diff --git a/books/bookvol7.1.pamphlet b/books/bookvol7.1.pamphlet index 6d546a9..2ad4111 100644 --- a/books/bookvol7.1.pamphlet +++ b/books/bookvol7.1.pamphlet @@ -1107,7 +1107,7 @@ have to go hunting when moving between Unix versions. @ \subsection{Bitmaps and bitmap manipulation macros} <>= -\newcommand{\htbmdir}{\env{AXIOM}/doc/hypertex/bitmaps} +\newcommand{\htbmdir}{\env{AXIOM}/doc/bitmaps} \newcommand{\htbmfile}[1]{\htbmdir /#1.bitmap} \newcommand{\htbitmap}[1]{\inputbitmap{\htbmfile{#1}}} \newcommand{\ControlBitmap}[1]{\controlbitmap{\htbmfile{#1}}} @@ -1126,7 +1126,7 @@ have to go hunting when moving between Unix versions. % Including control panel pixmaps for help pages: \newcommand{\helpbit}[1] -{\centerline{\inputpixmap{\env{AXIOM}/doc/hypertex/pixmaps/{#1}}}} +{\centerline{\inputpixmap{\env{AXIOM}/doc/pixmaps/{#1}}}} @ \subsection{HyperDoc button objects} @@ -2147,6 +2147,193 @@ see \downlink{`List'}{ListXmpPage}\ignore{List}. \autobuttons \end{page} +\begin{patch}{AssociationListXmpPagePatch1} +\begin{paste}{AssociationListXmpPageFull1}{AssociationListXmpPageEmpty1} +\pastebutton{AssociationListXmpPageFull1}{\hidepaste} +\tab{5}\spadcommand{ +Data := Record(monthsOld : Integer, gender : String)\bound{Data }} +\indentrel{3}\begin{verbatim} + (1) Record(monthsOld: Integer,gender: String) + Type: Domain +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{AssociationListXmpPageEmpty1} +\begin{paste}{AssociationListXmpPageEmpty1}{AssociationListXmpPagePatch1} +\pastebutton{AssociationListXmpPageEmpty1}{\showpaste} +\tab{5}\spadcommand{ +Data := Record(monthsOld : Integer, gender : String)\bound{Data }} +\end{paste}\end{patch} + +\begin{patch}{AssociationListXmpPagePatch2} +\begin{paste}{AssociationListXmpPageFull2}{AssociationListXmpPageEmpty2} +\pastebutton{AssociationListXmpPageFull2}{\hidepaste} +\tab{5}\spadcommand{ +al : AssociationList(String,Data)\free{Data }\bound{al }} +\indentrel{3}\begin{verbatim} + Type: Void +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{AssociationListXmpPageEmpty2} +\begin{paste}{AssociationListXmpPageEmpty2}{AssociationListXmpPagePatch2} +\pastebutton{AssociationListXmpPageEmpty2}{\showpaste} +\tab{5}\spadcommand{ +al : AssociationList(String,Data)\free{Data }\bound{al }} +\end{paste}\end{patch} + +\begin{patch}{AssociationListXmpPagePatch3} +\begin{paste}{AssociationListXmpPageFull3}{AssociationListXmpPageEmpty3} +\pastebutton{AssociationListXmpPageFull3}{\hidepaste} +\tab{5}\spadcommand{al := table()\free{al }\bound{al1 }} +\indentrel{3}\begin{verbatim} + (3) table() +Type: AssociationList(String,Record(monthsOld: Integer,gender: String)) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{AssociationListXmpPageEmpty3} +\begin{paste}{AssociationListXmpPageEmpty3}{AssociationListXmpPagePatch3} +\pastebutton{AssociationListXmpPageEmpty3}{\showpaste} +\tab{5}\spadcommand{al := table()\free{al }\bound{al1 }} +\end{paste}\end{patch} + +\begin{patch}{AssociationListXmpPagePatch4} +\begin{paste}{AssociationListXmpPageFull4}{AssociationListXmpPageEmpty4} +\pastebutton{AssociationListXmpPageFull4}{\hidepaste} +\tab{5}\spadcommand{al."bob" := [407,"male"]$Data\free{al1 }\bound{al2 }} +\indentrel{3}\begin{verbatim} + (4) [monthsOld= 407,gender= "male"] + Type: Record(monthsOld: Integer,gender: String) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{AssociationListXmpPageEmpty4} +\begin{paste}{AssociationListXmpPageEmpty4}{AssociationListXmpPagePatch4} +\pastebutton{AssociationListXmpPageEmpty4}{\showpaste} +\tab{5}\spadcommand{al."bob" := [407,"male"]$Data\free{al1 }\bound{al2 }} +\end{paste}\end{patch} + +\begin{patch}{AssociationListXmpPagePatch5} +\begin{paste}{AssociationListXmpPageFull5}{AssociationListXmpPageEmpty5} +\pastebutton{AssociationListXmpPageFull5}{\hidepaste} +\tab{5}\spadcommand{ +al."judith" := [366,"female"]$Data\free{al2 }\bound{al3 }} +\indentrel{3}\begin{verbatim} + (5) [monthsOld= 366,gender= "female"] + Type: Record(monthsOld: Integer,gender: String) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{AssociationListXmpPageEmpty5} +\begin{paste}{AssociationListXmpPageEmpty5}{AssociationListXmpPagePatch5} +\pastebutton{AssociationListXmpPageEmpty5}{\showpaste} +\tab{5}\spadcommand{ +al."judith" := [366,"female"]$Data\free{al2 }\bound{al3 }} +\end{paste}\end{patch} + +\begin{patch}{AssociationListXmpPagePatch6} +\begin{paste}{AssociationListXmpPageFull6}{AssociationListXmpPageEmpty6} +\pastebutton{AssociationListXmpPageFull6}{\hidepaste} +\tab{5}\spadcommand{ +al."katie" := [24,"female"]$Data\free{al3 }\bound{al4 }} +\indentrel{3}\begin{verbatim} + (6) [monthsOld= 24,gender= "female"] + Type: Record(monthsOld: Integer,gender: String) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{AssociationListXmpPageEmpty6} +\begin{paste}{AssociationListXmpPageEmpty6}{AssociationListXmpPagePatch6} +\pastebutton{AssociationListXmpPageEmpty6}{\showpaste} +\tab{5}\spadcommand{ +al."katie" := [24,"female"]$Data\free{al3 }\bound{al4 }} +\end{paste}\end{patch} + +\begin{patch}{AssociationListXmpPagePatch7} +\begin{paste}{AssociationListXmpPageFull7}{AssociationListXmpPageEmpty7} +\pastebutton{AssociationListXmpPageFull7}{\hidepaste} +\tab{5}\spadcommand{ +al."smokie" := [200,"female"]$Data\free{al4 }\bound{al5 }} +\indentrel{3}\begin{verbatim} + (7) [monthsOld= 200,gender= "female"] + Type: Record(monthsOld: Integer,gender: String) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{AssociationListXmpPageEmpty7} +\begin{paste}{AssociationListXmpPageEmpty7}{AssociationListXmpPagePatch7} +\pastebutton{AssociationListXmpPageEmpty7}{\showpaste} +\tab{5}\spadcommand{ +al."smokie" := [200,"female"]$Data\free{al4 }\bound{al5 }} +\end{paste}\end{patch} + +\begin{patch}{AssociationListXmpPagePatch8} +\begin{paste}{AssociationListXmpPageFull8}{AssociationListXmpPageEmpty8} +\pastebutton{AssociationListXmpPageFull8}{\hidepaste} +\tab{5}\spadcommand{al\free{al5 }} +\indentrel{3}\begin{verbatim} + (8) + table + "smokie"= [monthsOld= 200,gender= "female"] + , + "katie"= [monthsOld= 24,gender= "female"] + , + "judith"= [monthsOld= 366,gender= "female"] + , + "bob"= [monthsOld= 407,gender= "male"] +Type: AssociationList(String,Record(monthsOld: Integer,gender: String)) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{AssociationListXmpPageEmpty8} +\begin{paste}{AssociationListXmpPageEmpty8}{AssociationListXmpPagePatch8} +\pastebutton{AssociationListXmpPageEmpty8}{\showpaste} +\tab{5}\spadcommand{al\free{al5 }} +\end{paste}\end{patch} + +\begin{patch}{AssociationListXmpPagePatch9} +\begin{paste}{AssociationListXmpPageFull9}{AssociationListXmpPageEmpty9} +\pastebutton{AssociationListXmpPageFull9}{\hidepaste} +\tab{5}\spadcommand{ +al."katie" := [23,"female"]$Data\free{al5 }\bound{al6 }} +\indentrel{3}\begin{verbatim} + (9) [monthsOld= 23,gender= "female"] + Type: Record(monthsOld: Integer,gender: String) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{AssociationListXmpPageEmpty9} +\begin{paste}{AssociationListXmpPageEmpty9}{AssociationListXmpPagePatch9} +\pastebutton{AssociationListXmpPageEmpty9}{\showpaste} +\tab{5}\spadcommand{ +al."katie" := [23,"female"]$Data\free{al5 }\bound{al6 }} +\end{paste}\end{patch} + +\begin{patch}{AssociationListXmpPagePatch10} +\begin{paste}{AssociationListXmpPageFull10}{AssociationListXmpPageEmpty10} +\pastebutton{AssociationListXmpPageFull10}{\hidepaste} +\tab{5}\spadcommand{delete!(al,1)\free{al6 }\bound{al7 }} +\indentrel{3}\begin{verbatim} + (10) + table + "katie"= [monthsOld= 23,gender= "female"] + , + "judith"= [monthsOld= 366,gender= "female"] + , + "bob"= [monthsOld= 407,gender= "male"] +Type: AssociationList(String,Record(monthsOld: Integer,gender: String)) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{AssociationListXmpPageEmpty10} +\begin{paste} +{AssociationListXmpPageEmpty10}{AssociationListXmpPagePatch10} +\pastebutton{AssociationListXmpPageEmpty10}{\showpaste} +\tab{5}\spadcommand{delete!(al,1)\free{al6 }\bound{al7 }} +\end{paste}\end{patch} + + @ \section{array1.ht} \pagehead{OneDimensionalArrayXmpPage}{array1.ht}{OneDimensionalArray} @@ -2155,15 +2342,13 @@ see \downlink{`List'}{ListXmpPage}\ignore{List}. <>= \begin{page}{OneDimensionalArrayXmpPage}{OneDimensionalArray} \beginscroll -The \spadtype{OneDimensionalArray} domain is used for storing data in a -one-dimensional indexed data structure. -Such an array is a homogeneous data structure in that all the entries of -the array must belong to the same Axiom domain. -Each array has a fixed length specified by the user and arrays are not -extensible. -The indexing of one-dimensional arrays is one-based. -This means that the ``first'' element of an array is given the index -\spad{1}. +The \spadtype{OneDimensionalArray} domain is used for storing data in +a one-dimensional indexed data structure. Such an array is a +homogeneous data structure in that all the entries of the array must +belong to the same Axiom domain. Each array has a fixed length +specified by the user and arrays are not extensible. The indexing of +one-dimensional arrays is one-based. This means that the ``first'' +element of an array is given the index \spad{1}. See also \downlink{`Vector'}{VectorXmpPage}\ignore{Vector} and \downlink{`FlexibleArray'}{FlexibleArrayXmpPage}\ignore{FlexibleArray}. \xtc{ @@ -2222,6 +2407,170 @@ Replace the first 5 elements of \spad{a} with those of \spad{b}. \autobuttons \end{page} +\begin{patch}{OneDimensionalArrayXmpPagePatch1} +\begin{paste}{OneDimensionalArrayXmpPageFull1} +{OneDimensionalArrayXmpPageEmpty1} +\pastebutton{OneDimensionalArrayXmpPageFull1}{\hidepaste} +\tab{5}\spadcommand{oneDimensionalArray [i**2 for i in 1..10]} +\indentrel{3}\begin{verbatim} + (1) [1,4,9,16,25,36,49,64,81,100] + Type: OneDimensionalArray PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{OneDimensionalArrayXmpPageEmpty1} +\begin{paste}{OneDimensionalArrayXmpPageEmpty1} +{OneDimensionalArrayXmpPagePatch1} +\pastebutton{OneDimensionalArrayXmpPageEmpty1}{\showpaste} +\tab{5}\spadcommand{oneDimensionalArray [i**2 for i in 1..10]} +\end{paste}\end{patch} + +\begin{patch}{OneDimensionalArrayXmpPagePatch2} +\begin{paste}{OneDimensionalArrayXmpPageFull2} +{OneDimensionalArrayXmpPageEmpty2} +\pastebutton{OneDimensionalArrayXmpPageFull2}{\hidepaste} +\tab{5}\spadcommand{a : ARRAY1 INT := new(10,0)\bound{a }} +\indentrel{3}\begin{verbatim} + (2) [0,0,0,0,0,0,0,0,0,0] + Type: OneDimensionalArray Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{OneDimensionalArrayXmpPageEmpty2} +\begin{paste}{OneDimensionalArrayXmpPageEmpty2} +{OneDimensionalArrayXmpPagePatch2} +\pastebutton{OneDimensionalArrayXmpPageEmpty2}{\showpaste} +\tab{5}\spadcommand{a : ARRAY1 INT := new(10,0)\bound{a }} +\end{paste}\end{patch} + +\begin{patch}{OneDimensionalArrayXmpPagePatch3} +\begin{paste}{OneDimensionalArrayXmpPageFull3} +{OneDimensionalArrayXmpPageEmpty3} +\pastebutton{OneDimensionalArrayXmpPageFull3}{\hidepaste} +\tab{5}\spadcommand{ +for i in 1..10 repeat a.i := i; a\bound{a1 }\free{a }} +\indentrel{3}\begin{verbatim} + (3) [1,2,3,4,5,6,7,8,9,10] + Type: OneDimensionalArray Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{OneDimensionalArrayXmpPageEmpty3} +\begin{paste}{OneDimensionalArrayXmpPageEmpty3} +{OneDimensionalArrayXmpPagePatch3} +\pastebutton{OneDimensionalArrayXmpPageEmpty3}{\showpaste} +\tab{5}\spadcommand{ +for i in 1..10 repeat a.i := i; a\bound{a1 }\free{a }} +\end{paste}\end{patch} + +\begin{patch}{OneDimensionalArrayXmpPagePatch4} +\begin{paste}{OneDimensionalArrayXmpPageFull4} +{OneDimensionalArrayXmpPageEmpty4} +\pastebutton{OneDimensionalArrayXmpPageFull4}{\hidepaste} +\tab{5}\spadcommand{map!(i +-> i ** 2,a); a\bound{a3 }\free{a2 }} +\indentrel{3}\begin{verbatim} + (4) [1,4,9,16,25,36,49,64,81,100] + Type: OneDimensionalArray Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{OneDimensionalArrayXmpPageEmpty4} +\begin{paste}{OneDimensionalArrayXmpPageEmpty4} +{OneDimensionalArrayXmpPagePatch4} +\pastebutton{OneDimensionalArrayXmpPageEmpty4}{\showpaste} +\tab{5}\spadcommand{map!(i +-> i ** 2,a); a\bound{a3 }\free{a2 }} +\end{paste}\end{patch} + +\begin{patch}{OneDimensionalArrayXmpPagePatch5} +\begin{paste}{OneDimensionalArrayXmpPageFull5} +{OneDimensionalArrayXmpPageEmpty5} +\pastebutton{OneDimensionalArrayXmpPageFull5}{\hidepaste} +\tab{5}\spadcommand{reverse! a\bound{a4 }\free{a3 }} +\indentrel{3}\begin{verbatim} + (5) [100,81,64,49,36,25,16,9,4,1] + Type: OneDimensionalArray Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{OneDimensionalArrayXmpPageEmpty5} +\begin{paste}{OneDimensionalArrayXmpPageEmpty5} +{OneDimensionalArrayXmpPagePatch5} +\pastebutton{OneDimensionalArrayXmpPageEmpty5}{\showpaste} +\tab{5}\spadcommand{reverse! a\bound{a4 }\free{a3 }} +\end{paste}\end{patch} + +\begin{patch}{OneDimensionalArrayXmpPagePatch6} +\begin{paste}{OneDimensionalArrayXmpPageFull6} +{OneDimensionalArrayXmpPageEmpty6} +\pastebutton{OneDimensionalArrayXmpPageFull6}{\hidepaste} +\tab{5}\spadcommand{swap!(a,4,5); a\bound{a5 }\free{a4 }} +\indentrel{3}\begin{verbatim} + (6) [100,81,64,36,49,25,16,9,4,1] + Type: OneDimensionalArray Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{OneDimensionalArrayXmpPageEmpty6} +\begin{paste}{OneDimensionalArrayXmpPageEmpty6} +{OneDimensionalArrayXmpPagePatch6} +\pastebutton{OneDimensionalArrayXmpPageEmpty6}{\showpaste} +\tab{5}\spadcommand{swap!(a,4,5); a\bound{a5 }\free{a4 }} +\end{paste}\end{patch} + +\begin{patch}{OneDimensionalArrayXmpPagePatch7} +\begin{paste}{OneDimensionalArrayXmpPageFull7} +{OneDimensionalArrayXmpPageEmpty7} +\pastebutton{OneDimensionalArrayXmpPageFull7}{\hidepaste} +\tab{5}\spadcommand{sort! a\bound{a6 }\free{a5 }} +\indentrel{3}\begin{verbatim} + (7) [1,4,9,16,25,36,49,64,81,100] + Type: OneDimensionalArray Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{OneDimensionalArrayXmpPageEmpty7} +\begin{paste}{OneDimensionalArrayXmpPageEmpty7} +{OneDimensionalArrayXmpPagePatch7} +\pastebutton{OneDimensionalArrayXmpPageEmpty7}{\showpaste} +\tab{5}\spadcommand{sort! a\bound{a6 }\free{a5 }} +\end{paste}\end{patch} + +\begin{patch}{OneDimensionalArrayXmpPagePatch8} +\begin{paste}{OneDimensionalArrayXmpPageFull8} +{OneDimensionalArrayXmpPageEmpty8} +\pastebutton{OneDimensionalArrayXmpPageFull8}{\hidepaste} +\tab{5}\spadcommand{b := a(6..10)\bound{b }\free{a6 }} +\indentrel{3}\begin{verbatim} + (8) [36,49,64,81,100] + Type: OneDimensionalArray Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{OneDimensionalArrayXmpPageEmpty8} +\begin{paste}{OneDimensionalArrayXmpPageEmpty8} +{OneDimensionalArrayXmpPagePatch8} +\pastebutton{OneDimensionalArrayXmpPageEmpty8}{\showpaste} +\tab{5}\spadcommand{b := a(6..10)\bound{b }\free{a6 }} +\end{paste}\end{patch} + +\begin{patch}{OneDimensionalArrayXmpPagePatch9} +\begin{paste}{OneDimensionalArrayXmpPageFull9} +{OneDimensionalArrayXmpPageEmpty9} +\pastebutton{OneDimensionalArrayXmpPageFull9}{\hidepaste} +\tab{5}\spadcommand{copyInto!(a,b,1)\free{b }} +\indentrel{3}\begin{verbatim} + (9) [36,49,64,81,100,36,49,64,81,100] + Type: OneDimensionalArray Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{OneDimensionalArrayXmpPageEmpty9} +\begin{paste}{OneDimensionalArrayXmpPageEmpty9} +{OneDimensionalArrayXmpPagePatch9} +\pastebutton{OneDimensionalArrayXmpPageEmpty9}{\showpaste} +\tab{5}\spadcommand{copyInto!(a,b,1)\free{b }} +\end{paste}\end{patch} + @ \section{array2.ht} \pagehead{TwoDimensionalArrayXmpPage}{array2.ht}{TwoDimensionalArray} @@ -2390,7 +2739,431 @@ For information on related topics, see \endscroll \autobuttons \end{page} -% + +\begin{patch}{TwoDimensionalArrayXmpPagePatch1} +\begin{paste}{TwoDimensionalArrayXmpPageFull1} +{TwoDimensionalArrayXmpPageEmpty1} +\pastebutton{TwoDimensionalArrayXmpPageFull1}{\hidepaste} +\tab{5}\spadcommand{arr : ARRAY2 INT := new(5,4,0)\bound{arr }} +\indentrel{3}\begin{verbatim} + Ú0 0 0 0¿ + ³ ³ + ³0 0 0 0³ + ³ ³ + (1) ³0 0 0 0³ + ³ ³ + ³0 0 0 0³ + ³ ³ + À0 0 0 0Ù + Type: TwoDimensionalArray Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{TwoDimensionalArrayXmpPageEmpty1} +\begin{paste}{TwoDimensionalArrayXmpPageEmpty1} +{TwoDimensionalArrayXmpPagePatch1} +\pastebutton{TwoDimensionalArrayXmpPageEmpty1}{\showpaste} +\tab{5}\spadcommand{arr : ARRAY2 INT := new(5,4,0)\bound{arr }} +\end{paste}\end{patch} + +\begin{patch}{TwoDimensionalArrayXmpPagePatch2} +\begin{paste}{TwoDimensionalArrayXmpPageFull2} +{TwoDimensionalArrayXmpPageEmpty2} +\pastebutton{TwoDimensionalArrayXmpPageFull2}{\hidepaste} +\tab{5}\spadcommand{setelt(arr,1,1,17)\free{arr }\bound{arr1 }} +\indentrel{3}\begin{verbatim} + (2) 17 + Type: PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{TwoDimensionalArrayXmpPageEmpty2} +\begin{paste}{TwoDimensionalArrayXmpPageEmpty2} +{TwoDimensionalArrayXmpPagePatch2} +\pastebutton{TwoDimensionalArrayXmpPageEmpty2}{\showpaste} +\tab{5}\spadcommand{setelt(arr,1,1,17)\free{arr }\bound{arr1 }} +\end{paste}\end{patch} + +\begin{patch}{TwoDimensionalArrayXmpPagePatch3} +\begin{paste}{TwoDimensionalArrayXmpPageFull3} +{TwoDimensionalArrayXmpPageEmpty3} +\pastebutton{TwoDimensionalArrayXmpPageFull3}{\hidepaste} +\tab{5}\spadcommand{arr\free{arr1 }} +\indentrel{3}\begin{verbatim} + Ú17 0 0 0¿ + ³ ³ + ³0 0 0 0³ + ³ ³ + (3) ³0 0 0 0³ + ³ ³ + ³0 0 0 0³ + ³ ³ + À0 0 0 0Ù + Type: TwoDimensionalArray Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{TwoDimensionalArrayXmpPageEmpty3} +\begin{paste}{TwoDimensionalArrayXmpPageEmpty3} +{TwoDimensionalArrayXmpPagePatch3} +\pastebutton{TwoDimensionalArrayXmpPageEmpty3}{\showpaste} +\tab{5}\spadcommand{arr\free{arr1 }} +\end{paste}\end{patch} + +\begin{patch}{TwoDimensionalArrayXmpPagePatch4} +\begin{paste}{TwoDimensionalArrayXmpPageFull4} +{TwoDimensionalArrayXmpPageEmpty4} +\pastebutton{TwoDimensionalArrayXmpPageFull4}{\hidepaste} +\tab{5}\spadcommand{elt(arr,1,1)\free{arr1 }} +\indentrel{3}\begin{verbatim} + (4) 17 + Type: PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{TwoDimensionalArrayXmpPageEmpty4} +\begin{paste}{TwoDimensionalArrayXmpPageEmpty4} +{TwoDimensionalArrayXmpPagePatch4} +\pastebutton{TwoDimensionalArrayXmpPageEmpty4}{\showpaste} +\tab{5}\spadcommand{elt(arr,1,1)\free{arr1 }} +\end{paste}\end{patch} + +\begin{patch}{TwoDimensionalArrayXmpPagePatch5} +\begin{paste}{TwoDimensionalArrayXmpPageFull5} +{TwoDimensionalArrayXmpPageEmpty5} +\pastebutton{TwoDimensionalArrayXmpPageFull5}{\hidepaste} +\tab{5}\spadcommand{arr(3,2) := 15\free{arr1 }\bound{arr2 }} +\indentrel{3}\begin{verbatim} + (5) 15 + Type: PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{TwoDimensionalArrayXmpPageEmpty5} +\begin{paste}{TwoDimensionalArrayXmpPageEmpty5} +{TwoDimensionalArrayXmpPagePatch5} +\pastebutton{TwoDimensionalArrayXmpPageEmpty5}{\showpaste} +\tab{5}\spadcommand{arr(3,2) := 15\free{arr1 }\bound{arr2 }} +\end{paste}\end{patch} + +\begin{patch}{TwoDimensionalArrayXmpPagePatch6} +\begin{paste}{TwoDimensionalArrayXmpPageFull6} +{TwoDimensionalArrayXmpPageEmpty6} +\pastebutton{TwoDimensionalArrayXmpPageFull6}{\hidepaste} +\tab{5}\spadcommand{arr(3,2)\free{arr2 }} +\indentrel{3}\begin{verbatim} + (6) 15 + Type: PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{TwoDimensionalArrayXmpPageEmpty6} +\begin{paste}{TwoDimensionalArrayXmpPageEmpty6} +{TwoDimensionalArrayXmpPagePatch6} +\pastebutton{TwoDimensionalArrayXmpPageEmpty6}{\showpaste} +\tab{5}\spadcommand{arr(3,2)\free{arr2 }} +\end{paste}\end{patch} + +\begin{patch}{TwoDimensionalArrayXmpPagePatch7} +\begin{paste}{TwoDimensionalArrayXmpPageFull7} +{TwoDimensionalArrayXmpPageEmpty7} +\pastebutton{TwoDimensionalArrayXmpPageFull7}{\hidepaste} +\tab{5}\spadcommand{row(arr,1)\free{arr2 }} +\indentrel{3}\begin{verbatim} + (7) [17,0,0,0] + Type: OneDimensionalArray Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{TwoDimensionalArrayXmpPageEmpty7} +\begin{paste}{TwoDimensionalArrayXmpPageEmpty7} +{TwoDimensionalArrayXmpPagePatch7} +\pastebutton{TwoDimensionalArrayXmpPageEmpty7}{\showpaste} +\tab{5}\spadcommand{row(arr,1)\free{arr2 }} +\end{paste}\end{patch} + +\begin{patch}{TwoDimensionalArrayXmpPagePatch8} +\begin{paste}{TwoDimensionalArrayXmpPageFull8} +{TwoDimensionalArrayXmpPageEmpty8} +\pastebutton{TwoDimensionalArrayXmpPageFull8}{\hidepaste} +\tab{5}\spadcommand{column(arr,1)\free{arr2 }} +\indentrel{3}\begin{verbatim} + (8) [17,0,0,0,0] + Type: