Symbol,NonNegativeInteger) -> % if MachineFloat has PDRING SYMBOL +--R differentiate : (%,List Symbol,List NonNegativeInteger) -> % if MachineFloat has PDRING SYMBOL +--R differentiate : (%,(MachineFloat -> MachineFloat),NonNegativeInteger) -> % +--R differentiate : (%,(MachineFloat -> MachineFloat)) -> % +--R discreteLog : % -> NonNegativeInteger if MachineFloat has FFIELDC +--R discreteLog : (%,%) -> Union(NonNegativeInteger,"failed") if MachineFloat has FFIELDC +--R discriminant : Vector % -> MachineFloat +--R divide : (%,%) -> Record(quotient: %,remainder: %) if MachineFloat has EUCDOM +--R ?.? : (%,MachineFloat) -> % if MachineFloat has ELTAB(MFLOAT,MFLOAT) +--R euclideanSize : % -> NonNegativeInteger if MachineFloat has EUCDOM +--R eval : (%,List MachineFloat,List MachineFloat) -> % if MachineFloat has EVALAB MFLOAT +--R eval : (%,MachineFloat,MachineFloat) -> % if MachineFloat has EVALAB MFLOAT +--R eval : (%,Equation MachineFloat) -> % if MachineFloat has EVALAB MFLOAT +--R eval : (%,List Equation MachineFloat) -> % if MachineFloat has EVALAB MFLOAT +--R eval : (%,List Symbol,List MachineFloat) -> % if MachineFloat has IEVALAB(SYMBOL,MFLOAT) +--R eval : (%,Symbol,MachineFloat) -> % if MachineFloat has IEVALAB(SYMBOL,MFLOAT) +--R exp : % -> % if MachineFloat has TRANFUN +--R expressIdealMember : (List %,%) -> Union(List %,"failed") if MachineFloat has EUCDOM +--R exquo : (%,MachineFloat) -> Union(%,"failed") if MachineFloat has INTDOM +--R exquo : (%,%) -> Union(%,"failed") +--R extendedEuclidean : (%,%) -> Record(coef1: %,coef2: %,generator: %) if MachineFloat has EUCDOM +--R extendedEuclidean : (%,%,%) -> Union(Record(coef1: %,coef2: %),"failed") if MachineFloat has EUCDOM +--R factor : % -> Factored % if MachineFloat has EUCDOM and MachineFloat has PFECAT or MachineFloat has FIELD +--R factorPolynomial : SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if MachineFloat has EUCDOM and MachineFloat has PFECAT +--R factorSquareFreePolynomial : SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if MachineFloat has EUCDOM and MachineFloat has PFECAT +--R factorsOfCyclicGroupSize : () -> List Record(factor: Integer,exponent: Integer) if MachineFloat has FFIELDC +--R gcd : (%,%) -> % if MachineFloat has EUCDOM +--R gcd : List % -> % if MachineFloat has EUCDOM +--R gcdPolynomial : (SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial % if MachineFloat has EUCDOM +--R index : PositiveInteger -> % if MachineFloat has FINITE +--R init : () -> % if MachineFloat has FFIELDC +--R inv : % -> % if MachineFloat has FIELD +--R lcm : (%,%) -> % if MachineFloat has EUCDOM +--R lcm : List % -> % if MachineFloat has EUCDOM +--R lift : % -> SparseUnivariatePolynomial MachineFloat +--R log : % -> % if MachineFloat has TRANFUN +--R lookup : % -> PositiveInteger if MachineFloat has FINITE +--R map : ((MachineFloat -> MachineFloat),%) -> % +--R minimalPolynomial : % -> SparseUnivariatePolynomial MachineFloat if MachineFloat has FIELD +--R multiEuclidean : (List %,%) -> Union(List %,"failed") if MachineFloat has EUCDOM +--R nextItem : % -> Union(%,"failed") if MachineFloat has FFIELDC +--R nthRoot : (%,Integer) -> % if MachineFloat has RADCAT and MachineFloat has TRANFUN +--R order : % -> PositiveInteger if MachineFloat has FFIELDC +--R order : % -> OnePointCompletion PositiveInteger if MachineFloat has FFIELDC +--R patternMatch : (%,Pattern Integer,PatternMatchResult(Integer,%)) -> PatternMatchResult(Integer,%) if MachineFloat has PATMAB INT +--R patternMatch : (%,Pattern Float,PatternMatchResult(Float,%)) -> PatternMatchResult(Float,%) if MachineFloat has PATMAB FLOAT +--R pi : () -> % if MachineFloat has TRANFUN +--R polarCoordinates : % -> Record(r: MachineFloat,phi: MachineFloat) if MachineFloat has RNS and MachineFloat has TRANFUN +--R prime? : % -> Boolean if MachineFloat has EUCDOM and MachineFloat has PFECAT or MachineFloat has FIELD +--R primeFrobenius : (%,NonNegativeInteger) -> % if MachineFloat has FFIELDC +--R primeFrobenius : % -> % if MachineFloat has FFIELDC +--R primitive? : % -> Boolean if MachineFloat has FFIELDC +--R primitiveElement : () -> % if MachineFloat has FFIELDC +--R principalIdeal : List % -> Record(coef: List %,generator: %) if MachineFloat has EUCDOM +--R ?quo? : (%,%) -> % if MachineFloat has EUCDOM +--R random : () -> % if MachineFloat has FINITE +--R rational : % -> Fraction Integer if MachineFloat has INS +--R rational? : % -> Boolean if MachineFloat has INS +--R rationalIfCan : % -> Union(Fraction Integer,"failed") if MachineFloat has INS +--R reduce : SparseUnivariatePolynomial MachineFloat -> % +--R reduce : Fraction SparseUnivariatePolynomial MachineFloat -> Union(%,"failed") if MachineFloat has FIELD +--R reducedSystem : Matrix % -> Matrix Integer if MachineFloat has LINEXP INT +--R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix Integer,vec: Vector Integer) if MachineFloat has LINEXP INT +--R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix MachineFloat,vec: Vector MachineFloat) +--R reducedSystem : Matrix % -> Matrix MachineFloat +--R regularRepresentation : (%,Vector %) -> Matrix MachineFloat +--R regularRepresentation : % -> Matrix MachineFloat +--R ?rem? : (%,%) -> % if MachineFloat has EUCDOM +--R representationType : () -> Union("prime",polynomial,normal,cyclic) if MachineFloat has FFIELDC +--R represents : (Vector MachineFloat,Vector %) -> % +--R represents : Vector MachineFloat -> % +--R retract : % -> Fraction Integer if MachineFloat has RETRACT FRAC INT +--R retractIfCan : % -> Union(Fraction Integer,"failed") if MachineFloat has RETRACT FRAC INT +--R retractIfCan : % -> Union(MachineFloat,"failed") +--R retractIfCan : % -> Union(Integer,"failed") +--R sec : % -> % if MachineFloat has TRANFUN +--R sech : % -> % if MachineFloat has TRANFUN +--R sin : % -> % if MachineFloat has TRANFUN +--R sinh : % -> % if MachineFloat has TRANFUN +--R size : () -> NonNegativeInteger if MachineFloat has FINITE +--R sizeLess? : (%,%) -> Boolean if MachineFloat has EUCDOM +--R solveLinearPolynomialEquation : (List SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> Union(List SparseUnivariatePolynomial %,"failed") if MachineFloat has EUCDOM and MachineFloat has PFECAT +--R sqrt : % -> % if MachineFloat has RADCAT and MachineFloat has TRANFUN +--R squareFree : % -> Factored % if MachineFloat has EUCDOM and MachineFloat has PFECAT or MachineFloat has FIELD +--R squareFreePart : % -> % if MachineFloat has EUCDOM and MachineFloat has PFECAT or MachineFloat has FIELD +--R squareFreePolynomial : SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if MachineFloat has EUCDOM and MachineFloat has PFECAT +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R tableForDiscreteLogarithm : Integer -> Table(PositiveInteger,NonNegativeInteger) if MachineFloat has FFIELDC +--R tan : % -> % if MachineFloat has TRANFUN +--R tanh : % -> % if MachineFloat has TRANFUN +--R traceMatrix : Vector % -> Matrix MachineFloat +--R traceMatrix : () -> Matrix MachineFloat +--R unitNormal : % -> Record(unit: %,canonical: %,associate: %) +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +MachineComplex examples +==================================================================== + +See Also: +o )show MachineComplex + +@ + \pagehead{MachineComplex}{MCMPLX} \pagepic{ps/v103machinecomplex.ps}{MCMPLX}{1.00} {\bf See}\\ @@ -59465,6 +70463,112 @@ MachineComplex():Exports == Implementation where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain MFLOAT MachineFloat} + +<>= +)set break resume +)sys rm -f MachineFloat.output +)spool MachineFloat.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show MachineFloat +--R MachineFloat is a domain constructor +--R Abbreviation for MachineFloat is MFLOAT +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for MFLOAT +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (Fraction Integer,%) -> % ?*? : (%,Fraction Integer) -> % +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?**? : (%,Fraction Integer) -> % +--R ?**? : (%,Integer) -> % ?**? : (%,PositiveInteger) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ?/? : (%,%) -> % +--R ? Boolean ?<=? : (%,%) -> Boolean +--R ?=? : (%,%) -> Boolean ?>? : (%,%) -> Boolean +--R ?>=? : (%,%) -> Boolean 1 : () -> % +--R 0 : () -> % ?^? : (%,Integer) -> % +--R ?^? : (%,PositiveInteger) -> % abs : % -> % +--R associates? : (%,%) -> Boolean base : () -> PositiveInteger +--R bits : () -> PositiveInteger ceiling : % -> % +--R coerce : MachineInteger -> % coerce : % -> Float +--R coerce : Float -> % coerce : Fraction Integer -> % +--R coerce : Integer -> % coerce : Fraction Integer -> % +--R coerce : % -> % coerce : Integer -> % +--R coerce : % -> OutputForm convert : % -> Pattern Float +--R convert : % -> DoubleFloat convert : % -> Float +--R digits : () -> PositiveInteger exponent : % -> Integer +--R factor : % -> Factored % float : (Integer,Integer) -> % +--R floor : % -> % fractionPart : % -> % +--R gcd : List % -> % gcd : (%,%) -> % +--R hash : % -> SingleInteger inv : % -> % +--R latex : % -> String lcm : List % -> % +--R lcm : (%,%) -> % mantissa : % -> Integer +--R max : (%,%) -> % maximumExponent : () -> Integer +--R min : (%,%) -> % minimumExponent : () -> Integer +--R negative? : % -> Boolean norm : % -> % +--R nthRoot : (%,Integer) -> % one? : % -> Boolean +--R order : % -> Integer positive? : % -> Boolean +--R precision : () -> PositiveInteger prime? : % -> Boolean +--R ?quo? : (%,%) -> % recip : % -> Union(%,"failed") +--R ?rem? : (%,%) -> % retract : % -> Float +--R retract : % -> Fraction Integer retract : % -> Integer +--R round : % -> % sample : () -> % +--R sign : % -> Integer sizeLess? : (%,%) -> Boolean +--R sqrt : % -> % squareFree : % -> Factored % +--R squareFreePart : % -> % truncate : % -> % +--R unit? : % -> Boolean unitCanonical : % -> % +--R wholePart : % -> Integer zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean +--R ?*? : (NonNegativeInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % +--R ?^? : (%,NonNegativeInteger) -> % +--R base : PositiveInteger -> PositiveInteger +--R bits : PositiveInteger -> PositiveInteger if $ has arbitraryPrecision +--R changeBase : (Integer,Integer,PositiveInteger) -> % +--R characteristic : () -> NonNegativeInteger +--R decreasePrecision : Integer -> PositiveInteger if $ has arbitraryPrecision +--R digits : PositiveInteger -> PositiveInteger if $ has arbitraryPrecision +--R divide : (%,%) -> Record(quotient: %,remainder: %) +--R euclideanSize : % -> NonNegativeInteger +--R expressIdealMember : (List %,%) -> Union(List %,"failed") +--R exquo : (%,%) -> Union(%,"failed") +--R extendedEuclidean : (%,%,%) -> Union(Record(coef1: %,coef2: %),"failed") +--R extendedEuclidean : (%,%) -> Record(coef1: %,coef2: %,generator: %) +--R float : (Integer,Integer,PositiveInteger) -> % +--R gcdPolynomial : (SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial % +--R increasePrecision : Integer -> PositiveInteger if $ has arbitraryPrecision +--R max : () -> % if not has($,arbitraryExponent) and not has($,arbitraryPrecision) +--R maximumExponent : Integer -> Integer +--R min : () -> % if not has($,arbitraryExponent) and not has($,arbitraryPrecision) +--R minimumExponent : Integer -> Integer +--R multiEuclidean : (List %,%) -> Union(List %,"failed") +--R patternMatch : (%,Pattern Float,PatternMatchResult(Float,%)) -> PatternMatchResult(Float,%) +--R precision : PositiveInteger -> PositiveInteger +--R principalIdeal : List % -> Record(coef: List %,generator: %) +--R retractIfCan : % -> Union(Float,"failed") +--R retractIfCan : % -> Union(Fraction Integer,"failed") +--R retractIfCan : % -> Union(Integer,"failed") +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R unitNormal : % -> Record(unit: %,canonical: %,associate: %) +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +MachineFloat examples +==================================================================== + +See Also: +o )show MachineFloat + +@ + \pagehead{MachineFloat}{MFLOAT} \pagepic{ps/v103machinefloat.ps}{MFLOAT}{1.00} {\bf See}\\ @@ -59865,6 +70969,104 @@ MachineFloat(): Exports == Implementation where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain MINT MachineInteger} + +<>= +)set break resume +)sys rm -f MachineInteger.output +)spool MachineInteger.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show MachineInteger +--R MachineInteger is a domain constructor +--R Abbreviation for MachineInteger is MINT +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for MINT +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ? Boolean +--R ?<=? : (%,%) -> Boolean ?=? : (%,%) -> Boolean +--R ?>? : (%,%) -> Boolean ?>=? : (%,%) -> Boolean +--R D : (%,NonNegativeInteger) -> % D : % -> % +--R 1 : () -> % 0 : () -> % +--R ?^? : (%,PositiveInteger) -> % abs : % -> % +--R addmod : (%,%,%) -> % associates? : (%,%) -> Boolean +--R base : () -> % binomial : (%,%) -> % +--R bit? : (%,%) -> Boolean coerce : Integer -> % +--R coerce : % -> % coerce : Integer -> % +--R coerce : % -> OutputForm convert : % -> Integer +--R convert : % -> InputForm convert : % -> Pattern Integer +--R convert : % -> Float convert : % -> DoubleFloat +--R copy : % -> % dec : % -> % +--R differentiate : % -> % even? : % -> Boolean +--R factor : % -> Factored % factorial : % -> % +--R gcd : (%,%) -> % gcd : List % -> % +--R hash : % -> % hash : % -> SingleInteger +--R inc : % -> % init : () -> % +--R invmod : (%,%) -> % latex : % -> String +--R lcm : (%,%) -> % lcm : List % -> % +--R length : % -> % mask : % -> % +--R max : (%,%) -> % maxint : () -> PositiveInteger +--R min : (%,%) -> % mulmod : (%,%,%) -> % +--R negative? : % -> Boolean odd? : % -> Boolean +--R one? : % -> Boolean permutation : (%,%) -> % +--R positive? : % -> Boolean positiveRemainder : (%,%) -> % +--R powmod : (%,%,%) -> % prime? : % -> Boolean +--R ?quo? : (%,%) -> % random : () -> % +--R random : % -> % rational : % -> Fraction Integer +--R rational? : % -> Boolean recip : % -> Union(%,"failed") +--R ?rem? : (%,%) -> % retract : % -> Integer +--R sample : () -> % shift : (%,%) -> % +--R sign : % -> Integer sizeLess? : (%,%) -> Boolean +--R squareFree : % -> Factored % squareFreePart : % -> % +--R submod : (%,%,%) -> % symmetricRemainder : (%,%) -> % +--R unit? : % -> Boolean unitCanonical : % -> % +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean +--R ?*? : (NonNegativeInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % +--R ?^? : (%,NonNegativeInteger) -> % +--R characteristic : () -> NonNegativeInteger +--R coerce : Expression Integer -> Expression % +--R differentiate : (%,NonNegativeInteger) -> % +--R divide : (%,%) -> Record(quotient: %,remainder: %) +--R euclideanSize : % -> NonNegativeInteger +--R expressIdealMember : (List %,%) -> Union(List %,"failed") +--R exquo : (%,%) -> Union(%,"failed") +--R extendedEuclidean : (%,%,%) -> Union(Record(coef1: %,coef2: %),"failed") +--R extendedEuclidean : (%,%) -> Record(coef1: %,coef2: %,generator: %) +--R gcdPolynomial : (SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial % +--R maxint : PositiveInteger -> PositiveInteger +--R multiEuclidean : (List %,%) -> Union(List %,"failed") +--R nextItem : % -> Union(%,"failed") +--R patternMatch : (%,Pattern Integer,PatternMatchResult(Integer,%)) -> PatternMatchResult(Integer,%) +--R principalIdeal : List % -> Record(coef: List %,generator: %) +--R rationalIfCan : % -> Union(Fraction Integer,"failed") +--R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix Integer,vec: Vector Integer) +--R reducedSystem : Matrix % -> Matrix Integer +--R retractIfCan : % -> Union(Integer,"failed") +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R unitNormal : % -> Record(unit: %,canonical: %,associate: %) +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +MachineInteger examples +==================================================================== + +See Also: +o )show MachineInteger + +@ + \pagehead{MachineInteger}{MINT} \pagepic{ps/v103machineinteger.ps}{MINT}{1.00} {\bf See}\\ @@ -60022,6 +71224,7 @@ MachineInteger(): Exports == Implementation where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain MAGMA Magma} + <>= )set break resume )sys rm -f Magma.output @@ -60505,6 +71708,48 @@ Magma(VarSet:OrderedSet):Public == Private where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain MKCHSET MakeCachableSet} + +<>= +)set break resume +)sys rm -f MakeCachableSet.output +)spool MakeCachableSet.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show MakeCachableSet +--R MakeCachableSet S: SetCategory is a domain constructor +--R Abbreviation for MakeCachableSet is MKCHSET +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for MKCHSET +--R +--R------------------------------- Operations -------------------------------- +--R ? Boolean ?<=? : (%,%) -> Boolean +--R ?=? : (%,%) -> Boolean ?>? : (%,%) -> Boolean +--R ?>=? : (%,%) -> Boolean coerce : S -> % +--R coerce : % -> S coerce : % -> OutputForm +--R hash : % -> SingleInteger latex : % -> String +--R max : (%,%) -> % min : (%,%) -> % +--R ?~=? : (%,%) -> Boolean +--R position : % -> NonNegativeInteger +--R setPosition : (%,NonNegativeInteger) -> Void +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +MakeCachableSet examples +==================================================================== + +See Also: +o )show MakeCachableSet + +@ + \pagehead{MakeCachableSet}{MKCHSET} \pagepic{ps/v103makecachableset.ps}{MKCHSET}{1.00} {\bf See}\\ @@ -60573,6 +71818,44 @@ MakeCachableSet(S:SetCategory): Exports == Implementation where %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain MMLFORM MathMLFormat} +<>= +)set break resume +)sys rm -f MathMLFormat.output +)spool MathMLFormat.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show MathMLFormat +--R MathMLFormat is a domain constructor +--R Abbreviation for MathMLFormat is MMLFORM +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for MMLFORM +--R +--R------------------------------- Operations -------------------------------- +--R ?=? : (%,%) -> Boolean coerce : OutputForm -> String +--R coerce : % -> OutputForm coerceL : OutputForm -> String +--R coerceS : OutputForm -> String display : String -> Void +--R exprex : OutputForm -> String hash : % -> SingleInteger +--R latex : % -> String ?~=? : (%,%) -> Boolean +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +MathMLFormat examples +==================================================================== + +See Also: +o )show MathMLFormat + +@ + + Both this code and documentation are still under development and I don't pretend they are anywhere close to perfect or even finished. However the code does work and I hope it might be useful to somebody @@ -62193,6 +73476,7 @@ o )show MathMLFormat @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain MATRIX Matrix} + <>= )set break resume )sys rm -f Matrix.output @@ -63372,6 +74656,218 @@ Matrix(R): Exports == Implementation where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain MODMON ModMonic} + +<>= +)set break resume +)sys rm -f ModMonic.output +)spool ModMonic.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show ModMonic +--R ModMonic(R: Ring,Rep: UnivariatePolynomialCategory R) is a domain constructor +--R Abbreviation for ModMonic is MODMON +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for MODMON +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (%,R) -> % ?*? : (R,%) -> % +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ?=? : (%,%) -> Boolean +--R An : % -> Vector R D : (%,(R -> R)) -> % +--R D : % -> % D : (%,NonNegativeInteger) -> % +--R 1 : () -> % UnVectorise : Vector R -> % +--R Vectorise : % -> Vector R 0 : () -> % +--R ?^? : (%,PositiveInteger) -> % coefficients : % -> List R +--R coerce : Rep -> % coerce : R -> % +--R coerce : Integer -> % coerce : % -> OutputForm +--R degree : % -> NonNegativeInteger differentiate : % -> % +--R ?.? : (%,%) -> % ?.? : (%,R) -> R +--R eval : (%,List %,List %) -> % eval : (%,%,%) -> % +--R eval : (%,Equation %) -> % eval : (%,List Equation %) -> % +--R ground : % -> R ground? : % -> Boolean +--R hash : % -> SingleInteger init : () -> % if R has STEP +--R latex : % -> String leadingCoefficient : % -> R +--R leadingMonomial : % -> % lift : % -> Rep +--R map : ((R -> R),%) -> % modulus : () -> Rep +--R monomial? : % -> Boolean monomials : % -> List % +--R one? : % -> Boolean pow : () -> PrimitiveArray % +--R primitiveMonomials : % -> List % pseudoRemainder : (%,%) -> % +--R recip : % -> Union(%,"failed") reduce : Rep -> % +--R reductum : % -> % retract : % -> R +--R sample : () -> % setPoly : Rep -> Rep +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean +--R ?*? : (Fraction Integer,%) -> % if R has ALGEBRA FRAC INT +--R ?*? : (%,Fraction Integer) -> % if R has ALGEBRA FRAC INT +--R ?*? : (NonNegativeInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % +--R ?/? : (%,R) -> % if R has FIELD +--R ? Boolean if R has ORDSET +--R ?<=? : (%,%) -> Boolean if R has ORDSET +--R ?>? : (%,%) -> Boolean if R has ORDSET +--R ?>=? : (%,%) -> Boolean if R has ORDSET +--R D : (%,(R -> R),NonNegativeInteger) -> % +--R D : (%,List Symbol,List NonNegativeInteger) -> % if R has PDRING SYMBOL +--R D : (%,Symbol,NonNegativeInteger) -> % if R has PDRING SYMBOL +--R D : (%,List Symbol) -> % if R has PDRING SYMBOL +--R D : (%,Symbol) -> % if R has PDRING SYMBOL +--R D : (%,List SingletonAsOrderedSet,List NonNegativeInteger) -> % +--R D : (%,SingletonAsOrderedSet,NonNegativeInteger) -> % +--R D : (%,List SingletonAsOrderedSet) -> % +--R D : (%,SingletonAsOrderedSet) -> % +--R ?^? : (%,NonNegativeInteger) -> % +--R associates? : (%,%) -> Boolean if R has INTDOM +--R binomThmExpt : (%,%,NonNegativeInteger) -> % if R has COMRING +--R characteristic : () -> NonNegativeInteger +--R charthRoot : % -> Union(%,"failed") if $ has CHARNZ and R has PFECAT or R has CHARNZ +--R coefficient : (%,List SingletonAsOrderedSet,List NonNegativeInteger) -> % +--R coefficient : (%,SingletonAsOrderedSet,NonNegativeInteger) -> % +--R coefficient : (%,NonNegativeInteger) -> R +--R coerce : % -> % if R has INTDOM +--R coerce : Fraction Integer -> % if R has ALGEBRA FRAC INT or R has RETRACT FRAC INT +--R coerce : SingletonAsOrderedSet -> % +--R composite : (Fraction %,%) -> Union(Fraction %,"failed") if R has INTDOM +--R composite : (%,%) -> Union(%,"failed") if R has INTDOM +--R computePowers : () -> PrimitiveArray % +--R conditionP : Matrix % -> Union(Vector %,"failed") if $ has CHARNZ and R has PFECAT +--R content : (%,SingletonAsOrderedSet) -> % if R has GCDDOM +--R content : % -> R if R has GCDDOM +--R convert : % -> InputForm if SingletonAsOrderedSet has KONVERT INFORM and R has KONVERT INFORM +--R convert : % -> Pattern Integer if SingletonAsOrderedSet has KONVERT PATTERN INT and R has KONVERT PATTERN INT +--R convert : % -> Pattern Float if SingletonAsOrderedSet has KONVERT PATTERN FLOAT and R has KONVERT PATTERN FLOAT +--R degree : (%,List SingletonAsOrderedSet) -> List NonNegativeInteger +--R degree : (%,SingletonAsOrderedSet) -> NonNegativeInteger +--R differentiate : (%,(R -> R),%) -> % +--R differentiate : (%,(R -> R)) -> % +--R differentiate : (%,(R -> R),NonNegativeInteger) -> % +--R differentiate : (%,List Symbol,List NonNegativeInteger) -> % if R has PDRING SYMBOL +--R differentiate : (%,Symbol,NonNegativeInteger) -> % if R has PDRING SYMBOL +--R differentiate : (%,List Symbol) -> % if R has PDRING SYMBOL +--R differentiate : (%,Symbol) -> % if R has PDRING SYMBOL +--R differentiate : (%,NonNegativeInteger) -> % +--R differentiate : (%,List SingletonAsOrderedSet,List NonNegativeInteger) -> % +--R differentiate : (%,SingletonAsOrderedSet,NonNegativeInteger) -> % +--R differentiate : (%,List SingletonAsOrderedSet) -> % +--R differentiate : (%,SingletonAsOrderedSet) -> % +--R discriminant : % -> R if R has COMRING +--R discriminant : (%,SingletonAsOrderedSet) -> % if R has COMRING +--R divide : (%,%) -> Record(quotient: %,remainder: %) if R has FIELD +--R divideExponents : (%,NonNegativeInteger) -> Union(%,"failed") +--R ?.? : (%,Fraction %) -> Fraction % if R has INTDOM +--R elt : (Fraction %,R) -> R if R has FIELD +--R elt : (Fraction %,Fraction %) -> Fraction % if R has INTDOM +--R euclideanSize : % -> NonNegativeInteger if R has FIELD +--R eval : (%,List SingletonAsOrderedSet,List %) -> % +--R eval : (%,SingletonAsOrderedSet,%) -> % +--R eval : (%,List SingletonAsOrderedSet,List R) -> % +--R eval : (%,SingletonAsOrderedSet,R) -> % +--R expressIdealMember : (List %,%) -> Union(List %,"failed") if R has FIELD +--R exquo : (%,%) -> Union(%,"failed") if R has INTDOM +--R exquo : (%,R) -> Union(%,"failed") if R has INTDOM +--R extendedEuclidean : (%,%) -> Record(coef1: %,coef2: %,generator: %) if R has FIELD +--R extendedEuclidean : (%,%,%) -> Union(Record(coef1: %,coef2: %),"failed") if R has FIELD +--R factor : % -> Factored % if R has PFECAT +--R factorPolynomial : SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if R has PFECAT +--R factorSquareFreePolynomial : SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if R has PFECAT +--R frobenius : % -> % if R has FFIELDC +--R gcd : (%,%) -> % if R has GCDDOM +--R gcd : List % -> % if R has GCDDOM +--R gcdPolynomial : (SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial % if R has GCDDOM +--R index : PositiveInteger -> % if R has FINITE +--R integrate : % -> % if R has ALGEBRA FRAC INT +--R isExpt : % -> Union(Record(var: SingletonAsOrderedSet,exponent: NonNegativeInteger),"failed") +--R isPlus : % -> Union(List %,"failed") +--R isTimes : % -> Union(List %,"failed") +--R karatsubaDivide : (%,NonNegativeInteger) -> Record(quotient: %,remainder: %) +--R lcm : (%,%) -> % if R has GCDDOM +--R lcm : List % -> % if R has GCDDOM +--R lookup : % -> PositiveInteger if R has FINITE +--R mainVariable : % -> Union(SingletonAsOrderedSet,"failed") +--R makeSUP : % -> SparseUnivariatePolynomial R +--R mapExponents : ((NonNegativeInteger -> NonNegativeInteger),%) -> % +--R max : (%,%) -> % if R has ORDSET +--R min : (%,%) -> % if R has ORDSET +--R minimumDegree : (%,List SingletonAsOrderedSet) -> List NonNegativeInteger +--R minimumDegree : (%,SingletonAsOrderedSet) -> NonNegativeInteger +--R minimumDegree : % -> NonNegativeInteger +--R monicDivide : (%,%) -> Record(quotient: %,remainder: %) +--R monicDivide : (%,%,SingletonAsOrderedSet) -> Record(quotient: %,remainder: %) +--R monomial : (%,List SingletonAsOrderedSet,List NonNegativeInteger) -> % +--R monomial : (%,SingletonAsOrderedSet,NonNegativeInteger) -> % +--R monomial : (R,NonNegativeInteger) -> % +--R multiEuclidean : (List %,%) -> Union(List %,"failed") if R has FIELD +--R multiplyExponents : (%,NonNegativeInteger) -> % +--R multivariate : (SparseUnivariatePolynomial %,SingletonAsOrderedSet) -> % +--R multivariate : (SparseUnivariatePolynomial R,SingletonAsOrderedSet) -> % +--R nextItem : % -> Union(%,"failed") if R has STEP +--R numberOfMonomials : % -> NonNegativeInteger +--R order : (%,%) -> NonNegativeInteger if R has INTDOM +--R patternMatch : (%,Pattern Integer,PatternMatchResult(Integer,%)) -> PatternMatchResult(Integer,%) if SingletonAsOrderedSet has PATMAB INT and R has PATMAB INT +--R patternMatch : (%,Pattern Float,PatternMatchResult(Float,%)) -> PatternMatchResult(Float,%) if SingletonAsOrderedSet has PATMAB FLOAT and R has PATMAB FLOAT +--R pomopo! : (%,R,NonNegativeInteger,%) -> % +--R prime? : % -> Boolean if R has PFECAT +--R primitivePart : (%,SingletonAsOrderedSet) -> % if R has GCDDOM +--R primitivePart : % -> % if R has GCDDOM +--R principalIdeal : List % -> Record(coef: List %,generator: %) if R has FIELD +--R pseudoDivide : (%,%) -> Record(coef: R,quotient: %,remainder: %) if R has INTDOM +--R pseudoQuotient : (%,%) -> % if R has INTDOM +--R ?quo? : (%,%) -> % if R has FIELD +--R random : () -> % if R has FINITE +--R reducedSystem : Matrix % -> Matrix R +--R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix R,vec: Vector R) +--R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix Integer,vec: Vector Integer) if R has LINEXP INT +--R reducedSystem : Matrix % -> Matrix Integer if R has LINEXP INT +--R ?rem? : (%,%) -> % if R has FIELD +--R resultant : (%,%) -> R if R has COMRING +--R resultant : (%,%,SingletonAsOrderedSet) -> % if R has COMRING +--R retract : % -> SingletonAsOrderedSet +--R retract : % -> Integer if R has RETRACT INT +--R retract : % -> Fraction Integer if R has RETRACT FRAC INT +--R retractIfCan : % -> Union(SingletonAsOrderedSet,"failed") +--R retractIfCan : % -> Union(Integer,"failed") if R has RETRACT INT +--R retractIfCan : % -> Union(Fraction Integer,"failed") if R has RETRACT FRAC INT +--R retractIfCan : % -> Union(R,"failed") +--R separate : (%,%) -> Record(primePart: %,commonPart: %) if R has GCDDOM +--R shiftLeft : (%,NonNegativeInteger) -> % +--R shiftRight : (%,NonNegativeInteger) -> % +--R size : () -> NonNegativeInteger if R has FINITE +--R sizeLess? : (%,%) -> Boolean if R has FIELD +--R solveLinearPolynomialEquation : (List SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> Union(List SparseUnivariatePolynomial %,"failed") if R has PFECAT +--R squareFree : % -> Factored % if R has GCDDOM +--R squareFreePart : % -> % if R has GCDDOM +--R squareFreePolynomial : SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if R has PFECAT +--R subResultantGcd : (%,%) -> % if R has INTDOM +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R totalDegree : (%,List SingletonAsOrderedSet) -> NonNegativeInteger +--R totalDegree : % -> NonNegativeInteger +--R unit? : % -> Boolean if R has INTDOM +--R unitCanonical : % -> % if R has INTDOM +--R unitNormal : % -> Record(unit: %,canonical: %,associate: %) if R has INTDOM +--R univariate : % -> SparseUnivariatePolynomial R +--R univariate : (%,SingletonAsOrderedSet) -> SparseUnivariatePolynomial % +--R unmakeSUP : SparseUnivariatePolynomial R -> % +--R variables : % -> List SingletonAsOrderedSet +--R vectorise : (%,NonNegativeInteger) -> Vector R +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +ModMonic examples +==================================================================== + +See Also: +o )show ModMonic + +@ + \pagehead{ModMonic}{MODMON} \pagepic{ps/v103modmonic.ps}{MODMON}{1.00} @@ -63683,6 +75179,78 @@ ModMonic(R,Rep): C == T @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain MODFIELD ModularField} + +<>= +)set break resume +)sys rm -f ModularField.output +)spool ModularField.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show ModularField +--R ModularField(R: CommutativeRing,Mod: AbelianMonoid,reduction: ((R,Mod) -> R),merge: ((Mod,Mod) -> Union(Mod,"failed")),exactQuo: ((R,R,Mod) -> Union(R,"failed"))) is a domain constructor +--R Abbreviation for ModularField is MODFIELD +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for MODFIELD +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (Fraction Integer,%) -> % ?*? : (%,Fraction Integer) -> % +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?**? : (%,Integer) -> % +--R ?**? : (%,PositiveInteger) -> % ?+? : (%,%) -> % +--R ?-? : (%,%) -> % -? : % -> % +--R ?/? : (%,%) -> % ?=? : (%,%) -> Boolean +--R 1 : () -> % 0 : () -> % +--R ?^? : (%,Integer) -> % ?^? : (%,PositiveInteger) -> % +--R associates? : (%,%) -> Boolean coerce : % -> R +--R coerce : Fraction Integer -> % coerce : % -> % +--R coerce : Integer -> % coerce : % -> OutputForm +--R factor : % -> Factored % gcd : List % -> % +--R gcd : (%,%) -> % hash : % -> SingleInteger +--R inv : % -> % latex : % -> String +--R lcm : List % -> % lcm : (%,%) -> % +--R modulus : % -> Mod one? : % -> Boolean +--R prime? : % -> Boolean ?quo? : (%,%) -> % +--R recip : % -> Union(%,"failed") reduce : (R,Mod) -> % +--R ?rem? : (%,%) -> % sample : () -> % +--R sizeLess? : (%,%) -> Boolean squareFree : % -> Factored % +--R squareFreePart : % -> % unit? : % -> Boolean +--R unitCanonical : % -> % zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean +--R ?*? : (NonNegativeInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % +--R ?^? : (%,NonNegativeInteger) -> % +--R characteristic : () -> NonNegativeInteger +--R divide : (%,%) -> Record(quotient: %,remainder: %) +--R euclideanSize : % -> NonNegativeInteger +--R exQuo : (%,%) -> Union(%,"failed") +--R expressIdealMember : (List %,%) -> Union(List %,"failed") +--R exquo : (%,%) -> Union(%,"failed") +--R extendedEuclidean : (%,%,%) -> Union(Record(coef1: %,coef2: %),"failed") +--R extendedEuclidean : (%,%) -> Record(coef1: %,coef2: %,generator: %) +--R gcdPolynomial : (SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial % +--R multiEuclidean : (List %,%) -> Union(List %,"failed") +--R principalIdeal : List % -> Record(coef: List %,generator: %) +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R unitNormal : % -> Record(unit: %,canonical: %,associate: %) +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +ModularField examples +==================================================================== + +See Also: +o )show ModularField + +@ + \pagehead{ModularField}{MODFIELD} \pagepic{ps/v103modularfield.ps}{MODFIELD}{1.00} {\bf See}\\ @@ -63775,6 +75343,57 @@ ModularField(R,Mod,reduction:(R,Mod) -> R, @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain MODRING ModularRing} + +<>= +)set break resume +)sys rm -f ModularRing.output +)spool ModularRing.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show ModularRing +--R ModularRing(R: CommutativeRing,Mod: AbelianMonoid,reduction: ((R,Mod) -> R),merge: ((Mod,Mod) -> Union(Mod,"failed")),exactQuo: ((R,R,Mod) -> Union(R,"failed"))) is a domain constructor +--R Abbreviation for ModularRing is MODRING +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for MODRING +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ?=? : (%,%) -> Boolean +--R 1 : () -> % 0 : () -> % +--R ?^? : (%,PositiveInteger) -> % coerce : % -> R +--R coerce : Integer -> % coerce : % -> OutputForm +--R hash : % -> SingleInteger inv : % -> % +--R latex : % -> String modulus : % -> Mod +--R one? : % -> Boolean recip : % -> Union(%,"failed") +--R reduce : (R,Mod) -> % sample : () -> % +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean +--R ?*? : (NonNegativeInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % +--R ?^? : (%,NonNegativeInteger) -> % +--R characteristic : () -> NonNegativeInteger +--R exQuo : (%,%) -> Union(%,"failed") +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +ModularRing examples +==================================================================== + +See Also: +o )show ModularRing + +@ + \pagehead{ModularRing}{MODRING} \pagepic{ps/v103modularring.ps}{MODRING}{1.00} {\bf See}\\ @@ -63907,6 +75526,48 @@ ModularRing(R,Mod,reduction:(R,Mod) -> R, @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain MODMONOM ModuleMonomial} + +<>= +)set break resume +)sys rm -f ModuleMonomial.output +)spool ModuleMonomial.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show ModuleMonomial +--R ModuleMonomial(IS: OrderedSet,E: SetCategory,ff: ((Record(index: IS,exponent: E),Record(index: IS,exponent: E)) -> Boolean)) is a domain constructor +--R Abbreviation for ModuleMonomial is MODMONOM +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for MODMONOM +--R +--R------------------------------- Operations -------------------------------- +--R ? Boolean ?<=? : (%,%) -> Boolean +--R ?=? : (%,%) -> Boolean ?>? : (%,%) -> Boolean +--R ?>=? : (%,%) -> Boolean coerce : % -> OutputForm +--R construct : (IS,E) -> % exponent : % -> E +--R hash : % -> SingleInteger index : % -> IS +--R latex : % -> String max : (%,%) -> % +--R min : (%,%) -> % ?~=? : (%,%) -> Boolean +--R coerce : % -> Record(index: IS,exponent: E) +--R coerce : Record(index: IS,exponent: E) -> % +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +ModuleMonomial examples +==================================================================== + +See Also: +o )show ModuleMonomial + +@ + \pagehead{ModuleMonomial}{MODMONOM} \pagepic{ps/v103modulemonomial.ps}{MODMONOM}{1.00} {\bf See}\\ @@ -63971,6 +75632,69 @@ ModuleMonomial(IS: OrderedSet, @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain MODOP ModuleOperator} + +<>= +)set break resume +)sys rm -f ModuleOperator.output +)spool ModuleOperator.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show ModuleOperator +--R ModuleOperator(R: Ring,M: LeftModule R) is a domain constructor +--R Abbreviation for ModuleOperator is MODOP +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for MODOP +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?**? : (%,Integer) -> % +--R ?**? : (%,PositiveInteger) -> % ?+? : (%,%) -> % +--R ?-? : (%,%) -> % -? : % -> % +--R ?=? : (%,%) -> Boolean 1 : () -> % +--R 0 : () -> % ?^? : (%,PositiveInteger) -> % +--R coerce : BasicOperator -> % coerce : R -> % +--R coerce : Integer -> % coerce : % -> OutputForm +--R ?.? : (%,M) -> M evaluate : (%,(M -> M)) -> % +--R hash : % -> SingleInteger latex : % -> String +--R one? : % -> Boolean opeval : (BasicOperator,M) -> M +--R recip : % -> Union(%,"failed") retract : % -> BasicOperator +--R retract : % -> R sample : () -> % +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean +--R ?*? : (%,R) -> % if R has COMRING +--R ?*? : (R,%) -> % if R has COMRING +--R ?*? : (NonNegativeInteger,%) -> % +--R ?**? : (BasicOperator,Integer) -> % +--R ?**? : (%,NonNegativeInteger) -> % +--R ?^? : (%,NonNegativeInteger) -> % +--R adjoint : (%,%) -> % if R has COMRING +--R adjoint : % -> % if R has COMRING +--R characteristic : () -> NonNegativeInteger +--R charthRoot : % -> Union(%,"failed") if R has CHARNZ +--R conjug : R -> R if R has COMRING +--R evaluateInverse : (%,(M -> M)) -> % +--R makeop : (R,FreeGroup BasicOperator) -> % +--R retractIfCan : % -> Union(BasicOperator,"failed") +--R retractIfCan : % -> Union(R,"failed") +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +ModuleOperator examples +==================================================================== + +See Also: +o )show ModuleOperator + +@ + \pagehead{ModuleOperator}{MODOP} \pagepic{ps/v103moduleoperator.ps}{MODOP}{1.00} {\bf See}\\ @@ -64247,6 +75971,55 @@ ModuleOperator(R: Ring, M:LeftModule(R)): Exports == Implementation where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain MOEBIUS MoebiusTransform} + +<>= +)set break resume +)sys rm -f MoebiusTransform.output +)spool MoebiusTransform.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show MoebiusTransform +--R MoebiusTransform F: Field is a domain constructor +--R Abbreviation for MoebiusTransform is MOEBIUS +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for MOEBIUS +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (%,%) -> % ?**? : (%,Integer) -> % +--R ?**? : (%,PositiveInteger) -> % ?/? : (%,%) -> % +--R ?=? : (%,%) -> Boolean 1 : () -> % +--R ?^? : (%,Integer) -> % ?^? : (%,PositiveInteger) -> % +--R coerce : % -> OutputForm commutator : (%,%) -> % +--R conjugate : (%,%) -> % eval : (%,F) -> F +--R hash : % -> SingleInteger inv : % -> % +--R latex : % -> String moebius : (F,F,F,F) -> % +--R one? : % -> Boolean recip : % -> % +--R recip : () -> % recip : % -> Union(%,"failed") +--R sample : () -> % scale : (%,F) -> % +--R scale : F -> % shift : (%,F) -> % +--R shift : F -> % ?~=? : (%,%) -> Boolean +--R ?**? : (%,NonNegativeInteger) -> % +--R ?^? : (%,NonNegativeInteger) -> % +--R eval : (%,OnePointCompletion F) -> OnePointCompletion F +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +MoebiusTransform examples +==================================================================== + +See Also: +o )show MoebiusTransform + +@ + \pagehead{MoebiusTransform}{MOEBIUS} \pagepic{ps/v103moebiustransform.ps}{MOEBIUS}{1.00} @@ -64385,6 +76158,74 @@ MoebiusTransform(F): Exports == Implementation where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain MRING MonoidRing} + +<>= +)set break resume +)sys rm -f MonoidRing.output +)spool MonoidRing.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show MonoidRing +--R MonoidRing(R: Ring,M: Monoid) is a domain constructor +--R Abbreviation for MonoidRing is MRING +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for MRING +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ?=? : (%,%) -> Boolean +--R 1 : () -> % 0 : () -> % +--R ?^? : (%,PositiveInteger) -> % coefficient : (%,M) -> R +--R coefficients : % -> List R coerce : R -> % +--R coerce : M -> % coerce : Integer -> % +--R coerce : % -> OutputForm hash : % -> SingleInteger +--R latex : % -> String map : ((R -> R),%) -> % +--R monomial : (R,M) -> % monomial? : % -> Boolean +--R monomials : % -> List % one? : % -> Boolean +--R recip : % -> Union(%,"failed") retract : % -> R +--R retract : % -> M sample : () -> % +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean +--R ?*? : (%,R) -> % if R has COMRING +--R ?*? : (R,%) -> % if R has COMRING +--R ?*? : (NonNegativeInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % +--R ?^? : (%,NonNegativeInteger) -> % +--R characteristic : () -> NonNegativeInteger +--R charthRoot : % -> Union(%,"failed") if R has CHARNZ +--R coerce : List Record(coef: R,monom: M) -> % +--R index : PositiveInteger -> % if M has FINITE and R has FINITE +--R leadingCoefficient : % -> R if M has ORDSET +--R leadingMonomial : % -> M if M has ORDSET +--R lookup : % -> PositiveInteger if M has FINITE and R has FINITE +--R numberOfMonomials : % -> NonNegativeInteger +--R random : () -> % if M has FINITE and R has FINITE +--R reductum : % -> % if M has ORDSET +--R retractIfCan : % -> Union(R,"failed") +--R retractIfCan : % -> Union(M,"failed") +--R size : () -> NonNegativeInteger if M has FINITE and R has FINITE +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R terms : % -> List Record(coef: R,monom: M) +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +MonoidRing examples +==================================================================== + +See Also: +o )show MonoidRing + +@ + \pagehead{MonoidRing}{MRING} \pagepic{ps/v103monoidring.ps}{MRING}{1.00} @@ -64757,6 +76598,7 @@ MonoidRing(R: Ring, M: Monoid): MRcategory == MRdefinition where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain MSET Multiset} + <>= )set break resume )sys rm -f Multiset.output @@ -65320,6 +77162,7 @@ Multiset(S: SetCategory): MultisetAggregate S with @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain MPOLY MultivariatePolynomial} + <>= )set break resume )sys rm -f MultivariatePolynomial.output @@ -65645,6 +77488,200 @@ MultivariatePolynomial(vl:List Symbol, R:Ring) @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain MYEXPR MyExpression} + +<>= +)set break resume +)sys rm -f MyExpression.output +)spool MyExpression.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show MyExpression +--R MyExpression(q: Symbol,R: Join(Ring,OrderedSet,IntegralDomain)) is a domain constructor +--R Abbreviation for MyExpression is MYEXPR +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for MYEXPR +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (PositiveInteger,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (%,%) -> % ?**? : (%,%) -> % +--R ?**? : (%,PositiveInteger) -> % ?+? : (%,%) -> % +--R -? : % -> % ?-? : (%,%) -> % +--R ?/? : (%,%) -> % ? Boolean +--R ?<=? : (%,%) -> Boolean ?=? : (%,%) -> Boolean +--R ?>? : (%,%) -> Boolean ?>=? : (%,%) -> Boolean +--R D : (%,Symbol) -> % D : (%,List Symbol) -> % +--R 1 : () -> % 0 : () -> % +--R ?^? : (%,PositiveInteger) -> % applyQuote : (Symbol,%,%) -> % +--R applyQuote : (Symbol,%) -> % associates? : (%,%) -> Boolean +--R belong? : BasicOperator -> Boolean binomial : (%,%) -> % +--R box : List % -> % box : % -> % +--R coerce : Integer -> % coerce : % -> % +--R coerce : R -> % coerce : Symbol -> % +--R coerce : Kernel % -> % coerce : % -> OutputForm +--R denominator : % -> % differentiate : (%,Symbol) -> % +--R distribute : (%,%) -> % distribute : % -> % +--R elt : (BasicOperator,%,%) -> % elt : (BasicOperator,%) -> % +--R eval : (%,List %,List %) -> % eval : (%,%,%) -> % +--R eval : (%,Equation %) -> % eval : (%,List Equation %) -> % +--R eval : (%,Kernel %,%) -> % factorial : % -> % +--R factorials : % -> % factorials : (%,Symbol) -> % +--R freeOf? : (%,Symbol) -> Boolean freeOf? : (%,%) -> Boolean +--R ground : % -> R ground? : % -> Boolean +--R hash : % -> SingleInteger height : % -> NonNegativeInteger +--R is? : (%,Symbol) -> Boolean kernel : (BasicOperator,%) -> % +--R kernels : % -> List Kernel % latex : % -> String +--R map : ((% -> %),Kernel %) -> % max : (%,%) -> % +--R min : (%,%) -> % numerator : % -> % +--R one? : % -> Boolean paren : List % -> % +--R paren : % -> % permutation : (%,%) -> % +--R product : (%,Symbol) -> % recip : % -> Union(%,"failed") +--R retract : % -> Integer retract : % -> R +--R retract : % -> Symbol retract : % -> Kernel % +--R sample : () -> % subst : (%,Equation %) -> % +--R summation : (%,Symbol) -> % tower : % -> List Kernel % +--R unit? : % -> Boolean unitCanonical : % -> % +--R variables : % -> List Symbol zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean +--R ?*? : (NonNegativeInteger,%) -> % +--R ?*? : (%,R) -> % if R has COMRING +--R ?*? : (R,%) -> % if R has COMRING +--R ?*? : (%,Fraction Integer) -> % if R has INTDOM +--R ?*? : (Fraction Integer,%) -> % if R has INTDOM +--R ?**? : (%,Integer) -> % if R has GROUP or R has INTDOM +--R ?**? : (%,NonNegativeInteger) -> % +--R ?/? : (SparseMultivariatePolynomial(R,Kernel %),SparseMultivariatePolynomial(R,Kernel %)) -> % if R has INTDOM +--R D : (%,Symbol,NonNegativeInteger) -> % +--R D : (%,List Symbol,List NonNegativeInteger) -> % +--R ?^? : (%,Integer) -> % if R has GROUP or R has INTDOM +--R ?^? : (%,NonNegativeInteger) -> % +--R applyQuote : (Symbol,List %) -> % +--R applyQuote : (Symbol,%,%,%,%) -> % +--R applyQuote : (Symbol,%,%,%) -> % +--R characteristic : () -> NonNegativeInteger +--R charthRoot : % -> Union(%,"failed") if R has CHARNZ +--R coerce : Fraction Integer -> % if R has INTDOM or R has RETRACT FRAC INT +--R coerce : Fraction MyUnivariatePolynomial(q,R) -> % +--R coerce : MyUnivariatePolynomial(q,R) -> % +--R coerce : Polynomial R -> % if R has RING +--R coerce : Fraction Polynomial R -> % if R has INTDOM +--R coerce : Fraction Polynomial Fraction R -> % if R has INTDOM +--R coerce : Polynomial Fraction R -> % if R has INTDOM +--R coerce : Fraction R -> % if R has INTDOM +--R coerce : SparseMultivariatePolynomial(R,Kernel %) -> % if R has RING +--R commutator : (%,%) -> % if R has GROUP +--R conjugate : (%,%) -> % if R has GROUP +--R convert : % -> InputForm if R has KONVERT INFORM +--R convert : Factored % -> % if R has INTDOM +--R convert : % -> Pattern Float if R has KONVERT PATTERN FLOAT +--R convert : % -> Pattern Integer if R has KONVERT PATTERN INT +--R definingPolynomial : % -> % if $ has RING +--R denom : % -> SparseMultivariatePolynomial(R,Kernel %) if R has INTDOM +--R differentiate : (%,List Symbol) -> % +--R differentiate : (%,Symbol,NonNegativeInteger) -> % +--R differentiate : (%,List Symbol,List NonNegativeInteger) -> % +--R divide : (%,%) -> Record(quotient: %,remainder: %) if R has INTDOM +--R elt : (BasicOperator,List %) -> % +--R elt : (BasicOperator,%,%,%,%) -> % +--R elt : (BasicOperator,%,%,%) -> % +--R euclideanSize : % -> NonNegativeInteger if R has INTDOM +--R eval : (%,Symbol,NonNegativeInteger,(% -> %)) -> % if R has RING +--R eval : (%,Symbol,NonNegativeInteger,(List % -> %)) -> % if R has RING +--R eval : (%,List Symbol,List NonNegativeInteger,List (List % -> %)) -> % if R has RING +--R eval : (%,List Symbol,List NonNegativeInteger,List (% -> %)) -> % if R has RING +--R eval : (%,List BasicOperator,List %,Symbol) -> % if R has KONVERT INFORM +--R eval : (%,BasicOperator,%,Symbol) -> % if R has KONVERT INFORM +--R eval : % -> % if R has KONVERT INFORM +--R eval : (%,List Symbol) -> % if R has KONVERT INFORM +--R eval : (%,Symbol) -> % if R has KONVERT INFORM +--R eval : (%,BasicOperator,(% -> %)) -> % +--R eval : (%,BasicOperator,(List % -> %)) -> % +--R eval : (%,List BasicOperator,List (List % -> %)) -> % +--R eval : (%,List BasicOperator,List (% -> %)) -> % +--R eval : (%,Symbol,(% -> %)) -> % +--R eval : (%,Symbol,(List % -> %)) -> % +--R eval : (%,List Symbol,List (List % -> %)) -> % +--R eval : (%,List Symbol,List (% -> %)) -> % +--R eval : (%,List Kernel %,List %) -> % +--R even? : % -> Boolean if $ has RETRACT INT +--R expressIdealMember : (List %,%) -> Union(List %,"failed") if R has INTDOM +--R exquo : (%,%) -> Union(%,"failed") +--R extendedEuclidean : (%,%) -> Record(coef1: %,coef2: %,generator: %) if R has INTDOM +--R extendedEuclidean : (%,%,%) -> Union(Record(coef1: %,coef2: %),"failed") if R has INTDOM +--R factor : % -> Factored % if R has INTDOM +--R gcd : (%,%) -> % if R has INTDOM +--R gcd : List % -> % if R has INTDOM +--R gcdPolynomial : (SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial % if R has INTDOM +--R inv : % -> % if R has GROUP or R has INTDOM +--R is? : (%,BasicOperator) -> Boolean +--R isExpt : (%,Symbol) -> Union(Record(var: Kernel %,exponent: Integer),"failed") if R has RING +--R isExpt : (%,BasicOperator) -> Union(Record(var: Kernel %,exponent: Integer),"failed") if R has RING +--R isExpt : % -> Union(Record(var: Kernel %,exponent: Integer),"failed") if R has SGROUP +--R isMult : % -> Union(Record(coef: Integer,var: Kernel %),"failed") if R has ABELSG +--R isPlus : % -> Union(List %,"failed") if R has ABELSG +--R isPower : % -> Union(Record(val: %,exponent: Integer),"failed") if R has RING +--R isTimes : % -> Union(List %,"failed") if R has SGROUP +--R kernel : (BasicOperator,List %) -> % +--R lcm : (%,%) -> % if R has INTDOM +--R lcm : List % -> % if R has INTDOM +--R mainKernel : % -> Union(Kernel %,"failed") +--R minPoly : Kernel % -> SparseUnivariatePolynomial % if $ has RING +--R multiEuclidean : (List %,%) -> Union(List %,"failed") if R has INTDOM +--R numer : % -> SparseMultivariatePolynomial(R,Kernel %) if R has RING +--R odd? : % -> Boolean if $ has RETRACT INT +--R operator : BasicOperator -> BasicOperator +--R operators : % -> List BasicOperator +--R patternMatch : (%,Pattern Float,PatternMatchResult(Float,%)) -> PatternMatchResult(Float,%) if R has PATMAB FLOAT +--R patternMatch : (%,Pattern Integer,PatternMatchResult(Integer,%)) -> PatternMatchResult(Integer,%) if R has PATMAB INT +--R prime? : % -> Boolean if R has INTDOM +--R principalIdeal : List % -> Record(coef: List %,generator: %) if R has INTDOM +--R product : (%,SegmentBinding %) -> % +--R ?quo? : (%,%) -> % if R has INTDOM +--R reducedSystem : Matrix % -> Matrix Integer if R has LINEXP INT and R has RING +--R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix Integer,vec: Vector Integer) if R has LINEXP INT and R has RING +--R reducedSystem : Matrix % -> Matrix R if R has RING +--R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix R,vec: Vector R) if R has RING +--R ?rem? : (%,%) -> % if R has INTDOM +--R retract : % -> Fraction Integer if R has INTDOM and R has RETRACT INT or R has RETRACT FRAC INT +--R retract : % -> Fraction MyUnivariatePolynomial(q,R) +--R retract : % -> MyUnivariatePolynomial(q,R) +--R retract : % -> Polynomial R if R has RING +--R retract : % -> Fraction Polynomial R if R has INTDOM +--R retractIfCan : % -> Union(Fraction Integer,"failed") if R has INTDOM and R has RETRACT INT or R has RETRACT FRAC INT +--R retractIfCan : % -> Union(Integer,"failed") +--R retractIfCan : % -> Union(MyUnivariatePolynomial(q,R),"failed") +--R retractIfCan : % -> Union(Polynomial R,"failed") if R has RING +--R retractIfCan : % -> Union(Fraction Polynomial R,"failed") if R has INTDOM +--R retractIfCan : % -> Union(R,"failed") +--R retractIfCan : % -> Union(Symbol,"failed") +--R retractIfCan : % -> Union(Kernel %,"failed") +--R sizeLess? : (%,%) -> Boolean if R has INTDOM +--R squareFree : % -> Factored % if R has INTDOM +--R squareFreePart : % -> % if R has INTDOM +--R subst : (%,List Kernel %,List %) -> % +--R subst : (%,List Equation %) -> % +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R summation : (%,SegmentBinding %) -> % +--R unitNormal : % -> Record(unit: %,canonical: %,associate: %) +--R univariate : (%,Kernel %) -> Fraction SparseUnivariatePolynomial % if R has INTDOM +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +MyExpression examples +==================================================================== + +See Also: +o )show MyExpression + +@ + \pagehead{MyExpression}{MYEXPR} \pagepic{ps/v103myexpression.ps}{MYEXPR}{1.00} {\bf See}\\ @@ -65817,6 +77854,212 @@ MyExpression(q: Symbol, R): Exports == Implementation where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain MYUP MyUnivariatePolynomial} + +<>= +)set break resume +)sys rm -f MyUnivariatePolynomial.output +)spool MyUnivariatePolynomial.