OneDimensionalArray Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{TwoDimensionalArrayXmpPageEmpty8} +\begin{paste}{TwoDimensionalArrayXmpPageEmpty8} +{TwoDimensionalArrayXmpPagePatch8} +\pastebutton{TwoDimensionalArrayXmpPageEmpty8}{\showpaste} +\tab{5}\spadcommand{column(arr,1)\free{arr2 }} +\end{paste}\end{patch} + +\begin{patch}{TwoDimensionalArrayXmpPagePatch9} +\begin{paste}{TwoDimensionalArrayXmpPageFull9} +{TwoDimensionalArrayXmpPageEmpty9} +\pastebutton{TwoDimensionalArrayXmpPageFull9}{\hidepaste} +\tab{5}\spadcommand{nrows(arr)\free{arr2 }} +\indentrel{3}\begin{verbatim} + (9) 5 + Type: PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{TwoDimensionalArrayXmpPageEmpty9} +\begin{paste}{TwoDimensionalArrayXmpPageEmpty9} +{TwoDimensionalArrayXmpPagePatch9} +\pastebutton{TwoDimensionalArrayXmpPageEmpty9}{\showpaste} +\tab{5}\spadcommand{nrows(arr)\free{arr2 }} +\end{paste}\end{patch} + +\begin{patch}{TwoDimensionalArrayXmpPagePatch10} +\begin{paste}{TwoDimensionalArrayXmpPageFull10} +{TwoDimensionalArrayXmpPageEmpty10} +\pastebutton{TwoDimensionalArrayXmpPageFull10}{\hidepaste} +\tab{5}\spadcommand{ncols(arr)\free{arr2 }} +\indentrel{3}\begin{verbatim} + (10) 4 + Type: PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{TwoDimensionalArrayXmpPageEmpty10} +\begin{paste}{TwoDimensionalArrayXmpPageEmpty10} +{TwoDimensionalArrayXmpPagePatch10} +\pastebutton{TwoDimensionalArrayXmpPageEmpty10}{\showpaste} +\tab{5}\spadcommand{ncols(arr)\free{arr2 }} +\end{paste}\end{patch} + +\begin{patch}{TwoDimensionalArrayXmpPagePatch11} +\begin{paste}{TwoDimensionalArrayXmpPageFull11} +{TwoDimensionalArrayXmpPageEmpty11} +\pastebutton{TwoDimensionalArrayXmpPageFull11}{\hidepaste} +\tab{5}\spadcommand{map(-,arr)\free{arr2 }} +\indentrel{3}\begin{verbatim} + Ú- 17 0 0 0¿ + ³ ³ + ³ 0 0 0 0³ + ³ ³ + (11) ³ 0 - 15 0 0³ + ³ ³ + ³ 0 0 0 0³ + ³ ³ + À 0 0 0 0Ù + Type: TwoDimensionalArray Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{TwoDimensionalArrayXmpPageEmpty11} +\begin{paste}{TwoDimensionalArrayXmpPageEmpty11} +{TwoDimensionalArrayXmpPagePatch11} +\pastebutton{TwoDimensionalArrayXmpPageEmpty11}{\showpaste} +\tab{5}\spadcommand{map(-,arr)\free{arr2 }} +\end{paste}\end{patch} + +\begin{patch}{TwoDimensionalArrayXmpPagePatch12} +\begin{paste}{TwoDimensionalArrayXmpPageFull12} +{TwoDimensionalArrayXmpPageEmpty12} +\pastebutton{TwoDimensionalArrayXmpPageFull12}{\hidepaste} +\tab{5}\spadcommand{map((x +-> x + x),arr)\free{arr2 }} +\indentrel{3}\begin{verbatim} + Ú34 0 0 0¿ + ³ ³ + ³0 0 0 0³ + ³ ³ + (12) ³0 30 0 0³ + ³ ³ + ³0 0 0 0³ + ³ ³ + À0 0 0 0Ù + Type: TwoDimensionalArray Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{TwoDimensionalArrayXmpPageEmpty12} +\begin{paste}{TwoDimensionalArrayXmpPageEmpty12} +{TwoDimensionalArrayXmpPagePatch12} +\pastebutton{TwoDimensionalArrayXmpPageEmpty12}{\showpaste} +\tab{5}\spadcommand{map((x +-> x + x),arr)\free{arr2 }} +\end{paste}\end{patch} + +\begin{patch}{TwoDimensionalArrayXmpPagePatch13} +\begin{paste}{TwoDimensionalArrayXmpPageFull13} +{TwoDimensionalArrayXmpPageEmpty13} +\pastebutton{TwoDimensionalArrayXmpPageFull13}{\hidepaste} +\tab{5}\spadcommand{arrc := copy(arr)\bound{arrc }\free{arr2 }} +\indentrel{3}\begin{verbatim} + Ú17 0 0 0¿ + ³ ³ + ³0 0 0 0³ + ³ ³ + (13) ³0 15 0 0³ + ³ ³ + ³0 0 0 0³ + ³ ³ + À0 0 0 0Ù + Type: TwoDimensionalArray Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{TwoDimensionalArrayXmpPageEmpty13} +\begin{paste}{TwoDimensionalArrayXmpPageEmpty13} +{TwoDimensionalArrayXmpPagePatch13} +\pastebutton{TwoDimensionalArrayXmpPageEmpty13}{\showpaste} +\tab{5}\spadcommand{arrc := copy(arr)\bound{arrc }\free{arr2 }} +\end{paste}\end{patch} + +\begin{patch}{TwoDimensionalArrayXmpPagePatch14} +\begin{paste}{TwoDimensionalArrayXmpPageFull14} +{TwoDimensionalArrayXmpPageEmpty14} +\pastebutton{TwoDimensionalArrayXmpPageFull14}{\hidepaste} +\tab{5}\spadcommand{map!(-,arrc)\free{arrc }} +\indentrel{3}\begin{verbatim} + Ú- 17 0 0 0¿ + ³ ³ + ³ 0 0 0 0³ + ³ ³ + (14) ³ 0 - 15 0 0³ + ³ ³ + ³ 0 0 0 0³ + ³ ³ + À 0 0 0 0Ù + Type: TwoDimensionalArray Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{TwoDimensionalArrayXmpPageEmpty14} +\begin{paste}{TwoDimensionalArrayXmpPageEmpty14} +{TwoDimensionalArrayXmpPagePatch14} +\pastebutton{TwoDimensionalArrayXmpPageEmpty14}{\showpaste} +\tab{5}\spadcommand{map!(-,arrc)\free{arrc }} +\end{paste}\end{patch} + +\begin{patch}{TwoDimensionalArrayXmpPagePatch15} +\begin{paste}{TwoDimensionalArrayXmpPageFull15} +{TwoDimensionalArrayXmpPageEmpty15} +\pastebutton{TwoDimensionalArrayXmpPageFull15}{\hidepaste} +\tab{5}\spadcommand{arrc\free{arrc }} +\indentrel{3}\begin{verbatim} + Ú- 17 0 0 0¿ + ³ ³ + ³ 0 0 0 0³ + ³ ³ + (15) ³ 0 - 15 0 0³ + ³ ³ + ³ 0 0 0 0³ + ³ ³ + À 0 0 0 0Ù + Type: TwoDimensionalArray Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{TwoDimensionalArrayXmpPageEmpty15} +\begin{paste}{TwoDimensionalArrayXmpPageEmpty15} +{TwoDimensionalArrayXmpPagePatch15} +\pastebutton{TwoDimensionalArrayXmpPageEmpty15}{\showpaste} +\tab{5}\spadcommand{arrc\free{arrc }} +\end{paste}\end{patch} + +\begin{patch}{TwoDimensionalArrayXmpPagePatch16} +\begin{paste}{TwoDimensionalArrayXmpPageFull16} +{TwoDimensionalArrayXmpPageEmpty16} +\pastebutton{TwoDimensionalArrayXmpPageFull16}{\hidepaste} +\tab{5}\spadcommand{arr\free{arr2 }} +\indentrel{3}\begin{verbatim} + Ú17 0 0 0¿ + ³ ³ + ³0 0 0 0³ + ³ ³ + (16) ³0 15 0 0³ + ³ ³ + ³0 0 0 0³ + ³ ³ + À0 0 0 0Ù + Type: TwoDimensionalArray Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{TwoDimensionalArrayXmpPageEmpty16} +\begin{paste}{TwoDimensionalArrayXmpPageEmpty16} +{TwoDimensionalArrayXmpPagePatch16} +\pastebutton{TwoDimensionalArrayXmpPageEmpty16}{\showpaste} +\tab{5}\spadcommand{arr\free{arr2 }} +\end{paste}\end{patch} + +\begin{patch}{TwoDimensionalArrayXmpPagePatch17} +\begin{paste}{TwoDimensionalArrayXmpPageFull17} +{TwoDimensionalArrayXmpPageEmpty17} +\pastebutton{TwoDimensionalArrayXmpPageFull17}{\hidepaste} +\tab{5}\spadcommand{member?(17,arr)\free{arr2 }} +\indentrel{3}\begin{verbatim} + (17) true + Type: Boolean +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{TwoDimensionalArrayXmpPageEmpty17} +\begin{paste}{TwoDimensionalArrayXmpPageEmpty17} +{TwoDimensionalArrayXmpPagePatch17} +\pastebutton{TwoDimensionalArrayXmpPageEmpty17}{\showpaste} +\tab{5}\spadcommand{member?(17,arr)\free{arr2 }} +\end{paste}\end{patch} + +\begin{patch}{TwoDimensionalArrayXmpPagePatch18} +\begin{paste}{TwoDimensionalArrayXmpPageFull18} +{TwoDimensionalArrayXmpPageEmpty18} +\pastebutton{TwoDimensionalArrayXmpPageFull18}{\hidepaste} +\tab{5}\spadcommand{member?(10317,arr)\free{arr2 }} +\indentrel{3}\begin{verbatim} + (18) false + Type: Boolean +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{TwoDimensionalArrayXmpPageEmpty18} +\begin{paste}{TwoDimensionalArrayXmpPageEmpty18} +{TwoDimensionalArrayXmpPagePatch18} +\pastebutton{TwoDimensionalArrayXmpPageEmpty18}{\showpaste} +\tab{5}\spadcommand{member?(10317,arr)\free{arr2 }} +\end{paste}\end{patch} + +\begin{patch}{TwoDimensionalArrayXmpPagePatch19} +\begin{paste}{TwoDimensionalArrayXmpPageFull19} +{TwoDimensionalArrayXmpPageEmpty19} +\pastebutton{TwoDimensionalArrayXmpPageFull19}{\hidepaste} +\tab{5}\spadcommand{count(17,arr)\free{arr2 }} +\indentrel{3}\begin{verbatim} + (19) 1 + Type: PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{TwoDimensionalArrayXmpPageEmpty19} +\begin{paste}{TwoDimensionalArrayXmpPageEmpty19} +{TwoDimensionalArrayXmpPagePatch19} +\pastebutton{TwoDimensionalArrayXmpPageEmpty19}{\showpaste} +\tab{5}\spadcommand{count(17,arr)\free{arr2 }} +\end{paste}\end{patch} + +\begin{patch}{TwoDimensionalArrayXmpPagePatch20} +\begin{paste}{TwoDimensionalArrayXmpPageFull20} +{TwoDimensionalArrayXmpPageEmpty20} +\pastebutton{TwoDimensionalArrayXmpPageFull20}{\hidepaste} +\tab{5}\spadcommand{count(0,arr)\free{arr2 }} +\indentrel{3}\begin{verbatim} + (20) 18 + Type: PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{TwoDimensionalArrayXmpPageEmpty20} +\begin{paste}{TwoDimensionalArrayXmpPageEmpty20} +{TwoDimensionalArrayXmpPagePatch20} +\pastebutton{TwoDimensionalArrayXmpPageEmpty20}{\showpaste} +\tab{5}\spadcommand{count(0,arr)\free{arr2 }} +\end{paste}\end{patch} + @ \section{basic.ht} @@ -2575,6 +3348,189 @@ answer for \texht{$12^2$}{12**2}. \autobuttons \end{page} +\begin{patch}{BalancedBinaryTreeXmpPagePatch1} +\begin{paste}{BalancedBinaryTreeXmpPageFull1} +{BalancedBinaryTreeXmpPageEmpty1} +\pastebutton{BalancedBinaryTreeXmpPageFull1}{\hidepaste} +\tab{5}\spadcommand{lm := [3,5,7,11]\bound{lm }} +\indentrel{3}\begin{verbatim} + (1) [3,5,7,11] + Type: List PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{BalancedBinaryTreeXmpPageEmpty1} +\begin{paste}{BalancedBinaryTreeXmpPageEmpty1} +{BalancedBinaryTreeXmpPagePatch1} +\pastebutton{BalancedBinaryTreeXmpPageEmpty1}{\showpaste} +\tab{5}\spadcommand{lm := [3,5,7,11]\bound{lm }} +\end{paste}\end{patch} + +\begin{patch}{BalancedBinaryTreeXmpPagePatch2} +\begin{paste}{BalancedBinaryTreeXmpPageFull2} +{BalancedBinaryTreeXmpPageEmpty2} +\pastebutton{BalancedBinaryTreeXmpPageFull2}{\hidepaste} +\tab{5}\spadcommand{modTree(12,lm)\free{lm }} +\indentrel{3}\begin{verbatim} + (2) [0,2,5,1] + Type: List Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{BalancedBinaryTreeXmpPageEmpty2} +\begin{paste}{BalancedBinaryTreeXmpPageEmpty2} +{BalancedBinaryTreeXmpPagePatch2} +\pastebutton{BalancedBinaryTreeXmpPageEmpty2}{\showpaste} +\tab{5}\spadcommand{modTree(12,lm)\free{lm }} +\end{paste}\end{patch} + +\begin{patch}{BalancedBinaryTreeXmpPagePatch3} +\begin{paste}{BalancedBinaryTreeXmpPageFull3} +{BalancedBinaryTreeXmpPageEmpty3} +\pastebutton{BalancedBinaryTreeXmpPageFull3}{\hidepaste} +\tab{5}\spadcommand{ +t := balancedBinaryTree(\#lm, 0)\bound{t }\free{lm }} +\indentrel{3}\begin{verbatim} + (3) [[0,0,0],0,[0,0,0]] + Type: BalancedBinaryTree NonNegativeInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{BalancedBinaryTreeXmpPageEmpty3} +\begin{paste}{BalancedBinaryTreeXmpPageEmpty3} +{BalancedBinaryTreeXmpPagePatch3} +\pastebutton{BalancedBinaryTreeXmpPageEmpty3}{\showpaste} +\tab{5}\spadcommand{t := balancedBinaryTree(\#lm, 0)\bound{t }\free{lm }} +\end{paste}\end{patch} + +\begin{patch}{BalancedBinaryTreeXmpPagePatch4} +\begin{paste}{BalancedBinaryTreeXmpPageFull4} +{BalancedBinaryTreeXmpPageEmpty4} +\pastebutton{BalancedBinaryTreeXmpPageFull4}{\hidepaste} +\tab{5}\spadcommand{setleaves!(t,lm)\bound{t1 }\free{t }} +\indentrel{3}\begin{verbatim} + (4) [[3,0,5],0,[7,0,11]] + Type: BalancedBinaryTree NonNegativeInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{BalancedBinaryTreeXmpPageEmpty4} +\begin{paste}{BalancedBinaryTreeXmpPageEmpty4} +{BalancedBinaryTreeXmpPagePatch4} +\pastebutton{BalancedBinaryTreeXmpPageEmpty4}{\showpaste} +\tab{5}\spadcommand{setleaves!(t,lm)\bound{t1 }\free{t }} +\end{paste}\end{patch} + +\begin{patch}{BalancedBinaryTreeXmpPagePatch5} +\begin{paste}{BalancedBinaryTreeXmpPageFull5} +{BalancedBinaryTreeXmpPageEmpty5} +\pastebutton{BalancedBinaryTreeXmpPageFull5}{\hidepaste} +\tab{5}\spadcommand{mapUp!(t,_*)\bound{t2 }\free{t1 }} +\indentrel{3}\begin{verbatim} + (5) 1155 + Type: PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{BalancedBinaryTreeXmpPageEmpty5} +\begin{paste}{BalancedBinaryTreeXmpPageEmpty5} +{BalancedBinaryTreeXmpPagePatch5} +\pastebutton{BalancedBinaryTreeXmpPageEmpty5}{\showpaste} +\tab{5}\spadcommand{mapUp!(t,_*)\bound{t2 }\free{t1 }} +\end{paste}\end{patch} + +\begin{patch}{BalancedBinaryTreeXmpPagePatch6} +\begin{paste}{BalancedBinaryTreeXmpPageFull6} +{BalancedBinaryTreeXmpPageEmpty6} +\pastebutton{BalancedBinaryTreeXmpPageFull6}{\hidepaste} +\tab{5}\spadcommand{t\bound{t3 }\free{t2 }} +\indentrel{3}\begin{verbatim} + (6) [[3,15,5],1155,[7,77,11]] + Type: BalancedBinaryTree NonNegativeInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{BalancedBinaryTreeXmpPageEmpty6} +\begin{paste}{BalancedBinaryTreeXmpPageEmpty6} +{BalancedBinaryTreeXmpPagePatch6} +\pastebutton{BalancedBinaryTreeXmpPageEmpty6}{\showpaste} +\tab{5}\spadcommand{t\bound{t3 }\free{t2 }} +\end{paste}\end{patch} + +\begin{patch}{BalancedBinaryTreeXmpPagePatch7} +\begin{paste}{BalancedBinaryTreeXmpPageFull7} +{BalancedBinaryTreeXmpPageEmpty7} +\pastebutton{BalancedBinaryTreeXmpPageFull7}{\hidepaste} +\tab{5}\spadcommand{mapDown!(t,12,_rem)\bound{t4 }\free{t3 }} +\indentrel{3}\begin{verbatim} + (7) [[0,12,2],12,[5,12,1]] + Type: BalancedBinaryTree NonNegativeInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{BalancedBinaryTreeXmpPageEmpty7} +\begin{paste}{BalancedBinaryTreeXmpPageEmpty7} +{BalancedBinaryTreeXmpPagePatch7} +\pastebutton{BalancedBinaryTreeXmpPageEmpty7}{\showpaste} +\tab{5}\spadcommand{mapDown!(t,12,_rem)\bound{t4 }\free{t3 }} +\end{paste}\end{patch} + +\begin{patch}{BalancedBinaryTreeXmpPagePatch8} +\begin{paste}{BalancedBinaryTreeXmpPageFull8} +{BalancedBinaryTreeXmpPageEmpty8} +\pastebutton{BalancedBinaryTreeXmpPageFull8}{\hidepaste} +\tab{5}\spadcommand{leaves \%\bound{t5 }\free{t4 }} +\indentrel{3}\begin{verbatim} + (8) [0,2,5,1] + Type: List NonNegativeInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{BalancedBinaryTreeXmpPageEmpty8} +\begin{paste}{BalancedBinaryTreeXmpPageEmpty8} +{BalancedBinaryTreeXmpPagePatch8} +\pastebutton{BalancedBinaryTreeXmpPageEmpty8}{\showpaste} +\tab{5}\spadcommand{leaves \%\bound{t5 }\free{t4 }} +\end{paste}\end{patch} + +\begin{patch}{BalancedBinaryTreeXmpPagePatch9} +\begin{paste}{BalancedBinaryTreeXmpPageFull9} +{BalancedBinaryTreeXmpPageEmpty9} +\pastebutton{BalancedBinaryTreeXmpPageFull9}{\hidepaste} +\tab{5}\spadcommand{ +squares := [x**2 rem m for x in \% for m in lm]\bound{t6 }\free{t5 }} +\indentrel{3}\begin{verbatim} + (9) [0,4,4,1] + Type: List NonNegativeInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{BalancedBinaryTreeXmpPageEmpty9} +\begin{paste}{BalancedBinaryTreeXmpPageEmpty9} +{BalancedBinaryTreeXmpPagePatch9} +\pastebutton{BalancedBinaryTreeXmpPageEmpty9}{\showpaste} +\tab{5}\spadcommand{ +squares := [x**2 rem m for x in \% for m in lm]\bound{t6 }\free{t5 }} +\end{paste}\end{patch} + +\begin{patch}{BalancedBinaryTreeXmpPagePatch10} +\begin{paste}{BalancedBinaryTreeXmpPageFull10} +{BalancedBinaryTreeXmpPageEmpty10} +\pastebutton{BalancedBinaryTreeXmpPageFull10}{\hidepaste} +\tab{5}\spadcommand{chineseRemainder(\%,lm)\free{t6 }} +\indentrel{3}\begin{verbatim} + (10) 144 + Type: PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{BalancedBinaryTreeXmpPageEmpty10} +\begin{paste}{BalancedBinaryTreeXmpPageEmpty10} +{BalancedBinaryTreeXmpPagePatch10} +\pastebutton{BalancedBinaryTreeXmpPageEmpty10}{\showpaste} +\tab{5}\spadcommand{chineseRemainder(\%,lm)\free{t6 }} +\end{paste}\end{patch} + @ \section{binary.ht} \pagehead{BinaryExpansionXmpPage}{binary.ht}{BinaryExpansion} @@ -2635,6 +3591,148 @@ These numbers are bona fide algebraic objects. \autobuttons \end{page} +\begin{patch}{BinaryExpansionXmpPagePatch1} +\begin{paste}{BinaryExpansionXmpPageFull1}{BinaryExpansionXmpPageEmpty1} +\pastebutton{BinaryExpansionXmpPageFull1}{\hidepaste} +\tab{5}\spadcommand{r := binary(22/7)\bound{r }} +\indentrel{3}\begin{verbatim} + ___ + (1) 11.001 + Type: BinaryExpansion +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{BinaryExpansionXmpPageEmpty1} +\begin{paste}{BinaryExpansionXmpPageEmpty1}{BinaryExpansionXmpPagePatch1} +\pastebutton{BinaryExpansionXmpPageEmpty1}{\showpaste} +\tab{5}\spadcommand{r := binary(22/7)\bound{r }} +\end{paste}\end{patch} + +\begin{patch}{BinaryExpansionXmpPagePatch2} +\begin{paste}{BinaryExpansionXmpPageFull2}{BinaryExpansionXmpPageEmpty2} +\pastebutton{BinaryExpansionXmpPageFull2}{\hidepaste} +\tab{5}\spadcommand{r + binary(6/7)\free{r }} +\indentrel{3}\begin{verbatim} + (2) 100 + Type: BinaryExpansion +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{BinaryExpansionXmpPageEmpty2} +\begin{paste}{BinaryExpansionXmpPageEmpty2}{BinaryExpansionXmpPagePatch2} +\pastebutton{BinaryExpansionXmpPageEmpty2}{\showpaste} +\tab{5}\spadcommand{r + binary(6/7)\free{r }} +\end{paste}\end{patch} + +\begin{patch}{BinaryExpansionXmpPagePatch3} +\begin{paste}{BinaryExpansionXmpPageFull3}{BinaryExpansionXmpPageEmpty3} +\pastebutton{BinaryExpansionXmpPageFull3}{\hidepaste} +\tab{5}\spadcommand{[binary(1/i) for i in 102..106]} +\indentrel{3}\begin{verbatim} + (3) + ________ + [0.000000101, + ___________________________________________________ + 0.000000100111110001000101100101111001110010010101001, + ____________ ____________ + 0.000000100111011, 0.000000100111, + + 0.0 + OVERBAR + 00000100110101001000011100111110110010101101111 + 00011 + ] + Type: List BinaryExpansion +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{BinaryExpansionXmpPageEmpty3} +\begin{paste}{BinaryExpansionXmpPageEmpty3}{BinaryExpansionXmpPagePatch3} +\pastebutton{BinaryExpansionXmpPageEmpty3}{\showpaste} +\tab{5}\spadcommand{[binary(1/i) for i in 102..106]} +\end{paste}\end{patch} + +\begin{patch}{BinaryExpansionXmpPagePatch4} +\begin{paste}{BinaryExpansionXmpPageFull4}{BinaryExpansionXmpPageEmpty4} +\pastebutton{BinaryExpansionXmpPageFull4}{\hidepaste} +\tab{5}\spadcommand{binary(1/1007)} +\indentrel{3}\begin{verbatim} + (4) + 0. + OVERBAR + 0000000001000001000101001001011110000011111100001 + 01111110010110001111101000100111001001100110001 + 10010010101011110110100110000000011000011001111 + 01110001101000101111010010001111011000010101110 + 11100111010101110011001010010111000000011100011 + 11001000000100100100110111001010100111010001101 + 11011010111000100100000110010110110000001011001 + 01111100010100000101010101101011000001101101110 + 10010101111111010111010100110010000101001101100 + 0100110001000100001000011000111010011110001 + Type: BinaryExpansion +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{BinaryExpansionXmpPageEmpty4} +\begin{paste}{BinaryExpansionXmpPageEmpty4}{BinaryExpansionXmpPagePatch4} +\pastebutton{BinaryExpansionXmpPageEmpty4}{\showpaste} +\tab{5}\spadcommand{binary(1/1007)} +\end{paste}\end{patch} + +\begin{patch}{BinaryExpansionXmpPagePatch5} +\begin{paste}{BinaryExpansionXmpPageFull5}{BinaryExpansionXmpPageEmpty5} +\pastebutton{BinaryExpansionXmpPageFull5}{\hidepaste} +\tab{5}\spadcommand{ +p := binary(1/4)*x**2 + binary(2/3)*x + binary(4/9)\bound{p }} +\indentrel{3}\begin{verbatim} + 2 __ ______ + (5) 0.01x + 0.10x + 0.011100 + Type: Polynomial BinaryExpansion +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{BinaryExpansionXmpPageEmpty5} +\begin{paste}{BinaryExpansionXmpPageEmpty5}{BinaryExpansionXmpPagePatch5} +\pastebutton{BinaryExpansionXmpPageEmpty5}{\showpaste} +\tab{5}\spadcommand{ +p := binary(1/4)*x**2 + binary(2/3)*x + binary(4/9)\bound{p }} +\end{paste}\end{patch} + +\begin{patch}{BinaryExpansionXmpPagePatch6} +\begin{paste}{BinaryExpansionXmpPageFull6}{BinaryExpansionXmpPageEmpty6} +\pastebutton{BinaryExpansionXmpPageFull6}{\hidepaste} +\tab{5}\spadcommand{q := D(p, x)\free{p }\bound{q }} +\indentrel{3}\begin{verbatim} + __ + (6) 0.1x + 0.10 + Type: Polynomial BinaryExpansion +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{BinaryExpansionXmpPageEmpty6} +\begin{paste}{BinaryExpansionXmpPageEmpty6}{BinaryExpansionXmpPagePatch6} +\pastebutton{BinaryExpansionXmpPageEmpty6}{\showpaste} +\tab{5}\spadcommand{q := D(p, x)\free{p }\bound{q }} +\end{paste}\end{patch} + +\begin{patch}{BinaryExpansionXmpPagePatch7} +\begin{paste}{BinaryExpansionXmpPageFull7}{BinaryExpansionXmpPageEmpty7} +\pastebutton{BinaryExpansionXmpPageFull7}{\hidepaste} +\tab{5}\spadcommand{g := gcd(p, q)\free{p q }\bound{g }} +\indentrel{3}\begin{verbatim} + __ + (7) x + 1.01 + Type: Polynomial BinaryExpansion +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{BinaryExpansionXmpPageEmpty7} +\begin{paste}{BinaryExpansionXmpPageEmpty7}{BinaryExpansionXmpPagePatch7} +\pastebutton{BinaryExpansionXmpPageEmpty7}{\showpaste} +\tab{5}\spadcommand{g := gcd(p, q)\free{p q }\bound{g }} +\end{paste}\end{patch} + @ \section{bmcat.ht} \pagehead{BitMaps}{bmcat.ht}{Bit Map Catalog} @@ -2845,7 +3943,309 @@ remove a property. \endscroll \autobuttons \end{page} -% + +\begin{patch}{BasicOperatorXmpPagePatch1} +\begin{paste}{BasicOperatorXmpPageFull1}{BasicOperatorXmpPageEmpty1} +\pastebutton{BasicOperatorXmpPageFull1}{\hidepaste} +\tab{5}\spadcommand{y := operator 'y\bound{y }} +\indentrel{3}\begin{verbatim} + (1) y + Type: BasicOperator +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{BasicOperatorXmpPageEmpty1} +\begin{paste}{BasicOperatorXmpPageEmpty1}{BasicOperatorXmpPagePatch1} +\pastebutton{BasicOperatorXmpPageEmpty1}{\showpaste} +\tab{5}\spadcommand{y := operator 'y\bound{y }} +\end{paste}\end{patch} + +\begin{patch}{BasicOperatorXmpPagePatch2} +\begin{paste}{BasicOperatorXmpPageFull2}{BasicOperatorXmpPageEmpty2} +\pastebutton{BasicOperatorXmpPageFull2}{\hidepaste} +\tab{5}\spadcommand{ +deq := D(y x, x, 2) + D(y x, x) + y x = 0\bound{e1 }\free{y }} +\indentrel{3}\begin{verbatim} + ,, , + (2) y (x) + y (x) + y(x)= 0 + + Type: Equation Expression Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{BasicOperatorXmpPageEmpty2} +\begin{paste}{BasicOperatorXmpPageEmpty2}{BasicOperatorXmpPagePatch2} +\pastebutton{BasicOperatorXmpPageEmpty2}{\showpaste} +\tab{5}\spadcommand{ +deq := D(y x, x, 2) + D(y x, x) + y x = 0\bound{e1 }\free{y }} +\end{paste}\end{patch} + +\begin{patch}{BasicOperatorXmpPagePatch3} +\begin{paste}{BasicOperatorXmpPageFull3}{BasicOperatorXmpPageEmpty3} +\pastebutton{BasicOperatorXmpPageFull3}{\hidepaste} +\tab{5}\spadcommand{solve(deq, y, x)\free{e1 }\free{y }} +\indentrel{3}\begin{verbatim} + (3) + [particular= 0, + x x + ÚÄ¿ - Ä - Ä ÚÄ¿ + x\³3 2 2 x\³3 + basis= [cos(ÄÄÄÄÄ)%e ,%e sin(ÄÄÄÄÄ)]] + 2 2 +Type: Union(Record(particular: Expression Integer, + basis: List Expression Integer),...) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{BasicOperatorXmpPageEmpty3} +\begin{paste}{BasicOperatorXmpPageEmpty3}{BasicOperatorXmpPagePatch3} +\pastebutton{BasicOperatorXmpPageEmpty3}{\showpaste} +\tab{5}\spadcommand{solve(deq, y, x)\free{e1 }\free{y }} +\end{paste}\end{patch} + +\begin{patch}{BasicOperatorXmpPagePatch4} +\begin{paste}{BasicOperatorXmpPageFull4}{BasicOperatorXmpPageEmpty4} +\pastebutton{BasicOperatorXmpPageFull4}{\hidepaste} +\tab{5}\spadcommand{nary? y\free{y }} +\indentrel{3}\begin{verbatim} + (4) true + Type: Boolean +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{BasicOperatorXmpPageEmpty4} +\begin{paste}{BasicOperatorXmpPageEmpty4}{BasicOperatorXmpPagePatch4} +\pastebutton{BasicOperatorXmpPageEmpty4}{\showpaste} +\tab{5}\spadcommand{nary? y\free{y }} +\end{paste}\end{patch} + +\begin{patch}{BasicOperatorXmpPagePatch5} +\begin{paste}{BasicOperatorXmpPageFull5}{BasicOperatorXmpPageEmpty5} +\pastebutton{BasicOperatorXmpPageFull5}{\hidepaste} +\tab{5}\spadcommand{unary? y\free{y }} +\indentrel{3}\begin{verbatim} + (5) false + Type: Boolean +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{BasicOperatorXmpPageEmpty5} +\begin{paste}{BasicOperatorXmpPageEmpty5}{BasicOperatorXmpPagePatch5} +\pastebutton{BasicOperatorXmpPageEmpty5}{\showpaste} +\tab{5}\spadcommand{unary? y\free{y }} +\end{paste}\end{patch} + +\begin{patch}{BasicOperatorXmpPagePatch6} +\begin{paste}{BasicOperatorXmpPageFull6}{BasicOperatorXmpPageEmpty6} +\pastebutton{BasicOperatorXmpPageFull6}{\hidepaste} +\tab{5}\spadcommand{opOne := operator('opOne, 1)\bound{opOne }} +\indentrel{3}\begin{verbatim} + (6) opOne + Type: BasicOperator +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{BasicOperatorXmpPageEmpty6} +\begin{paste}{BasicOperatorXmpPageEmpty6}{BasicOperatorXmpPagePatch6} +\pastebutton{BasicOperatorXmpPageEmpty6}{\showpaste} +\tab{5}\spadcommand{opOne := operator('opOne, 1)\bound{opOne }} +\end{paste}\end{patch} + +\begin{patch}{BasicOperatorXmpPagePatch7} +\begin{paste}{BasicOperatorXmpPageFull7}{BasicOperatorXmpPageEmpty7} +\pastebutton{BasicOperatorXmpPageFull7}{\hidepaste} +\tab{5}\spadcommand{nary? opOne\free{opOne }} +\indentrel{3}\begin{verbatim} + (7) false + Type: Boolean +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{BasicOperatorXmpPageEmpty7} +\begin{paste}{BasicOperatorXmpPageEmpty7}{BasicOperatorXmpPagePatch7} +\pastebutton{BasicOperatorXmpPageEmpty7}{\showpaste} +\tab{5}\spadcommand{nary? opOne\free{opOne }} +\end{paste}\end{patch} + +\begin{patch}{BasicOperatorXmpPagePatch8} +\begin{paste}{BasicOperatorXmpPageFull8}{BasicOperatorXmpPageEmpty8} +\pastebutton{BasicOperatorXmpPageFull8}{\hidepaste} +\tab{5}\spadcommand{unary? opOne\free{opOne }} +\indentrel{3}\begin{verbatim} + (8) true + Type: Boolean +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{BasicOperatorXmpPageEmpty8} +\begin{paste}{BasicOperatorXmpPageEmpty8}{BasicOperatorXmpPagePatch8} +\pastebutton{BasicOperatorXmpPageEmpty8}{\showpaste} +\tab{5}\spadcommand{unary? opOne\free{opOne }} +\end{paste}\end{patch} + +\begin{patch}{BasicOperatorXmpPagePatch9} +\begin{paste}{BasicOperatorXmpPageFull9}{BasicOperatorXmpPageEmpty9} +\pastebutton{BasicOperatorXmpPageFull9}{\hidepaste} +\tab{5}\spadcommand{arity opOne\free{opOne }} +\indentrel{3}\begin{verbatim} + (9) 1 + Type: Union(NonNegativeInteger,...) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{BasicOperatorXmpPageEmpty9} +\begin{paste}{BasicOperatorXmpPageEmpty9}{BasicOperatorXmpPagePatch9} +\pastebutton{BasicOperatorXmpPageEmpty9}{\showpaste} +\tab{5}\spadcommand{arity opOne\free{opOne }} +\end{paste}\end{patch} + +\begin{patch}{BasicOperatorXmpPagePatch10} +\begin{paste}{BasicOperatorXmpPageFull10}{BasicOperatorXmpPageEmpty10} +\pastebutton{BasicOperatorXmpPageFull10}{\hidepaste} +\tab{5}\spadcommand{name opOne\free{opOne }} +\indentrel{3}\begin{verbatim} + (10) opOne + Type: Symbol +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{BasicOperatorXmpPageEmpty10} +\begin{paste}{BasicOperatorXmpPageEmpty10}{BasicOperatorXmpPagePatch10} +\pastebutton{BasicOperatorXmpPageEmpty10}{\showpaste} +\tab{5}\spadcommand{name opOne\free{opOne }} +\end{paste}\end{patch} + +\begin{patch}{BasicOperatorXmpPagePatch11} +\begin{paste}{BasicOperatorXmpPageFull11}{BasicOperatorXmpPageEmpty11} +\pastebutton{BasicOperatorXmpPageFull11}{\hidepaste} +\tab{5}\spadcommand{is?(opOne, 'z2)\free{opOne }} +\indentrel{3}\begin{verbatim} + (11) false + Type: Boolean +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{BasicOperatorXmpPageEmpty11} +\begin{paste}{BasicOperatorXmpPageEmpty11}{BasicOperatorXmpPagePatch11} +\pastebutton{BasicOperatorXmpPageEmpty11}{\showpaste} +\tab{5}\spadcommand{is?(opOne, 'z2)\free{opOne }} +\end{paste}\end{patch} + +\begin{patch}{BasicOperatorXmpPagePatch12} +\begin{paste}{BasicOperatorXmpPageFull12}{BasicOperatorXmpPageEmpty12} +\pastebutton{BasicOperatorXmpPageFull12}{\hidepaste} +\tab{5}\spadcommand{is?(opOne, "opOne")\free{opOne }} +\indentrel{3}\begin{verbatim} + (12) true + Type: Boolean +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{BasicOperatorXmpPageEmpty12} +\begin{paste}{BasicOperatorXmpPageEmpty12}{BasicOperatorXmpPagePatch12} +\pastebutton{BasicOperatorXmpPageEmpty12}{\showpaste} +\tab{5}\spadcommand{is?(opOne, "opOne")\free{opOne }} +\end{paste}\end{patch} + +\begin{patch}{BasicOperatorXmpPagePatch13} +\begin{paste}{BasicOperatorXmpPageFull13}{BasicOperatorXmpPageEmpty13} +\pastebutton{BasicOperatorXmpPageFull13}{\hidepaste} +\tab{5}\spadcommand{properties y\free{y }} +\indentrel{3}\begin{verbatim} + (13) table() + Type: AssociationList(String,None) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{BasicOperatorXmpPageEmpty13} +\begin{paste}{BasicOperatorXmpPageEmpty13}{BasicOperatorXmpPagePatch13} +\pastebutton{BasicOperatorXmpPageEmpty13}{\showpaste} +\tab{5}\spadcommand{properties y\free{y }} +\end{paste}\end{patch} + +\begin{patch}{BasicOperatorXmpPagePatch14} +\begin{paste}{BasicOperatorXmpPageFull14}{BasicOperatorXmpPageEmpty14} +\pastebutton{BasicOperatorXmpPageFull14}{\hidepaste} +\tab{5}\spadcommand{ +setProperty(y, "use", "unknown function" :: None )\free{y }\bound{spy }} +\indentrel{3}\begin{verbatim} + (14) y + Type: BasicOperator +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{BasicOperatorXmpPageEmpty14} +\begin{paste}{BasicOperatorXmpPageEmpty14}{BasicOperatorXmpPagePatch14} +\pastebutton{BasicOperatorXmpPageEmpty14}{\showpaste} +\tab{5}\spadcommand{ +setProperty(y, "use", "unknown function" :: None )\free{y }\bound{spy }} +\end{paste}\end{patch} + +\begin{patch}{BasicOperatorXmpPagePatch15} +\begin{paste}{BasicOperatorXmpPageFull15}{BasicOperatorXmpPageEmpty15} +\pastebutton{BasicOperatorXmpPageFull15}{\hidepaste} +\tab{5}\spadcommand{properties y\free{y spy }} +\indentrel{3}\begin{verbatim} + (15) table("use"= NONE) + Type: AssociationList(String,None) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{BasicOperatorXmpPageEmpty15} +\begin{paste}{BasicOperatorXmpPageEmpty15}{BasicOperatorXmpPagePatch15} +\pastebutton{BasicOperatorXmpPageEmpty15}{\showpaste} +\tab{5}\spadcommand{properties y\free{y spy }} +\end{paste}\end{patch} + +\begin{patch}{BasicOperatorXmpPagePatch16} +\begin{paste}{BasicOperatorXmpPageFull16}{BasicOperatorXmpPageEmpty16} +\pastebutton{BasicOperatorXmpPageFull16}{\hidepaste} +\tab{5}\spadcommand{property(y, "use") :: None pretend String\free{y spy }} +\indentrel{3}\begin{verbatim} + (16) "unknown function" + Type: String +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{BasicOperatorXmpPageEmpty16} +\begin{paste}{BasicOperatorXmpPageEmpty16}{BasicOperatorXmpPagePatch16} +\pastebutton{BasicOperatorXmpPageEmpty16}{\showpaste} +\tab{5}\spadcommand{property(y, "use") :: None pretend String\free{y spy }} +\end{paste}\end{patch} + +\begin{patch}{BasicOperatorXmpPagePatch17} +\begin{paste}{BasicOperatorXmpPageFull17}{BasicOperatorXmpPageEmpty17} +\pastebutton{BasicOperatorXmpPageFull17}{\hidepaste} +\tab{5}\spadcommand{deleteProperty!(y, "use")\free{y spy }\bound{dpy }} +\indentrel{3}\begin{verbatim} + (17) y + Type: BasicOperator +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{BasicOperatorXmpPageEmpty17} +\begin{paste}{BasicOperatorXmpPageEmpty17}{BasicOperatorXmpPagePatch17} +\pastebutton{BasicOperatorXmpPageEmpty17}{\showpaste} +\tab{5}\spadcommand{deleteProperty!(y, "use")\free{y spy }\bound{dpy }} +\end{paste}\end{patch} + +\begin{patch}{BasicOperatorXmpPagePatch18} +\begin{paste}{BasicOperatorXmpPageFull18}{BasicOperatorXmpPageEmpty18} +\pastebutton{BasicOperatorXmpPageFull18}{\hidepaste} +\tab{5}\spadcommand{properties y\free{dpy }} +\indentrel{3}\begin{verbatim} + (18) table() + Type: AssociationList(String,None) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{BasicOperatorXmpPageEmpty18} +\begin{paste}{BasicOperatorXmpPageEmpty18}{BasicOperatorXmpPagePatch18} +\pastebutton{BasicOperatorXmpPageEmpty18}{\showpaste} +\tab{5}\spadcommand{properties y\free{dpy }} +\end{paste}\end{patch} + + @ \section{bstree.ht} \pagehead{BinarySearchTreeXmpPage}{bstree.ht}{BinarySearchTree} @@ -2946,6 +4346,210 @@ Have Axiom check that these are equal. \autobuttons \end{page} +\begin{patch}{BinarySearchTreeXmpPagePatch1} +\begin{paste}{BinarySearchTreeXmpPageFull1}{BinarySearchTreeXmpPageEmpty1} +\pastebutton{BinarySearchTreeXmpPageFull1}{\hidepaste} +\tab{5}\spadcommand{lv := [8,3,5,4,6,2,1,5,7]\bound{lv }} +\indentrel{3}\begin{verbatim} + (1) [8,3,5,4,6,2,1,5,7] + Type: List PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{BinarySearchTreeXmpPageEmpty1} +\begin{paste}{BinarySearchTreeXmpPageEmpty1}{BinarySearchTreeXmpPagePatch1} +\pastebutton{BinarySearchTreeXmpPageEmpty1}{\showpaste} +\tab{5}\spadcommand{lv := [8,3,5,4,6,2,1,5,7]\bound{lv }} +\end{paste}\end{patch} + +\begin{patch}{BinarySearchTreeXmpPagePatch2} +\begin{paste}{BinarySearchTreeXmpPageFull2}{BinarySearchTreeXmpPageEmpty2} +\pastebutton{BinarySearchTreeXmpPageFull2}{\hidepaste} +\tab{5}\spadcommand{t := binarySearchTree lv\free{lv }\bound{t }} +\indentrel{3}\begin{verbatim} + (2) [[[1,2,.],3,[4,5,[5,6,7]]],8,.] + Type: BinarySearchTree PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{BinarySearchTreeXmpPageEmpty2} +\begin{paste}{BinarySearchTreeXmpPageEmpty2}{BinarySearchTreeXmpPagePatch2} +\pastebutton{BinarySearchTreeXmpPageEmpty2}{\showpaste} +\tab{5}\spadcommand{t := binarySearchTree lv\free{lv }\bound{t }} +\end{paste}\end{patch} + +\begin{patch}{BinarySearchTreeXmpPagePatch3} +\begin{paste}{BinarySearchTreeXmpPageFull3}{BinarySearchTreeXmpPageEmpty3} +\pastebutton{BinarySearchTreeXmpPageFull3}{\hidepaste} +\tab{5}\spadcommand{emptybst := empty()$BSTREE(INT)\bound{e }} +\indentrel{3}\begin{verbatim} + (3) [] + Type: BinarySearchTree Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{BinarySearchTreeXmpPageEmpty3} +\begin{paste}{BinarySearchTreeXmpPageEmpty3}{BinarySearchTreeXmpPagePatch3} +\pastebutton{BinarySearchTreeXmpPageEmpty3}{\showpaste} +\tab{5}\spadcommand{emptybst := empty()$BSTREE(INT)\bound{e }} +\end{paste}\end{patch} + +\begin{patch}{BinarySearchTreeXmpPagePatch4} +\begin{paste}{BinarySearchTreeXmpPageFull4}{BinarySearchTreeXmpPageEmpty4} +\pastebutton{BinarySearchTreeXmpPageFull4}{\hidepaste} +\tab{5}\spadcommand{t1 := insert!(8,emptybst)\free{e }\bound{t1 }} +\indentrel{3}\begin{verbatim} + (4) 8 + Type: BinarySearchTree Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{BinarySearchTreeXmpPageEmpty4} +\begin{paste}{BinarySearchTreeXmpPageEmpty4}{BinarySearchTreeXmpPagePatch4} +\pastebutton{BinarySearchTreeXmpPageEmpty4}{\showpaste} +\tab{5}\spadcommand{t1 := insert!(8,emptybst)\free{e }\bound{t1 }} +\end{paste}\end{patch} + +\begin{patch}{BinarySearchTreeXmpPagePatch5} +\begin{paste}{BinarySearchTreeXmpPageFull5}{BinarySearchTreeXmpPageEmpty5} +\pastebutton{BinarySearchTreeXmpPageFull5}{\hidepaste} +\tab{5}\spadcommand{insert!(3,t1)\free{t1 }} +\indentrel{3}\begin{verbatim} + (5) [3,8,.] + Type: BinarySearchTree Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{BinarySearchTreeXmpPageEmpty5} +\begin{paste}{BinarySearchTreeXmpPageEmpty5}{BinarySearchTreeXmpPagePatch5} +\pastebutton{BinarySearchTreeXmpPageEmpty5}{\showpaste} +\tab{5}\spadcommand{insert!(3,t1)\free{t1 }} +\end{paste}\end{patch} + +\begin{patch}{BinarySearchTreeXmpPagePatch6} +\begin{paste}{BinarySearchTreeXmpPageFull6}{BinarySearchTreeXmpPageEmpty6} +\pastebutton{BinarySearchTreeXmpPageFull6}{\hidepaste} +\tab{5}\spadcommand{leaves t\free{t }} +\indentrel{3}\begin{verbatim} + (6) [1,4,5,7] + Type: List PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{BinarySearchTreeXmpPageEmpty6} +\begin{paste}{BinarySearchTreeXmpPageEmpty6}{BinarySearchTreeXmpPagePatch6} +\pastebutton{BinarySearchTreeXmpPageEmpty6}{\showpaste} +\tab{5}\spadcommand{leaves t\free{t }} +\end{paste}\end{patch} + +\begin{patch}{BinarySearchTreeXmpPagePatch7} +\begin{paste}{BinarySearchTreeXmpPageFull7}{BinarySearchTreeXmpPageEmpty7} +\pastebutton{BinarySearchTreeXmpPageFull7}{\hidepaste} +\tab{5}\spadcommand{split(3,t)\free{t }} +\indentrel{3}\begin{verbatim} + (7) + [less= [1,2,.],greater= [[.,3,[4,5,[5,6,7]]],8,.]] +Type: Record(less: BinarySearchTree PositiveInteger, + greater: BinarySearchTree PositiveInteger) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{BinarySearchTreeXmpPageEmpty7} +\begin{paste}{BinarySearchTreeXmpPageEmpty7}{BinarySearchTreeXmpPagePatch7} +\pastebutton{BinarySearchTreeXmpPageEmpty7}{\showpaste} +\tab{5}\spadcommand{split(3,t)\free{t }} +\end{paste}\end{patch} + +\begin{patch}{BinarySearchTreeXmpPagePatch8} +\begin{paste}{BinarySearchTreeXmpPageFull8}{BinarySearchTreeXmpPageEmpty8} +\pastebutton{BinarySearchTreeXmpPageFull8}{\hidepaste} +\tab{5}\spadcommand{insertRoot: (INT,BSTREE INT) -> BSTREE INT\bound{x }} +\indentrel{3}\begin{verbatim} + Type: Void +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{BinarySearchTreeXmpPageEmpty8} +\begin{paste}{BinarySearchTreeXmpPageEmpty8}{BinarySearchTreeXmpPagePatch8} +\pastebutton{BinarySearchTreeXmpPageEmpty8}{\showpaste} +\tab{5}\spadcommand{insertRoot: (INT,BSTREE INT) -> BSTREE INT\bound{x }} +\end{paste}\end{patch} + +\begin{patch}{BinarySearchTreeXmpPagePatch9} +\begin{paste}{BinarySearchTreeXmpPageFull9}{BinarySearchTreeXmpPageEmpty9} +\pastebutton{BinarySearchTreeXmpPageFull9}{\hidepaste} +\tab{5}\spadcommand{insertRoot(x, t) == + a := split(x, t) + node(a.less, x, a.greater) +\bound{x1 }\free{x }} +\indentrel{3}\begin{verbatim} + Type: Void +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{BinarySearchTreeXmpPageEmpty9} +\begin{paste}{BinarySearchTreeXmpPageEmpty9}{BinarySearchTreeXmpPagePatch9} +\pastebutton{BinarySearchTreeXmpPageEmpty9}{\showpaste} +\tab{5}\spadcommand{insertRoot(x, t) == + a := split(x, t) + node(a.less, x, a.greater) +\bound{x1 }\free{x }} +\end{paste}\end{patch} + +\begin{patch}{BinarySearchTreeXmpPagePatch10} +\begin{paste}{BinarySearchTreeXmpPageFull10}{BinarySearchTreeXmpPageEmpty10} +\pastebutton{BinarySearchTreeXmpPageFull10}{\hidepaste} +\tab{5}\spadcommand{ +buildFromRoot ls == reduce(insertRoot,ls,emptybst)\bound{x2 }\free{x1 e }} +\indentrel{3}\begin{verbatim} + Type: Void +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{BinarySearchTreeXmpPageEmpty10} +\begin{paste}{BinarySearchTreeXmpPageEmpty10} +{BinarySearchTreeXmpPagePatch10} +\pastebutton{BinarySearchTreeXmpPageEmpty10}{\showpaste} +\tab{5}\spadcommand{ +buildFromRoot ls == reduce(insertRoot,ls,emptybst)\bound{x2 }\free{x1 e }} +\end{paste}\end{patch} + +\begin{patch}{BinarySearchTreeXmpPagePatch11} +\begin{paste}{BinarySearchTreeXmpPageFull11} +{BinarySearchTreeXmpPageEmpty11} +\pastebutton{BinarySearchTreeXmpPageFull11}{\hidepaste} +\tab{5}\spadcommand{rt := buildFromRoot reverse lv\bound{rt }\free{lv x2 }} +\indentrel{3}\begin{verbatim} + (11) [[[1,2,.],3,[4,5,[5,6,7]]],8,.] + Type: BinarySearchTree Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{BinarySearchTreeXmpPageEmpty11} +\begin{paste}{BinarySearchTreeXmpPageEmpty11} +{BinarySearchTreeXmpPagePatch11} +\pastebutton{BinarySearchTreeXmpPageEmpty11}{\showpaste} +\tab{5}\spadcommand{rt := buildFromRoot reverse lv\bound{rt }\free{lv x2 }} +\end{paste}\end{patch} + +\begin{patch}{BinarySearchTreeXmpPagePatch12} +\begin{paste}{BinarySearchTreeXmpPageFull12} +{BinarySearchTreeXmpPageEmpty12} +\pastebutton{BinarySearchTreeXmpPageFull12}{\hidepaste} +\tab{5}\spadcommand{(t = rt)@Boolean\free{rt t }} +\indentrel{3}\begin{verbatim} + (12) true + Type: Boolean +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{BinarySearchTreeXmpPageEmpty12} +\begin{paste}{BinarySearchTreeXmpPageEmpty12} +{BinarySearchTreeXmpPagePatch12} +\pastebutton{BinarySearchTreeXmpPageEmpty12}{\showpaste} +\tab{5}\spadcommand{(t = rt)@Boolean\free{rt t }} +\end{paste}\end{patch} + @ \section{card.ht} \pagehead{CardinalNumberXmpPage}{card.ht}{CardinalNumber} @@ -2963,8 +4567,8 @@ The non-negative integers have a natural construction as cardinals \begin{verbatim} 0 = #{ }, 1 = {0}, 2 = {0, 1}, ..., n = {i | 0 <= i < n}. \end{verbatim} -The fact that \spad{0} acts as a zero for the multiplication of cardinals is -equivalent to the axiom of choice. +The fact that \spad{0} acts as a zero for the multiplication of +cardinals is equivalent to the axiom of choice. \xtc{ Cardinal numbers can be created by conversion from non-negative integers. @@ -2993,8 +4597,8 @@ They can also be obtained as the named cardinal \spad{Aleph(n)}. \spadpaste{A1 := Aleph 1 \bound{A1}} } \xtc{ -The \spadfunFrom{finite?}{CardinalNumber} operation tests whether a value is a -finite cardinal, that is, a non-negative integer. +The \spadfunFrom{finite?}{CardinalNumber} operation tests whether a +value is a finite cardinal, that is, a non-negative integer. }{ \spadpaste{finite? c2 \free{c2}} } @@ -3099,6 +4703,337 @@ generalized continuum hypothesis in this way. \autobuttons \end{page} +\begin{patch}{CardinalNumberXmpPagePatch1} +\begin{paste}{CardinalNumberXmpPageFull1}{CardinalNumberXmpPageEmpty1} +\pastebutton{CardinalNumberXmpPageFull1}{\hidepaste} +\tab{5}\spadcommand{c0 := 0 :: CardinalNumber\bound{c0 }} +\indentrel{3}\begin{verbatim} + (1) 0 + Type: CardinalNumber +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{CardinalNumberXmpPageEmpty1} +\begin{paste}{CardinalNumberXmpPageEmpty1}{CardinalNumberXmpPagePatch1} +\pastebutton{CardinalNumberXmpPageEmpty1}{\showpaste} +\tab{5}\spadcommand{c0 := 0 :: CardinalNumber\bound{c0 }} +\end{paste}\end{patch} + +\begin{patch}{CardinalNumberXmpPagePatch2} +\begin{paste}{CardinalNumberXmpPageFull2}{CardinalNumberXmpPageEmpty2} +\pastebutton{CardinalNumberXmpPageFull2}{\hidepaste} +\tab{5}\spadcommand{c1 := 1 :: CardinalNumber\bound{c1 }} +\indentrel{3}\begin{verbatim} + (2) 1 + Type: CardinalNumber +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{CardinalNumberXmpPageEmpty2} +\begin{paste}{CardinalNumberXmpPageEmpty2}{CardinalNumberXmpPagePatch2} +\pastebutton{CardinalNumberXmpPageEmpty2}{\showpaste} +\tab{5}\spadcommand{c1 := 1 :: CardinalNumber\bound{c1 }} +\end{paste}\end{patch} + +\begin{patch}{CardinalNumberXmpPagePatch3} +\begin{paste}{CardinalNumberXmpPageFull3}{CardinalNumberXmpPageEmpty3} +\pastebutton{CardinalNumberXmpPageFull3}{\hidepaste} +\tab{5}\spadcommand{c2 := 2 :: CardinalNumber\bound{c2 }} +\indentrel{3}\begin{verbatim} + (3) 2 + Type: CardinalNumber +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{CardinalNumberXmpPageEmpty3} +\begin{paste}{CardinalNumberXmpPageEmpty3}{CardinalNumberXmpPagePatch3} +\pastebutton{CardinalNumberXmpPageEmpty3}{\showpaste} +\tab{5}\spadcommand{c2 := 2 :: CardinalNumber\bound{c2 }} +\end{paste}\end{patch} + +\begin{patch}{CardinalNumberXmpPagePatch4} +\begin{paste}{CardinalNumberXmpPageFull4}{CardinalNumberXmpPageEmpty4} +\pastebutton{CardinalNumberXmpPageFull4}{\hidepaste} +\tab{5}\spadcommand{c3 := 3 :: CardinalNumber\bound{c3 }} +\indentrel{3}\begin{verbatim} + (4) 3 + Type: CardinalNumber +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{CardinalNumberXmpPageEmpty4} +\begin{paste}{CardinalNumberXmpPageEmpty4}{CardinalNumberXmpPagePatch4} +\pastebutton{CardinalNumberXmpPageEmpty4}{\showpaste} +\tab{5}\spadcommand{c3 := 3 :: CardinalNumber\bound{c3 }} +\end{paste}\end{patch} + +\begin{patch}{CardinalNumberXmpPagePatch5} +\begin{paste}{CardinalNumberXmpPageFull5}{CardinalNumberXmpPageEmpty5} +\pastebutton{CardinalNumberXmpPageFull5}{\hidepaste} +\tab{5}\spadcommand{A0 := Aleph 0\bound{A0 }} +\indentrel{3}\begin{verbatim} + (5) Aleph(0) + Type: CardinalNumber +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{CardinalNumberXmpPageEmpty5} +\begin{paste}{CardinalNumberXmpPageEmpty5}{CardinalNumberXmpPagePatch5} +\pastebutton{CardinalNumberXmpPageEmpty5}{\showpaste} +\tab{5}\spadcommand{A0 := Aleph 0\bound{A0 }} +\end{paste}\end{patch} + +\begin{patch}{CardinalNumberXmpPagePatch6} +\begin{paste}{CardinalNumberXmpPageFull6}{CardinalNumberXmpPageEmpty6} +\pastebutton{CardinalNumberXmpPageFull6}{\hidepaste} +\tab{5}\spadcommand{A1 := Aleph 1\bound{A1 }} +\indentrel{3}\begin{verbatim} + (6) Aleph(1) + Type: CardinalNumber +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{CardinalNumberXmpPageEmpty6} +\begin{paste}{CardinalNumberXmpPageEmpty6}{CardinalNumberXmpPagePatch6} +\pastebutton{CardinalNumberXmpPageEmpty6}{\showpaste} +\tab{5}\spadcommand{A1 := Aleph 1\bound{A1 }} +\end{paste}\end{patch} + +\begin{patch}{CardinalNumberXmpPagePatch7} +\begin{paste}{CardinalNumberXmpPageFull7}{CardinalNumberXmpPageEmpty7} +\pastebutton{CardinalNumberXmpPageFull7}{\hidepaste} +\tab{5}\spadcommand{finite? c2\free{c2 }} +\indentrel{3}\begin{verbatim} + (7) true + Type: Boolean +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{CardinalNumberXmpPageEmpty7} +\begin{paste}{CardinalNumberXmpPageEmpty7}{CardinalNumberXmpPagePatch7} +\pastebutton{CardinalNumberXmpPageEmpty7}{\showpaste} +\tab{5}\spadcommand{finite? c2\free{c2 }} +\end{paste}\end{patch} + +\begin{patch}{CardinalNumberXmpPagePatch8} +\begin{paste}{CardinalNumberXmpPageFull8}{CardinalNumberXmpPageEmpty8} +\pastebutton{CardinalNumberXmpPageFull8}{\hidepaste} +\tab{5}\spadcommand{finite? A0\free{A0 }} +\indentrel{3}\begin{verbatim} + (8) false + Type: Boolean +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{CardinalNumberXmpPageEmpty8} +\begin{paste}{CardinalNumberXmpPageEmpty8}{CardinalNumberXmpPagePatch8} +\pastebutton{CardinalNumberXmpPageEmpty8}{\showpaste} +\tab{5}\spadcommand{finite? A0\free{A0 }} +\end{paste}\end{patch} + +\begin{patch}{CardinalNumberXmpPagePatch9} +\begin{paste}{CardinalNumberXmpPageFull9}{CardinalNumberXmpPageEmpty9} +\pastebutton{CardinalNumberXmpPageFull9}{\hidepaste} +\tab{5}\spadcommand{countable? c2\free{c2 }} +\indentrel{3}\begin{verbatim} + (9) true + Type: Boolean +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{CardinalNumberXmpPageEmpty9} +\begin{paste}{CardinalNumberXmpPageEmpty9}{CardinalNumberXmpPagePatch9} +\pastebutton{CardinalNumberXmpPageEmpty9}{\showpaste} +\tab{5}\spadcommand{countable? c2\free{c2 }} +\end{paste}\end{patch} + +\begin{patch}{CardinalNumberXmpPagePatch10} +\begin{paste}{CardinalNumberXmpPageFull10}{CardinalNumberXmpPageEmpty10} +\pastebutton{CardinalNumberXmpPageFull10}{\hidepaste} +\tab{5}\spadcommand{countable? A0\free{A0 }} +\indentrel{3}\begin{verbatim} + (10) true + Type: Boolean +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{CardinalNumberXmpPageEmpty10} +\begin{paste}{CardinalNumberXmpPageEmpty10}{CardinalNumberXmpPagePatch10} +\pastebutton{CardinalNumberXmpPageEmpty10}{\showpaste} +\tab{5}\spadcommand{countable? A0\free{A0 }} +\end{paste}\end{patch} + +\begin{patch}{CardinalNumberXmpPagePatch11} +\begin{paste}{CardinalNumberXmpPageFull11}{CardinalNumberXmpPageEmpty11} +\pastebutton{CardinalNumberXmpPageFull11}{\hidepaste} +\tab{5}\spadcommand{countable? A1\free{A1 }} +\indentrel{3}\begin{verbatim} + (11) false + Type: Boolean +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{CardinalNumberXmpPageEmpty11} +\begin{paste}{CardinalNumberXmpPageEmpty11}{CardinalNumberXmpPagePatch11} +\pastebutton{CardinalNumberXmpPageEmpty11}{\showpaste} +\tab{5}\spadcommand{countable? A1\free{A1 }} +\end{paste}\end{patch} + +\begin{patch}{CardinalNumberXmpPagePatch12} +\begin{paste}{CardinalNumberXmpPageFull12}{CardinalNumberXmpPageEmpty12} +\pastebutton{CardinalNumberXmpPageFull12}{\hidepaste} +\tab{5}\spadcommand{[c2 + c2, c2 + A1]\free{c2 A1 }} +\indentrel{3}\begin{verbatim} + (12) [4,Aleph(1)] + Type: List CardinalNumber +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{CardinalNumberXmpPageEmpty12} +\begin{paste}{CardinalNumberXmpPageEmpty12}{CardinalNumberXmpPagePatch12} +\pastebutton{CardinalNumberXmpPageEmpty12}{\showpaste} +\tab{5}\spadcommand{[c2 + c2, c2 + A1]\free{c2 A1 }} +\end{paste}\end{patch} + +\begin{patch}{CardinalNumberXmpPagePatch13} +\begin{paste}{CardinalNumberXmpPageFull13}{CardinalNumberXmpPageEmpty13} +\pastebutton{CardinalNumberXmpPageFull13}{\hidepaste} +\tab{5}\spadcommand{ +[c0*c2, c1*c2, c2*c2, c0*A1, c1*A1, c2*A1, A0*A1]\free{c0 c1 c2 A0 A1 }} +\indentrel{3}\begin{verbatim} + (13) [0,2,4,0,Aleph(1),Aleph(1),Aleph(1)] + Type: List CardinalNumber +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{CardinalNumberXmpPageEmpty13} +\begin{paste}{CardinalNumberXmpPageEmpty13}{CardinalNumberXmpPagePatch13} +\pastebutton{CardinalNumberXmpPageEmpty13}{\showpaste} +\tab{5}\spadcommand{ +[c0*c2, c1*c2, c2*c2, c0*A1, c1*A1, c2*A1, A0*A1]\free{c0 c1 c2 A0 A1 }} +\end{paste}\end{patch} + +\begin{patch}{CardinalNumberXmpPagePatch14} +\begin{paste}{CardinalNumberXmpPageFull14}{CardinalNumberXmpPageEmpty14} +\pastebutton{CardinalNumberXmpPageFull14}{\hidepaste} +\tab{5}\spadcommand{ +[c2**c0, c2**c1, c2**c2, A1**c0, A1**c1, A1**c2]\free{c0 c1 c2 A1 }} +\indentrel{3}\begin{verbatim} + (14) [1,2,4,1,Aleph(1),Aleph(1)] + Type: List CardinalNumber +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{CardinalNumberXmpPageEmpty14} +\begin{paste}{CardinalNumberXmpPageEmpty14}{CardinalNumberXmpPagePatch14} +\pastebutton{CardinalNumberXmpPageEmpty14}{\showpaste} +\tab{5}\spadcommand{ +[c2**c0, c2**c1, c2**c2, A1**c0, A1**c1, A1**c2]\free{c0 c1 c2 A1 }} +\end{paste}\end{patch} + +\begin{patch}{CardinalNumberXmpPagePatch15} +\begin{paste}{CardinalNumberXmpPageFull15}{CardinalNumberXmpPageEmpty15} +\pastebutton{CardinalNumberXmpPageFull15}{\hidepaste} +\tab{5}\spadcommand{ +[c2-c1, c2-c2, c2-c3, A1-c2, A1-A0, A1-A1]\free{c1 c2 c3 A0 A1 }} +\indentrel{3}\begin{verbatim} + (15) [1,0,"failed",Aleph(1),Aleph(1),"failed"] + Type: List Union(CardinalNumber,"failed") +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{CardinalNumberXmpPageEmpty15} +\begin{paste}{CardinalNumberXmpPageEmpty15}{CardinalNumberXmpPagePatch15} +\pastebutton{CardinalNumberXmpPageEmpty15}{\showpaste} +\tab{5}\spadcommand{ +[c2-c1, c2-c2, c2-c3, A1-c2, A1-A0, A1-A1]\free{c1 c2 c3 A0 A1 }} +\end{paste}\end{patch} + +\begin{patch}{CardinalNumberXmpPagePatch16} +\begin{paste}{CardinalNumberXmpPageFull16}{CardinalNumberXmpPageEmpty16} +\pastebutton{CardinalNumberXmpPageFull16}{\hidepaste} +\tab{5}\spadcommand{generalizedContinuumHypothesisAssumed true\bound{GCH }} +\indentrel{3}\begin{verbatim} + (16) true + Type: Boolean +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{CardinalNumberXmpPageEmpty16} +\begin{paste}{CardinalNumberXmpPageEmpty16}{CardinalNumberXmpPagePatch16} +\pastebutton{CardinalNumberXmpPageEmpty16}{\showpaste} +\tab{5}\spadcommand{generalizedContinuumHypothesisAssumed true\bound{GCH }} +\end{paste}\end{patch} + +\begin{patch}{CardinalNumberXmpPagePatch17} +\begin{paste}{CardinalNumberXmpPageFull17}{CardinalNumberXmpPageEmpty17} +\pastebutton{CardinalNumberXmpPageFull17}{\hidepaste} +\tab{5}\spadcommand{ +[c0**A0, c1**A0, c2**A0, A0**A0, A0**A1, A1**A0, A1**A1] +\free{c0 c1 c2 A0 A1 GCH }} +\indentrel{3}\begin{verbatim} + (17) + [0,1,Aleph(1),Aleph(1),Aleph(2),Aleph(1),Aleph(2)] + Type: List CardinalNumber +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{CardinalNumberXmpPageEmpty17} +\begin{paste}{CardinalNumberXmpPageEmpty17}{CardinalNumberXmpPagePatch17} +\pastebutton{CardinalNumberXmpPageEmpty17}{\showpaste} +\tab{5}\spadcommand{ +[c0**A0, c1**A0, c2**A0, A0**A0, A0**A1, A1**A0, A1**A1] +\free{c0 c1 c2 A0 A1 GCH }} +\end{paste}\end{patch} + +\begin{patch}{CardinalNumberXmpPagePatch18} +\begin{paste}{CardinalNumberXmpPageFull18}{CardinalNumberXmpPageEmpty18} +\pastebutton{CardinalNumberXmpPageFull18}{\hidepaste} +\tab{5}\spadcommand{a := Aleph 0\free{GCH }\bound{a }} +\indentrel{3}\begin{verbatim} + (18) Aleph(0) + Type: CardinalNumber +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{CardinalNumberXmpPageEmpty18} +\begin{paste}{CardinalNumberXmpPageEmpty18}{CardinalNumberXmpPagePatch18} +\pastebutton{CardinalNumberXmpPageEmpty18}{\showpaste} +\tab{5}\spadcommand{a := Aleph 0\free{GCH }\bound{a }} +\end{paste}\end{patch} + +\begin{patch}{CardinalNumberXmpPagePatch19} +\begin{paste}{CardinalNumberXmpPageFull19}{CardinalNumberXmpPageEmpty19} +\pastebutton{CardinalNumberXmpPageFull19}{\hidepaste} +\tab{5}\spadcommand{c := 2**a\free{a }\bound{c }} +\indentrel{3}\begin{verbatim} + (19) Aleph(1) + Type: CardinalNumber +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{CardinalNumberXmpPageEmpty19} +\begin{paste}{CardinalNumberXmpPageEmpty19}{CardinalNumberXmpPagePatch19} +\pastebutton{CardinalNumberXmpPageEmpty19}{\showpaste} +\tab{5}\spadcommand{c := 2**a\free{a }\bound{c }} +\end{paste}\end{patch} + +\begin{patch}{CardinalNumberXmpPagePatch20} +\begin{paste}{CardinalNumberXmpPageFull20}{CardinalNumberXmpPageEmpty20} +\pastebutton{CardinalNumberXmpPageFull20}{\hidepaste} +\tab{5}\spadcommand{f := 2**c\free{c }\bound{f }} +\indentrel{3}\begin{verbatim} + (20) Aleph(2) + Type: CardinalNumber +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{CardinalNumberXmpPageEmpty20} +\begin{paste}{CardinalNumberXmpPageEmpty20}{CardinalNumberXmpPagePatch20} +\pastebutton{CardinalNumberXmpPageEmpty20}{\showpaste} +\tab{5}\spadcommand{f := 2**c\free{c }\bound{f }} +\end{paste}\end{patch} + @ \section{carten.ht} \pagehead{CartesianTensorXmpPage}{carten.ht}{CartesianTensor} @@ -3495,21 +5430,886 @@ the degree \spad{k} module is \spad{T[k](V)}. %\head{subsection}{Tensor Calculus}{ugxCartenCalculus} It should be noted here that often tensors are used in the context of -tensor-valued manifold maps. -This leads to the notion of covariant and contravariant bases with tensor -component functions transforming in specific ways under a change of -coordinates on the manifold. -This is no more directly supported by the \spadtype{CartesianTensor} -domain than it is by the \spadtype{Vector} domain. -However, it is possible to have the components implicitly represent -component maps by choosing a polynomial or expression type for the -components. -In this case, it is up to the user to satisfy any constraints which arise -on the basis of this interpretation. +tensor-valued manifold maps. This leads to the notion of covariant +and contravariant bases with tensor component functions transforming +in specific ways under a change of coordinates on the manifold. This +is no more directly supported by the \spadtype{CartesianTensor} domain +than it is by the \spadtype{Vector} domain. However, it is possible +to have the components implicitly represent component maps by choosing +a polynomial or expression type for the components. In this case, it +is up to the user to satisfy any constraints which arise on the basis +of this interpretation. \endscroll \autobuttons \end{page} +\begin{patch}{CartesianTensorXmpPagePatch1} +\begin{paste}{CartesianTensorXmpPageFull1}{CartesianTensorXmpPageEmpty1} +\pastebutton{CartesianTensorXmpPageFull1}{\hidepaste} +\tab{5}\spadcommand{CT := CARTEN(i0 := 1, 2, Integer)\bound{CT i0 }} +\indentrel{3}\begin{verbatim} + (1) CartesianTensor(1,2,Integer) + Type: Domain +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{CartesianTensorXmpPageEmpty1} +\begin{paste}{CartesianTensorXmpPageEmpty1}{CartesianTensorXmpPagePatch1} +\pastebutton{CartesianTensorXmpPageEmpty1}{\showpaste} +\tab{5}\spadcommand{CT := CARTEN(i0 := 1, 2, Integer)\bound{CT i0 }} +\end{paste}\end{patch} + +\begin{patch}{CartesianTensorXmpPagePatch2} +\begin{paste}{CartesianTensorXmpPageFull2}{CartesianTensorXmpPageEmpty2} +\pastebutton{CartesianTensorXmpPageFull2}{\hidepaste} +\tab{5}\spadcommand{t0: CT := 8\free{CT }\bound{t0 }} +\indentrel{3}\begin{verbatim} + (2) 8 + Type: CartesianTensor(1,2,Integer) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{CartesianTensorXmpPageEmpty2} +\begin{paste}{CartesianTensorXmpPageEmpty2}{CartesianTensorXmpPagePatch2} +\pastebutton{CartesianTensorXmpPageEmpty2}{\showpaste} +\tab{5}\spadcommand{t0: CT := 8\free{CT }\bound{t0 }} +\end{paste}\end{patch} + +\begin{patch}{CartesianTensorXmpPagePatch3} +\begin{paste}{CartesianTensorXmpPageFull3}{CartesianTensorXmpPageEmpty3} +\pastebutton{CartesianTensorXmpPageFull3}{\hidepaste} +\tab{5}\spadcommand{rank t0\free{t0 }} +\indentrel{3}\begin{verbatim} + (3) 0 + Type: NonNegativeInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{CartesianTensorXmpPageEmpty3} +\begin{paste}{CartesianTensorXmpPageEmpty3}{CartesianTensorXmpPagePatch3} +\pastebutton{CartesianTensorXmpPageEmpty3}{\showpaste} +\tab{5}\spadcommand{rank t0\free{t0 }} +\end{paste}\end{patch} + +\begin{patch}{CartesianTensorXmpPagePatch4} +\begin{paste}{CartesianTensorXmpPageFull4}{CartesianTensorXmpPageEmpty4} +\pastebutton{CartesianTensorXmpPageFull4}{\hidepaste} +\tab{5}\spadcommand{ +v: DirectProduct(2, Integer) := directProduct [3,4]\bound{v }} +\indentrel{3}\begin{verbatim} + (4) [3,4] + Type: DirectProduct(2,Integer) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{CartesianTensorXmpPageEmpty4} +\begin{paste}{CartesianTensorXmpPageEmpty4}{CartesianTensorXmpPagePatch4} +\pastebutton{CartesianTensorXmpPageEmpty4}{\showpaste} +\tab{5}\spadcommand{ +v: DirectProduct(2, Integer) := directProduct [3,4]\bound{v }} +\end{paste}\end{patch} + +\begin{patch}{CartesianTensorXmpPagePatch5} +\begin{paste}{CartesianTensorXmpPageFull5}{CartesianTensorXmpPageEmpty5} +\pastebutton{CartesianTensorXmpPageFull5}{\hidepaste} +\tab{5}\spadcommand{Tv: CT := v\free{v CT }\bound{Tv }} +\indentrel{3}\begin{verbatim} + (5) [3,4] + Type: CartesianTensor(1,2,Integer) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{CartesianTensorXmpPageEmpty5} +\begin{paste}{CartesianTensorXmpPageEmpty5}{CartesianTensorXmpPagePatch5} +\pastebutton{CartesianTensorXmpPageEmpty5}{\showpaste} +\tab{5}\spadcommand{Tv: CT := v\free{v CT }\bound{Tv }} +\end{paste}\end{patch} + +\begin{patch}{CartesianTensorXmpPagePatch6} +\begin{paste}{CartesianTensorXmpPageFull6}{CartesianTensorXmpPageEmpty6} +\pastebutton{CartesianTensorXmpPageFull6}{\hidepaste} +\tab{5}\spadcommand{ +m: SquareMatrix(2, Integer) := matrix [[1,2],[4,5]]\bound{m }} +\indentrel{3}\begin{verbatim} + Ú1 2¿ + (6) ³ ³ + À4 5Ù + Type: SquareMatrix(2,Integer) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{CartesianTensorXmpPageEmpty6} +\begin{paste}{CartesianTensorXmpPageEmpty6}{CartesianTensorXmpPagePatch6} +\pastebutton{CartesianTensorXmpPageEmpty6}{\showpaste} +\tab{5}\spadcommand{ +m: SquareMatrix(2, Integer) := matrix [[1,2],[4,5]]\bound{m }} +\end{paste}\end{patch} + +\begin{patch}{CartesianTensorXmpPagePatch7} +\begin{paste}{CartesianTensorXmpPageFull7}{CartesianTensorXmpPageEmpty7} +\pastebutton{CartesianTensorXmpPageFull7}{\hidepaste} +\tab{5}\spadcommand{Tm: CT := m\bound{Tm }\free{CT m }} +\indentrel{3}\begin{verbatim} + Ú1 2¿ + (7) ³ ³ + À4 5Ù + Type: CartesianTensor(1,2,Integer) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{CartesianTensorXmpPageEmpty7} +\begin{paste}{CartesianTensorXmpPageEmpty7}{CartesianTensorXmpPagePatch7} +\pastebutton{CartesianTensorXmpPageEmpty7}{\showpaste} +\tab{5}\spadcommand{Tm: CT := m\bound{Tm }\free{CT m }} +\end{paste}\end{patch} + +\begin{patch}{CartesianTensorXmpPagePatch8} +\begin{paste}{CartesianTensorXmpPageFull8}{CartesianTensorXmpPageEmpty8} +\pastebutton{CartesianTensorXmpPageFull8}{\hidepaste} +\tab{5}\spadcommand{ +n: SquareMatrix(2, Integer) := matrix [[2,3],[0,1]]\bound{n }} +\indentrel{3}\begin{verbatim} + Ú2 3¿ + (8) ³ ³ + À0 1Ù + Type: SquareMatrix(2,Integer) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{CartesianTensorXmpPageEmpty8} +\begin{paste}{CartesianTensorXmpPageEmpty8}{CartesianTensorXmpPagePatch8} +\pastebutton{CartesianTensorXmpPageEmpty8}{\showpaste} +\tab{5}\spadcommand{ +n: SquareMatrix(2, Integer) := matrix [[2,3],[0,1]]\bound{n }} +\end{paste}\end{patch} + +\begin{patch}{CartesianTensorXmpPagePatch9} +\begin{paste}{CartesianTensorXmpPageFull9}{CartesianTensorXmpPageEmpty9} +\pastebutton{CartesianTensorXmpPageFull9}{\hidepaste} +\tab{5}\spadcommand{Tn: CT := n\bound{Tn }\free{CT n }} +\indentrel{3}\begin{verbatim} + Ú2 3¿ + (9) ³ ³ + À0 1Ù + Type: CartesianTensor(1,2,Integer) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{CartesianTensorXmpPageEmpty9} +\begin{paste}{CartesianTensorXmpPageEmpty9}{CartesianTensorXmpPagePatch9} +\pastebutton{CartesianTensorXmpPageEmpty9}{\showpaste} +\tab{5}\spadcommand{Tn: CT := n\bound{Tn }\free{CT n }} +\end{paste}\end{patch} + +\begin{patch}{CartesianTensorXmpPagePatch10} +\begin{paste}{CartesianTensorXmpPageFull10}{CartesianTensorXmpPageEmpty10} +\pastebutton{CartesianTensorXmpPageFull10}{\hidepaste} +\tab{5}\spadcommand{t1: CT := [2, 3]\free{CT }\bound{t1 }} +\indentrel{3}\begin{verbatim} + (10) [2,3] + Type: CartesianTensor(1,2,Integer) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{CartesianTensorXmpPageEmpty10} +\begin{paste}{CartesianTensorXmpPageEmpty10}{CartesianTensorXmpPagePatch10} +\pastebutton{CartesianTensorXmpPageEmpty10}{\showpaste} +\tab{5}\spadcommand{t1: CT := [2, 3]\free{CT }\bound{t1 }} +\end{paste}\end{patch} + +\begin{patch}{CartesianTensorXmpPagePatch11} +\begin{paste}{CartesianTensorXmpPageFull11}{CartesianTensorXmpPageEmpty11} +\pastebutton{CartesianTensorXmpPageFull11}{\hidepaste} +\tab{5}\spadcommand{rank t1\free{t1 }} +\indentrel{3}\begin{verbatim} + (11) 1 + Type: PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{CartesianTensorXmpPageEmpty11} +\begin{paste}{CartesianTensorXmpPageEmpty11}{CartesianTensorXmpPagePatch11} +\pastebutton{CartesianTensorXmpPageEmpty11}{\showpaste} +\tab{5}\spadcommand{rank t1\free{t1 }} +\end{paste}\end{patch} + +\begin{patch}{CartesianTensorXmpPagePatch12} +\begin{paste}{CartesianTensorXmpPageFull12}{CartesianTensorXmpPageEmpty12} +\pastebutton{CartesianTensorXmpPageFull12}{\hidepaste} +\tab{5}\spadcommand{t2: CT := [t1, t1]\free{CT t1 }\bound{t2 }} +\indentrel{3}\begin{verbatim} + Ú2 3¿ + (12) ³ ³ + À2 3Ù + Type: CartesianTensor(1,2,Integer) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{CartesianTensorXmpPageEmpty12} +\begin{paste}{CartesianTensorXmpPageEmpty12}{CartesianTensorXmpPagePatch12} +\pastebutton{CartesianTensorXmpPageEmpty12}{\showpaste} +\tab{5}\spadcommand{t2: CT := [t1, t1]\free{CT t1 }\bound{t2 }} +\end{paste}\end{patch} + +\begin{patch}{CartesianTensorXmpPagePatch13} +\begin{paste}{CartesianTensorXmpPageFull13}{CartesianTensorXmpPageEmpty13} +\pastebutton{CartesianTensorXmpPageFull13}{\hidepaste} +\tab{5}\spadcommand{t3: CT := [t2, t2]\free{CT t2 }\bound{t3 }} +\indentrel{3}\begin{verbatim} + Ú2 3¿ Ú2 3¿ + (13) [³ ³,³ ³] + À2 3Ù À2 3Ù + Type: CartesianTensor(1,2,Integer) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{CartesianTensorXmpPageEmpty13} +\begin{paste}{CartesianTensorXmpPageEmpty13}{CartesianTensorXmpPagePatch13} +\pastebutton{CartesianTensorXmpPageEmpty13}{\showpaste} +\tab{5}\spadcommand{t3: CT := [t2, t2]\free{CT t2 }\bound{t3 }} +\end{paste}\end{patch} + +\begin{patch}{CartesianTensorXmpPagePatch14} +\begin{paste}{CartesianTensorXmpPageFull14}{CartesianTensorXmpPageEmpty14} +\pastebutton{CartesianTensorXmpPageFull14}{\hidepaste} +\tab{5}\spadcommand{ +tt: CT := [t3, t3]; tt := [tt, tt]\free{CT t3 }\bound{tt }} +\indentrel{3}\begin{verbatim} + ÚÚ2 3¿ Ú2 3¿¿ ÚÚ2 3¿ Ú2 3¿¿ + ³³ ³ ³ ³³ ³³ ³ ³ ³³ + ³À2 3Ù À2 3Ù³ ³À2 3Ù À2 3Ù³ + (14) [³ ³,³ ³] + ³Ú2 3¿ Ú2 3¿³ ³Ú2 3¿ Ú2 3¿³ + ³³ ³ ³ ³³ ³³ ³ ³ ³³ + ÀÀ2 3Ù À2 3ÙÙ ÀÀ2 3Ù À2 3ÙÙ + Type: CartesianTensor(1,2,Integer) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{CartesianTensorXmpPageEmpty14} +\begin{paste}{CartesianTensorXmpPageEmpty14}{CartesianTensorXmpPagePatch14} +\pastebutton{CartesianTensorXmpPageEmpty14}{\showpaste} +\tab{5}\spadcommand{ +tt: CT := [t3, t3]; tt := [tt, tt]\free{CT t3 }\bound{tt }} +\end{paste}\end{patch} + +\begin{patch}{CartesianTensorXmpPagePatch15} +\begin{paste}{CartesianTensorXmpPageFull15}{CartesianTensorXmpPageEmpty15} +\pastebutton{CartesianTensorXmpPageFull15}{\hidepaste} +\tab{5}\spadcommand{rank tt\free{tt }} +\indentrel{3}\begin{verbatim} + (15) 5 + Type: PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{CartesianTensorXmpPageEmpty15} +\begin{paste}{CartesianTensorXmpPageEmpty15}{CartesianTensorXmpPagePatch15} 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+\pastebutton{CartesianTensorXmpPageFull20}{\hidepaste} +\tab{5}\spadcommand{t0()\free{t0 }} +\indentrel{3}\begin{verbatim} + (20) 8 + Type: PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{CartesianTensorXmpPageEmpty20} +\begin{paste}{CartesianTensorXmpPageEmpty20}{CartesianTensorXmpPagePatch20} +\pastebutton{CartesianTensorXmpPageEmpty20}{\showpaste} +\tab{5}\spadcommand{t0()\free{t0 }} +\end{paste}\end{patch} + +\begin{patch}{CartesianTensorXmpPagePatch21} +\begin{paste}{CartesianTensorXmpPageFull21}{CartesianTensorXmpPageEmpty21} +\pastebutton{CartesianTensorXmpPageFull21}{\hidepaste} +\tab{5}\spadcommand{t1(1+1)\free{t1 }} +\indentrel{3}\begin{verbatim} + (21) 3 + Type: PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{CartesianTensorXmpPageEmpty21} +\begin{paste}{CartesianTensorXmpPageEmpty21}{CartesianTensorXmpPagePatch21} +\pastebutton{CartesianTensorXmpPageEmpty21}{\showpaste} 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+\pastebutton{CartesianTensorXmpPageFull25}{\hidepaste} +\tab{5}\spadcommand{t0[]\free{t0 }} +\indentrel{3}\begin{verbatim} + (25) 8 + Type: PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{CartesianTensorXmpPageEmpty25} +\begin{paste}{CartesianTensorXmpPageEmpty25}{CartesianTensorXmpPagePatch25} +\pastebutton{CartesianTensorXmpPageEmpty25}{\showpaste} +\tab{5}\spadcommand{t0[]\free{t0 }} +\end{paste}\end{patch} + +\begin{patch}{CartesianTensorXmpPagePatch26} +\begin{paste}{CartesianTensorXmpPageFull26}{CartesianTensorXmpPageEmpty26} +\pastebutton{CartesianTensorXmpPageFull26}{\hidepaste} +\tab{5}\spadcommand{t1[2]\free{t1 }} +\indentrel{3}\begin{verbatim} + (26) 3 + Type: PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{CartesianTensorXmpPageEmpty26} +\begin{paste}{CartesianTensorXmpPageEmpty26}{CartesianTensorXmpPagePatch26} +\pastebutton{CartesianTensorXmpPageEmpty26}{\showpaste} 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+\pastebutton{CartesianTensorXmpPageFull30}{\hidepaste} +\tab{5}\spadcommand{cTmn := contract(Tmn,1,2)\free{Tmn }\bound{cTmn }} +\indentrel{3}\begin{verbatim} + Ú12 18¿ + (30) ³ ³ + À0 6 Ù + Type: CartesianTensor(1,2,Integer) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{CartesianTensorXmpPageEmpty30} +\begin{paste}{CartesianTensorXmpPageEmpty30}{CartesianTensorXmpPagePatch30} +\pastebutton{CartesianTensorXmpPageEmpty30}{\showpaste} +\tab{5}\spadcommand{cTmn := contract(Tmn,1,2)\free{Tmn }\bound{cTmn }} +\end{paste}\end{patch} + +\begin{patch}{CartesianTensorXmpPagePatch31} +\begin{paste}{CartesianTensorXmpPageFull31}{CartesianTensorXmpPageEmpty31} +\pastebutton{CartesianTensorXmpPageFull31}{\hidepaste} +\tab{5}\spadcommand{trace(m) * n\free{m n }} +\indentrel{3}\begin{verbatim} + Ú12 18¿ + (31) ³ ³ + À0 6 Ù + Type: SquareMatrix(2,Integer) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{CartesianTensorXmpPageEmpty31} 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+\begin{paste}{CartesianTensorXmpPageEmpty42}{CartesianTensorXmpPagePatch42} +\pastebutton{CartesianTensorXmpPageEmpty42}{\showpaste} +\tab{5}\spadcommand{ +tt := transpose(Tm)*Tn - Tn*transpose(Tm)\free{Tm Tn }\bound{tt2 }} +\end{paste}\end{patch} + +\begin{patch}{CartesianTensorXmpPagePatch43} +\begin{paste}{CartesianTensorXmpPageFull43}{CartesianTensorXmpPageEmpty43} +\pastebutton{CartesianTensorXmpPageFull43}{\hidepaste} +\tab{5}\spadcommand{Tv*(tt+Tn)\free{tt2 Tv Tn }} +\indentrel{3}\begin{verbatim} + (43) [- 4,- 11] + Type: CartesianTensor(1,2,Integer) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{CartesianTensorXmpPageEmpty43} +\begin{paste}{CartesianTensorXmpPageEmpty43}{CartesianTensorXmpPagePatch43} +\pastebutton{CartesianTensorXmpPageEmpty43}{\showpaste} +\tab{5}\spadcommand{Tv*(tt+Tn)\free{tt2 Tv Tn }} +\end{paste}\end{patch} + +\begin{patch}{CartesianTensorXmpPagePatch44} +\begin{paste}{CartesianTensorXmpPageFull44}{CartesianTensorXmpPageEmpty44} +\pastebutton{CartesianTensorXmpPageFull44}{\hidepaste} +\tab{5}\spadcommand{ +reindex(product(Tn,Tn),[4,3,2,1])+3*Tn*product(Tm,Tm)\free{Tm Tn }} +\indentrel{3}\begin{verbatim} + ÚÚ46 84 ¿ Ú57 114¿¿ + ³³ ³ ³ ³³ + ³À174 212Ù À228 285Ù³ + (44) ³ ³ + ³ Ú18 24¿ Ú17 30¿ ³ + ³ ³ ³ ³ ³ ³ + À À57 63Ù À63 76Ù Ù + Type: CartesianTensor(1,2,Integer) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{CartesianTensorXmpPageEmpty44} +\begin{paste}{CartesianTensorXmpPageEmpty44}{CartesianTensorXmpPagePatch44} +\pastebutton{CartesianTensorXmpPageEmpty44}{\showpaste} +\tab{5}\spadcommand{ +reindex(product(Tn,Tn),[4,3,2,1])+3*Tn*product(Tm,Tm)\free{Tm Tn }} +\end{paste}\end{patch} + +\begin{patch}{CartesianTensorXmpPagePatch45} +\begin{paste}{CartesianTensorXmpPageFull45}{CartesianTensorXmpPageEmpty45} +\pastebutton{CartesianTensorXmpPageFull45}{\hidepaste} +\tab{5}\spadcommand{delta: CT := kroneckerDelta()\free{CT }\bound{delta }} +\indentrel{3}\begin{verbatim} + Ú1 0¿ + (45) ³ ³ + À0 1Ù + Type: CartesianTensor(1,2,Integer) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{CartesianTensorXmpPageEmpty45} +\begin{paste}{CartesianTensorXmpPageEmpty45}{CartesianTensorXmpPagePatch45} +\pastebutton{CartesianTensorXmpPageEmpty45}{\showpaste} +\tab{5}\spadcommand{delta: CT := kroneckerDelta()\free{CT }\bound{delta }} +\end{paste}\end{patch} + +\begin{patch}{CartesianTensorXmpPagePatch46} +\begin{paste}{CartesianTensorXmpPageFull46}{CartesianTensorXmpPageEmpty46} +\pastebutton{CartesianTensorXmpPageFull46}{\hidepaste} +\tab{5}\spadcommand{ +contract(Tmn, 2, delta, 1) = reindex(Tmn, [1,3,4,2])\free{Tmn delta }} +\indentrel{3}\begin{verbatim} + Ú Ú2 4¿ Ú0 0¿¿ Ú Ú2 4¿ Ú0 0¿¿ + ³ ³ ³ ³ ³³ ³ ³ ³ ³ ³³ + ³ À3 6Ù À1 2Ù³ ³ À3 6Ù À1 2Ù³ + (46) ³ ³= ³ ³ + ³Ú8 10¿ Ú0 0¿³ ³Ú8 10¿ Ú0 0¿³ + ³³ ³ ³ ³³ ³³ ³ ³ ³³ + ÀÀ12 15Ù À4 5ÙÙ ÀÀ12 15Ù À4 5ÙÙ + Type: Equation CartesianTensor(1,2,Integer) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{CartesianTensorXmpPageEmpty46} +\begin{paste}{CartesianTensorXmpPageEmpty46}{CartesianTensorXmpPagePatch46} +\pastebutton{CartesianTensorXmpPageEmpty46}{\showpaste} +\tab{5}\spadcommand{ +contract(Tmn, 2, delta, 1) = reindex(Tmn, [1,3,4,2])\free{Tmn delta }} +\end{paste}\end{patch} + +\begin{patch}{CartesianTensorXmpPagePatch47} +\begin{paste}{CartesianTensorXmpPageFull47}{CartesianTensorXmpPageEmpty47} +\pastebutton{CartesianTensorXmpPageFull47}{\hidepaste} +\tab{5}\spadcommand{ +epsilon:CT := leviCivitaSymbol()\free{CT }\bound{epsilon }} +\indentrel{3}\begin{verbatim} + Ú 0 1¿ + (47) ³ ³ + À- 1 0Ù + Type: CartesianTensor(1,2,Integer) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{CartesianTensorXmpPageEmpty47} +\begin{paste}{CartesianTensorXmpPageEmpty47} +{CartesianTensorXmpPagePatch47} +\pastebutton{CartesianTensorXmpPageEmpty47}{\showpaste} +\tab{5}\spadcommand{ +epsilon:CT := leviCivitaSymbol()\free{CT }\bound{epsilon }} +\end{paste}\end{patch} + +\begin{patch}{CartesianTensorXmpPagePatch48} +\begin{paste}{CartesianTensorXmpPageFull48}{CartesianTensorXmpPageEmpty48} +\pastebutton{CartesianTensorXmpPageFull48}{\hidepaste} +\tab{5}\spadcommand{ +contract(epsilon*Tm*epsilon, 1,2) = 2 * determinant m\free{epsilon Tm m }} +\indentrel{3}\begin{verbatim} + (48) - 6= - 6 + Type: Equation CartesianTensor(1,2,Integer) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{CartesianTensorXmpPageEmpty48} +\begin{paste}{CartesianTensorXmpPageEmpty48}{CartesianTensorXmpPagePatch48} +\pastebutton{CartesianTensorXmpPageEmpty48}{\showpaste} +\tab{5}\spadcommand{ +contract(epsilon*Tm*epsilon, 1,2) = 2 * determinant m\free{epsilon Tm m }} +\end{paste}\end{patch} + @ \section{cclass.ht} \pagehead{CharacterClassXmpPage}{cclass.ht}{CharacterClass} @@ -3604,6 +6404,269 @@ For more information on related topics, see \autobuttons \end{page} +\begin{patch}{CharacterClassXmpPagePatch1} +\begin{paste}{CharacterClassXmpPageFull1}{CharacterClassXmpPageEmpty1} +\pastebutton{CharacterClassXmpPageFull1}{\hidepaste} +\tab{5}\spadcommand{ +cl1:=charClass[char "a", char "e", char "i", char "o", char "u", char "y"] +\bound{cl1 }} +\indentrel{3}\begin{verbatim} + (1) "aeiouy" + Type: CharacterClass +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{CharacterClassXmpPageEmpty1} +\begin{paste}{CharacterClassXmpPageEmpty1}{CharacterClassXmpPagePatch1} +\pastebutton{CharacterClassXmpPageEmpty1}{\showpaste} +\tab{5}\spadcommand{ +cl1:=charClass [char "a", char "e", char "i", char "o", char "u", char "y"] +\bound{cl1 }} +\end{paste}\end{patch} + +\begin{patch}{CharacterClassXmpPagePatch2} +\begin{paste}{CharacterClassXmpPageFull2}{CharacterClassXmpPageEmpty2} +\pastebutton{CharacterClassXmpPageFull2}{\hidepaste} +\tab{5}\spadcommand{cl2 := charClass "bcdfghjklmnpqrstvwxyz"\bound{cl2 }} +\indentrel{3}\begin{verbatim} + (2) "bcdfghjklmnpqrstvwxyz" + Type: CharacterClass +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{CharacterClassXmpPageEmpty2} +\begin{paste}{CharacterClassXmpPageEmpty2}{CharacterClassXmpPagePatch2} +\pastebutton{CharacterClassXmpPageEmpty2}{\showpaste} +\tab{5}\spadcommand{cl2 := charClass "bcdfghjklmnpqrstvwxyz"\bound{cl2 }} +\end{paste}\end{patch} + +\begin{patch}{CharacterClassXmpPagePatch3} +\begin{paste}{CharacterClassXmpPageFull3}{CharacterClassXmpPageEmpty3} +\pastebutton{CharacterClassXmpPageFull3}{\hidepaste} +\tab{5}\spadcommand{digit()} +\indentrel{3}\begin{verbatim} + (3) "0123456789" + Type: CharacterClass +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{CharacterClassXmpPageEmpty3} +\begin{paste}{CharacterClassXmpPageEmpty3}{CharacterClassXmpPagePatch3} +\pastebutton{CharacterClassXmpPageEmpty3}{\showpaste} +\tab{5}\spadcommand{digit()} +\end{paste}\end{patch} + +\begin{patch}{CharacterClassXmpPagePatch4} +\begin{paste}{CharacterClassXmpPageFull4}{CharacterClassXmpPageEmpty4} +\pastebutton{CharacterClassXmpPageFull4}{\hidepaste} +\tab{5}\spadcommand{hexDigit()} +\indentrel{3}\begin{verbatim} + (4) "0123456789ABCDEFabcdef" + Type: CharacterClass +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{CharacterClassXmpPageEmpty4} +\begin{paste}{CharacterClassXmpPageEmpty4}{CharacterClassXmpPagePatch4} +\pastebutton{CharacterClassXmpPageEmpty4}{\showpaste} +\tab{5}\spadcommand{hexDigit()} +\end{paste}\end{patch} + +\begin{patch}{CharacterClassXmpPagePatch5} +\begin{paste}{CharacterClassXmpPageFull5}{CharacterClassXmpPageEmpty5} +\pastebutton{CharacterClassXmpPageFull5}{\hidepaste} +\tab{5}\spadcommand{upperCase()} +\indentrel{3}\begin{verbatim} + (5) "ABCDEFGHIJKLMNOPQRSTUVWXYZ" + Type: CharacterClass +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{CharacterClassXmpPageEmpty5} +\begin{paste}{CharacterClassXmpPageEmpty5}{CharacterClassXmpPagePatch5} +\pastebutton{CharacterClassXmpPageEmpty5}{\showpaste} +\tab{5}\spadcommand{upperCase()} +\end{paste}\end{patch} + +\begin{patch}{CharacterClassXmpPagePatch6} +\begin{paste}{CharacterClassXmpPageFull6}{CharacterClassXmpPageEmpty6} +\pastebutton{CharacterClassXmpPageFull6}{\hidepaste} +\tab{5}\spadcommand{lowerCase()} +\indentrel{3}\begin{verbatim} + (6) "abcdefghijklmnopqrstuvwxyz" + Type: CharacterClass +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{CharacterClassXmpPageEmpty6} +\begin{paste}{CharacterClassXmpPageEmpty6}{CharacterClassXmpPagePatch6} +\pastebutton{CharacterClassXmpPageEmpty6}{\showpaste} +\tab{5}\spadcommand{lowerCase()} +\end{paste}\end{patch} + +\begin{patch}{CharacterClassXmpPagePatch7} +\begin{paste}{CharacterClassXmpPageFull7}{CharacterClassXmpPageEmpty7} +\pastebutton{CharacterClassXmpPageFull7}{\hidepaste} +\tab{5}\spadcommand{alphabetic()} +\indentrel{3}\begin{verbatim} + (7) + "ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz" + Type: CharacterClass +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{CharacterClassXmpPageEmpty7} +\begin{paste}{CharacterClassXmpPageEmpty7}{CharacterClassXmpPagePatch7} +\pastebutton{CharacterClassXmpPageEmpty7}{\showpaste} +\tab{5}\spadcommand{alphabetic()} +\end{paste}\end{patch} + +\begin{patch}{CharacterClassXmpPagePatch8} +\begin{paste}{CharacterClassXmpPageFull8}{CharacterClassXmpPageEmpty8} +\pastebutton{CharacterClassXmpPageFull8}{\hidepaste} +\tab{5}\spadcommand{alphanumeric()} +\indentrel{3}\begin{verbatim} + (8) + "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqr + stuvwxyz" + Type: CharacterClass +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{CharacterClassXmpPageEmpty8} +\begin{paste}{CharacterClassXmpPageEmpty8}{CharacterClassXmpPagePatch8} +\pastebutton{CharacterClassXmpPageEmpty8}{\showpaste} +\tab{5}\spadcommand{alphanumeric()} +\end{paste}\end{patch} + +\begin{patch}{CharacterClassXmpPagePatch9} +\begin{paste}{CharacterClassXmpPageFull9}{CharacterClassXmpPageEmpty9} +\pastebutton{CharacterClassXmpPageFull9}{\hidepaste} +\tab{5}\spadcommand{member?(char "a", cl1)\free{cl1 }} +\indentrel{3}\begin{verbatim} + (9) true + Type: Boolean +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{CharacterClassXmpPageEmpty9} +\begin{paste}{CharacterClassXmpPageEmpty9}{CharacterClassXmpPagePatch9} +\pastebutton{CharacterClassXmpPageEmpty9}{\showpaste} +\tab{5}\spadcommand{member?(char "a", cl1)\free{cl1 }} +\end{paste}\end{patch} + +\begin{patch}{CharacterClassXmpPagePatch10} +\begin{paste}{CharacterClassXmpPageFull10}{CharacterClassXmpPageEmpty10} +\pastebutton{CharacterClassXmpPageFull10}{\hidepaste} +\tab{5}\spadcommand{member?(char "a", cl2)\free{cl2 }} +\indentrel{3}\begin{verbatim} + (10) false + Type: Boolean +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{CharacterClassXmpPageEmpty10} +\begin{paste}{CharacterClassXmpPageEmpty10}{CharacterClassXmpPagePatch10} +\pastebutton{CharacterClassXmpPageEmpty10}{\showpaste} +\tab{5}\spadcommand{member?(char "a", cl2)\free{cl2 }} +\end{paste}\end{patch} + +\begin{patch}{CharacterClassXmpPagePatch11} +\begin{paste}{CharacterClassXmpPageFull11}{CharacterClassXmpPageEmpty11} +\pastebutton{CharacterClassXmpPageFull11}{\hidepaste} +\tab{5}\spadcommand{intersect(cl1, cl2)\free{cl1 cl2 }} +\indentrel{3}\begin{verbatim} + (11) "y" + Type: CharacterClass +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{CharacterClassXmpPageEmpty11} +\begin{paste}{CharacterClassXmpPageEmpty11}{CharacterClassXmpPagePatch11} +\pastebutton{CharacterClassXmpPageEmpty11}{\showpaste} +\tab{5}\spadcommand{intersect(cl1, cl2)\free{cl1 cl2 }} +\end{paste}\end{patch} + +\begin{patch}{CharacterClassXmpPagePatch12} +\begin{paste}{CharacterClassXmpPageFull12}{CharacterClassXmpPageEmpty12} +\pastebutton{CharacterClassXmpPageFull12}{\hidepaste} +\tab{5}\spadcommand{union(cl1,cl2)\free{cl1 cl2 }} +\indentrel{3}\begin{verbatim} + (12) "abcdefghijklmnopqrstuvwxyz" + Type: CharacterClass +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{CharacterClassXmpPageEmpty12} +\begin{paste}{CharacterClassXmpPageEmpty12}{CharacterClassXmpPagePatch12} +\pastebutton{CharacterClassXmpPageEmpty12}{\showpaste} +\tab{5}\spadcommand{union(cl1,cl2)\free{cl1 cl2 }} +\end{paste}\end{patch} + +\begin{patch}{CharacterClassXmpPagePatch13} +\begin{paste}{CharacterClassXmpPageFull13}{CharacterClassXmpPageEmpty13} +\pastebutton{CharacterClassXmpPageFull13}{\hidepaste} +\tab{5}\spadcommand{difference(cl1,cl2)\free{cl1 cl2 }} +\indentrel{3}\begin{verbatim} + (13) "aeiou" + Type: CharacterClass +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{CharacterClassXmpPageEmpty13} +\begin{paste}{CharacterClassXmpPageEmpty13}{CharacterClassXmpPagePatch13} +\pastebutton{CharacterClassXmpPageEmpty13}{\showpaste} +\tab{5}\spadcommand{difference(cl1,cl2)\free{cl1 cl2 }} +\end{paste}\end{patch} + +\begin{patch}{CharacterClassXmpPagePatch14} +\begin{paste}{CharacterClassXmpPageFull14}{CharacterClassXmpPageEmpty14} +\pastebutton{CharacterClassXmpPageFull14}{\hidepaste} +\tab{5}\spadcommand{intersect(complement(cl1),cl2)\free{cl1 cl2 }} +\indentrel{3}\begin{verbatim} + (14) "bcdfghjklmnpqrstvwxz" + Type: CharacterClass +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{CharacterClassXmpPageEmpty14} +\begin{paste}{CharacterClassXmpPageEmpty14}{CharacterClassXmpPagePatch14} +\pastebutton{CharacterClassXmpPageEmpty14}{\showpaste} +\tab{5}\spadcommand{intersect(complement(cl1),cl2)\free{cl1 cl2 }} +\end{paste}\end{patch} + +\begin{patch}{CharacterClassXmpPagePatch15} +\begin{paste}{CharacterClassXmpPageFull15}{CharacterClassXmpPageEmpty15} +\pastebutton{CharacterClassXmpPageFull15}{\hidepaste} +\tab{5}\spadcommand{insert!(char "a", cl2)\free{cl2 }\bound{cl22 }} +\indentrel{3}\begin{verbatim} + (15) "abcdfghjklmnpqrstvwxyz" + Type: CharacterClass +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{CharacterClassXmpPageEmpty15} +\begin{paste}{CharacterClassXmpPageEmpty15}{CharacterClassXmpPagePatch15} +\pastebutton{CharacterClassXmpPageEmpty15}{\showpaste} +\tab{5}\spadcommand{insert!(char "a", cl2)\free{cl2 }\bound{cl22 }} +\end{paste}\end{patch} + +\begin{patch}{CharacterClassXmpPagePatch16} +\begin{paste}{CharacterClassXmpPageFull16}{CharacterClassXmpPageEmpty16} +\pastebutton{CharacterClassXmpPageFull16}{\hidepaste} +\tab{5}\spadcommand{remove!(char "b", cl2)\free{cl22 }\bound{cl23 }} +\indentrel{3}\begin{verbatim} + (16) "acdfghjklmnpqrstvwxyz" + Type: CharacterClass +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{CharacterClassXmpPageEmpty16} +\begin{paste}{CharacterClassXmpPageEmpty16}{CharacterClassXmpPagePatch16} +\pastebutton{CharacterClassXmpPageEmpty16}{\showpaste} +\tab{5}\spadcommand{remove!