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show MyUnivariatePolynomial +--R MyUnivariatePolynomial(x: Symbol,R: Ring) is a domain constructor +--R Abbreviation for MyUnivariatePolynomial is MYUP +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for MYUP +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (%,R) -> % ?*? : (R,%) -> % +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ?=? : (%,%) -> Boolean +--R D : (%,(R -> R)) -> % D : % -> % +--R D : (%,NonNegativeInteger) -> % 1 : () -> % +--R 0 : () -> % ?^? : (%,PositiveInteger) -> % +--R coefficients : % -> List R coerce : Symbol -> % +--R coerce : Polynomial R -> % coerce : Variable x -> % +--R coerce : R -> % coerce : Integer -> % +--R coerce : % -> OutputForm degree : % -> NonNegativeInteger +--R differentiate : % -> % ?.? : (%,%) -> % +--R ?.? : (%,R) -> R eval : (%,List %,List %) -> % +--R eval : (%,%,%) -> % eval : (%,Equation %) -> % +--R eval : (%,List Equation %) -> % ground : % -> R +--R ground? : % -> Boolean hash : % -> SingleInteger +--R init : () -> % if R has STEP latex : % -> String +--R leadingCoefficient : % -> R leadingMonomial : % -> % +--R map : ((R -> R),%) -> % monomial? : % -> Boolean +--R monomials : % -> List % one? : % -> Boolean +--R primitiveMonomials : % -> List % pseudoRemainder : (%,%) -> % +--R recip : % -> Union(%,"failed") reductum : % -> % +--R retract : % -> Symbol retract : % -> R +--R sample : () -> % zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean +--R ?*? : (Fraction Integer,%) -> % if R has ALGEBRA FRAC INT +--R ?*? : (%,Fraction Integer) -> % if R has ALGEBRA FRAC INT +--R ?*? : (NonNegativeInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % +--R ?/? : (%,R) -> % if R has FIELD +--R ? Boolean if R has ORDSET +--R ?<=? : (%,%) -> Boolean if R has ORDSET +--R ?>? : (%,%) -> Boolean if R has ORDSET +--R ?>=? : (%,%) -> Boolean if R has ORDSET +--R D : (%,(R -> R),NonNegativeInteger) -> % +--R D : (%,List Symbol,List NonNegativeInteger) -> % if R has PDRING SYMBOL +--R D : (%,Symbol,NonNegativeInteger) -> % if R has PDRING SYMBOL +--R D : (%,List Symbol) -> % if R has PDRING SYMBOL +--R D : (%,Symbol) -> % if R has PDRING SYMBOL +--R D : (%,List SingletonAsOrderedSet,List NonNegativeInteger) -> % +--R D : (%,SingletonAsOrderedSet,NonNegativeInteger) -> % +--R D : (%,List SingletonAsOrderedSet) -> % +--R D : (%,SingletonAsOrderedSet) -> % +--R ?^? : (%,NonNegativeInteger) -> % +--R associates? : (%,%) -> Boolean if R has INTDOM +--R binomThmExpt : (%,%,NonNegativeInteger) -> % if R has COMRING +--R characteristic : () -> NonNegativeInteger +--R charthRoot : % -> Union(%,"failed") if $ has CHARNZ and R has PFECAT or R has CHARNZ +--R coefficient : (%,List SingletonAsOrderedSet,List NonNegativeInteger) -> % +--R coefficient : (%,SingletonAsOrderedSet,NonNegativeInteger) -> % +--R coefficient : (%,NonNegativeInteger) -> R +--R coerce : % -> % if R has INTDOM +--R coerce : Fraction Integer -> % if R has ALGEBRA FRAC INT or R has RETRACT FRAC INT +--R coerce : SingletonAsOrderedSet -> % +--R composite : (Fraction %,%) -> Union(Fraction %,"failed") if R has INTDOM +--R composite : (%,%) -> Union(%,"failed") if R has INTDOM +--R conditionP : Matrix % -> Union(Vector %,"failed") if $ has CHARNZ and R has PFECAT +--R content : (%,SingletonAsOrderedSet) -> % if R has GCDDOM +--R content : % -> R if R has GCDDOM +--R convert : % -> InputForm if SingletonAsOrderedSet has KONVERT INFORM and R has KONVERT INFORM +--R convert : % -> Pattern Integer if SingletonAsOrderedSet has KONVERT PATTERN INT and R has KONVERT PATTERN INT +--R convert : % -> Pattern Float if SingletonAsOrderedSet has KONVERT PATTERN FLOAT and R has KONVERT PATTERN FLOAT +--R degree : (%,List SingletonAsOrderedSet) -> List NonNegativeInteger +--R degree : (%,SingletonAsOrderedSet) -> NonNegativeInteger +--R differentiate : (%,(R -> R),%) -> % +--R differentiate : (%,(R -> R)) -> % +--R differentiate : (%,(R -> R),NonNegativeInteger) -> % +--R differentiate : (%,List Symbol,List NonNegativeInteger) -> % if R has PDRING SYMBOL +--R differentiate : (%,Symbol,NonNegativeInteger) -> % if R has PDRING SYMBOL +--R differentiate : (%,List Symbol) -> % if R has PDRING SYMBOL +--R differentiate : (%,Symbol) -> % if R has PDRING SYMBOL +--R differentiate : (%,NonNegativeInteger) -> % +--R differentiate : (%,List SingletonAsOrderedSet,List NonNegativeInteger) -> % +--R differentiate : (%,SingletonAsOrderedSet,NonNegativeInteger) -> % +--R differentiate : (%,List SingletonAsOrderedSet) -> % +--R differentiate : (%,SingletonAsOrderedSet) -> % +--R discriminant : % -> R if R has COMRING +--R discriminant : (%,SingletonAsOrderedSet) -> % if R has COMRING +--R divide : (%,%) -> Record(quotient: %,remainder: %) if R has FIELD +--R divideExponents : (%,NonNegativeInteger) -> Union(%,"failed") +--R ?.? : (%,Fraction %) -> Fraction % if R has INTDOM +--R elt : (Fraction %,R) -> R if R has FIELD +--R elt : (Fraction %,Fraction %) -> Fraction % if R has INTDOM +--R euclideanSize : % -> NonNegativeInteger if R has FIELD +--R eval : (%,List SingletonAsOrderedSet,List %) -> % +--R eval : (%,SingletonAsOrderedSet,%) -> % +--R eval : (%,List SingletonAsOrderedSet,List R) -> % +--R eval : (%,SingletonAsOrderedSet,R) -> % +--R expressIdealMember : (List %,%) -> Union(List %,"failed") if R has FIELD +--R exquo : (%,%) -> Union(%,"failed") if R has INTDOM +--R exquo : (%,R) -> Union(%,"failed") if R has INTDOM +--R extendedEuclidean : (%,%) -> Record(coef1: %,coef2: %,generator: %) if R has FIELD +--R extendedEuclidean : (%,%,%) -> Union(Record(coef1: %,coef2: %),"failed") if R has FIELD +--R factor : % -> Factored % if R has PFECAT +--R factorPolynomial : SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if R has PFECAT +--R factorSquareFreePolynomial : SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if R has PFECAT +--R fmecg : (%,NonNegativeInteger,R,%) -> % +--R gcd : (%,%) -> % if R has GCDDOM +--R gcd : List % -> % if R has GCDDOM +--R gcdPolynomial : (SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial % if R has GCDDOM +--R integrate : % -> % if R has ALGEBRA FRAC INT +--R isExpt : % -> Union(Record(var: SingletonAsOrderedSet,exponent: NonNegativeInteger),"failed") +--R isPlus : % -> Union(List %,"failed") +--R isTimes : % -> Union(List %,"failed") +--R karatsubaDivide : (%,NonNegativeInteger) -> Record(quotient: %,remainder: %) +--R lcm : (%,%) -> % if R has GCDDOM +--R lcm : List % -> % if R has GCDDOM +--R mainVariable : % -> Union(SingletonAsOrderedSet,"failed") +--R makeSUP : % -> SparseUnivariatePolynomial R +--R mapExponents : ((NonNegativeInteger -> NonNegativeInteger),%) -> % +--R max : (%,%) -> % if R has ORDSET +--R min : (%,%) -> % if R has ORDSET +--R minimumDegree : (%,List SingletonAsOrderedSet) -> List NonNegativeInteger +--R minimumDegree : (%,SingletonAsOrderedSet) -> NonNegativeInteger +--R minimumDegree : % -> NonNegativeInteger +--R monicDivide : (%,%) -> Record(quotient: %,remainder: %) +--R monicDivide : (%,%,SingletonAsOrderedSet) -> Record(quotient: %,remainder: %) +--R monomial : (%,List SingletonAsOrderedSet,List NonNegativeInteger) -> % +--R monomial : (%,SingletonAsOrderedSet,NonNegativeInteger) -> % +--R monomial : (R,NonNegativeInteger) -> % +--R multiEuclidean : (List %,%) -> Union(List %,"failed") if R has FIELD +--R multiplyExponents : (%,NonNegativeInteger) -> % +--R multivariate : (SparseUnivariatePolynomial %,SingletonAsOrderedSet) -> % +--R multivariate : (SparseUnivariatePolynomial R,SingletonAsOrderedSet) -> % +--R nextItem : % -> Union(%,"failed") if R has STEP +--R numberOfMonomials : % -> NonNegativeInteger +--R order : (%,%) -> NonNegativeInteger if R has INTDOM +--R patternMatch : (%,Pattern Integer,PatternMatchResult(Integer,%)) -> PatternMatchResult(Integer,%) if SingletonAsOrderedSet has PATMAB INT and R has PATMAB INT +--R patternMatch : (%,Pattern Float,PatternMatchResult(Float,%)) -> PatternMatchResult(Float,%) if SingletonAsOrderedSet has PATMAB FLOAT and R has PATMAB FLOAT +--R pomopo! : (%,R,NonNegativeInteger,%) -> % +--R prime? : % -> Boolean if R has PFECAT +--R primitivePart : (%,SingletonAsOrderedSet) -> % if R has GCDDOM +--R primitivePart : % -> % if R has GCDDOM +--R principalIdeal : List % -> Record(coef: List %,generator: %) if R has FIELD +--R pseudoDivide : (%,%) -> Record(coef: R,quotient: %,remainder: %) if R has INTDOM +--R pseudoQuotient : (%,%) -> % if R has INTDOM +--R ?quo? : (%,%) -> % if R has FIELD +--R reducedSystem : Matrix % -> Matrix R +--R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix R,vec: Vector R) +--R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix Integer,vec: Vector Integer) if R has LINEXP INT +--R reducedSystem : Matrix % -> Matrix Integer if R has LINEXP INT +--R ?rem? : (%,%) -> % if R has FIELD +--R resultant : (%,%) -> R if R has COMRING +--R resultant : (%,%,SingletonAsOrderedSet) -> % if R has COMRING +--R retract : % -> SingletonAsOrderedSet +--R retract : % -> Integer if R has RETRACT INT +--R retract : % -> Fraction Integer if R has RETRACT FRAC INT +--R retractIfCan : % -> Union(Symbol,"failed") +--R retractIfCan : % -> Union(SingletonAsOrderedSet,"failed") +--R retractIfCan : % -> Union(Integer,"failed") if R has RETRACT INT +--R retractIfCan : % -> Union(Fraction Integer,"failed") if R has RETRACT FRAC INT +--R retractIfCan : % -> Union(R,"failed") +--R separate : (%,%) -> Record(primePart: %,commonPart: %) if R has GCDDOM +--R shiftLeft : (%,NonNegativeInteger) -> % +--R shiftRight : (%,NonNegativeInteger) -> % +--R sizeLess? : (%,%) -> Boolean if R has FIELD +--R solveLinearPolynomialEquation : (List SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> Union(List SparseUnivariatePolynomial %,"failed") if R has PFECAT +--R squareFree : % -> Factored % if R has GCDDOM +--R squareFreePart : % -> % if R has GCDDOM +--R squareFreePolynomial : SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if R has PFECAT +--R subResultantGcd : (%,%) -> % if R has INTDOM +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R totalDegree : (%,List SingletonAsOrderedSet) -> NonNegativeInteger +--R totalDegree : % -> NonNegativeInteger +--R unit? : % -> Boolean if R has INTDOM +--R unitCanonical : % -> % if R has INTDOM +--R unitNormal : % -> Record(unit: %,canonical: %,associate: %) if R has INTDOM +--R univariate : % -> SparseUnivariatePolynomial R +--R univariate : (%,SingletonAsOrderedSet) -> SparseUnivariatePolynomial % +--R unmakeSUP : SparseUnivariatePolynomial R -> % +--R variables : % -> List SingletonAsOrderedSet +--R vectorise : (%,NonNegativeInteger) -> Vector R +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +MyUnivariatePolynomial examples +==================================================================== + +See Also: +o )show MyUnivariatePolynomial + +@ + \pagehead{MyUnivariatePolynomial}{MYUP} \pagepic{ps/v103myunivariatepolynomial.ps}{MYUP}{1.00} {\bf See}\\ @@ -65985,6 +78228,7 @@ MyUnivariatePolynomial(x:Symbol, R:Ring): \chapter{Chapter N} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain NSDPS NeitherSparseOrDensePowerSeries} + <>= )set break resume )sys rm -f NeitherSparseOrDensePowerSeries.output @@ -66592,11 +78836,225 @@ NeitherSparseOrDensePowerSeries(K):Exports == Implementation where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain NSMP NewSparseMultivariatePolynomial} + Based on the {\bf PseudoRemainderSequence} package, the domain constructor {\bf NewSparseMulitvariatePolynomial} extends the constructor {\bf SparseMultivariatePolynomial}. It also provides some additional operations related to polynomial system solving by means of triangular sets. + +<>= +)set break resume +)sys rm -f NewSparseMultivariatePolynomial.output +)spool NewSparseMultivariatePolynomial.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show NewSparseMultivariatePolynomial +--R NewSparseMultivariatePolynomial(R: Ring,VarSet: OrderedSet) is a domain constructor +--R Abbreviation for NewSparseMultivariatePolynomial is NSMP +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for NSMP +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (%,R) -> % ?*? : (R,%) -> % +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ?=? : (%,%) -> Boolean +--R D : (%,List VarSet) -> % D : (%,VarSet) -> % +--R 1 : () -> % 0 : () -> % +--R ?^? : (%,PositiveInteger) -> % coefficients : % -> List R +--R coerce : VarSet -> % coerce : R -> % +--R coerce : Integer -> % coerce : % -> OutputForm +--R deepestInitial : % -> % deepestTail : % -> % +--R differentiate : (%,VarSet) -> % eval : (%,VarSet,%) -> % +--R eval : (%,VarSet,R) -> % eval : (%,List %,List %) -> % +--R eval : (%,%,%) -> % eval : (%,Equation %) -> % +--R eval : (%,List Equation %) -> % ground : % -> R +--R ground? : % -> Boolean hash : % -> SingleInteger +--R head : % -> % headReduce : (%,%) -> % +--R headReduced? : (%,%) -> Boolean infRittWu? : (%,%) -> Boolean +--R init : % -> % initiallyReduce : (%,%) -> % +--R iteratedInitials : % -> List % latex : % -> String +--R lazyPquo : (%,%,VarSet) -> % lazyPquo : (%,%) -> % +--R lazyPrem : (%,%,VarSet) -> % lazyPrem : (%,%) -> % +--R leadingCoefficient : % -> R leadingMonomial : % -> % +--R leastMonomial : % -> % mainCoefficients : % -> List % +--R mainMonomial : % -> % mainMonomials : % -> List % +--R map : ((R -> R),%) -> % mdeg : % -> NonNegativeInteger +--R monic? : % -> Boolean monicModulo : (%,%) -> % +--R monomial? : % -> Boolean monomials : % -> List % +--R mvar : % -> VarSet normalized? : (%,%) -> Boolean +--R one? : % -> Boolean pquo : (%,%,VarSet) -> % +--R pquo : (%,%) -> % prem : (%,%,VarSet) -> % +--R prem : (%,%) -> % primitiveMonomials : % -> List % +--R quasiMonic? : % -> Boolean recip : % -> Union(%,"failed") +--R reduced? : (%,List %) -> Boolean reduced? : (%,%) -> Boolean +--R reductum : (%,VarSet) -> % reductum : % -> % +--R retract : % -> VarSet retract : % -> R +--R sample : () -> % supRittWu? : (%,%) -> Boolean +--R tail : % -> % variables : % -> List VarSet +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean +--R ?*? : (Fraction Integer,%) -> % if R has ALGEBRA FRAC INT +--R ?*? : (%,Fraction Integer) -> % if R has ALGEBRA FRAC INT +--R ?*? : (NonNegativeInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % +--R ?/? : (%,R) -> % if R has FIELD +--R ? Boolean if R has ORDSET +--R ?<=? : (%,%) -> Boolean if R has ORDSET +--R ?>? : (%,%) -> Boolean if R has ORDSET +--R ?>=? : (%,%) -> Boolean if R has ORDSET +--R D : (%,List VarSet,List NonNegativeInteger) -> % +--R D : (%,VarSet,NonNegativeInteger) -> % +--R LazardQuotient : (%,%,NonNegativeInteger) -> % if R has INTDOM +--R LazardQuotient2 : (%,%,%,NonNegativeInteger) -> % if R has INTDOM +--R RittWuCompare : (%,%) -> Union(Boolean,"failed") +--R ?^? : (%,NonNegativeInteger) -> % +--R associates? : (%,%) -> Boolean if R has INTDOM +--R binomThmExpt : (%,%,NonNegativeInteger) -> % if R has COMRING +--R characteristic : () -> NonNegativeInteger +--R charthRoot : % -> Union(%,"failed") if $ has CHARNZ and R has PFECAT or R has CHARNZ +--R coefficient : (%,List VarSet,List NonNegativeInteger) -> % +--R coefficient : (%,VarSet,NonNegativeInteger) -> % +--R coefficient : (%,IndexedExponents VarSet) -> R +--R coerce : % -> % if R has INTDOM +--R coerce : Fraction Integer -> % if R has ALGEBRA FRAC INT or R has RETRACT FRAC INT +--R coerce : SparseMultivariatePolynomial(R,VarSet) -> % +--R coerce : % -> SparseMultivariatePolynomial(R,VarSet) +--R coerce : % -> Polynomial R if VarSet has KONVERT SYMBOL +--R conditionP : Matrix % -> Union(Vector %,"failed") if $ has CHARNZ and R has PFECAT +--R content : (%,VarSet) -> % if R has GCDDOM +--R content : % -> R if R has GCDDOM +--R convert : % -> Polynomial R if VarSet has KONVERT SYMBOL +--R convert : % -> String if R has RETRACT INT and VarSet has KONVERT SYMBOL +--R convert : Polynomial R -> % if VarSet has KONVERT SYMBOL +--R convert : Polynomial Integer -> % if R has ALGEBRA INT and VarSet has KONVERT SYMBOL and not has(R,Algebra Fraction Integer) or R has ALGEBRA FRAC INT and VarSet has KONVERT SYMBOL +--R convert : Polynomial Fraction Integer -> % if R has ALGEBRA FRAC INT and VarSet has KONVERT SYMBOL +--R convert : % -> InputForm if R has KONVERT INFORM and VarSet has KONVERT INFORM +--R convert : % -> Pattern Integer if R has KONVERT PATTERN INT and VarSet has KONVERT PATTERN INT +--R convert : % -> Pattern Float if R has KONVERT PATTERN FLOAT and VarSet has KONVERT PATTERN FLOAT +--R degree : (%,List VarSet) -> List NonNegativeInteger +--R degree : (%,VarSet) -> NonNegativeInteger +--R degree : % -> IndexedExponents VarSet +--R differentiate : (%,List VarSet,List NonNegativeInteger) -> % +--R differentiate : (%,VarSet,NonNegativeInteger) -> % +--R differentiate : (%,List VarSet) -> % +--R discriminant : (%,VarSet) -> % if R has COMRING +--R eval : (%,List VarSet,List %) -> % +--R eval : (%,List VarSet,List R) -> % +--R exactQuotient : (%,%) -> % if R has INTDOM +--R exactQuotient : (%,R) -> % if R has INTDOM +--R exactQuotient! : (%,%) -> % if R has INTDOM +--R exactQuotient! : (%,R) -> % if R has INTDOM +--R exquo : (%,%) -> Union(%,"failed") if R has INTDOM +--R exquo : (%,R) -> Union(%,"failed") if R has INTDOM +--R extendedSubResultantGcd : (%,%) -> Record(gcd: %,coef1: %,coef2: %) if R has INTDOM +--R factor : % -> Factored % if R has PFECAT +--R factorPolynomial : SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if R has PFECAT +--R factorSquareFreePolynomial : SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if R has PFECAT +--R gcd : (%,%) -> % if R has GCDDOM +--R gcd : List % -> % if R has GCDDOM +--R gcd : (R,%) -> R if R has GCDDOM +--R gcdPolynomial : (SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial % if R has GCDDOM +--R halfExtendedSubResultantGcd1 : (%,%) -> Record(gcd: %,coef1: %) if R has INTDOM +--R halfExtendedSubResultantGcd2 : (%,%) -> Record(gcd: %,coef2: %) if R has INTDOM +--R headReduced? : (%,List %) -> Boolean +--R initiallyReduced? : (%,List %) -> Boolean +--R initiallyReduced? : (%,%) -> Boolean +--R isExpt : % -> Union(Record(var: VarSet,exponent: NonNegativeInteger),"failed") +--R isPlus : % -> Union(List %,"failed") +--R isTimes : % -> Union(List %,"failed") +--R lastSubResultant : (%,%) -> % if R has INTDOM +--R lazyPremWithDefault : (%,%,VarSet) -> Record(coef: %,gap: NonNegativeInteger,remainder: %) +--R lazyPremWithDefault : (%,%) -> Record(coef: %,gap: NonNegativeInteger,remainder: %) +--R lazyPseudoDivide : (%,%,VarSet) -> Record(coef: %,gap: NonNegativeInteger,quotient: %,remainder: %) +--R lazyPseudoDivide : (%,%) -> Record(coef: %,gap: NonNegativeInteger,quotient: %,remainder: %) +--R lazyResidueClass : (%,%) -> Record(polnum: %,polden: %,power: NonNegativeInteger) +--R lcm : (%,%) -> % if R has GCDDOM +--R lcm : List % -> % if R has GCDDOM +--R leadingCoefficient : (%,VarSet) -> % +--R mainContent : % -> % if R has GCDDOM +--R mainPrimitivePart : % -> % if R has GCDDOM +--R mainSquareFreePart : % -> % if R has GCDDOM +--R mainVariable : % -> Union(VarSet,"failed") +--R mapExponents : ((IndexedExponents VarSet -> IndexedExponents VarSet),%) -> % +--R max : (%,%) -> % if R has ORDSET +--R min : (%,%) -> % if R has ORDSET +--R minimumDegree : (%,List VarSet) -> List NonNegativeInteger +--R minimumDegree : (%,VarSet) -> NonNegativeInteger +--R minimumDegree : % -> IndexedExponents VarSet +--R monicDivide : (%,%,VarSet) -> Record(quotient: %,remainder: %) +--R monomial : (%,List VarSet,List NonNegativeInteger) -> % +--R monomial : (%,VarSet,NonNegativeInteger) -> % +--R monomial : (R,IndexedExponents VarSet) -> % +--R multivariate : (SparseUnivariatePolynomial %,VarSet) -> % +--R multivariate : (SparseUnivariatePolynomial R,VarSet) -> % +--R nextsubResultant2 : (%,%,%,%) -> % if R has INTDOM +--R normalized? : (%,List %) -> Boolean +--R numberOfMonomials : % -> NonNegativeInteger +--R patternMatch : (%,Pattern Integer,PatternMatchResult(Integer,%)) -> PatternMatchResult(Integer,%) if R has PATMAB INT and VarSet has PATMAB INT +--R patternMatch : (%,Pattern Float,PatternMatchResult(Float,%)) -> PatternMatchResult(Float,%) if R has PATMAB FLOAT and VarSet has PATMAB FLOAT +--R pomopo! : (%,R,IndexedExponents VarSet,%) -> % +--R primPartElseUnitCanonical : % -> % if R has INTDOM +--R primPartElseUnitCanonical! : % -> % if R has INTDOM +--R prime? : % -> Boolean if R has PFECAT +--R primitivePart : (%,VarSet) -> % if R has GCDDOM +--R primitivePart : % -> % if R has GCDDOM +--R primitivePart! : % -> % if R has GCDDOM +--R pseudoDivide : (%,%) -> Record(quotient: %,remainder: %) +--R reducedSystem : Matrix % -> Matrix R +--R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix R,vec: Vector R) +--R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix Integer,vec: Vector Integer) if R has LINEXP INT +--R reducedSystem : Matrix % -> Matrix Integer if R has LINEXP INT +--R resultant : (%,%) -> % if R has INTDOM +--R resultant : (%,%,VarSet) -> % if R has COMRING +--R retract : % -> SparseMultivariatePolynomial(R,VarSet) +--R retract : Polynomial R -> % if VarSet has KONVERT SYMBOL and not has(R,Algebra Fraction Integer) and not has(R,Algebra Integer) or R has ALGEBRA INT and VarSet has KONVERT SYMBOL and not has(R,Algebra Fraction Integer) and not has(R,IntegerNumberSystem) or R has ALGEBRA FRAC INT and VarSet has KONVERT SYMBOL and not has(R,QuotientFieldCategory Integer) +--R retract : Polynomial Integer -> % if R has ALGEBRA INT and VarSet has KONVERT SYMBOL and not has(R,Algebra Fraction Integer) or R has ALGEBRA FRAC INT and VarSet has KONVERT SYMBOL +--R retract : Polynomial Fraction Integer -> % if R has ALGEBRA FRAC INT and VarSet has KONVERT SYMBOL +--R retract : % -> Integer if R has RETRACT INT +--R retract : % -> Fraction Integer if R has RETRACT FRAC INT +--R retractIfCan : % -> Union(SparseMultivariatePolynomial(R,VarSet),"failed") +--R retractIfCan : Polynomial R -> Union(%,"failed") if VarSet has KONVERT SYMBOL and not has(R,Algebra Fraction Integer) and not has(R,Algebra Integer) or R has ALGEBRA INT and VarSet has KONVERT SYMBOL and not has(R,Algebra Fraction Integer) and not has(R,IntegerNumberSystem) or R has ALGEBRA FRAC INT and VarSet has KONVERT SYMBOL and not has(R,QuotientFieldCategory Integer) +--R retractIfCan : Polynomial Integer -> Union(%,"failed") if R has ALGEBRA INT and VarSet has KONVERT SYMBOL and not has(R,Algebra Fraction Integer) or R has ALGEBRA FRAC INT and VarSet has KONVERT SYMBOL +--R retractIfCan : Polynomial Fraction Integer -> Union(%,"failed") if R has ALGEBRA FRAC INT and VarSet has KONVERT SYMBOL +--R retractIfCan : % -> Union(VarSet,"failed") +--R retractIfCan : % -> Union(Integer,"failed") if R has RETRACT INT +--R retractIfCan : % -> Union(Fraction Integer,"failed") if R has RETRACT FRAC INT +--R retractIfCan : % -> Union(R,"failed") +--R solveLinearPolynomialEquation : (List SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> Union(List SparseUnivariatePolynomial %,"failed") if R has PFECAT +--R squareFree : % -> Factored % if R has GCDDOM +--R squareFreePart : % -> % if R has GCDDOM +--R squareFreePolynomial : SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if R has PFECAT +--R subResultantChain : (%,%) -> List % if R has INTDOM +--R subResultantGcd : (%,%) -> % if R has INTDOM +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R totalDegree : (%,List VarSet) -> NonNegativeInteger +--R totalDegree : % -> NonNegativeInteger +--R unit? : % -> Boolean if R has INTDOM +--R unitCanonical : % -> % if R has INTDOM +--R unitNormal : % -> Record(unit: %,canonical: %,associate: %) if R has INTDOM +--R univariate : % -> SparseUnivariatePolynomial R +--R univariate : (%,VarSet) -> SparseUnivariatePolynomial % +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +NewSparseMultivariatePolynomial examples +==================================================================== + +See Also: +o )show NewSparseMultivariatePolynomial + +@ + \pagehead{NewSparseMultivariatePolynomial}{NSMP} \pagepic{ps/v103newsparsemultivariatepolynomial.ps}{NSMP}{1.00} {\bf See}\\ @@ -67151,9 +79609,229 @@ NewSparseMultivariatePolynomial(R,VarSet) : Exports == Implementation where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain NSUP NewSparseUnivariatePolynomial} + Based on the {\bf PseudoRemainderSequence} package, the domain constructor {\bf NewSparseUnivariatePolynomial} extends the constructur {\bf SparseUnivariatePolynomial}. + +<>= +)set break resume +)sys rm -f NewSparseUnivariatePolynomial.output +)spool NewSparseUnivariatePolynomial.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show NewSparseUnivariatePolynomial +--R NewSparseUnivariatePolynomial R: Ring is a domain constructor +--R Abbreviation for NewSparseUnivariatePolynomial is NSUP +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for NSUP +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (%,R) -> % ?*? : (R,%) -> % +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ?=? : (%,%) -> Boolean +--R D : (%,(R -> R)) -> % D : % -> % +--R D : (%,NonNegativeInteger) -> % 1 : () -> % +--R 0 : () -> % ?^? : (%,PositiveInteger) -> % +--R coefficients : % -> List R coerce : R -> % +--R coerce : Integer -> % coerce : % -> OutputForm +--R degree : % -> NonNegativeInteger differentiate : % -> % +--R ?.? : (%,%) -> % ?.? : (%,R) -> R +--R eval : (%,List %,List %) -> % eval : (%,%,%) -> % +--R eval : (%,Equation %) -> % eval : (%,List Equation %) -> % +--R ground : % -> R ground? : % -> Boolean +--R hash : % -> SingleInteger init : () -> % if R has STEP +--R latex : % -> String lazyPseudoQuotient : (%,%) -> % +--R leadingCoefficient : % -> R leadingMonomial : % -> % +--R map : ((R -> R),%) -> % monicModulo : (%,%) -> % +--R monomial? : % -> Boolean monomials : % -> List % +--R one? : % -> Boolean primitiveMonomials : % -> List % +--R pseudoRemainder : (%,%) -> % recip : % -> Union(%,"failed") +--R reductum : % -> % retract : % -> R +--R sample : () -> % zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean +--R ?*? : (Fraction Integer,%) -> % if R has ALGEBRA FRAC INT +--R ?*? : (%,Fraction Integer) -> % if R has ALGEBRA FRAC INT +--R ?*? : (NonNegativeInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % +--R ?/? : (%,R) -> % if R has FIELD +--R ? Boolean if R has ORDSET +--R ?<=? : (%,%) -> Boolean if R has ORDSET +--R ?>? : (%,%) -> Boolean if R has ORDSET +--R ?>=? : (%,%) -> Boolean if R has ORDSET +--R D : (%,(R -> R),NonNegativeInteger) -> % +--R D : (%,List Symbol,List NonNegativeInteger) -> % if R has PDRING SYMBOL +--R D : (%,Symbol,NonNegativeInteger) -> % if R has PDRING SYMBOL +--R D : (%,List Symbol) -> % if R has PDRING SYMBOL +--R D : (%,Symbol) -> % if R has PDRING SYMBOL +--R D : (%,List SingletonAsOrderedSet,List NonNegativeInteger) -> % +--R D : (%,SingletonAsOrderedSet,NonNegativeInteger) -> % +--R D : (%,List SingletonAsOrderedSet) -> % +--R D : (%,SingletonAsOrderedSet) -> % +--R ?^? : (%,NonNegativeInteger) -> % +--R associates? : (%,%) -> Boolean if R has INTDOM +--R binomThmExpt : (%,%,NonNegativeInteger) -> % if R has COMRING +--R characteristic : () -> NonNegativeInteger +--R charthRoot : % -> Union(%,"failed") if $ has CHARNZ and R has PFECAT or R has CHARNZ +--R coefficient : (%,List SingletonAsOrderedSet,List NonNegativeInteger) -> % +--R coefficient : (%,SingletonAsOrderedSet,NonNegativeInteger) -> % +--R coefficient : (%,NonNegativeInteger) -> R +--R coerce : % -> % if R has INTDOM +--R coerce : Fraction Integer -> % if R has ALGEBRA FRAC INT or R has RETRACT FRAC INT +--R coerce : SparseUnivariatePolynomial R -> % +--R coerce : % -> SparseUnivariatePolynomial R +--R coerce : SingletonAsOrderedSet -> % +--R composite : (Fraction %,%) -> Union(Fraction %,"failed") if R has INTDOM +--R composite : (%,%) -> Union(%,"failed") if R has INTDOM +--R conditionP : Matrix % -> Union(Vector %,"failed") if $ has CHARNZ and R has PFECAT +--R content : (%,SingletonAsOrderedSet) -> % if R has GCDDOM +--R content : % -> R if R has GCDDOM +--R convert : % -> InputForm if SingletonAsOrderedSet has KONVERT INFORM and R has KONVERT INFORM +--R convert : % -> Pattern Integer if SingletonAsOrderedSet has KONVERT PATTERN INT and R has KONVERT PATTERN INT +--R convert : % -> Pattern Float if SingletonAsOrderedSet has KONVERT PATTERN FLOAT and R has KONVERT PATTERN FLOAT +--R degree : (%,List SingletonAsOrderedSet) -> List NonNegativeInteger +--R degree : (%,SingletonAsOrderedSet) -> NonNegativeInteger +--R differentiate : (%,(R -> R),%) -> % +--R differentiate : (%,(R -> R)) -> % +--R differentiate : (%,(R -> R),NonNegativeInteger) -> % +--R differentiate : (%,List Symbol,List NonNegativeInteger) -> % if R has PDRING SYMBOL +--R differentiate : (%,Symbol,NonNegativeInteger) -> % if R has PDRING SYMBOL +--R differentiate : (%,List Symbol) -> % if R has PDRING SYMBOL +--R differentiate : (%,Symbol) -> % if R has PDRING SYMBOL +--R differentiate : (%,NonNegativeInteger) -> % +--R differentiate : (%,List SingletonAsOrderedSet,List NonNegativeInteger) -> % +--R differentiate : (%,SingletonAsOrderedSet,NonNegativeInteger) -> % +--R differentiate : (%,List SingletonAsOrderedSet) -> % +--R differentiate : (%,SingletonAsOrderedSet) -> % +--R discriminant : % -> R if R has COMRING +--R discriminant : (%,SingletonAsOrderedSet) -> % if R has COMRING +--R divide : (%,%) -> Record(quotient: %,remainder: %) if R has FIELD +--R divideExponents : (%,NonNegativeInteger) -> Union(%,"failed") +--R ?.? : (%,Fraction %) -> Fraction % if R has INTDOM +--R elt : (Fraction %,R) -> R if R has FIELD +--R elt : (Fraction %,Fraction %) -> Fraction % if R has INTDOM +--R euclideanSize : % -> NonNegativeInteger if R has FIELD +--R eval : (%,List SingletonAsOrderedSet,List %) -> % +--R eval : (%,SingletonAsOrderedSet,%) -> % +--R eval : (%,List SingletonAsOrderedSet,List R) -> % +--R eval : (%,SingletonAsOrderedSet,R) -> % +--R expressIdealMember : (List %,%) -> Union(List %,"failed") if R has FIELD +--R exquo : (%,%) -> Union(%,"failed") if R has INTDOM +--R exquo : (%,R) -> Union(%,"failed") if R has INTDOM +--R extendedEuclidean : (%,%) -> Record(coef1: %,coef2: %,generator: %) if R has FIELD +--R extendedEuclidean : (%,%,%) -> Union(Record(coef1: %,coef2: %),"failed") if R has FIELD +--R extendedResultant : (%,%) -> Record(resultant: R,coef1: %,coef2: %) if R has INTDOM +--R extendedSubResultantGcd : (%,%) -> Record(gcd: %,coef1: %,coef2: %) if R has INTDOM +--R factor : % -> Factored % if R has PFECAT +--R factorPolynomial : SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if R has PFECAT +--R factorSquareFreePolynomial : SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if R has PFECAT +--R fmecg : (%,NonNegativeInteger,R,%) -> % +--R gcd : (%,%) -> % if R has GCDDOM +--R gcd : List % -> % if R has GCDDOM +--R gcdPolynomial : (SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial % if R has GCDDOM +--R halfExtendedResultant1 : (%,%) -> Record(resultant: R,coef1: %) if R has INTDOM +--R halfExtendedResultant2 : (%,%) -> Record(resultant: R,coef2: %) if R has INTDOM +--R halfExtendedSubResultantGcd1 : (%,%) -> Record(gcd: %,coef1: %) if R has INTDOM +--R halfExtendedSubResultantGcd2 : (%,%) -> Record(gcd: %,coef2: %) if R has INTDOM +--R integrate : % -> % if R has ALGEBRA FRAC INT +--R isExpt : % -> Union(Record(var: SingletonAsOrderedSet,exponent: NonNegativeInteger),"failed") +--R isPlus : % -> Union(List %,"failed") +--R isTimes : % -> Union(List %,"failed") +--R karatsubaDivide : (%,NonNegativeInteger) -> Record(quotient: %,remainder: %) +--R lastSubResultant : (%,%) -> % if R has INTDOM +--R lazyPseudoDivide : (%,%) -> Record(coef: R,gap: NonNegativeInteger,quotient: %,remainder: %) +--R lazyPseudoRemainder : (%,%) -> % +--R lazyResidueClass : (%,%) -> Record(polnum: %,polden: R,power: NonNegativeInteger) +--R lcm : (%,%) -> % if R has GCDDOM +--R lcm : List % -> % if R has GCDDOM +--R mainVariable : % -> Union(SingletonAsOrderedSet,"failed") +--R makeSUP : % -> SparseUnivariatePolynomial R +--R mapExponents : ((NonNegativeInteger -> NonNegativeInteger),%) -> % +--R max : (%,%) -> % if R has ORDSET +--R min : (%,%) -> % if R has ORDSET +--R minimumDegree : (%,List SingletonAsOrderedSet) -> List NonNegativeInteger +--R minimumDegree : (%,SingletonAsOrderedSet) -> NonNegativeInteger +--R minimumDegree : % -> NonNegativeInteger +--R monicDivide : (%,%) -> Record(quotient: %,remainder: %) +--R monicDivide : (%,%,SingletonAsOrderedSet) -> Record(quotient: %,remainder: %) +--R monomial : (%,List SingletonAsOrderedSet,List NonNegativeInteger) -> % +--R monomial : (%,SingletonAsOrderedSet,NonNegativeInteger) -> % +--R monomial : (R,NonNegativeInteger) -> % +--R multiEuclidean : (List %,%) -> Union(List %,"failed") if R has FIELD +--R multiplyExponents : (%,NonNegativeInteger) -> % +--R multivariate : (SparseUnivariatePolynomial %,SingletonAsOrderedSet) -> % +--R multivariate : (SparseUnivariatePolynomial R,SingletonAsOrderedSet) -> % +--R nextItem : % -> Union(%,"failed") if R has STEP +--R numberOfMonomials : % -> NonNegativeInteger +--R order : (%,%) -> NonNegativeInteger if R has INTDOM +--R patternMatch : (%,Pattern Integer,PatternMatchResult(Integer,%)) -> PatternMatchResult(Integer,%) if SingletonAsOrderedSet has PATMAB INT and R has PATMAB INT +--R patternMatch : (%,Pattern Float,PatternMatchResult(Float,%)) -> PatternMatchResult(Float,%) if SingletonAsOrderedSet has PATMAB FLOAT and R has PATMAB FLOAT +--R pomopo! : (%,R,NonNegativeInteger,%) -> % +--R prime? : % -> Boolean if R has PFECAT +--R primitivePart : (%,SingletonAsOrderedSet) -> % if R has GCDDOM +--R primitivePart : % -> % if R has GCDDOM +--R principalIdeal : List % -> Record(coef: List %,generator: %) if R has FIELD +--R pseudoDivide : (%,%) -> Record(coef: R,quotient: %,remainder: %) if R has INTDOM +--R pseudoQuotient : (%,%) -> % if R has INTDOM +--R ?quo? : (%,%) -> % if R has FIELD +--R reducedSystem : Matrix % -> Matrix R +--R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix R,vec: Vector R) +--R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix Integer,vec: Vector Integer) if R has LINEXP INT +--R reducedSystem : Matrix % -> Matrix Integer if R has LINEXP INT +--R ?rem? : (%,%) -> % if R has FIELD +--R resultant : (%,%) -> R if R has COMRING +--R resultant : (%,%,SingletonAsOrderedSet) -> % if R has COMRING +--R retract : % -> SparseUnivariatePolynomial R +--R retract : % -> SingletonAsOrderedSet +--R retract : % -> Integer if R has RETRACT INT +--R retract : % -> Fraction Integer if R has RETRACT FRAC INT +--R retractIfCan : % -> Union(SparseUnivariatePolynomial R,"failed") +--R retractIfCan : % -> Union(SingletonAsOrderedSet,"failed") +--R retractIfCan : % -> Union(Integer,"failed") if R has RETRACT INT +--R retractIfCan : % -> Union(Fraction Integer,"failed") if R has RETRACT FRAC INT +--R retractIfCan : % -> Union(R,"failed") +--R separate : (%,%) -> Record(primePart: %,commonPart: %) if R has GCDDOM +--R shiftLeft : (%,NonNegativeInteger) -> % +--R shiftRight : (%,NonNegativeInteger) -> % +--R sizeLess? : (%,%) -> Boolean if R has FIELD +--R solveLinearPolynomialEquation : (List SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> Union(List SparseUnivariatePolynomial %,"failed") if R has PFECAT +--R squareFree : % -> Factored % if R has GCDDOM +--R squareFreePart : % -> % if R has GCDDOM +--R squareFreePolynomial : SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if R has PFECAT +--R subResultantGcd : (%,%) -> % if R has INTDOM +--R subResultantsChain : (%,%) -> List % if R has INTDOM +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R totalDegree : (%,List SingletonAsOrderedSet) -> NonNegativeInteger +--R totalDegree : % -> NonNegativeInteger +--R unit? : % -> Boolean if R has INTDOM +--R unitCanonical : % -> % if R has INTDOM +--R unitNormal : % -> Record(unit: %,canonical: %,associate: %) if R has INTDOM +--R univariate : % -> SparseUnivariatePolynomial R +--R univariate : (%,SingletonAsOrderedSet) -> SparseUnivariatePolynomial % +--R unmakeSUP : SparseUnivariatePolynomial R -> % +--R variables : % -> List SingletonAsOrderedSet +--R vectorise : (%,NonNegativeInteger) -> Vector R +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +NewSparseUnivariatePolynomial examples +==================================================================== + +See Also: +o )show NewSparseUnivariatePolynomial + +@ + \pagehead{NewSparseUnivariatePolynomial}{NSUP} \pagepic{ps/v103newsparseunivariatepolynomial.ps}{NSUP}{1.00} {\bf See}\\ @@ -67560,6 +80238,7 @@ NewSparseUnivariatePolynomial(R): Exports == Implementation where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain NONE None} + <>= )set break resume )sys rm -f None.output @@ -67670,6 +80349,59 @@ None():SetCategory == add @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain NNI NonNegativeInteger} + +<>= +)set break resume +)sys rm -f NonNegativeInteger.output +)spool NonNegativeInteger.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show NonNegativeInteger +--R NonNegativeInteger is a domain constructor +--R Abbreviation for NonNegativeInteger is NNI +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for NNI +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (%,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,PositiveInteger) -> % ?+? : (%,%) -> % +--R ? Boolean ?<=? : (%,%) -> Boolean +--R ?=? : (%,%) -> Boolean ?>? : (%,%) -> Boolean +--R ?>=? : (%,%) -> Boolean 1 : () -> % +--R 0 : () -> % ?^? : (%,PositiveInteger) -> % +--R coerce : % -> OutputForm gcd : (%,%) -> % +--R hash : % -> SingleInteger latex : % -> String +--R max : (%,%) -> % min : (%,%) -> % +--R one? : % -> Boolean ?quo? : (%,%) -> % +--R random : % -> % recip : % -> Union(%,"failed") +--R ?rem? : (%,%) -> % sample : () -> % +--R shift : (%,Integer) -> % sup : (%,%) -> % +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean +--R ?*? : (NonNegativeInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % +--R ?^? : (%,NonNegativeInteger) -> % +--R divide : (%,%) -> Record(quotient: %,remainder: %) +--R exquo : (%,%) -> Union(%,"failed") +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +NonNegativeInteger examples +==================================================================== + +See Also: +o )show NonNegativeInteger + +@ + \pagehead{NonNegativeInteger}{NNI} \pagepic{ps/v103nonnegativeinteger.ps}{NNI}{1.00} {\bf See}\\ @@ -67763,6 +80495,7 @@ NonNegativeInteger: Join(OrderedAbelianMonoidSup,Monoid) with @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain NOTTING NottinghamGroup} + <>= )set break resume )sys rm -f NottinghamGroup.output @@ -67960,6 +80693,46 @@ NottinghamGroup(F:FiniteFieldCategory): Group with @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain NIPROB NumericalIntegrationProblem} + +<>= +)set break resume +)sys rm -f NumericalIntegrationProblem.output +)spool NumericalIntegrationProblem.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show NumericalIntegrationProblem +--R NumericalIntegrationProblem is a domain constructor +--R Abbreviation for NumericalIntegrationProblem is NIPROB +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for NIPROB +--R +--R------------------------------- Operations -------------------------------- +--R ?=? : (%,%) -> Boolean coerce : % -> OutputForm +--R hash : % -> SingleInteger latex : % -> String +--R ?~=? : (%,%) -> Boolean +--R coerce : Union(nia: Record(var: Symbol,fn: Expression DoubleFloat,range: Segment OrderedCompletion DoubleFloat,abserr: DoubleFloat,relerr: DoubleFloat),mdnia: Record(fn: Expression DoubleFloat,range: List Segment OrderedCompletion DoubleFloat,abserr: DoubleFloat,relerr: DoubleFloat)) -> % +--R coerce : Record(fn: Expression DoubleFloat,range: List Segment OrderedCompletion DoubleFloat,abserr: DoubleFloat,relerr: DoubleFloat) -> % +--R coerce : Record(var: Symbol,fn: Expression DoubleFloat,range: Segment OrderedCompletion DoubleFloat,abserr: DoubleFloat,relerr: DoubleFloat) -> % +--R retract : % -> Union(nia: Record(var: Symbol,fn: Expression DoubleFloat,range: Segment OrderedCompletion DoubleFloat,abserr: DoubleFloat,relerr: DoubleFloat),mdnia: Record(fn: Expression DoubleFloat,range: List Segment OrderedCompletion DoubleFloat,abserr: DoubleFloat,relerr: DoubleFloat)) +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +NumericalIntegrationProblem examples +==================================================================== + +See Also: +o )show NumericalIntegrationProblem + +@ + \pagehead{NumericalIntegrationProblem}{NIPROB} \pagepic{ps/v103numericalintegrationproblem.ps}{NIPROB}{1.00} @@ -68046,6 +80819,44 @@ NumericalIntegrationProblem(): EE == II where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain ODEPROB NumericalODEProblem} + +<>= +)set break resume +)sys rm -f NumericalODEProblem.output +)spool NumericalODEProblem.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show NumericalODEProblem +--R NumericalODEProblem is a domain constructor +--R Abbreviation for NumericalODEProblem is ODEPROB +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for ODEPROB +--R +--R------------------------------- Operations -------------------------------- +--R ?=? : (%,%) -> Boolean coerce : % -> OutputForm +--R hash : % -> SingleInteger latex : % -> String +--R ?~=? : (%,%) -> Boolean +--R coerce : Record(xinit: DoubleFloat,xend: DoubleFloat,fn: Vector Expression DoubleFloat,yinit: List DoubleFloat,intvals: List DoubleFloat,g: Expression DoubleFloat,abserr: DoubleFloat,relerr: DoubleFloat) -> % +--R retract : % -> Record(xinit: DoubleFloat,xend: DoubleFloat,fn: Vector Expression DoubleFloat,yinit: List DoubleFloat,intvals: List DoubleFloat,g: Expression DoubleFloat,abserr: DoubleFloat,relerr: DoubleFloat) +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +NumericalODEProblem examples +==================================================================== + +See Also: +o )show NumericalODEProblem + +@ + \pagehead{NumericalODEProblem}{ODEPROB} \pagepic{ps/v103numericalodeproblem.ps}{ODEPROB}{1.00} @@ -68116,6 +80927,46 @@ NumericalODEProblem(): EE == II where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain OPTPROB NumericalOptimizationProblem} + +<>= +)set break resume +)sys rm -f NumericalOptimizationProblem.output +)spool NumericalOptimizationProblem.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show NumericalOptimizationProblem +--R NumericalOptimizationProblem is a domain constructor +--R Abbreviation for NumericalOptimizationProblem is OPTPROB +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for OPTPROB +--R +--R------------------------------- Operations -------------------------------- +--R ?=? : (%,%) -> Boolean coerce : % -> OutputForm +--R hash : % -> SingleInteger latex : % -> String +--R ?~=? : (%,%) -> Boolean +--R coerce : Union(noa: Record(fn: Expression DoubleFloat,init: List DoubleFloat,lb: List OrderedCompletion DoubleFloat,cf: List Expression DoubleFloat,ub: List OrderedCompletion DoubleFloat),lsa: Record(lfn: List Expression DoubleFloat,init: List DoubleFloat)) -> % +--R coerce : Record(lfn: List Expression DoubleFloat,init: List DoubleFloat) -> % +--R coerce : Record(fn: Expression DoubleFloat,init: List DoubleFloat,lb: List OrderedCompletion DoubleFloat,cf: List Expression DoubleFloat,ub: List OrderedCompletion DoubleFloat) -> % +--R retract : % -> Union(noa: Record(fn: Expression DoubleFloat,init: List DoubleFloat,lb: List OrderedCompletion DoubleFloat,cf: List Expression DoubleFloat,ub: List OrderedCompletion DoubleFloat),lsa: Record(lfn: List Expression DoubleFloat,init: List DoubleFloat)) +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +NumericalOptimizationProblem examples +==================================================================== + +See Also: +o )show NumericalOptimizationProblem + +@ + \pagehead{NumericalOptimizationProblem}{OPTPROB} \pagepic{ps/v103numericaloptimizationproblem.ps}{OPTPROB}{1.00} @@ -68203,6 +81054,44 @@ NumericalOptimizationProblem(): EE == II where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain PDEPROB NumericalPDEProblem} + +<>= +)set break resume +)sys rm -f NumericalPDEProblem.output +)spool NumericalPDEProblem.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show NumericalPDEProblem +--R NumericalPDEProblem is a domain constructor +--R Abbreviation for NumericalPDEProblem is PDEPROB +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for PDEPROB +--R +--R------------------------------- Operations -------------------------------- +--R ?=? : (%,%) -> Boolean coerce : % -> OutputForm +--R hash : % -> SingleInteger latex : % -> String +--R ?~=? : (%,%) -> Boolean +--R coerce : Record(pde: List Expression DoubleFloat,constraints: List Record(start: DoubleFloat,finish: DoubleFloat,grid: NonNegativeInteger,boundaryType: Integer,dStart: Matrix DoubleFloat,dFinish: Matrix DoubleFloat),f: List List Expression DoubleFloat,st: String,tol: DoubleFloat) -> % +--R retract : % -> Record(pde: List Expression DoubleFloat,constraints: List Record(start: DoubleFloat,finish: DoubleFloat,grid: NonNegativeInteger,boundaryType: Integer,dStart: Matrix DoubleFloat,dFinish: Matrix DoubleFloat),f: List List Expression DoubleFloat,st: String,tol: DoubleFloat) +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +NumericalPDEProblem examples +==================================================================== + +See Also: +o )show NumericalPDEProblem + +@ + \pagehead{NumericalPDEProblem}{PDEPROB} \pagepic{ps/v103numericalpdeproblem.ps}{PDEPROB}{1.00} @@ -68700,6 +81589,44 @@ Octonion(R:CommutativeRing): export == impl where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain ODEIFTBL ODEIntensityFunctionsTable} + +<>= +)set break resume +)sys rm -f ODEIntensityFunctionsTable.output +)spool ODEIntensityFunctionsTable.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show ODEIntensityFunctionsTable +--R ODEIntensityFunctionsTable is a domain constructor +--R Abbreviation for ODEIntensityFunctionsTable is ODEIFTBL +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for ODEIFTBL +--R +--R------------------------------- Operations -------------------------------- +--R clearTheIFTable : () -> Void showTheIFTable : () -> % +--R iFTable : List Record(key: Record(xinit: DoubleFloat,xend: DoubleFloat,fn: Vector Expression DoubleFloat,yinit: List DoubleFloat,intvals: List DoubleFloat,g: Expression DoubleFloat,abserr: DoubleFloat,relerr: DoubleFloat),entry: Record(stiffness: Float,stability: Float,expense: Float,accuracy: Float,intermediateResults: Float)) -> % +--R insert! : Record(key: Record(xinit: DoubleFloat,xend: DoubleFloat,fn: Vector Expression DoubleFloat,yinit: List DoubleFloat,intvals: List DoubleFloat,g: Expression DoubleFloat,abserr: DoubleFloat,relerr: DoubleFloat),entry: Record(stiffness: Float,stability: Float,expense: Float,accuracy: Float,intermediateResults: Float)) -> % +--R keys : % -> List Record(xinit: DoubleFloat,xend: DoubleFloat,fn: Vector Expression DoubleFloat,yinit: List DoubleFloat,intvals: List DoubleFloat,g: Expression DoubleFloat,abserr: DoubleFloat,relerr: DoubleFloat) +--R showIntensityFunctions : Record(xinit: DoubleFloat,xend: DoubleFloat,fn: Vector Expression DoubleFloat,yinit: List DoubleFloat,intvals: List DoubleFloat,g: Expression DoubleFloat,abserr: DoubleFloat,relerr: DoubleFloat) -> Union(Record(stiffness: Float,stability: Float,expense: Float,accuracy: Float,intermediateResults: Float),"failed") +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +ODEIntensityFunctionsTable examples +==================================================================== + +See Also: +o )show ODEIntensityFunctionsTable + +@ + \pagehead{ODEIntensityFunctionsTable}{ODEIFTBL} \pagepic{ps/v103odeintensityfunctionstable.ps}{ODEIFTBL}{1.00} @@ -68799,6 +81726,7 @@ ODEIntensityFunctionsTable(): E == I where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain ARRAY1 OneDimensionalArray} + <>= )set break resume )sys rm -f OneDimensionalArray.output @@ -69068,6 +81996,82 @@ OneDimensionalArray(S:Type): Exports == Implementation where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain ONECOMP OnePointCompletion} + +<>= +)set break resume +)sys rm -f OnePointCompletion.output +)spool OnePointCompletion.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show OnePointCompletion +--R OnePointCompletion R: SetCategory is a domain constructor +--R Abbreviation for OnePointCompletion is ONECOMP +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for ONECOMP +--R +--R------------------------------- Operations -------------------------------- +--R -? : % -> % if R has ABELGRP ?=? : (%,%) -> Boolean +--R 1 : () -> % if R has ORDRING 0 : () -> % if R has ABELGRP +--R coerce : R -> % coerce : % -> OutputForm +--R finite? : % -> Boolean hash : % -> SingleInteger +--R infinite? : % -> Boolean infinity : () -> % +--R latex : % -> String retract : % -> R +--R ?~=? : (%,%) -> Boolean +--R ?*? : (PositiveInteger,%) -> % if R has ABELGRP +--R ?*? : (NonNegativeInteger,%) -> % if R has ABELGRP +--R ?*? : (Integer,%) -> % if R has ABELGRP +--R ?*? : (%,%) -> % if R has ORDRING +--R ?**? : (%,NonNegativeInteger) -> % if R has ORDRING +--R ?**? : (%,PositiveInteger) -> % if R has ORDRING +--R ?+? : (%,%) -> % if R has ABELGRP +--R ?-? : (%,%) -> % if R has ABELGRP +--R ? Boolean if R has ORDRING +--R ?<=? : (%,%) -> Boolean if R has ORDRING +--R ?>? : (%,%) -> Boolean if R has ORDRING +--R ?>=? : (%,%) -> Boolean if R has ORDRING +--R ?^? : (%,NonNegativeInteger) -> % if R has ORDRING +--R ?^? : (%,PositiveInteger) -> % if R has ORDRING +--R abs : % -> % if R has ORDRING +--R characteristic : () -> NonNegativeInteger if R has ORDRING +--R coerce : Integer -> % if R has ORDRING or R has RETRACT INT +--R coerce : Fraction Integer -> % if R has RETRACT FRAC INT +--R max : (%,%) -> % if R has ORDRING +--R min : (%,%) -> % if R has ORDRING +--R negative? : % -> Boolean if R has ORDRING +--R one? : % -> Boolean if R has ORDRING +--R positive? : % -> Boolean if R has ORDRING +--R rational : % -> Fraction Integer if R has INS +--R rational? : % -> Boolean if R has INS +--R rationalIfCan : % -> Union(Fraction Integer,"failed") if R has INS +--R recip : % -> Union(%,"failed") if R has ORDRING +--R retract : % -> Fraction Integer if R has RETRACT FRAC INT +--R retract : % -> Integer if R has RETRACT INT +--R retractIfCan : % -> Union(R,"failed") +--R retractIfCan : % -> Union(Fraction Integer,"failed") if R has RETRACT FRAC INT +--R retractIfCan : % -> Union(Integer,"failed") if R has RETRACT INT +--R sample : () -> % if R has ABELGRP +--R sign : % -> Integer if R has ORDRING +--R subtractIfCan : (%,%) -> Union(%,"failed") if R has ABELGRP +--R zero? : % -> Boolean if R has ABELGRP +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +OnePointCompletion examples +==================================================================== + +See Also: +o )show OnePointCompletion + +@ + \pagehead{OnePointCompletion}{ONECOMP} \pagepic{ps/v103onepointcompletion.ps}{ONECOMP}{1.00} {\bf See}\\ @@ -69228,6 +82232,44 @@ OnePointCompletion(R:SetCategory): Exports == Implementation where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain OMCONN OpenMathConnection} + +<>= +)set break resume +)sys rm -f OpenMathConnection.output +)spool OpenMathConnection.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show OpenMathConnection +--R OpenMathConnection is a domain constructor +--R Abbreviation for OpenMathConnection is OMCONN +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for OMCONN +--R +--R------------------------------- Operations -------------------------------- +--R OMcloseConn : % -> Void OMmakeConn : SingleInteger -> % +--R OMbindTCP : (%,SingleInteger) -> Boolean +--R OMconnInDevice : % -> OpenMathDevice +--R OMconnOutDevice : % -> OpenMathDevice +--R OMconnectTCP : (%,String,SingleInteger) -> Boolean +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +OpenMathConnection examples +==================================================================== + +See Also: +o )show OpenMathConnection + +@ + \pagehead{OpenMathConnection}{OMCONN} \pagepic{ps/v103openmathconnection.ps}{OMCONN}{1.00} {\bf See}\\ @@ -69289,6 +82331,65 @@ OpenMathConnection(): with @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain OMDEV OpenMathDevice} + +<>= +)set break resume +)sys rm -f OpenMathDevice.output +)spool OpenMathDevice.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show OpenMathDevice +--R OpenMathDevice is a domain constructor +--R Abbreviation for OpenMathDevice is OMDEV +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for OMDEV +--R +--R------------------------------- Operations -------------------------------- +--R OMclose : % -> Void OMgetApp : % -> Void +--R OMgetAtp : % -> Void OMgetAttr : % -> Void +--R OMgetBVar : % -> Void OMgetBind : % -> Void +--R OMgetEndApp : % -> Void OMgetEndAtp : % -> Void +--R OMgetEndAttr : % -> Void OMgetEndBVar : % -> Void +--R OMgetEndBind : % -> Void OMgetEndError : % -> Void +--R OMgetEndObject : % -> Void OMgetError : % -> Void +--R OMgetFloat : % -> DoubleFloat OMgetInteger : % -> Integer +--R OMgetObject : % -> Void OMgetString : % -> String +--R OMgetType : % -> Symbol OMgetVariable : % -> Symbol +--R OMputApp : % -> Void OMputAtp : % -> Void +--R OMputAttr : % -> Void OMputBVar : % -> Void +--R OMputBind : % -> Void OMputEndApp : % -> Void +--R OMputEndAtp : % -> Void OMputEndAttr : % -> Void +--R OMputEndBVar : % -> Void OMputEndBind : % -> Void +--R OMputEndError : % -> Void OMputEndObject : % -> Void +--R OMputError : % -> Void OMputObject : % -> Void +--R OMputString : (%,String) -> Void +--R OMgetSymbol : % -> Record(cd: String,name: String) +--R OMopenFile : (String,String,OpenMathEncoding) -> % +--R OMopenString : (String,OpenMathEncoding) -> % +--R OMputFloat : (%,DoubleFloat) -> Void +--R OMputInteger : (%,Integer) -> Void +--R OMputSymbol : (%,String,String) -> Void +--R OMputVariable : (%,Symbol) -> Void +--R OMsetEncoding : (%,OpenMathEncoding) -> Void +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +OpenMathDevice examples +==================================================================== + +See Also: +o )show OpenMathDevice + +@ + \pagehead{OpenMathDevice}{OMDEV} \pagepic{ps/v103openmathdevice.ps}{OMDEV}{1.00} {\bf See}\\ @@ -69516,6 +82617,44 @@ OpenMathDevice(): with @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain OMENC OpenMathEncoding} + +<>= +)set break resume +)sys rm -f OpenMathEncoding.output +)spool OpenMathEncoding.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show OpenMathEncoding +--R OpenMathEncoding is a domain constructor +--R Abbreviation for OpenMathEncoding is OMENC +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for OMENC +--R +--R------------------------------- Operations -------------------------------- +--R ?=? : (%,%) -> Boolean OMencodingBinary : () -> % +--R OMencodingSGML : () -> % OMencodingUnknown : () -> % +--R OMencodingXML : () -> % coerce : % -> OutputForm +--R hash : % -> SingleInteger latex : % -> String +--R ?~=? : (%,%) -> Boolean +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +OpenMathEncoding examples +==================================================================== + +See Also: +o )show OpenMathEncoding + +@ + \pagehead{OpenMathEncoding}{OMENC} \pagepic{ps/v103openmathencoding.ps}{OMENC}{1.00} {\bf See}\\ @@ -69590,6 +82729,44 @@ OpenMathEncoding(): SetCategory with @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain OMERR OpenMathError} + +<>= +)set break resume +)sys rm -f OpenMathError.output +)spool OpenMathError.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show OpenMathError +--R OpenMathError is a domain constructor +--R Abbreviation for OpenMathError is OMERR +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for OMERR +--R +--R------------------------------- Operations -------------------------------- +--R ?=? : (%,%) -> Boolean coerce : % -> OutputForm +--R errorInfo : % -> List Symbol hash : % -> SingleInteger +--R latex : % -> String ?~=? : (%,%) -> Boolean +--R errorKind : % -> OpenMathErrorKind +--R omError : (OpenMathErrorKind,List Symbol) -> % +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +OpenMathError examples +==================================================================== + +See Also: +o )show OpenMathError + +@ + \pagehead{OpenMathError}{OMERR} \pagepic{ps/v103openmatherror.ps}{OMERR}{1.00} {\bf See}\\ @@ -69662,6 +82839,44 @@ OpenMathError() : SetCategory with @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain OMERRK OpenMathErrorKind} + +<>= +)set break resume +)sys rm -f OpenMathErrorKind.output +)spool OpenMathErrorKind.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show OpenMathErrorKind +--R OpenMathErrorKind is a domain constructor +--R Abbreviation for OpenMathErrorKind is OMERRK +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for OMERRK +--R +--R------------------------------- Operations -------------------------------- +--R ?=? : (%,%) -> Boolean OMParseError? : % -> Boolean +--R OMReadError? : % -> Boolean OMUnknownCD? : % -> Boolean +--R OMUnknownSymbol? : % -> Boolean coerce : Symbol -> % +--R coerce : % -> OutputForm hash : % -> SingleInteger +--R latex : % -> String ?~=? : (%,%) -> Boolean +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +OpenMathErrorKind examples +==================================================================== + +See Also: +o )show OpenMathErrorKind + +@ + \pagehead{OpenMathErrorKind}{OMERRK} \pagepic{ps/v103openmatherrorkind.ps}{OMERRK}{1.00} {\bf See}\\ @@ -69739,6 +82954,7 @@ OpenMathErrorKind() : SetCategory with @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain OP Operator} + <>= )set break resume )sys rm -f Operator.output @@ -70182,6 +83398,65 @@ Operator(R: Ring) == ModuleOperator(R,R) @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain OMLO OppositeMonogenicLinearOperator} + +<>= +)set break resume +)sys rm -f OppositeMonogenicLinearOperator.output +)spool OppositeMonogenicLinearOperator.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show OppositeMonogenicLinearOperator +--R OppositeMonogenicLinearOperator(P: MonogenicLinearOperator R,R: Ring) is a domain constructor +--R Abbreviation for OppositeMonogenicLinearOperator is OMLO +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for OMLO +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (R,%) -> % ?*? : (%,R) -> % +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ?=? : (%,%) -> Boolean +--R D : % -> % if P has DIFRING 1 : () -> % +--R 0 : () -> % ?^? : (%,PositiveInteger) -> % +--R coerce : Integer -> % coerce : % -> OutputForm +--R degree : % -> NonNegativeInteger hash : % -> SingleInteger +--R latex : % -> String leadingCoefficient : % -> R +--R one? : % -> Boolean op : P -> % +--R po : % -> P recip : % -> Union(%,"failed") +--R reductum : % -> % sample : () -> % +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean +--R ?*? : (NonNegativeInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % +--R D : (%,NonNegativeInteger) -> % if P has DIFRING +--R ?^? : (%,NonNegativeInteger) -> % +--R characteristic : () -> NonNegativeInteger +--R coefficient : (%,NonNegativeInteger) -> R +--R coerce : R -> % if R has COMRING +--R differentiate : % -> % if P has DIFRING +--R differentiate : (%,NonNegativeInteger) -> % if P has DIFRING +--R minimumDegree : % -> NonNegativeInteger +--R monomial : (R,NonNegativeInteger) -> % +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +OppositeMonogenicLinearOperator examples +==================================================================== + +See Also: +o )show OppositeMonogenicLinearOperator + +@ + \pagehead{OppositeMonogenicLinearOperator}{OMLO} \pagepic{ps/v103oppositemonogeniclinearoperator.ps}{OMLO}{1.00} {\bf See}\\ @@ -70267,6 +83542,83 @@ OppositeMonogenicLinearOperator(P, R): OPRcat == OPRdef where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain ORDCOMP OrderedCompletion} + +<>= +)set break resume +)sys rm -f OrderedCompletion.output +)spool OrderedCompletion.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show OrderedCompletion +--R OrderedCompletion R: SetCategory is a domain constructor +--R Abbreviation for OrderedCompletion is ORDCOMP +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for ORDCOMP +--R +--R------------------------------- Operations -------------------------------- +--R -? : % -> % if R has ABELGRP ?=? : (%,%) -> Boolean +--R 1 : () -> % if R has ORDRING 0 : () -> % if R has ABELGRP +--R coerce : R -> % coerce : % -> OutputForm +--R finite? : % -> Boolean hash : % -> SingleInteger +--R infinite? : % -> Boolean latex : % -> String +--R minusInfinity : () -> % plusInfinity : () -> % +--R retract : % -> R whatInfinity : % -> SingleInteger +--R ?~=? : (%,%) -> Boolean +--R ?*? : (PositiveInteger,%) -> % if R has ABELGRP +--R ?*? : (NonNegativeInteger,%) -> % if R has ABELGRP +--R ?*? : (Integer,%) -> % if R has ABELGRP +--R ?*? : (%,%) -> % if R has ORDRING +--R ?**? : (%,NonNegativeInteger) -> % if R has ORDRING +--R ?**? : (%,PositiveInteger) -> % if R has ORDRING +--R ?+? : (%,%) -> % if R has ABELGRP +--R ?-? : (%,%) -> % if R has ABELGRP +--R ? Boolean if R has ORDRING +--R ?<=? : (%,%) -> Boolean if R has ORDRING +--R ?>? : (%,%) -> Boolean if R has ORDRING +--R ?>=? : (%,%) -> Boolean if R has ORDRING +--R ?^? : (%,NonNegativeInteger) -> % if R has ORDRING +--R ?^? : (%,PositiveInteger) -> % if R has ORDRING +--R abs : % -> % if R has ORDRING +--R characteristic : () -> NonNegativeInteger if R has ORDRING +--R coerce : Integer -> % if R has ORDRING or R has RETRACT INT +--R coerce : Fraction Integer -> % if R has RETRACT FRAC INT +--R max : (%,%) -> % if R has ORDRING +--R min : (%,%) -> % if R has ORDRING +--R negative? : % -> Boolean if R has ORDRING +--R one? : % -> Boolean if R has ORDRING +--R positive? : % -> Boolean if R has ORDRING +--R rational : % -> Fraction Integer if R has INS +--R rational? : % -> Boolean if R has INS +--R rationalIfCan : % -> Union(Fraction Integer,"failed") if R has INS +--R recip : % -> Union(%,"failed") if R has ORDRING +--R retract : % -> Fraction Integer if R has RETRACT FRAC INT +--R retract : % -> Integer if R has RETRACT INT +--R retractIfCan : % -> Union(R,"failed") +--R retractIfCan : % -> Union(Fraction Integer,"failed") if R has RETRACT FRAC INT +--R retractIfCan : % -> Union(Integer,"failed") if R has RETRACT INT +--R sample : () -> % if R has ABELGRP +--R sign : % -> Integer if R has ORDRING +--R subtractIfCan : (%,%) -> Union(%,"failed") if R has ABELGRP +--R zero? : % -> Boolean if R has ABELGRP +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +OrderedCompletion examples +==================================================================== + +See Also: +o )show OrderedCompletion + +@ + \pagehead{OrderedCompletion}{ORDCOMP} \pagepic{ps/v103orderedcompletion.ps}{ORDCOMP}{1.00} {\bf See}\\ @@ -70454,6 +83806,142 @@ OrderedCompletion(R:SetCategory): Exports == Implementation where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain ODP OrderedDirectProduct} + +<>= +)set break resume +)sys rm -f OrderedDirectProduct.output +)spool OrderedDirectProduct.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show OrderedDirectProduct +--R OrderedDirectProduct(dim: NonNegativeInteger,S: OrderedAbelianMonoidSup,f: ((Vector S,Vector S) -> Boolean)) is a domain constructor +--R Abbreviation for OrderedDirectProduct is ODP +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for ODP +--R +--R------------------------------- Operations -------------------------------- +--R -? : % -> % if S has RING 1 : () -> % if S has MONOID +--R 0 : () -> % if S has CABMON coerce : % -> Vector S +--R copy : % -> % directProduct : Vector S -> % +--R ?.? : (%,Integer) -> S elt : (%,Integer,S) -> S +--R empty : () -> % empty? : % -> Boolean +--R entries : % -> List S eq? : (%,%) -> Boolean +--R index? : (Integer,%) -> Boolean indices : % -> List Integer +--R map : ((S -> S),%) -> % qelt : (%,Integer) -> S +--R sample : () -> % +--R #? : % -> NonNegativeInteger if $ has finiteAggregate +--R ?*? : (PositiveInteger,%) -> % if S has ABELSG +--R ?*? : (NonNegativeInteger,%) -> % if S has CABMON +--R ?*? : (S,%) -> % if S has RING +--R ?*? : (%,S) -> % if S has RING +--R ?*? : (%,%) -> % if S has MONOID +--R ?*? : (Integer,%) -> % if S has RING +--R ?**? : (%,PositiveInteger) -> % if S has MONOID +--R ?**? : (%,NonNegativeInteger) -> % if S has MONOID +--R ?+? : (%,%) -> % if S has ABELSG +--R ?-? : (%,%) -> % if S has RING +--R ?/? : (%,S) -> % if S has FIELD +--R ? Boolean if S has OAMONS or S has ORDRING +--R ?<=? : (%,%) -> Boolean if S has OAMONS or S has ORDRING +--R ?=? : (%,%) -> Boolean if S has SETCAT +--R ?>? : (%,%) -> Boolean if S has OAMONS or S has ORDRING +--R ?>=? : (%,%) -> Boolean if S has OAMONS or S has ORDRING +--R D : (%,(S -> S)) -> % if S has RING +--R D : (%,(S -> S),NonNegativeInteger) -> % if S has RING +--R D : (%,List Symbol,List NonNegativeInteger) -> % if S has PDRING SYMBOL and S has RING +--R D : (%,Symbol,NonNegativeInteger) -> % if S has PDRING SYMBOL and S has RING +--R D : (%,List Symbol) -> % if S has PDRING SYMBOL and S has RING +--R D : (%,Symbol) -> % if S has PDRING SYMBOL and S has RING +--R D : (%,NonNegativeInteger) -> % if S has DIFRING and S has RING +--R D : % -> % if S has DIFRING and S has RING +--R ?^? : (%,PositiveInteger) -> % if S has MONOID +--R ?^? : (%,NonNegativeInteger) -> % if S has MONOID +--R abs : % -> % if S has ORDRING +--R any? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate +--R characteristic : () -> NonNegativeInteger if S has RING +--R coerce : S -> % if S has SETCAT +--R coerce : Fraction Integer -> % if S has RETRACT FRAC INT and S has SETCAT +--R coerce : Integer -> % if S has RETRACT INT and S has SETCAT or S has RING +--R coerce : % -> OutputForm if S has SETCAT +--R count : (S,%) -> NonNegativeInteger if $ has finiteAggregate and S has SETCAT +--R count : ((S -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate +--R differentiate : (%,(S -> S)) -> % if S has RING +--R differentiate : (%,(S -> S),NonNegativeInteger) -> % if S has RING +--R differentiate : (%,List Symbol,List NonNegativeInteger) -> % if S has PDRING SYMBOL and S has RING +--R differentiate : (%,Symbol,NonNegativeInteger) -> % if S has PDRING SYMBOL and S has RING +--R differentiate : (%,List Symbol) -> % if S has PDRING SYMBOL and S has RING +--R differentiate : (%,Symbol) -> % if S has PDRING SYMBOL and S has RING +--R differentiate : (%,NonNegativeInteger) -> % if S has DIFRING and S has RING +--R differentiate : % -> % if S has DIFRING and S has RING +--R dimension : () -> CardinalNumber if S has FIELD +--R dot : (%,%) -> S if S has RING +--R entry? : (S,%) -> Boolean if $ has finiteAggregate and S has SETCAT +--R eval : (%,List S,List S) -> % if S has EVALAB S and S has SETCAT +--R eval : (%,S,S) -> % if S has EVALAB S and S has SETCAT +--R eval : (%,Equation S) -> % if S has EVALAB S and S has SETCAT +--R eval : (%,List Equation S) -> % if S has EVALAB S and S has SETCAT +--R every? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate +--R fill! : (%,S) -> % if $ has shallowlyMutable +--R first : % -> S if Integer has ORDSET +--R hash : % -> SingleInteger if S has SETCAT +--R index : PositiveInteger -> % if S has FINITE +--R latex : % -> String if S has SETCAT +--R less? : (%,NonNegativeInteger) -> Boolean +--R lookup : % -> PositiveInteger if S has FINITE +--R map! : ((S -> S),%) -> % if $ has shallowlyMutable +--R max : (%,%) -> % if S has OAMONS or S has ORDRING +--R maxIndex : % -> Integer if Integer has ORDSET +--R member? : (S,%) -> Boolean if $ has finiteAggregate and S has SETCAT +--R members : % -> List S if $ has finiteAggregate +--R min : (%,%) -> % if S has OAMONS or S has ORDRING +--R minIndex : % -> Integer if Integer has ORDSET +--R more? : (%,NonNegativeInteger) -> Boolean +--R negative? : % -> Boolean if S has ORDRING +--R one? : % -> Boolean if S has MONOID +--R parts : % -> List S if $ has finiteAggregate +--R positive? : % -> Boolean if S has ORDRING +--R qsetelt! : (%,Integer,S) -> S if $ has shallowlyMutable +--R random : () -> % if S has FINITE +--R recip : % -> Union(%,"failed") if S has MONOID +--R reducedSystem : Matrix % -> Matrix S if S has RING +--R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix S,vec: Vector S) if S has RING +--R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix Integer,vec: Vector Integer) if S has LINEXP INT and S has RING +--R reducedSystem : Matrix % -> Matrix Integer if S has LINEXP INT and S has RING +--R retract : % -> S if S has SETCAT +--R retract : % -> Fraction Integer if S has RETRACT FRAC INT and S has SETCAT +--R retract : % -> Integer if S has RETRACT INT and S has SETCAT +--R retractIfCan : % -> Union(S,"failed") if S has SETCAT +--R retractIfCan : % -> Union(Fraction Integer,"failed") if S has RETRACT FRAC INT and S has SETCAT +--R retractIfCan : % -> Union(Integer,"failed") if S has RETRACT INT and S has SETCAT +--R setelt : (%,Integer,S) -> S if $ has shallowlyMutable +--R sign : % -> Integer if S has ORDRING +--R size : () -> NonNegativeInteger if S has FINITE +--R size? : (%,NonNegativeInteger) -> Boolean +--R subtractIfCan : (%,%) -> Union(%,"failed") if S has CABMON +--R sup : (%,%) -> % if S has OAMONS +--R swap! : (%,Integer,Integer) -> Void if $ has shallowlyMutable +--R unitVector : PositiveInteger -> % if S has RING +--R zero? : % -> Boolean if S has CABMON +--R ?~=? : (%,%) -> Boolean if S has SETCAT +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +OrderedDirectProduct examples +==================================================================== + +See Also: +o )show OrderedDirectProduct + +@ + \pagehead{OrderedDirectProduct}{ODP} \pagepic{ps/v103ordereddirectproduct.ps}{ODP}{1.00} {\bf See}\\ @@ -70579,6 +84067,7 @@ OrderedDirectProduct(dim:NonNegativeInteger, @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain OFMONOID OrderedFreeMonoid} + <>= )set break resume )sys rm -f OrderedFreeMonoid.output @@ -71388,6 +84877,7 @@ OrderedFreeMonoid(S: OrderedSet): OFMcategory == OFMdefinition where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain OVAR OrderedVariableList} + <>= )set break resume )sys rm -f OrderedVariableList.output @@ -71547,11 +85037,7 @@ OrderedVariableList(VariableList:List Symbol): @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain ODPOL OrderlyDifferentialPolynomial} -{\bf See}\\ -\pageto{OrderlyDifferentialVariable}{ODVAR} -\pageto{SequentialDifferentialVariable}{SDVAR} -\pageto{DifferentialSparseMultivariatePolynomial}{DSMP} -\pageto{SequentialDifferentialPolynomial}{SDPOL} + <>= )set break resume )sys rm -f OrderlyDifferentialPolynomial.output @@ -72204,9 +85690,16 @@ See Also: o )show OrderlyDifferentialPolynomial @ + \pagehead{OrderlyDifferentialPolynomial}{ODPOL} \pagepic{ps/v103orderlydifferentialpolynomial.ps}{ODPOL}{1.00} +{\bf See}\\ +\pageto{OrderlyDifferentialVariable}{ODVAR} +\pageto{SequentialDifferentialVariable}{SDVAR} +\pageto{DifferentialSparseMultivariatePolynomial}{DSMP} +\pageto{SequentialDifferentialPolynomial}{SDPOL} + {\bf Exports:}\\ \begin{tabular}{lll} \cross{ODPOL}{0} & @@ -72344,6 +85837,51 @@ OrderlyDifferentialPolynomial(R): @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain ODVAR OrderlyDifferentialVariable} + +<>= +)set break resume +)sys rm -f OrderlyDifferentialVariable.output +)spool OrderlyDifferentialVariable.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show OrderlyDifferentialVariable +--R OrderlyDifferentialVariable S: OrderedSet is a domain constructor +--R Abbreviation for OrderlyDifferentialVariable is ODVAR +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for ODVAR +--R +--R------------------------------- Operations -------------------------------- +--R ? Boolean ?<=? : (%,%) -> Boolean +--R ?=? : (%,%) -> Boolean ?>? : (%,%) -> Boolean +--R ?>=? : (%,%) -> Boolean coerce : S -> % +--R coerce : % -> OutputForm differentiate : % -> % +--R hash : % -> SingleInteger latex : % -> String +--R max : (%,%) -> % min : (%,%) -> % +--R order : % -> NonNegativeInteger retract : % -> S +--R variable : % -> S weight : % -> NonNegativeInteger +--R ?~=? : (%,%) -> Boolean +--R differentiate : (%,NonNegativeInteger) -> % +--R makeVariable : (S,NonNegativeInteger) -> % +--R retractIfCan : % -> Union(S,"failed") +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +OrderlyDifferentialVariable examples +==================================================================== + +See Also: +o )show OrderlyDifferentialVariable + +@ + \pagehead{OrderlyDifferentialVariable}{ODVAR} \pagepic{ps/v103orderlydifferentialvariable.ps}{ODVAR}{1.00} {\bf See}\\ @@ -72417,6 +85955,90 @@ OrderlyDifferentialVariable(S:OrderedSet):DifferentialVariableCategory(S) @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain ODR OrdinaryDifferentialRing} + +<>= +)set break resume +)sys rm -f OrdinaryDifferentialRing.output +)spool OrdinaryDifferentialRing.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show OrdinaryDifferentialRing +--R OrdinaryDifferentialRing(Kernels: SetCategory,R: PartialDifferentialRing Kernels,var: Kernels) is a domain constructor +--R Abbreviation for OrdinaryDifferentialRing is ODR +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for ODR +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (%,%) -> % ?*? : (%,%) -> % +--R ?*? : (Integer,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,PositiveInteger) -> % ?+? : (%,%) -> % +--R ?-? : (%,%) -> % -? : % -> % +--R ?=? : (%,%) -> Boolean D : % -> % +--R D : (%,NonNegativeInteger) -> % 1 : () -> % +--R 0 : () -> % ?^? : (%,PositiveInteger) -> % +--R coerce : % -> R coerce : R -> % +--R coerce : Integer -> % coerce : % -> OutputForm +--R differentiate : % -> % hash : % -> SingleInteger +--R inv : % -> % if R has FIELD latex : % -> String +--R one? : % -> Boolean recip : % -> Union(%,"failed") +--R sample : () -> % zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean +--R ?*? : (%,Fraction Integer) -> % if R has FIELD +--R ?*? : (Fraction Integer,%) -> % if R has FIELD +--R ?*? : (NonNegativeInteger,%) -> % +--R ?**? : (%,Integer) -> % if R has FIELD +--R ?**? : (%,NonNegativeInteger) -> % +--R ?/? : (%,%) -> % if R has FIELD +--R ?^? : (%,Integer) -> % if R has FIELD +--R ?^? : (%,NonNegativeInteger) -> % +--R associates? : (%,%) -> Boolean if R has FIELD +--R characteristic : () -> NonNegativeInteger +--R coerce : % -> % if R has FIELD +--R coerce : Fraction Integer -> % if R has FIELD +--R differentiate : (%,NonNegativeInteger) -> % +--R divide : (%,%) -> Record(quotient: %,remainder: %) if R has FIELD +--R euclideanSize : % -> NonNegativeInteger if R has FIELD +--R expressIdealMember : (List %,%) -> Union(List %,"failed") if R has FIELD +--R exquo : (%,%) -> Union(%,"failed") if R has FIELD +--R extendedEuclidean : (%,%) -> Record(coef1: %,coef2: %,generator: %) if R has FIELD +--R extendedEuclidean : (%,%,%) -> Union(Record(coef1: %,coef2: %),"failed") if R has FIELD +--R factor : % -> Factored % if R has FIELD +--R gcd : (%,%) -> % if R has FIELD +--R gcd : List % -> % if R has FIELD +--R gcdPolynomial : (SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial % if R has FIELD +--R lcm : (%,%) -> % if R has FIELD +--R lcm : List % -> % if R has FIELD +--R multiEuclidean : (List %,%) -> Union(List %,"failed") if R has FIELD +--R prime? : % -> Boolean if R has FIELD +--R principalIdeal : List % -> Record(coef: List %,generator: %) if R has FIELD +--R ?quo? : (%,%) -> % if R has FIELD +--R ?rem? : (%,%) -> % if R has FIELD +--R sizeLess? : (%,%) -> Boolean if R has FIELD +--R squareFree : % -> Factored % if R has FIELD +--R squareFreePart : % -> % if R has FIELD +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R unit? : % -> Boolean if R has FIELD +--R unitCanonical : % -> % if R has FIELD +--R unitNormal : % -> Record(unit: %,canonical: %,associate: %) if R has FIELD +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +OrdinaryDifferentialRing examples +==================================================================== + +See Also: +o )show OrdinaryDifferentialRing + +@ + \pagehead{OrdinaryDifferentialRing}{ODR} \pagepic{ps/v103ordinarydifferentialring.ps}{ODR}{1.00} {\bf See}\\ @@ -72519,6 +86141,60 @@ OrdinaryDifferentialRing(Kernels,R,var): DRcategory == DRcapsule where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain OWP OrdinaryWeightedPolynomials} + +<>= +)set break resume +)sys rm -f OrdinaryWeightedPolynomials.output +)spool OrdinaryWeightedPolynomials.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show OrdinaryWeightedPolynomials +--R OrdinaryWeightedPolynomials(R: Ring,vl: List Symbol,wl: List NonNegativeInteger,wtlevel: NonNegativeInteger) is a domain constructor +--R Abbreviation for OrdinaryWeightedPolynomials is OWP +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for OWP +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ?=? : (%,%) -> Boolean +--R 1 : () -> % 0 : () -> % +--R ?^? : (%,PositiveInteger) -> % coerce : Polynomial R -> % +--R coerce : % -> Polynomial R coerce : Integer -> % +--R coerce : % -> OutputForm hash : % -> SingleInteger +--R latex : % -> String one? : % -> Boolean +--R recip : % -> Union(%,"failed") sample : () -> % +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean +--R ?*? : (%,R) -> % if R has COMRING +--R ?*? : (R,%) -> % if R has COMRING +--R ?*? : (NonNegativeInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % +--R ?/? : (%,%) -> Union(%,"failed") if R has FIELD +--R ?^? : (%,NonNegativeInteger) -> % +--R changeWeightLevel : NonNegativeInteger -> Void +--R characteristic : () -> NonNegativeInteger +--R coerce : R -> % if R has COMRING +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +OrdinaryWeightedPolynomials examples +==================================================================== + +See Also: +o )show OrdinaryWeightedPolynomials + +@ + \pagehead{OrdinaryWeightedPolynomials}{OWP} \pagepic{ps/v103ordinaryweightedpolynomials.ps}{OWP}{1.00} @@ -72595,6 +86271,46 @@ OrdinaryWeightedPolynomials(R:Ring, @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain OSI OrdSetInts} + +<>= +)set break resume +)sys rm -f OrdSetInts.output +)spool OrdSetInts.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show OrdSetInts +--R OrdSetInts is a domain constructor +--R Abbreviation for OrdSetInts is OSI +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for OSI +--R +--R------------------------------- Operations -------------------------------- +--R ? Boolean ?<=? : (%,%) -> Boolean +--R ?=? : (%,%) -> Boolean ?>? : (%,%) -> Boolean +--R ?>=? : (%,%) -> Boolean coerce : Integer -> % +--R coerce : % -> OutputForm hash : % -> SingleInteger +--R latex : % -> String max : (%,%) -> % +--R min : (%,%) -> % value : % -> Integer +--R ?~=? : (%,%) -> Boolean +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +OrdSetInts examples +==================================================================== + +See Also: +o )show OrdSetInts + +@ + \pagehead{OrdSetInts}{OSI} \pagepic{ps/v103ordsetints.ps}{OSI}{1.00} {\bf See}\\ @@ -72661,6 +86377,93 @@ OrdSetInts: Export == Implement where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain OUTFORM OutputForm} + +<>= +)set break resume +)sys rm -f OutputForm.output +)spool OutputForm.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show OutputForm +--R OutputForm is a domain constructor +--R Abbreviation for OutputForm is OUTFORM +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for OUTFORM +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (%,%) -> % ?**? : (%,%) -> % +--R ?+? : (%,%) -> % -? : % -> % +--R ?-? : (%,%) -> % ?/? : (%,%) -> % +--R ? % ?<=? : (%,%) -> % +--R ?=? : (%,%) -> % ?=? : (%,%) -> Boolean +--R ?>? : (%,%) -> % ?>=? : (%,%) -> % +--R ?SEGMENT : % -> % ?..? : (%,%) -> % +--R ?^=? : (%,%) -> % ?and? : (%,%) -> % +--R assign : (%,%) -> % binomial : (%,%) -> % +--R blankSeparate : List % -> % box : % -> % +--R brace : List % -> % brace : % -> % +--R bracket : List % -> % bracket : % -> % +--R center : % -> % center : (%,Integer) -> % +--R coerce : % -> OutputForm commaSeparate : List % -> % +--R ?div? : (%,%) -> % dot : % -> % +--R ?.? : (%,List %) -> % empty : () -> % +--R exquo : (%,%) -> % hash : % -> SingleInteger +--R hconcat : List % -> % hconcat : (%,%) -> % +--R height : () -> Integer height : % -> Integer +--R hspace : Integer -> % infix : (%,%,%) -> % +--R infix : (%,List %) -> % infix? : % -> Boolean +--R int : (%,%,%) -> % int : (%,%) -> % +--R int : % -> % label : (%,%) -> % +--R latex : % -> String left : % -> % +--R left : (%,Integer) -> % matrix : List List % -> % +--R message : String -> % messagePrint : String -> Void +--R not? : % -> % ?or? : (%,%) -> % +--R outputForm : DoubleFloat -> % outputForm : String -> % +--R outputForm : Symbol -> % outputForm : Integer -> % +--R over : (%,%) -> % overbar : % -> % +--R overlabel : (%,%) -> % paren : List % -> % +--R paren : % -> % pile : List % -> % +--R postfix : (%,%) -> % prefix : (%,List %) -> % +--R presub : (%,%) -> % presuper : (%,%) -> % +--R prime : % -> % print : % -> Void +--R prod : (%,%,%) -> % prod : (%,%) -> % +--R prod : % -> % ?quo? : (%,%) -> % +--R quote : % -> % rarrow : (%,%) -> % +--R ?rem? : (%,%) -> % right : % -> % +--R right : (%,Integer) -> % root : (%,%) -> % +--R root : % -> % rspace : (Integer,Integer) -> % +--R scripts : (%,List %) -> % semicolonSeparate : List % -> % +--R slash : (%,%) -> % string : % -> % +--R sub : (%,%) -> % subHeight : % -> Integer +--R sum : (%,%,%) -> % sum : (%,%) -> % +--R sum : % -> % super : (%,%) -> % +--R superHeight : % -> Integer supersub : (%,List %) -> % +--R vconcat : List % -> % vconcat : (%,%) -> % +--R vspace : Integer -> % width : () -> Integer +--R width : % -> Integer zag : (%,%) -> % +--R ?~=? : (%,%) -> Boolean +--R differentiate : (%,NonNegativeInteger) -> % +--R dot : (%,NonNegativeInteger) -> % +--R prime : (%,NonNegativeInteger) -> % +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +OutputForm examples +==================================================================== + +See Also: +o )show OutputForm + +@ + \pagehead{OutputForm}{OUTFORM} \pagepic{ps/v103outputform.ps}{OUTFORM}{1.00} @@ -73213,6 +87016,76 @@ OutputForm(): SetCategory with %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain PADIC PAdicInteger} + +<>= +)set break resume +)sys rm -f PAdicInteger.output +)spool PAdicInteger.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show PAdicInteger +--R PAdicInteger p: Integer is a domain constructor +--R Abbreviation for PAdicInteger is PADIC +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for PADIC +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ?=? : (%,%) -> Boolean +--R 1 : () -> % 0 : () -> % +--R ?^? : (%,PositiveInteger) -> % associates? : (%,%) -> Boolean +--R coerce : % -> % coerce : Integer -> % +--R coerce : % -> OutputForm complete : % -> % +--R digits : % -> Stream Integer extend : (%,Integer) -> % +--R gcd : List % -> % gcd : (%,%) -> % +--R hash : % -> SingleInteger latex : % -> String +--R lcm : List % -> % lcm : (%,%) -> % +--R moduloP : % -> Integer modulus : () -> Integer +--R one? : % -> Boolean order : % -> NonNegativeInteger +--R ?quo? : (%,%) -> % quotientByP : % -> % +--R recip : % -> Union(%,"failed") ?rem? : (%,%) -> % +--R sample : () -> % sizeLess? : (%,%) -> Boolean +--R sqrt : (%,Integer) -> % unit? : % -> Boolean +--R unitCanonical : % -> % zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean +--R ?*? : (NonNegativeInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % +--R ?^? : (%,NonNegativeInteger) -> % +--R approximate : (%,Integer) -> Integer +--R characteristic : () -> NonNegativeInteger +--R divide : (%,%) -> Record(quotient: %,remainder: %) +--R euclideanSize : % -> NonNegativeInteger +--R expressIdealMember : (List %,%) -> Union(List %,"failed") +--R exquo : (%,%) -> Union(%,"failed") +--R extendedEuclidean : (%,%,%) -> Union(Record(coef1: %,coef2: %),"failed") +--R extendedEuclidean : (%,%) -> Record(coef1: %,coef2: %,generator: %) +--R gcdPolynomial : (SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial % +--R multiEuclidean : (List %,%) -> Union(List %,"failed") +--R principalIdeal : List % -> Record(coef: List %,generator: %) +--R root : (SparseUnivariatePolynomial Integer,Integer) -> % +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R unitNormal : % -> Record(unit: %,canonical: %,associate: %) +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +PAdicInteger examples +==================================================================== + +See Also: +o )show PAdicInteger + +@ + \pagehead{PAdicInteger}{PADIC} \pagepic{ps/v103padicinteger.ps}{PADIC}{1.00} {\bf See}\\ @@ -73301,6 +87174,149 @@ PAdicInteger(p:Integer) == InnerPAdicInteger(p,true$Boolean) @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain PADICRAT PAdicRational} + +<>= +)set break resume +)sys rm -f PAdicRational.output +)spool PAdicRational.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show PAdicRational +--R PAdicRational p: Integer is a domain constructor +--R Abbreviation for PAdicRational is PADICRAT +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for PADICRAT +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (%,PAdicInteger p) -> % ?*? : (PAdicInteger p,%) -> % +--R ?*? : (Fraction Integer,%) -> % ?*? : (%,Fraction Integer) -> % +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?**? : (%,Integer) -> % +--R ?**? : (%,PositiveInteger) -> % ?+? : (%,%) -> % +--R ?-? : (%,%) -> % -? : % -> % +--R ?/? : (%,%) -> % ?=? : (%,%) -> Boolean +--R 1 : () -> % 0 : () -> % +--R ?^? : (%,Integer) -> % ?^? : (%,PositiveInteger) -> % +--R associates? : (%,%) -> Boolean coerce : PAdicInteger p -> % +--R coerce : Fraction Integer -> % coerce : % -> % +--R coerce : Integer -> % coerce : % -> OutputForm +--R denom : % -> PAdicInteger p denominator : % -> % +--R factor : % -> Factored % gcd : List % -> % +--R gcd : (%,%) -> % hash : % -> SingleInteger +--R inv : % -> % latex : % -> String +--R lcm : List % -> % lcm : (%,%) -> % +--R numer : % -> PAdicInteger p numerator : % -> % +--R one? : % -> Boolean prime? : % -> Boolean +--R ?quo? : (%,%) -> % recip : % -> Union(%,"failed") +--R ?rem? : (%,%) -> % removeZeroes : (Integer,%) -> % +--R removeZeroes : % -> % retract : % -> PAdicInteger p +--R sample : () -> % sizeLess? : (%,%) -> Boolean +--R squareFree : % -> Factored % squareFreePart : % -> % +--R unit? : % -> Boolean unitCanonical : % -> % +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean +--R ?*? : (NonNegativeInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % +--R ?/? : (PAdicInteger p,PAdicInteger p) -> % +--R ? Boolean if PAdicInteger p has ORDSET +--R ?<=? : (%,%) -> Boolean if PAdicInteger p has ORDSET +--R ?>? : (%,%) -> Boolean if PAdicInteger p has ORDSET +--R ?>=? : (%,%) -> Boolean if PAdicInteger p has ORDSET +--R D : (%,(PAdicInteger p -> PAdicInteger p)) -> % +--R D : (%,(PAdicInteger p -> PAdicInteger p),NonNegativeInteger) -> % +--R D : (%,List Symbol,List NonNegativeInteger) -> % if PAdicInteger p has PDRING SYMBOL +--R D : (%,Symbol,NonNegativeInteger) -> % if PAdicInteger p has PDRING SYMBOL +--R D : (%,List Symbol) -> % if PAdicInteger p has PDRING SYMBOL +--R D : (%,Symbol) -> % if PAdicInteger p has PDRING SYMBOL +--R D : (%,NonNegativeInteger) -> % if PAdicInteger p has DIFRING +--R D : % -> % if PAdicInteger p has DIFRING +--R ?^? : (%,NonNegativeInteger) -> % +--R abs : % -> % if PAdicInteger p has OINTDOM +--R approximate : (%,Integer) -> Fraction Integer +--R ceiling : % -> PAdicInteger p if PAdicInteger p has INS +--R characteristic : () -> NonNegativeInteger +--R charthRoot : % -> Union(%,"failed") if $ has CHARNZ and PAdicInteger p has PFECAT or PAdicInteger p has CHARNZ +--R coerce : Symbol -> % if PAdicInteger p has RETRACT SYMBOL +--R conditionP : Matrix % -> Union(Vector %,"failed") if $ has CHARNZ and PAdicInteger p has PFECAT +--R continuedFraction : % -> ContinuedFraction Fraction Integer +--R convert : % -> DoubleFloat if PAdicInteger p has REAL +--R convert : % -> Float if PAdicInteger p has REAL +--R convert : % -> InputForm if PAdicInteger p has KONVERT INFORM +--R convert : % -> Pattern Float if PAdicInteger p has KONVERT PATTERN FLOAT +--R convert : % -> Pattern Integer if PAdicInteger p has KONVERT PATTERN INT +--R differentiate : (%,(PAdicInteger p -> PAdicInteger p)) -> % +--R differentiate : (%,(PAdicInteger p -> PAdicInteger p),NonNegativeInteger) -> % +--R differentiate : (%,List Symbol,List NonNegativeInteger) -> % if PAdicInteger p has PDRING SYMBOL +--R differentiate : (%,Symbol,NonNegativeInteger) -> % if PAdicInteger p has PDRING SYMBOL +--R differentiate : (%,List Symbol) -> % if PAdicInteger p has PDRING SYMBOL +--R differentiate : (%,Symbol) -> % if PAdicInteger p has PDRING SYMBOL +--R differentiate : (%,NonNegativeInteger) -> % if PAdicInteger p has DIFRING +--R differentiate : % -> % if PAdicInteger p has DIFRING +--R divide : (%,%) -> Record(quotient: %,remainder: %) +--R ?.? : (%,PAdicInteger p) -> % if PAdicInteger p has ELTAB(PADIC p,PADIC p) +--R euclideanSize : % -> NonNegativeInteger +--R eval : (%,Symbol,PAdicInteger p) -> % if PAdicInteger p has IEVALAB(SYMBOL,PADIC p) +--R eval : (%,List Symbol,List PAdicInteger p) -> % if PAdicInteger p has IEVALAB(SYMBOL,PADIC p) +--R eval : (%,List Equation PAdicInteger p) -> % if PAdicInteger p has EVALAB PADIC p +--R eval : (%,Equation PAdicInteger p) -> % if PAdicInteger p has EVALAB PADIC p +--R eval : (%,PAdicInteger p,PAdicInteger p) -> % if PAdicInteger p has EVALAB PADIC p +--R eval : (%,List PAdicInteger p,List PAdicInteger p) -> % if PAdicInteger p has EVALAB PADIC p +--R expressIdealMember : (List %,%) -> Union(List %,"failed") +--R exquo : (%,%) -> Union(%,"failed") +--R extendedEuclidean : (%,%,%) -> Union(Record(coef1: %,coef2: %),"failed") +--R extendedEuclidean : (%,%) -> Record(coef1: %,coef2: %,generator: %) +--R factorPolynomial : SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if PAdicInteger p has PFECAT +--R factorSquareFreePolynomial : SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if PAdicInteger p has PFECAT +--R floor : % -> PAdicInteger p if PAdicInteger p has INS +--R fractionPart : % -> % if PAdicInteger p has EUCDOM +--R gcdPolynomial : (SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial % +--R init : () -> % if PAdicInteger p has STEP +--R map : ((PAdicInteger p -> PAdicInteger p),%) -> % +--R max : (%,%) -> % if PAdicInteger p has ORDSET +--R min : (%,%) -> % if PAdicInteger p has ORDSET +--R multiEuclidean : (List %,%) -> Union(List %,"failed") +--R negative? : % -> Boolean if PAdicInteger p has OINTDOM +--R nextItem : % -> Union(%,"failed") if PAdicInteger p has STEP +--R patternMatch : (%,Pattern Float,PatternMatchResult(Float,%)) -> PatternMatchResult(Float,%) if PAdicInteger p has PATMAB FLOAT +--R patternMatch : (%,Pattern Integer,PatternMatchResult(Integer,%)) -> PatternMatchResult(Integer,%) if PAdicInteger p has PATMAB INT +--R positive? : % -> Boolean if PAdicInteger p has OINTDOM +--R principalIdeal : List % -> Record(coef: List %,generator: %) +--R random : () -> % if PAdicInteger p has INS +--R reducedSystem : Matrix % -> Matrix PAdicInteger p +--R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix PAdicInteger p,vec: Vector PAdicInteger p) +--R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix Integer,vec: Vector Integer) if PAdicInteger p has LINEXP INT +--R reducedSystem : Matrix % -> Matrix Integer if PAdicInteger p has LINEXP INT +--R retract : % -> Integer if PAdicInteger p has RETRACT INT +--R retract : % -> Fraction Integer if PAdicInteger p has RETRACT INT +--R retract : % -> Symbol if PAdicInteger p has RETRACT SYMBOL +--R retractIfCan : % -> Union(Integer,"failed") if PAdicInteger p has RETRACT INT +--R retractIfCan : % -> Union(Fraction Integer,"failed") if PAdicInteger p has RETRACT INT +--R retractIfCan : % -> Union(Symbol,"failed") if PAdicInteger p has RETRACT SYMBOL +--R retractIfCan : % -> Union(PAdicInteger p,"failed") +--R sign : % -> Integer if PAdicInteger p has OINTDOM +--R solveLinearPolynomialEquation : (List SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> Union(List SparseUnivariatePolynomial %,"failed") if PAdicInteger p has PFECAT +--R squareFreePolynomial : SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if PAdicInteger p has PFECAT +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R unitNormal : % -> Record(unit: %,canonical: %,associate: %) +--R wholePart : % -> PAdicInteger p if PAdicInteger p has EUCDOM +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +PAdicRational examples +==================================================================== + +See Also: +o )show PAdicRational + +@ + \pagehead{PAdicRational}{PADICRAT} \pagepic{ps/v103padicrational.ps}{PADICRAT}{1.00} {\bf See}\\ @@ -73424,6 +87440,148 @@ PAdicRational(p:Integer) == PAdicRationalConstructor(p,PAdicInteger p) @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain PADICRC PAdicRationalConstructor} + +<>= +)set break resume +)sys rm -f PAdicRationalConstructor.output +)spool PAdicRationalConstructor.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show PAdicRationalConstructor +--R PAdicRationalConstructor(p: Integer,PADIC: PAdicIntegerCategory p) is a domain constructor +--R Abbreviation for PAdicRationalConstructor is PADICRC +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for PADICRC +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (%,PADIC) -> % ?*? : (PADIC,%) -> % +--R ?*? : (Fraction Integer,%) -> % ?*? : (%,Fraction Integer) -> % +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?**? : (%,Integer) -> % +--R ?**? : (%,PositiveInteger) -> % ?+? : (%,%) -> % +--R ?-? : (%,%) -> % -? : % -> % +--R ?/? : (PADIC,PADIC) -> % ?/? : (%,%) -> % +--R ?=? : (%,%) -> Boolean D : (%,(PADIC -> PADIC)) -> % +--R 1 : () -> % 0 : () -> % +--R ?^? : (%,Integer) -> % ?^? : (%,PositiveInteger) -> % +--R associates? : (%,%) -> Boolean coerce : PADIC -> % +--R coerce : Fraction Integer -> % coerce : % -> % +--R coerce : Integer -> % coerce : % -> OutputForm +--R denom : % -> PADIC denominator : % -> % +--R factor : % -> Factored % gcd : List % -> % +--R gcd : (%,%) -> % hash : % -> SingleInteger +--R inv : % -> % latex : % -> String +--R lcm : List % -> % lcm : (%,%) -> % +--R map : ((PADIC -> PADIC),%) -> % numer : % -> PADIC +--R numerator : % -> % one? : % -> Boolean +--R prime? : % -> Boolean ?quo? : (%,%) -> % +--R recip : % -> Union(%,"failed") ?rem? : (%,%) -> % +--R removeZeroes : (Integer,%) -> % removeZeroes : % -> % +--R retract : % -> PADIC sample : () -> % +--R sizeLess? : (%,%) -> Boolean squareFree : % -> Factored % +--R squareFreePart : % -> % unit? : % -> Boolean +--R unitCanonical : % -> % zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean +--R ?*? : (NonNegativeInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % +--R ? Boolean if PADIC has ORDSET +--R ?<=? : (%,%) -> Boolean if PADIC has ORDSET +--R ?>? : (%,%) -> Boolean if PADIC has ORDSET +--R ?>=? : (%,%) -> Boolean if PADIC has ORDSET +--R D : (%,(PADIC -> PADIC),NonNegativeInteger) -> % +--R D : (%,List Symbol,List NonNegativeInteger) -> % if PADIC has PDRING SYMBOL +--R D : (%,Symbol,NonNegativeInteger) -> % if PADIC has PDRING SYMBOL +--R D : (%,List Symbol) -> % if PADIC has PDRING SYMBOL +--R D : (%,Symbol) -> % if PADIC has PDRING SYMBOL +--R D : (%,NonNegativeInteger) -> % if PADIC has DIFRING +--R D : % -> % if PADIC has DIFRING +--R ?^? : (%,NonNegativeInteger) -> % +--R abs : % -> % if PADIC has OINTDOM +--R approximate : (%,Integer) -> Fraction Integer +--R ceiling : % -> PADIC if PADIC has INS +--R characteristic : () -> NonNegativeInteger +--R charthRoot : % -> Union(%,"failed") if $ has CHARNZ and PADIC has PFECAT or PADIC has CHARNZ +--R coerce : Symbol -> % if PADIC has RETRACT SYMBOL +--R conditionP : Matrix % -> Union(Vector %,"failed") if $ has CHARNZ and PADIC has PFECAT +--R continuedFraction : % -> ContinuedFraction Fraction Integer +--R convert : % -> DoubleFloat if PADIC has REAL +--R convert : % -> Float if PADIC has REAL +--R convert : % -> InputForm if PADIC has KONVERT INFORM +--R convert : % -> Pattern Float if PADIC has KONVERT PATTERN FLOAT +--R convert : % -> Pattern Integer if PADIC has KONVERT PATTERN INT +--R differentiate : (%,(PADIC -> PADIC)) -> % +--R differentiate : (%,(PADIC -> PADIC),NonNegativeInteger) -> % +--R differentiate : (%,List Symbol,List NonNegativeInteger) -> % if PADIC has PDRING SYMBOL +--R differentiate : (%,Symbol,NonNegativeInteger) -> % if PADIC has PDRING SYMBOL +--R differentiate : (%,List Symbol) -> % if PADIC has PDRING SYMBOL +--R differentiate : (%,Symbol) -> % if PADIC has PDRING SYMBOL +--R differentiate : (%,NonNegativeInteger) -> % if PADIC has DIFRING +--R differentiate : % -> % if PADIC has DIFRING +--R divide : (%,%) -> Record(quotient: %,remainder: %) +--R ?.? : (%,PADIC) -> % if PADIC has ELTAB(PADIC,PADIC) +--R euclideanSize : % -> NonNegativeInteger +--R eval : (%,Symbol,PADIC) -> % if PADIC has IEVALAB(SYMBOL,PADIC) +--R eval : (%,List Symbol,List PADIC) -> % if PADIC has IEVALAB(SYMBOL,PADIC) +--R eval : (%,List Equation PADIC) -> % if PADIC has EVALAB PADIC +--R eval : (%,Equation PADIC) -> % if PADIC has EVALAB PADIC +--R eval : (%,PADIC,PADIC) -> % if PADIC has EVALAB PADIC +--R eval : (%,List PADIC,List PADIC) -> % if PADIC has EVALAB PADIC +--R expressIdealMember : (List %,%) -> Union(List %,"failed") +--R exquo : (%,%) -> Union(%,"failed") +--R extendedEuclidean : (%,%,%) -> Union(Record(coef1: %,coef2: %),"failed") +--R extendedEuclidean : (%,%) -> Record(coef1: %,coef2: %,generator: %) +--R factorPolynomial : SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if PADIC has PFECAT +--R factorSquareFreePolynomial : SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if PADIC has PFECAT +--R floor : % -> PADIC if PADIC has INS +--R fractionPart : % -> % if PADIC has EUCDOM +--R gcdPolynomial : (SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial % +--R init : () -> % if PADIC has STEP +--R max : (%,%) -> % if PADIC has ORDSET +--R min : (%,%) -> % if PADIC has ORDSET +--R multiEuclidean : (List %,%) -> Union(List %,"failed") +--R negative? : % -> Boolean if PADIC has OINTDOM +--R nextItem : % -> Union(%,"failed") if PADIC has STEP +--R patternMatch : (%,Pattern Float,PatternMatchResult(Float,%)) -> PatternMatchResult(Float,%) if PADIC has PATMAB FLOAT +--R patternMatch : (%,Pattern Integer,PatternMatchResult(Integer,%)) -> PatternMatchResult(Integer,%) if PADIC has PATMAB INT +--R positive? : % -> Boolean if PADIC has OINTDOM +--R principalIdeal : List % -> Record(coef: List %,generator: %) +--R random : () -> % if PADIC has INS +--R reducedSystem : Matrix % -> Matrix PADIC +--R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix PADIC,vec: Vector PADIC) +--R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix Integer,vec: Vector Integer) if PADIC has LINEXP INT +--R reducedSystem : Matrix % -> Matrix Integer if PADIC has LINEXP INT +--R retract : % -> Integer if PADIC has RETRACT INT +--R retract : % -> Fraction Integer if PADIC has RETRACT INT +--R retract : % -> Symbol if PADIC has RETRACT SYMBOL +--R retractIfCan : % -> Union(Integer,"failed") if PADIC has RETRACT INT +--R retractIfCan : % -> Union(Fraction Integer,"failed") if PADIC has RETRACT INT +--R retractIfCan : % -> Union(Symbol,"failed") if PADIC has RETRACT SYMBOL +--R retractIfCan : % -> Union(PADIC,"failed") +--R sign : % -> Integer if PADIC has OINTDOM +--R solveLinearPolynomialEquation : (List SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> Union(List SparseUnivariatePolynomial %,"failed") if PADIC has PFECAT +--R squareFreePolynomial : SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if PADIC has PFECAT +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R unitNormal : % -> Record(unit: %,canonical: %,associate: %) +--R wholePart : % -> PADIC if PADIC has EUCDOM +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +PAdicRationalConstructor examples +==================================================================== + +See Also: +o )show PAdicRationalConstructor + +@ + \pagehead{PAdicRationalConstructor}{PADICRC} \pagepic{ps/v103padicrationalconstructor.ps}{PADICRC}{1.00} {\bf See}\\ @@ -73712,6 +87870,46 @@ PAdicRationalConstructor(p,PADIC): Exports == Implementation where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain PALETTE Palette} + +<>= +)set break resume +)sys rm -f Palette.output +)spool Palette.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show Palette +--R Palette is a domain constructor +--R Abbreviation for Palette is PALETTE +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for PALETTE +--R +--R------------------------------- Operations -------------------------------- +--R ?=? : (%,%) -> Boolean bright : Color -> % +--R coerce : Color -> % coerce : % -> OutputForm +--R dark : Color -> % dim : Color -> % +--R hash : % -> SingleInteger hue : % -> Color +--R latex : % -> String light : Color -> % +--R pastel : Color -> % shade : % -> Integer +--R ?~=? : (%,%) -> Boolean +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +Palette examples +==================================================================== + +See Also: +o )show Palette + +@ + \pagehead{Palette}{PALETTE} \pagepic{ps/v103palette.ps}{PALETTE}{1.00} {\bf See}\\ @@ -73798,6 +87996,41 @@ Palette(): Exports == Implementation where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain PARPCURV ParametricPlaneCurve} + +<>= +)set break resume +)sys rm -f ParametricPlaneCurve.output +)spool ParametricPlaneCurve.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show ParametricPlaneCurve +--R ParametricPlaneCurve ComponentFunction: Type is a domain constructor +--R Abbreviation for ParametricPlaneCurve is PARPCURV +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for PARPCURV +--R +--R------------------------------- Operations -------------------------------- +--R coordinate : (%,NonNegativeInteger) -> ComponentFunction +--R curve : (ComponentFunction,ComponentFunction) -> % +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +ParametricPlaneCurve examples +==================================================================== + +See Also: +o )show ParametricPlaneCurve + +@ + \pagehead{ParametricPlaneCurve}{PARPCURV} \pagepic{ps/v103parametricplanecurve.ps}{PARPCURV}{1.00} {\bf See}\\ @@ -73857,6 +88090,41 @@ ParametricPlaneCurve(ComponentFunction): Exports == Implementation where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain PARSCURV ParametricSpaceCurve} + +<>= +)set break resume +)sys rm -f ParametricSpaceCurve.output +)spool ParametricSpaceCurve.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show ParametricSpaceCurve +--R ParametricSpaceCurve ComponentFunction: Type is a domain constructor +--R Abbreviation for ParametricSpaceCurve is PARSCURV +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for PARSCURV +--R +--R------------------------------- Operations -------------------------------- +--R coordinate : (%,NonNegativeInteger) -> ComponentFunction +--R curve : (ComponentFunction,ComponentFunction,ComponentFunction) -> % +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +ParametricSpaceCurve examples +==================================================================== + +See Also: +o )show ParametricSpaceCurve + +@ + \pagehead{ParametricSpaceCurve}{PARSCURV} \pagepic{ps/v103parametricspacecurve.ps}{PARSCURV}{1.00} {\bf See}\\ @@ -73919,6 +88187,41 @@ ParametricSpaceCurve(ComponentFunction): Exports == Implementation where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain PARSURF ParametricSurface} + +<>= +)set break resume +)sys rm -f ParametricSurface.output +)spool ParametricSurface.