(char "b", cl2)\free{cl22 }\bound{cl23 }} +\end{paste}\end{patch} + @ \section{char.ht} \pagehead{CharacterXmpPage}{char.ht}{Character} @@ -3696,7 +6759,217 @@ belong to certain families. \endscroll \autobuttons \end{page} -% + +\begin{patch}{CharacterXmpPagePatch1} +\begin{paste}{CharacterXmpPageFull1}{CharacterXmpPageEmpty1} +\pastebutton{CharacterXmpPageFull1}{\hidepaste} +\tab{5}\spadcommand{ +chars := [char "a", char "A", char "X", char "8", char "+"]\bound{chars }} +\indentrel{3}\begin{verbatim} + (1) [a,A,X,8,+] + Type: List Character +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{CharacterXmpPageEmpty1} +\begin{paste}{CharacterXmpPageEmpty1}{CharacterXmpPagePatch1} +\pastebutton{CharacterXmpPageEmpty1}{\showpaste} +\tab{5}\spadcommand{ +chars := [char "a", char "A", char "X", char "8", char "+"]\bound{chars }} +\end{paste}\end{patch} + +\begin{patch}{CharacterXmpPagePatch2} +\begin{paste}{CharacterXmpPageFull2}{CharacterXmpPageEmpty2} +\pastebutton{CharacterXmpPageFull2}{\hidepaste} +\tab{5}\spadcommand{space()} +\indentrel{3}\begin{verbatim} + (2) + Type: Character +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{CharacterXmpPageEmpty2} +\begin{paste}{CharacterXmpPageEmpty2}{CharacterXmpPagePatch2} +\pastebutton{CharacterXmpPageEmpty2}{\showpaste} +\tab{5}\spadcommand{space()} +\end{paste}\end{patch} + +\begin{patch}{CharacterXmpPagePatch3} +\begin{paste}{CharacterXmpPageFull3}{CharacterXmpPageEmpty3} +\pastebutton{CharacterXmpPageFull3}{\hidepaste} +\tab{5}\spadcommand{quote()} +\indentrel{3}\begin{verbatim} + (3) " + Type: Character +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{CharacterXmpPageEmpty3} +\begin{paste}{CharacterXmpPageEmpty3}{CharacterXmpPagePatch3} +\pastebutton{CharacterXmpPageEmpty3}{\showpaste} +\tab{5}\spadcommand{quote()} +\end{paste}\end{patch} + +\begin{patch}{CharacterXmpPagePatch4} +\begin{paste}{CharacterXmpPageFull4}{CharacterXmpPageEmpty4} +\pastebutton{CharacterXmpPageFull4}{\hidepaste} +\tab{5}\spadcommand{escape()} +\indentrel{3}\begin{verbatim} + (4) _ + Type: Character +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{CharacterXmpPageEmpty4} +\begin{paste}{CharacterXmpPageEmpty4}{CharacterXmpPagePatch4} +\pastebutton{CharacterXmpPageEmpty4}{\showpaste} +\tab{5}\spadcommand{escape()} +\end{paste}\end{patch} + +\begin{patch}{CharacterXmpPagePatch5} +\begin{paste}{CharacterXmpPageFull5}{CharacterXmpPageEmpty5} +\pastebutton{CharacterXmpPageFull5}{\hidepaste} +\tab{5}\spadcommand{[ord c for c in chars]\free{chars }} +\indentrel{3}\begin{verbatim} + (5) [97,65,88,56,43] + Type: List Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{CharacterXmpPageEmpty5} +\begin{paste}{CharacterXmpPageEmpty5}{CharacterXmpPagePatch5} +\pastebutton{CharacterXmpPageEmpty5}{\showpaste} +\tab{5}\spadcommand{[ord c for c in chars]\free{chars }} +\end{paste}\end{patch} + +\begin{patch}{CharacterXmpPagePatch6} +\begin{paste}{CharacterXmpPageFull6}{CharacterXmpPageEmpty6} +\pastebutton{CharacterXmpPageFull6}{\hidepaste} +\tab{5}\spadcommand{[upperCase c for c in chars]\free{chars }} +\indentrel{3}\begin{verbatim} + (6) [A,A,X,8,+] + Type: List Character +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{CharacterXmpPageEmpty6} +\begin{paste}{CharacterXmpPageEmpty6}{CharacterXmpPagePatch6} +\pastebutton{CharacterXmpPageEmpty6}{\showpaste} +\tab{5}\spadcommand{[upperCase c for c in chars]\free{chars }} +\end{paste}\end{patch} + +\begin{patch}{CharacterXmpPagePatch7} +\begin{paste}{CharacterXmpPageFull7}{CharacterXmpPageEmpty7} +\pastebutton{CharacterXmpPageFull7}{\hidepaste} +\tab{5}\spadcommand{[lowerCase c for c in chars]\free{chars }} +\indentrel{3}\begin{verbatim} + (7) [a,a,x,8,+] + Type: List Character +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{CharacterXmpPageEmpty7} +\begin{paste}{CharacterXmpPageEmpty7}{CharacterXmpPagePatch7} +\pastebutton{CharacterXmpPageEmpty7}{\showpaste} +\tab{5}\spadcommand{[lowerCase c for c in chars]\free{chars }} +\end{paste}\end{patch} + +\begin{patch}{CharacterXmpPagePatch8} +\begin{paste}{CharacterXmpPageFull8}{CharacterXmpPageEmpty8} +\pastebutton{CharacterXmpPageFull8}{\hidepaste} +\tab{5}\spadcommand{[alphabetic? c for c in chars]\free{chars }} +\indentrel{3}\begin{verbatim} + (8) [true,true,true,false,false] + Type: List Boolean +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{CharacterXmpPageEmpty8} +\begin{paste}{CharacterXmpPageEmpty8}{CharacterXmpPagePatch8} +\pastebutton{CharacterXmpPageEmpty8}{\showpaste} +\tab{5}\spadcommand{[alphabetic? c for c in chars]\free{chars }} +\end{paste}\end{patch} + +\begin{patch}{CharacterXmpPagePatch9} +\begin{paste}{CharacterXmpPageFull9}{CharacterXmpPageEmpty9} +\pastebutton{CharacterXmpPageFull9}{\hidepaste} +\tab{5}\spadcommand{[upperCase? c for c in chars]\free{chars }} +\indentrel{3}\begin{verbatim} + (9) [false,true,true,false,false] + Type: List Boolean +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{CharacterXmpPageEmpty9} +\begin{paste}{CharacterXmpPageEmpty9}{CharacterXmpPagePatch9} +\pastebutton{CharacterXmpPageEmpty9}{\showpaste} +\tab{5}\spadcommand{[upperCase? c for c in chars]\free{chars }} +\end{paste}\end{patch} + +\begin{patch}{CharacterXmpPagePatch10} +\begin{paste}{CharacterXmpPageFull10}{CharacterXmpPageEmpty10} +\pastebutton{CharacterXmpPageFull10}{\hidepaste} +\tab{5}\spadcommand{[lowerCase? c for c in chars]\free{chars }} +\indentrel{3}\begin{verbatim} + (10) [true,false,false,false,false] + Type: List Boolean +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{CharacterXmpPageEmpty10} +\begin{paste}{CharacterXmpPageEmpty10}{CharacterXmpPagePatch10} +\pastebutton{CharacterXmpPageEmpty10}{\showpaste} +\tab{5}\spadcommand{[lowerCase? c for c in chars]\free{chars }} +\end{paste}\end{patch} + +\begin{patch}{CharacterXmpPagePatch11} +\begin{paste}{CharacterXmpPageFull11}{CharacterXmpPageEmpty11} +\pastebutton{CharacterXmpPageFull11}{\hidepaste} +\tab{5}\spadcommand{[digit? c for c in chars]\free{chars }} +\indentrel{3}\begin{verbatim} + (11) [false,false,false,true,false] + Type: List Boolean +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{CharacterXmpPageEmpty11} +\begin{paste}{CharacterXmpPageEmpty11}{CharacterXmpPagePatch11} +\pastebutton{CharacterXmpPageEmpty11}{\showpaste} +\tab{5}\spadcommand{[digit? c for c in chars]\free{chars }} +\end{paste}\end{patch} + +\begin{patch}{CharacterXmpPagePatch12} +\begin{paste}{CharacterXmpPageFull12}{CharacterXmpPageEmpty12} +\pastebutton{CharacterXmpPageFull12}{\hidepaste} +\tab{5}\spadcommand{[hexDigit? c for c in chars]\free{chars }} +\indentrel{3}\begin{verbatim} + (12) [true,true,false,true,false] + Type: List Boolean +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{CharacterXmpPageEmpty12} +\begin{paste}{CharacterXmpPageEmpty12}{CharacterXmpPagePatch12} +\pastebutton{CharacterXmpPageEmpty12}{\showpaste} +\tab{5}\spadcommand{[hexDigit? c for c in chars]\free{chars }} +\end{paste}\end{patch} + +\begin{patch}{CharacterXmpPagePatch13} +\begin{paste}{CharacterXmpPageFull13}{CharacterXmpPageEmpty13} +\pastebutton{CharacterXmpPageFull13}{\hidepaste} +\tab{5}\spadcommand{[alphanumeric? c for c in chars]\free{chars }} +\indentrel{3}\begin{verbatim} + (13) [true,true,true,true,false] + Type: List Boolean +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{CharacterXmpPageEmpty13} +\begin{paste}{CharacterXmpPageEmpty13}{CharacterXmpPagePatch13} +\pastebutton{CharacterXmpPageEmpty13}{\showpaste} +\tab{5}\spadcommand{[alphanumeric? c for c in chars]\free{chars }} +\end{paste}\end{patch} + @ \pagehead{CliffordAlgebraXmpPage}{clif.ht}{CliffordAlgebra} @@ -3801,6 +7074,125 @@ implementing complex numbers. \autobuttons \end{page} +\begin{patch}{ugxCliffordComplexPagePatch1} +\begin{paste}{ugxCliffordComplexPageFull1}{ugxCliffordComplexPageEmpty1} +\pastebutton{ugxCliffordComplexPageFull1}{\hidepaste} +\tab{5}\spadcommand{K := Fraction Polynomial Integer\bound{K }} +\indentrel{3}\begin{verbatim} + (1) Fraction Polynomial Integer + Type: Domain +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxCliffordComplexPageEmpty1} +\begin{paste}{ugxCliffordComplexPageEmpty1}{ugxCliffordComplexPagePatch1} +\pastebutton{ugxCliffordComplexPageEmpty1}{\showpaste} +\tab{5}\spadcommand{K := Fraction Polynomial Integer\bound{K }} +\end{paste}\end{patch} + +\begin{patch}{ugxCliffordComplexPagePatch2} +\begin{paste}{ugxCliffordComplexPageFull2}{ugxCliffordComplexPageEmpty2} +\pastebutton{ugxCliffordComplexPageFull2}{\hidepaste} +\tab{5}\spadcommand{m := matrix [[-1]]\bound{m }} +\indentrel{3}\begin{verbatim} + (2) [- 1] + Type: Matrix Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxCliffordComplexPageEmpty2} +\begin{paste}{ugxCliffordComplexPageEmpty2}{ugxCliffordComplexPagePatch2} +\pastebutton{ugxCliffordComplexPageEmpty2}{\showpaste} +\tab{5}\spadcommand{m := matrix [[-1]]\bound{m }} +\end{paste}\end{patch} + +\begin{patch}{ugxCliffordComplexPagePatch3} +\begin{paste}{ugxCliffordComplexPageFull3}{ugxCliffordComplexPageEmpty3} +\pastebutton{ugxCliffordComplexPageFull3}{\hidepaste} +\tab{5}\spadcommand{ +C := CliffordAlgebra(1, K, quadraticForm m)\free{K m }\bound{C }} +\indentrel{3}\begin{verbatim} + (3) + CliffordAlgebra(1,Fraction Polynomial Integer,MATRIX) + Type: Domain +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxCliffordComplexPageEmpty3} +\begin{paste}{ugxCliffordComplexPageEmpty3}{ugxCliffordComplexPagePatch3} +\pastebutton{ugxCliffordComplexPageEmpty3}{\showpaste} +\tab{5}\spadcommand{ +C := CliffordAlgebra(1, K, quadraticForm m)\free{K m }\bound{C }} +\end{paste}\end{patch} + +\begin{patch}{ugxCliffordComplexPagePatch4} +\begin{paste}{ugxCliffordComplexPageFull4}{ugxCliffordComplexPageEmpty4} +\pastebutton{ugxCliffordComplexPageFull4}{\hidepaste} +\tab{5}\spadcommand{i: C := e(1)\bound{i }\free{C }} +\indentrel{3}\begin{verbatim} + (4) e + 1 +Type: CliffordAlgebra(1,Fraction Polynomial Integer,MATRIX) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxCliffordComplexPageEmpty4} +\begin{paste}{ugxCliffordComplexPageEmpty4}{ugxCliffordComplexPagePatch4} +\pastebutton{ugxCliffordComplexPageEmpty4}{\showpaste} +\tab{5}\spadcommand{i: C := e(1)\bound{i }\free{C }} +\end{paste}\end{patch} + +\begin{patch}{ugxCliffordComplexPagePatch5} +\begin{paste}{ugxCliffordComplexPageFull5}{ugxCliffordComplexPageEmpty5} +\pastebutton{ugxCliffordComplexPageFull5}{\hidepaste} +\tab{5}\spadcommand{x := a + b * i\bound{x }\free{i }} +\indentrel{3}\begin{verbatim} + (5) a + b e + 1 +Type: CliffordAlgebra(1,Fraction Polynomial Integer,MATRIX) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxCliffordComplexPageEmpty5} +\begin{paste}{ugxCliffordComplexPageEmpty5}{ugxCliffordComplexPagePatch5} +\pastebutton{ugxCliffordComplexPageEmpty5}{\showpaste} +\tab{5}\spadcommand{x := a + b * i\bound{x }\free{i }} +\end{paste}\end{patch} + +\begin{patch}{ugxCliffordComplexPagePatch6} +\begin{paste}{ugxCliffordComplexPageFull6}{ugxCliffordComplexPageEmpty6} +\pastebutton{ugxCliffordComplexPageFull6}{\hidepaste} +\tab{5}\spadcommand{y := c + d * i\bound{y }\free{i }} +\indentrel{3}\begin{verbatim} + (6) c + d e + 1 +Type: CliffordAlgebra(1,Fraction Polynomial Integer,MATRIX) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxCliffordComplexPageEmpty6} +\begin{paste}{ugxCliffordComplexPageEmpty6}{ugxCliffordComplexPagePatch6} +\pastebutton{ugxCliffordComplexPageEmpty6}{\showpaste} +\tab{5}\spadcommand{y := c + d * i\bound{y }\free{i }} +\end{paste}\end{patch} + +\begin{patch}{ugxCliffordComplexPagePatch7} +\begin{paste}{ugxCliffordComplexPageFull7}{ugxCliffordComplexPageEmpty7} +\pastebutton{ugxCliffordComplexPageFull7}{\hidepaste} +\tab{5}\spadcommand{x * y\free{x y }} +\indentrel{3}\begin{verbatim} + (7) - b d + a c + (a d + b c)e + 1 +Type: CliffordAlgebra(1,Fraction Polynomial Integer,MATRIX) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxCliffordComplexPageEmpty7} +\begin{paste}{ugxCliffordComplexPageEmpty7}{ugxCliffordComplexPagePatch7} +\pastebutton{ugxCliffordComplexPageEmpty7}{\showpaste} +\tab{5}\spadcommand{x * y\free{x y }} +\end{paste}\end{patch} + @ \pagehead{ugxCliffordQuaternPage}{clif.ht} {The Quaternion Numbers as a Clifford Algebra} @@ -3868,6 +7260,206 @@ implementing quaternions. \autobuttons \end{page} +\begin{patch}{ugxCliffordQuaternPagePatch1} +\begin{paste}{ugxCliffordQuaternPageFull1}{ugxCliffordQuaternPageEmpty1} +\pastebutton{ugxCliffordQuaternPageFull1}{\hidepaste} +\tab{5}\spadcommand{K := Fraction Polynomial Integer\bound{K }} +\indentrel{3}\begin{verbatim} + (1) Fraction Polynomial Integer + Type: Domain +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxCliffordQuaternPageEmpty1} +\begin{paste}{ugxCliffordQuaternPageEmpty1}{ugxCliffordQuaternPagePatch1} +\pastebutton{ugxCliffordQuaternPageEmpty1}{\showpaste} +\tab{5}\spadcommand{K := Fraction Polynomial Integer\bound{K }} +\end{paste}\end{patch} + +\begin{patch}{ugxCliffordQuaternPagePatch2} +\begin{paste}{ugxCliffordQuaternPageFull2}{ugxCliffordQuaternPageEmpty2} +\pastebutton{ugxCliffordQuaternPageFull2}{\hidepaste} +\tab{5}\spadcommand{m := matrix [[-1,0],[0,-1]]\bound{m }} +\indentrel{3}\begin{verbatim} + Ú- 1 0 ¿ + (2) ³ ³ + À 0 - 1Ù + Type: Matrix Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxCliffordQuaternPageEmpty2} +\begin{paste}{ugxCliffordQuaternPageEmpty2}{ugxCliffordQuaternPagePatch2} +\pastebutton{ugxCliffordQuaternPageEmpty2}{\showpaste} +\tab{5}\spadcommand{m := matrix [[-1,0],[0,-1]]\bound{m }} +\end{paste}\end{patch} + +\begin{patch}{ugxCliffordQuaternPagePatch3} +\begin{paste}{ugxCliffordQuaternPageFull3}{ugxCliffordQuaternPageEmpty3} +\pastebutton{ugxCliffordQuaternPageFull3}{\hidepaste} +\tab{5}\spadcommand{ +H := CliffordAlgebra(2, K, quadraticForm m)\free{K m }\bound{H }} +\indentrel{3}\begin{verbatim} + (3) + CliffordAlgebra(2,Fraction Polynomial Integer,MATRIX) + Type: Domain +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxCliffordQuaternPageEmpty3} +\begin{paste}{ugxCliffordQuaternPageEmpty3}{ugxCliffordQuaternPagePatch3} +\pastebutton{ugxCliffordQuaternPageEmpty3}{\showpaste} +\tab{5}\spadcommand{ +H := CliffordAlgebra(2, K, quadraticForm m)\free{K m }\bound{H }} +\end{paste}\end{patch} + +\begin{patch}{ugxCliffordQuaternPagePatch4} +\begin{paste}{ugxCliffordQuaternPageFull4}{ugxCliffordQuaternPageEmpty4} +\pastebutton{ugxCliffordQuaternPageFull4}{\hidepaste} +\tab{5}\spadcommand{i: H := e(1)\free{H }\bound{i }} +\indentrel{3}\begin{verbatim} + (4) e + 1 +Type: CliffordAlgebra(2,Fraction Polynomial Integer,MATRIX) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxCliffordQuaternPageEmpty4} +\begin{paste}{ugxCliffordQuaternPageEmpty4}{ugxCliffordQuaternPagePatch4} +\pastebutton{ugxCliffordQuaternPageEmpty4}{\showpaste} +\tab{5}\spadcommand{i: H := e(1)\free{H }\bound{i }} +\end{paste}\end{patch} + +\begin{patch}{ugxCliffordQuaternPagePatch5} +\begin{paste}{ugxCliffordQuaternPageFull5}{ugxCliffordQuaternPageEmpty5} +\pastebutton{ugxCliffordQuaternPageFull5}{\hidepaste} +\tab{5}\spadcommand{j: H := e(2)\free{H }\bound{j }} +\indentrel{3}\begin{verbatim} + (5) e + 2 +Type: CliffordAlgebra(2,Fraction Polynomial Integer,MATRIX) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxCliffordQuaternPageEmpty5} +\begin{paste}{ugxCliffordQuaternPageEmpty5}{ugxCliffordQuaternPagePatch5} +\pastebutton{ugxCliffordQuaternPageEmpty5}{\showpaste} +\tab{5}\spadcommand{j: H := e(2)\free{H }\bound{j }} +\end{paste}\end{patch} + +\begin{patch}{ugxCliffordQuaternPagePatch6} +\begin{paste}{ugxCliffordQuaternPageFull6}{ugxCliffordQuaternPageEmpty6} +\pastebutton{ugxCliffordQuaternPageFull6}{\hidepaste} +\tab{5}\spadcommand{k: H := i * j\free{H i j }\bound{k }} +\indentrel{3}\begin{verbatim} + (6) e e + 1 2 +Type: CliffordAlgebra(2,Fraction Polynomial Integer,MATRIX) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxCliffordQuaternPageEmpty6} +\begin{paste}{ugxCliffordQuaternPageEmpty6}{ugxCliffordQuaternPagePatch6} +\pastebutton{ugxCliffordQuaternPageEmpty6}{\showpaste} +\tab{5}\spadcommand{k: H := i * j\free{H i j }\bound{k }} +\end{paste}\end{patch} + +\begin{patch}{ugxCliffordQuaternPagePatch7} +\begin{paste}{ugxCliffordQuaternPageFull7}{ugxCliffordQuaternPageEmpty7} +\pastebutton{ugxCliffordQuaternPageFull7}{\hidepaste} +\tab{5}\spadcommand{x := a + b * i + c * j + d * k\free{i j k }\bound{x }} +\indentrel{3}\begin{verbatim} + (7) a + b e + c e + d e e + 1 2 1 2 +Type: CliffordAlgebra(2,Fraction Polynomial Integer,MATRIX) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxCliffordQuaternPageEmpty7} +\begin{paste}{ugxCliffordQuaternPageEmpty7}{ugxCliffordQuaternPagePatch7} +\pastebutton{ugxCliffordQuaternPageEmpty7}{\showpaste} +\tab{5}\spadcommand{x := a + b * i + c * j + d * k\free{i j k }\bound{x }} +\end{paste}\end{patch} + +\begin{patch}{ugxCliffordQuaternPagePatch8} +\begin{paste}{ugxCliffordQuaternPageFull8}{ugxCliffordQuaternPageEmpty8} +\pastebutton{ugxCliffordQuaternPageFull8}{\hidepaste} +\tab{5}\spadcommand{y := e + f * i + g * j + h * k\free{i j k }\bound{y }} +\indentrel{3}\begin{verbatim} + (8) e + f e + g e + h e e + 1 2 1 2 +Type: CliffordAlgebra(2,Fraction Polynomial Integer,MATRIX) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxCliffordQuaternPageEmpty8} +\begin{paste}{ugxCliffordQuaternPageEmpty8}{ugxCliffordQuaternPagePatch8} +\pastebutton{ugxCliffordQuaternPageEmpty8}{\showpaste} +\tab{5}\spadcommand{y := e + f * i + g * j + h * k\free{i j k }\bound{y }} +\end{paste}\end{patch} + +\begin{patch}{ugxCliffordQuaternPagePatch9} +\begin{paste}{ugxCliffordQuaternPageFull9}{ugxCliffordQuaternPageEmpty9} +\pastebutton{ugxCliffordQuaternPageFull9}{\hidepaste} +\tab{5}\spadcommand{x + y\free{x y }} +\indentrel{3}\begin{verbatim} + (9) e + a + (f + b)e + (g + c)e + (h + d)e e + 1 2 1 2 +Type: CliffordAlgebra(2,Fraction Polynomial Integer,MATRIX) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxCliffordQuaternPageEmpty9} +\begin{paste}{ugxCliffordQuaternPageEmpty9}{ugxCliffordQuaternPagePatch9} +\pastebutton{ugxCliffordQuaternPageEmpty9}{\showpaste} +\tab{5}\spadcommand{x + y\free{x y }} +\end{paste}\end{patch} + +\begin{patch}{ugxCliffordQuaternPagePatch10} +\begin{paste}{ugxCliffordQuaternPageFull10}{ugxCliffordQuaternPageEmpty10} +\pastebutton{ugxCliffordQuaternPageFull10}{\hidepaste} +\tab{5}\spadcommand{x * y\free{x y }} +\indentrel{3}\begin{verbatim} + (10) + - d h - c g - b f + a e + (c h - d g + a f + b e)e + 1 + + + (- b h + a g + d f + c e)e + 2 + + + (a h + b g - c f + d e)e e + 1 2 +Type: CliffordAlgebra(2,Fraction Polynomial Integer,MATRIX) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxCliffordQuaternPageEmpty10} +\begin{paste}{ugxCliffordQuaternPageEmpty10}{ugxCliffordQuaternPagePatch10} +\pastebutton{ugxCliffordQuaternPageEmpty10}{\showpaste} +\tab{5}\spadcommand{x * y\free{x y }} +\end{paste}\end{patch} + +\begin{patch}{ugxCliffordQuaternPagePatch11} +\begin{paste}{ugxCliffordQuaternPageFull11}{ugxCliffordQuaternPageEmpty11} +\pastebutton{ugxCliffordQuaternPageFull11}{\hidepaste} +\tab{5}\spadcommand{y * x\free{x y }} +\indentrel{3}\begin{verbatim} + (11) + - d h - c g - b f + a e + (- c h + d g + a f + b e)e + 1 + + + (b h + a g - d f + c e)e + (a h - b g + c f + d e)e e + 2 1 2 +Type: CliffordAlgebra(2,Fraction Polynomial Integer,MATRIX) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxCliffordQuaternPageEmpty11} +\begin{paste}{ugxCliffordQuaternPageEmpty11}{ugxCliffordQuaternPagePatch11} +\pastebutton{ugxCliffordQuaternPageEmpty11}{\showpaste} +\tab{5}\spadcommand{y * x\free{x y }} +\end{paste}\end{patch} + @ \pagehead{ugxCliffordExteriorPage}{clif.ht} {The Exterior Algebra on a Three Space} @@ -3938,6 +7530,199 @@ The vector cross product is then given by this. \autobuttons \end{page} +\begin{patch}{ugxCliffordExteriorPagePatch1} +\begin{paste}{ugxCliffordExteriorPageFull1}{ugxCliffordExteriorPageEmpty1} +\pastebutton{ugxCliffordExteriorPageFull1}{\hidepaste} +\tab{5}\spadcommand{K := Fraction Polynomial Integer\bound{K }} +\indentrel{3}\begin{verbatim} + (1) Fraction Polynomial Integer + Type: Domain +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxCliffordExteriorPageEmpty1} +\begin{paste}{ugxCliffordExteriorPageEmpty1}{ugxCliffordExteriorPagePatch1} +\pastebutton{ugxCliffordExteriorPageEmpty1}{\showpaste} +\tab{5}\spadcommand{K := Fraction Polynomial Integer\bound{K }} +\end{paste}\end{patch} + +\begin{patch}{ugxCliffordExteriorPagePatch2} +\begin{paste}{ugxCliffordExteriorPageFull2}{ugxCliffordExteriorPageEmpty2} +\pastebutton{ugxCliffordExteriorPageFull2}{\hidepaste} +\tab{5}\spadcommand{ +Ext := CliffordAlgebra(3, K, quadraticForm 0)\bound{Ext }\free{K }} +\indentrel{3}\begin{verbatim} + (2) + CliffordAlgebra(3,Fraction Polynomial Integer,MATRIX) + Type: Domain +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxCliffordExteriorPageEmpty2} +\begin{paste}{ugxCliffordExteriorPageEmpty2}{ugxCliffordExteriorPagePatch2} +\pastebutton{ugxCliffordExteriorPageEmpty2}{\showpaste} +\tab{5}\spadcommand{ +Ext := CliffordAlgebra(3, K, quadraticForm 0)\bound{Ext }\free{K }} +\end{paste}\end{patch} + +\begin{patch}{ugxCliffordExteriorPagePatch3} +\begin{paste}{ugxCliffordExteriorPageFull3}{ugxCliffordExteriorPageEmpty3} +\pastebutton{ugxCliffordExteriorPageFull3}{\hidepaste} +\tab{5}\spadcommand{i: Ext := e(1)\free{Ext }\bound{i }} +\indentrel{3}\begin{verbatim} + (3) e + 1 +Type: CliffordAlgebra(3,Fraction Polynomial Integer,MATRIX) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxCliffordExteriorPageEmpty3} +\begin{paste}{ugxCliffordExteriorPageEmpty3}{ugxCliffordExteriorPagePatch3} +\pastebutton{ugxCliffordExteriorPageEmpty3}{\showpaste} +\tab{5}\spadcommand{i: Ext := e(1)\free{Ext }\bound{i }} +\end{paste}\end{patch} + +\begin{patch}{ugxCliffordExteriorPagePatch4} +\begin{paste}{ugxCliffordExteriorPageFull4}{ugxCliffordExteriorPageEmpty4} +\pastebutton{ugxCliffordExteriorPageFull4}{\hidepaste} +\tab{5}\spadcommand{j: Ext := e(2)\free{Ext }\bound{j }} +\indentrel{3}\begin{verbatim} + (4) e + 2 +Type: CliffordAlgebra(3,Fraction Polynomial Integer,MATRIX) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxCliffordExteriorPageEmpty4} +\begin{paste}{ugxCliffordExteriorPageEmpty4}{ugxCliffordExteriorPagePatch4} +\pastebutton{ugxCliffordExteriorPageEmpty4}{\showpaste} +\tab{5}\spadcommand{j: Ext := e(2)\free{Ext }\bound{j }} +\end{paste}\end{patch} + +\begin{patch}{ugxCliffordExteriorPagePatch5} +\begin{paste}{ugxCliffordExteriorPageFull5}{ugxCliffordExteriorPageEmpty5} +\pastebutton{ugxCliffordExteriorPageFull5}{\hidepaste} +\tab{5}\spadcommand{k: Ext := e(3)\free{Ext }\bound{k }} +\indentrel{3}\begin{verbatim} + (5) e + 3 +Type: CliffordAlgebra(3,Fraction Polynomial Integer,MATRIX) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxCliffordExteriorPageEmpty5} +\begin{paste}{ugxCliffordExteriorPageEmpty5}{ugxCliffordExteriorPagePatch5} +\pastebutton{ugxCliffordExteriorPageEmpty5}{\showpaste} +\tab{5}\spadcommand{k: Ext := e(3)\free{Ext }\bound{k }} +\end{paste}\end{patch} + +\begin{patch}{ugxCliffordExteriorPagePatch6} +\begin{paste}{ugxCliffordExteriorPageFull6}{ugxCliffordExteriorPageEmpty6} +\pastebutton{ugxCliffordExteriorPageFull6}{\hidepaste} +\tab{5}\spadcommand{x := x1*i + x2*j + x3*k\free{i j k }\bound{x }} +\indentrel{3}\begin{verbatim} + (6) x1 e + x2 e + x3 e + 1 2 3 +Type: CliffordAlgebra(3,Fraction Polynomial Integer,MATRIX) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxCliffordExteriorPageEmpty6} +\begin{paste}{ugxCliffordExteriorPageEmpty6}{ugxCliffordExteriorPagePatch6} +\pastebutton{ugxCliffordExteriorPageEmpty6}{\showpaste} +\tab{5}\spadcommand{x := x1*i + x2*j + x3*k\free{i j k }\bound{x }} +\end{paste}\end{patch} + +\begin{patch}{ugxCliffordExteriorPagePatch7} +\begin{paste}{ugxCliffordExteriorPageFull7}{ugxCliffordExteriorPageEmpty7} +\pastebutton{ugxCliffordExteriorPageFull7}{\hidepaste} +\tab{5}\spadcommand{y := y1*i + y2*j + y3*k\free{i j k }\bound{y }} +\indentrel{3}\begin{verbatim} + (7) y1 e + y2 e + y3 e + 1 2 3 +Type: CliffordAlgebra(3,Fraction Polynomial Integer,MATRIX) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxCliffordExteriorPageEmpty7} +\begin{paste}{ugxCliffordExteriorPageEmpty7}{ugxCliffordExteriorPagePatch7} +\pastebutton{ugxCliffordExteriorPageEmpty7}{\showpaste} +\tab{5}\spadcommand{y := y1*i + y2*j + y3*k\free{i j k }\bound{y }} +\end{paste}\end{patch} + +\begin{patch}{ugxCliffordExteriorPagePatch8} +\begin{paste}{ugxCliffordExteriorPageFull8}{ugxCliffordExteriorPageEmpty8} +\pastebutton{ugxCliffordExteriorPageFull8}{\hidepaste} +\tab{5}\spadcommand{x + y\free{x y }} +\indentrel{3}\begin{verbatim} + (8) (y1 + x1)e + (y2 + x2)e + (y3 + x3)e + 1 2 3 +Type: CliffordAlgebra(3,Fraction Polynomial Integer,MATRIX) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxCliffordExteriorPageEmpty8} +\begin{paste}{ugxCliffordExteriorPageEmpty8}{ugxCliffordExteriorPagePatch8} +\pastebutton{ugxCliffordExteriorPageEmpty8}{\showpaste} +\tab{5}\spadcommand{x + y\free{x y }} +\end{paste}\end{patch} + +\begin{patch}{ugxCliffordExteriorPagePatch9} +\begin{paste}{ugxCliffordExteriorPageFull9}{ugxCliffordExteriorPageEmpty9} +\pastebutton{ugxCliffordExteriorPageFull9}{\hidepaste} +\tab{5}\spadcommand{x * y + y * x\free{x y }} +\indentrel{3}\begin{verbatim} + (9) 0 +Type: CliffordAlgebra(3,Fraction Polynomial Integer,MATRIX) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxCliffordExteriorPageEmpty9} +\begin{paste}{ugxCliffordExteriorPageEmpty9}{ugxCliffordExteriorPagePatch9} +\pastebutton{ugxCliffordExteriorPageEmpty9}{\showpaste} +\tab{5}\spadcommand{x * y + y * x\free{x y }} +\end{paste}\end{patch} + +\begin{patch}{ugxCliffordExteriorPagePatch10} +\begin{paste}{ugxCliffordExteriorPageFull10}{ugxCliffordExteriorPageEmpty10} +\pastebutton{ugxCliffordExteriorPageFull10}{\hidepaste} +\tab{5}\spadcommand{ +dual2 a == coefficient(a,[2,3]) * i + coefficient(a,[3,1]) * _ + j + coefficient(a,[1,2]) * k\free{i j k }\bound{dual2 }} +\indentrel{3}\begin{verbatim} + Type: Void +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxCliffordExteriorPageEmpty10} +\begin{paste}{ugxCliffordExteriorPageEmpty10}{ugxCliffordExteriorPagePatch10} +\pastebutton{ugxCliffordExteriorPageEmpty10}{\showpaste} +\tab{5}\spadcommand{ +dual2 a == coefficient(a,[2,3]) * i + coefficient(a,[3,1]) * _ + j + coefficient(a,[1,2]) * k\free{i j k }\bound{dual2 }} +\end{paste}\end{patch} + +\begin{patch}{ugxCliffordExteriorPagePatch11} +\begin{paste}{ugxCliffordExteriorPageFull11}{ugxCliffordExteriorPageEmpty11} +\pastebutton{ugxCliffordExteriorPageFull11}{\hidepaste} +\tab{5}\spadcommand{dual2(x*y)\free{x y dual2 }} +\indentrel{3}\begin{verbatim} + (11) + (x2 y3 - x3 y2)e + (- x1 y3 + x3 y1)e + 1 2 + + + (x1 y2 - x2 y1)e + 3 +Type: CliffordAlgebra(3,Fraction Polynomial Integer,MATRIX) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxCliffordExteriorPageEmpty11} +\begin{paste}{ugxCliffordExteriorPageEmpty11}{ugxCliffordExteriorPagePatch11} +\pastebutton{ugxCliffordExteriorPageEmpty11}{\showpaste} +\tab{5}\spadcommand{dual2(x*y)\free{x y dual2 }} +\end{paste}\end{patch} + @ \pagehead{ugxCliffordDiracPage}{clif.ht}{The Dirac Spin Algebra} <>= @@ -4000,6 +7785,139 @@ for t in 1..4]) \bound{lhs}\free{g gam m n r s}} \autobuttons \end{page} +\begin{patch}{ugxCliffordDiracPagePatch1} +\begin{paste}{ugxCliffordDiracPageFull1}{ugxCliffordDiracPageEmpty1} +\pastebutton{ugxCliffordDiracPageFull1}{\hidepaste} +\tab{5}\spadcommand{K := Fraction Integer\bound{K }} +\indentrel{3}\begin{verbatim} + (1) Fraction Integer + Type: Domain +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxCliffordDiracPageEmpty1} +\begin{paste}{ugxCliffordDiracPageEmpty1}{ugxCliffordDiracPagePatch1} +\pastebutton{ugxCliffordDiracPageEmpty1}{\showpaste} +\tab{5}\spadcommand{K := Fraction Integer\bound{K }} +\end{paste}\end{patch} + +\begin{patch}{ugxCliffordDiracPagePatch2} +\begin{paste}{ugxCliffordDiracPageFull2}{ugxCliffordDiracPageEmpty2} +\pastebutton{ugxCliffordDiracPageFull2}{\hidepaste} +\tab{5}\spadcommand{g := matrix [[1,0,0,0], [0,-1,0,0], [0,0,-1,0], [0,0,0,-1]]\bound{g }} +\indentrel{3}\begin{verbatim} + Ú1 0 0 0 ¿ + ³ ³ + ³0 - 1 0 0 ³ + (2) ³ ³ + ³0 0 - 1 0 ³ + ³ ³ + À0 0 0 - 1Ù + Type: Matrix Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxCliffordDiracPageEmpty2} +\begin{paste}{ugxCliffordDiracPageEmpty2}{ugxCliffordDiracPagePatch2} +\pastebutton{ugxCliffordDiracPageEmpty2}{\showpaste} +\tab{5}\spadcommand{ +g := matrix [[1,0,0,0], [0,-1,0,0], [0,0,-1,0], [0,0,0,-1]]\bound{g }} +\end{paste}\end{patch} + +\begin{patch}{ugxCliffordDiracPagePatch3} +\begin{paste}{ugxCliffordDiracPageFull3}{ugxCliffordDiracPageEmpty3} +\pastebutton{ugxCliffordDiracPageFull3}{\hidepaste} +\tab{5}\spadcommand{ +D := CliffordAlgebra(4,K, quadraticForm g)\free{K g }\bound{D }} +\indentrel{3}\begin{verbatim} + (3) CliffordAlgebra(4,Fraction Integer,MATRIX) + Type: Domain +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxCliffordDiracPageEmpty3} +\begin{paste}{ugxCliffordDiracPageEmpty3}{ugxCliffordDiracPagePatch3} +\pastebutton{ugxCliffordDiracPageEmpty3}{\showpaste} +\tab{5}\spadcommand{ +D := CliffordAlgebra(4,K, quadraticForm g)\free{K g }\bound{D }} +\end{paste}\end{patch} + +\begin{patch}{ugxCliffordDiracPagePatch4} +\begin{paste}{ugxCliffordDiracPageFull4}{ugxCliffordDiracPageEmpty4} +\pastebutton{ugxCliffordDiracPageFull4}{\hidepaste} +\tab{5}\spadcommand{gam := [e(i)$D for i in 1..4]\free{D }\bound{gam }} +\indentrel{3}\begin{verbatim} + (4) [e ,e ,e ,e ] + 1 2 3 4 + Type: List CliffordAlgebra(4,Fraction Integer,MATRIX) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxCliffordDiracPageEmpty4} +\begin{paste}{ugxCliffordDiracPageEmpty4}{ugxCliffordDiracPagePatch4} +\pastebutton{ugxCliffordDiracPageEmpty4}{\showpaste} +\tab{5}\spadcommand{gam := [e(i)$D for i in 1..4]\free{D }\bound{gam }} +\end{paste}\end{patch} + +\begin{patch}{ugxCliffordDiracPagePatch5} +\begin{paste}{ugxCliffordDiracPageFull5}{ugxCliffordDiracPageEmpty5} +\pastebutton{ugxCliffordDiracPageFull5}{\hidepaste} +\tab{5}\spadcommand{m := 1; n:= 2; r := 3; s := 4;\bound{m n r s }} +\indentrel{3}\begin{verbatim} + Type: PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxCliffordDiracPageEmpty5} +\begin{paste}{ugxCliffordDiracPageEmpty5}{ugxCliffordDiracPagePatch5} +\pastebutton{ugxCliffordDiracPageEmpty5}{\showpaste} +\tab{5}\spadcommand{m := 1; n:= 2; r := 3; s := 4;\bound{m n r s }} +\end{paste}\end{patch} + +\begin{patch}{ugxCliffordDiracPagePatch6} +\begin{paste}{ugxCliffordDiracPageFull6}{ugxCliffordDiracPageEmpty6} +\pastebutton{ugxCliffordDiracPageFull6}{\hidepaste} +\tab{5}\spadcommand{ +lhs := reduce(+, [reduce(+, _ + [ g(l,t)*gam(l)*gam(m)*gam(n)*gam(r)*gam(s)*gam(t) for l in 1..4]) _ + for t in 1..4])\bound{lhs }\free{g gam m n r s }} +\indentrel{3}\begin{verbatim} + (6) - 4e e e e + 1 2 3 4 + Type: CliffordAlgebra(4,Fraction Integer,MATRIX) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxCliffordDiracPageEmpty6} +\begin{paste}{ugxCliffordDiracPageEmpty6}{ugxCliffordDiracPagePatch6} +\pastebutton{ugxCliffordDiracPageEmpty6}{\showpaste} +\tab{5}\spadcommand{ +lhs := reduce(+, [reduce(+, _ + [ g(l,t)*gam(l)*gam(m)*gam(n)*gam(r)*gam(s)*gam(t) for l in 1..4]) _ + for t in 1..4])\bound{lhs }\free{g gam m n r s }} +\end{paste}\end{patch} + +\begin{patch}{ugxCliffordDiracPagePatch7} +\begin{paste}{ugxCliffordDiracPageFull7}{ugxCliffordDiracPageEmpty7} +\pastebutton{ugxCliffordDiracPageFull7}{\hidepaste} +\tab{5}\spadcommand{ +rhs := 2*(gam s * gam m*gam n*gam r + gam r*gam n*gam m*gam s) +\bound{rhs }\free{lhs g gam m n r s }} +\indentrel{3}\begin{verbatim} + (7) - 4e e e e + 1 2 3 4 + Type: CliffordAlgebra(4,Fraction Integer,MATRIX) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxCliffordDiracPageEmpty7} +\begin{paste}{ugxCliffordDiracPageEmpty7}{ugxCliffordDiracPagePatch7} +\pastebutton{ugxCliffordDiracPageEmpty7}{\showpaste} +\tab{5}\spadcommand{ +rhs := 2*(gam s * gam m*gam n*gam r + gam r*gam n*gam m*gam s) +\bound{rhs }\free{lhs g gam m n r s }} +\end{paste}\end{patch} + @ \section{complex.ht} \pagehead{ComplexXmpPage}{complex.ht}{Complex} @@ -4107,6 +8025,283 @@ You can \spadfunFrom{factor}{Complex} Gaussian integers. \autobuttons \end{page} +\begin{patch}{ComplexXmpPagePatch1} +\begin{paste}{ComplexXmpPageFull1}{ComplexXmpPageEmpty1} +\pastebutton{ComplexXmpPageFull1}{\hidepaste} +\tab{5}\spadcommand{a := complex(4/3,5/2)\bound{a }} +\indentrel{3}\begin{verbatim} + 4 5 + (1) Ä + Ä %i + 3 2 + Type: Complex Fraction Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ComplexXmpPageEmpty1} +\begin{paste}{ComplexXmpPageEmpty1}{ComplexXmpPagePatch1} +\pastebutton{ComplexXmpPageEmpty1}{\showpaste} +\tab{5}\spadcommand{a := complex(4/3,5/2)\bound{a }} +\end{paste}\end{patch} + +\begin{patch}{ComplexXmpPagePatch2} +\begin{paste}{ComplexXmpPageFull2}{ComplexXmpPageEmpty2} +\pastebutton{ComplexXmpPageFull2}{\hidepaste} +\tab{5}\spadcommand{b := complex(4/3,-5/2)\bound{b }} +\indentrel{3}\begin{verbatim} + 4 5 + (2) Ä - Ä %i + 3 2 + Type: Complex Fraction Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ComplexXmpPageEmpty2} +\begin{paste}{ComplexXmpPageEmpty2}{ComplexXmpPagePatch2} +\pastebutton{ComplexXmpPageEmpty2}{\showpaste} +\tab{5}\spadcommand{b := complex(4/3,-5/2)\bound{b }} +\end{paste}\end{patch} + +\begin{patch}{ComplexXmpPagePatch3} +\begin{paste}{ComplexXmpPageFull3}{ComplexXmpPageEmpty3} +\pastebutton{ComplexXmpPageFull3}{\hidepaste} +\tab{5}\spadcommand{a + b\free{a b }} +\indentrel{3}\begin{verbatim} + 8 + (3) Ä + 3 + Type: Complex Fraction Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ComplexXmpPageEmpty3} +\begin{paste}{ComplexXmpPageEmpty3}{ComplexXmpPagePatch3} +\pastebutton{ComplexXmpPageEmpty3}{\showpaste} +\tab{5}\spadcommand{a + b\free{a b }} +\end{paste}\end{patch} + +\begin{patch}{ComplexXmpPagePatch4} +\begin{paste}{ComplexXmpPageFull4}{ComplexXmpPageEmpty4} +\pastebutton{ComplexXmpPageFull4}{\hidepaste} +\tab{5}\spadcommand{a - b\free{a b }} +\indentrel{3}\begin{verbatim} + (4) 5%i + Type: Complex Fraction Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ComplexXmpPageEmpty4} +\begin{paste}{ComplexXmpPageEmpty4}{ComplexXmpPagePatch4} +\pastebutton{ComplexXmpPageEmpty4}{\showpaste} +\tab{5}\spadcommand{a - b\free{a b }} +\end{paste}\end{patch} + +\begin{patch}{ComplexXmpPagePatch5} +\begin{paste}{ComplexXmpPageFull5}{ComplexXmpPageEmpty5} +\pastebutton{ComplexXmpPageFull5}{\hidepaste} +\tab{5}\spadcommand{a * b\free{a b }} +\indentrel{3}\begin{verbatim} + 289 + (5) ÄÄÄ + 36 + Type: Complex Fraction Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ComplexXmpPageEmpty5} +\begin{paste}{ComplexXmpPageEmpty5}{ComplexXmpPagePatch5} +\pastebutton{ComplexXmpPageEmpty5}{\showpaste} +\tab{5}\spadcommand{a * b\free{a b }} +\end{paste}\end{patch} + +\begin{patch}{ComplexXmpPagePatch6} +\begin{paste}{ComplexXmpPageFull6}{ComplexXmpPageEmpty6} +\pastebutton{ComplexXmpPageFull6}{\hidepaste} +\tab{5}\spadcommand{a / b\free{a b }\bound{adb }} +\indentrel{3}\begin{verbatim} + 161 240 + (6) - ÄÄÄ + ÄÄÄ %i + 289 289 + Type: Complex Fraction Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ComplexXmpPageEmpty6} +\begin{paste}{ComplexXmpPageEmpty6}{ComplexXmpPagePatch6} +\pastebutton{ComplexXmpPageEmpty6}{\showpaste} +\tab{5}\spadcommand{a / b\free{a b }\bound{adb }} +\end{paste}\end{patch} + +\begin{patch}{ComplexXmpPagePatch7} +\begin{paste}{ComplexXmpPageFull7}{ComplexXmpPageEmpty7} +\pastebutton{ComplexXmpPageFull7}{\hidepaste} +\tab{5}\spadcommand{\% :: Fraction Complex Integer\free{adb }} +\indentrel{3}\begin{verbatim} + - 15 + 8%i + (7) ÄÄÄÄÄÄÄÄÄÄ + 15 + 8%i + Type: Fraction Complex Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ComplexXmpPageEmpty7} +\begin{paste}{ComplexXmpPageEmpty7}{ComplexXmpPagePatch7} +\pastebutton{ComplexXmpPageEmpty7}{\showpaste} +\tab{5}\spadcommand{\% :: Fraction Complex Integer\free{adb }} +\end{paste}\end{patch} + +\begin{patch}{ComplexXmpPagePatch8} +\begin{paste}{ComplexXmpPageFull8}{ComplexXmpPageEmpty8} +\pastebutton{ComplexXmpPageFull8}{\hidepaste} +\tab{5}\spadcommand{3.4 + 6.7 * \%i} +\indentrel{3}\begin{verbatim} + (8) 3.4 + 6.7 %i + Type: Complex Float +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ComplexXmpPageEmpty8} +\begin{paste}{ComplexXmpPageEmpty8}{ComplexXmpPagePatch8} +\pastebutton{ComplexXmpPageEmpty8}{\showpaste} +\tab{5}\spadcommand{3.4 + 6.7 * \%i} +\end{paste}\end{patch} + +\begin{patch}{ComplexXmpPagePatch9} +\begin{paste}{ComplexXmpPageFull9}{ComplexXmpPageEmpty9} +\pastebutton{ComplexXmpPageFull9}{\hidepaste} +\tab{5}\spadcommand{conjugate a\free{a }} +\indentrel{3}\begin{verbatim} + 4 5 + (9) Ä - Ä %i + 3 2 + Type: Complex Fraction Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ComplexXmpPageEmpty9} +\begin{paste}{ComplexXmpPageEmpty9}{ComplexXmpPagePatch9} +\pastebutton{ComplexXmpPageEmpty9}{\showpaste} +\tab{5}\spadcommand{conjugate a\free{a }} +\end{paste}\end{patch} + +\begin{patch}{ComplexXmpPagePatch10} +\begin{paste}{ComplexXmpPageFull10}{ComplexXmpPageEmpty10} +\pastebutton{ComplexXmpPageFull10}{\hidepaste} +\tab{5}\spadcommand{norm a\free{a }} +\indentrel{3}\begin{verbatim} + 289 + (10) ÄÄÄ + 36 + Type: Fraction Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ComplexXmpPageEmpty10} +\begin{paste}{ComplexXmpPageEmpty10}{ComplexXmpPagePatch10} +\pastebutton{ComplexXmpPageEmpty10}{\showpaste} +\tab{5}\spadcommand{norm a\free{a }} +\end{paste}\end{patch} + +\begin{patch}{ComplexXmpPagePatch11} +\begin{paste}{ComplexXmpPageFull11}{ComplexXmpPageEmpty11} +\pastebutton{ComplexXmpPageFull11}{\hidepaste} +\tab{5}\spadcommand{real a\free{a }} +\indentrel{3}\begin{verbatim} + 4 + (11) Ä + 3 + Type: Fraction Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ComplexXmpPageEmpty11} +\begin{paste}{ComplexXmpPageEmpty11}{ComplexXmpPagePatch11} +\pastebutton{ComplexXmpPageEmpty11}{\showpaste} +\tab{5}\spadcommand{real a\free{a }} +\end{paste}\end{patch} + +\begin{patch}{ComplexXmpPagePatch12} +\begin{paste}{ComplexXmpPageFull12}{ComplexXmpPageEmpty12} +\pastebutton{ComplexXmpPageFull12}{\hidepaste} +\tab{5}\spadcommand{imag a\free{a }} +\indentrel{3}\begin{verbatim} + 5 + (12) Ä + 2 + Type: Fraction Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ComplexXmpPageEmpty12} +\begin{paste}{ComplexXmpPageEmpty12}{ComplexXmpPagePatch12} +\pastebutton{ComplexXmpPageEmpty12}{\showpaste} +\tab{5}\spadcommand{imag a\free{a }} +\end{paste}\end{patch} + +\begin{patch}{ComplexXmpPagePatch13} +\begin{paste}{ComplexXmpPageFull13}{ComplexXmpPageEmpty13} +\pastebutton{ComplexXmpPageFull13}{\hidepaste} +\tab{5}\spadcommand{gcd(13 - 13*\%i,31 + 27*\%i)} +\indentrel{3}\begin{verbatim} + (13) 5 + %i + Type: Complex Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ComplexXmpPageEmpty13} +\begin{paste}{ComplexXmpPageEmpty13}{ComplexXmpPagePatch13} +\pastebutton{ComplexXmpPageEmpty13}{\showpaste} +\tab{5}\spadcommand{gcd(13 - 13*\%i,31 + 27*\%i)} +\end{paste}\end{patch} + +\begin{patch}{ComplexXmpPagePatch14} +\begin{paste}{ComplexXmpPageFull14}{ComplexXmpPageEmpty14} +\pastebutton{ComplexXmpPageFull14}{\hidepaste} +\tab{5}\spadcommand{lcm(13 - 13*\%i,31 + 27*\%i)} +\indentrel{3}\begin{verbatim} + (14) 143 - 39%i + Type: Complex Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ComplexXmpPageEmpty14} +\begin{paste}{ComplexXmpPageEmpty14}{ComplexXmpPagePatch14} +\pastebutton{ComplexXmpPageEmpty14}{\showpaste} +\tab{5}\spadcommand{lcm(13 - 13*\%i,31 + 27*\%i)} +\end{paste}\end{patch} + +\begin{patch}{ComplexXmpPagePatch15} +\begin{paste}{ComplexXmpPageFull15}{ComplexXmpPageEmpty15} +\pastebutton{ComplexXmpPageFull15}{\hidepaste} +\tab{5}\spadcommand{factor(13 - 13*\%i)} +\indentrel{3}\begin{verbatim} + (15) - (1 + %i)(2 + 3%i)(3 + 2%i) + Type: Factored Complex Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ComplexXmpPageEmpty15} +\begin{paste}{ComplexXmpPageEmpty15}{ComplexXmpPagePatch15} +\pastebutton{ComplexXmpPageEmpty15}{\showpaste} +\tab{5}\spadcommand{factor(13 - 13*\%i)} +\end{paste}\end{patch} + +\begin{patch}{ComplexXmpPagePatch16} +\begin{paste}{ComplexXmpPageFull16}{ComplexXmpPageEmpty16} +\pastebutton{ComplexXmpPageFull16}{\hidepaste} +\tab{5}\spadcommand{factor complex(2,0)} +\indentrel{3}\begin{verbatim} + 2 + (16) - %i (1 + %i) + Type: Factored Complex Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ComplexXmpPageEmpty16} +\begin{paste}{ComplexXmpPageEmpty16}{ComplexXmpPagePatch16} +\pastebutton{ComplexXmpPageEmpty16}{\showpaste} +\tab{5}\spadcommand{factor complex(2,0)} +\end{paste}\end{patch} + @ \section{contfrac.ht} \pagehead{ContinuedFractionXmpPage}{contfrac.ht}{ContinuedFraction} @@ -4412,6 +8607,508 @@ is the expansion of \texht{$\sqrt{11}$}{the square root of \spad{11}}. \autobuttons \end{page} +\begin{patch}{ContinuedFractionXmpPagePatch1} +\begin{paste}{ContinuedFractionXmpPageFull1}{ContinuedFractionXmpPageEmpty1} +\pastebutton{ContinuedFractionXmpPageFull1}{\hidepaste} +\tab{5}\spadcommand{c := continuedFraction(314159/100000)\bound{c }} +\indentrel{3}\begin{verbatim} + (1) + 1 ³ 1 ³ 1 ³ 1 ³ 1 ³ 1 ³ + 3 + ÚÄÄÄÙ + ÚÄÄÄÄÙ + ÚÄÄÄÙ + ÚÄÄÄÄÙ + ÚÄÄÄÙ + ÚÄÄÄÙ + ³ 7 ³ 15 ³ 1 ³ 25 ³ 1 ³ 7 + + + 1 ³ + ÚÄÄÄÙ + ³ 4 + Type: ContinuedFraction Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ContinuedFractionXmpPageEmpty1} +\begin{paste}{ContinuedFractionXmpPageEmpty1} +{ContinuedFractionXmpPagePatch1} +\pastebutton{ContinuedFractionXmpPageEmpty1}{\showpaste} +\tab{5}\spadcommand{c := continuedFraction(314159/100000)\bound{c }} +\end{paste}\end{patch} + +\begin{patch}{ContinuedFractionXmpPagePatch2} +\begin{paste}{ContinuedFractionXmpPageFull2} +{ContinuedFractionXmpPageEmpty2} +\pastebutton{ContinuedFractionXmpPageFull2}{\hidepaste} +\tab{5}\spadcommand{partialQuotients c\free{c }} +\indentrel{3}\begin{verbatim} + (2) [3,7,15,1,25,1,7,4] + Type: Stream Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ContinuedFractionXmpPageEmpty2} +\begin{paste}{ContinuedFractionXmpPageEmpty2} +{ContinuedFractionXmpPagePatch2} +\pastebutton{ContinuedFractionXmpPageEmpty2}{\showpaste} +\tab{5}\spadcommand{partialQuotients c\free{c }} +\end{paste}\end{patch} + +\begin{patch}{ContinuedFractionXmpPagePatch3} +\begin{paste}{ContinuedFractionXmpPageFull3} +{ContinuedFractionXmpPageEmpty3} +\pastebutton{ContinuedFractionXmpPageFull3}{\hidepaste} +\tab{5}\spadcommand{convergents c\free{c }} +\indentrel{3}\begin{verbatim} + 22 333 355 9208 9563 76149 314159 + (3) [3,ÄÄ,ÄÄÄ,ÄÄÄ,ÄÄÄÄ,ÄÄÄÄ,ÄÄÄÄÄ,ÄÄÄÄÄÄ] + 7 106 113 2931 3044 24239 100000 + Type: Stream Fraction Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ContinuedFractionXmpPageEmpty3} +\begin{paste}{ContinuedFractionXmpPageEmpty3} +{ContinuedFractionXmpPagePatch3} +\pastebutton{ContinuedFractionXmpPageEmpty3}{\showpaste} +\tab{5}\spadcommand{convergents