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show ParametricSurface +--R ParametricSurface ComponentFunction: Type is a domain constructor +--R Abbreviation for ParametricSurface is PARSURF +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for PARSURF +--R +--R------------------------------- Operations -------------------------------- +--R coordinate : (%,NonNegativeInteger) -> ComponentFunction +--R surface : (ComponentFunction,ComponentFunction,ComponentFunction) -> % +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +ParametricSurface examples +==================================================================== + +See Also: +o )show ParametricSurface + +@ + \pagehead{ParametricSurface}{PARSURF} \pagepic{ps/v103parametricsurface.ps}{PARSURF}{1.00} {\bf See}\\ @@ -73981,6 +88284,7 @@ ParametricSurface(ComponentFunction): Exports == Implementation where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain PFR PartialFraction} + <>= )set break resume )sys rm -f PartialFraction.output @@ -74797,6 +89101,53 @@ PartialFraction(R: EuclideanDomain): Cat == Capsule where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain PRTITION Partition} + +<>= +)set break resume +)sys rm -f Partition.output +)spool Partition.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show Partition +--R Partition is a domain constructor +--R Abbreviation for Partition is PRTITION +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for PRTITION +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (PositiveInteger,%) -> % ?+? : (%,%) -> % +--R ? Boolean ?<=? : (%,%) -> Boolean +--R ?=? : (%,%) -> Boolean ?>? : (%,%) -> Boolean +--R ?>=? : (%,%) -> Boolean 0 : () -> % +--R coerce : % -> List Integer coerce : % -> OutputForm +--R conjugate : % -> % convert : % -> List Integer +--R hash : % -> SingleInteger latex : % -> String +--R max : (%,%) -> % min : (%,%) -> % +--R partition : List Integer -> % pdct : % -> Integer +--R sample : () -> % zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean +--R ?*? : (NonNegativeInteger,%) -> % +--R powers : List Integer -> List List Integer +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +Partition examples +==================================================================== + +See Also: +o )show Partition + +@ + \pagehead{Partition}{PRTITION} \pagepic{ps/v103partition.ps}{PRTITION}{1.00} {\bf See}\\ @@ -74967,6 +89318,73 @@ Partition: Exports == Implementation where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain PATTERN Pattern} + +<>= +)set break resume +)sys rm -f Pattern.output +)spool Pattern.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show Pattern +--R Pattern R: SetCategory is a domain constructor +--R Abbreviation for Pattern is PATTERN +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for PATTERN +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (%,%) -> % ?**? : (%,%) -> % +--R ?+? : (%,%) -> % ?/? : (%,%) -> % +--R ?=? : (%,%) -> Boolean 1 : () -> % +--R 0 : () -> % addBadValue : (%,Any) -> % +--R coerce : Symbol -> % coerce : R -> % +--R coerce : % -> OutputForm constant? : % -> Boolean +--R convert : List % -> % copy : % -> % +--R depth : % -> NonNegativeInteger generic? : % -> Boolean +--R getBadValues : % -> List Any hasPredicate? : % -> Boolean +--R hasTopPredicate? : % -> Boolean hash : % -> SingleInteger +--R inR? : % -> Boolean latex : % -> String +--R multiple? : % -> Boolean optional? : % -> Boolean +--R predicates : % -> List Any quoted? : % -> Boolean +--R resetBadValues : % -> % retract : % -> Symbol +--R retract : % -> R symbol? : % -> Boolean +--R variables : % -> List % ?~=? : (%,%) -> Boolean +--R ?**? : (%,NonNegativeInteger) -> % +--R elt : (BasicOperator,List %) -> % +--R isExpt : % -> Union(Record(val: %,exponent: NonNegativeInteger),"failed") +--R isList : % -> Union(List %,"failed") +--R isOp : % -> Union(Record(op: BasicOperator,arg: List %),"failed") +--R isOp : (%,BasicOperator) -> Union(List %,"failed") +--R isPlus : % -> Union(List %,"failed") +--R isPower : % -> Union(Record(val: %,exponent: %),"failed") +--R isQuotient : % -> Union(Record(num: %,den: %),"failed") +--R isTimes : % -> Union(List %,"failed") +--R optpair : List % -> Union(List %,"failed") +--R patternVariable : (Symbol,Boolean,Boolean,Boolean) -> % +--R retractIfCan : % -> Union(Symbol,"failed") +--R retractIfCan : % -> Union(R,"failed") +--R setPredicates : (%,List Any) -> % +--R setTopPredicate : (%,List Symbol,Any) -> % +--R topPredicate : % -> Record(var: List Symbol,pred: Any) +--R withPredicates : (%,List Any) -> % +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +Pattern examples +==================================================================== + +See Also: +o )show Pattern + +@ + \pagehead{Pattern}{PATTERN} \pagepic{ps/v103pattern.ps}{PATTERN}{1.00} @@ -75403,6 +89821,46 @@ Pattern(R:SetCategory): Exports == Implementation where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain PATLRES PatternMatchListResult} + +<>= +)set break resume +)sys rm -f PatternMatchListResult.output +)spool PatternMatchListResult.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show PatternMatchListResult +--R PatternMatchListResult(R: SetCategory,S: SetCategory,L: ListAggregate S) is a domain constructor +--R Abbreviation for PatternMatchListResult is PATLRES +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for PATLRES +--R +--R------------------------------- Operations -------------------------------- +--R ?=? : (%,%) -> Boolean coerce : % -> OutputForm +--R failed : () -> % failed? : % -> Boolean +--R hash : % -> SingleInteger latex : % -> String +--R new : () -> % ?~=? : (%,%) -> Boolean +--R atoms : % -> PatternMatchResult(R,S) +--R lists : % -> PatternMatchResult(R,L) +--R makeResult : (PatternMatchResult(R,S),PatternMatchResult(R,L)) -> % +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +PatternMatchListResult examples +==================================================================== + +See Also: +o )show PatternMatchListResult + +@ + \pagehead{PatternMatchListResult}{PATLRES} \pagepic{ps/v103patternmatchlistresult.ps}{PATLRES}{1.00} {\bf See}\\ @@ -75478,6 +89936,50 @@ PatternMatchListResult(R:SetCategory, S:SetCategory, L:ListAggregate S): @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain PATRES PatternMatchResult} + +<>= +)set break resume +)sys rm -f PatternMatchResult.output +)spool PatternMatchResult.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show PatternMatchResult +--R PatternMatchResult(R: SetCategory,S: SetCategory) is a domain constructor +--R Abbreviation for PatternMatchResult is PATRES +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for PATRES +--R +--R------------------------------- Operations -------------------------------- +--R ?=? : (%,%) -> Boolean addMatch : (Pattern R,S,%) -> % +--R coerce : % -> OutputForm failed : () -> % +--R failed? : % -> Boolean hash : % -> SingleInteger +--R latex : % -> String new : () -> % +--R union : (%,%) -> % ?~=? : (%,%) -> Boolean +--R addMatchRestricted : (Pattern R,S,%,S) -> % +--R construct : List Record(key: Symbol,entry: S) -> % +--R destruct : % -> List Record(key: Symbol,entry: S) +--R getMatch : (Pattern R,%) -> Union(S,"failed") +--R insertMatch : (Pattern R,S,%) -> % +--R satisfy? : (%,Pattern R) -> Union(Boolean,"failed") +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +PatternMatchResult examples +==================================================================== + +See Also: +o )show PatternMatchResult + +@ + \pagehead{PatternMatchResult}{PATRES} \pagepic{ps/v103patternmatchresult.ps}{PATRES}{1.00} {\bf See}\\ @@ -75613,6 +90115,80 @@ PatternMatchResult(R:SetCategory, S:SetCategory): SetCategory with @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain PENDTREE PendantTree} + +<>= +)set break resume +)sys rm -f PendantTree.output +)spool PendantTree.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show PendantTree +--R PendantTree S: SetCategory is a domain constructor +--R Abbreviation for PendantTree is PENDTREE +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for PENDTREE +--R +--R------------------------------- Operations -------------------------------- +--R children : % -> List % coerce : % -> Tree S +--R copy : % -> % cyclic? : % -> Boolean +--R distance : (%,%) -> Integer ?.right : (%,right) -> % +--R ?.left : (%,left) -> % ?.value : (%,value) -> S +--R empty : () -> % empty? : % -> Boolean +--R eq? : (%,%) -> Boolean leaf? : % -> Boolean +--R leaves : % -> List S left : % -> % +--R map : ((S -> S),%) -> % nodes : % -> List % +--R ptree : (%,%) -> % ptree : S -> % +--R right : % -> % sample : () -> % +--R value : % -> S +--R #? : % -> NonNegativeInteger if $ has finiteAggregate +--R ?=? : (%,%) -> Boolean if S has SETCAT +--R any? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate +--R child? : (%,%) -> Boolean if S has SETCAT +--R coerce : % -> OutputForm if S has SETCAT +--R count : (S,%) -> NonNegativeInteger if $ has finiteAggregate and S has SETCAT +--R count : ((S -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate +--R eval : (%,List S,List S) -> % if S has EVALAB S and S has SETCAT +--R eval : (%,S,S) -> % if S has EVALAB S and S has SETCAT +--R eval : (%,Equation S) -> % if S has EVALAB S and S has SETCAT +--R eval : (%,List Equation S) -> % if S has EVALAB S and S has SETCAT +--R every? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate +--R hash : % -> SingleInteger if S has SETCAT +--R latex : % -> String if S has SETCAT +--R less? : (%,NonNegativeInteger) -> Boolean +--R map! : ((S -> S),%) -> % if $ has shallowlyMutable +--R member? : (S,%) -> Boolean if $ has finiteAggregate and S has SETCAT +--R members : % -> List S if $ has finiteAggregate +--R more? : (%,NonNegativeInteger) -> Boolean +--R node? : (%,%) -> Boolean if S has SETCAT +--R parts : % -> List S if $ has finiteAggregate +--R setchildren! : (%,List %) -> % if $ has shallowlyMutable +--R setelt : (%,right,%) -> % if $ has shallowlyMutable +--R setelt : (%,left,%) -> % if $ has shallowlyMutable +--R setelt : (%,value,S) -> S if $ has shallowlyMutable +--R setleft! : (%,%) -> % if $ has shallowlyMutable +--R setright! : (%,%) -> % if $ has shallowlyMutable +--R setvalue! : (%,S) -> S if $ has shallowlyMutable +--R size? : (%,NonNegativeInteger) -> Boolean +--R ?~=? : (%,%) -> Boolean if S has SETCAT +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +PendantTree examples +==================================================================== + +See Also: +o )show PendantTree + +@ + A PendantTree(S)is either a leaf? and is an S or has a left and a right both PendantTree(S)'s \pagehead{PendantTree}{PENDTREE} @@ -75727,6 +90303,7 @@ PendantTree(S: SetCategory): T == C where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain PERM Permutation} + <>= )set break resume )sys rm -f Permutation.output @@ -76297,6 +90874,59 @@ Permutation(S:SetCategory): public == private where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain PERMGRP PermutationGroup} + +<>= +)set break resume +)sys rm -f PermutationGroup.output +)spool PermutationGroup.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show PermutationGroup +--R PermutationGroup S: SetCategory is a domain constructor +--R Abbreviation for PermutationGroup is PERMGRP +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for PERMGRP +--R +--R------------------------------- Operations -------------------------------- +--R ? Boolean ?<=? : (%,%) -> Boolean +--R ?=? : (%,%) -> Boolean base : % -> List S +--R coerce : List Permutation S -> % coerce : % -> List Permutation S +--R coerce : % -> OutputForm degree : % -> NonNegativeInteger +--R hash : % -> SingleInteger latex : % -> String +--R movedPoints : % -> Set S orbit : (%,List S) -> Set List S +--R orbit : (%,Set S) -> Set Set S orbit : (%,S) -> Set S +--R orbits : % -> Set Set S order : % -> NonNegativeInteger +--R random : % -> Permutation S ?~=? : (%,%) -> Boolean +--R ?.? : (%,NonNegativeInteger) -> Permutation S +--R generators : % -> List Permutation S +--R initializeGroupForWordProblem : (%,Integer,Integer) -> Void +--R initializeGroupForWordProblem : % -> Void +--R member? : (Permutation S,%) -> Boolean +--R permutationGroup : List Permutation S -> % +--R random : (%,Integer) -> Permutation S +--R strongGenerators : % -> List Permutation S +--R wordInGenerators : (Permutation S,%) -> List NonNegativeInteger +--R wordInStrongGenerators : (Permutation S,%) -> List NonNegativeInteger +--R wordsForStrongGenerators : % -> List List NonNegativeInteger +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +PermutationGroup examples +==================================================================== + +See Also: +o )show PermutationGroup + +@ + \pagehead{PermutationGroup}{PERMGRP} \pagepic{ps/v103permutationgroup.ps}{PERMGRP}{1.00} @@ -77094,6 +91724,82 @@ PermutationGroup(S:SetCategory): public == private where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain HACKPI Pi} + +<>= +)set break resume +)sys rm -f Pi.output +)spool Pi.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show Pi +--R Pi is a domain constructor +--R Abbreviation for Pi is HACKPI +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for HACKPI +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (Fraction Integer,%) -> % ?*? : (%,Fraction Integer) -> % +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?**? : (%,Integer) -> % +--R ?**? : (%,PositiveInteger) -> % ?+? : (%,%) -> % +--R ?-? : (%,%) -> % -? : % -> % +--R ?/? : (%,%) -> % ?=? : (%,%) -> Boolean +--R 1 : () -> % 0 : () -> % +--R ?^? : (%,Integer) -> % ?^? : (%,PositiveInteger) -> % +--R associates? : (%,%) -> Boolean coerce : % -> Float +--R coerce : % -> DoubleFloat coerce : Fraction Integer -> % +--R coerce : % -> % coerce : Integer -> % +--R coerce : % -> OutputForm convert : % -> InputForm +--R convert : % -> DoubleFloat convert : % -> Float +--R factor : % -> Factored % gcd : List % -> % +--R gcd : (%,%) -> % hash : % -> SingleInteger +--R inv : % -> % latex : % -> String +--R lcm : List % -> % lcm : (%,%) -> % +--R one? : % -> Boolean pi : () -> % +--R prime? : % -> Boolean ?quo? : (%,%) -> % +--R recip : % -> Union(%,"failed") ?rem? : (%,%) -> % +--R retract : % -> Fraction Integer retract : % -> Integer +--R sample : () -> % sizeLess? : (%,%) -> Boolean +--R squareFree : % -> Factored % squareFreePart : % -> % +--R unit? : % -> Boolean unitCanonical : % -> % +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean +--R ?*? : (NonNegativeInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % +--R ?^? : (%,NonNegativeInteger) -> % +--R characteristic : () -> NonNegativeInteger +--R convert : % -> Fraction SparseUnivariatePolynomial Integer +--R divide : (%,%) -> Record(quotient: %,remainder: %) +--R euclideanSize : % -> NonNegativeInteger +--R expressIdealMember : (List %,%) -> Union(List %,"failed") +--R exquo : (%,%) -> Union(%,"failed") +--R extendedEuclidean : (%,%,%) -> Union(Record(coef1: %,coef2: %),"failed") +--R extendedEuclidean : (%,%) -> Record(coef1: %,coef2: %,generator: %) +--R gcdPolynomial : (SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial % +--R multiEuclidean : (List %,%) -> Union(List %,"failed") +--R principalIdeal : List % -> Record(coef: List %,generator: %) +--R retractIfCan : % -> Union(Fraction Integer,"failed") +--R retractIfCan : % -> Union(Integer,"failed") +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R unitNormal : % -> Record(unit: %,canonical: %,associate: %) +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +Pi examples +==================================================================== + +See Also: +o )show Pi + +@ + \pagehead{Pi}{HACKPI} \pagepic{ps/v103pi.ps}{HACKPI}{1.00} {\bf See}\\ @@ -77225,6 +91931,7 @@ Pi(): Exports == Implementation where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain ACPLOT PlaneAlgebraicCurvePlot} + <>= )set break resume )sys rm -f PlaneAlgebraicCurvePlot.output @@ -79080,6 +93787,7 @@ PlaneAlgebraicCurvePlot(): PlottablePlaneCurveCategory _ @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain PLACES Places} + <>= )set break resume )sys rm -f Places.output @@ -79181,6 +93889,7 @@ Places(K):Exports == Implementation where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain PLACESPS PlacesOverPseudoAlgebraicClosureOfFiniteField} + <>= )set break resume )sys rm -f PlacesOverPseudoAlgebraicClosureOfFiniteField.output @@ -79284,6 +93993,7 @@ PlacesOverPseudoAlgebraicClosureOfFiniteField(K):Exports @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain PLCS Plcs} + <>= )set break resume )sys rm -f Plcs.output @@ -79479,6 +94189,7 @@ Plcs(K:Field,PCS:LocalPowerSeriesCategory(K)):Exports == Implementation where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain PLOT Plot} + <>= )set break resume )sys rm -f Plot.output @@ -80179,6 +94890,58 @@ Plot(): Exports == Implementation where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain PLOT3D Plot3D} + +<>= +)set break resume +)sys rm -f Plot3D.output +)spool Plot3D.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show Plot3D +--R Plot3D is a domain constructor +--R Abbreviation for Plot3D is PLOT3D +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for PLOT3D +--R +--R------------------------------- Operations -------------------------------- +--R adaptive3D? : () -> Boolean coerce : % -> OutputForm +--R debug3D : Boolean -> Boolean maxPoints3D : () -> Integer +--R minPoints3D : () -> Integer numFunEvals3D : () -> Integer +--R refine : % -> % screenResolution3D : () -> Integer +--R setAdaptive3D : Boolean -> Boolean tRange : % -> Segment DoubleFloat +--R xRange : % -> Segment DoubleFloat yRange : % -> Segment DoubleFloat +--R zRange : % -> Segment DoubleFloat +--R listBranches : % -> List List Point DoubleFloat +--R plot : (%,Segment DoubleFloat) -> % +--R plot : ((DoubleFloat -> DoubleFloat),(DoubleFloat -> DoubleFloat),(DoubleFloat -> DoubleFloat),(DoubleFloat -> DoubleFloat),Segment DoubleFloat,Segment DoubleFloat,Segment DoubleFloat,Segment DoubleFloat) -> % +--R plot : ((DoubleFloat -> DoubleFloat),(DoubleFloat -> DoubleFloat),(DoubleFloat -> DoubleFloat),(DoubleFloat -> DoubleFloat),Segment DoubleFloat) -> % +--R pointPlot : ((DoubleFloat -> Point DoubleFloat),Segment DoubleFloat,Segment DoubleFloat,Segment DoubleFloat,Segment DoubleFloat) -> % +--R pointPlot : ((DoubleFloat -> Point DoubleFloat),Segment DoubleFloat) -> % +--R refine : (%,Segment DoubleFloat) -> % +--R setMaxPoints3D : Integer -> Integer +--R setMinPoints3D : Integer -> Integer +--R setScreenResolution3D : Integer -> Integer +--R tValues : % -> List List DoubleFloat +--R zoom : (%,Segment DoubleFloat,Segment DoubleFloat,Segment DoubleFloat) -> % +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +Plot3D examples +==================================================================== + +See Also: +o )show Plot3D + +@ + \pagehead{Plot3D}{PLOT3D} \pagepic{ps/v103plot3d.ps}{PLOT3D}{1.00} @@ -80704,6 +95467,52 @@ Plot3D(): Exports == Implementation where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain PBWLB PoincareBirkhoffWittLyndonBasis} + +<>= +)set break resume +)sys rm -f PoincareBirkhoffWittLyndonBasis.output +)spool PoincareBirkhoffWittLyndonBasis.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show PoincareBirkhoffWittLyndonBasis +--R PoincareBirkhoffWittLyndonBasis VarSet: OrderedSet is a domain constructor +--R Abbreviation for PoincareBirkhoffWittLyndonBasis is PBWLB +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for PBWLB +--R +--R------------------------------- Operations -------------------------------- +--R ? Boolean ?<=? : (%,%) -> Boolean +--R ?=? : (%,%) -> Boolean ?>? : (%,%) -> Boolean +--R ?>=? : (%,%) -> Boolean 1 : () -> % +--R coerce : VarSet -> % coerce : LyndonWord VarSet -> % +--R coerce : % -> OutputForm first : % -> LyndonWord VarSet +--R hash : % -> SingleInteger latex : % -> String +--R length : % -> NonNegativeInteger max : (%,%) -> % +--R min : (%,%) -> % rest : % -> % +--R retract : % -> LyndonWord VarSet retractable? : % -> Boolean +--R varList : % -> List VarSet ?~=? : (%,%) -> Boolean +--R coerce : % -> OrderedFreeMonoid VarSet +--R listOfTerms : % -> List LyndonWord VarSet +--R retractIfCan : % -> Union(LyndonWord VarSet,"failed") +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +PoincareBirkhoffWittLyndonBasis examples +==================================================================== + +See Also: +o )show PoincareBirkhoffWittLyndonBasis + +@ + \pagehead{PoincareBirkhoffWittLyndonBasis}{PBWLB} \pagepic{ps/v103poincarebirkhoffwittlyndonbasis.ps}{PBWLB}{1.00} @@ -80849,6 +95658,124 @@ PoincareBirkhoffWittLyndonBasis(VarSet: OrderedSet): Public == Private where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain POINT Point} + +<>= +)set break resume +)sys rm -f Point.output +)spool Point.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show Point +--R Point R: Ring is a domain constructor +--R Abbreviation for Point is POINT +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for POINT +--R +--R------------------------------- Operations -------------------------------- +--R -? : % -> % if R has ABELGRP concat : List % -> % +--R concat : (%,%) -> % concat : (R,%) -> % +--R concat : (%,R) -> % construct : List R -> % +--R convert : List R -> % copy : % -> % +--R cross : (%,%) -> % delete : (%,Integer) -> % +--R dimension : % -> PositiveInteger ?.? : (%,Integer) -> R +--R elt : (%,Integer,R) -> R empty : () -> % +--R empty? : % -> Boolean entries : % -> List R +--R eq? : (%,%) -> Boolean extend : (%,List R) -> % +--R index? : (Integer,%) -> Boolean indices : % -> List Integer +--R insert : (%,%,Integer) -> % insert : (R,%,Integer) -> % +--R map : (((R,R) -> R),%,%) -> % map : ((R -> R),%) -> % +--R new : (NonNegativeInteger,R) -> % point : List R -> % +--R qelt : (%,Integer) -> R reverse : % -> % +--R sample : () -> % +--R #? : % -> NonNegativeInteger if $ has finiteAggregate +--R ?*? : (%,R) -> % if R has MONOID +--R ?*? : (R,%) -> % if R has MONOID +--R ?*? : (Integer,%) -> % if R has ABELGRP +--R ?+? : (%,%) -> % if R has ABELSG +--R ?-? : (%,%) -> % if R has ABELGRP +--R ? Boolean if R has ORDSET +--R ?<=? : (%,%) -> Boolean if R has ORDSET +--R ?=? : (%,%) -> Boolean if R has SETCAT +--R ?>? : (%,%) -> Boolean if R has ORDSET +--R ?>=? : (%,%) -> Boolean if R has ORDSET +--R any? : ((R -> Boolean),%) -> Boolean if $ has finiteAggregate +--R coerce : % -> OutputForm if R has SETCAT +--R convert : % -> InputForm if R has KONVERT INFORM +--R copyInto! : (%,%,Integer) -> % if $ has shallowlyMutable +--R count : (R,%) -> NonNegativeInteger if $ has finiteAggregate and R has SETCAT +--R count : ((R -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate +--R delete : (%,UniversalSegment Integer) -> % +--R dot : (%,%) -> R if R has RING +--R ?.? : (%,UniversalSegment Integer) -> % +--R entry? : (R,%) -> Boolean if $ has finiteAggregate and R has SETCAT +--R eval : (%,List R,List R) -> % if R has EVALAB R and R has SETCAT +--R eval : (%,R,R) -> % if R has EVALAB R and R has SETCAT +--R eval : (%,Equation R) -> % if R has EVALAB R and R has SETCAT +--R eval : (%,List Equation R) -> % if R has EVALAB R and R has SETCAT +--R every? : ((R -> Boolean),%) -> Boolean if $ has finiteAggregate +--R fill! : (%,R) -> % if $ has shallowlyMutable +--R find : ((R -> Boolean),%) -> Union(R,"failed") +--R first : % -> R if Integer has ORDSET +--R hash : % -> SingleInteger if R has SETCAT +--R latex : % -> String if R has SETCAT +--R length : % -> R if R has RADCAT and R has RING +--R less? : (%,NonNegativeInteger) -> Boolean +--R magnitude : % -> R if R has RADCAT and R has RING +--R map! : ((R -> R),%) -> % if $ has shallowlyMutable +--R max : (%,%) -> % if R has ORDSET +--R maxIndex : % -> Integer if Integer has ORDSET +--R member? : (R,%) -> Boolean if $ has finiteAggregate and R has SETCAT +--R members : % -> List R if $ has finiteAggregate +--R merge : (%,%) -> % if R has ORDSET +--R merge : (((R,R) -> Boolean),%,%) -> % +--R min : (%,%) -> % if R has ORDSET +--R minIndex : % -> Integer if Integer has ORDSET +--R more? : (%,NonNegativeInteger) -> Boolean +--R outerProduct : (%,%) -> Matrix R if R has RING +--R parts : % -> List R if $ has finiteAggregate +--R position : (R,%,Integer) -> Integer if R has SETCAT +--R position : (R,%) -> Integer if R has SETCAT +--R position : ((R -> Boolean),%) -> Integer +--R qsetelt! : (%,Integer,R) -> R if $ has shallowlyMutable +--R reduce : (((R,R) -> R),%) -> R if $ has finiteAggregate +--R reduce : (((R,R) -> R),%,R) -> R if $ has finiteAggregate +--R reduce : (((R,R) -> R),%,R,R) -> R if $ has finiteAggregate and R has SETCAT +--R remove : ((R -> Boolean),%) -> % if $ has finiteAggregate +--R remove : (R,%) -> % if $ has finiteAggregate and R has SETCAT +--R removeDuplicates : % -> % if $ has finiteAggregate and R has SETCAT +--R reverse! : % -> % if $ has shallowlyMutable +--R select : ((R -> Boolean),%) -> % if $ has finiteAggregate +--R setelt : (%,UniversalSegment Integer,R) -> R if $ has shallowlyMutable +--R setelt : (%,Integer,R) -> R if $ has shallowlyMutable +--R size? : (%,NonNegativeInteger) -> Boolean +--R sort : % -> % if R has ORDSET +--R sort : (((R,R) -> Boolean),%) -> % +--R sort! : % -> % if $ has shallowlyMutable and R has ORDSET +--R sort! : (((R,R) -> Boolean),%) -> % if $ has shallowlyMutable +--R sorted? : % -> Boolean if R has ORDSET +--R sorted? : (((R,R) -> Boolean),%) -> Boolean +--R swap! : (%,Integer,Integer) -> Void if $ has shallowlyMutable +--R zero : NonNegativeInteger -> % if R has ABELMON +--R ?~=? : (%,%) -> Boolean if R has SETCAT +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +Point examples +==================================================================== + +See Also: +o )show Point + +@ + \pagehead{Point}{POINT} \pagepic{ps/v103point.ps}{POINT}{1.00} {\bf See}\\ @@ -80976,6 +95903,7 @@ Point(R:Ring) : Exports == Implementation where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain POLY Polynomial} + <>= )set break resume )sys rm -f Polynomial.output @@ -81912,6 +96840,59 @@ Polynomial(R:Ring): @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain IDEAL PolynomialIdeals} + +<>= +)set break resume +)sys rm -f PolynomialIdeals.output +)spool PolynomialIdeals.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show PolynomialIdeals +--R PolynomialIdeals(F: Field,Expon: OrderedAbelianMonoidSup,VarSet: OrderedSet,DPoly: PolynomialCategory(F,Expon,VarSet)) is a domain constructor +--R Abbreviation for PolynomialIdeals is IDEAL +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for IDEAL +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (%,%) -> % ?+? : (%,%) -> % +--R ?=? : (%,%) -> Boolean coerce : List DPoly -> % +--R coerce : % -> OutputForm dimension : % -> Integer +--R element? : (DPoly,%) -> Boolean generators : % -> List DPoly +--R groebner : % -> % groebner? : % -> Boolean +--R groebnerIdeal : List DPoly -> % hash : % -> SingleInteger +--R ideal : List DPoly -> % in? : (%,%) -> Boolean +--R inRadical? : (DPoly,%) -> Boolean intersect : List % -> % +--R intersect : (%,%) -> % latex : % -> String +--R leadingIdeal : % -> % one? : % -> Boolean +--R quotient : (%,DPoly) -> % quotient : (%,%) -> % +--R saturate : (%,DPoly) -> % zero? : % -> Boolean +--R zeroDim? : % -> Boolean ?~=? : (%,%) -> Boolean +--R ?**? : (%,NonNegativeInteger) -> % +--R backOldPos : Record(mval: Matrix F,invmval: Matrix F,genIdeal: %) -> % +--R dimension : (%,List VarSet) -> Integer +--R generalPosition : (%,List VarSet) -> Record(mval: Matrix F,invmval: Matrix F,genIdeal: %) +--R relationsIdeal : List DPoly -> SuchThat(List Polynomial F,List Equation Polynomial F) if VarSet has KONVERT SYMBOL +--R saturate : (%,DPoly,List VarSet) -> % +--R zeroDim? : (%,List VarSet) -> Boolean +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +PolynomialIdeals examples +==================================================================== + +See Also: +o )show PolynomialIdeals + +@ + \pagehead{PolynomialIdeals}{IDEAL} \pagepic{ps/v103polynomialideals.ps}{IDEAL}{1.00} @@ -82379,6 +97360,85 @@ PolynomialIdeals(F,Expon,VarSet,DPoly) : C == T @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain PR PolynomialRing} + +<>= +)set break resume +)sys rm -f PolynomialRing.output +)spool PolynomialRing.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show PolynomialRing +--R PolynomialRing(R: Ring,E: OrderedAbelianMonoid) is a domain constructor +--R Abbreviation for PolynomialRing is PR +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for PR +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (R,%) -> % ?*? : (%,R) -> % +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ?=? : (%,%) -> Boolean +--R 1 : () -> % 0 : () -> % +--R ?^? : (%,PositiveInteger) -> % coefficient : (%,E) -> R +--R coefficients : % -> List R coerce : R -> % +--R coerce : Integer -> % coerce : % -> OutputForm +--R degree : % -> E ground : % -> R +--R ground? : % -> Boolean hash : % -> SingleInteger +--R latex : % -> String leadingCoefficient : % -> R +--R leadingMonomial : % -> % map : ((R -> R),%) -> % +--R mapExponents : ((E -> E),%) -> % minimumDegree : % -> E +--R monomial : (R,E) -> % monomial? : % -> Boolean +--R one? : % -> Boolean pomopo! : (%,R,E,%) -> % +--R recip : % -> Union(%,"failed") reductum : % -> % +--R retract : % -> R sample : () -> % +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean +--R ?*? : (%,Fraction Integer) -> % if R has ALGEBRA FRAC INT +--R ?*? : (Fraction Integer,%) -> % if R has ALGEBRA FRAC INT +--R ?*? : (NonNegativeInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % +--R ?/? : (%,R) -> % if R has FIELD +--R ?^? : (%,NonNegativeInteger) -> % +--R associates? : (%,%) -> Boolean if R has INTDOM +--R binomThmExpt : (%,%,NonNegativeInteger) -> % if R has COMRING +--R characteristic : () -> NonNegativeInteger +--R charthRoot : % -> Union(%,"failed") if R has CHARNZ +--R coerce : Fraction Integer -> % if R has ALGEBRA FRAC INT or R has RETRACT FRAC INT +--R coerce : % -> % if R has INTDOM +--R content : % -> R if R has GCDDOM +--R exquo : (%,R) -> Union(%,"failed") if R has INTDOM +--R exquo : (%,%) -> Union(%,"failed") if R has INTDOM +--R fmecg : (%,E,R,%) -> % if E has CABMON and R has INTDOM +--R numberOfMonomials : % -> NonNegativeInteger +--R primitivePart : % -> % if R has GCDDOM +--R retract : % -> Fraction Integer if R has RETRACT FRAC INT +--R retract : % -> Integer if R has RETRACT INT +--R retractIfCan : % -> Union(R,"failed") +--R retractIfCan : % -> Union(Fraction Integer,"failed") if R has RETRACT FRAC INT +--R retractIfCan : % -> Union(Integer,"failed") if R has RETRACT INT +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R unit? : % -> Boolean if R has INTDOM +--R unitCanonical : % -> % if R has INTDOM +--R unitNormal : % -> Record(unit: %,canonical: %,associate: %) if R has INTDOM +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +PolynomialRing examples +==================================================================== + +See Also: +o )show PolynomialRing + +@ + \pagehead{PolynomialRing}{PR} \pagepic{ps/v103polynomialring.ps}{PR}{1.00} {\bf See}\\ @@ -82752,6 +97812,52 @@ PolynomialRing(R:Ring,E:OrderedAbelianMonoid): T == C @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain PI PositiveInteger} + +<>= +)set break resume +)sys rm -f PositiveInteger.output +)spool PositiveInteger.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show PositiveInteger +--R PositiveInteger is a domain constructor +--R Abbreviation for PositiveInteger is PI +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for PI +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (%,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?**? : (%,PositiveInteger) -> % ?+? : (%,%) -> % +--R ? Boolean ?<=? : (%,%) -> Boolean +--R ?=? : (%,%) -> Boolean ?>? : (%,%) -> Boolean +--R ?>=? : (%,%) -> Boolean 1 : () -> % +--R ?^? : (%,PositiveInteger) -> % coerce : % -> OutputForm +--R gcd : (%,%) -> % hash : % -> SingleInteger +--R latex : % -> String max : (%,%) -> % +--R min : (%,%) -> % one? : % -> Boolean +--R recip : % -> Union(%,"failed") sample : () -> % +--R ?~=? : (%,%) -> Boolean +--R ?**? : (%,NonNegativeInteger) -> % +--R ?^? : (%,NonNegativeInteger) -> % +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +PositiveInteger examples +==================================================================== + +See Also: +o )show PositiveInteger + +@ + \pagehead{PositiveInteger}{PI} \pagepic{ps/v103positiveinteger.ps}{PI}{1.00} {\bf See}\\ @@ -82816,6 +97922,121 @@ PositiveInteger: Join(AbelianSemiGroup,OrderedSet,Monoid) with @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain PF PrimeField} + +<>= +)set break resume +)sys rm -f PrimeField.output +)spool PrimeField.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show PrimeField +--R PrimeField p: PositiveInteger is a domain constructor +--R Abbreviation for PrimeField is PF +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for PF +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (Fraction Integer,%) -> % ?*? : (%,Fraction Integer) -> % +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?**? : (%,Integer) -> % +--R ?**? : (%,PositiveInteger) -> % ?+? : (%,%) -> % +--R ?-? : (%,%) -> % -? : % -> % +--R ?/? : (%,%) -> % ?=? : (%,%) -> Boolean +--R D : % -> % D : (%,NonNegativeInteger) -> % +--R 1 : () -> % 0 : () -> % +--R ?^? : (%,Integer) -> % ?^? : (%,PositiveInteger) -> % +--R algebraic? : % -> Boolean associates? : (%,%) -> Boolean +--R basis : () -> Vector % charthRoot : % -> % +--R coerce : Fraction Integer -> % coerce : % -> % +--R coerce : Integer -> % coerce : % -> OutputForm +--R convert : % -> Integer coordinates : % -> Vector % +--R createPrimitiveElement : () -> % degree : % -> PositiveInteger +--R differentiate : % -> % dimension : () -> CardinalNumber +--R factor : % -> Factored % gcd : List % -> % +--R gcd : (%,%) -> % hash : % -> SingleInteger +--R inGroundField? : % -> Boolean index : PositiveInteger -> % +--R init : () -> % inv : % -> % +--R latex : % -> String lcm : List % -> % +--R lcm : (%,%) -> % lookup : % -> PositiveInteger +--R norm : % -> % one? : % -> Boolean +--R order : % -> PositiveInteger prime? : % -> Boolean +--R primeFrobenius : % -> % primitive? : % -> Boolean +--R primitiveElement : () -> % ?quo? : (%,%) -> % +--R random : () -> % recip : % -> Union(%,"failed") +--R ?rem? : (%,%) -> % represents : Vector % -> % +--R retract : % -> % sample : () -> % +--R size : () -> NonNegativeInteger sizeLess? : (%,%) -> Boolean +--R squareFree : % -> Factored % squareFreePart : % -> % +--R trace : % -> % transcendent? : % -> Boolean +--R unit? : % -> Boolean unitCanonical : % -> % +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean +--R ?*? : (NonNegativeInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % +--R Frobenius : % -> % if $ has FINITE +--R Frobenius : (%,NonNegativeInteger) -> % if $ has FINITE +--R ?^? : (%,NonNegativeInteger) -> % +--R basis : PositiveInteger -> Vector % +--R characteristic : () -> NonNegativeInteger +--R charthRoot : % -> Union(%,"failed") +--R conditionP : Matrix % -> Union(Vector %,"failed") +--R coordinates : Vector % -> Matrix % +--R createNormalElement : () -> % if $ has FINITE +--R definingPolynomial : () -> SparseUnivariatePolynomial % +--R degree : % -> OnePointCompletion PositiveInteger +--R differentiate : (%,NonNegativeInteger) -> % +--R discreteLog : % -> NonNegativeInteger +--R discreteLog : (%,%) -> Union(NonNegativeInteger,"failed") +--R divide : (%,%) -> Record(quotient: %,remainder: %) +--R euclideanSize : % -> NonNegativeInteger +--R expressIdealMember : (List %,%) -> Union(List %,"failed") +--R exquo : (%,%) -> Union(%,"failed") +--R extendedEuclidean : (%,%,%) -> Union(Record(coef1: %,coef2: %),"failed") +--R extendedEuclidean : (%,%) -> Record(coef1: %,coef2: %,generator: %) +--R extensionDegree : () -> OnePointCompletion PositiveInteger +--R extensionDegree : () -> PositiveInteger +--R factorsOfCyclicGroupSize : () -> List Record(factor: Integer,exponent: Integer) +--R gcdPolynomial : (SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial % +--R generator : () -> % if $ has FINITE +--R linearAssociatedExp : (%,SparseUnivariatePolynomial %) -> % if $ has FINITE +--R linearAssociatedLog : % -> SparseUnivariatePolynomial % if $ has FINITE +--R linearAssociatedLog : (%,%) -> Union(SparseUnivariatePolynomial %,"failed") if $ has FINITE +--R linearAssociatedOrder : % -> SparseUnivariatePolynomial % if $ has FINITE +--R minimalPolynomial : % -> SparseUnivariatePolynomial % +--R minimalPolynomial : (%,PositiveInteger) -> SparseUnivariatePolynomial % if $ has FINITE +--R multiEuclidean : (List %,%) -> Union(List %,"failed") +--R nextItem : % -> Union(%,"failed") +--R norm : (%,PositiveInteger) -> % if $ has FINITE +--R normal? : % -> Boolean if $ has FINITE +--R normalElement : () -> % if $ has FINITE +--R order : % -> OnePointCompletion PositiveInteger +--R primeFrobenius : (%,NonNegativeInteger) -> % +--R principalIdeal : List % -> Record(coef: List %,generator: %) +--R representationType : () -> Union("prime",polynomial,normal,cyclic) +--R retractIfCan : % -> Union(%,"failed") +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R tableForDiscreteLogarithm : Integer -> Table(PositiveInteger,NonNegativeInteger) +--R trace : (%,PositiveInteger) -> % if $ has FINITE +--R transcendenceDegree : () -> NonNegativeInteger +--R unitNormal : % -> Record(unit: %,canonical: %,associate: %) +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +PrimeField examples +==================================================================== + +See Also: +o )show PrimeField + +@ + \pagehead{PrimeField}{PF} \pagepic{ps/v103primefield.ps}{PF}{1.00} {\bf See}\\ @@ -82947,6 +98168,111 @@ PrimeField(p:PositiveInteger): Exp == Impl where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain PRIMARR PrimitiveArray} + +<>= +)set break resume +)sys rm -f PrimitiveArray.output +)spool PrimitiveArray.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show PrimitiveArray +--R PrimitiveArray S: Type is a domain constructor +--R Abbreviation for PrimitiveArray is PRIMARR +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for PRIMARR +--R +--R------------------------------- Operations -------------------------------- +--R concat : List % -> % concat : (%,%) -> % +--R concat : (S,%) -> % concat : (%,S) -> % +--R construct : List S -> % copy : % -> % +--R delete : (%,Integer) -> % ?.? : (%,Integer) -> S +--R elt : (%,Integer,S) -> S empty : () -> % +--R empty? : % -> Boolean entries : % -> List S +--R eq? : (%,%) -> Boolean index? : (Integer,%) -> Boolean +--R indices : % -> List Integer insert : (%,%,Integer) -> % +--R insert : (S,%,Integer) -> % map : (((S,S) -> S),%,%) -> % +--R map : ((S -> S),%) -> % new : (NonNegativeInteger,S) -> % +--R qelt : (%,Integer) -> S reverse : % -> % +--R sample : () -> % +--R #? : % -> NonNegativeInteger if $ has finiteAggregate +--R ? Boolean if S has ORDSET +--R ?<=? : (%,%) -> Boolean if S has ORDSET +--R ?=? : (%,%) -> Boolean if S has SETCAT +--R ?>? : (%,%) -> Boolean if S has ORDSET +--R ?>=? : (%,%) -> Boolean if S has ORDSET +--R any? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate +--R coerce : % -> OutputForm if S has SETCAT +--R convert : % -> InputForm if S has KONVERT INFORM +--R copyInto! : (%,%,Integer) -> % if $ has shallowlyMutable +--R count : (S,%) -> NonNegativeInteger if $ has finiteAggregate and S has SETCAT +--R count : ((S -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate +--R delete : (%,UniversalSegment Integer) -> % +--R ?.? : (%,UniversalSegment Integer) -> % +--R entry? : (S,%) -> Boolean if $ has finiteAggregate and S has SETCAT +--R eval : (%,List S,List S) -> % if S has EVALAB S and S has SETCAT +--R eval : (%,S,S) -> % if S has EVALAB S and S has SETCAT +--R eval : (%,Equation S) -> % if S has EVALAB S and S has SETCAT +--R eval : (%,List Equation S) -> % if S has EVALAB S and S has SETCAT +--R every? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate +--R fill! : (%,S) -> % if $ has shallowlyMutable +--R find : ((S -> Boolean),%) -> Union(S,"failed") +--R first : % -> S if Integer has ORDSET +--R hash : % -> SingleInteger if S has SETCAT +--R latex : % -> String if S has SETCAT +--R less? : (%,NonNegativeInteger) -> Boolean +--R map! : ((S -> S),%) -> % if $ has shallowlyMutable +--R max : (%,%) -> % if S has ORDSET +--R maxIndex : % -> Integer if Integer has ORDSET +--R member? : (S,%) -> Boolean if $ has finiteAggregate and S has SETCAT +--R members : % -> List S if $ has finiteAggregate +--R merge : (%,%) -> % if S has ORDSET +--R merge : (((S,S) -> Boolean),%,%) -> % +--R min : (%,%) -> % if S has ORDSET +--R minIndex : % -> Integer if Integer has ORDSET +--R more? : (%,NonNegativeInteger) -> Boolean +--R parts : % -> List S if $ has finiteAggregate +--R position : (S,%,Integer) -> Integer if S has SETCAT +--R position : (S,%) -> Integer if S has SETCAT +--R position : ((S -> Boolean),%) -> Integer +--R qsetelt! : (%,Integer,S) -> S if $ has shallowlyMutable +--R reduce : (((S,S) -> S),%) -> S if $ has finiteAggregate +--R reduce : (((S,S) -> S),%,S) -> S if $ has finiteAggregate +--R reduce : (((S,S) -> S),%,S,S) -> S if $ has finiteAggregate and S has SETCAT +--R remove : ((S -> Boolean),%) -> % if $ has finiteAggregate +--R remove : (S,%) -> % if $ has finiteAggregate and S has SETCAT +--R removeDuplicates : % -> % if $ has finiteAggregate and S has SETCAT +--R reverse! : % -> % if $ has shallowlyMutable +--R select : ((S -> Boolean),%) -> % if $ has finiteAggregate +--R setelt : (%,UniversalSegment Integer,S) -> S if $ has shallowlyMutable +--R setelt : (%,Integer,S) -> S if $ has shallowlyMutable +--R size? : (%,NonNegativeInteger) -> Boolean +--R sort : % -> % if S has ORDSET +--R sort : (((S,S) -> Boolean),%) -> % +--R sort! : % -> % if $ has shallowlyMutable and S has ORDSET +--R sort! : (((S,S) -> Boolean),%) -> % if $ has shallowlyMutable +--R sorted? : % -> Boolean if S has ORDSET +--R sorted? : (((S,S) -> Boolean),%) -> Boolean +--R swap! : (%,Integer,Integer) -> Void if $ has shallowlyMutable +--R ?~=? : (%,%) -> Boolean if S has SETCAT +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +PrimitiveArray examples +==================================================================== + +See Also: +o )show PrimitiveArray + +@ + \pagehead{PrimitiveArray}{PRIMARR} \pagepic{ps/v103primitivearray.ps}{PRIMARR}{1.00} {\bf See}\\ @@ -83059,6 +98385,7 @@ PrimitiveArray(S:Type): OneDimensionalArrayAggregate S == add @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain PRODUCT Product} + <>= )set break resume )sys rm -f Product.output @@ -83302,6 +98629,7 @@ Product (A:SetCategory,B:SetCategory) : C == T @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain PROJPL ProjectivePlane} + <>= )set break resume )sys rm -f ProjectivePlane.output @@ -83399,6 +98727,7 @@ ProjectivePlane(K):Exports == Implementation where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain PROJPLPS ProjectivePlaneOverPseudoAlgebraicClosureOfFiniteField} + <>= )set break resume )sys rm -f ProjectivePlaneOverPseudoAlgebraicClosureOfFiniteField.output @@ -83502,6 +98831,7 @@ ProjectivePlaneOverPseudoAlgebraicClosureOfFiniteField(K):Exp == Impl where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain PROJSP ProjectiveSpace} + <>= )set break resume )sys rm -f ProjectiveSpace.output @@ -83713,6 +99043,7 @@ ProjectiveSpace(dim,K):Exports == Implementation where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain PACEXT PseudoAlgebraicClosureOfAlgExtOfRationalNumber} + <>= )set break resume )sys rm -f PseudoAlgebraicClosureOfAlgExtOfRationalNumber.output @@ -84052,6 +99383,7 @@ PseudoAlgebraicClosureOfAlgExtOfRationalNumber(downLevel:K):Exp == Impl where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain PACOFF PseudoAlgebraicClosureOfFiniteField} + <>= )set break resume )sys rm -f PseudoAlgebraicClosureOfFiniteField.output @@ -84590,6 +99922,7 @@ PseudoAlgebraicClosureOfFiniteField(K):Exports == Implementation where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain PACRAT PseudoAlgebraicClosureOfRationalNumber} + <>= )set break resume )sys rm -f PseudoAlgebraicClosureOfRationalNumber.output @@ -85064,6 +100397,50 @@ PseudoAlgebraicClosureOfRationalNumber:Exports == Implementation where \chapter{Chapter Q} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain QFORM QuadraticForm} + +<>= +)set break resume +)sys rm -f QuadraticForm.output +)spool QuadraticForm.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show QuadraticForm +--R QuadraticForm(n: PositiveInteger,K: Field) is a domain constructor +--R Abbreviation for QuadraticForm is QFORM +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for QFORM +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (Integer,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ?=? : (%,%) -> Boolean +--R 0 : () -> % coerce : % -> OutputForm +--R ?.? : (%,DirectProduct(n,K)) -> K hash : % -> SingleInteger +--R latex : % -> String matrix : % -> SquareMatrix(n,K) +--R sample : () -> % zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean +--R ?*? : (NonNegativeInteger,%) -> % +--R quadraticForm : SquareMatrix(n,K) -> % +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +QuadraticForm examples +==================================================================== + +See Also: +o )show QuadraticForm + +@ + \pagehead{QuadraticForm}{QFORM} \pagepic{ps/v103quadraticform.ps}{QFORM}{1.00} {\bf See}\\ @@ -85140,6 +100517,49 @@ QuadraticForm(n, K): T == Impl where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain QALGSET QuasiAlgebraicSet} + +<>= +)set break resume +)sys rm -f QuasiAlgebraicSet.output +)spool QuasiAlgebraicSet.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show QuasiAlgebraicSet +--R QuasiAlgebraicSet(R: GcdDomain,Var: OrderedSet,Expon: OrderedAbelianMonoidSup,Dpoly: PolynomialCategory(R,Expon,Var)) is a domain constructor +--R Abbreviation for QuasiAlgebraicSet is QALGSET +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for QALGSET +--R +--R------------------------------- Operations -------------------------------- +--R ?=? : (%,%) -> Boolean coerce : % -> OutputForm +--R definingInequation : % -> Dpoly empty : () -> % +--R empty? : % -> Boolean hash : % -> SingleInteger +--R idealSimplify : % -> % latex : % -> String +--R ?~=? : (%,%) -> Boolean +--R definingEquations : % -> List Dpoly +--R quasiAlgebraicSet : (List Dpoly,Dpoly) -> % +--R setStatus : (%,Union(Boolean,"failed")) -> % +--R simplify : % -> % if R has CHARZ and R has EUCDOM +--R status : % -> Union(Boolean,"failed") +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +QuasiAlgebraicSet examples +==================================================================== + +See Also: +o )show QuasiAlgebraicSet + +@ + \pagehead{QuasiAlgebraicSet}{QALGSET} \pagepic{ps/v103quasialgebraicset.ps}{QALGSET}{1.00} @@ -85355,6 +100775,7 @@ QuasiAlgebraicSet(R, Var,Expon,Dpoly) : C == T @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain QUAT Quaternion} + <>= )set break resume )sys rm -f Quaternion.output @@ -85697,6 +101118,41 @@ Quaternion(R:CommutativeRing): QuaternionCategory(R) == add @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain QEQUAT QueryEquation} + +<>= +)set break resume +)sys rm -f QueryEquation.output +)spool QueryEquation.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show QueryEquation +--R QueryEquation is a domain constructor +--R Abbreviation for QueryEquation is QEQUAT +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for QEQUAT +--R +--R------------------------------- Operations -------------------------------- +--R coerce : % -> OutputForm equation : (Symbol,String) -> % +--R value : % -> String variable : % -> Symbol +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +QueryEquation examples +==================================================================== + +See Also: +o )show QueryEquation + +@ + \pagehead{QueryEquation}{QEQUAT} \pagepic{ps/v103queryequation.ps}{QEQUAT}{1.00} {\bf See}\\ @@ -85742,6 +101198,7 @@ QueryEquation(): Exports == Implementation where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain QUEUE Queue} + <>= )set break resume )sys rm -f Queue.output @@ -86645,6 +102102,187 @@ Queue(S:SetCategory): QueueAggregate S with \chapter{Chapter R} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain RADFF RadicalFunctionField} + +<>= +)set break resume +)sys rm -f RadicalFunctionField.output +)spool RadicalFunctionField.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show RadicalFunctionField +--R RadicalFunctionField(F: UniqueFactorizationDomain,UP: UnivariatePolynomialCategory F,UPUP: UnivariatePolynomialCategory Fraction UP,radicnd: Fraction UP,n: NonNegativeInteger) is a domain constructor +--R Abbreviation for RadicalFunctionField is RADFF +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for RADFF +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (Fraction UP,%) -> % ?*? : (%,Fraction UP) -> % +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ?=? : (%,%) -> Boolean +--R 1 : () -> % 0 : () -> % +--R ?^? : (%,PositiveInteger) -> % basis : () -> Vector % +--R branchPoint? : UP -> Boolean branchPoint? : F -> Boolean +--R coerce : Fraction UP -> % coerce : Integer -> % +--R coerce : % -> OutputForm convert : UPUP -> % +--R convert : % -> UPUP convert : Vector Fraction UP -> % +--R convert : % -> Vector Fraction UP definingPolynomial : () -> UPUP +--R discriminant : () -> Fraction UP elt : (%,F,F) -> F +--R generator : () -> % genus : () -> NonNegativeInteger +--R hash : % -> SingleInteger integral? : (%,UP) -> Boolean +--R integral? : (%,F) -> Boolean integral? : % -> Boolean +--R integralBasis : () -> Vector % latex : % -> String +--R lift : % -> UPUP norm : % -> Fraction UP +--R one? : % -> Boolean primitivePart : % -> % +--R ramified? : UP -> Boolean ramified? : F -> Boolean +--R rank : () -> PositiveInteger rationalPoint? : (F,F) -> Boolean +--R recip : % -> Union(%,"failed") reduce : UPUP -> % +--R represents : (Vector UP,UP) -> % retract : % -> Fraction UP +--R sample : () -> % singular? : UP -> Boolean +--R singular? : F -> Boolean trace : % -> Fraction UP +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean +--R ?*? : (%,Fraction Integer) -> % if Fraction UP has FIELD +--R ?*? : (Fraction Integer,%) -> % if Fraction UP has FIELD +--R ?*? : (NonNegativeInteger,%) -> % +--R ?**? : (%,Integer) -> % if Fraction UP has FIELD +--R ?**? : (%,NonNegativeInteger) -> % +--R ?/? : (%,%) -> % if Fraction UP has FIELD +--R D : % -> % if Fraction UP has DIFRING and Fraction UP has FIELD or Fraction UP has FFIELDC +--R D : (%,NonNegativeInteger) -> % if Fraction UP has DIFRING and Fraction UP has FIELD or Fraction UP has FFIELDC +--R D : (%,Symbol) -> % if Fraction UP has FIELD and Fraction UP has PDRING SYMBOL +--R D : (%,List Symbol) -> % if Fraction UP has FIELD and Fraction UP has PDRING SYMBOL +--R D : (%,Symbol,NonNegativeInteger) -> % if Fraction UP has FIELD and Fraction UP has PDRING SYMBOL +--R D : (%,List Symbol,List NonNegativeInteger) -> % if Fraction UP has FIELD and Fraction UP has PDRING SYMBOL +--R D : (%,(Fraction UP -> Fraction UP)) -> % if Fraction UP has FIELD +--R D : (%,(Fraction UP -> Fraction UP),NonNegativeInteger) -> % if Fraction UP has FIELD +--R ?^? : (%,Integer) -> % if Fraction UP has FIELD +--R ?^? : (%,NonNegativeInteger) -> % +--R absolutelyIrreducible? : () -> Boolean +--R algSplitSimple : (%,(UP -> UP)) -> Record(num: %,den: UP,derivden: UP,gd: UP) +--R associates? : (%,%) -> Boolean if Fraction UP has FIELD +--R branchPointAtInfinity? : () -> Boolean +--R characteristic : () -> NonNegativeInteger +--R characteristicPolynomial : % -> UPUP +--R charthRoot : % -> Union(%,"failed") if Fraction UP has CHARNZ +--R charthRoot : % -> % if Fraction UP has FFIELDC +--R coerce : % -> % if Fraction UP has FIELD +--R coerce : Fraction Integer -> % if Fraction UP has FIELD or Fraction UP has RETRACT FRAC INT +--R complementaryBasis : Vector % -> Vector % +--R conditionP : Matrix % -> Union(Vector %,"failed") if Fraction UP has FFIELDC +--R coordinates : Vector % -> Matrix Fraction UP +--R coordinates : % -> Vector Fraction UP +--R coordinates : (Vector %,Vector %) -> Matrix Fraction UP +--R coordinates : (%,Vector %) -> Vector Fraction UP +--R createPrimitiveElement : () -> % if Fraction UP has FFIELDC +--R derivationCoordinates : (Vector %,(Fraction UP -> Fraction UP)) -> Matrix Fraction UP if Fraction UP has FIELD +--R differentiate : % -> % if Fraction UP has DIFRING and Fraction UP has FIELD or Fraction UP has FFIELDC +--R differentiate : (%,NonNegativeInteger) -> % if Fraction UP has DIFRING and Fraction UP has FIELD or Fraction UP has FFIELDC +--R differentiate : (%,Symbol) -> % if Fraction UP has FIELD and Fraction UP has PDRING SYMBOL +--R differentiate : (%,List Symbol) -> % if Fraction UP has FIELD and Fraction UP has PDRING SYMBOL +--R differentiate : (%,Symbol,NonNegativeInteger) -> % if Fraction UP has FIELD and Fraction UP has PDRING SYMBOL +--R differentiate : (%,List Symbol,List NonNegativeInteger) -> % if Fraction UP has FIELD and Fraction UP has PDRING SYMBOL +--R differentiate : (%,(UP -> UP)) -> % +--R differentiate : (%,(Fraction UP -> Fraction UP)) -> % if Fraction UP has FIELD +--R differentiate : (%,(Fraction UP -> Fraction UP),NonNegativeInteger) -> % if Fraction UP has FIELD +--R discreteLog : (%,%) -> Union(NonNegativeInteger,"failed") if Fraction UP has FFIELDC +--R discreteLog : % -> NonNegativeInteger if Fraction UP has FFIELDC +--R discriminant : Vector % -> Fraction UP +--R divide : (%,%) -> Record(quotient: %,remainder: %) if Fraction UP has FIELD +--R elliptic : () -> Union(UP,"failed") +--R euclideanSize : % -> NonNegativeInteger if Fraction UP has FIELD +--R expressIdealMember : (List %,%) -> Union(List %,"failed") if Fraction UP has FIELD +--R exquo : (%,%) -> Union(%,"failed") if Fraction UP has FIELD +--R extendedEuclidean : (%,%) -> Record(coef1: %,coef2: %,generator: %) if Fraction UP has FIELD +--R extendedEuclidean : (%,%,%) -> Union(Record(coef1: %,coef2: %),"failed") if Fraction UP has FIELD +--R factor : % -> Factored % if Fraction UP has FIELD +--R factorsOfCyclicGroupSize : () -> List Record(factor: Integer,exponent: Integer) if Fraction UP has FFIELDC +--R gcd : (%,%) -> % if Fraction UP has FIELD +--R gcd : List % -> % if Fraction UP has FIELD +--R gcdPolynomial : (SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial % if Fraction UP has FIELD +--R hyperelliptic : () -> Union(UP,"failed") +--R index : PositiveInteger -> % if Fraction UP has FINITE +--R init : () -> % if Fraction UP has FFIELDC +--R integralAtInfinity? : % -> Boolean +--R integralBasisAtInfinity : () -> Vector % +--R integralCoordinates : % -> Record(num: Vector UP,den: UP) +--R integralDerivationMatrix : (UP -> UP) -> Record(num: Matrix UP,den: UP) +--R integralMatrix : () -> Matrix Fraction UP +--R integralMatrixAtInfinity : () -> Matrix Fraction UP +--R integralRepresents : (Vector UP,UP) -> % +--R inv : % -> % if Fraction UP has FIELD +--R inverseIntegralMatrix : () -> Matrix Fraction UP +--R inverseIntegralMatrixAtInfinity : () -> Matrix Fraction UP +--R lcm : (%,%) -> % if Fraction UP has FIELD +--R lcm : List % -> % if Fraction UP has FIELD +--R lookup : % -> PositiveInteger if Fraction UP has FINITE +--R minimalPolynomial : % -> UPUP if Fraction UP has FIELD +--R multiEuclidean : (List %,%) -> Union(List %,"failed") if Fraction UP has FIELD +--R nextItem : % -> Union(%,"failed") if Fraction UP has FFIELDC +--R nonSingularModel : Symbol -> List Polynomial F if F has FIELD +--R normalizeAtInfinity : Vector % -> Vector % +--R numberOfComponents : () -> NonNegativeInteger +--R order : % -> OnePointCompletion PositiveInteger if Fraction UP has FFIELDC +--R order : % -> PositiveInteger if Fraction UP has FFIELDC +--R prime? : % -> Boolean if Fraction UP has FIELD +--R primeFrobenius : % -> % if Fraction UP has FFIELDC +--R primeFrobenius : (%,NonNegativeInteger) -> % if Fraction UP has FFIELDC +--R primitive? : % -> Boolean if Fraction UP has FFIELDC +--R primitiveElement : () -> % if Fraction UP has FFIELDC +--R principalIdeal : List % -> Record(coef: List %,generator: %) if Fraction UP has FIELD +--R ?quo? : (%,%) -> % if Fraction UP has FIELD +--R ramifiedAtInfinity? : () -> Boolean +--R random : () -> % if Fraction UP has FINITE +--R rationalPoints : () -> List List F if F has FINITE +--R reduce : Fraction UPUP -> Union(%,"failed") if Fraction UP has FIELD +--R reduceBasisAtInfinity : Vector % -> Vector % +--R reducedSystem : Matrix % -> Matrix Fraction UP +--R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix Fraction UP,vec: Vector Fraction UP) +--R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix Integer,vec: Vector Integer) if Fraction UP has LINEXP INT +--R reducedSystem : Matrix % -> Matrix Integer if Fraction UP has LINEXP INT +--R regularRepresentation : % -> Matrix Fraction UP +--R regularRepresentation : (%,Vector %) -> Matrix Fraction UP +--R ?rem? : (%,%) -> % if Fraction UP has FIELD +--R representationType : () -> Union("prime",polynomial,normal,cyclic) if Fraction UP has FFIELDC +--R represents : Vector Fraction UP -> % +--R represents : (Vector Fraction UP,Vector %) -> % +--R retract : % -> Fraction Integer if Fraction UP has RETRACT FRAC INT +--R retract : % -> Integer if Fraction UP has RETRACT INT +--R retractIfCan : % -> Union(Fraction UP,"failed") +--R retractIfCan : % -> Union(Fraction Integer,"failed") if Fraction UP has RETRACT FRAC INT +--R retractIfCan : % -> Union(Integer,"failed") if Fraction UP has RETRACT INT +--R singularAtInfinity? : () -> Boolean +--R size : () -> NonNegativeInteger if Fraction UP has FINITE +--R sizeLess? : (%,%) -> Boolean if Fraction UP has FIELD +--R squareFree : % -> Factored % if Fraction UP has FIELD +--R squareFreePart : % -> % if Fraction UP has FIELD +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R tableForDiscreteLogarithm : Integer -> Table(PositiveInteger,NonNegativeInteger) if Fraction UP has FFIELDC +--R traceMatrix : () -> Matrix Fraction UP +--R traceMatrix : Vector % -> Matrix Fraction UP +--R unit? : % -> Boolean if Fraction UP has FIELD +--R unitCanonical : % -> % if Fraction UP has FIELD +--R unitNormal : % -> Record(unit: %,canonical: %,associate: %) if Fraction UP has FIELD +--R yCoordinates : % -> Record(num: Vector UP,den: UP) +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +RadicalFunctionField examples +==================================================================== + +See Also: +o )show RadicalFunctionField + +@ + \pagehead{RadicalFunctionField}{RADFF} \pagepic{ps/v103radicalfunctionfield.ps}{RADFF}{1.00} {\bf See}\\ @@ -86977,6 +102615,7 @@ RadicalFunctionField(F, UP, UPUP, radicnd, n): Exports == Impl where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain RADIX RadixExpansion} + <>= )set break resume )sys rm -f RadixExpansion.output @@ -87647,6 +103286,7 @@ particular problem to solve or want to use these versions. Be aware that approximations behave as post-processing and that all computations are done excatly. They can thus be quite time consuming when depending on several "real roots". + <>= )set break resume )sys rm -f RealClosure.output @@ -89221,6 +104861,86 @@ RealClosure(TheField): PUB == PRIV where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain RMATRIX RectangularMatrix} + +<>= +)set break resume +)sys rm -f RectangularMatrix.output +)spool RectangularMatrix.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show RectangularMatrix +--R RectangularMatrix(m: NonNegativeInteger,n: NonNegativeInteger,R: Ring) is a domain constructor +--R Abbreviation for RectangularMatrix is RMATRIX +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for RMATRIX +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (%,R) -> % ?*? : (R,%) -> % +--R ?*? : (Integer,%) -> % ?*? : (PositiveInteger,%) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ?=? : (%,%) -> Boolean +--R 0 : () -> % antisymmetric? : % -> Boolean +--R coerce : % -> Matrix R coerce : % -> OutputForm +--R copy : % -> % diagonal? : % -> Boolean +--R elt : (%,Integer,Integer,R) -> R elt : (%,Integer,Integer) -> R +--R empty : () -> % empty? : % -> Boolean +--R eq? : (%,%) -> Boolean hash : % -> SingleInteger +--R latex : % -> String listOfLists : % -> List List R +--R map : (((R,R) -> R),%,%) -> % map : ((R -> R),%) -> % +--R matrix : List List R -> % maxColIndex : % -> Integer +--R maxRowIndex : % -> Integer minColIndex : % -> Integer +--R minRowIndex : % -> Integer ncols : % -> NonNegativeInteger +--R nrows : % -> NonNegativeInteger qelt : (%,Integer,Integer) -> R +--R rectangularMatrix : Matrix R -> % sample : () -> % +--R square? : % -> Boolean symmetric? : % -> Boolean +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean +--R #? : % -> NonNegativeInteger if $ has finiteAggregate +--R ?*? : (NonNegativeInteger,%) -> % +--R ?/? : (%,R) -> % if R has FIELD +--R any? : ((R -> Boolean),%) -> Boolean if $ has finiteAggregate +--R column : (%,Integer) -> DirectProduct(m,R) +--R convert : % -> InputForm if R has KONVERT INFORM +--R count : ((R -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate +--R count : (R,%) -> NonNegativeInteger if $ has finiteAggregate and R has SETCAT +--R dimension : () -> CardinalNumber if R has FIELD +--R eval : (%,List Equation R) -> % if R has EVALAB R and R has SETCAT +--R eval : (%,Equation R) -> % if R has EVALAB R and R has SETCAT +--R eval : (%,R,R) -> % if R has EVALAB R and R has SETCAT +--R eval : (%,List R,List R) -> % if R has EVALAB R and R has SETCAT +--R every? : ((R -> Boolean),%) -> Boolean if $ has finiteAggregate +--R exquo : (%,R) -> Union(%,"failed") if R has INTDOM +--R less? : (%,NonNegativeInteger) -> Boolean +--R map! : ((R -> R),%) -> % if $ has shallowlyMutable +--R member? : (R,%) -> Boolean if $ has finiteAggregate and R has SETCAT +--R members : % -> List R if $ has finiteAggregate +--R more? : (%,NonNegativeInteger) -> Boolean +--R nullSpace : % -> List DirectProduct(m,R) if R has INTDOM +--R nullity : % -> NonNegativeInteger if R has INTDOM +--R parts : % -> List R if $ has finiteAggregate +--R rank : % -> NonNegativeInteger if R has INTDOM +--R row : (%,Integer) -> DirectProduct(n,R) +--R rowEchelon : % -> % if R has EUCDOM +--R size? : (%,NonNegativeInteger) -> Boolean +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +RectangularMatrix examples +==================================================================== + +See Also: +o )show RectangularMatrix + +@ + \pagehead{RectangularMatrix}{RMATRIX} \pagepic{ps/v103rectangularmatrix.ps}{RMATRIX}{1.00} {\bf See}\\ @@ -89385,6 +105105,46 @@ RectangularMatrix(m,n,R): Exports == Implementation where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain REF Reference} + +<>= +)set break resume +)sys rm -f Reference.output +)spool Reference.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show Reference +--R Reference S: Type is a domain constructor +--R Abbreviation for Reference is REF +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for REF +--R +--R------------------------------- Operations -------------------------------- +--R ?=? : (%,%) -> Boolean deref : % -> S +--R elt : % -> S ref : S -> % +--R setelt : (%,S) -> S setref : (%,S) -> S +--R coerce : % -> OutputForm if S has SETCAT +--R hash : % -> SingleInteger if S has SETCAT +--R latex : % -> String if S has SETCAT +--R ?~=? : (%,%) -> Boolean if S has SETCAT +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +Reference examples +==================================================================== + +See Also: +o )show Reference + +@ + \pagehead{Reference}{REF} \pagepic{ps/v103reference.ps}{REF}{1.00} {\bf See}\\ @@ -89461,6 +105221,150 @@ Reference(S:Type): Type with @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain RGCHAIN RegularChain} + +<>= +)set break resume +)sys rm -f RegularChain.output +)spool RegularChain.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show RegularChain +--R RegularChain(R: GcdDomain,ls: List Symbol) is a domain constructor +--R Abbreviation for RegularChain is RGCHAIN +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for RGCHAIN +--R +--R------------------------------- Operations -------------------------------- +--R ?=? : (%,%) -> Boolean coerce : % -> OutputForm +--R collectQuasiMonic : % -> % copy : % -> % +--R degree : % -> NonNegativeInteger empty : () -> % +--R empty? : % -> Boolean eq? : (%,%) -> Boolean +--R hash : % -> SingleInteger headReduced? : % -> Boolean +--R infRittWu? : (%,%) -> Boolean initiallyReduced? : % -> Boolean +--R latex : % -> String normalized? : % -> Boolean +--R purelyAlgebraic? : % -> Boolean rest : % -> Union(%,"failed") +--R sample : () -> % stronglyReduced? : % -> Boolean +--R trivialIdeal? : % -> Boolean ?~=? : (%,%) -> Boolean +--R #? : % -> NonNegativeInteger if $ has finiteAggregate +--R algebraic? : (OrderedVariableList ls,%) -> Boolean +--R algebraicCoefficients? : (NewSparseMultivariatePolynomial(R,OrderedVariableList ls),%) -> Boolean +--R algebraicVariables : % -> List OrderedVariableList ls +--R any? : ((NewSparseMultivariatePolynomial(R,OrderedVariableList ls) -> Boolean),%) -> Boolean if $ has finiteAggregate +--R augment : (List NewSparseMultivariatePolynomial(R,OrderedVariableList ls),List %) -> List % +--R augment : (List NewSparseMultivariatePolynomial(R,OrderedVariableList ls),%) -> List % +--R augment : (NewSparseMultivariatePolynomial(R,OrderedVariableList ls),List %) -> List % +--R augment : (NewSparseMultivariatePolynomial(R,OrderedVariableList ls),%) -> List % +--R autoReduced? : (%,((NewSparseMultivariatePolynomial(R,OrderedVariableList ls),List NewSparseMultivariatePolynomial(R,OrderedVariableList ls)) -> Boolean)) -> Boolean +--R basicSet : (List NewSparseMultivariatePolynomial(R,OrderedVariableList ls),(NewSparseMultivariatePolynomial(R,OrderedVariableList ls) -> Boolean),((NewSparseMultivariatePolynomial(R,OrderedVariableList ls),NewSparseMultivariatePolynomial(R,OrderedVariableList ls)) -> Boolean)) -> Union(Record(bas: %,top: List NewSparseMultivariatePolynomial(R,OrderedVariableList ls)),"failed") +--R basicSet : (List NewSparseMultivariatePolynomial(R,OrderedVariableList ls),((NewSparseMultivariatePolynomial(R,OrderedVariableList ls),NewSparseMultivariatePolynomial(R,OrderedVariableList ls)) -> Boolean)) -> Union(Record(bas: %,top: List NewSparseMultivariatePolynomial(R,OrderedVariableList ls)),"failed") +--R coHeight : % -> NonNegativeInteger if OrderedVariableList ls has FINITE +--R coerce : % -> List NewSparseMultivariatePolynomial(R,OrderedVariableList ls) +--R collect : (%,OrderedVariableList ls) -> % +--R collectUnder : (%,OrderedVariableList ls) -> % +--R collectUpper : (%,OrderedVariableList ls) -> % +--R construct : List NewSparseMultivariatePolynomial(R,OrderedVariableList ls) -> % +--R convert : % -> InputForm if NewSparseMultivariatePolynomial(R,OrderedVariableList ls) has KONVERT INFORM +--R count : ((NewSparseMultivariatePolynomial(R,OrderedVariableList ls) -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate +--R count : (NewSparseMultivariatePolynomial(R,OrderedVariableList ls),%) -> NonNegativeInteger if $ has finiteAggregate and NewSparseMultivariatePolynomial(R,OrderedVariableList ls) has SETCAT +--R eval : (%,List Equation NewSparseMultivariatePolynomial(R,OrderedVariableList ls)) -> % if NewSparseMultivariatePolynomial(R,OrderedVariableList ls) has EVALAB NSMP(R,OVAR ls) and NewSparseMultivariatePolynomial(R,OrderedVariableList ls) has SETCAT +--R eval : (%,Equation NewSparseMultivariatePolynomial(R,OrderedVariableList ls)) -> % if NewSparseMultivariatePolynomial(R,OrderedVariableList ls) has EVALAB NSMP(R,OVAR ls) and NewSparseMultivariatePolynomial(R,OrderedVariableList ls) has SETCAT +--R eval : (%,NewSparseMultivariatePolynomial(R,OrderedVariableList ls),NewSparseMultivariatePolynomial(R,OrderedVariableList ls)) -> % if NewSparseMultivariatePolynomial(R,OrderedVariableList ls) has EVALAB NSMP(R,OVAR ls) and NewSparseMultivariatePolynomial(R,OrderedVariableList ls) has SETCAT +--R eval : (%,List NewSparseMultivariatePolynomial(R,OrderedVariableList ls),List NewSparseMultivariatePolynomial(R,OrderedVariableList ls)) -> % if NewSparseMultivariatePolynomial(R,OrderedVariableList ls) has EVALAB NSMP(R,OVAR ls) and NewSparseMultivariatePolynomial(R,OrderedVariableList ls) has SETCAT +--R every? : ((NewSparseMultivariatePolynomial(R,OrderedVariableList ls) -> Boolean),%) -> Boolean if $ has finiteAggregate +--R extend : (List NewSparseMultivariatePolynomial(R,OrderedVariableList ls),List %) -> List % +--R extend : (List NewSparseMultivariatePolynomial(R,OrderedVariableList ls),%) -> List % +--R extend : (NewSparseMultivariatePolynomial(R,OrderedVariableList ls),List %) -> List % +--R extend : (NewSparseMultivariatePolynomial(R,OrderedVariableList ls),%) -> List % +--R extend : (%,NewSparseMultivariatePolynomial(R,OrderedVariableList ls)) -> % +--R extendIfCan : (%,NewSparseMultivariatePolynomial(R,OrderedVariableList ls)) -> Union(%,"failed") +--R find : ((NewSparseMultivariatePolynomial(R,OrderedVariableList ls) -> Boolean),%) -> Union(NewSparseMultivariatePolynomial(R,OrderedVariableList ls),"failed") +--R first : % -> Union(NewSparseMultivariatePolynomial(R,OrderedVariableList ls),"failed") +--R headReduce : (NewSparseMultivariatePolynomial(R,OrderedVariableList ls),%) -> NewSparseMultivariatePolynomial(R,OrderedVariableList ls) +--R headReduced? : (NewSparseMultivariatePolynomial(R,OrderedVariableList ls),%) -> Boolean +--R headRemainder : (NewSparseMultivariatePolynomial(R,OrderedVariableList ls),%) -> Record(num: NewSparseMultivariatePolynomial(R,OrderedVariableList ls),den: R) if R has INTDOM +--R initiallyReduce : (NewSparseMultivariatePolynomial(R,OrderedVariableList ls),%) -> NewSparseMultivariatePolynomial(R,OrderedVariableList ls) +--R initiallyReduced? : (NewSparseMultivariatePolynomial(R,OrderedVariableList ls),%) -> Boolean +--R initials : % -> List NewSparseMultivariatePolynomial(R,OrderedVariableList ls) +--R internalAugment : (List NewSparseMultivariatePolynomial(R,OrderedVariableList ls),%) -> % +--R internalAugment : (NewSparseMultivariatePolynomial(R,OrderedVariableList ls),%) -> % +--R intersect : (NewSparseMultivariatePolynomial(R,OrderedVariableList ls),List %) -> List % +--R intersect : (List NewSparseMultivariatePolynomial(R,OrderedVariableList ls),List %) -> List % +--R intersect : (List NewSparseMultivariatePolynomial(R,OrderedVariableList ls),%) -> List % +--R intersect : (NewSparseMultivariatePolynomial(R,OrderedVariableList ls),%) -> List % +--R invertible? : (NewSparseMultivariatePolynomial(R,OrderedVariableList ls),%) -> Boolean +--R invertible? : (NewSparseMultivariatePolynomial(R,OrderedVariableList ls),%) -> List Record(val: Boolean,tower: %) +--R invertibleElseSplit? : (NewSparseMultivariatePolynomial(R,OrderedVariableList ls),%) -> Union(Boolean,List %) +--R invertibleSet : (NewSparseMultivariatePolynomial(R,OrderedVariableList ls),%) -> List % +--R last : % -> Union(NewSparseMultivariatePolynomial(R,OrderedVariableList ls),"failed") +--R lastSubResultant : (NewSparseMultivariatePolynomial(R,OrderedVariableList ls),NewSparseMultivariatePolynomial(R,OrderedVariableList ls),%) -> List Record(val: NewSparseMultivariatePolynomial(R,OrderedVariableList ls),tower: %) +--R lastSubResultantElseSplit : (NewSparseMultivariatePolynomial(R,OrderedVariableList ls),NewSparseMultivariatePolynomial(R,OrderedVariableList ls),%) -> Union(NewSparseMultivariatePolynomial(R,OrderedVariableList ls),List %) +--R less? : (%,NonNegativeInteger) -> Boolean +--R mainVariable? : (OrderedVariableList ls,%) -> Boolean +--R mainVariables : % -> List OrderedVariableList ls +--R map : ((NewSparseMultivariatePolynomial(R,OrderedVariableList ls) -> NewSparseMultivariatePolynomial(R,OrderedVariableList ls)),%) -> % +--R map! : ((NewSparseMultivariatePolynomial(R,OrderedVariableList ls) -> NewSparseMultivariatePolynomial(R,OrderedVariableList ls)),%) -> % if $ has shallowlyMutable +--R member? : (NewSparseMultivariatePolynomial(R,OrderedVariableList ls),%) -> Boolean if $ has finiteAggregate and NewSparseMultivariatePolynomial(R,OrderedVariableList ls) has SETCAT +--R members : % -> List NewSparseMultivariatePolynomial(R,OrderedVariableList ls) if $ has finiteAggregate +--R more? : (%,NonNegativeInteger) -> Boolean +--R mvar : % -> OrderedVariableList ls +--R normalized? : (NewSparseMultivariatePolynomial(R,OrderedVariableList ls),%) -> Boolean +--R parts : % -> List NewSparseMultivariatePolynomial(R,OrderedVariableList ls) if $ has finiteAggregate +--R purelyAlgebraic? : (NewSparseMultivariatePolynomial(R,OrderedVariableList ls),%) -> Boolean +--R purelyAlgebraicLeadingMonomial? : (NewSparseMultivariatePolynomial(R,OrderedVariableList ls),%) -> Boolean +--R purelyTranscendental? : (NewSparseMultivariatePolynomial(R,OrderedVariableList ls),%) -> Boolean +--R quasiComponent : % -> Record(close: List NewSparseMultivariatePolynomial(R,OrderedVariableList ls),open: List NewSparseMultivariatePolynomial(R,OrderedVariableList ls)) +--R reduce : (NewSparseMultivariatePolynomial(R,OrderedVariableList ls),%,((NewSparseMultivariatePolynomial(R,OrderedVariableList ls),NewSparseMultivariatePolynomial(R,OrderedVariableList ls)) -> NewSparseMultivariatePolynomial(R,OrderedVariableList ls)),((NewSparseMultivariatePolynomial(R,OrderedVariableList ls),NewSparseMultivariatePolynomial(R,OrderedVariableList ls)) -> Boolean)) -> NewSparseMultivariatePolynomial(R,OrderedVariableList ls) +--R reduce : (((NewSparseMultivariatePolynomial(R,OrderedVariableList ls),NewSparseMultivariatePolynomial(R,OrderedVariableList ls)) -> NewSparseMultivariatePolynomial(R,OrderedVariableList ls)),%) -> NewSparseMultivariatePolynomial(R,OrderedVariableList ls) if $ has finiteAggregate +--R reduce : (((NewSparseMultivariatePolynomial(R,OrderedVariableList ls),NewSparseMultivariatePolynomial(R,OrderedVariableList ls)) -> NewSparseMultivariatePolynomial(R,OrderedVariableList ls)),%,NewSparseMultivariatePolynomial(R,OrderedVariableList ls)) -> NewSparseMultivariatePolynomial(R,OrderedVariableList ls) if $ has finiteAggregate +--R reduce : (((NewSparseMultivariatePolynomial(R,OrderedVariableList ls),NewSparseMultivariatePolynomial(R,OrderedVariableList ls)) -> NewSparseMultivariatePolynomial(R,OrderedVariableList ls)),%,NewSparseMultivariatePolynomial(R,OrderedVariableList ls),NewSparseMultivariatePolynomial(R,OrderedVariableList ls)) -> NewSparseMultivariatePolynomial(R,OrderedVariableList ls) if $ has finiteAggregate and NewSparseMultivariatePolynomial(R,OrderedVariableList ls) has SETCAT +--R reduceByQuasiMonic : (NewSparseMultivariatePolynomial(R,OrderedVariableList ls),%) -> NewSparseMultivariatePolynomial(R,OrderedVariableList ls) +--R reduced? : (NewSparseMultivariatePolynomial(R,OrderedVariableList ls),%,((NewSparseMultivariatePolynomial(R,OrderedVariableList ls),NewSparseMultivariatePolynomial(R,OrderedVariableList ls)) -> Boolean)) -> Boolean +--R remainder : (NewSparseMultivariatePolynomial(R,OrderedVariableList ls),%) -> Record(rnum: R,polnum: NewSparseMultivariatePolynomial(R,OrderedVariableList ls),den: R) if R has INTDOM +--R remove : ((NewSparseMultivariatePolynomial(R,OrderedVariableList ls) -> Boolean),%) -> % if $ has finiteAggregate +--R remove : (NewSparseMultivariatePolynomial(R,OrderedVariableList ls),%) -> % if $ has finiteAggregate and NewSparseMultivariatePolynomial(R,OrderedVariableList ls) has SETCAT +--R removeDuplicates : % -> % if $ has finiteAggregate and NewSparseMultivariatePolynomial(R,OrderedVariableList ls) has SETCAT +--R removeZero : (NewSparseMultivariatePolynomial(R,OrderedVariableList ls),%) -> NewSparseMultivariatePolynomial(R,OrderedVariableList ls) +--R retract : List NewSparseMultivariatePolynomial(R,OrderedVariableList ls) -> % +--R retractIfCan : List NewSparseMultivariatePolynomial(R,OrderedVariableList ls) -> Union(%,"failed") +--R rewriteIdealWithHeadRemainder : (List NewSparseMultivariatePolynomial(R,OrderedVariableList ls),%) -> List NewSparseMultivariatePolynomial(R,OrderedVariableList ls) if R has INTDOM +--R rewriteIdealWithRemainder : (List NewSparseMultivariatePolynomial(R,OrderedVariableList ls),%) -> List NewSparseMultivariatePolynomial(R,OrderedVariableList ls) if R has INTDOM +--R rewriteSetWithReduction : (List NewSparseMultivariatePolynomial(R,OrderedVariableList ls),%,((NewSparseMultivariatePolynomial(R,OrderedVariableList ls),NewSparseMultivariatePolynomial(R,OrderedVariableList ls)) -> NewSparseMultivariatePolynomial(R,OrderedVariableList ls)),((NewSparseMultivariatePolynomial(R,OrderedVariableList ls),NewSparseMultivariatePolynomial(R,OrderedVariableList ls)) -> Boolean)) -> List NewSparseMultivariatePolynomial(R,OrderedVariableList ls) +--R roughBase? : % -> Boolean if R has INTDOM +--R roughEqualIdeals? : (%,%) -> Boolean if R has INTDOM +--R roughSubIdeal? : (%,%) -> Boolean if R has INTDOM +--R roughUnitIdeal? : % -> Boolean if R has INTDOM +--R select : (%,OrderedVariableList ls) -> Union(NewSparseMultivariatePolynomial(R,OrderedVariableList ls),"failed") +--R select : ((NewSparseMultivariatePolynomial(R,OrderedVariableList ls) -> Boolean),%) -> % if $ has finiteAggregate +--R size? : (%,NonNegativeInteger) -> Boolean +--R sort : (%,OrderedVariableList ls) -> Record(under: %,floor: %,upper: %) +--R squareFreePart : (NewSparseMultivariatePolynomial(R,OrderedVariableList ls),%) -> List Record(val: NewSparseMultivariatePolynomial(R,OrderedVariableList ls),tower: %) +--R stronglyReduce : (NewSparseMultivariatePolynomial(R,OrderedVariableList ls),%) -> NewSparseMultivariatePolynomial(R,OrderedVariableList ls) +--R stronglyReduced? : (NewSparseMultivariatePolynomial(R,OrderedVariableList ls),%) -> Boolean +--R triangular? : % -> Boolean if R has INTDOM +--R variables : % -> List OrderedVariableList ls +--R zeroSetSplit : (List NewSparseMultivariatePolynomial(R,OrderedVariableList ls),Boolean,Boolean) -> List % +--R zeroSetSplit : (List NewSparseMultivariatePolynomial(R,OrderedVariableList ls),Boolean) -> List % +--R zeroSetSplit : List NewSparseMultivariatePolynomial(R,OrderedVariableList ls) -> List % +--R zeroSetSplitIntoTriangularSystems : List NewSparseMultivariatePolynomial(R,OrderedVariableList ls) -> List Record(close: %,open: List NewSparseMultivariatePolynomial(R,OrderedVariableList ls)) +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +RegularChain examples +==================================================================== + +See Also: +o )show RegularChain + +@ + \pagehead{RegularChain}{RGCHAIN} \pagepic{ps/v103regularchain.ps}{RGCHAIN}{1.00} @@ -89607,6 +105511,7 @@ chains). Among them {\bf RegularTriangularSet} and by Marc Moreno Maza for computing triangular decompositions of polynomial systems. This method is refined in the package {\bf LazardSetSolvingPackage} in order to produce decompositions by means of Lazard triangular sets. + <>= )set break resume )sys rm -f RegularTriangularSet.output @@ -91471,6 +107376,57 @@ RegularTriangularSet(R,E,V,P) : Exports == Implementation where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain RESRING ResidueRing} + +<>= +)set break resume +)sys rm -f ResidueRing.output +)spool ResidueRing.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show ResidueRing +--R ResidueRing(F: Field,Expon: OrderedAbelianMonoidSup,VarSet: OrderedSet,FPol: PolynomialCategory(F,Expon,VarSet),LFPol: List FPol) is a domain constructor +--R Abbreviation for ResidueRing is RESRING +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for RESRING +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (%,F) -> % ?*? : (F,%) -> % +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ?=? : (%,%) -> Boolean +--R 1 : () -> % 0 : () -> % +--R ?^? : (%,PositiveInteger) -> % coerce : FPol -> % +--R coerce : F -> % coerce : Integer -> % +--R coerce : % -> OutputForm hash : % -> SingleInteger +--R latex : % -> String lift : % -> FPol +--R one? : % -> Boolean recip : % -> Union(%,"failed") +--R reduce : FPol -> % sample : () -> % +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean +--R ?*? : (NonNegativeInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % +--R ?^? : (%,NonNegativeInteger) -> % +--R characteristic : () -> NonNegativeInteger +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +ResidueRing examples +==================================================================== + +See Also: +o )show ResidueRing + +@ + \pagehead{ResidueRing}{RESRING} \pagepic{ps/v103residuering.ps}{RESRING}{1.00} @@ -91562,6 +107518,113 @@ ResidueRing(F,Expon,VarSet,FPol,LFPol) : Dom == Body @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain RESULT Result} + +<>= +)set break resume +)sys rm -f Result.output +)spool Result.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show Result +--R Result is a domain constructor +--R Abbreviation for Result is RESULT +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for RESULT +--R +--R------------------------------- Operations -------------------------------- +--R copy : % -> % dictionary : () -> % +--R elt : (%,Symbol,Any) -> Any ?.? : (%,Symbol) -> Any +--R empty : () -> % empty? : % -> Boolean +--R entries : % -> List Any eq? : (%,%) -> Boolean +--R index? : (Symbol,%) -> Boolean indices : % -> List Symbol +--R key? : (Symbol,%) -> Boolean keys : % -> List Symbol +--R map : ((Any -> Any),%) -> % qelt : (%,Symbol) -> Any +--R sample : () -> % setelt : (%,Symbol,Any) -> Any +--R table : () -> % +--R #? : % -> NonNegativeInteger if $ has finiteAggregate +--R ?=? : (%,%) -> Boolean if Any has SETCAT or Record(key: Symbol,entry: Any) has SETCAT +--R any? : ((Any -> Boolean),%) -> Boolean if $ has finiteAggregate +--R any? : ((Record(key: Symbol,entry: Any) -> Boolean),%) -> Boolean if $ has finiteAggregate +--R bag : List Record(key: Symbol,entry: Any) -> % +--R coerce : % -> OutputForm if Any has SETCAT or Record(key: Symbol,entry: Any) has SETCAT +--R construct : List Record(key: Symbol,entry: Any) -> % +--R convert : % -> InputForm if Record(key: Symbol,entry: Any) has KONVERT INFORM +--R count : ((Any -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate +--R count : (Any,%) -> NonNegativeInteger if $ has finiteAggregate and Any has SETCAT +--R count : (Record(key: Symbol,entry: Any),%) -> NonNegativeInteger if $ has finiteAggregate and Record(key: Symbol,entry: Any) has SETCAT +--R count : ((Record(key: Symbol,entry: Any) -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate +--R dictionary : List Record(key: Symbol,entry: Any) -> % +--R entry? : (Any,%) -> Boolean if $ has finiteAggregate and Any has SETCAT +--R eval : (%,List Equation Any) -> % if Any has EVALAB ANY and Any has SETCAT +--R eval : (%,Equation Any) -> % if Any has EVALAB ANY and Any has SETCAT +--R eval : (%,Any,Any) -> % if Any has EVALAB ANY and Any has SETCAT +--R eval : (%,List Any,List Any) -> % if Any has EVALAB ANY and Any has SETCAT +--R eval : (%,List Record(key: Symbol,entry: Any),List Record(key: Symbol,entry: Any)) -> % if Record(key: Symbol,entry: Any) has EVALAB Record(key: Symbol,entry: Any) and Record(key: Symbol,entry: Any) has SETCAT +--R eval : (%,Record(key: Symbol,entry: Any),Record(key: Symbol,entry: Any)) -> % if Record(key: Symbol,entry: Any) has EVALAB Record(key: Symbol,entry: Any) and Record(key: Symbol,entry: Any) has SETCAT +--R eval : (%,Equation Record(key: Symbol,entry: Any)) -> % if Record(key: Symbol,entry: Any) has EVALAB Record(key: Symbol,entry: Any) and Record(key: Symbol,entry: Any) has SETCAT +--R eval : (%,List Equation Record(key: Symbol,entry: Any)) -> % if Record(key: Symbol,entry: Any) has EVALAB Record(key: Symbol,entry: Any) and Record(key: Symbol,entry: Any) has SETCAT +--R every? : ((Any -> Boolean),%) -> Boolean if $ has finiteAggregate +--R every? : ((Record(key: Symbol,entry: Any) -> Boolean),%) -> Boolean if $ has finiteAggregate +--R extract! : % -> Record(key: Symbol,entry: Any) +--R fill! : (%,Any) -> % if $ has shallowlyMutable +--R find : ((Record(key: Symbol,entry: Any) -> Boolean),%) -> Union(Record(key: Symbol,entry: Any),"failed") +--R first : % -> Any if Symbol has ORDSET +--R hash : % -> SingleInteger if Any has SETCAT or Record(key: Symbol,entry: Any) has SETCAT +--R insert! : (Record(key: Symbol,entry: Any),%) -> % +--R inspect : % -> Record(key: Symbol,entry: Any) +--R latex : % -> String if Any has SETCAT or Record(key: Symbol,entry: Any) has SETCAT +--R less? : (%,NonNegativeInteger) -> Boolean +--R map : (((Any,Any) -> Any),%,%) -> % +--R map : ((Record(key: Symbol,entry: Any) -> Record(key: Symbol,entry: Any)),%) -> % +--R map! : ((Any -> Any),%) -> % if $ has shallowlyMutable +--R map! : ((Record(key: Symbol,entry: Any) -> Record(key: Symbol,entry: Any)),%) -> % if $ has shallowlyMutable +--R maxIndex : % -> Symbol if Symbol has ORDSET +--R member? : (Any,%) -> Boolean if $ has finiteAggregate and Any has SETCAT +--R member? : (Record(key: Symbol,entry: Any),%) -> Boolean if $ has finiteAggregate and Record(key: Symbol,entry: Any) has SETCAT +--R members : % -> List Any if $ has finiteAggregate +--R members : % -> List Record(key: Symbol,entry: Any) if $ has finiteAggregate +--R minIndex : % -> Symbol if Symbol has ORDSET +--R more? : (%,NonNegativeInteger) -> Boolean +--R parts : % -> List Any if $ has finiteAggregate +--R parts : % -> List Record(key: Symbol,entry: Any) if $ has finiteAggregate +--R qsetelt! : (%,Symbol,Any) -> Any if $ has shallowlyMutable +--R reduce : (((Record(key: Symbol,entry: Any),Record(key: Symbol,entry: Any)) -> Record(key: Symbol,entry: Any)),%) -> Record(key: Symbol,entry: Any) if $ has finiteAggregate +--R reduce : (((Record(key: Symbol,entry: Any),Record(key: Symbol,entry: Any)) -> Record(key: Symbol,entry: Any)),%,Record(key: Symbol,entry: Any)) -> Record(key: Symbol,entry: Any) if $ has finiteAggregate +--R reduce : (((Record(key: Symbol,entry: Any),Record(key: Symbol,entry: Any)) -> Record(key: Symbol,entry: Any)),%,Record(key: Symbol,entry: Any),Record(key: Symbol,entry: Any)) -> Record(key: Symbol,entry: Any) if $ has finiteAggregate and Record(key: Symbol,entry: Any) has SETCAT +--R remove : ((Record(key: Symbol,entry: Any) -> Boolean),%) -> % if $ has finiteAggregate +--R remove : (Record(key: Symbol,entry: Any),%) -> % if $ has finiteAggregate and Record(key: Symbol,entry: Any) has SETCAT +--R remove! : (Symbol,%) -> Union(Any,"failed") +--R remove! : ((Record(key: Symbol,entry: Any) -> Boolean),%) -> % if $ has finiteAggregate +--R remove! : (Record(key: Symbol,entry: Any),%) -> % if $ has finiteAggregate +--R removeDuplicates : % -> % if $ has finiteAggregate and Record(key: Symbol,entry: Any) has SETCAT +--R search : (Symbol,%) -> Union(Any,"failed") +--R select : ((Record(key: Symbol,entry: Any) -> Boolean),%) -> % if $ has finiteAggregate +--R select! : ((Record(key: Symbol,entry: Any) -> Boolean),%) -> % if $ has finiteAggregate +--R showArrayValues : Boolean -> Boolean +--R showScalarValues : Boolean -> Boolean +--R size? : (%,NonNegativeInteger) -> Boolean +--R swap! : (%,Symbol,Symbol) -> Void if $ has shallowlyMutable +--R table : List Record(key: Symbol,entry: Any) -> % +--R ?~=? : (%,%) -> Boolean if Any has SETCAT or Record(key: Symbol,entry: Any) has SETCAT +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +Result examples +==================================================================== + +See Also: +o )show Result + +@ + \pagehead{Result}{RESULT} \pagepic{ps/v103result.ps}{RESULT}{1.00} {\bf See}\\ @@ -91712,6 +107775,49 @@ Result():Exports==Implementation where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain RULE RewriteRule} + +<>= +)set break resume +)sys rm -f RewriteRule.output +)spool RewriteRule.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show RewriteRule +--R RewriteRule(Base: SetCategory,R: Join(Ring,PatternMatchable Base,OrderedSet,ConvertibleTo Pattern Base),F: Join(FunctionSpace R,PatternMatchable Base,ConvertibleTo Pattern Base)) is a domain constructor +--R Abbreviation for RewriteRule is RULE +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for RULE +--R +--R------------------------------- Operations -------------------------------- +--R ?=? : (%,%) -> Boolean coerce : Equation F -> % +--R coerce : % -> OutputForm elt : (%,F,PositiveInteger) -> F +--R ?.? : (%,F) -> F hash : % -> SingleInteger +--R latex : % -> String lhs : % -> F +--R pattern : % -> Pattern Base retract : % -> Equation F +--R rhs : % -> F rule : (F,F,List Symbol) -> % +--R rule : (F,F) -> % ?~=? : (%,%) -> Boolean +--R quotedOperators : % -> List Symbol +--R retractIfCan : % -> Union(Equation F,"failed") +--R suchThat : (%,List Symbol,(List F -> Boolean)) -> % +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +RewriteRule examples +==================================================================== + +See Also: +o )show RewriteRule + +@ + \pagehead{RewriteRule}{RULE} \pagepic{ps/v103rewriterule.ps}{RULE}{1.00} {\bf See}\\ @@ -91909,8 +108015,56 @@ algorithms and cannot be distributed. Please contact the author if you have a particular problem to solve or want to use these versions. Be aware that approximations behave as post-processing and that all -computations are done excatly. They can thus be quite time consuming when +computations are done exactly. They can thus be quite time consuming when depending on several "real roots". + +<>= +)set break resume +)sys rm -f RightOpenIntervalRootCharacterization.output +)spool RightOpenIntervalRootCharacterization.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show RightOpenIntervalRootCharacterization +--R RightOpenIntervalRootCharacterization(TheField: Join(OrderedRing,Field),ThePolDom: UnivariatePolynomialCategory TheField) is a domain constructor +--R Abbreviation for RightOpenIntervalRootCharacterization is ROIRC +--R This constructor is exposed in this frame. +--R Issue )edit NIL to see algebra source code for ROIRC +--R +--R------------------------------- Operations -------------------------------- +--R ?=? : (%,%) -> Boolean allRootsOf : ThePolDom -> List % +--R coerce : % -> OutputForm hash : % -> SingleInteger +--R latex : % -> String left : % -> TheField +--R middle : % -> TheField refine : % -> % +--R right : % -> TheField sign : (ThePolDom,%) -> Integer +--R size : % -> TheField zero? : (ThePolDom,%) -> Boolean +--R ?~=? : (%,%) -> Boolean +--R approximate : (ThePolDom,%,TheField) -> TheField +--R definingPolynomial : % -> ThePolDom +--R mightHaveRoots : (ThePolDom,%) -> Boolean +--R negative? : (ThePolDom,%) -> Boolean +--R positive? : (ThePolDom,%) -> Boolean +--R recip : (ThePolDom,%) -> Union(ThePolDom,"failed") +--R relativeApprox : (ThePolDom,%,TheField) -> TheField +--R rootOf : (ThePolDom,PositiveInteger) -> Union(%,"failed") +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +RightOpenIntervalRootCharacterization examples +==================================================================== + +See Also: +o )show RightOpenIntervalRootCharacterization + +@ + \pagehead{RightOpenIntervalRootCharacterization}{ROIRC} \pagepic{ps/v103rightopenintervalrootcharacterization.ps}{ROIRC}{1.00} {\bf See}\\ @@ -92412,6 +108566,7 @@ RightOpenIntervalRootCharacterization(TheField,ThePolDom) : PUB == PRIV where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain ROMAN RomanNumeral} + <>= )set break resume )sys rm -f RomanNumeral.output @@ -92838,6 +108993,123 @@ RomanNumeral(): IntegerNumberSystem with @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain ROUTINE RoutinesTable} + +<>= +)set break resume +)sys rm -f RoutinesTable.output +)spool RoutinesTable.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show RoutinesTable +--R RoutinesTable is a domain constructor +--R Abbreviation for RoutinesTable is ROUTINE +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for ROUTINE +--R +--R------------------------------- Operations -------------------------------- +--R concat : (%,%) -> % copy : % -> % +--R deleteRoutine! : (%,Symbol) -> % dictionary : () -> % +--R elt : (%,Symbol,Any) -> Any ?.? : (%,Symbol) -> Any +--R empty : () -> % empty? : % -> Boolean +--R entries : % -> List Any eq? : (%,%) -> Boolean +--R getMeasure : (%,Symbol) -> Float index? : (Symbol,%) -> Boolean +--R indices : % -> List Symbol key? : (Symbol,%) -> Boolean +--R keys : % -> List Symbol map : ((Any -> Any),%) -> % +--R qelt : (%,Symbol) -> Any routines : () -> % +--R sample : () -> % selectFiniteRoutines : % -> % +--R selectNonFiniteRoutines : % -> % selectODEIVPRoutines : % -> % +--R selectPDERoutines : % -> % setelt : (%,Symbol,Any) -> Any +--R showTheRoutinesTable : () -> % table : () -> % +--R #? : % -> NonNegativeInteger if $ has finiteAggregate +--R ?=? : (%,%) -> Boolean if Any has SETCAT or Record(key: Symbol,entry: Any) has SETCAT +--R any? : ((Any -> Boolean),%) -> Boolean if $ has finiteAggregate +--R any? : ((Record(key: Symbol,entry: Any) -> Boolean),%) -> Boolean if $ has finiteAggregate +--R bag : List Record(key: Symbol,entry: Any) -> % +--R changeMeasure : (%,Symbol,Float) -> % +--R changeThreshhold : (%,Symbol,Float) -> % +--R coerce : % -> OutputForm if Any has SETCAT or Record(key: Symbol,entry: Any) has SETCAT +--R construct : List Record(key: Symbol,entry: Any) -> % +--R convert : % -> InputForm if Record(key: Symbol,entry: Any) has KONVERT INFORM +--R count : ((Any -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate +--R count : (Any,%) -> NonNegativeInteger if $ has finiteAggregate and Any has SETCAT +--R count : (Record(key: Symbol,entry: Any),%) -> NonNegativeInteger if $ has finiteAggregate and Record(key: Symbol,entry: Any) has SETCAT +--R count : ((Record(key: Symbol,entry: Any) -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate +--R dictionary : List Record(key: Symbol,entry: Any) -> % +--R entry? : (Any,%) -> Boolean if $ has finiteAggregate and Any has SETCAT +--R eval : (%,List Equation Any) -> % if Any has EVALAB ANY and Any has SETCAT +--R eval : (%,Equation Any) -> % if Any has EVALAB ANY and Any has SETCAT +--R eval : (%,Any,Any) -> % if Any has EVALAB ANY and Any has SETCAT +--R eval : (%,List Any,List Any) -> % if Any has EVALAB ANY and Any has SETCAT +--R eval : (%,List Record(key: Symbol,entry: Any),List Record(key: Symbol,entry: Any)) -> % if Record(key: Symbol,entry: Any) has EVALAB Record(key: Symbol,entry: Any) and Record(key: Symbol,entry: Any) has SETCAT +--R eval : (%,Record(key: Symbol,entry: Any),Record(key: Symbol,entry: Any)) -> % if Record(key: Symbol,entry: Any) has EVALAB Record(key: Symbol,entry: Any) and Record(key: Symbol,entry: Any) has SETCAT +--R eval : (%,Equation Record(key: Symbol,entry: Any)) -> % if Record(key: Symbol,entry: Any) has EVALAB Record(key: Symbol,entry: Any) and Record(key: Symbol,entry: Any) has SETCAT +--R eval : (%,List Equation Record(key: Symbol,entry: Any)) -> % if Record(key: Symbol,entry: Any) has EVALAB Record(key: Symbol,entry: Any) and Record(key: Symbol,entry: Any) has SETCAT +--R every? : ((Any -> Boolean),%) -> Boolean if $ has finiteAggregate +--R every? : ((Record(key: Symbol,entry: Any) -> Boolean),%) -> Boolean if $ has finiteAggregate +--R extract! : % -> Record(key: Symbol,entry: Any) +--R fill! : (%,Any) -> % if $ has shallowlyMutable +--R find : ((Record(key: Symbol,entry: Any) -> Boolean),%) -> Union(Record(key: Symbol,entry: Any),"failed") +--R first : % -> Any if Symbol has ORDSET +--R getExplanations : (%,String) -> List String +--R hash : % -> SingleInteger if Any has SETCAT or Record(key: Symbol,entry: Any) has SETCAT +--R insert! : (Record(key: Symbol,entry: Any),%) -> % +--R inspect : % -> Record(key: Symbol,entry: Any) +--R latex : % -> String if Any has SETCAT or Record(key: Symbol,entry: Any) has SETCAT +--R less? : (%,NonNegativeInteger) -> Boolean +--R map : (((Any,Any) -> Any),%,%) -> % +--R map : ((Record(key: Symbol,entry: Any) -> Record(key: Symbol,entry: Any)),%) -> % +--R map! : ((Any -> Any),%) -> % if $ has shallowlyMutable +--R map! : ((Record(key: Symbol,entry: Any) -> Record(key: Symbol,entry: Any)),%) -> % if $ has shallowlyMutable +--R maxIndex : % -> Symbol if Symbol has ORDSET +--R member? : (Any,%) -> Boolean if $ has finiteAggregate and Any has SETCAT +--R member? : (Record(key: Symbol,entry: Any),%) -> Boolean if $ has finiteAggregate and Record(key: Symbol,entry: Any) has SETCAT +--R members : % -> List Any if $ has finiteAggregate +--R members : % -> List Record(key: Symbol,entry: Any) if $ has finiteAggregate +--R minIndex : % -> Symbol if Symbol has ORDSET +--R more? : (%,NonNegativeInteger) -> Boolean +--R parts : % -> List Any if $ has finiteAggregate +--R parts : % -> List Record(key: Symbol,entry: Any) if $ has finiteAggregate +--R qsetelt! : (%,Symbol,Any) -> Any if $ has shallowlyMutable +--R recoverAfterFail : (%,String,Integer) -> Union(String,"failed") +--R reduce : (((Record(key: Symbol,entry: Any),Record(key: Symbol,entry: Any)) -> Record(key: Symbol,entry: Any)),%) -> Record(key: Symbol,entry: Any) if $ has finiteAggregate +--R reduce : (((Record(key: Symbol,entry: Any),Record(key: Symbol,entry: Any)) -> Record(key: Symbol,entry: Any)),%,Record(key: Symbol,entry: Any)) -> Record(key: Symbol,entry: Any) if $ has finiteAggregate +--R reduce : (((Record(key: Symbol,entry: Any),Record(key: Symbol,entry: Any)) -> Record(key: Symbol,entry: Any)),%,Record(key: Symbol,entry: Any),Record(key: Symbol,entry: Any)) -> Record(key: Symbol,entry: Any) if $ has finiteAggregate and Record(key: Symbol,entry: Any) has SETCAT +--R remove : ((Record(key: Symbol,entry: Any) -> Boolean),%) -> % if $ has finiteAggregate +--R remove : (Record(key: Symbol,entry: Any),%) -> % if $ has finiteAggregate and Record(key: Symbol,entry: Any) has SETCAT +--R remove! : (Symbol,%) -> Union(Any,"failed") +--R remove! : ((Record(key: Symbol,entry: Any) -> Boolean),%) -> % if $ has finiteAggregate +--R remove! : (Record(key: Symbol,entry: Any),%) -> % if $ has finiteAggregate +--R removeDuplicates : % -> % if $ has finiteAggregate and Record(key: Symbol,entry: Any) has SETCAT +--R search : (Symbol,%) -> Union(Any,"failed") +--R select : ((Record(key: Symbol,entry: Any) -> Boolean),%) -> % if $ has finiteAggregate +--R select! : ((Record(key: Symbol,entry: Any) -> Boolean),%) -> % if $ has finiteAggregate +--R selectIntegrationRoutines : % -> % +--R selectMultiDimensionalRoutines : % -> % +--R selectOptimizationRoutines : % -> % +--R selectSumOfSquaresRoutines : % -> % +--R size? : (%,NonNegativeInteger) -> Boolean +--R swap! : (%,Symbol,Symbol) -> Void if $ has shallowlyMutable +--R table : List Record(key: Symbol,entry: Any) -> % +--R ?~=? : (%,%) -> Boolean if Any has SETCAT or Record(key: Symbol,entry: Any) has SETCAT +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +RoutinesTable examples +==================================================================== + +See Also: +o )show RoutinesTable + +@ + \pagehead{RoutinesTable}{ROUTINE} \pagepic{ps/v103routinestable.ps}{ROUTINE}{1.00} @@ -93305,6 +109577,42 @@ RoutinesTable(): E == I where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain RULECOLD RuleCalled} + +<>= +)set break resume +)sys rm -f RuleCalled.output +)spool RuleCalled.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show RuleCalled +--R RuleCalled f: Symbol is a domain constructor +--R Abbreviation for RuleCalled is RULECOLD +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for RULECOLD +--R +--R------------------------------- Operations -------------------------------- +--R ?=? : (%,%) -> Boolean coerce : % -> OutputForm +--R hash : % -> SingleInteger latex : % -> String +--R name : % -> Symbol ?~=? : (%,%) -> Boolean +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +RuleCalled examples +==================================================================== + +See Also: +o )show RuleCalled + +@ + \pagehead{RuleCalled}{RULECOLD} \pagepic{ps/v103rulecalled.ps}{RULECOLD}{1.00} @@ -93342,6 +109650,45 @@ RuleCalled(f:Symbol): SetCategory with @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain RULESET Ruleset} + +<>= +)set break resume +)sys rm -f Ruleset.output +)spool Ruleset.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show Ruleset +--R Ruleset(Base: SetCategory,R: Join(Ring,PatternMatchable Base,OrderedSet,ConvertibleTo Pattern Base),F: Join(FunctionSpace R,PatternMatchable Base,ConvertibleTo Pattern Base)) is a domain constructor +--R Abbreviation for Ruleset is RULESET +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for RULESET +--R +--R------------------------------- Operations -------------------------------- +--R ?=? : (%,%) -> Boolean coerce : % -> OutputForm +--R elt : (%,F,PositiveInteger) -> F ?.? : (%,F) -> F +--R hash : % -> SingleInteger latex : % -> String +--R ?~=? : (%,%) -> Boolean +--R rules : % -> List RewriteRule(Base,R,F) +--R ruleset : List RewriteRule(Base,R,F) -> % +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +Ruleset examples +==================================================================== + +See Also: +o )show Ruleset + +@ + \pagehead{Ruleset}{RULESET} \pagepic{ps/v103ruleset.ps}{RULESET}{1.00} {\bf See}\\ @@ -93410,6 +109757,49 @@ Ruleset(Base, R, F): Exports == Implementation where \chapter{Chapter S} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain FORMULA ScriptFormulaFormat} + +<>= +)set break resume +)sys rm -f ScriptFormulaFormat.output +)spool ScriptFormulaFormat.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show ScriptFormulaFormat +--R ScriptFormulaFormat is a domain constructor +--R Abbreviation for ScriptFormulaFormat is FORMULA +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for FORMULA +--R +--R------------------------------- Operations -------------------------------- +--R ?=? : (%,%) -> Boolean coerce : OutputForm -> % +--R coerce : % -> OutputForm display : % -> Void +--R display : (%,Integer) -> Void epilogue : % -> List String +--R formula : % -> List String hash : % -> SingleInteger +--R latex : % -> String new : () -> % +--R prologue : % -> List String ?~=? : (%,%) -> Boolean +--R convert : (OutputForm,Integer) -> % +--R setEpilogue! : (%,List String) -> List String +--R setFormula! : (%,List String) -> List String +--R setPrologue! : (%,List String) -> List String +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +ScriptFormulaFormat examples +==================================================================== + +See Also: +o )show ScriptFormulaFormat + +@ + \pagehead{ScriptFormulaFormat}{FORMULA} \pagepic{ps/v103scriptformulaformat.ps}{FORMULA}{1.00} @@ -93867,6 +110257,7 @@ ScriptFormulaFormat(): public == private where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain SEG Segment} + <>= )set break resume )sys rm -f Segment.output @@ -94148,6 +110539,7 @@ Segment(S:Type): SegmentCategory(S) with @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain SEGBIND SegmentBinding} + <>= )set break resume )sys rm -f SegmentBinding.output @@ -94331,6 +110723,7 @@ SegmentBinding(S:Type): Type with @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain SET Set} + <>= )set break resume )sys rm -f Set.output @@ -94888,6 +111281,50 @@ Set(S:SetCategory): FiniteSetAggregate S == add @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain SETMN SetOfMIntegersInOneToN} + +<>= +)set break resume +)sys rm -f SetOfMIntegersInOneToN.output +)spool SetOfMIntegersInOneToN.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show SetOfMIntegersInOneToN +--R SetOfMIntegersInOneToN(m: PositiveInteger,n: PositiveInteger) is a domain constructor +--R Abbreviation for SetOfMIntegersInOneToN is SETMN +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for SETMN +--R +--R------------------------------- Operations -------------------------------- +--R ?=? : (%,%) -> Boolean coerce : % -> OutputForm +--R enumerate : () -> Vector % hash : % -> SingleInteger +--R index : PositiveInteger -> % latex : % -> String +--R lookup : % -> PositiveInteger random : () -> % +--R size : () -> NonNegativeInteger ?~=? : (%,%) -> Boolean +--R delta : (%,PositiveInteger,PositiveInteger) -> NonNegativeInteger +--R elements : % -> List PositiveInteger +--R incrementKthElement : (%,PositiveInteger) -> Union(%,"failed") +--R member? : (PositiveInteger,%) -> Boolean +--R replaceKthElement : (%,PositiveInteger,PositiveInteger) -> Union(%,"failed") +--R setOfMinN : List PositiveInteger -> % +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +SetOfMIntegersInOneToN examples +==================================================================== + +See Also: +o )show SetOfMIntegersInOneToN + +@ + \pagehead{SetOfMIntegersInOneToN}{SETMN} \pagepic{ps/v103setofmintegersinoneton.ps}{SETMN}{1.00} @@ -95066,6 +111503,194 @@ SetOfMIntegersInOneToN(m, n): Exports == Implementation where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain SDPOL SequentialDifferentialPolynomial} + +<>= +)set break resume +)sys rm -f SequentialDifferentialPolynomial.output +)spool SequentialDifferentialPolynomial.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show SequentialDifferentialPolynomial +--R SequentialDifferentialPolynomial R: Ring is a domain constructor +--R Abbreviation for SequentialDifferentialPolynomial is SDPOL +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for SDPOL +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (%,R) -> % ?*? : (R,%) -> % +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ?=? : (%,%) -> Boolean +--R D : (%,(R -> R)) -> % D : % -> % if R has DIFRING +--R 1 : () -> % 0 : () -> % +--R ?^? : (%,PositiveInteger) -> % coefficients : % -> List R +--R coerce : Symbol -> % coerce : R -> % +--R coerce : Integer -> % coerce : % -> OutputForm +--R eval : (%,List %,List %) -> % eval : (%,%,%) -> % +--R eval : (%,Equation %) -> % eval : (%,List Equation %) -> % +--R ground : % -> R ground? : % -> Boolean +--R hash : % -> SingleInteger initial : % -> % +--R isobaric? : % -> Boolean latex : % -> String +--R leadingCoefficient : % -> R leadingMonomial : % -> % +--R map : ((R -> R),%) -> % monomial? : % -> Boolean +--R monomials : % -> List % one? : % -> Boolean +--R order : % -> NonNegativeInteger primitiveMonomials : % -> List % +--R recip : % -> Union(%,"failed") reductum : % -> % +--R retract : % -> Symbol retract : % -> R +--R sample : () -> % separant : % -> % +--R weight : % -> NonNegativeInteger zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean +--R ?*? : (Fraction Integer,%) -> % if R has ALGEBRA FRAC INT +--R ?*? : (%,Fraction Integer) -> % if R has ALGEBRA FRAC INT +--R ?*? : (NonNegativeInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % +--R ?/? : (%,R) -> % if R has FIELD +--R ? Boolean if R has ORDSET +--R ?<=? : (%,%) -> Boolean if R has ORDSET +--R ?>? : (%,%) -> Boolean if R has ORDSET +--R ?>=? : (%,%) -> Boolean if R has ORDSET +--R D : (%,(R -> R),NonNegativeInteger) -> % +--R D : (%,List Symbol,List NonNegativeInteger) -> % if R has PDRING SYMBOL +--R D : (%,Symbol,NonNegativeInteger) -> % if R has PDRING SYMBOL +--R D : (%,List Symbol) -> % if R has PDRING SYMBOL +--R D : (%,Symbol) -> % if R has PDRING SYMBOL +--R D : (%,NonNegativeInteger) -> % if R has DIFRING +--R D : (%,List SequentialDifferentialVariable Symbol,List NonNegativeInteger) -> % +--R D : (%,SequentialDifferentialVariable Symbol,NonNegativeInteger) -> % +--R D : (%,List SequentialDifferentialVariable Symbol) -> % +--R D : (%,SequentialDifferentialVariable Symbol) -> % +--R ?^? : (%,NonNegativeInteger) -> % +--R associates? : (%,%) -> Boolean if R has INTDOM +--R binomThmExpt : (%,%,NonNegativeInteger) -> % if R has COMRING +--R characteristic : () -> NonNegativeInteger +--R charthRoot : % -> Union(%,"failed") if $ has CHARNZ and R has PFECAT or R has CHARNZ +--R coefficient : (%,List SequentialDifferentialVariable Symbol,List NonNegativeInteger) -> % +--R coefficient : (%,SequentialDifferentialVariable Symbol,NonNegativeInteger) -> % +--R coefficient : (%,IndexedExponents SequentialDifferentialVariable Symbol) -> R +--R coerce : % -> % if R has INTDOM +--R coerce : Fraction Integer -> % if R has ALGEBRA FRAC INT or R has RETRACT FRAC INT +--R coerce : SparseMultivariatePolynomial(R,Symbol) -> % +--R coerce : SequentialDifferentialVariable Symbol -> % +--R conditionP : Matrix % -> Union(Vector %,"failed") if $ has CHARNZ and R has PFECAT +--R content : (%,SequentialDifferentialVariable Symbol) -> % if R has GCDDOM +--R content : % -> R if R has GCDDOM +--R convert : % -> InputForm if SequentialDifferentialVariable Symbol has KONVERT INFORM and R has KONVERT INFORM +--R convert : % -> Pattern Integer if SequentialDifferentialVariable Symbol has KONVERT PATTERN INT and R has KONVERT PATTERN INT +--R convert : % -> Pattern Float if SequentialDifferentialVariable Symbol has KONVERT PATTERN FLOAT and R has KONVERT PATTERN FLOAT +--R degree : (%,Symbol) -> NonNegativeInteger +--R degree : (%,List SequentialDifferentialVariable Symbol) -> List NonNegativeInteger +--R degree : (%,SequentialDifferentialVariable Symbol) -> NonNegativeInteger +--R degree : % -> IndexedExponents SequentialDifferentialVariable Symbol +--R differentialVariables : % -> List Symbol +--R differentiate : (%,(R -> R)) -> % +--R differentiate : (%,(R -> R),NonNegativeInteger) -> % +--R differentiate : (%,List Symbol,List NonNegativeInteger) -> % if R has PDRING SYMBOL +--R differentiate : (%,Symbol,NonNegativeInteger) -> % if R has PDRING SYMBOL +--R differentiate : (%,List Symbol) -> % if R has PDRING SYMBOL +--R differentiate : (%,Symbol) -> % if R has PDRING SYMBOL +--R differentiate : (%,NonNegativeInteger) -> % if R has DIFRING +--R differentiate : % -> % if R has DIFRING +--R differentiate : (%,List SequentialDifferentialVariable Symbol,List NonNegativeInteger) -> % +--R differentiate : (%,SequentialDifferentialVariable Symbol,NonNegativeInteger) -> % +--R differentiate : (%,List SequentialDifferentialVariable Symbol) -> % +--R differentiate : (%,SequentialDifferentialVariable Symbol) -> % +--R discriminant : (%,SequentialDifferentialVariable Symbol) -> % if R has COMRING +--R eval : (%,List Symbol,List R) -> % if R has DIFRING +--R eval : (%,Symbol,R) -> % if R has DIFRING +--R eval : (%,List Symbol,List %) -> % if R has DIFRING +--R eval : (%,Symbol,%) -> % if R has DIFRING +--R eval : (%,List SequentialDifferentialVariable Symbol,List %) -> % +--R eval : (%,SequentialDifferentialVariable Symbol,%) -> % +--R eval : (%,List SequentialDifferentialVariable Symbol,List R) -> % +--R eval : (%,SequentialDifferentialVariable Symbol,R) -> % +--R exquo : (%,%) -> Union(%,"failed") if R has INTDOM +--R exquo : (%,R) -> Union(%,"failed") if R has INTDOM +--R factor : % -> Factored % if R has PFECAT +--R factorPolynomial : SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if R has PFECAT +--R factorSquareFreePolynomial : SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if R has PFECAT +--R gcd : (%,%) -> % if R has GCDDOM +--R gcd : List % -> % if R has GCDDOM +--R gcdPolynomial : (SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial % if R has GCDDOM +--R isExpt : % -> Union(Record(var: SequentialDifferentialVariable Symbol,exponent: NonNegativeInteger),"failed") +--R isPlus : % -> Union(List %,"failed") +--R isTimes : % -> Union(List %,"failed") +--R lcm : (%,%) -> % if R has GCDDOM +--R lcm : List % -> % if R has GCDDOM +--R leader : % -> SequentialDifferentialVariable Symbol +--R mainVariable : % -> Union(SequentialDifferentialVariable Symbol,"failed") +--R makeVariable : % -> (NonNegativeInteger -> %) if R has DIFRING +--R makeVariable : Symbol -> (NonNegativeInteger -> %) +--R mapExponents : ((IndexedExponents SequentialDifferentialVariable Symbol -> IndexedExponents SequentialDifferentialVariable Symbol),%) -> % +--R max : (%,%) -> % if R has ORDSET +--R min : (%,%) -> % if R has ORDSET +--R minimumDegree : (%,List SequentialDifferentialVariable Symbol) -> List NonNegativeInteger +--R minimumDegree : (%,SequentialDifferentialVariable Symbol) -> NonNegativeInteger +--R minimumDegree : % -> IndexedExponents SequentialDifferentialVariable Symbol +--R monicDivide : (%,%,SequentialDifferentialVariable Symbol) -> Record(quotient: %,remainder: %) +--R monomial : (%,List SequentialDifferentialVariable Symbol,List NonNegativeInteger) -> % +--R monomial : (%,SequentialDifferentialVariable Symbol,NonNegativeInteger) -> % +--R monomial : (R,IndexedExponents SequentialDifferentialVariable Symbol) -> % +--R multivariate : (SparseUnivariatePolynomial %,SequentialDifferentialVariable Symbol) -> % +--R multivariate : (SparseUnivariatePolynomial R,SequentialDifferentialVariable Symbol) -> % +--R numberOfMonomials : % -> NonNegativeInteger +--R order : (%,Symbol) -> NonNegativeInteger +--R patternMatch : (%,Pattern Integer,PatternMatchResult(Integer,%)) -> PatternMatchResult(Integer,%) if SequentialDifferentialVariable Symbol has PATMAB INT and R has PATMAB INT +--R patternMatch : (%,Pattern Float,PatternMatchResult(Float,%)) -> PatternMatchResult(Float,%) if SequentialDifferentialVariable Symbol has PATMAB FLOAT and R has PATMAB FLOAT +--R pomopo! : (%,R,IndexedExponents SequentialDifferentialVariable Symbol,%) -> % +--R prime? : % -> Boolean if R has PFECAT +--R primitivePart : (%,SequentialDifferentialVariable Symbol) -> % if R has GCDDOM +--R primitivePart : % -> % if R has GCDDOM +--R reducedSystem : Matrix % -> Matrix R +--R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix R,vec: Vector R) +--R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix Integer,vec: Vector Integer) if R has LINEXP INT +--R reducedSystem : Matrix % -> Matrix Integer if R has LINEXP INT +--R resultant : (%,%,SequentialDifferentialVariable Symbol) -> % if R has COMRING +--R retract : % -> SparseMultivariatePolynomial(R,Symbol) +--R retract : % -> SequentialDifferentialVariable Symbol +--R retract : % -> Integer if R has RETRACT INT +--R retract : % -> Fraction Integer if R has RETRACT FRAC INT +--R retractIfCan : % -> Union(SparseMultivariatePolynomial(R,Symbol),"failed") +--R retractIfCan : % -> Union(Symbol,"failed") +--R retractIfCan : % -> Union(SequentialDifferentialVariable Symbol,"failed") +--R retractIfCan : % -> Union(Integer,"failed") if R has RETRACT INT +--R retractIfCan : % -> Union(Fraction Integer,"failed") if R has RETRACT FRAC INT +--R retractIfCan : % -> Union(R,"failed") +--R solveLinearPolynomialEquation : (List SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> Union(List SparseUnivariatePolynomial %,"failed") if R has PFECAT +--R squareFree : % -> Factored % if R has GCDDOM +--R squareFreePart : % -> % if R has GCDDOM +--R squareFreePolynomial : SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if R has PFECAT +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R totalDegree : (%,List SequentialDifferentialVariable Symbol) -> NonNegativeInteger +--R totalDegree : % -> NonNegativeInteger +--R unit? : % -> Boolean if R has INTDOM +--R unitCanonical : % -> % if R has INTDOM +--R unitNormal : % -> Record(unit: %,canonical: %,associate: %) if R has INTDOM +--R univariate : % -> SparseUnivariatePolynomial R +--R univariate : (%,SequentialDifferentialVariable Symbol) -> SparseUnivariatePolynomial % +--R variables : % -> List SequentialDifferentialVariable Symbol +--R weight : (%,Symbol) -> NonNegativeInteger +--R weights : (%,Symbol) -> List NonNegativeInteger +--R weights : % -> List NonNegativeInteger +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +SequentialDifferentialPolynomial examples +==================================================================== + +See Also: +o )show SequentialDifferentialPolynomial + +@ + \pagehead{SequentialDifferentialPolynomial}{SDPOL} \pagepic{ps/v103sequentialdifferentialpolynomial.ps}{SDPOL}{1.00} {\bf See}\\ @@ -95210,6 +111835,51 @@ SequentialDifferentialPolynomial(R): @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain SDVAR SequentialDifferentialVariable} + +<>= +)set break resume +)sys rm -f SequentialDifferentialVariable.output +)spool SequentialDifferentialVariable.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show SequentialDifferentialVariable +--R SequentialDifferentialVariable S: OrderedSet is a domain constructor +--R Abbreviation for SequentialDifferentialVariable is SDVAR +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for SDVAR +--R +--R------------------------------- Operations -------------------------------- +--R ? Boolean ?<=? : (%,%) -> Boolean +--R ?=? : (%,%) -> Boolean ?>? : (%,%) -> Boolean +--R ?>=? : (%,%) -> Boolean coerce : S -> % +--R coerce : % -> OutputForm differentiate : % -> % +--R hash : % -> SingleInteger latex : % -> String +--R max : (%,%) -> % min : (%,%) -> % +--R order : % -> NonNegativeInteger retract : % -> S +--R variable : % -> S weight : % -> NonNegativeInteger +--R ?~=? : (%,%) -> Boolean +--R differentiate : (%,NonNegativeInteger) -> % +--R makeVariable : (S,NonNegativeInteger) -> % +--R retractIfCan : % -> Union(S,"failed") +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +SequentialDifferentialVariable examples +==================================================================== + +See Also: +o )show SequentialDifferentialVariable + +@ + \pagehead{SequentialDifferentialVariable}{SDVAR} \pagepic{ps/v103sequentialdifferentialvariable.ps}{SDVAR}{1.00} {\bf See}\\ @@ -95286,6 +111956,55 @@ SequentialDifferentialVariable(S:OrderedSet):DifferentialVariableCategory(S) @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain SEX SExpression} + +<>= +)set break resume +)sys rm -f SExpression.output +)spool SExpression.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show SExpression +--R SExpression is a domain constructor +--R Abbreviation for SExpression is SEX +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for SEX +--R +--R------------------------------- Operations -------------------------------- +--R #? : % -> Integer ?=? : (%,%) -> Boolean +--R atom? : % -> Boolean car : % -> % +--R cdr : % -> % coerce : % -> OutputForm +--R convert : OutputForm -> % convert : DoubleFloat -> % +--R convert : Integer -> % convert : Symbol -> % +--R convert : String -> % convert : List % -> % +--R destruct : % -> List % ?.? : (%,List Integer) -> % +--R ?.? : (%,Integer) -> % eq : (%,%) -> Boolean +--R expr : % -> OutputForm float : % -> DoubleFloat +--R float? : % -> Boolean hash : % -> SingleInteger +--R integer : % -> Integer integer? : % -> Boolean +--R latex : % -> String list? : % -> Boolean +--R null? : % -> Boolean pair? : % -> Boolean +--R string : % -> String string? : % -> Boolean +--R symbol : % -> Symbol symbol? : % -> Boolean +--R ?~=? : (%,%) -> Boolean +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +SExpression examples +==================================================================== + +See Also: +o )show SExpression + +@ + \pagehead{SExpression}{SEX} \pagepic{ps/v103sexpression.ps}{SEX}{1.00} {\bf See}\\ @@ -95340,6 +112059,55 @@ SExpression() @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain SEXOF SExpressionOf} + +<>= +)set break resume +)sys rm -f SExpressionOf.output +)spool SExpressionOf.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show SExpressionOf +--R SExpressionOf(Str: SetCategory,Sym: SetCategory,Int: SetCategory,Flt: SetCategory,Expr: SetCategory) is a domain constructor +--R Abbreviation for SExpressionOf is SEXOF +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for SEXOF +--R +--R------------------------------- Operations -------------------------------- +--R #? : % -> Integer ?=? : (%,%) -> Boolean +--R atom? : % -> Boolean car : % -> % +--R cdr : % -> % coerce : % -> OutputForm +--R convert : Expr -> % convert : Flt -> % +--R convert : Int -> % convert : Sym -> % +--R convert : Str -> % convert : List % -> % +--R destruct : % -> List % ?.? : (%,List Integer) -> % +--R ?.? : (%,Integer) -> % eq : (%,%) -> Boolean +--R expr : % -> Expr float : % -> Flt +--R float? : % -> Boolean hash : % -> SingleInteger +--R integer : % -> Int integer? : % -> Boolean +--R latex : % -> String list? : % -> Boolean +--R null? : % -> Boolean pair? : % -> Boolean +--R string : % -> Str string? : % -> Boolean +--R symbol : % -> Sym symbol? : % -> Boolean +--R ?~=? : (%,%) -> Boolean +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +SExpressionOf examples +==================================================================== + +See Also: +o )show SExpressionOf + +@ + \pagehead{SExpressionOf}{SEXOF} \pagepic{ps/v103sexpressionof.ps}{SEXOF}{1.00} {\bf See}\\ @@ -95453,6 +112221,153 @@ SExpressionOf(Str, Sym, Int, Flt, Expr): Decl == Body where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain SAE SimpleAlgebraicExtension} + +<>= +)set break resume +)sys rm -f SimpleAlgebraicExtension.output +)spool SimpleAlgebraicExtension.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show SimpleAlgebraicExtension +--R SimpleAlgebraicExtension(R: CommutativeRing,UP: UnivariatePolynomialCategory R,M: UP) is a domain constructor +--R Abbreviation for SimpleAlgebraicExtension is SAE +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for SAE +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (R,%) -> % ?*? : (%,R) -> % +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ?=? : (%,%) -> Boolean +--R 1 : () -> % 0 : () -> % +--R ?^? : (%,PositiveInteger) -> % basis : () -> Vector % +--R coerce : R -> % coerce : Integer -> % +--R coerce : % -> OutputForm convert : UP -> % +--R convert : % -> UP convert : Vector R -> % +--R convert : % -> Vector R coordinates : % -> Vector R +--R definingPolynomial : () -> UP discriminant : () -> R +--R discriminant : Vector % -> R generator : () -> % +--R hash : % -> SingleInteger inv : % -> % if R has FIELD +--R latex : % -> String lift : % -> UP +--R norm : % -> R one? : % -> Boolean +--R rank : () -> PositiveInteger recip : % -> Union(%,"failed") +--R reduce : UP -> % represents : Vector R -> % +--R retract : % -> R sample : () -> % +--R trace : % -> R traceMatrix : () -> Matrix R +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean +--R ?*? : (%,Fraction Integer) -> % if R has FIELD +--R ?*? : (Fraction Integer,%) -> % if R has FIELD +--R ?*? : (NonNegativeInteger,%) -> % +--R ?**? : (%,Integer) -> % if R has FIELD +--R ?**? : (%,NonNegativeInteger) -> % +--R ?/? : (%,%) -> % if R has FIELD +--R D : (%,(R -> R)) -> % if R has FIELD +--R D : (%,(R -> R),NonNegativeInteger) -> % if R has FIELD +--R D : (%,List Symbol,List NonNegativeInteger) -> % if R has FIELD and R has PDRING SYMBOL +--R D : (%,Symbol,NonNegativeInteger) -> % if R has FIELD and R has PDRING SYMBOL +--R D : (%,List Symbol) -> % if R has FIELD and R has PDRING SYMBOL +--R D : (%,Symbol) -> % if R has FIELD and R has PDRING SYMBOL +--R D : (%,NonNegativeInteger) -> % if R has DIFRING and R has FIELD or R has FFIELDC +--R D : % -> % if R has DIFRING and R has FIELD or R has FFIELDC +--R ?^? : (%,Integer) -> % if R has FIELD +--R ?^? : (%,NonNegativeInteger) -> % +--R associates? : (%,%) -> Boolean if R has FIELD +--R characteristic : () -> NonNegativeInteger +--R characteristicPolynomial : % -> UP +--R charthRoot : % -> Union(%,"failed") if R has CHARNZ +--R charthRoot : % -> % if R has FFIELDC +--R coerce : Fraction Integer -> % if R has FIELD or R has RETRACT FRAC INT +--R coerce : % -> % if R has FIELD +--R conditionP : Matrix % -> Union(Vector %,"failed") if R has FFIELDC +--R coordinates : Vector % -> Matrix R +--R coordinates : (Vector %,Vector %) -> Matrix R +--R coordinates : (%,Vector %) -> Vector R +--R createPrimitiveElement : () -> % if R has FFIELDC +--R derivationCoordinates : (Vector %,(R -> R)) -> Matrix R if R has FIELD +--R differentiate : (%,(R -> R)) -> % if R has FIELD +--R differentiate : (%,(R -> R),NonNegativeInteger) -> % if R has FIELD +--R differentiate : (%,List Symbol,List NonNegativeInteger) -> % if R has FIELD and R has PDRING SYMBOL +--R differentiate : (%,Symbol,NonNegativeInteger) -> % if R has FIELD and R has PDRING SYMBOL +--R differentiate : (%,List Symbol) -> % if R has FIELD and R has PDRING SYMBOL +--R differentiate : (%,Symbol) -> % if R has FIELD and R has PDRING SYMBOL +--R differentiate : (%,NonNegativeInteger) -> % if R has DIFRING and R has FIELD or R has FFIELDC +--R differentiate : % -> % if R has DIFRING and R has FIELD or R has FFIELDC +--R discreteLog : (%,%) -> Union(NonNegativeInteger,"failed") if R has FFIELDC +--R discreteLog : % -> NonNegativeInteger if R has FFIELDC +--R divide : (%,%) -> Record(quotient: %,remainder: %) if R has FIELD +--R euclideanSize : % -> NonNegativeInteger if R has FIELD +--R expressIdealMember : (List %,%) -> Union(List %,"failed") if R has FIELD +--R exquo : (%,%) -> Union(%,"failed") if R has FIELD +--R extendedEuclidean : (%,%) -> Record(coef1: %,coef2: %,generator: %) if R has FIELD +--R extendedEuclidean : (%,%,%) -> Union(Record(coef1: %,coef2: %),"failed") if R has FIELD +--R factor : % -> Factored % if R has FIELD +--R factorsOfCyclicGroupSize : () -> List Record(factor: Integer,exponent: Integer) if R has FFIELDC +--R gcd : (%,%) -> % if R has FIELD +--R gcd : List % -> % if R has FIELD +--R gcdPolynomial : (SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial % if R has FIELD +--R index : PositiveInteger -> % if R has FINITE +--R init : () -> % if R has FFIELDC +--R lcm : (%,%) -> % if R has FIELD +--R lcm : List % -> % if R has FIELD +--R lookup : % -> PositiveInteger if R has FINITE +--R minimalPolynomial : % -> UP if R has FIELD +--R multiEuclidean : (List %,%) -> Union(List %,"failed") if R has FIELD +--R nextItem : % -> Union(%,"failed") if R has FFIELDC +--R order : % -> OnePointCompletion PositiveInteger if R has FFIELDC +--R order : % -> PositiveInteger if R has FFIELDC +--R prime? : % -> Boolean if R has FIELD +--R primeFrobenius : % -> % if R has FFIELDC +--R primeFrobenius : (%,NonNegativeInteger) -> % if R has FFIELDC +--R primitive? : % -> Boolean if R has FFIELDC +--R primitiveElement : () -> % if R has FFIELDC +--R principalIdeal : List % -> Record(coef: List %,generator: %) if R has FIELD +--R ?quo? : (%,%) -> % if R has FIELD +--R random : () -> % if R has FINITE +--R reduce : Fraction UP -> Union(%,"failed") if R has FIELD +--R reducedSystem : Matrix % -> Matrix R +--R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix R,vec: Vector R) +--R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix Integer,vec: Vector Integer) if R has LINEXP INT +--R reducedSystem : Matrix % -> Matrix Integer if R has LINEXP INT +--R regularRepresentation : % -> Matrix R +--R regularRepresentation : (%,Vector %) -> Matrix R +--R ?rem? : (%,%) -> % if R has FIELD +--R representationType : () -> Union("prime",polynomial,normal,cyclic) if R has FFIELDC +--R represents : (Vector R,Vector %) -> % +--R retract : % -> Fraction Integer if R has RETRACT FRAC INT +--R retract : % -> Integer if R has RETRACT INT +--R retractIfCan : % -> Union(R,"failed") +--R retractIfCan : % -> Union(Fraction Integer,"failed") if R has RETRACT FRAC INT +--R retractIfCan : % -> Union(Integer,"failed") if R has RETRACT INT +--R size : () -> NonNegativeInteger if R has FINITE +--R sizeLess? : (%,%) -> Boolean if R has FIELD +--R squareFree : % -> Factored % if R has FIELD +--R squareFreePart : % -> % if R has FIELD +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R tableForDiscreteLogarithm : Integer -> Table(PositiveInteger,NonNegativeInteger) if R has FFIELDC +--R traceMatrix : Vector % -> Matrix R +--R unit? : % -> Boolean if R has FIELD +--R unitCanonical : % -> % if R has FIELD +--R unitNormal : % -> Record(unit: %,canonical: %,associate: %) if R has FIELD +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +SimpleAlgebraicExtension examples +==================================================================== + +See Also: +o )show SimpleAlgebraicExtension + +@ + \pagehead{SimpleAlgebraicExtension}{SAE} \pagepic{ps/v103simplealgebraicextension.ps}{SAE}{1.00} @@ -95729,6 +112644,41 @@ SimpleAlgebraicExtension(R:CommutativeRing, @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain SFORT SimpleFortranProgram} + +<>= +)set break resume +)sys rm -f SimpleFortranProgram.output +)spool SimpleFortranProgram.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show SimpleFortranProgram +--R SimpleFortranProgram(R: OrderedSet,FS: FunctionSpace R) is a domain constructor +--R Abbreviation for SimpleFortranProgram is SFORT +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for SFORT +--R +--R------------------------------- Operations -------------------------------- +--R coerce : % -> OutputForm outputAsFortran : % -> Void +--R fortran : (Symbol,FortranScalarType,FS) -> % +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +SimpleFortranProgram examples +==================================================================== + +See Also: +o )show SimpleFortranProgram + +@ + \pagehead{SimpleFortranProgram}{SFORT} \pagepic{ps/v103simplefortranprogram.ps}{SFORT}{1.00} {\bf See}\\ @@ -95822,6 +112772,7 @@ SimpleFortranProgram(R,FS): Exports == Implementation where The definition of {\bf one?} has been rewritten as it relies on calling {\bf ONEP} which is a function specific to Codemist Common Lisp but is not defined in Common Lisp. + <>= )set break resume )sys rm -f SingleInteger.output @@ -96315,6 +113266,46 @@ SingleInteger(): Join(IntegerNumberSystem,Logic,OpenMath) with @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain SAOS SingletonAsOrderedSet} + +<>= +)set break resume +)sys rm -f SingletonAsOrderedSet.output +)spool SingletonAsOrderedSet.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show SingletonAsOrderedSet +--R SingletonAsOrderedSet is a domain constructor +--R Abbreviation for SingletonAsOrderedSet is SAOS +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for SAOS +--R +--R------------------------------- Operations -------------------------------- +--R ? Boolean ?<=? : (%,%) -> Boolean +--R ?=? : (%,%) -> Boolean ?>? : (%,%) -> Boolean +--R ?>=? : (%,%) -> Boolean coerce : % -> OutputForm +--R convert : % -> Symbol create : () -> % +--R hash : % -> SingleInteger latex : % -> String +--R max : (%,%) -> % min : (%,%) -> % +--R ?~=? : (%,%) -> Boolean +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +SingletonAsOrderedSet examples +==================================================================== + +See Also: +o )show SingletonAsOrderedSet + +@ + \pagehead{SingletonAsOrderedSet}{SAOS} \pagepic{ps/v103singletonasorderedset.ps}{SAOS}{1.00} @@ -96363,6 +113354,154 @@ SingletonAsOrderedSet(): OrderedSet with @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain SMP SparseMultivariatePolynomial} + +<>= +)set break resume +)sys rm -f SparseMultivariatePolynomial.output +)spool SparseMultivariatePolynomial.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show SparseMultivariatePolynomial +--R SparseMultivariatePolynomial(R: Ring,VarSet: OrderedSet) is a domain constructor +--R Abbreviation for SparseMultivariatePolynomial is SMP +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for SMP +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (%,R) -> % ?*? : (R,%) -> % +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ?=? : (%,%) -> Boolean +--R D : (%,List VarSet) -> % D : (%,VarSet) -> % +--R 1 : () -> % 0 : () -> % +--R ?^? : (%,PositiveInteger) -> % coefficients : % -> List R +--R coerce : VarSet -> % coerce : R -> % +--R coerce : Integer -> % coerce : % -> OutputForm +--R differentiate : (%,VarSet) -> % eval : (%,VarSet,%) -> % +--R eval : (%,VarSet,R) -> % eval : (%,List %,List %) -> % +--R eval : (%,%,%) -> % eval : (%,Equation %) -> % +--R eval : (%,List Equation %) -> % ground : % -> R +--R ground? : % -> Boolean hash : % -> SingleInteger +--R latex : % -> String leadingCoefficient : % -> R +--R leadingMonomial : % -> % map : ((R -> R),%) -> % +--R monomial? : % -> Boolean monomials : % -> List % +--R one? : % -> Boolean primitiveMonomials : % -> List % +--R recip : % -> Union(%,"failed") reductum : % -> % +--R retract : % -> VarSet retract : % -> R +--R sample : () -> % variables : % -> List VarSet +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean +--R ?*? : (Fraction Integer,%) -> % if R has ALGEBRA FRAC INT +--R ?*? : (%,Fraction Integer) -> % if R has ALGEBRA FRAC INT +--R ?*? : (NonNegativeInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % +--R ?/? : (%,R) -> % if R has FIELD +--R ? Boolean if R has ORDSET +--R ?<=? : (%,%) -> Boolean if R has ORDSET +--R ?>? : (%,%) -> Boolean if R has ORDSET +--R ?>=? : (%,%) -> Boolean if R has ORDSET +--R D : (%,List VarSet,List NonNegativeInteger) -> % +--R D : (%,VarSet,NonNegativeInteger) -> % +--R ?^? : (%,NonNegativeInteger) -> % +--R associates? : (%,%) -> Boolean if R has INTDOM +--R binomThmExpt : (%,%,NonNegativeInteger) -> % if R has COMRING +--R characteristic : () -> NonNegativeInteger +--R charthRoot : % -> Union(%,"failed") if $ has CHARNZ and R has PFECAT or R has CHARNZ +--R coefficient : (%,List VarSet,List NonNegativeInteger) -> % +--R coefficient : (%,VarSet,NonNegativeInteger) -> % +--R coefficient : (%,IndexedExponents VarSet) -> R +--R coerce : Fraction Integer -> % if R has ALGEBRA FRAC INT or R has RETRACT FRAC INT +--R coerce : % -> % if R has INTDOM +--R conditionP : Matrix % -> Union(Vector %,"failed") if $ has CHARNZ and R has PFECAT +--R content : (%,VarSet) -> % if R has GCDDOM +--R content : % -> R if R has GCDDOM +--R convert : % -> InputForm if R has KONVERT INFORM and VarSet has KONVERT INFORM +--R convert : % -> Pattern Integer if R has KONVERT PATTERN INT and VarSet has KONVERT PATTERN INT +--R convert : % -> Pattern Float if R has KONVERT PATTERN FLOAT and VarSet has KONVERT PATTERN FLOAT +--R degree : (%,List VarSet) -> List NonNegativeInteger +--R degree : (%,VarSet) -> NonNegativeInteger +--R degree : % -> IndexedExponents VarSet +--R differentiate : (%,List VarSet,List NonNegativeInteger) -> % +--R differentiate : (%,VarSet,NonNegativeInteger) -> % +--R differentiate : (%,List VarSet) -> % +--R discriminant : (%,VarSet) -> % if R has COMRING +--R eval : (%,List VarSet,List %) -> % +--R eval : (%,List VarSet,List R) -> % +--R exquo : (%,%) -> Union(%,"failed") if R has INTDOM +--R exquo : (%,R) -> Union(%,"failed") if R has INTDOM +--R factor : % -> Factored % if R has PFECAT +--R factorPolynomial : SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if R has PFECAT +--R factorSquareFreePolynomial : SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if R has PFECAT +--R gcd : (%,%) -> % if R has GCDDOM +--R gcd : List % -> % if R has GCDDOM +--R gcdPolynomial : (SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial % if R has GCDDOM +--R isExpt : % -> Union(Record(var: VarSet,exponent: NonNegativeInteger),"failed") +--R isPlus : % -> Union(List %,"failed") +--R isTimes : % -> Union(List %,"failed") +--R lcm : (%,%) -> % if R has GCDDOM +--R lcm : List % -> % if R has GCDDOM +--R mainVariable : % -> Union(VarSet,"failed") +--R mapExponents : ((IndexedExponents VarSet -> IndexedExponents VarSet),%) -> % +--R max : (%,%) -> % if R has ORDSET +--R min : (%,%) -> % if R has ORDSET +--R minimumDegree : (%,List VarSet) -> List NonNegativeInteger +--R minimumDegree : (%,VarSet) -> NonNegativeInteger +--R minimumDegree : % -> IndexedExponents VarSet +--R monicDivide : (%,%,VarSet) -> Record(quotient: %,remainder: %) +--R monomial : (%,List VarSet,List NonNegativeInteger) -> % +--R monomial : (%,VarSet,NonNegativeInteger) -> % +--R monomial : (R,IndexedExponents VarSet) -> % +--R multivariate : (SparseUnivariatePolynomial %,VarSet) -> % +--R multivariate : (SparseUnivariatePolynomial R,VarSet) -> % +--R numberOfMonomials : % -> NonNegativeInteger +--R patternMatch : (%,Pattern Integer,PatternMatchResult(Integer,%)) -> PatternMatchResult(Integer,%) if R has PATMAB INT and VarSet has PATMAB INT +--R patternMatch : (%,Pattern Float,PatternMatchResult(Float,%)) -> PatternMatchResult(Float,%) if R has PATMAB FLOAT and VarSet has PATMAB FLOAT +--R pomopo! : (%,R,IndexedExponents VarSet,%) -> % +--R prime? : % -> Boolean if R has PFECAT +--R primitivePart : (%,VarSet) -> % if R has GCDDOM +--R primitivePart : % -> % if R has GCDDOM +--R reducedSystem : Matrix % -> Matrix R +--R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix R,vec: Vector R) +--R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix Integer,vec: Vector Integer) if R has LINEXP INT +--R reducedSystem : Matrix % -> Matrix Integer if R has LINEXP INT +--R resultant : (%,%,VarSet) -> % if R has COMRING +--R retract : % -> Integer if R has RETRACT INT +--R retract : % -> Fraction Integer if R has RETRACT FRAC INT +--R retractIfCan : % -> Union(VarSet,"failed") +--R retractIfCan : % -> Union(Integer,"failed") if R has RETRACT INT +--R retractIfCan : % -> Union(Fraction Integer,"failed") if R has RETRACT FRAC INT +--R retractIfCan : % -> Union(R,"failed") +--R solveLinearPolynomialEquation : (List SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> Union(List SparseUnivariatePolynomial %,"failed") if R has PFECAT +--R squareFree : % -> Factored % if R has GCDDOM +--R squareFreePart : % -> % if R has GCDDOM +--R squareFreePolynomial : SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if R has PFECAT +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R totalDegree : (%,List VarSet) -> NonNegativeInteger +--R totalDegree : % -> NonNegativeInteger +--R unit? : % -> Boolean if R has INTDOM +--R unitCanonical : % -> % if R has INTDOM +--R unitNormal : % -> Record(unit: %,canonical: %,associate: %) if R has INTDOM +--R univariate : % -> SparseUnivariatePolynomial R +--R univariate : (%,VarSet) -> SparseUnivariatePolynomial % +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +SparseMultivariatePolynomial examples +==================================================================== + +See Also: +o )show SparseMultivariatePolynomial + +@ + \pagehead{SparseMultivariatePolynomial}{SMP} \pagepic{ps/v103sparsemultivariatepolynomial.ps}{SMP}{1.00} {\bf See}\\ @@ -97044,6 +114183,7 @@ SparseMultivariatePolynomial(R: Ring,VarSet: OrderedSet): C == T where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain SMTS SparseMultivariateTaylorSeries} + <>= )set break resume )sys rm -f SparseMultivariateTaylorSeries.output @@ -97659,6 +114799,7 @@ SparseMultivariateTaylorSeries(Coef,Var,SMP):_ @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain STBL SparseTable} + <>= )set break resume )sys rm -f SparseTable.output @@ -97878,6 +115019,226 @@ SparseTable(Key:SetCategory, Ent:SetCategory, dent:Ent) == @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain SULS SparseUnivariateLaurentSeries} + +<>= +)set break resume +)sys rm -f SparseUnivariateLaurentSeries.output +)spool SparseUnivariateLaurentSeries.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show SparseUnivariateLaurentSeries +--R SparseUnivariateLaurentSeries(Coef: Ring,var: Symbol,cen: Coef) is a domain constructor +--R Abbreviation for SparseUnivariateLaurentSeries is SULS +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for SULS +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (Coef,%) -> % ?*? : (%,Coef) -> % +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ?=? : (%,%) -> Boolean +--R 1 : () -> % 0 : () -> % +--R ?^? : (%,PositiveInteger) -> % center : % -> Coef +--R coefficient : (%,Integer) -> Coef coerce : Variable var -> % +--R coerce : Integer -> % coerce : % -> OutputForm +--R complete : % -> % degree : % -> Integer +--R ?.? : (%,Integer) -> Coef extend : (%,Integer) -> % +--R hash : % -> SingleInteger latex : % -> String +--R leadingCoefficient : % -> Coef leadingMonomial : % -> % +--R map : ((Coef -> Coef),%) -> % monomial : (Coef,Integer) -> % +--R monomial? : % -> Boolean one? : % -> Boolean +--R order : (%,Integer) -> Integer order : % -> Integer +--R pole? : % -> Boolean recip : % -> Union(%,"failed") +--R reductum : % -> % removeZeroes : (Integer,%) -> % +--R removeZeroes : % -> % sample : () -> % +--R truncate : (%,Integer) -> % variable : % -> Symbol +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean +--R ?*? : (%,Fraction Integer) -> % if Coef has ALGEBRA FRAC INT +--R ?*? : (Fraction Integer,%) -> % if Coef has ALGEBRA FRAC INT +--R ?*? : (SparseUnivariateTaylorSeries(Coef,var,cen),%) -> % if Coef has FIELD +--R ?*? : (%,SparseUnivariateTaylorSeries(Coef,var,cen)) -> % if Coef has FIELD +--R ?*? : (NonNegativeInteger,%) -> % +--R ?**? : (%,Fraction Integer) -> % if Coef has ALGEBRA FRAC INT +--R ?**? : (%,%) -> % if Coef has ALGEBRA FRAC INT +--R ?**? : (%,Integer) -> % if Coef has FIELD +--R ?**? : (%,NonNegativeInteger) -> % +--R ?/? : (SparseUnivariateTaylorSeries(Coef,var,cen),SparseUnivariateTaylorSeries(Coef,var,cen)) -> % if Coef has FIELD +--R ?/? : (%,%) -> % if Coef has FIELD +--R ?/? : (%,Coef) -> % if Coef has FIELD +--R ? Boolean if SparseUnivariateTaylorSeries(Coef,var,cen) has OINTDOM and Coef has FIELD or SparseUnivariateTaylorSeries(Coef,var,cen) has ORDSET and Coef has FIELD +--R ?<=? : (%,%) -> Boolean if SparseUnivariateTaylorSeries(Coef,var,cen) has OINTDOM and Coef has FIELD or SparseUnivariateTaylorSeries(Coef,var,cen) has ORDSET and Coef has FIELD +--R ?>? : (%,%) -> Boolean if SparseUnivariateTaylorSeries(Coef,var,cen) has OINTDOM and Coef has FIELD or SparseUnivariateTaylorSeries(Coef,var,cen) has ORDSET and Coef has FIELD +--R ?>=? : (%,%) -> Boolean if SparseUnivariateTaylorSeries(Coef,var,cen) has OINTDOM and Coef has FIELD or SparseUnivariateTaylorSeries(Coef,var,cen) has ORDSET and Coef has FIELD +--R D : (%,Symbol) -> % if SparseUnivariateTaylorSeries(Coef,var,cen) has PDRING SYMBOL and Coef has FIELD or Coef has *: (Integer,Coef) -> Coef and Coef has PDRING SYMBOL +--R D : (%,List Symbol) -> % if SparseUnivariateTaylorSeries(Coef,var,cen) has PDRING SYMBOL and Coef has FIELD or Coef has *: (Integer,Coef) -> Coef and Coef has PDRING SYMBOL +--R D : (%,Symbol,NonNegativeInteger) -> % if SparseUnivariateTaylorSeries(Coef,var,cen) has PDRING SYMBOL and Coef has FIELD or Coef has *: (Integer,Coef) -> Coef and Coef has PDRING SYMBOL +--R D : (%,List Symbol,List NonNegativeInteger) -> % if SparseUnivariateTaylorSeries(Coef,var,cen) has PDRING SYMBOL and Coef has FIELD or Coef has *: (Integer,Coef) -> Coef and Coef has PDRING SYMBOL +--R D : % -> % if SparseUnivariateTaylorSeries(Coef,var,cen) has DIFRING and Coef has FIELD or Coef has *: (Integer,Coef) -> Coef +--R D : (%,NonNegativeInteger) -> % if SparseUnivariateTaylorSeries(Coef,var,cen) has DIFRING and Coef has FIELD or Coef has *: (Integer,Coef) -> Coef +--R D : (%,(SparseUnivariateTaylorSeries(Coef,var,cen) -> SparseUnivariateTaylorSeries(Coef,var,cen)),NonNegativeInteger) -> % if Coef has FIELD +--R D : (%,(SparseUnivariateTaylorSeries(Coef,var,cen) -> SparseUnivariateTaylorSeries(Coef,var,cen))) -> % if Coef has FIELD +--R ?^? : (%,Integer) -> % if Coef has FIELD +--R ?^? : (%,NonNegativeInteger) -> % +--R abs : % -> % if SparseUnivariateTaylorSeries(Coef,var,cen) has OINTDOM and Coef has FIELD +--R acos : % -> % if Coef has ALGEBRA FRAC INT +--R acosh : % -> % if Coef has ALGEBRA FRAC INT +--R acot : % -> % if Coef has ALGEBRA FRAC INT +--R acoth : % -> % if Coef has ALGEBRA FRAC INT +--R acsc : % -> % if Coef has ALGEBRA FRAC INT +--R acsch : % -> % if Coef has ALGEBRA FRAC INT +--R approximate : (%,Integer) -> Coef if Coef has **: (Coef,Integer) -> Coef and Coef has coerce: Symbol -> Coef +--R asec : % -> % if Coef has ALGEBRA FRAC INT +--R asech : % -> % if Coef has ALGEBRA FRAC INT +--R asin : % -> % if Coef has ALGEBRA FRAC INT +--R asinh : % -> % if Coef has ALGEBRA FRAC INT +--R associates? : (%,%) -> Boolean if SparseUnivariateTaylorSeries(Coef,var,cen) has OINTDOM and Coef has FIELD or SparseUnivariateTaylorSeries(Coef,var,cen) has PFECAT and Coef has FIELD or Coef has INTDOM +--R atan : % -> % if Coef has ALGEBRA FRAC INT +--R atanh : % -> % if Coef has ALGEBRA FRAC INT +--R ceiling : % -> SparseUnivariateTaylorSeries(Coef,var,cen) if SparseUnivariateTaylorSeries(Coef,var,cen) has INS and Coef has FIELD +--R characteristic : () -> NonNegativeInteger +--R charthRoot : % -> Union(%,"failed") if $ has CHARNZ and SparseUnivariateTaylorSeries(Coef,var,cen) has PFECAT and Coef has FIELD or SparseUnivariateTaylorSeries(Coef,var,cen) has CHARNZ and Coef has FIELD or Coef has CHARNZ +--R coerce : Fraction Integer -> % if SparseUnivariateTaylorSeries(Coef,var,cen) has RETRACT INT and Coef has FIELD or Coef has ALGEBRA FRAC INT +--R coerce : % -> % if SparseUnivariateTaylorSeries(Coef,var,cen) has OINTDOM and Coef has FIELD or SparseUnivariateTaylorSeries(Coef,var,cen) has PFECAT and Coef has FIELD or Coef has INTDOM +--R coerce : Symbol -> % if SparseUnivariateTaylorSeries(Coef,var,cen) has RETRACT SYMBOL and Coef has FIELD +--R coerce : SparseUnivariateTaylorSeries(Coef,var,cen) -> % +--R coerce : Coef -> % if Coef has COMRING +--R conditionP : Matrix % -> Union(Vector %,"failed") if $ has CHARNZ and SparseUnivariateTaylorSeries(Coef,var,cen) has PFECAT and Coef has FIELD +--R convert : % -> Pattern Integer if SparseUnivariateTaylorSeries(Coef,var,cen) has KONVERT PATTERN INT and Coef has FIELD +--R convert : % -> Pattern Float if SparseUnivariateTaylorSeries(Coef,var,cen) has KONVERT PATTERN FLOAT and Coef has FIELD +--R convert : % -> DoubleFloat if SparseUnivariateTaylorSeries(Coef,var,cen) has REAL and Coef has FIELD +--R convert : % -> Float if SparseUnivariateTaylorSeries(Coef,var,cen) has REAL and Coef has FIELD +--R convert : % -> InputForm if SparseUnivariateTaylorSeries(Coef,var,cen) has KONVERT INFORM and Coef has FIELD +--R cos : % -> % if Coef has ALGEBRA FRAC INT +--R cosh : % -> % if Coef has ALGEBRA FRAC INT +--R cot : % -> % if Coef has ALGEBRA FRAC INT +--R coth : % -> % if Coef has ALGEBRA FRAC INT +--R csc : % -> % if Coef has ALGEBRA FRAC INT +--R csch : % -> % if Coef has ALGEBRA FRAC INT +--R denom : % -> SparseUnivariateTaylorSeries(Coef,var,cen) if Coef has FIELD +--R denominator : % -> % if Coef has FIELD +--R differentiate : (%,Symbol) -> % if SparseUnivariateTaylorSeries(Coef,var,cen) has PDRING SYMBOL and Coef has FIELD or Coef has *: (Integer,Coef) -> Coef and Coef has PDRING SYMBOL +--R differentiate : (%,List Symbol) -> % if SparseUnivariateTaylorSeries(Coef,var,cen) has PDRING SYMBOL and Coef has FIELD or Coef has *: (Integer,Coef) -> Coef and Coef has PDRING SYMBOL +--R differentiate : (%,Symbol,NonNegativeInteger) -> % if SparseUnivariateTaylorSeries(Coef,var,cen) has PDRING SYMBOL and Coef has FIELD or Coef has *: (Integer,Coef) -> Coef and Coef has PDRING SYMBOL +--R differentiate : (%,List Symbol,List NonNegativeInteger) -> % if SparseUnivariateTaylorSeries(Coef,var,cen) has PDRING SYMBOL and Coef has FIELD or Coef has *: (Integer,Coef) -> Coef and Coef has PDRING SYMBOL +--R differentiate : % -> % if SparseUnivariateTaylorSeries(Coef,var,cen) has DIFRING and Coef has FIELD or Coef has *: (Integer,Coef) -> Coef +--R differentiate : (%,NonNegativeInteger) -> % if SparseUnivariateTaylorSeries(Coef,var,cen) has DIFRING and Coef has FIELD or Coef has *: (Integer,Coef) -> Coef +--R differentiate : (%,Variable var) -> % +--R differentiate : (%,(SparseUnivariateTaylorSeries(Coef,var,cen) -> SparseUnivariateTaylorSeries(Coef,var,cen)),NonNegativeInteger) -> % if Coef has FIELD +--R differentiate : (%,(SparseUnivariateTaylorSeries(Coef,var,cen) -> SparseUnivariateTaylorSeries(Coef,var,cen))) -> % if Coef has FIELD +--R divide : (%,%) -> Record(quotient: %,remainder: %) if Coef has FIELD +--R ?.? : (%,SparseUnivariateTaylorSeries(Coef,var,cen)) -> % if SparseUnivariateTaylorSeries(Coef,var,cen) has ELTAB(SUTS(Coef,var,cen),SUTS(Coef,var,cen)) and Coef has FIELD +--R ?.? : (%,%) -> % if Integer has SGROUP +--R euclideanSize : % -> NonNegativeInteger if Coef has FIELD +--R eval : (%,List SparseUnivariateTaylorSeries(Coef,var,cen),List SparseUnivariateTaylorSeries(Coef,var,cen)) -> % if SparseUnivariateTaylorSeries(Coef,var,cen) has EVALAB SUTS(Coef,var,cen) and Coef has FIELD +--R eval : (%,SparseUnivariateTaylorSeries(Coef,var,cen),SparseUnivariateTaylorSeries(Coef,var,cen)) -> % if SparseUnivariateTaylorSeries(Coef,var,cen) has EVALAB SUTS(Coef,var,cen) and Coef has FIELD +--R eval : (%,Equation SparseUnivariateTaylorSeries(Coef,var,cen)) -> % if SparseUnivariateTaylorSeries(Coef,var,cen) has EVALAB SUTS(Coef,var,cen) and Coef has FIELD +--R eval : (%,List Equation SparseUnivariateTaylorSeries(Coef,var,cen)) -> % if SparseUnivariateTaylorSeries(Coef,var,cen) has EVALAB SUTS(Coef,var,cen) and Coef has FIELD +--R eval : (%,List Symbol,List SparseUnivariateTaylorSeries(Coef,var,cen)) -> % if SparseUnivariateTaylorSeries(Coef,var,cen) has IEVALAB(SYMBOL,SUTS(Coef,var,cen)) and Coef has FIELD +--R eval : (%,Symbol,SparseUnivariateTaylorSeries(Coef,var,cen)) -> % if SparseUnivariateTaylorSeries(Coef,var,cen) has IEVALAB(SYMBOL,SUTS(Coef,var,cen)) and Coef has FIELD +--R eval : (%,Coef) -> Stream Coef if Coef has **: (Coef,Integer) -> Coef +--R exp : % -> % if Coef has ALGEBRA FRAC INT +--R expressIdealMember : (List %,%) -> Union(List %,"failed") if Coef has FIELD +--R exquo : (%,%) -> Union(%,"failed") if SparseUnivariateTaylorSeries(Coef,var,cen) has OINTDOM and Coef has FIELD or SparseUnivariateTaylorSeries(Coef,var,cen) has PFECAT and Coef has FIELD or Coef has INTDOM +--R extendedEuclidean : (%,%) -> Record(coef1: %,coef2: %,generator: %) if Coef has FIELD +--R extendedEuclidean : (%,%,%) -> Union(Record(coef1: %,coef2: %),"failed") if Coef has FIELD +--R factor : % -> Factored % if Coef has FIELD +--R factorPolynomial : SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if SparseUnivariateTaylorSeries(Coef,var,cen) has PFECAT and Coef has FIELD +--R factorSquareFreePolynomial : SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if SparseUnivariateTaylorSeries(Coef,var,cen) has PFECAT and Coef has FIELD +--R floor : % -> SparseUnivariateTaylorSeries(Coef,var,cen) if SparseUnivariateTaylorSeries(Coef,var,cen) has INS and Coef has FIELD +--R fractionPart : % -> % if SparseUnivariateTaylorSeries(Coef,var,cen) has EUCDOM and Coef has FIELD +--R gcd : (%,%) -> % if Coef has FIELD +--R gcd : List % -> % if Coef has FIELD +--R gcdPolynomial : (SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial % if Coef has FIELD +--R init : () -> % if SparseUnivariateTaylorSeries(Coef,var,cen) has STEP and Coef has FIELD +--R integrate : (%,Variable var) -> % if Coef has ALGEBRA FRAC INT +--R integrate : (%,Symbol) -> % if Coef has integrate: (Coef,Symbol) -> Coef and Coef has variables: Coef -> List Symbol and Coef has ALGEBRA FRAC INT or Coef has ACFS INT and Coef has ALGEBRA FRAC INT and Coef has PRIMCAT and Coef has TRANFUN +--R integrate : % -> % if Coef has ALGEBRA FRAC INT +--R inv : % -> % if Coef has FIELD +--R laurent : (Integer,SparseUnivariateTaylorSeries(Coef,var,cen)) -> % +--R lcm : (%,%) -> % if Coef has FIELD +--R lcm : List % -> % if Coef has FIELD +--R log : % -> % if Coef has ALGEBRA FRAC INT +--R map : ((SparseUnivariateTaylorSeries(Coef,var,cen) -> SparseUnivariateTaylorSeries(Coef,var,cen)),%) -> % if Coef has FIELD +--R max : (%,%) -> % if SparseUnivariateTaylorSeries(Coef,var,cen) has OINTDOM and Coef has FIELD or SparseUnivariateTaylorSeries(Coef,var,cen) has ORDSET and Coef has FIELD +--R min : (%,%) -> % if SparseUnivariateTaylorSeries(Coef,var,cen) has OINTDOM and Coef has FIELD or SparseUnivariateTaylorSeries(Coef,var,cen) has ORDSET and Coef has FIELD +--R monomial : (%,List SingletonAsOrderedSet,List Integer) -> % +--R monomial : (%,SingletonAsOrderedSet,Integer) -> % +--R multiEuclidean : (List %,%) -> Union(List %,"failed") if Coef has FIELD +--R multiplyCoefficients : ((Integer -> Coef),%) -> % +--R multiplyExponents : (%,PositiveInteger) -> % +--R negative? : % -> Boolean if SparseUnivariateTaylorSeries(Coef,var,cen) has OINTDOM and Coef has FIELD +--R nextItem : % -> Union(%,"failed") if SparseUnivariateTaylorSeries(Coef,var,cen) has STEP and Coef has FIELD +--R nthRoot : (%,Integer) -> % if Coef has ALGEBRA FRAC INT +--R numer : % -> SparseUnivariateTaylorSeries(Coef,var,cen) if Coef has FIELD +--R numerator : % -> % if Coef has FIELD +--R patternMatch : (%,Pattern Float,PatternMatchResult(Float,%)) -> PatternMatchResult(Float,%) if SparseUnivariateTaylorSeries(Coef,var,cen) has PATMAB FLOAT and Coef has FIELD +--R patternMatch : (%,Pattern Integer,PatternMatchResult(Integer,%)) -> PatternMatchResult(Integer,%) if SparseUnivariateTaylorSeries(Coef,var,cen) has PATMAB INT and Coef has FIELD +--R pi : () -> % if Coef has ALGEBRA FRAC INT +--R positive? : % -> Boolean if SparseUnivariateTaylorSeries(Coef,var,cen) has OINTDOM and Coef has FIELD +--R prime? : % -> Boolean if Coef has FIELD +--R principalIdeal : List % -> Record(coef: List %,generator: %) if Coef has FIELD +--R ?quo? : (%,%) -> % if Coef has FIELD +--R random : () -> % if SparseUnivariateTaylorSeries(Coef,var,cen) has INS and Coef has FIELD +--R rationalFunction : (%,Integer,Integer) -> Fraction Polynomial Coef if Coef has INTDOM +--R rationalFunction : (%,Integer) -> Fraction Polynomial Coef if Coef has INTDOM +--R reducedSystem : Matrix % -> Matrix Integer if SparseUnivariateTaylorSeries(Coef,var,cen) has LINEXP INT and Coef has FIELD +--R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix Integer,vec: Vector Integer) if SparseUnivariateTaylorSeries(Coef,var,cen) has LINEXP INT and Coef has FIELD +--R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix SparseUnivariateTaylorSeries(Coef,var,cen),vec: Vector SparseUnivariateTaylorSeries(Coef,var,cen)) if Coef has FIELD +--R reducedSystem : Matrix % -> Matrix SparseUnivariateTaylorSeries(Coef,var,cen) if Coef has FIELD +--R ?rem? : (%,%) -> % if Coef has FIELD +--R retract : % -> Integer if SparseUnivariateTaylorSeries(Coef,var,cen) has RETRACT INT and Coef has FIELD +--R retract : % -> Fraction Integer if SparseUnivariateTaylorSeries(Coef,var,cen) has RETRACT INT and Coef has FIELD +--R retract : % -> Symbol if SparseUnivariateTaylorSeries(Coef,var,cen) has RETRACT SYMBOL and Coef has FIELD +--R retract : % -> SparseUnivariateTaylorSeries(Coef,var,cen) +--R retractIfCan : % -> Union(Integer,"failed") if SparseUnivariateTaylorSeries(Coef,var,cen) has RETRACT INT and Coef has FIELD +--R retractIfCan : % -> Union(Fraction Integer,"failed") if SparseUnivariateTaylorSeries(Coef,var,cen) has RETRACT INT and Coef has FIELD +--R retractIfCan : % -> Union(Symbol,"failed") if SparseUnivariateTaylorSeries(Coef,var,cen) has RETRACT SYMBOL and Coef has FIELD +--R retractIfCan : % -> Union(SparseUnivariateTaylorSeries(Coef,var,cen),"failed") +--R sec : % -> % if Coef has ALGEBRA FRAC INT +--R sech : % -> % if Coef has ALGEBRA FRAC INT +--R series : Stream Record(k: Integer,c: Coef) -> % +--R sign : % -> Integer if SparseUnivariateTaylorSeries(Coef,var,cen) has OINTDOM and Coef has FIELD +--R sin : % -> % if Coef has ALGEBRA FRAC INT +--R sinh : % -> % if Coef has ALGEBRA FRAC INT +--R sizeLess? : (%,%) -> Boolean if Coef has FIELD +--R solveLinearPolynomialEquation : (List SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> Union(List SparseUnivariatePolynomial %,"failed") if SparseUnivariateTaylorSeries(Coef,var,cen) has PFECAT and Coef has FIELD +--R sqrt : % -> % if Coef has ALGEBRA FRAC INT +--R squareFree : % -> Factored % if Coef has FIELD +--R squareFreePart : % -> % if Coef has FIELD +--R squareFreePolynomial : SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if SparseUnivariateTaylorSeries(Coef,var,cen) has PFECAT and Coef has FIELD +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R tan : % -> % if Coef has ALGEBRA FRAC INT +--R tanh : % -> % if Coef has ALGEBRA FRAC INT +--R taylor : % -> SparseUnivariateTaylorSeries(Coef,var,cen) +--R taylorIfCan : % -> Union(SparseUnivariateTaylorSeries(Coef,var,cen),"failed") +--R taylorRep : % -> SparseUnivariateTaylorSeries(Coef,var,cen) +--R terms : % -> Stream Record(k: Integer,c: Coef) +--R truncate : (%,Integer,Integer) -> % +--R unit? : % -> Boolean if SparseUnivariateTaylorSeries(Coef,var,cen) has OINTDOM and Coef has FIELD or SparseUnivariateTaylorSeries(Coef,var,cen) has PFECAT and Coef has FIELD or Coef has INTDOM +--R unitCanonical : % -> % if SparseUnivariateTaylorSeries(Coef,var,cen) has OINTDOM and Coef has FIELD or SparseUnivariateTaylorSeries(Coef,var,cen) has PFECAT and Coef has FIELD or Coef has INTDOM +--R unitNormal : % -> Record(unit: %,canonical: %,associate: %) if SparseUnivariateTaylorSeries(Coef,var,cen) has OINTDOM and Coef has FIELD or SparseUnivariateTaylorSeries(Coef,var,cen) has PFECAT and Coef has FIELD or Coef has INTDOM +--R variables : % -> List SingletonAsOrderedSet +--R wholePart : % -> SparseUnivariateTaylorSeries(Coef,var,cen) if SparseUnivariateTaylorSeries(Coef,var,cen) has EUCDOM and Coef has FIELD +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +SparseUnivariateLaurentSeries examples +==================================================================== + +See Also: +o )show SparseUnivariateLaurentSeries + +@ + \pagehead{SparseUnivariateLaurentSeries}{SULS} \pagepic{ps/v103sparseunivariatelaurentseries.ps}{SULS}{1.00} @@ -98226,6 +115587,210 @@ SparseUnivariateLaurentSeries(Coef,var,cen): Exports == Implementation where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain SUP SparseUnivariatePolynomial} + +<>= +)set break resume +)sys rm -f SparseUnivariatePolynomial.output +)spool SparseUnivariatePolynomial.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show SparseUnivariatePolynomial +--R SparseUnivariatePolynomial R: Ring is a domain constructor +--R Abbreviation for SparseUnivariatePolynomial is SUP +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for SUP +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (%,R) -> % ?*? : (R,%) -> % +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ?=? : (%,%) -> Boolean +--R D : (%,(R -> R)) -> % D : % -> % +--R D : (%,NonNegativeInteger) -> % 1 : () -> % +--R 0 : () -> % ?^? : (%,PositiveInteger) -> % +--R coefficients : % -> List R coerce : R -> % +--R coerce : Integer -> % coerce : % -> OutputForm +--R degree : % -> NonNegativeInteger differentiate : % -> % +--R ?.? : (%,%) -> % ?.? : (%,R) -> R +--R eval : (%,List %,List %) -> % eval : (%,%,%) -> % +--R eval : (%,Equation %) -> % eval : (%,List Equation %) -> % +--R ground : % -> R ground? : % -> Boolean +--R hash : % -> SingleInteger init : () -> % if R has STEP +--R latex : % -> String leadingCoefficient : % -> R +--R leadingMonomial : % -> % map : ((R -> R),%) -> % +--R monomial? : % -> Boolean monomials : % -> List % +--R one? : % -> Boolean primitiveMonomials : % -> List % +--R pseudoRemainder : (%,%) -> % recip : % -> Union(%,"failed") +--R reductum : % -> % retract : % -> R +--R sample : () -> % zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean +--R ?*? : (Fraction Integer,%) -> % if R has ALGEBRA FRAC INT +--R ?*? : (%,Fraction Integer) -> % if R has ALGEBRA FRAC INT +--R ?*? : (NonNegativeInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % +--R ?/? : (%,R) -> % if R has FIELD +--R ? Boolean if R has ORDSET +--R ?<=? : (%,%) -> Boolean if R has ORDSET +--R ?>? : (%,%) -> Boolean if R has ORDSET +--R ?>=? : (%,%) -> Boolean if R has ORDSET +--R D : (%,(R -> R),NonNegativeInteger) -> % +--R D : (%,List Symbol,List NonNegativeInteger) -> % if R has PDRING SYMBOL +--R D : (%,Symbol,NonNegativeInteger) -> % if R has PDRING SYMBOL +--R D : (%,List Symbol) -> % if R has PDRING SYMBOL +--R D : (%,Symbol) -> % if R has PDRING SYMBOL +--R D : (%,List SingletonAsOrderedSet,List NonNegativeInteger) -> % +--R D : (%,SingletonAsOrderedSet,NonNegativeInteger) -> % +--R D : (%,List SingletonAsOrderedSet) -> % +--R D : (%,SingletonAsOrderedSet) -> % +--R ?^? : (%,NonNegativeInteger) -> % +--R associates? : (%,%) -> Boolean if R has INTDOM +--R binomThmExpt : (%,%,NonNegativeInteger) -> % if R has COMRING +--R characteristic : () -> NonNegativeInteger +--R charthRoot : % -> Union(%,"failed") if $ has CHARNZ and R has PFECAT or R has CHARNZ +--R coefficient : (%,List SingletonAsOrderedSet,List NonNegativeInteger) -> % +--R coefficient : (%,SingletonAsOrderedSet,NonNegativeInteger) -> % +--R coefficient : (%,NonNegativeInteger) -> R +--R coerce : % -> % if R has INTDOM +--R coerce : Fraction Integer -> % if R has ALGEBRA FRAC INT or R has RETRACT FRAC INT +--R coerce : SingletonAsOrderedSet -> % +--R composite : (Fraction %,%) -> Union(Fraction %,"failed") if R has INTDOM +--R composite : (%,%) -> Union(%,"failed") if R has INTDOM +--R conditionP : Matrix % -> Union(Vector %,"failed") if $ has CHARNZ and R has PFECAT +--R content : (%,SingletonAsOrderedSet) -> % if R has GCDDOM +--R content : % -> R if R has GCDDOM +--R convert : % -> InputForm if SingletonAsOrderedSet has KONVERT INFORM and R has KONVERT INFORM +--R convert : % -> Pattern Integer if SingletonAsOrderedSet has KONVERT PATTERN INT and R has KONVERT PATTERN INT +--R convert : % -> Pattern Float if SingletonAsOrderedSet has KONVERT PATTERN FLOAT and R has KONVERT PATTERN FLOAT +--R degree : (%,List SingletonAsOrderedSet) -> List NonNegativeInteger +--R degree : (%,SingletonAsOrderedSet) -> NonNegativeInteger +--R differentiate : (%,(R -> R),%) -> % +--R differentiate : (%,(R -> R)) -> % +--R differentiate : (%,(R -> R),NonNegativeInteger) -> % +--R differentiate : (%,List Symbol,List NonNegativeInteger) -> % if R has PDRING SYMBOL +--R differentiate : (%,Symbol,NonNegativeInteger) -> % if R has PDRING SYMBOL +--R differentiate : (%,List Symbol) -> % if R has PDRING SYMBOL +--R differentiate : (%,Symbol) -> % if R has PDRING SYMBOL +--R differentiate : (%,NonNegativeInteger) -> % +--R differentiate : (%,List SingletonAsOrderedSet,List NonNegativeInteger) -> % +--R differentiate : (%,SingletonAsOrderedSet,NonNegativeInteger) -> % +--R differentiate : (%,List SingletonAsOrderedSet) -> % +--R differentiate : (%,SingletonAsOrderedSet) -> % +--R discriminant : % -> R if R has COMRING +--R discriminant : (%,SingletonAsOrderedSet) -> % if R has COMRING +--R divide : (%,%) -> Record(quotient: %,remainder: %) if R has FIELD +--R divideExponents : (%,NonNegativeInteger) -> Union(%,"failed") +--R ?.? : (%,Fraction %) -> Fraction % if R has INTDOM +--R elt : (Fraction %,R) -> R if R has FIELD +--R elt : (Fraction %,Fraction %) -> Fraction % if R has INTDOM +--R euclideanSize : % -> NonNegativeInteger if R has FIELD +--R eval : (%,List SingletonAsOrderedSet,List %) -> % +--R eval : (%,SingletonAsOrderedSet,%) -> % +--R eval : (%,List SingletonAsOrderedSet,List R) -> % +--R eval : (%,SingletonAsOrderedSet,R) -> % +--R expressIdealMember : (List %,%) -> Union(List %,"failed") if R has FIELD +--R exquo : (%,%) -> Union(%,"failed") if R has INTDOM +--R exquo : (%,R) -> Union(%,"failed") if R has INTDOM +--R extendedEuclidean : (%,%) -> Record(coef1: %,coef2: %,generator: %) if R has FIELD +--R extendedEuclidean : (%,%,%) -> Union(Record(coef1: %,coef2: %),"failed") if R has FIELD +--R factor : % -> Factored % if R has PFECAT +--R factorPolynomial : SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if R has PFECAT +--R factorSquareFreePolynomial : SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if R has PFECAT +--R fmecg : (%,NonNegativeInteger,R,%) -> % +--R gcd : (%,%) -> % if R has GCDDOM +--R gcd : List % -> % if R has GCDDOM +--R gcdPolynomial : (SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial % if R has GCDDOM +--R integrate : % -> % if R has ALGEBRA FRAC INT +--R isExpt : % -> Union(Record(var: SingletonAsOrderedSet,exponent: NonNegativeInteger),"failed") +--R isPlus : % -> Union(List %,"failed") +--R isTimes : % -> Union(List %,"failed") +--R karatsubaDivide : (%,NonNegativeInteger) -> Record(quotient: %,remainder: %) +--R lcm : (%,%) -> % if R has GCDDOM +--R lcm : List % -> % if R has GCDDOM +--R mainVariable : % -> Union(SingletonAsOrderedSet,"failed") +--R makeSUP : % -> SparseUnivariatePolynomial R +--R mapExponents : ((NonNegativeInteger -> NonNegativeInteger),%) -> % +--R max : (%,%) -> % if R has ORDSET +--R min : (%,%) -> % if R has ORDSET +--R minimumDegree : (%,List SingletonAsOrderedSet) -> List NonNegativeInteger +--R minimumDegree : (%,SingletonAsOrderedSet) -> NonNegativeInteger +--R minimumDegree : % -> NonNegativeInteger +--R monicDivide : (%,%) -> Record(quotient: %,remainder: %) +--R monicDivide : (%,%,SingletonAsOrderedSet) -> Record(quotient: %,remainder: %) +--R monomial : (%,List SingletonAsOrderedSet,List NonNegativeInteger) -> % +--R monomial : (%,SingletonAsOrderedSet,NonNegativeInteger) -> % +--R monomial : (R,NonNegativeInteger) -> % +--R multiEuclidean : (List %,%) -> Union(List %,"failed") if R has FIELD +--R multiplyExponents : (%,NonNegativeInteger) -> % +--R multivariate : (SparseUnivariatePolynomial %,SingletonAsOrderedSet) -> % +--R multivariate : (SparseUnivariatePolynomial R,SingletonAsOrderedSet) -> % +--R nextItem : % -> Union(%,"failed") if R has STEP +--R numberOfMonomials : % -> NonNegativeInteger +--R order : (%,%) -> NonNegativeInteger if R has INTDOM +--R outputForm : (%,OutputForm) -> OutputForm +--R patternMatch : (%,Pattern Integer,PatternMatchResult(Integer,%)) -> PatternMatchResult(Integer,%) if SingletonAsOrderedSet has PATMAB INT and R has PATMAB INT +--R patternMatch : (%,Pattern Float,PatternMatchResult(Float,%)) -> PatternMatchResult(Float,%) if SingletonAsOrderedSet has PATMAB FLOAT and R has PATMAB FLOAT +--R pomopo! : (%,R,NonNegativeInteger,%) -> % +--R prime? : % -> Boolean if R has PFECAT +--R primitivePart : (%,SingletonAsOrderedSet) -> % if R has GCDDOM +--R primitivePart : % -> % if R has GCDDOM +--R principalIdeal : List % -> Record(coef: List %,generator: %) if R has FIELD +--R pseudoDivide : (%,%) -> Record(coef: R,quotient: %,remainder: %) if R has INTDOM +--R pseudoQuotient : (%,%) -> % if R has INTDOM +--R ?quo? : (%,%) -> % if R has FIELD +--R reducedSystem : Matrix % -> Matrix R +--R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix R,vec: Vector R) +--R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix Integer,vec: Vector Integer) if R has LINEXP INT +--R reducedSystem : Matrix % -> Matrix Integer if R has LINEXP INT +--R ?rem? : (%,%) -> % if R has FIELD +--R resultant : (%,%) -> R if R has COMRING +--R resultant : (%,%,SingletonAsOrderedSet) -> % if R has COMRING +--R retract : % -> SingletonAsOrderedSet +--R retract : % -> Integer if R has RETRACT INT +--R retract : % -> Fraction Integer if R has RETRACT FRAC INT +--R retractIfCan : % -> Union(SingletonAsOrderedSet,"failed") +--R retractIfCan : % -> Union(Integer,"failed") if R has RETRACT INT +--R retractIfCan : % -> Union(Fraction Integer,"failed") if R has RETRACT FRAC INT +--R retractIfCan : % -> Union(R,"failed") +--R separate : (%,%) -> Record(primePart: %,commonPart: %) if R has GCDDOM +--R shiftLeft : (%,NonNegativeInteger) -> % +--R shiftRight : (%,NonNegativeInteger) -> % +--R sizeLess? : (%,%) -> Boolean if R has FIELD +--R solveLinearPolynomialEquation : (List SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> Union(List SparseUnivariatePolynomial %,"failed") if R has PFECAT +--R squareFree : % -> Factored % if R has GCDDOM +--R squareFreePart : % -> % if R has GCDDOM +--R squareFreePolynomial : SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if R has PFECAT +--R subResultantGcd : (%,%) -> % if R has INTDOM +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R totalDegree : (%,List SingletonAsOrderedSet) -> NonNegativeInteger +--R totalDegree : % -> NonNegativeInteger +--R unit? : % -> Boolean if R has INTDOM +--R unitCanonical : % -> % if R has INTDOM +--R unitNormal : % -> Record(unit: %,canonical: %,associate: %) if R has INTDOM +--R univariate : % -> SparseUnivariatePolynomial R +--R univariate : (%,SingletonAsOrderedSet) -> SparseUnivariatePolynomial % +--R unmakeSUP : SparseUnivariatePolynomial R -> % +--R variables : % -> List SingletonAsOrderedSet +--R vectorise : (%,NonNegativeInteger) -> Vector R +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +SparseUnivariatePolynomial examples +==================================================================== + +See Also: +o )show SparseUnivariatePolynomial + +@ + \pagehead{SparseUnivariatePolynomial}{SUP} \pagepic{ps/v103sparseunivariatepolynomial.ps}{SUP}{1.00} {\bf See}\\ @@ -98717,6 +116282,235 @@ domain, as long as the polynomials can be retracted to that domain, i.e., as long as they are just constants. I don't see another way to do this, unfortunately. +<>= +)set break resume +)sys rm -f SparseUnivariatePolynomialExpressions.output +)spool SparseUnivariatePolynomialExpressions.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show SparseUnivariatePolynomialExpressions +--R SparseUnivariatePolynomialExpressions R: Ring is a domain constructor +--R Abbreviation for SparseUnivariatePolynomialExpressions is SUPEXPR +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for SUPEXPR +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (%,R) -> % ?*? : (R,%) -> % +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ?=? : (%,%) -> Boolean +--R D : (%,(R -> R)) -> % D : % -> % +--R D : (%,NonNegativeInteger) -> % 1 : () -> % +--R 0 : () -> % ?^? : (%,PositiveInteger) -> % +--R coefficients : % -> List R coerce : R -> % +--R coerce : Integer -> % coerce : % -> OutputForm +--R degree : % -> NonNegativeInteger differentiate : % -> % +--R ?.? : (%,%) -> % ?.? : (%,R) -> R +--R eval : (%,List %,List %) -> % eval : (%,%,%) -> % +--R eval : (%,Equation %) -> % eval : (%,List Equation %) -> % +--R ground : % -> R ground? : % -> Boolean +--R hash : % -> SingleInteger init : () -> % if R has STEP +--R latex : % -> String leadingCoefficient : % -> R +--R leadingMonomial : % -> % map : ((R -> R),%) -> % +--R monomial? : % -> Boolean monomials : % -> List % +--R one? : % -> Boolean pi : () -> % if R has TRANFUN +--R primitiveMonomials : % -> List % pseudoRemainder : (%,%) -> % +--R recip : % -> Union(%,"failed") reductum : % -> % +--R retract : % -> R sample : () -> % +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean +--R ?*? : (Fraction Integer,%) -> % if R has ALGEBRA FRAC INT +--R ?*? : (%,Fraction Integer) -> % if R has ALGEBRA FRAC INT +--R ?*? : (NonNegativeInteger,%) -> % +--R ?**? : (%,%) -> % if R has TRANFUN +--R ?**? : (%,NonNegativeInteger) -> % +--R ?/? : (%,R) -> % if R has FIELD +--R ? Boolean if R has ORDSET +--R ?<=? : (%,%) -> Boolean if R has ORDSET +--R ?>? : (%,%) -> Boolean if R has ORDSET +--R ?>=? : (%,%) -> Boolean if R has ORDSET +--R D : (%,(R -> R),NonNegativeInteger) -> % +--R D : (%,List Symbol,List NonNegativeInteger) -> % if R has PDRING SYMBOL +--R D : (%,Symbol,NonNegativeInteger) -> % if R has PDRING SYMBOL +--R D : (%,List Symbol) -> % if R has PDRING SYMBOL +--R D : (%,Symbol) -> % if R has PDRING SYMBOL +--R D : (%,List SingletonAsOrderedSet,List NonNegativeInteger) -> % +--R D : (%,SingletonAsOrderedSet,NonNegativeInteger) -> % +--R D : (%,List SingletonAsOrderedSet) -> % +--R D : (%,SingletonAsOrderedSet) -> % +--R ?^? : (%,NonNegativeInteger) -> % +--R acos : % -> % if R has TRANFUN +--R acosh : % -> % if R has TRANFUN +--R acot : % -> % if R has TRANFUN +--R acoth : % -> % if R has TRANFUN +--R acsc : % -> % if R has TRANFUN +--R acsch : % -> % if R has TRANFUN +--R asec : % -> % if R has TRANFUN +--R asech : % -> % if R has TRANFUN +--R asin : % -> % if R has TRANFUN +--R asinh : % -> % if R has TRANFUN +--R associates? : (%,%) -> Boolean if R has INTDOM +--R atan : % -> % if R has TRANFUN +--R atanh : % -> % if R has TRANFUN +--R binomThmExpt : (%,%,NonNegativeInteger) -> % if R has COMRING +--R characteristic : () -> NonNegativeInteger +--R charthRoot : % -> Union(%,"failed") if $ has CHARNZ and R has PFECAT or R has CHARNZ +--R coefficient : (%,List SingletonAsOrderedSet,List NonNegativeInteger) -> % +--R coefficient : (%,SingletonAsOrderedSet,NonNegativeInteger) -> % +--R coefficient : (%,NonNegativeInteger) -> R +--R coerce : % -> % if R has INTDOM +--R coerce : Fraction Integer -> % if R has ALGEBRA FRAC INT or R has RETRACT FRAC INT +--R coerce : SingletonAsOrderedSet -> % +--R composite : (Fraction %,%) -> Union(Fraction %,"failed") if R has INTDOM +--R composite : (%,%) -> Union(%,"failed") if R has INTDOM +--R conditionP : Matrix % -> Union(Vector %,"failed") if $ has CHARNZ and R has PFECAT +--R content : (%,SingletonAsOrderedSet) -> % if R has GCDDOM +--R content : % -> R if R has GCDDOM +--R convert : % -> InputForm if SingletonAsOrderedSet has KONVERT INFORM and R has KONVERT INFORM +--R convert : % -> Pattern Integer if SingletonAsOrderedSet has KONVERT PATTERN INT and R has KONVERT PATTERN INT +--R convert : % -> Pattern Float if SingletonAsOrderedSet has KONVERT PATTERN FLOAT and R has KONVERT PATTERN FLOAT +--R cos : % -> % if R has TRANFUN +--R cosh : % -> % if R has TRANFUN +--R cot : % -> % if R has TRANFUN +--R coth : % -> % if R has TRANFUN +--R csc : % -> % if R has TRANFUN +--R csch : % -> % if R has TRANFUN +--R degree : (%,List SingletonAsOrderedSet) -> List NonNegativeInteger +--R degree : (%,SingletonAsOrderedSet) -> NonNegativeInteger +--R differentiate : (%,(R -> R),%) -> % +--R differentiate : (%,(R -> R)) -> % +--R differentiate : (%,(R -> R),NonNegativeInteger) -> % +--R differentiate : (%,List Symbol,List NonNegativeInteger) -> % if R has PDRING SYMBOL +--R differentiate : (%,Symbol,NonNegativeInteger) -> % if R has PDRING SYMBOL +--R differentiate : (%,List Symbol) -> % if R has PDRING SYMBOL +--R differentiate : (%,Symbol) -> % if R has PDRING SYMBOL +--R differentiate : (%,NonNegativeInteger) -> % +--R differentiate : (%,List SingletonAsOrderedSet,List NonNegativeInteger) -> % +--R differentiate : (%,SingletonAsOrderedSet,NonNegativeInteger) -> % +--R differentiate : (%,List SingletonAsOrderedSet) -> % +--R differentiate : (%,SingletonAsOrderedSet) -> % +--R discriminant : % -> R if R has COMRING +--R discriminant : (%,SingletonAsOrderedSet) -> % if R has COMRING +--R divide : (%,%) -> Record(quotient: %,remainder: %) if R has FIELD +--R divideExponents : (%,NonNegativeInteger) -> Union(%,"failed") +--R ?.? : (%,Fraction %) -> Fraction % if R has INTDOM +--R elt : (Fraction %,R) -> R if R has FIELD +--R elt : (Fraction %,Fraction %) -> Fraction % if R has INTDOM +--R euclideanSize : % -> NonNegativeInteger if R has FIELD +--R eval : (%,List SingletonAsOrderedSet,List %) -> % +--R eval : (%,SingletonAsOrderedSet,%) -> % +--R eval : (%,List SingletonAsOrderedSet,List R) -> % +--R eval : (%,SingletonAsOrderedSet,R) -> % +--R exp : % -> % if R has TRANFUN +--R expressIdealMember : (List %,%) -> Union(List %,"failed") if R has FIELD +--R exquo : (%,%) -> Union(%,"failed") if R has INTDOM +--R exquo : (%,R) -> Union(%,"failed") if R has INTDOM +--R extendedEuclidean : (%,%) -> Record(coef1: %,coef2: %,generator: %) if R has FIELD +--R extendedEuclidean : (%,%,%) -> Union(Record(coef1: %,coef2: %),"failed") if R has FIELD +--R factor : % -> Factored % if R has PFECAT +--R factorPolynomial : SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if R has PFECAT +--R factorSquareFreePolynomial : SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if R has PFECAT +--R gcd : (%,%) -> % if R has GCDDOM +--R gcd : List % -> % if R has GCDDOM +--R gcdPolynomial : (SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial % if R has GCDDOM +--R integrate : % -> % if R has ALGEBRA FRAC INT +--R isExpt : % -> Union(Record(var: SingletonAsOrderedSet,exponent: NonNegativeInteger),"failed") +--R isPlus : % -> Union(List %,"failed") +--R isTimes : % -> Union(List %,"failed") +--R karatsubaDivide : (%,NonNegativeInteger) -> Record(quotient: %,remainder: %) +--R lcm : (%,%) -> % if R has GCDDOM +--R lcm : List % -> % if R has GCDDOM +--R log : % -> % if R has TRANFUN +--R mainVariable : % -> Union(SingletonAsOrderedSet,"failed") +--R makeSUP : % -> SparseUnivariatePolynomial R +--R mapExponents : ((NonNegativeInteger -> NonNegativeInteger),%) -> % +--R max : (%,%) -> % if R has ORDSET +--R min : (%,%) -> % if R has ORDSET +--R minimumDegree : (%,List SingletonAsOrderedSet) -> List NonNegativeInteger +--R minimumDegree : (%,SingletonAsOrderedSet) -> NonNegativeInteger +--R minimumDegree : % -> NonNegativeInteger +--R monicDivide : (%,%) -> Record(quotient: %,remainder: %) +--R monicDivide : (%,%,SingletonAsOrderedSet) -> Record(quotient: %,remainder: %) +--R monomial : (%,List SingletonAsOrderedSet,List NonNegativeInteger) -> % +--R monomial : (%,SingletonAsOrderedSet,NonNegativeInteger) -> % +--R monomial : (R,NonNegativeInteger) -> % +--R multiEuclidean : (List %,%) -> Union(List %,"failed") if R has FIELD +--R multiplyExponents : (%,NonNegativeInteger) -> % +--R multivariate : (SparseUnivariatePolynomial %,SingletonAsOrderedSet) -> % +--R multivariate : (SparseUnivariatePolynomial R,SingletonAsOrderedSet) -> % +--R nextItem : % -> Union(%,"failed") if R has STEP +--R numberOfMonomials : % -> NonNegativeInteger +--R order : (%,%) -> NonNegativeInteger if R has INTDOM +--R patternMatch : (%,Pattern Integer,PatternMatchResult(Integer,%)) -> PatternMatchResult(Integer,%) if SingletonAsOrderedSet has PATMAB INT and R has PATMAB INT +--R patternMatch : (%,Pattern Float,PatternMatchResult(Float,%)) -> PatternMatchResult(Float,%) if SingletonAsOrderedSet has PATMAB FLOAT and R has PATMAB FLOAT +--R pomopo! : (%,R,NonNegativeInteger,%) -> % +--R prime? : % -> Boolean if R has PFECAT +--R primitivePart : (%,SingletonAsOrderedSet) -> % if R has GCDDOM +--R primitivePart : % -> % if R has GCDDOM +--R principalIdeal : List % -> Record(coef: List %,generator: %) if R has FIELD +--R pseudoDivide : (%,%) -> Record(coef: R,quotient: %,remainder: %) if R has INTDOM +--R pseudoQuotient : (%,%) -> % if R has INTDOM +--R ?quo? : (%,%) -> % if R has FIELD +--R reducedSystem : Matrix % -> Matrix R +--R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix R,vec: Vector R) +--R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix Integer,vec: Vector Integer) if R has LINEXP INT +--R reducedSystem : Matrix % -> Matrix Integer if R has LINEXP INT +--R ?rem? : (%,%) -> % if R has FIELD +--R resultant : (%,%) -> R if R has COMRING +--R resultant : (%,%,SingletonAsOrderedSet) -> % if R has COMRING +--R retract : % -> SingletonAsOrderedSet +--R retract : % -> Integer if R has RETRACT INT +--R retract : % -> Fraction Integer if R has RETRACT FRAC INT +--R retractIfCan : % -> Union(SingletonAsOrderedSet,"failed") +--R retractIfCan : % -> Union(Integer,"failed") if R has RETRACT INT +--R retractIfCan : % -> Union(Fraction Integer,"failed") if R has RETRACT FRAC INT +--R retractIfCan : % -> Union(R,"failed") +--R sec : % -> % if R has TRANFUN +--R sech : % -> % if R has TRANFUN +--R separate : (%,%) -> Record(primePart: %,commonPart: %) if R has GCDDOM +--R shiftLeft : (%,NonNegativeInteger) -> % +--R shiftRight : (%,NonNegativeInteger) -> % +--R sin : % -> % if R has TRANFUN +--R sinh : % -> % if R has TRANFUN +--R sizeLess? : (%,%) -> Boolean if R has FIELD +--R solveLinearPolynomialEquation : (List SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> Union(List SparseUnivariatePolynomial %,"failed") if R has PFECAT +--R squareFree : % -> Factored % if R has GCDDOM +--R squareFreePart : % -> % if R has GCDDOM +--R squareFreePolynomial : SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if R has PFECAT +--R subResultantGcd : (%,%) -> % if R has INTDOM +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R tan : % -> % if R has TRANFUN +--R tanh : % -> % if R has TRANFUN +--R totalDegree : (%,List SingletonAsOrderedSet) -> NonNegativeInteger +--R totalDegree : % -> NonNegativeInteger +--R unit? : % -> Boolean if R has INTDOM +--R unitCanonical : % -> % if R has INTDOM +--R unitNormal : % -> Record(unit: %,canonical: %,associate: %) if R has INTDOM +--R univariate : % -> SparseUnivariatePolynomial R +--R univariate : (%,SingletonAsOrderedSet) -> SparseUnivariatePolynomial % +--R unmakeSUP : SparseUnivariatePolynomial R -> % +--R variables : % -> List SingletonAsOrderedSet +--R vectorise : (%,NonNegativeInteger) -> Vector R +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +SparseUnivariatePolynomialExpressions examples +==================================================================== + +See Also: +o )show SparseUnivariatePolynomialExpressions + +@ + + \pagehead{SparseUnivariatePolynomialExpressions}{SUPEXPR} \pagepic{ps/v103sparseunivariatepolynomialexpressions.ps}{SUPEXPR}{1.00} @@ -98913,6 +116707,171 @@ SparseUnivariatePolynomialExpressions(R: Ring): Exports == Implementation where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain SUPXS SparseUnivariatePuiseuxSeries} + +<>= +)set break resume +)sys rm -f SparseUnivariatePuiseuxSeries.output +)spool SparseUnivariatePuiseuxSeries.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show SparseUnivariatePuiseuxSeries +--R SparseUnivariatePuiseuxSeries(Coef: Ring,var: Symbol,cen: Coef) is a domain constructor +--R Abbreviation for SparseUnivariatePuiseuxSeries is SUPXS +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for SUPXS +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (Coef,%) -> % ?*? : (%,Coef) -> % +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ?=? : (%,%) -> Boolean +--R 1 : () -> % 0 : () -> % +--R ?^? : (%,PositiveInteger) -> % center : % -> Coef +--R coerce : Variable var -> % coerce : Integer -> % +--R coerce : % -> OutputForm complete : % -> % +--R degree : % -> Fraction Integer hash : % -> SingleInteger +--R latex : % -> String leadingCoefficient : % -> Coef +--R leadingMonomial : % -> % map : ((Coef -> Coef),%) -> % +--R monomial? : % -> Boolean one? : % -> Boolean +--R order : % -> Fraction Integer pole? : % -> Boolean +--R recip : % -> Union(%,"failed") reductum : % -> % +--R sample : () -> % variable : % -> Symbol +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean +--R ?*? : (%,Fraction Integer) -> % if Coef has ALGEBRA FRAC INT +--R ?*? : (Fraction Integer,%) -> % if Coef has ALGEBRA FRAC INT +--R ?*? : (NonNegativeInteger,%) -> % +--R ?**? : (%,Fraction Integer) -> % if Coef has ALGEBRA FRAC INT +--R ?**? : (%,%) -> % if Coef has ALGEBRA FRAC INT +--R ?**? : (%,Integer) -> % if Coef has FIELD +--R ?**? : (%,NonNegativeInteger) -> % +--R ?/? : (%,%) -> % if Coef has FIELD +--R ?/? : (%,Coef) -> % if Coef has FIELD +--R D : % -> % if Coef has *: (Fraction Integer,Coef) -> Coef +--R D : (%,NonNegativeInteger) -> % if Coef has *: (Fraction Integer,Coef) -> Coef +--R D : (%,Symbol) -> % if Coef has *: (Fraction Integer,Coef) -> Coef and Coef has PDRING SYMBOL +--R D : (%,List Symbol) -> % if Coef has *: (Fraction Integer,Coef) -> Coef and Coef has PDRING SYMBOL +--R D : (%,Symbol,NonNegativeInteger) -> % if Coef has *: (Fraction Integer,Coef) -> Coef and Coef has PDRING SYMBOL +--R D : (%,List Symbol,List NonNegativeInteger) -> % if Coef has *: (Fraction Integer,Coef) -> Coef and Coef has PDRING SYMBOL +--R ?^? : (%,Integer) -> % if Coef has FIELD +--R ?^? : (%,NonNegativeInteger) -> % +--R acos : % -> % if Coef has ALGEBRA FRAC INT +--R acosh : % -> % if Coef has ALGEBRA FRAC INT +--R acot : % -> % if Coef has ALGEBRA FRAC INT +--R acoth : % -> % if Coef has ALGEBRA FRAC INT +--R acsc : % -> % if Coef has ALGEBRA FRAC INT +--R acsch : % -> % if Coef has ALGEBRA FRAC INT +--R approximate : (%,Fraction Integer) -> Coef if Coef has **: (Coef,Fraction Integer) -> Coef and Coef has coerce: Symbol -> Coef +--R asec : % -> % if Coef has ALGEBRA FRAC INT +--R asech : % -> % if Coef has ALGEBRA FRAC INT +--R asin : % -> % if Coef has ALGEBRA FRAC INT +--R asinh : % -> % if Coef has ALGEBRA FRAC INT +--R associates? : (%,%) -> Boolean if Coef has INTDOM +--R atan : % -> % if Coef has ALGEBRA FRAC INT +--R atanh : % -> % if Coef has ALGEBRA FRAC INT +--R characteristic : () -> NonNegativeInteger +--R charthRoot : % -> Union(%,"failed") if Coef has CHARNZ +--R coefficient : (%,Fraction Integer) -> Coef +--R coerce : % -> % if Coef has INTDOM +--R coerce : Fraction Integer -> % if Coef has ALGEBRA FRAC INT +--R coerce : SparseUnivariateTaylorSeries(Coef,var,cen) -> % +--R coerce : SparseUnivariateLaurentSeries(Coef,var,cen) -> % +--R coerce : Coef -> % if Coef has COMRING +--R cos : % -> % if Coef has ALGEBRA FRAC INT +--R cosh : % -> % if Coef has ALGEBRA FRAC INT +--R cot : % -> % if Coef has ALGEBRA FRAC INT +--R coth : % -> % if Coef has ALGEBRA FRAC INT +--R csc : % -> % if Coef has ALGEBRA FRAC INT +--R csch : % -> % if Coef has ALGEBRA FRAC INT +--R differentiate : (%,Variable var) -> % +--R differentiate : % -> % if Coef has *: (Fraction Integer,Coef) -> Coef +--R differentiate : (%,NonNegativeInteger) -> % if Coef has *: (Fraction Integer,Coef) -> Coef +--R differentiate : (%,Symbol) -> % if Coef has *: (Fraction Integer,Coef) -> Coef and Coef has PDRING SYMBOL +--R differentiate : (%,List Symbol) -> % if Coef has *: (Fraction Integer,Coef) -> Coef and Coef has PDRING SYMBOL +--R differentiate : (%,Symbol,NonNegativeInteger) -> % if Coef has *: (Fraction Integer,Coef) -> Coef and Coef has PDRING SYMBOL +--R differentiate : (%,List Symbol,List NonNegativeInteger) -> % if Coef has *: (Fraction Integer,Coef) -> Coef and Coef has PDRING SYMBOL +--R divide : (%,%) -> Record(quotient: %,remainder: %) if Coef has FIELD +--R ?.? : (%,%) -> % if Fraction Integer has SGROUP +--R ?.? : (%,Fraction Integer) -> Coef +--R euclideanSize : % -> NonNegativeInteger if Coef has FIELD +--R eval : (%,Coef) -> Stream Coef if Coef has **: (Coef,Fraction Integer) -> Coef +--R exp : % -> % if Coef has ALGEBRA FRAC INT +--R expressIdealMember : (List %,%) -> Union(List %,"failed") if Coef has FIELD +--R exquo : (%,%) -> Union(%,"failed") if Coef has INTDOM +--R extend : (%,Fraction Integer) -> % +--R extendedEuclidean : (%,%) -> Record(coef1: %,coef2: %,generator: %) if Coef has FIELD +--R extendedEuclidean : (%,%,%) -> Union(Record(coef1: %,coef2: %),"failed") if Coef has FIELD +--R factor : % -> Factored % if Coef has FIELD +--R gcd : (%,%) -> % if Coef has FIELD +--R gcd : List % -> % if Coef has FIELD +--R gcdPolynomial : (SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial % if Coef has FIELD +--R integrate : (%,Variable var) -> % if Coef has ALGEBRA FRAC INT +--R integrate : (%,Symbol) -> % if Coef has integrate: (Coef,Symbol) -> Coef and Coef has variables: Coef -> List Symbol and Coef has ALGEBRA FRAC INT or Coef has ACFS INT and Coef has ALGEBRA FRAC INT and Coef has PRIMCAT and Coef has TRANFUN +--R integrate : % -> % if Coef has ALGEBRA FRAC INT +--R inv : % -> % if Coef has FIELD +--R laurent : % -> SparseUnivariateLaurentSeries(Coef,var,cen) +--R laurentIfCan : % -> Union(SparseUnivariateLaurentSeries(Coef,var,cen),"failed") +--R laurentRep : % -> SparseUnivariateLaurentSeries(Coef,var,cen) +--R lcm : (%,%) -> % if Coef has FIELD +--R lcm : List % -> % if Coef has FIELD +--R log : % -> % if Coef has ALGEBRA FRAC INT +--R monomial : (%,List SingletonAsOrderedSet,List Fraction Integer) -> % +--R monomial : (%,SingletonAsOrderedSet,Fraction Integer) -> % +--R monomial : (Coef,Fraction Integer) -> % +--R multiEuclidean : (List %,%) -> Union(List %,"failed") if Coef has FIELD +--R multiplyExponents : (%,Fraction Integer) -> % +--R multiplyExponents : (%,PositiveInteger) -> % +--R nthRoot : (%,Integer) -> % if Coef has ALGEBRA FRAC INT +--R order : (%,Fraction Integer) -> Fraction Integer +--R pi : () -> % if Coef has ALGEBRA FRAC INT +--R prime? : % -> Boolean if Coef has FIELD +--R principalIdeal : List % -> Record(coef: List %,generator: %) if Coef has FIELD +--R puiseux : (Fraction Integer,SparseUnivariateLaurentSeries(Coef,var,cen)) -> % +--R ?quo? : (%,%) -> % if Coef has FIELD +--R rationalPower : % -> Fraction Integer +--R ?rem? : (%,%) -> % if Coef has FIELD +--R retract : % -> SparseUnivariateTaylorSeries(Coef,var,cen) +--R retract : % -> SparseUnivariateLaurentSeries(Coef,var,cen) +--R retractIfCan : % -> Union(SparseUnivariateTaylorSeries(Coef,var,cen),"failed") +--R retractIfCan : % -> Union(SparseUnivariateLaurentSeries(Coef,var,cen),"failed") +--R sec : % -> % if Coef has ALGEBRA FRAC INT +--R sech : % -> % if Coef has ALGEBRA FRAC INT +--R series : (NonNegativeInteger,Stream Record(k: Fraction Integer,c: Coef)) -> % +--R sin : % -> % if Coef has ALGEBRA FRAC INT +--R sinh : % -> % if Coef has ALGEBRA FRAC INT +--R sizeLess? : (%,%) -> Boolean if Coef has FIELD +--R sqrt : % -> % if Coef has ALGEBRA FRAC INT +--R squareFree : % -> Factored % if Coef has FIELD +--R squareFreePart : % -> % if Coef has FIELD +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R tan : % -> % if Coef has ALGEBRA FRAC INT +--R tanh : % -> % if Coef has ALGEBRA FRAC INT +--R terms : % -> Stream Record(k: Fraction Integer,c: Coef) +--R truncate : (%,Fraction Integer,Fraction Integer) -> % +--R truncate : (%,Fraction Integer) -> % +--R unit? : % -> Boolean if Coef has INTDOM +--R unitCanonical : % -> % if Coef has INTDOM +--R unitNormal : % -> Record(unit: %,canonical: %,associate: %) if Coef has INTDOM +--R variables : % -> List SingletonAsOrderedSet +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +SparseUnivariatePuiseuxSeries examples +==================================================================== + +See Also: +o )show SparseUnivariatePuiseuxSeries + +@ + \pagehead{SparseUnivariatePuiseuxSeries}{SUPXS} \pagepic{ps/v103sparseunivariatepuiseuxseries.ps}{SUPXS}{1.00} @@ -99121,6 +117080,88 @@ SparseUnivariatePuiseuxSeries(Coef,var,cen): Exports == Implementation where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain ORESUP SparseUnivariateSkewPolynomial} + +<>= +)set break resume +)sys rm -f SparseUnivariateSkewPolynomial.output +)spool SparseUnivariateSkewPolynomial.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show SparseUnivariateSkewPolynomial +--R SparseUnivariateSkewPolynomial(R: Ring,sigma: Automorphism R,delta: (R -> R)) is a domain constructor +--R Abbreviation for SparseUnivariateSkewPolynomial is ORESUP +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for ORESUP +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (R,%) -> % ?*? : (%,R) -> % +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ?=? : (%,%) -> Boolean +--R 1 : () -> % 0 : () -> % +--R ?^? : (%,PositiveInteger) -> % apply : (%,R,R) -> R +--R coefficients : % -> List R coerce : R -> % +--R coerce : Integer -> % coerce : % -> OutputForm +--R degree : % -> NonNegativeInteger hash : % -> SingleInteger +--R latex : % -> String leadingCoefficient : % -> R +--R one? : % -> Boolean recip : % -> Union(%,"failed") +--R reductum : % -> % retract : % -> R +--R sample : () -> % zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean +--R ?*? : (NonNegativeInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % +--R ?^? : (%,NonNegativeInteger) -> % +--R characteristic : () -> NonNegativeInteger +--R coefficient : (%,NonNegativeInteger) -> R +--R coerce : Fraction Integer -> % if R has RETRACT FRAC INT +--R content : % -> R if R has GCDDOM +--R exquo : (%,R) -> Union(%,"failed") if R has INTDOM +--R leftDivide : (%,%) -> Record(quotient: %,remainder: %) if R has FIELD +--R leftExactQuotient : (%,%) -> Union(%,"failed") if R has FIELD +--R leftExtendedGcd : (%,%) -> Record(coef1: %,coef2: %,generator: %) if R has FIELD +--R leftGcd : (%,%) -> % if R has FIELD +--R leftLcm : (%,%) -> % if R has FIELD +--R leftQuotient : (%,%) -> % if R has FIELD +--R leftRemainder : (%,%) -> % if R has FIELD +--R minimumDegree : % -> NonNegativeInteger +--R monicLeftDivide : (%,%) -> Record(quotient: %,remainder: %) if R has INTDOM +--R monicRightDivide : (%,%) -> Record(quotient: %,remainder: %) if R has INTDOM +--R monomial : (R,NonNegativeInteger) -> % +--R outputForm : (%,OutputForm) -> OutputForm +--R primitivePart : % -> % if R has GCDDOM +--R retract : % -> Fraction Integer if R has RETRACT FRAC INT +--R retract : % -> Integer if R has RETRACT INT +--R retractIfCan : % -> Union(R,"failed") +--R retractIfCan : % -> Union(Fraction Integer,"failed") if R has RETRACT FRAC INT +--R retractIfCan : % -> Union(Integer,"failed") if R has RETRACT INT +--R rightDivide : (%,%) -> Record(quotient: %,remainder: %) if R has FIELD +--R rightExactQuotient : (%,%) -> Union(%,"failed") if R has FIELD +--R rightExtendedGcd : (%,%) -> Record(coef1: %,coef2: %,generator: %) if R has FIELD +--R rightGcd : (%,%) -> % if R has FIELD +--R rightLcm : (%,%) -> % if R has FIELD +--R rightQuotient : (%,%) -> % if R has FIELD +--R rightRemainder : (%,%) -> % if R has FIELD +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +SparseUnivariateSkewPolynomial examples +==================================================================== + +See Also: +o )show SparseUnivariateSkewPolynomial + +@ + \pagehead{SparseUnivariateSkewPolynomial}{ORESUP} \pagepic{ps/v103sparseunivariateskewpolynomial.ps}{ORESUP}{1.00} {\bf See}\\ @@ -99218,6 +117259,144 @@ SparseUnivariateSkewPolynomial(R:Ring, sigma:Automorphism R, delta: R -> R): @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain SUTS SparseUnivariateTaylorSeries} + +<>= +)set break resume +)sys rm -f SparseUnivariateTaylorSeries.output +)spool SparseUnivariateTaylorSeries.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show SparseUnivariateTaylorSeries +--R SparseUnivariateTaylorSeries(Coef: Ring,var: Symbol,cen: Coef) is a domain constructor +--R Abbreviation for SparseUnivariateTaylorSeries is SUTS +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for SUTS +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (Coef,%) -> % ?*? : (%,Coef) -> % +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ?=? : (%,%) -> Boolean +--R 1 : () -> % 0 : () -> % +--R ?^? : (%,PositiveInteger) -> % center : % -> Coef +--R coefficients : % -> Stream Coef coerce : Variable var -> % +--R coerce : Integer -> % coerce : % -> OutputForm +--R complete : % -> % degree : % -> NonNegativeInteger +--R hash : % -> SingleInteger latex : % -> String +--R leadingCoefficient : % -> Coef leadingMonomial : % -> % +--R map : ((Coef -> Coef),%) -> % monomial? : % -> Boolean +--R one? : % -> Boolean order : % -> NonNegativeInteger +--R pole? : % -> Boolean quoByVar : % -> % +--R recip : % -> Union(%,"failed") reductum : % -> % +--R sample : () -> % series : Stream Coef -> % +--R variable : % -> Symbol zero? : % -> Boolean +--R ?~=? : (%,%) -> Boolean +--R ?*? : (%,Fraction Integer) -> % if Coef has ALGEBRA FRAC INT +--R ?*? : (Fraction Integer,%) -> % if Coef has ALGEBRA FRAC INT +--R ?*? : (NonNegativeInteger,%) -> % +--R ?**? : (%,Fraction Integer) -> % if Coef has ALGEBRA FRAC INT +--R ?**? : (%,%) -> % if Coef has ALGEBRA FRAC INT +--R ?**? : (%,Coef) -> % if Coef has FIELD +--R ?**? : (%,NonNegativeInteger) -> % +--R ?/? : (%,Coef) -> % if Coef has FIELD +--R D : % -> % if Coef has *: (NonNegativeInteger,Coef) -> Coef +--R D : (%,NonNegativeInteger) -> % if Coef has *: (NonNegativeInteger,Coef) -> Coef +--R D : (%,Symbol) -> % if Coef has *: (NonNegativeInteger,Coef) -> Coef and Coef has PDRING SYMBOL +--R D : (%,List Symbol) -> % if Coef has *: (NonNegativeInteger,Coef) -> Coef and Coef has PDRING SYMBOL +--R D : (%,Symbol,NonNegativeInteger) -> % if Coef has *: (NonNegativeInteger,Coef) -> Coef and Coef has PDRING SYMBOL +--R D : (%,List Symbol,List NonNegativeInteger) -> % if Coef has *: (NonNegativeInteger,Coef) -> Coef and Coef has PDRING SYMBOL +--R ?^? : (%,NonNegativeInteger) -> % +--R acos : % -> % if Coef has ALGEBRA FRAC INT +--R acosh : % -> % if Coef has ALGEBRA FRAC INT +--R acot : % -> % if Coef has ALGEBRA FRAC INT +--R acoth : % -> % if Coef has ALGEBRA FRAC INT +--R acsc : % -> % if Coef has ALGEBRA FRAC INT +--R acsch : % -> % if Coef has ALGEBRA FRAC INT +--R approximate : (%,NonNegativeInteger) -> Coef if Coef has **: (Coef,NonNegativeInteger) -> Coef and Coef has coerce: Symbol -> Coef +--R asec : % -> % if Coef has ALGEBRA FRAC INT +--R asech : % -> % if Coef has ALGEBRA FRAC INT +--R asin : % -> % if Coef has ALGEBRA FRAC INT +--R asinh : % -> % if Coef has ALGEBRA FRAC INT +--R associates? : (%,%) -> Boolean if Coef has INTDOM +--R atan : % -> % if Coef has ALGEBRA FRAC INT +--R atanh : % -> % if Coef has ALGEBRA FRAC INT +--R characteristic : () -> NonNegativeInteger +--R charthRoot : % -> Union(%,"failed") if Coef has CHARNZ +--R coefficient : (%,NonNegativeInteger) -> Coef +--R coerce : UnivariatePolynomial(var,Coef) -> % +--R coerce : Coef -> % if Coef has COMRING +--R coerce : % -> % if Coef has INTDOM +--R coerce : Fraction Integer -> % if Coef has ALGEBRA FRAC INT +--R cos : % -> % if Coef has ALGEBRA FRAC INT +--R cosh : % -> % if Coef has ALGEBRA FRAC INT +--R cot : % -> % if Coef has ALGEBRA FRAC INT +--R coth : % -> % if Coef has ALGEBRA FRAC INT +--R csc : % -> % if Coef has ALGEBRA FRAC INT +--R csch : % -> % if Coef has ALGEBRA FRAC INT +--R differentiate : (%,Variable var) -> % +--R differentiate : % -> % if Coef has *: (NonNegativeInteger,Coef) -> Coef +--R differentiate : (%,NonNegativeInteger) -> % if Coef has *: (NonNegativeInteger,Coef) -> Coef +--R differentiate : (%,Symbol) -> % if Coef has *: (NonNegativeInteger,Coef) -> Coef and Coef has PDRING SYMBOL +--R differentiate : (%,List Symbol) -> % if Coef has *: (NonNegativeInteger,Coef) -> Coef and Coef has PDRING SYMBOL +--R differentiate : (%,Symbol,NonNegativeInteger) -> % if Coef has *: (NonNegativeInteger,Coef) -> Coef and Coef has PDRING SYMBOL +--R differentiate : (%,List Symbol,List NonNegativeInteger) -> % if Coef has *: (NonNegativeInteger,Coef) -> Coef and Coef has PDRING SYMBOL +--R ?.? : (%,%) -> % if NonNegativeInteger has SGROUP +--R ?.? : (%,NonNegativeInteger) -> Coef +--R eval : (%,Coef) -> Stream Coef if Coef has **: (Coef,NonNegativeInteger) -> Coef +--R exp : % -> % if Coef has ALGEBRA FRAC INT +--R exquo : (%,%) -> Union(%,"failed") if Coef has INTDOM +--R extend : (%,NonNegativeInteger) -> % +--R integrate : (%,Variable var) -> % if Coef has ALGEBRA FRAC INT +--R integrate : (%,Symbol) -> % if Coef has integrate: (Coef,Symbol) -> Coef and Coef has variables: Coef -> List Symbol and Coef has ALGEBRA FRAC INT or Coef has ACFS INT and Coef has ALGEBRA FRAC INT and Coef has PRIMCAT and Coef has TRANFUN +--R integrate : % -> % if Coef has ALGEBRA FRAC INT +--R log : % -> % if Coef has ALGEBRA FRAC INT +--R monomial : (%,List SingletonAsOrderedSet,List NonNegativeInteger) -> % +--R monomial : (%,SingletonAsOrderedSet,NonNegativeInteger) -> % +--R monomial : (Coef,NonNegativeInteger) -> % +--R multiplyCoefficients : ((Integer -> Coef),%) -> % +--R multiplyExponents : (%,PositiveInteger) -> % +--R nthRoot : (%,Integer) -> % if Coef has ALGEBRA FRAC INT +--R order : (%,NonNegativeInteger) -> NonNegativeInteger +--R pi : () -> % if Coef has ALGEBRA FRAC INT +--R polynomial : (%,NonNegativeInteger,NonNegativeInteger) -> Polynomial Coef +--R polynomial : (%,NonNegativeInteger) -> Polynomial Coef +--R sec : % -> % if Coef has ALGEBRA FRAC INT +--R sech : % -> % if Coef has ALGEBRA FRAC INT +--R series : Stream Record(k: NonNegativeInteger,c: Coef) -> % +--R sin : % -> % if Coef has ALGEBRA FRAC INT +--R sinh : % -> % if Coef has ALGEBRA FRAC INT +--R sqrt : % -> % if Coef has ALGEBRA FRAC INT +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R tan : % -> % if Coef has ALGEBRA FRAC INT +--R tanh : % -> % if Coef has ALGEBRA FRAC INT +--R terms : % -> Stream Record(k: NonNegativeInteger,c: Coef) +--R truncate : (%,NonNegativeInteger,NonNegativeInteger) -> % +--R truncate : (%,NonNegativeInteger) -> % +--R unit? : % -> Boolean if Coef has INTDOM +--R unitCanonical : % -> % if Coef has INTDOM +--R unitNormal : % -> Record(unit: %,canonical: %,associate: %) if Coef has INTDOM +--R univariatePolynomial : (%,NonNegativeInteger) -> UnivariatePolynomial(var,Coef) +--R variables : % -> List SingletonAsOrderedSet +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +SparseUnivariateTaylorSeries examples +==================================================================== + +See Also: +o )show SparseUnivariateTaylorSeries + +@ + \pagehead{SparseUnivariateTaylorSeries}{SUTS} \pagepic{ps/v103sparseunivariatetaylorseries.ps}{SUTS}{1.00} @@ -99706,6 +117885,142 @@ SparseUnivariateTaylorSeries(Coef,var,cen): Exports == Implementation where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain SHDP SplitHomogeneousDirectProduct} + +<>= +)set break resume +)sys rm -f SplitHomogeneousDirectProduct.output +)spool SplitHomogeneousDirectProduct.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show SplitHomogeneousDirectProduct +--R SplitHomogeneousDirectProduct(dimtot: NonNegativeInteger,dim1: NonNegativeInteger,S: OrderedAbelianMonoidSup) is a domain constructor +--R Abbreviation for SplitHomogeneousDirectProduct is SHDP +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for SHDP +--R +--R------------------------------- Operations -------------------------------- +--R -? : % -> % if S has RING 1 : () -> % if S has MONOID +--R 0 : () -> % if S has CABMON coerce : % -> Vector S +--R copy : % -> % directProduct : Vector S -> % +--R ?.? : (%,Integer) -> S elt : (%,Integer,S) -> S +--R empty : () -> % empty? : % -> Boolean +--R entries : % -> List S eq? : (%,%) -> Boolean +--R index? : (Integer,%) -> Boolean indices : % -> List Integer +--R map : ((S -> S),%) -> % qelt : (%,Integer) -> S +--R sample : () -> % +--R #? : % -> NonNegativeInteger if $ has finiteAggregate +--R ?*? : (PositiveInteger,%) -> % if S has ABELSG +--R ?*? : (NonNegativeInteger,%) -> % if S has CABMON +--R ?*? : (S,%) -> % if S has RING +--R ?*? : (%,S) -> % if S has RING +--R ?*? : (%,%) -> % if S has MONOID +--R ?*? : (Integer,%) -> % if S has RING +--R ?**? : (%,PositiveInteger) -> % if S has MONOID +--R ?**? : (%,NonNegativeInteger) -> % if S has MONOID +--R ?+? : (%,%) -> % if S has ABELSG +--R ?-? : (%,%) -> % if S has RING +--R ?/? : (%,S) -> % if S has FIELD +--R ? Boolean if S has OAMONS or S has ORDRING +--R ?<=? : (%,%) -> Boolean if S has OAMONS or S has ORDRING +--R ?=? : (%,%) -> Boolean if S has SETCAT +--R ?>? : (%,%) -> Boolean if S has OAMONS or S has ORDRING +--R ?>=? : (%,%) -> Boolean if S has OAMONS or S has ORDRING +--R D : (%,(S -> S)) -> % if S has RING +--R D : (%,(S -> S),NonNegativeInteger) -> % if S has RING +--R D : (%,List Symbol,List NonNegativeInteger) -> % if S has PDRING SYMBOL and S has RING +--R D : (%,Symbol,NonNegativeInteger) -> % if S has PDRING SYMBOL and S has RING +--R D : (%,List Symbol) -> % if S has PDRING SYMBOL and S has RING +--R D : (%,Symbol) -> % if S has PDRING SYMBOL and S has RING +--R D : (%,NonNegativeInteger) -> % if S has DIFRING and S has RING +--R D : % -> % if S has DIFRING and S has RING +--R ?^? : (%,PositiveInteger) -> % if S has MONOID +--R ?^? : (%,NonNegativeInteger) -> % if S has MONOID +--R abs : % -> % if S has ORDRING +--R any? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate +--R characteristic : () -> NonNegativeInteger if S has RING +--R coerce : S -> % if S has SETCAT +--R coerce : Fraction Integer -> % if S has RETRACT FRAC INT and S has SETCAT +--R coerce : Integer -> % if S has RETRACT INT and S has SETCAT or S has RING +--R coerce : % -> OutputForm if S has SETCAT +--R count : (S,%) -> NonNegativeInteger if $ has finiteAggregate and S has SETCAT +--R count : ((S -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate +--R differentiate : (%,(S -> S)) -> % if S has RING +--R differentiate : (%,(S -> S),NonNegativeInteger) -> % if S has RING +--R differentiate : (%,List Symbol,List NonNegativeInteger) -> % if S has PDRING SYMBOL and S has RING +--R differentiate : (%,Symbol,NonNegativeInteger) -> % if S has PDRING SYMBOL and S has RING +--R differentiate : (%,List Symbol) -> % if S has PDRING SYMBOL and S has RING +--R differentiate : (%,Symbol) -> % if S has PDRING SYMBOL and S has RING +--R differentiate : (%,NonNegativeInteger) -> % if S has DIFRING and S has RING +--R differentiate : % -> % if S has DIFRING and S has RING +--R dimension : () -> CardinalNumber if S has FIELD +--R dot : (%,%) -> S if S has RING +--R entry? : (S,%) -> Boolean if $ has finiteAggregate and S has SETCAT +--R eval : (%,List S,List S) -> % if S has EVALAB S and S has SETCAT +--R eval : (%,S,S) -> % if S has EVALAB S and S has SETCAT +--R eval : (%,Equation S) -> % if S has EVALAB S and S has SETCAT +--R eval : (%,List Equation S) -> % if S has EVALAB S and S has SETCAT +--R every? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate +--R fill! : (%,S) -> % if $ has shallowlyMutable +--R first : % -> S if Integer has ORDSET +--R hash : % -> SingleInteger if S has SETCAT +--R index : PositiveInteger -> % if S has FINITE +--R latex : % -> String if S has SETCAT +--R less? : (%,NonNegativeInteger) -> Boolean +--R lookup : % -> PositiveInteger if S has FINITE +--R map! : ((S -> S),%) -> % if $ has shallowlyMutable +--R max : (%,%) -> % if S has OAMONS or S has ORDRING +--R maxIndex : % -> Integer if Integer has ORDSET +--R member? : (S,%) -> Boolean if $ has finiteAggregate and S has SETCAT +--R members : % -> List S if $ has finiteAggregate +--R min : (%,%) -> % if S has OAMONS or S has ORDRING +--R minIndex : % -> Integer if Integer has ORDSET +--R more? : (%,NonNegativeInteger) -> Boolean +--R negative? : % -> Boolean if S has ORDRING +--R one? : % -> Boolean if S has MONOID +--R parts : % -> List S if $ has finiteAggregate +--R positive? : % -> Boolean if S has ORDRING +--R qsetelt! : (%,Integer,S) -> S if $ has shallowlyMutable +--R random : () -> % if S has FINITE +--R recip : % -> Union(%,"failed") if S has MONOID +--R reducedSystem : Matrix % -> Matrix S if S has RING +--R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix S,vec: Vector S) if S has RING +--R reducedSystem : (Matrix %,Vector %) -> Record(mat: Matrix Integer,vec: Vector Integer) if S has LINEXP INT and S has RING +--R reducedSystem : Matrix % -> Matrix Integer if S has LINEXP INT and S has RING +--R retract : % -> S if S has SETCAT +--R retract : % -> Fraction Integer if S has RETRACT FRAC INT and S has SETCAT +--R retract : % -> Integer if S has RETRACT INT and S has SETCAT +--R retractIfCan : % -> Union(S,"failed") if S has SETCAT +--R retractIfCan : % -> Union(Fraction Integer,"failed") if S has RETRACT FRAC INT and S has SETCAT +--R retractIfCan : % -> Union(Integer,"failed") if S has RETRACT INT and S has SETCAT +--R setelt : (%,Integer,S) -> S if $ has shallowlyMutable +--R sign : % -> Integer if S has ORDRING +--R size : () -> NonNegativeInteger if S has FINITE +--R size? : (%,NonNegativeInteger) -> Boolean +--R subtractIfCan : (%,%) -> Union(%,"failed") if S has CABMON +--R sup : (%,%) -> % if S has OAMONS +--R swap! : (%,Integer,Integer) -> Void if $ has shallowlyMutable +--R unitVector : PositiveInteger -> % if S has RING +--R zero? : % -> Boolean if S has CABMON +--R ?~=? : (%,%) -> Boolean if S has SETCAT +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +SplitHomogeneousDirectProduct examples +==================================================================== + +See Also: +o )show SplitHomogeneousDirectProduct + +@ + \pagehead{SplitHomogeneousDirectProduct}{SHDP} \pagepic{ps/v103splithomogeneousdirectproduct.ps}{SHDP}{1.00} {\bf See}\\ @@ -99848,6 +118163,52 @@ SplitHomogeneousDirectProduct(dimtot,dim1,S) : T == C where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain SPLNODE SplittingNode} + +<>= +)set break resume +)sys rm -f SplittingNode.output +)spool SplittingNode.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show SplittingNode +--R SplittingNode(V: Join(SetCategory,Aggregate),C: Join(SetCategory,Aggregate)) is a domain constructor +--R Abbreviation for SplittingNode is SPLNODE +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for SPLNODE +--R +--R------------------------------- Operations -------------------------------- +--R ?=? : (%,%) -> Boolean coerce : % -> OutputForm +--R condition : % -> C construct : (V,List C) -> List % +--R construct : (V,C) -> % construct : (V,C,Boolean) -> % +--R copy : % -> % empty : () -> % +--R empty? : % -> Boolean hash : % -> SingleInteger +--R latex : % -> String setCondition! : (%,C) -> % +--R setEmpty! : % -> % setStatus! : (%,Boolean) -> % +--R setValue! : (%,V) -> % status : % -> Boolean +--R value : % -> V ?~=? : (%,%) -> Boolean +--R construct : List Record(val: V,tower: C) -> List % +--R construct : Record(val: V,tower: C) -> % +--R infLex? : (%,%,((V,V) -> Boolean),((C,C) -> Boolean)) -> Boolean +--R subNode? : (%,%,((C,C) -> Boolean)) -> Boolean +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +SplittingNode examples +==================================================================== + +See Also: +o )show SplittingNode + +@ + \pagehead{SplittingNode}{SPLNODE} \pagepic{ps/v103splittingnode.ps}{SPLNODE}{1.00} {\bf See}\\ @@ -100038,6 +118399,86 @@ SplittingNode(V,C) : Exports == Implementation where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain SPLTREE SplittingTree} + +<>= +)set break resume +)sys rm -f SplittingTree.output +)spool SplittingTree.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show SplittingTree +--R SplittingTree(V: Join(SetCategory,Aggregate),C: Join(SetCategory,Aggregate)) is a domain constructor +--R Abbreviation for SplittingTree is SPLTREE +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for SPLTREE +--R +--R------------------------------- Operations -------------------------------- +--R children : % -> List % conditions : % -> List C +--R construct : (V,C,V,List C) -> % construct : (V,C,List %) -> % +--R copy : % -> % cyclic? : % -> Boolean +--R distance : (%,%) -> Integer empty : () -> % +--R empty? : % -> Boolean eq? : (%,%) -> Boolean +--R leaf? : % -> Boolean nodes : % -> List % +--R sample : () -> % updateStatus! : % -> % +--R value : % -> SplittingNode(V,C) +--R #? : % -> NonNegativeInteger if $ has finiteAggregate +--R ?=? : (%,%) -> Boolean if SplittingNode(V,C) has SETCAT +--R any? : ((SplittingNode(V,C) -> Boolean),%) -> Boolean if $ has finiteAggregate +--R child? : (%,%) -> Boolean if SplittingNode(V,C) has SETCAT +--R coerce : % -> OutputForm if SplittingNode(V,C) has SETCAT +--R construct : (V,C,List SplittingNode(V,C)) -> % +--R construct : SplittingNode(V,C) -> % +--R count : (SplittingNode(V,C),%) -> NonNegativeInteger if $ has finiteAggregate and SplittingNode(V,C) has SETCAT +--R count : ((SplittingNode(V,C) -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate +--R ?.value : (%,value) -> SplittingNode(V,C) +--R eval : (%,List SplittingNode(V,C),List SplittingNode(V,C)) -> % if SplittingNode(V,C) has EVALAB SPLNODE(V,C) and SplittingNode(V,C) has SETCAT +--R eval : (%,SplittingNode(V,C),SplittingNode(V,C)) -> % if SplittingNode(V,C) has EVALAB SPLNODE(V,C) and SplittingNode(V,C) has SETCAT +--R eval : (%,Equation SplittingNode(V,C)) -> % if SplittingNode(V,C) has EVALAB SPLNODE(V,C) and SplittingNode(V,C) has SETCAT +--R eval : (%,List Equation SplittingNode(V,C)) -> % if SplittingNode(V,C) has EVALAB SPLNODE(V,C) and SplittingNode(V,C) has SETCAT +--R every? : ((SplittingNode(V,C) -> Boolean),%) -> Boolean if $ has finiteAggregate +--R extractSplittingLeaf : % -> Union(%,"failed") +--R hash : % -> SingleInteger if SplittingNode(V,C) has SETCAT +--R latex : % -> String if SplittingNode(V,C) has SETCAT +--R leaves : % -> List SplittingNode(V,C) +--R less? : (%,NonNegativeInteger) -> Boolean +--R map : ((SplittingNode(V,C) -> SplittingNode(V,C)),%) -> % +--R map! : ((SplittingNode(V,C) -> SplittingNode(V,C)),%) -> % if $ has shallowlyMutable +--R member? : (SplittingNode(V,C),%) -> Boolean if $ has finiteAggregate and SplittingNode(V,C) has SETCAT +--R members : % -> List SplittingNode(V,C) if $ has finiteAggregate +--R more? : (%,NonNegativeInteger) -> Boolean +--R node? : (%,%) -> Boolean if SplittingNode(V,C) has SETCAT +--R nodeOf? : (SplittingNode(V,C),%) -> Boolean +--R parts : % -> List SplittingNode(V,C) if $ has finiteAggregate +--R remove : (SplittingNode(V,C),%) -> % +--R remove! : (SplittingNode(V,C),%) -> % +--R result : % -> List Record(val: V,tower: C) +--R setchildren! : (%,List %) -> % if $ has shallowlyMutable +--R setelt : (%,value,SplittingNode(V,C)) -> SplittingNode(V,C) if $ has shallowlyMutable +--R setvalue! : (%,SplittingNode(V,C)) -> SplittingNode(V,C) if $ has shallowlyMutable +--R size? : (%,NonNegativeInteger) -> Boolean +--R splitNodeOf! : (%,%,List SplittingNode(V,C),((C,C) -> Boolean)) -> % +--R splitNodeOf! : (%,%,List SplittingNode(V,C)) -> % +--R subNodeOf? : (SplittingNode(V,C),%,((C,C) -> Boolean)) -> Boolean +--R ?~=? : (%,%) -> Boolean if SplittingNode(V,C) has SETCAT +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +SplittingTree examples +==================================================================== + +See Also: +o )show SplittingTree + +@ + \pagehead{SplittingTree}{SPLTREE} \pagepic{ps/v103splittingtree.ps}{SPLTREE}{1.00} {\bf See}\\ @@ -100409,6 +118850,7 @@ SplittingTree(V,C) : Exports == Implementation where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain SREGSET SquareFreeRegularTriangularSet} + <>= )set break resume )sys rm -f SquareFreeRegularTriangularSet.output @@ -101384,6 +119826,7 @@ SquareFreeRegularTriangularSet(R,E,V,P) : Exports == Implementation where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain SQMATRIX SquareMatrix} + <>= )set break resume )sys rm -f SquareMatrix.output @@ -101760,6 +120203,7 @@ SquareMatrix(ndim,R): Exports == Implementation where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain STACK Stack} + <>= )set break resume )sys rm -f Stack.output @@ -102583,6 +121027,7 @@ Stack(S:SetCategory): StackAggregate S with @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain STREAM Stream} + <>= )set break resume )sys rm -f Stream.output @@ -103531,6 +121976,7 @@ Stream(S): Exports == Implementation where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain STRING String} + <>= )set break resume )sys rm -f String.output @@ -104177,6 +122623,7 @@ String(): StringCategory == IndexedString(1) add @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain STRTBL StringTable} + <>= )set break resume )sys rm -f StringTable.output @@ -104346,6 +122793,7 @@ StringTable(Entry: SetCategory) == @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain SUBSPACE SubSpace} + The first argument n is the dimension of the subSpace The SubSpace domain is implemented as a tree. The root of the tree @@ -104392,6 +122840,64 @@ extend a path to a leaf of depth 3 that points to the data held in p. The subspace s would now have a new component which has one child which, in turn, has one child (the leaf). The new component is then a point. + +<>= +)set break resume +)sys rm -f SubSpace.output +)spool SubSpace.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show SubSpace +--R SubSpace(n: PositiveInteger,R: Ring) is a domain constructor +--R Abbreviation for SubSpace is SUBSPACE +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for SUBSPACE +--R +--R------------------------------- Operations -------------------------------- +--R ?=? : (%,%) -> Boolean addPoint2 : (%,Point R) -> % +--R birth : % -> % children : % -> List % +--R coerce : % -> OutputForm deepCopy : % -> % +--R extractClosed : % -> Boolean extractPoint : % -> Point R +--R hash : % -> SingleInteger internal? : % -> Boolean +--R latex : % -> String leaf? : % -> Boolean +--R level : % -> NonNegativeInteger merge : List % -> % +--R merge : (%,%) -> % new : () -> % +--R parent : % -> % pointData : % -> List Point R +--R root? : % -> Boolean separate : % -> List % +--R shallowCopy : % -> % subspace : () -> % +--R ?~=? : (%,%) -> Boolean +--R addPoint : (%,Point R) -> NonNegativeInteger +--R addPoint : (%,List NonNegativeInteger,NonNegativeInteger) -> % +--R addPoint : (%,List NonNegativeInteger,Point R) -> % +--R addPointLast : (%,%,Point R,NonNegativeInteger) -> % +--R child : (%,NonNegativeInteger) -> % +--R closeComponent : (%,List NonNegativeInteger,Boolean) -> % +--R defineProperty : (%,List NonNegativeInteger,SubSpaceComponentProperty) -> % +--R extractIndex : % -> NonNegativeInteger +--R extractProperty : % -> SubSpaceComponentProperty +--R modifyPoint : (%,NonNegativeInteger,Point R) -> % +--R modifyPoint : (%,List NonNegativeInteger,NonNegativeInteger) -> % +--R modifyPoint : (%,List NonNegativeInteger,Point R) -> % +--R numberOfChildren : % -> NonNegativeInteger +--R traverse : (%,List NonNegativeInteger) -> % +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +SubSpace examples +==================================================================== + +See Also: +o )show SubSpace + +@ \pagehead{SubSpace}{SUBSPACE} \pagepic{ps/v103subspace.ps}{SUBSPACE}{1.00} @@ -104865,6 +123371,45 @@ SubSpace(n:PI,R:Ring) : Exports == Implementation where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain COMPPROP SubSpaceComponentProperty} + +<>= +)set break resume +)sys rm -f SubSpaceComponentProperty.output +)spool SubSpaceComponentProperty.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show SubSpaceComponentProperty +--R SubSpaceComponentProperty is a domain constructor +--R Abbreviation for SubSpaceComponentProperty is COMPPROP +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for COMPPROP +--R +--R------------------------------- Operations -------------------------------- +--R ?=? : (%,%) -> Boolean close : (%,Boolean) -> Boolean +--R closed? : % -> Boolean coerce : % -> OutputForm +--R copy : % -> % hash : % -> SingleInteger +--R latex : % -> String new : () -> % +--R solid : (%,Boolean) -> Boolean solid? : % -> Boolean +--R ?~=? : (%,%) -> Boolean +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +SubSpaceComponentProperty examples +==================================================================== + +See Also: +o )show SubSpaceComponentProperty + +@ + \pagehead{SubSpaceComponentProperty}{COMPPROP} \pagepic{ps/v103subspacecomponentproperty.ps}{COMPPROP}{1.00} {\bf See}\\ @@ -104943,6 +123488,43 @@ SubSpaceComponentProperty() : Exports == Implementation where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain SUCH SuchThat} + +<>= +)set break resume +)sys rm -f SuchThat.output +)spool SuchThat.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show SuchThat +--R SuchThat(S1: SetCategory,S2: SetCategory) is a domain constructor +--R Abbreviation for SuchThat is SUCH +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for SUCH +--R +--R------------------------------- Operations -------------------------------- +--R ?=? : (%,%) -> Boolean coerce : % -> OutputForm +--R construct : (S1,S2) -> % hash : % -> SingleInteger +--R latex : % -> String lhs : % -> S1 +--R rhs : % -> S2 ?~=? : (%,%) -> Boolean +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +SuchThat examples +==================================================================== + +See Also: +o )show SuchThat + +@ + \pagehead{SuchThat}{SUCH} \pagepic{ps/v103suchthat.ps}{SUCH}{1.00} @@ -104994,6 +123576,49 @@ SuchThat(S1, S2): Cat == Capsule where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain SWITCH Switch} + +<>= +)set break resume +)sys rm -f Switch.output +)spool Switch.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show Switch +--R Switch is a domain constructor +--R Abbreviation for Switch is SWITCH +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for SWITCH +--R +--R------------------------------- Operations -------------------------------- +--R NOT : % -> % coerce : Symbol -> % +--R coerce : % -> OutputForm +--R AND : (Union(I: Expression Integer,F: Expression Float,CF: Expression Complex Float,switch: %),Union(I: Expression Integer,F: Expression Float,CF: Expression Complex Float,switch: %)) -> % +--R EQ : (Union(I: Expression Integer,F: Expression Float,CF: Expression Complex Float,switch: %),Union(I: Expression Integer,F: Expression Float,CF: Expression Complex Float,switch: %)) -> % +--R GE : (Union(I: Expression Integer,F: Expression Float,CF: Expression Complex Float,switch: %),Union(I: Expression Integer,F: Expression Float,CF: Expression Complex Float,switch: %)) -> % +--R GT : (Union(I: Expression Integer,F: Expression Float,CF: Expression Complex Float,switch: %),Union(I: Expression Integer,F: Expression Float,CF: Expression Complex Float,switch: %)) -> % +--R LE : (Union(I: Expression Integer,F: Expression Float,CF: Expression Complex Float,switch: %),Union(I: Expression Integer,F: Expression Float,CF: Expression Complex Float,switch: %)) -> % +--R LT : (Union(I: Expression Integer,F: Expression Float,CF: Expression Complex Float,switch: %),Union(I: Expression Integer,F: Expression Float,CF: Expression Complex Float,switch: %)) -> % +--R NOT : Union(I: Expression Integer,F: Expression Float,CF: Expression Complex Float,switch: %) -> % +--R OR : (Union(I: Expression Integer,F: Expression Float,CF: Expression Complex Float,switch: %),Union(I: Expression Integer,F: Expression Float,CF: Expression Complex Float,switch: %)) -> % +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +Switch examples +==================================================================== + +See Also: +o )show Switch + +@ + \pagehead{Switch}{SWITCH} \pagepic{ps/v103switch.ps}{SWITCH}{1.00} {\bf See}\\ @@ -105115,6 +123740,7 @@ Switch():public == private where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain SYMBOL Symbol} + <>= )set break resume )sys rm -f Symbol.output @@ -105849,6 +124475,49 @@ Symbol(): Exports == Implementation where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain SYMTAB SymbolTable} + +<>= +)set break resume +)sys rm -f SymbolTable.output +)spool SymbolTable.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show SymbolTable +--R SymbolTable is a domain constructor +--R Abbreviation for SymbolTable is SYMTAB +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for SYMTAB +--R +--R------------------------------- Operations -------------------------------- +--R coerce : % -> OutputForm empty : () -> % +--R externalList : % -> List Symbol newTypeLists : % -> SExpression +--R parametersOf : % -> List Symbol printTypes : % -> Void +--R coerce : % -> Table(Symbol,FortranType) +--R declare! : (Symbol,FortranType,%) -> FortranType +--R declare! : (List Symbol,FortranType,%) -> FortranType +--R fortranTypeOf : (Symbol,%) -> FortranType +--R symbolTable : List Record(key: Symbol,entry: FortranType) -> % +--R typeList : (FortranScalarType,%) -> List Union(name: Symbol,bounds: List Union(S: Symbol,P: Polynomial Integer)) +--R typeLists : % -> List List Union(name: Symbol,bounds: List Union(S: Symbol,P: Polynomial Integer)) +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +SymbolTable examples +==================================================================== + +See Also: +o )show SymbolTable + +@ + \pagehead{SymbolTable}{SYMTAB} \pagepic{ps/v103symboltable.ps}{SYMTAB}{1.00} {\bf See}\\ @@ -106062,6 +124731,86 @@ SymbolTable() : exports == implementation where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain SYMPOLY SymmetricPolynomial} + +<>= +)set break resume +)sys rm -f SymmetricPolynomial.output +)spool SymmetricPolynomial.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show SymmetricPolynomial +--R SymmetricPolynomial R: Ring is a domain constructor +--R Abbreviation for SymmetricPolynomial is SYMPOLY +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for SYMPOLY +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (R,%) -> % ?*? : (%,R) -> % +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ?=? : (%,%) -> Boolean +--R 1 : () -> % 0 : () -> % +--R ?^? : (%,PositiveInteger) -> % coefficient : (%,Partition) -> R +--R coefficients : % -> List R coerce : R -> % +--R coerce : Integer -> % coerce : % -> OutputForm +--R degree : % -> Partition ground : % -> R +--R ground? : % -> Boolean hash : % -> SingleInteger +--R latex : % -> String leadingCoefficient : % -> R +--R leadingMonomial : % -> % map : ((R -> R),%) -> % +--R minimumDegree : % -> Partition monomial : (R,Partition) -> % +--R monomial? : % -> Boolean one? : % -> Boolean +--R recip : % -> Union(%,"failed") reductum : % -> % +--R retract : % -> R sample : () -> % +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean +--R ?*? : (%,Fraction Integer) -> % if R has ALGEBRA FRAC INT +--R ?*? : (Fraction Integer,%) -> % if R has ALGEBRA FRAC INT +--R ?*? : (NonNegativeInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % +--R ?/? : (%,R) -> % if R has FIELD +--R ?^? : (%,NonNegativeInteger) -> % +--R associates? : (%,%) -> Boolean if R has INTDOM +--R binomThmExpt : (%,%,NonNegativeInteger) -> % if R has COMRING +--R characteristic : () -> NonNegativeInteger +--R charthRoot : % -> Union(%,"failed") if R has CHARNZ +--R coerce : Fraction Integer -> % if R has ALGEBRA FRAC INT or R has RETRACT FRAC INT +--R coerce : % -> % if R has INTDOM +--R content : % -> R if R has GCDDOM +--R exquo : (%,R) -> Union(%,"failed") if R has INTDOM +--R exquo : (%,%) -> Union(%,"failed") if R has INTDOM +--R fmecg : (%,Partition,R,%) -> % if Partition has CABMON and R has INTDOM +--R mapExponents : ((Partition -> Partition),%) -> % +--R numberOfMonomials : % -> NonNegativeInteger +--R pomopo! : (%,R,Partition,%) -> % +--R primitivePart : % -> % if R has GCDDOM +--R retract : % -> Fraction Integer if R has RETRACT FRAC INT +--R retract : % -> Integer if R has RETRACT INT +--R retractIfCan : % -> Union(R,"failed") +--R retractIfCan : % -> Union(Fraction Integer,"failed") if R has RETRACT FRAC INT +--R retractIfCan : % -> Union(Integer,"failed") if R has RETRACT INT +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R unit? : % -> Boolean if R has INTDOM +--R unitCanonical : % -> % if R has INTDOM +--R unitNormal : % -> Record(unit: %,canonical: %,associate: %) if R has INTDOM +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +SymmetricPolynomial examples +==================================================================== + +See Also: +o )show SymmetricPolynomial + +@ + \pagehead{SymmetricPolynomial}{SYMPOLY} \pagepic{ps/v103symmetricpolynomial.ps}{SYMPOLY}{1.00} {\bf See}\\ @@ -106165,6 +124914,7 @@ SymmetricPolynomial(R:Ring) == PolynomialRing(R,Partition) add \chapter{Chapter T} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain TABLE Table} + <>= )set break resume )sys rm -f Table.output @@ -106573,6 +125323,41 @@ Table(Key: SetCategory, Entry: SetCategory):Exports == Implementation where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain TABLEAU Tableau} + +<>= +)set break resume +)sys rm -f Tableau.output +)spool Tableau.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show Tableau +--R Tableau S: SetCategory is a domain constructor +--R Abbreviation for Tableau is TABLEAU +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for TABLEAU +--R +--R------------------------------- Operations -------------------------------- +--R coerce : % -> OutputForm listOfLists : % -> List List S +--R tableau : List List S -> % +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +Tableau examples +==================================================================== + +See Also: +o )show Tableau + +@ + \pagehead{Tableau}{TABLEAU} \pagepic{ps/v103tableau.ps}{TABLEAU}{1.00} @@ -106642,6 +125427,131 @@ Tableau(S:SetCategory):Exports == Implementation where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain TS TaylorSeries} + +<>= +)set break resume +)sys rm -f TaylorSeries.output +)spool TaylorSeries.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show TaylorSeries +--R TaylorSeries Coef: Ring is a domain constructor +--R Abbreviation for TaylorSeries is TS +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for TS +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (%,Coef) -> % ?*? : (Coef,%) -> % +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ?=? : (%,%) -> Boolean +--R D : (%,List Symbol) -> % D : (%,Symbol) -> % +--R 1 : () -> % 0 : () -> % +--R ?^? : (%,PositiveInteger) -> % coerce : Polynomial Coef -> % +--R coerce : Symbol -> % coerce : Integer -> % +--R coerce : % -> OutputForm complete : % -> % +--R differentiate : (%,Symbol) -> % eval : (%,List %,List %) -> % +--R eval : (%,%,%) -> % eval : (%,Equation %) -> % +--R eval : (%,List Equation %) -> % eval : (%,Symbol,%) -> % +--R hash : % -> SingleInteger latex : % -> String +--R leadingCoefficient : % -> Coef leadingMonomial : % -> % +--R map : ((Coef -> Coef),%) -> % monomial? : % -> Boolean +--R one? : % -> Boolean pole? : % -> Boolean +--R recip : % -> Union(%,"failed") reductum : % -> % +--R sample : () -> % variables : % -> List Symbol +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean +--R ?*? : (Fraction Integer,%) -> % if Coef has ALGEBRA FRAC INT +--R ?*? : (%,Fraction Integer) -> % if Coef has ALGEBRA FRAC INT +--R ?*? : (NonNegativeInteger,%) -> % +--R ?**? : (%,Fraction Integer) -> % if Coef has ALGEBRA FRAC INT +--R ?**? : (%,%) -> % if Coef has ALGEBRA FRAC INT +--R ?**? : (%,NonNegativeInteger) -> % +--R ?/? : (%,Coef) -> % if Coef has FIELD +--R D : (%,List Symbol,List NonNegativeInteger) -> % +--R D : (%,Symbol,NonNegativeInteger) -> % +--R ?^? : (%,NonNegativeInteger) -> % +--R acos : % -> % if Coef has ALGEBRA FRAC INT +--R acosh : % -> % if Coef has ALGEBRA FRAC INT +--R acot : % -> % if Coef has ALGEBRA FRAC INT +--R acoth : % -> % if Coef has ALGEBRA FRAC INT +--R acsc : % -> % if Coef has ALGEBRA FRAC INT +--R acsch : % -> % if Coef has ALGEBRA FRAC INT +--R asec : % -> % if Coef has ALGEBRA FRAC INT +--R asech : % -> % if Coef has ALGEBRA FRAC INT +--R asin : % -> % if Coef has ALGEBRA FRAC INT +--R asinh : % -> % if Coef has ALGEBRA FRAC INT +--R associates? : (%,%) -> Boolean if Coef has INTDOM +--R atan : % -> % if Coef has ALGEBRA FRAC INT +--R atanh : % -> % if Coef has ALGEBRA FRAC INT +--R characteristic : () -> NonNegativeInteger +--R charthRoot : % -> Union(%,"failed") if Coef has CHARNZ +--R coefficient : (%,NonNegativeInteger) -> Polynomial Coef +--R coefficient : (%,List Symbol,List NonNegativeInteger) -> % +--R coefficient : (%,Symbol,NonNegativeInteger) -> % +--R coefficient : (%,IndexedExponents Symbol) -> Coef +--R coerce : Fraction Integer -> % if Coef has ALGEBRA FRAC INT +--R coerce : % -> % if Coef has INTDOM +--R coerce : Coef -> % if Coef has COMRING +--R cos : % -> % if Coef has ALGEBRA FRAC INT +--R cosh : % -> % if Coef has ALGEBRA FRAC INT +--R cot : % -> % if Coef has ALGEBRA FRAC INT +--R coth : % -> % if Coef has ALGEBRA FRAC INT +--R csc : % -> % if Coef has ALGEBRA FRAC INT +--R csch : % -> % if Coef has ALGEBRA FRAC INT +--R degree : % -> IndexedExponents Symbol +--R differentiate : (%,List Symbol,List NonNegativeInteger) -> % +--R differentiate : (%,Symbol,NonNegativeInteger) -> % +--R differentiate : (%,List Symbol) -> % +--R eval : (%,List Symbol,List %) -> % +--R exp : % -> % if Coef has ALGEBRA FRAC INT +--R exquo : (%,%) -> Union(%,"failed") if Coef has INTDOM +--R extend : (%,NonNegativeInteger) -> % +--R fintegrate : ((() -> %),Symbol,Coef) -> % if Coef has ALGEBRA FRAC INT +--R integrate : (%,Symbol,Coef) -> % if Coef has ALGEBRA FRAC INT +--R integrate : (%,Symbol) -> % if Coef has ALGEBRA FRAC INT +--R log : % -> % if Coef has ALGEBRA FRAC INT +--R monomial : (%,List Symbol,List NonNegativeInteger) -> % +--R monomial : (%,Symbol,NonNegativeInteger) -> % +--R monomial : (Coef,IndexedExponents Symbol) -> % +--R monomial : (%,Symbol,IndexedExponents Symbol) -> % +--R monomial : (%,List Symbol,List IndexedExponents Symbol) -> % +--R nthRoot : (%,Integer) -> % if Coef has ALGEBRA FRAC INT +--R order : (%,Symbol,NonNegativeInteger) -> NonNegativeInteger +--R order : (%,Symbol) -> NonNegativeInteger +--R pi : () -> % if Coef has ALGEBRA FRAC INT +--R polynomial : (%,NonNegativeInteger,NonNegativeInteger) -> Polynomial Coef +--R polynomial : (%,NonNegativeInteger) -> Polynomial Coef +--R sec : % -> % if Coef has ALGEBRA FRAC INT +--R sech : % -> % if Coef has ALGEBRA FRAC INT +--R sin : % -> % if Coef has ALGEBRA FRAC INT +--R sinh : % -> % if Coef has ALGEBRA FRAC INT +--R sqrt : % -> % if Coef has ALGEBRA FRAC INT +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R tan : % -> % if Coef has ALGEBRA FRAC INT +--R tanh : % -> % if Coef has ALGEBRA FRAC INT +--R unit? : % -> Boolean if Coef has INTDOM +--R unitCanonical : % -> % if Coef has INTDOM +--R unitNormal : % -> Record(unit: %,canonical: %,associate: %) if Coef has INTDOM +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +TaylorSeries examples +==================================================================== + +See Also: +o )show TaylorSeries + +@ + \pagehead{TaylorSeries}{TS} \pagepic{ps/v103taylorseries.ps}{TS}{1.00} {\bf See}\\ @@ -107606,6 +126516,7 @@ TexFormat(): public == private where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain TEXTFILE TextFile} + <>= )set break resume )sys rm -f TextFile.output @@ -107897,6 +126808,59 @@ TextFile: Cat == Def where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain SYMS TheSymbolTable} + +<>= +)set break resume +)sys rm -f TheSymbolTable.output +)spool TheSymbolTable.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show TheSymbolTable +--R TheSymbolTable is a domain constructor +--R Abbreviation for TheSymbolTable is SYMS +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for SYMS +--R +--R------------------------------- Operations -------------------------------- +--R clearTheSymbolTable : () -> Void coerce : % -> OutputForm +--R currentSubProgram : () -> Symbol empty : () -> % +--R endSubProgram : () -> Symbol newSubProgram : Symbol -> Void +--R printHeader : () -> Void printHeader : Symbol -> Void +--R printHeader : (Symbol,%) -> Void printTypes : Symbol -> Void +--R showTheSymbolTable : () -> % +--R argumentList! : List Symbol -> Void +--R argumentList! : (Symbol,List Symbol) -> Void +--R argumentList! : (Symbol,List Symbol,%) -> Void +--R argumentListOf : (Symbol,%) -> List Symbol +--R clearTheSymbolTable : Symbol -> Void +--R declare! : (Symbol,FortranType,Symbol) -> FortranType +--R declare! : (Symbol,FortranType) -> FortranType +--R declare! : (List Symbol,FortranType,Symbol,%) -> FortranType +--R declare! : (Symbol,FortranType,Symbol,%) -> FortranType +--R returnType! : Union(fst: FortranScalarType,void: void) -> Void +--R returnType! : (Symbol,Union(fst: FortranScalarType,void: void)) -> Void +--R returnType! : (Symbol,Union(fst: FortranScalarType,void: void),%) -> Void +--R returnTypeOf : (Symbol,%) -> Union(fst: FortranScalarType,void: void) +--R symbolTableOf : (Symbol,%) -> SymbolTable +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +TheSymbolTable examples +==================================================================== + +See Also: +o )show TheSymbolTable + +@ + \pagehead{TheSymbolTable}{SYMS} \pagepic{ps/v103thesymboltable.ps}{SYMS}{1.00} {\bf See}\\ @@ -108135,6 +127099,73 @@ TheSymbolTable() : Exports == Implementation where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain M3D ThreeDimensionalMatrix} + +<>= +)set break resume +)sys rm -f ThreeDimensionalMatrix.output +)spool ThreeDimensionalMatrix.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show ThreeDimensionalMatrix +--R ThreeDimensionalMatrix R: SetCategory is a domain constructor +--R Abbreviation for ThreeDimensionalMatrix is M3D +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for M3D +--R +--R------------------------------- Operations -------------------------------- +--R construct : List List List R -> % copy : % -> % +--R empty : () -> % empty? : % -> Boolean +--R eq? : (%,%) -> Boolean map : ((R -> R),%) -> % +--R sample : () -> % +--R #? : % -> NonNegativeInteger if $ has finiteAggregate +--R ?=? : (%,%) -> Boolean if R has SETCAT +--R any? : ((R -> Boolean),%) -> Boolean if $ has finiteAggregate +--R coerce : % -> PrimitiveArray PrimitiveArray PrimitiveArray R +--R coerce : PrimitiveArray PrimitiveArray PrimitiveArray R -> % +--R coerce : % -> OutputForm if R has SETCAT +--R count : (R,%) -> NonNegativeInteger if $ has finiteAggregate and R has SETCAT +--R count : ((R -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate +--R elt : (%,NonNegativeInteger,NonNegativeInteger,NonNegativeInteger) -> R +--R eval : (%,List R,List R) -> % if R has EVALAB R and R has SETCAT +--R eval : (%,R,R) -> % if R has EVALAB R and R has SETCAT +--R eval : (%,Equation R) -> % if R has EVALAB R and R has SETCAT +--R eval : (%,List Equation R) -> % if R has EVALAB R and R has SETCAT +--R every? : ((R -> Boolean),%) -> Boolean if $ has finiteAggregate +--R hash : % -> SingleInteger if R has SETCAT +--R identityMatrix : NonNegativeInteger -> % if R has RING +--R latex : % -> String if R has SETCAT +--R less? : (%,NonNegativeInteger) -> Boolean +--R map! : ((R -> R),%) -> % if $ has shallowlyMutable +--R matrixConcat3D : (Symbol,%,%) -> % +--R matrixDimensions : % -> Vector NonNegativeInteger +--R member? : (R,%) -> Boolean if $ has finiteAggregate and R has SETCAT +--R members : % -> List R if $ has finiteAggregate +--R more? : (%,NonNegativeInteger) -> Boolean +--R parts : % -> List R if $ has finiteAggregate +--R plus : (%,%) -> % if R has RING +--R setelt! : (%,NonNegativeInteger,NonNegativeInteger,NonNegativeInteger,R) -> R +--R size? : (%,NonNegativeInteger) -> Boolean +--R zeroMatrix : (NonNegativeInteger,NonNegativeInteger,NonNegativeInteger) -> % if R has RING +--R ?~=? : (%,%) -> Boolean if R has SETCAT +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +ThreeDimensionalMatrix examples +==================================================================== + +See Also: +o )show ThreeDimensionalMatrix + +@ + \pagehead{ThreeDimensionalMatrix}{M3D} \pagepic{ps/v103threedimensionalmatrix.ps}{M3D}{1.00} {\bf See}\\ @@ -108438,6 +127469,81 @@ ThreeDimensionalMatrix(R) : Exports == Implementation where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain VIEW3D ThreeDimensionalViewport} + +<>= +)set break resume +)sys rm -f ThreeDimensionalViewport.output +)spool ThreeDimensionalViewport.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show ThreeDimensionalViewport +--R ThreeDimensionalViewport is a domain constructor +--R Abbreviation for ThreeDimensionalViewport is VIEW3D +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for VIEW3D +--R +--R------------------------------- Operations -------------------------------- +--R ?=? : (%,%) -> Boolean axes : (%,String) -> Void +--R clipSurface : (%,String) -> Void close : % -> Void +--R coerce : % -> OutputForm controlPanel : (%,String) -> Void +--R diagonals : (%,String) -> Void drawStyle : (%,String) -> Void +--R eyeDistance : (%,Float) -> Void hash : % -> SingleInteger +--R hitherPlane : (%,Float) -> Void intensity : (%,Float) -> Void +--R key : % -> Integer latex : % -> String +--R makeViewport3D : % -> % options : % -> List DrawOption +--R perspective : (%,String) -> Void reset : % -> Void +--R rotate : (%,Float,Float) -> Void showRegion : (%,String) -> Void +--R title : (%,String) -> Void viewDeltaXDefault : Float -> Float +--R viewDeltaXDefault : () -> Float viewDeltaYDefault : Float -> Float +--R viewDeltaYDefault : () -> Float viewPhiDefault : Float -> Float +--R viewPhiDefault : () -> Float viewThetaDefault : Float -> Float +--R viewThetaDefault : () -> Float viewZoomDefault : Float -> Float +--R viewZoomDefault : () -> Float viewport3D : () -> % +--R write : (%,String) -> String zoom : (%,Float) -> Void +--R ?~=? : (%,%) -> Boolean +--R colorDef : (%,Color,Color) -> Void +--R dimensions : (%,NonNegativeInteger,NonNegativeInteger,PositiveInteger,PositiveInteger) -> Void +--R lighting : (%,Float,Float,Float) -> Void +--R makeViewport3D : (ThreeSpace DoubleFloat,List DrawOption) -> % +--R makeViewport3D : (ThreeSpace DoubleFloat,String) -> % +--R modifyPointData : (%,NonNegativeInteger,Point DoubleFloat) -> Void +--R move : (%,NonNegativeInteger,NonNegativeInteger) -> Void +--R options : (%,List DrawOption) -> % +--R outlineRender : (%,String) -> Void +--R resize : (%,PositiveInteger,PositiveInteger) -> Void +--R rotate : (%,Integer,Integer) -> Void +--R showClipRegion : (%,String) -> Void +--R subspace : (%,ThreeSpace DoubleFloat) -> % +--R subspace : % -> ThreeSpace DoubleFloat +--R translate : (%,Float,Float) -> Void +--R viewpoint : (%,Float,Float,Float) -> Void +--R viewpoint : (%,Float,Float) -> Void +--R viewpoint : (%,Integer,Integer,Float,Float,Float) -> Void +--R viewpoint : (%,Record(theta: DoubleFloat,phi: DoubleFloat,scale: DoubleFloat,scaleX: DoubleFloat,scaleY: DoubleFloat,scaleZ: DoubleFloat,deltaX: DoubleFloat,deltaY: DoubleFloat)) -> Void +--R viewpoint : % -> Record(theta: DoubleFloat,phi: DoubleFloat,scale: DoubleFloat,scaleX: DoubleFloat,scaleY: DoubleFloat,scaleZ: DoubleFloat,deltaX: DoubleFloat,deltaY: DoubleFloat) +--R viewpoint : (%,Float,Float,Float,Float,Float) -> Void +--R write : (%,String,List String) -> String +--R write : (%,String,String) -> String +--R zoom : (%,Float,Float,Float) -> Void +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +ThreeDimensionalViewport examples +==================================================================== + +See Also: +o )show ThreeDimensionalViewport + +@ + \pagehead{ThreeDimensionalViewport}{VIEW3D} \pagepic{ps/v103threedimensionalviewport.ps}{VIEW3D}{1.00} @@ -109443,6 +128549,75 @@ ThreeDimensionalViewport(): Exports == Implementation where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain SPACE3 ThreeSpace} + +<>= +)set break resume +)sys rm -f ThreeSpace.output +)spool ThreeSpace.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show ThreeSpace +--R ThreeSpace R: Ring is a domain constructor +--R Abbreviation for ThreeSpace is SPACE3 +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for SPACE3 +--R +--R------------------------------- Operations -------------------------------- +--R ?=? : (%,%) -> Boolean check : % -> % +--R closedCurve : % -> List Point R closedCurve : List Point R -> % +--R closedCurve? : % -> Boolean coerce : % -> OutputForm +--R components : % -> List % composite : List % -> % +--R composites : % -> List % copy : % -> % +--R create3Space : SubSpace(3,R) -> % create3Space : () -> % +--R curve : % -> List Point R curve : List Point R -> % +--R curve : (%,List List R) -> % curve : (%,List Point R) -> % +--R curve? : % -> Boolean hash : % -> SingleInteger +--R latex : % -> String lp : % -> List Point R +--R merge : (%,%) -> % merge : List % -> % +--R mesh : % -> List List Point R mesh : List List Point R -> % +--R mesh? : % -> Boolean point : % -> Point R +--R point : Point R -> % point : (%,List R) -> % +--R point : (%,Point R) -> % point? : % -> Boolean +--R polygon : % -> List Point R polygon : List Point R -> % +--R polygon : (%,List List R) -> % polygon : (%,List Point R) -> % +--R polygon? : % -> Boolean subspace : % -> SubSpace(3,R) +--R ?~=? : (%,%) -> Boolean +--R closedCurve : (%,List List R) -> % +--R closedCurve : (%,List Point R) -> % +--R enterPointData : (%,List Point R) -> NonNegativeInteger +--R lllip : % -> List List List NonNegativeInteger +--R lllp : % -> List List List Point R +--R llprop : % -> List List SubSpaceComponentProperty +--R lprop : % -> List SubSpaceComponentProperty +--R mesh : (List List Point R,Boolean,Boolean) -> % +--R mesh : (%,List List List R,Boolean,Boolean) -> % +--R mesh : (%,List List Point R,Boolean,Boolean) -> % +--R mesh : (%,List List List R,List SubSpaceComponentProperty,SubSpaceComponentProperty) -> % +--R mesh : (%,List List Point R,List SubSpaceComponentProperty,SubSpaceComponentProperty) -> % +--R modifyPointData : (%,NonNegativeInteger,Point R) -> % +--R numberOfComponents : % -> NonNegativeInteger +--R numberOfComposites : % -> NonNegativeInteger +--R objects : % -> Record(points: NonNegativeInteger,curves: NonNegativeInteger,polygons: NonNegativeInteger,constructs: NonNegativeInteger) +--R point : (%,NonNegativeInteger) -> % +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +ThreeSpace examples +==================================================================== + +See Also: +o )show ThreeSpace + +@ + \pagehead{ThreeSpace}{SPACE3} \pagepic{ps/v103threespace.ps}{SPACE3}{1.00} @@ -109835,6 +129010,76 @@ ThreeSpace(R:Ring):Exports == Implementation where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain TREE Tree} + +<>= +)set break resume +)sys rm -f Tree.output +)spool Tree.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show Tree +--R Tree S: SetCategory is a domain constructor +--R Abbreviation for Tree is TREE +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for TREE +--R +--R------------------------------- Operations -------------------------------- +--R children : % -> List % copy : % -> % +--R cyclic? : % -> Boolean cyclicCopy : % -> % +--R cyclicEntries : % -> List % cyclicEqual? : (%,%) -> Boolean +--R cyclicParents : % -> List % distance : (%,%) -> Integer +--R ?.value : (%,value) -> S empty : () -> % +--R empty? : % -> Boolean eq? : (%,%) -> Boolean +--R leaf? : % -> Boolean leaves : % -> List S +--R map : ((S -> S),%) -> % nodes : % -> List % +--R sample : () -> % tree : S -> % +--R tree : List S -> % tree : (S,List %) -> % +--R value : % -> S +--R #? : % -> NonNegativeInteger if $ has finiteAggregate +--R ?=? : (%,%) -> Boolean if S has SETCAT +--R any? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate +--R child? : (%,%) -> Boolean if S has SETCAT +--R coerce : % -> OutputForm if S has SETCAT +--R count : (S,%) -> NonNegativeInteger if $ has finiteAggregate and S has SETCAT +--R count : ((S -> Boolean),%) -> NonNegativeInteger if $ has finiteAggregate +--R eval : (%,List S,List S) -> % if S has EVALAB S and S has SETCAT +--R eval : (%,S,S) -> % if S has EVALAB S and S has SETCAT +--R eval : (%,Equation S) -> % if S has EVALAB S and S has SETCAT +--R eval : (%,List Equation S) -> % if S has EVALAB S and S has SETCAT +--R every? : ((S -> Boolean),%) -> Boolean if $ has finiteAggregate +--R hash : % -> SingleInteger if S has SETCAT +--R latex : % -> String if S has SETCAT +--R less? : (%,NonNegativeInteger) -> Boolean +--R map! : ((S -> S),%) -> % if $ has shallowlyMutable +--R member? : (S,%) -> Boolean if $ has finiteAggregate and S has SETCAT +--R members : % -> List S if $ has finiteAggregate +--R more? : (%,NonNegativeInteger) -> Boolean +--R node? : (%,%) -> Boolean if S has SETCAT +--R parts : % -> List S if $ has finiteAggregate +--R setchildren! : (%,List %) -> % if $ has shallowlyMutable +--R setelt : (%,value,S) -> S if $ has shallowlyMutable +--R setvalue! : (%,S) -> S if $ has shallowlyMutable +--R size? : (%,NonNegativeInteger) -> Boolean +--R ?~=? : (%,%) -> Boolean if S has SETCAT +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +Tree examples +==================================================================== + +See Also: +o )show Tree + +@ + \pagehead{Tree}{TREE} \pagepic{ps/v103tree.ps}{TREE}{1.00} {\bf See}\\ @@ -110234,6 +129479,44 @@ Tree(S: SetCategory): T==C where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain TUBE TubePlot} + +<>= +)set break resume +)sys rm -f TubePlot.output +)spool TubePlot.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show TubePlot +--R TubePlot Curve: PlottableSpaceCurveCategory is a domain constructor +--R Abbreviation for TubePlot is TUBE +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for TUBE +--R +--R------------------------------- Operations -------------------------------- +--R closed? : % -> Boolean getCurve : % -> Curve +--R open? : % -> Boolean +--R listLoops : % -> List List Point DoubleFloat +--R setClosed : (%,Boolean) -> Boolean +--R tube : (Curve,List List Point DoubleFloat,Boolean) -> % +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +TubePlot examples +==================================================================== + +See Also: +o )show TubePlot + +@ + \pagehead{TubePlot}{TUBE} \pagepic{ps/v103tubeplot.ps}{TUBE}{1.00} @@ -110312,6 +129595,47 @@ TubePlot(Curve): Exports == Implementation where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain TUPLE Tuple} + +<>= +)set break resume +)sys rm -f Tuple.output +)spool Tuple.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show Tuple +--R Tuple S: Type is a domain constructor +--R Abbreviation for Tuple is TUPLE +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for TUPLE +--R +--R------------------------------- Operations -------------------------------- +--R coerce : PrimitiveArray S -> % coerce : % -> PrimitiveArray S +--R length : % -> NonNegativeInteger +--R ?=? : (%,%) -> Boolean if S has SETCAT +--R coerce : % -> OutputForm if S has SETCAT +--R hash : % -> SingleInteger if S has SETCAT +--R latex : % -> String if S has SETCAT +--R select : (%,NonNegativeInteger) -> S +--R ?~=? : (%,%) -> Boolean if S has SETCAT +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +Tuple examples +==================================================================== + +See Also: +o )show Tuple + +@ + \pagehead{Tuple}{TUPLE} \pagepic{ps/v103tuple.ps}{TUPLE}{1.00} {\bf See}\\ @@ -110390,6 +129714,7 @@ Tuple(S:Type): CoercibleTo(PrimitiveArray S) with @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain ARRAY2 TwoDimensionalArray} + <>= )set break resume )sys rm -f TwoDimensionalArray.output @@ -110914,6 +130239,7 @@ TwoDimensionalArray(R):Exports == Implementation where @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain VIEW2D TwoDimensionalViewport} + <>= ==================================================================== TwoDimensionalViewport examples @@ -111849,6 +131175,149 @@ TwoDimensionalViewport ():Exports == Implementation where \chapter{Chapter U} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain UFPS UnivariateFormalPowerSeries} + +<>= +)set break resume +)sys rm -f UnivariateFormalPowerSeries.output +)spool UnivariateFormalPowerSeries.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show UnivariateFormalPowerSeries +--R UnivariateFormalPowerSeries Coef: Ring is a domain constructor +--R Abbreviation for UnivariateFormalPowerSeries is UFPS +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for UFPS +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (Coef,%) -> % ?*? : (%,Coef) -> % +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ?=? : (%,%) -> Boolean +--R 1 : () -> % 0 : () -> % +--R ?^? : (%,PositiveInteger) -> % center : % -> Coef +--R coefficients : % -> Stream Coef coerce : Variable QUOTE x -> % +--R coerce : Integer -> % coerce : % -> OutputForm +--R complete : % -> % degree : % -> NonNegativeInteger +--R evenlambert : % -> % hash : % -> SingleInteger +--R lagrange : % -> % lambert : % -> % +--R latex : % -> String leadingCoefficient : % -> Coef +--R leadingMonomial : % -> % map : ((Coef -> Coef),%) -> % +--R monomial? : % -> Boolean oddlambert : % -> % +--R one? : % -> Boolean order : % -> NonNegativeInteger +--R pole? : % -> Boolean quoByVar : % -> % +--R recip : % -> Union(%,"failed") reductum : % -> % +--R revert : % -> % sample : () -> % +--R series : Stream Coef -> % variable : % -> Symbol +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean +--R ?*? : (%,Fraction Integer) -> % if Coef has ALGEBRA FRAC INT +--R ?*? : (Fraction Integer,%) -> % if Coef has ALGEBRA FRAC INT +--R ?*? : (NonNegativeInteger,%) -> % +--R ?**? : (%,Fraction Integer) -> % if Coef has ALGEBRA FRAC INT +--R ?**? : (%,%) -> % if Coef has ALGEBRA FRAC INT +--R ?**? : (%,Coef) -> % if Coef has FIELD +--R ?**? : (%,NonNegativeInteger) -> % +--R ?/? : (%,Coef) -> % if Coef has FIELD +--R D : % -> % if Coef has *: (NonNegativeInteger,Coef) -> Coef +--R D : (%,NonNegativeInteger) -> % if Coef has *: (NonNegativeInteger,Coef) -> Coef +--R D : (%,Symbol) -> % if Coef has *: (NonNegativeInteger,Coef) -> Coef and Coef has PDRING SYMBOL +--R D : (%,List Symbol) -> % if Coef has *: (NonNegativeInteger,Coef) -> Coef and Coef has PDRING SYMBOL +--R D : (%,Symbol,NonNegativeInteger) -> % if Coef has *: (NonNegativeInteger,Coef) -> Coef and Coef has PDRING SYMBOL +--R D : (%,List Symbol,List NonNegativeInteger) -> % if Coef has *: (NonNegativeInteger,Coef) -> Coef and Coef has PDRING SYMBOL +--R ?^? : (%,NonNegativeInteger) -> % +--R acos : % -> % if Coef has ALGEBRA FRAC INT +--R acosh : % -> % if Coef has ALGEBRA FRAC INT +--R acot : % -> % if Coef has ALGEBRA FRAC INT +--R acoth : % -> % if Coef has ALGEBRA FRAC INT +--R acsc : % -> % if Coef has ALGEBRA FRAC INT +--R acsch : % -> % if Coef has ALGEBRA FRAC INT +--R approximate : (%,NonNegativeInteger) -> Coef if Coef has **: (Coef,NonNegativeInteger) -> Coef and Coef has coerce: Symbol -> Coef +--R asec : % -> % if Coef has ALGEBRA FRAC INT +--R asech : % -> % if Coef has ALGEBRA FRAC INT +--R asin : % -> % if Coef has ALGEBRA FRAC INT +--R asinh : % -> % if Coef has ALGEBRA FRAC INT +--R associates? : (%,%) -> Boolean if Coef has INTDOM +--R atan : % -> % if Coef has ALGEBRA FRAC INT +--R atanh : % -> % if Coef has ALGEBRA FRAC INT +--R characteristic : () -> NonNegativeInteger +--R charthRoot : % -> Union(%,"failed") if Coef has CHARNZ +--R coefficient : (%,NonNegativeInteger) -> Coef +--R coerce : UnivariatePolynomial(QUOTE x,Coef) -> % +--R coerce : Coef -> % if Coef has COMRING +--R coerce : % -> % if Coef has INTDOM +--R coerce : Fraction Integer -> % if Coef has ALGEBRA FRAC INT +--R cos : % -> % if Coef has ALGEBRA FRAC INT +--R cosh : % -> % if Coef has ALGEBRA FRAC INT +--R cot : % -> % if Coef has ALGEBRA FRAC INT +--R coth : % -> % if Coef has ALGEBRA FRAC INT +--R csc : % -> % if Coef has ALGEBRA FRAC INT +--R csch : % -> % if Coef has ALGEBRA FRAC INT +--R differentiate : (%,Variable QUOTE x) -> % +--R differentiate : % -> % if Coef has *: (NonNegativeInteger,Coef) -> Coef +--R differentiate : (%,NonNegativeInteger) -> % if Coef has *: (NonNegativeInteger,Coef) -> Coef +--R differentiate : (%,Symbol) -> % if Coef has *: (NonNegativeInteger,Coef) -> Coef and Coef has PDRING SYMBOL +--R differentiate : (%,List Symbol) -> % if Coef has *: (NonNegativeInteger,Coef) -> Coef and Coef has PDRING SYMBOL +--R differentiate : (%,Symbol,NonNegativeInteger) -> % if Coef has *: (NonNegativeInteger,Coef) -> Coef and Coef has PDRING SYMBOL +--R differentiate : (%,List Symbol,List NonNegativeInteger) -> % if Coef has *: (NonNegativeInteger,Coef) -> Coef and Coef has PDRING SYMBOL +--R ?.? : (%,%) -> % if NonNegativeInteger has SGROUP +--R ?.? : (%,NonNegativeInteger) -> Coef +--R eval : (%,Coef) -> Stream Coef if Coef has **: (Coef,NonNegativeInteger) -> Coef +--R exp : % -> % if Coef has ALGEBRA FRAC INT +--R exquo : (%,%) -> Union(%,"failed") if Coef has INTDOM +--R extend : (%,NonNegativeInteger) -> % +--R generalLambert : (%,Integer,Integer) -> % +--R integrate : (%,Variable QUOTE x) -> % if Coef has ALGEBRA FRAC INT +--R integrate : (%,Symbol) -> % if Coef has integrate: (Coef,Symbol) -> Coef and Coef has variables: Coef -> List Symbol and Coef has ALGEBRA FRAC INT or Coef has ACFS INT and Coef has ALGEBRA FRAC INT and Coef has PRIMCAT and Coef has TRANFUN +--R integrate : % -> % if Coef has ALGEBRA FRAC INT +--R invmultisect : (Integer,Integer,%) -> % +--R log : % -> % if Coef has ALGEBRA FRAC INT +--R monomial : (%,List SingletonAsOrderedSet,List NonNegativeInteger) -> % +--R monomial : (%,SingletonAsOrderedSet,NonNegativeInteger) -> % +--R monomial : (Coef,NonNegativeInteger) -> % +--R multiplyCoefficients : ((Integer -> Coef),%) -> % +--R multiplyExponents : (%,PositiveInteger) -> % +--R multisect : (Integer,Integer,%) -> % +--R nthRoot : (%,Integer) -> % if Coef has ALGEBRA FRAC INT +--R order : (%,NonNegativeInteger) -> NonNegativeInteger +--R pi : () -> % if Coef has ALGEBRA FRAC INT +--R polynomial : (%,NonNegativeInteger,NonNegativeInteger) -> Polynomial Coef +--R polynomial : (%,NonNegativeInteger) -> Polynomial Coef +--R sec : % -> % if Coef has ALGEBRA FRAC INT +--R sech : % -> % if Coef has ALGEBRA FRAC INT +--R series : Stream Record(k: NonNegativeInteger,c: Coef) -> % +--R sin : % -> % if Coef has ALGEBRA FRAC INT +--R sinh : % -> % if Coef has ALGEBRA FRAC INT +--R sqrt : % -> % if Coef has ALGEBRA FRAC INT +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R tan : % -> % if Coef has ALGEBRA FRAC INT +--R tanh : % -> % if Coef has ALGEBRA FRAC INT +--R terms : % -> Stream Record(k: NonNegativeInteger,c: Coef) +--R truncate : (%,NonNegativeInteger,NonNegativeInteger) -> % +--R truncate : (%,NonNegativeInteger) -> % +--R unit? : % -> Boolean if Coef has INTDOM +--R unitCanonical : % -> % if Coef has INTDOM +--R unitNormal : % -> Record(unit: %,canonical: %,associate: %) if Coef has INTDOM +--R univariatePolynomial : (%,NonNegativeInteger) -> UnivariatePolynomial(QUOTE x,Coef) +--R variables : % -> List SingletonAsOrderedSet +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +UnivariateFormalPowerSeries examples +==================================================================== + +See Also: +o )show UnivariateFormalPowerSeries + +@ + \pagehead{UnivariateFormalPowerSeries}{UFPS} \pagepic{ps/v103univariateformalpowerseries.ps}{UFPS}{1.00} @@ -111967,6 +131436,226 @@ UnivariateFormalPowerSeries(Coef: Ring) == @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain ULS UnivariateLaurentSeries} + +<>= +)set break resume +)sys rm -f UnivariateLaurentSeries.output +)spool UnivariateLaurentSeries.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show UnivariateLaurentSeries +--R UnivariateLaurentSeries(Coef: Ring,var: Symbol,cen: Coef) is a domain constructor +--R Abbreviation for UnivariateLaurentSeries is ULS +--R This constructor is not exposed in this frame. +--R Issue )edit bookvol10.3.pamphlet to see algebra source code for ULS +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (Coef,%) -> % ?*? : (%,Coef) -> % +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?**? : (%,PositiveInteger) -> % +--R ?+? : (%,%) -> % ?-? : (%,%) -> % +--R -? : % -> % ?=? : (%,%) -> Boolean +--R 1 : () -> % 0 : () -> % +--R ?^? : (%,PositiveInteger) -> % center : % -> Coef +--R coefficient : (%,Integer) -> Coef coerce : Variable var -> % +--R coerce : Integer -> % coerce : % -> OutputForm +--R complete : % -> % degree : % -> Integer +--R ?.? : (%,Integer) -> Coef extend : (%,Integer) -> % +--R hash : % -> SingleInteger latex : % -> String +--R leadingCoefficient : % -> Coef leadingMonomial : % -> % +--R map : ((Coef -> Coef),%) -> % monomial : (Coef,Integer) -> % +--R monomial? : % -> Boolean one? : % -> Boolean +--R order : (%,Integer) -> Integer order : % -> Integer +--R pole? : % -> Boolean recip : % -> Union(%,"failed") +--R reductum : % -> % removeZeroes : (Integer,%) -> % +--R removeZeroes : % -> % sample : () -> % +--R truncate : (%,Integer) -> % variable : % -> Symbol +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean +--R ?*? : (%,Fraction Integer) -> % if Coef has ALGEBRA FRAC INT +--R ?*? : (Fraction Integer,%) -> % if Coef has ALGEBRA FRAC INT +--R ?*? : (UnivariateTaylorSeries(Coef,var,cen),%) -> % if Coef has FIELD +--R ?*? : (%,UnivariateTaylorSeries(Coef,var,cen)) -> % if Coef has FIELD +--R ?*? : (NonNegativeInteger,%) -> % +--R ?**? : (%,Fraction Integer) -> % if Coef has ALGEBRA FRAC INT +--R ?**? : (%,%) -> % if Coef has ALGEBRA FRAC INT +--R ?**? : (%,Integer) -> % if Coef has FIELD +--R ?**? : (%,NonNegativeInteger) -> % +--R ?/? : (UnivariateTaylorSeries(Coef,var,cen),UnivariateTaylorSeries(Coef,var,cen)) -> % if Coef has FIELD +--R ?/? : (%,%) -> % if Coef has FIELD +--R ?/? : (%,Coef) -> % if Coef has FIELD +--R ? Boolean if UnivariateTaylorSeries(Coef,var,cen) has OINTDOM and Coef has FIELD or UnivariateTaylorSeries(Coef,var,cen) has ORDSET and Coef has FIELD +--R ?<=? : (%,%) -> Boolean if UnivariateTaylorSeries(Coef,var,cen) has OINTDOM and Coef has FIELD or UnivariateTaylorSeries(Coef,var,cen) has ORDSET and Coef has FIELD +--R ?>? : (%,%) -> Boolean if UnivariateTaylorSeries(Coef,var,cen) has OINTDOM and Coef has FIELD or UnivariateTaylorSeries(Coef,var,cen) has ORDSET and Coef has FIELD +--R ?>=? : (%,%) -> Boolean if UnivariateTaylorSeries(Coef,var,cen) has OINTDOM and Coef has FIELD or UnivariateTaylorSeries(Coef,var,cen) has ORDSET and Coef has FIELD +--R D : (%,Symbol) -> % if UnivariateTaylorSeries(Coef,var,cen) has PDRING SYMBOL and Coef has FIELD or Coef has *: (Integer,Coef) -> Coef and Coef has PDRING SYMBOL +--R D : (%,List Symbol) -> % if UnivariateTaylorSeries(Coef,var,cen) has PDRING SYMBOL and Coef has FIELD or Coef has *: (Integer,Coef) -> Coef and Coef has PDRING SYMBOL +--R D : (%,Symbol,NonNegativeInteger) -> % if UnivariateTaylorSeries(Coef,var,cen) has PDRING SYMBOL and Coef has FIELD or Coef has *: (Integer,Coef) -> Coef and Coef has PDRING SYMBOL +--R D : (%,List Symbol,List NonNegativeInteger) -> % if UnivariateTaylorSeries(Coef,var,cen) has PDRING SYMBOL and Coef has FIELD or Coef has *: (Integer,Coef) -> Coef and Coef has PDRING SYMBOL +--R D : % -> % if UnivariateTaylorSeries(Coef,var,cen) has DIFRING and Coef has FIELD or Coef has *: (Integer,Coef) -> Coef +--R D : (%,NonNegativeInteger) -> % if UnivariateTaylorSeries(Coef,var,cen) has DIFRING and Coef has FIELD or Coef has *: (Integer,Coef) -> Coef +--R D : (%,(UnivariateTaylorSeries(Coef,var,cen) -> UnivariateTaylorSeries(Coef,var,cen)),NonNegativeInteger) -> % if Coef has FIELD +--R D : (%,(UnivariateTaylorSeries(Coef,var,cen) -> UnivariateTaylorSeries(Coef,var,cen))) -> % if Coef has FIELD +--R ?^? : (%,Integer) -> % if Coef has FIELD +--R ?^? : (%,NonNegativeInteger) -> % +--R abs : % -> % if UnivariateTaylorSeries(Coef,var,cen) has OINTDOM and Coef has FIELD +--R acos : % -> % if Coef has ALGEBRA FRAC INT +--R acosh : % -> % if Coef has ALGEBRA FRAC INT +--R acot : % -> % if Coef has ALGEBRA FRAC INT +--R acoth : % -> % if Coef has ALGEBRA FRAC INT +--R acsc : % -> % if Coef has ALGEBRA FRAC INT +--R acsch : % -> % if Coef has ALGEBRA FRAC INT +--R approximate : (%,Integer) -> Coef if Coef has **: (Coef,Integer) -> Coef and Coef has coerce: Symbol -> Coef +--R asec : % -> % if Coef has ALGEBRA FRAC INT +--R asech : % -> % if Coef has ALGEBRA FRAC INT +--R asin : % -> % if Coef has ALGEBRA FRAC INT +--R asinh : % -> % if Coef has ALGEBRA FRAC INT +--R associates? : (%,%) -> Boolean if UnivariateTaylorSeries(Coef,var,cen) has OINTDOM and Coef has FIELD or UnivariateTaylorSeries(Coef,var,cen) has PFECAT and Coef has FIELD or Coef has INTDOM +--R atan : % -> % if Coef has ALGEBRA FRAC INT +--R atanh : % -> % if Coef has ALGEBRA FRAC INT +--R ceiling : % -> UnivariateTaylorSeries(Coef,var,cen) if UnivariateTaylorSeries(Coef,var,cen) has INS an