c\free{c }} +\end{paste}\end{patch} + +\begin{patch}{ContinuedFractionXmpPagePatch4} +\begin{paste}{ContinuedFractionXmpPageFull4} +{ContinuedFractionXmpPageEmpty4} +\pastebutton{ContinuedFractionXmpPageFull4}{\hidepaste} +\tab{5}\spadcommand{approximants c\free{c }} +\indentrel{3}\begin{verbatim} + ______ + 22 333 355 9208 9563 76149 314159 + (4) [3,ÄÄ,ÄÄÄ,ÄÄÄ,ÄÄÄÄ,ÄÄÄÄ,ÄÄÄÄÄ,ÄÄÄÄÄÄ] + 7 106 113 2931 3044 24239 100000 + Type: Stream Fraction Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ContinuedFractionXmpPageEmpty4} +\begin{paste}{ContinuedFractionXmpPageEmpty4} +{ContinuedFractionXmpPagePatch4} +\pastebutton{ContinuedFractionXmpPageEmpty4}{\showpaste} +\tab{5}\spadcommand{approximants c\free{c }} +\end{paste}\end{patch} + +\begin{patch}{ContinuedFractionXmpPagePatch5} +\begin{paste}{ContinuedFractionXmpPageFull5} +{ContinuedFractionXmpPageEmpty5} +\pastebutton{ContinuedFractionXmpPageFull5}{\hidepaste} +\tab{5}\spadcommand{pq := partialQuotients(1/c)\free{c }\bound{pq }} +\indentrel{3}\begin{verbatim} + (5) [0,3,7,15,1,25,1,7,4] + Type: Stream Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ContinuedFractionXmpPageEmpty5} +\begin{paste}{ContinuedFractionXmpPageEmpty5} +{ContinuedFractionXmpPagePatch5} +\pastebutton{ContinuedFractionXmpPageEmpty5}{\showpaste} +\tab{5}\spadcommand{pq := partialQuotients(1/c)\free{c }\bound{pq }} +\end{paste}\end{patch} + +\begin{patch}{ContinuedFractionXmpPagePatch6} +\begin{paste}{ContinuedFractionXmpPageFull6} +{ContinuedFractionXmpPageEmpty6} +\pastebutton{ContinuedFractionXmpPageFull6}{\hidepaste} +\tab{5}\spadcommand{ +continuedFraction(first pq,repeating [1],rest pq)\free{pq }} +\indentrel{3}\begin{verbatim} + (6) + 1 ³ 1 ³ 1 ³ 1 ³ 1 ³ 1 ³ + ÚÄÄÄÙ + ÚÄÄÄÙ + ÚÄÄÄÄÙ + ÚÄÄÄÙ + ÚÄÄÄÄÙ + ÚÄÄÄÙ + ³ 3 ³ 7 ³ 15 ³ 1 ³ 25 ³ 1 + + + 1 ³ 1 ³ + ÚÄÄÄÙ + ÚÄÄÄÙ + ³ 7 ³ 4 + Type: ContinuedFraction Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ContinuedFractionXmpPageEmpty6} +\begin{paste}{ContinuedFractionXmpPageEmpty6} +{ContinuedFractionXmpPagePatch6} +\pastebutton{ContinuedFractionXmpPageEmpty6}{\showpaste} +\tab{5}\spadcommand{ +continuedFraction(first pq,repeating [1],rest pq)\free{pq }} +\end{paste}\end{patch} + +\begin{patch}{ContinuedFractionXmpPagePatch7} +\begin{paste}{ContinuedFractionXmpPageFull7} +{ContinuedFractionXmpPageEmpty7} +\pastebutton{ContinuedFractionXmpPageFull7}{\hidepaste} +\tab{5}\spadcommand{ +z:=continuedFraction(3,repeating [1],repeating [3,6])\bound{z }} +\indentrel{3}\begin{verbatim} + (7) + 1 ³ 1 ³ 1 ³ 1 ³ 1 ³ 1 ³ + 3 + ÚÄÄÄÙ + ÚÄÄÄÙ + ÚÄÄÄÙ + ÚÄÄÄÙ + ÚÄÄÄÙ + ÚÄÄÄÙ + ³ 3 ³ 6 ³ 3 ³ 6 ³ 3 ³ 6 + + + 1 ³ 1 ³ 1 ³ 1 ³ + ÚÄÄÄÙ + ÚÄÄÄÙ + ÚÄÄÄÙ + ÚÄÄÄÙ + ... + ³ 3 ³ 6 ³ 3 ³ 6 + Type: ContinuedFraction Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ContinuedFractionXmpPageEmpty7} +\begin{paste}{ContinuedFractionXmpPageEmpty7} +{ContinuedFractionXmpPagePatch7} +\pastebutton{ContinuedFractionXmpPageEmpty7}{\showpaste} +\tab{5}\spadcommand{ +z:=continuedFraction(3,repeating [1],repeating [3,6])\bound{z }} +\end{paste}\end{patch} + +\begin{patch}{ContinuedFractionXmpPagePatch8} +\begin{paste}{ContinuedFractionXmpPageFull8} +{ContinuedFractionXmpPageEmpty8} +\pastebutton{ContinuedFractionXmpPageFull8}{\hidepaste} +\tab{5}\spadcommand{ +dens:Stream Integer := cons(1,generate((x+->x+4),6))\bound{dens }} +\indentrel{3}\begin{verbatim} + (8) [1,6,10,14,18,22,26,30,34,38,...] + Type: Stream Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ContinuedFractionXmpPageEmpty8} +\begin{paste}{ContinuedFractionXmpPageEmpty8} +{ContinuedFractionXmpPagePatch8} +\pastebutton{ContinuedFractionXmpPageEmpty8}{\showpaste} +\tab{5}\spadcommand{ +dens:Stream Integer := cons(1,generate((x+->x+4),6))\bound{dens }} +\end{paste}\end{patch} + +\begin{patch}{ContinuedFractionXmpPagePatch9} +\begin{paste}{ContinuedFractionXmpPageFull9} +{ContinuedFractionXmpPageEmpty9} +\pastebutton{ContinuedFractionXmpPageFull9}{\hidepaste} +\tab{5}\spadcommand{ +cf := continuedFraction(0,repeating [1],dens)\free{dens }\bound{cf }} +\indentrel{3}\begin{verbatim} + (9) + 1 ³ 1 ³ 1 ³ 1 ³ 1 ³ 1 ³ + ÚÄÄÄÙ + ÚÄÄÄÙ + ÚÄÄÄÄÙ + ÚÄÄÄÄÙ + ÚÄÄÄÄÙ + ÚÄÄÄÄÙ + ³ 1 ³ 6 ³ 10 ³ 14 ³ 18 ³ 22 + + + 1 ³ 1 ³ 1 ³ 1 ³ + ÚÄÄÄÄÙ + ÚÄÄÄÄÙ + ÚÄÄÄÄÙ + ÚÄÄÄÄÙ + ... + ³ 26 ³ 30 ³ 34 ³ 38 + Type: ContinuedFraction Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ContinuedFractionXmpPageEmpty9} +\begin{paste}{ContinuedFractionXmpPageEmpty9} +{ContinuedFractionXmpPagePatch9} +\pastebutton{ContinuedFractionXmpPageEmpty9}{\showpaste} +\tab{5}\spadcommand{ +cf := continuedFraction(0,repeating [1],dens)\free{dens }\bound{cf }} +\end{paste}\end{patch} + +\begin{patch}{ContinuedFractionXmpPagePatch10} +\begin{paste}{ContinuedFractionXmpPageFull10} +{ContinuedFractionXmpPageEmpty10} +\pastebutton{ContinuedFractionXmpPageFull10}{\hidepaste} +\tab{5}\spadcommand{ccf := convergents cf\free{cf }\bound{ccf }} +\indentrel{3}\begin{verbatim} + (10) + 6 61 860 15541 342762 8927353 + [0, 1, Ä, ÄÄ, ÄÄÄÄ, ÄÄÄÄÄ, ÄÄÄÄÄÄ, ÄÄÄÄÄÄÄÄ, + 7 71 1001 18089 398959 10391023 + 268163352 9126481321 + ÄÄÄÄÄÄÄÄÄ, ÄÄÄÄÄÄÄÄÄÄÄ, ...] + 312129649 10622799089 + Type: Stream Fraction Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ContinuedFractionXmpPageEmpty10} +\begin{paste}{ContinuedFractionXmpPageEmpty10} +{ContinuedFractionXmpPagePatch10} +\pastebutton{ContinuedFractionXmpPageEmpty10}{\showpaste} +\tab{5}\spadcommand{ccf := convergents cf\free{cf }\bound{ccf }} +\end{paste}\end{patch} + +\begin{patch}{ContinuedFractionXmpPagePatch11} +\begin{paste}{ContinuedFractionXmpPageFull11} +{ContinuedFractionXmpPageEmpty11} +\pastebutton{ContinuedFractionXmpPageFull11}{\hidepaste} +\tab{5}\spadcommand{ +eConvergents := [2*e + 1 for e in ccf]\bound{ec }\free{ccf }} +\indentrel{3}\begin{verbatim} + (11) + 19 193 2721 49171 1084483 28245729 + [1, 3, ÄÄ, ÄÄÄ, ÄÄÄÄ, ÄÄÄÄÄ, ÄÄÄÄÄÄÄ, ÄÄÄÄÄÄÄÄ, + 7 71 1001 18089 398959 10391023 + 848456353 28875761731 + ÄÄÄÄÄÄÄÄÄ, ÄÄÄÄÄÄÄÄÄÄÄ, ...] + 312129649 10622799089 + Type: Stream Fraction Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ContinuedFractionXmpPageEmpty11} +\begin{paste}{ContinuedFractionXmpPageEmpty11} +{ContinuedFractionXmpPagePatch11} +\pastebutton{ContinuedFractionXmpPageEmpty11}{\showpaste} +\tab{5}\spadcommand{ +eConvergents := [2*e + 1 for e in ccf]\bound{ec }\free{ccf }} +\end{paste}\end{patch} + +\begin{patch}{ContinuedFractionXmpPagePatch12} +\begin{paste}{ContinuedFractionXmpPageFull12} +{ContinuedFractionXmpPageEmpty12} +\pastebutton{ContinuedFractionXmpPageFull12}{\hidepaste} +\tab{5}\spadcommand{eConvergents :: Stream Float\free{ec }} +\indentrel{3}\begin{verbatim} + (12) + [1.0, 3.0, 2.7142857142 857142857, + 2.7183098591 549295775, 2.7182817182 817182817, + 2.7182818287 356957267, 2.7182818284 585634113, + 2.7182818284 590458514, 2.7182818284 590452348, + 2.7182818284 590452354, ...] + Type: Stream Float +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ContinuedFractionXmpPageEmpty12} +\begin{paste}{ContinuedFractionXmpPageEmpty12} +{ContinuedFractionXmpPagePatch12} +\pastebutton{ContinuedFractionXmpPageEmpty12}{\showpaste} +\tab{5}\spadcommand{eConvergents :: Stream Float\free{ec }} +\end{paste}\end{patch} + +\begin{patch}{ContinuedFractionXmpPagePatch13} +\begin{paste}{ContinuedFractionXmpPageFull13} +{ContinuedFractionXmpPageEmpty13} +\pastebutton{ContinuedFractionXmpPageFull13}{\hidepaste} +\tab{5}\spadcommand{exp 1.0} +\indentrel{3}\begin{verbatim} + (13) 2.7182818284 590452354 + Type: Float +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ContinuedFractionXmpPageEmpty13} +\begin{paste}{ContinuedFractionXmpPageEmpty13} +{ContinuedFractionXmpPagePatch13} +\pastebutton{ContinuedFractionXmpPageEmpty13}{\showpaste} +\tab{5}\spadcommand{exp 1.0} +\end{paste}\end{patch} + +\begin{patch}{ContinuedFractionXmpPagePatch14} +\begin{paste}{ContinuedFractionXmpPageFull14} +{ContinuedFractionXmpPageEmpty14} +\pastebutton{ContinuedFractionXmpPageFull14}{\hidepaste} +\tab{5}\spadcommand{ +cf := continuedFraction(1,[(2*i+1)**2 for i in 0..],repeating [2]) +\bound{cf1 }} +\indentrel{3}\begin{verbatim} + (14) + 1 ³ 9 ³ 25 ³ 49 ³ 81 ³ + 1 + ÚÄÄÄÙ + ÚÄÄÄÙ + ÚÄÄÄÄÙ + ÚÄÄÄÄÙ + ÚÄÄÄÄÙ + ³ 2 ³ 2 ³ 2 ³ 2 ³ 2 + + + 121 ³ 169 ³ 225 ³ 289 ³ 361 ³ + ÚÄÄÄÄÄÙ + ÚÄÄÄÄÄÙ + ÚÄÄÄÄÄÙ + ÚÄÄÄÄÄÙ + ÚÄÄÄÄÄÙ + ... + ³ 2 ³ 2 ³ 2 ³ 2 ³ 2 + Type: ContinuedFraction Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ContinuedFractionXmpPageEmpty14} +\begin{paste}{ContinuedFractionXmpPageEmpty14} +{ContinuedFractionXmpPagePatch14} +\pastebutton{ContinuedFractionXmpPageEmpty14}{\showpaste} +\tab{5}\spadcommand{ +cf := continuedFraction(1,[(2*i+1)**2 for i in 0..],repeating [2]) +\bound{cf1 }} +\end{paste}\end{patch} + +\begin{patch}{ContinuedFractionXmpPagePatch15} +\begin{paste}{ContinuedFractionXmpPageFull15} +{ContinuedFractionXmpPageEmpty15} +\pastebutton{ContinuedFractionXmpPageFull15}{\hidepaste} +\tab{5}\spadcommand{ccf := convergents cf\free{cf1 }\bound{ccf1 }} +\indentrel{3}\begin{verbatim} + (15) + 3 15 105 315 3465 45045 45045 765765 14549535 + [1,Ä,ÄÄ,ÄÄÄ,ÄÄÄ,ÄÄÄÄ,ÄÄÄÄÄ,ÄÄÄÄÄ,ÄÄÄÄÄÄ,ÄÄÄÄÄÄÄÄ,...] + 2 13 76 263 2578 36979 33976 622637 11064338 + Type: Stream Fraction Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ContinuedFractionXmpPageEmpty15} +\begin{paste}{ContinuedFractionXmpPageEmpty15} +{ContinuedFractionXmpPagePatch15} +\pastebutton{ContinuedFractionXmpPageEmpty15}{\showpaste} +\tab{5}\spadcommand{ccf := convergents cf\free{cf1 }\bound{ccf1 }} +\end{paste}\end{patch} + +\begin{patch}{ContinuedFractionXmpPagePatch16} +\begin{paste}{ContinuedFractionXmpPageFull16} +{ContinuedFractionXmpPageEmpty16} +\pastebutton{ContinuedFractionXmpPageFull16}{\hidepaste} +\tab{5}\spadcommand{ +piConvergents := [4/p for p in ccf]\bound{piConvergents }\free{ccf1 }} +\indentrel{3}\begin{verbatim} + (16) + 8 52 304 1052 10312 147916 135904 2490548 + [4, Ä, ÄÄ, ÄÄÄ, ÄÄÄÄ, ÄÄÄÄÄ, ÄÄÄÄÄÄ, ÄÄÄÄÄÄ, ÄÄÄÄÄÄÄ, + 3 15 105 315 3465 45045 45045 765765 + 44257352 + ÄÄÄÄÄÄÄÄ, ...] + 14549535 + Type: Stream Fraction Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ContinuedFractionXmpPageEmpty16} +\begin{paste}{ContinuedFractionXmpPageEmpty16} +{ContinuedFractionXmpPagePatch16} +\pastebutton{ContinuedFractionXmpPageEmpty16}{\showpaste} +\tab{5}\spadcommand{ +piConvergents := [4/p for p in ccf]\bound{piConvergents }\free{ccf1 }} +\end{paste}\end{patch} + +\begin{patch}{ContinuedFractionXmpPagePatch17} +\begin{paste}{ContinuedFractionXmpPageFull17} +{ContinuedFractionXmpPageEmpty17} +\pastebutton{ContinuedFractionXmpPageFull17}{\hidepaste} +\tab{5}\spadcommand{piConvergents :: Stream Float\free{piConvergents }} +\indentrel{3}\begin{verbatim} + (17) + [4.0, 2.6666666666 666666667, 3.4666666666 666666667, + 2.8952380952 380952381, 3.3396825396 825396825, + 2.9760461760 461760462, 3.2837384837 384837385, + 3.0170718170 718170718, 3.2523659347 188758953, + 3.0418396189 294022111, ...] + Type: Stream Float +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ContinuedFractionXmpPageEmpty17} +\begin{paste}{ContinuedFractionXmpPageEmpty17} +{ContinuedFractionXmpPagePatch17} +\pastebutton{ContinuedFractionXmpPageEmpty17}{\showpaste} +\tab{5}\spadcommand{piConvergents :: Stream Float\free{piConvergents }} +\end{paste}\end{patch} + +\begin{patch}{ContinuedFractionXmpPagePatch18} +\begin{paste}{ContinuedFractionXmpPageFull18} +{ContinuedFractionXmpPageEmpty18} +\pastebutton{ContinuedFractionXmpPageFull18}{\hidepaste} +\tab{5}\spadcommand{continuedFraction((- 122 + 597*\%i)/(4 - 4*\%i))} +\indentrel{3}\begin{verbatim} + 1 ³ 1 ³ + (18) - 90 + 59%i + ÚÄÄÄÄÄÄÄÄÄÙ + ÚÄÄÄÄÄÄÄÄÄÄÄÙ + ³ 1 - 2%i ³ - 1 + 2%i + Type: ContinuedFraction Complex Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ContinuedFractionXmpPageEmpty18} +\begin{paste}{ContinuedFractionXmpPageEmpty18} +{ContinuedFractionXmpPagePatch18} +\pastebutton{ContinuedFractionXmpPageEmpty18}{\showpaste} +\tab{5}\spadcommand{continuedFraction((- 122 + 597*\%i)/(4 - 4*\%i))} +\end{paste}\end{patch} + +\begin{patch}{ContinuedFractionXmpPagePatch19} +\begin{paste}{ContinuedFractionXmpPageFull19} +{ContinuedFractionXmpPageEmpty19} +\pastebutton{ContinuedFractionXmpPageFull19}{\hidepaste} +\tab{5}\spadcommand{ +r : Fraction UnivariatePolynomial(x,Fraction Integer)\bound{rdec }} +\indentrel{3}\begin{verbatim} + Type: Void +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ContinuedFractionXmpPageEmpty19} +\begin{paste}{ContinuedFractionXmpPageEmpty19} +{ContinuedFractionXmpPagePatch19} +\pastebutton{ContinuedFractionXmpPageEmpty19}{\showpaste} +\tab{5}\spadcommand{ +r : Fraction UnivariatePolynomial(x,Fraction Integer)\bound{rdec }} +\end{paste}\end{patch} + +\begin{patch}{ContinuedFractionXmpPagePatch20} +\begin{paste}{ContinuedFractionXmpPageFull20} +{ContinuedFractionXmpPageEmpty20} +\pastebutton{ContinuedFractionXmpPageFull20}{\hidepaste} +\tab{5}\spadcommand{ +r := ((x - 1) * (x - 2)) / ((x-3) * (x-4))\free{rdec }\bound{r }} +\indentrel{3}\begin{verbatim} + 2 + x - 3x + 2 + (20) ÄÄÄÄÄÄÄÄÄÄÄÄ + 2 + x - 7x + 12 +Type: Fraction UnivariatePolynomial(x,Fraction Integer) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ContinuedFractionXmpPageEmpty20} +\begin{paste}{ContinuedFractionXmpPageEmpty20} +{ContinuedFractionXmpPagePatch20} +\pastebutton{ContinuedFractionXmpPageEmpty20}{\showpaste} +\tab{5}\spadcommand{ +r := ((x - 1) * (x - 2)) / ((x-3) * (x-4))\free{rdec }\bound{r }} +\end{paste}\end{patch} + +\begin{patch}{ContinuedFractionXmpPagePatch21} +\begin{paste}{ContinuedFractionXmpPageFull21} +{ContinuedFractionXmpPageEmpty21} +\pastebutton{ContinuedFractionXmpPageFull21}{\hidepaste} +\tab{5}\spadcommand{continuedFraction r\free{r }} +\indentrel{3}\begin{verbatim} + 1 ³ 1 ³ + (21) 1 + ÚÄÄÄÄÄÄÄÄÄÙ + ÚÄÄÄÄÄÄÄÄÄÄÄÙ + ³ 1 9 ³ 16 40 + ³ Ä x - Ä ³ ÄÄ x - ÄÄ + ³ 4 8 ³ 3 3 +Type: ContinuedFraction UnivariatePolynomial(x,Fraction Integer) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ContinuedFractionXmpPageEmpty21} +\begin{paste}{ContinuedFractionXmpPageEmpty21} +{ContinuedFractionXmpPagePatch21} +\pastebutton{ContinuedFractionXmpPageEmpty21}{\showpaste} +\tab{5}\spadcommand{continuedFraction r\free{r }} +\end{paste}\end{patch} + +\begin{patch}{ContinuedFractionXmpPagePatch22} +\begin{paste}{ContinuedFractionXmpPageFull22} +{ContinuedFractionXmpPageEmpty22} +\pastebutton{ContinuedFractionXmpPageFull22}{\hidepaste} +\tab{5}\spadcommand{ +[i*i for i in convergents(z) :: Stream Float]\free{z }} +\indentrel{3}\begin{verbatim} + (22) + [9.0, 11.1111111111 11111111, 10.9944598337 9501385, + 11.0002777777 77777778, 10.9999860763 98799786, + 11.0000006979 29731039, 10.9999999650 15834446, + 11.0000000017 53603304, 10.9999999999 12099531, + 11.0000000000 04406066, ...] + Type: Stream Float +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ContinuedFractionXmpPageEmpty22} +\begin{paste}{ContinuedFractionXmpPageEmpty22} +{ContinuedFractionXmpPagePatch22} +\pastebutton{ContinuedFractionXmpPageEmpty22}{\showpaste} +\tab{5}\spadcommand{ +[i*i for i in convergents(z) :: Stream Float]\free{z }} +\end{paste}\end{patch} + @ \section{cphelp.ht} \pagehead{CPHelp}{cphelp.ht}{Control Panel Bits} @@ -4638,13 +9335,15 @@ The number of cubes with 4 red vertices and 4 blue vertices. The number of labeled graphs with degree sequence \spad{2 2 2 1 1} with no loops or multiple edges. }{ -\spadpaste{cap(complete 2**3*complete 1**2,wreath(elementary 4,elementary 2))} +\spadpaste{ +cap(complete 2**3*complete 1**2,wreath(elementary 4,elementary 2))} } \xtc{ Again, but with loops allowed but not multiple edges. }{ -\spadpaste{cap(complete 2**3*complete 1**2,wreath(elementary 4,complete 2))} +\spadpaste{ +cap(complete 2**3*complete 1**2,wreath(elementary 4,complete 2))} } \xtc{ Again, but @@ -4665,8 +9364,8 @@ we are at liberty to evaluate the components any way we please. For example we can produce enumerating generating functions. {CycleIndicators} -This is done by providing a function \spad{f} on an integer \spad{i} to the -value required of \subscriptIt{s}{i}, +This is done by providing a function \spad{f} on an integer \spad{i} +to the value required of \subscriptIt{s}{i}, and then evaluating \spad{eval(f, cycleindex)}. \xtc{ }{ @@ -4809,6 +9508,882 @@ The smallest is \autobuttons \end{page} +\begin{patch}{CycleIndicatorsXmpPagePatch1} +\begin{paste}{CycleIndicatorsXmpPageFull1}{CycleIndicatorsXmpPageEmpty1} +\pastebutton{CycleIndicatorsXmpPageFull1}{\hidepaste} +\tab{5}\spadcommand{)expose EVALCYC} +\indentrel{3}\begin{verbatim} +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{CycleIndicatorsXmpPageEmpty1} +\begin{paste}{CycleIndicatorsXmpPageEmpty1}{CycleIndicatorsXmpPagePatch1} +\pastebutton{CycleIndicatorsXmpPageEmpty1}{\showpaste} +\tab{5}\spadcommand{)expose EVALCYC} +\end{paste}\end{patch} + +\begin{patch}{CycleIndicatorsXmpPagePatch2} +\begin{paste}{CycleIndicatorsXmpPageFull2}{CycleIndicatorsXmpPageEmpty2} +\pastebutton{CycleIndicatorsXmpPageFull2}{\hidepaste} +\tab{5}\spadcommand{complete 1} +\indentrel{3}\begin{verbatim} + (1) (1) + Type: SymmetricPolynomial Fraction Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{CycleIndicatorsXmpPageEmpty2} +\begin{paste}{CycleIndicatorsXmpPageEmpty2}{CycleIndicatorsXmpPagePatch2} +\pastebutton{CycleIndicatorsXmpPageEmpty2}{\showpaste} +\tab{5}\spadcommand{complete 1} +\end{paste}\end{patch} + +\begin{patch}{CycleIndicatorsXmpPagePatch3} +\begin{paste}{CycleIndicatorsXmpPageFull3}{CycleIndicatorsXmpPageEmpty3} +\pastebutton{CycleIndicatorsXmpPageFull3}{\hidepaste} +\tab{5}\spadcommand{complete 2} +\indentrel{3}\begin{verbatim} + 1 1 2 + (2) Ä (2) + Ä (1 ) + 2 2 + Type: SymmetricPolynomial Fraction Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{CycleIndicatorsXmpPageEmpty3} +\begin{paste}{CycleIndicatorsXmpPageEmpty3}{CycleIndicatorsXmpPagePatch3} +\pastebutton{CycleIndicatorsXmpPageEmpty3}{\showpaste} +\tab{5}\spadcommand{complete 2} +\end{paste}\end{patch} + +\begin{patch}{CycleIndicatorsXmpPagePatch4} +\begin{paste}{CycleIndicatorsXmpPageFull4}{CycleIndicatorsXmpPageEmpty4} +\pastebutton{CycleIndicatorsXmpPageFull4}{\hidepaste} +\tab{5}\spadcommand{complete 3} +\indentrel{3}\begin{verbatim} + 1 1 1 3 + (3) Ä (3) + Ä (2 1) + Ä (1 ) + 3 2 6 + Type: SymmetricPolynomial Fraction Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{CycleIndicatorsXmpPageEmpty4} +\begin{paste}{CycleIndicatorsXmpPageEmpty4}{CycleIndicatorsXmpPagePatch4} +\pastebutton{CycleIndicatorsXmpPageEmpty4}{\showpaste} +\tab{5}\spadcommand{complete 3} +\end{paste}\end{patch} + +\begin{patch}{CycleIndicatorsXmpPagePatch5} +\begin{paste}{CycleIndicatorsXmpPageFull5}{CycleIndicatorsXmpPageEmpty5} +\pastebutton{CycleIndicatorsXmpPageFull5}{\hidepaste} +\tab{5}\spadcommand{complete 7} +\indentrel{3}\begin{verbatim} + (4) + 1 1 1 1 2 1 + Ä (7) + Ä (6 1) + ÄÄ (5 2) + ÄÄ (5 1 ) + ÄÄ (4 3) + 7 6 10 10 12 + + + 1 1 3 1 2 1 2 + Ä (4 2 1) + ÄÄ (4 1 ) + ÄÄ (3 1) + ÄÄ (3 2 ) + 8 24 18 24 + + + 1 2 1 4 1 3 1 2 3 + ÄÄ (3 2 1 ) + ÄÄ (3 1 ) + ÄÄ (2 1) + ÄÄ (2 1 ) + 12 72 48 48 + + + 1 5 1 7 + ÄÄÄ (2 1 ) + ÄÄÄÄ (1 ) + 240 5040 + Type: SymmetricPolynomial Fraction Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{CycleIndicatorsXmpPageEmpty5} +\begin{paste}{CycleIndicatorsXmpPageEmpty5}{CycleIndicatorsXmpPagePatch5} +\pastebutton{CycleIndicatorsXmpPageEmpty5}{\showpaste} +\tab{5}\spadcommand{complete 7} +\end{paste}\end{patch} + +\begin{patch}{CycleIndicatorsXmpPagePatch6} +\begin{paste}{CycleIndicatorsXmpPageFull6}{CycleIndicatorsXmpPageEmpty6} +\pastebutton{CycleIndicatorsXmpPageFull6}{\hidepaste} +\tab{5}\spadcommand{elementary 7} +\indentrel{3}\begin{verbatim} + (5) + 1 1 1 1 2 1 + Ä (7) - Ä (6 1) - ÄÄ (5 2) + ÄÄ (5 1 ) - ÄÄ (4 3) + 7 6 10 10 12 + + + 1 1 3 1 2 1 2 + Ä (4 2 1) - ÄÄ (4 1 ) + ÄÄ (3 1) + ÄÄ (3 2 ) + 8 24 18 24 + + + 1 2 1 4 1 3 1 2 3 + - ÄÄ (3 2 1 ) + ÄÄ (3 1 ) - ÄÄ (2 1) + ÄÄ (2 1 ) + 12 72 48 48 + + + 1 5 1 7 + - ÄÄÄ (2 1 ) + ÄÄÄÄ (1 ) + 240 5040 + Type: SymmetricPolynomial Fraction Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{CycleIndicatorsXmpPageEmpty6} +\begin{paste}{CycleIndicatorsXmpPageEmpty6}{CycleIndicatorsXmpPagePatch6} +\pastebutton{CycleIndicatorsXmpPageEmpty6}{\showpaste} +\tab{5}\spadcommand{elementary 7} +\end{paste}\end{patch} + +\begin{patch}{CycleIndicatorsXmpPagePatch7} +\begin{paste}{CycleIndicatorsXmpPageFull7}{CycleIndicatorsXmpPageEmpty7} +\pastebutton{CycleIndicatorsXmpPageFull7}{\hidepaste} +\tab{5}\spadcommand{alternating 7} +\indentrel{3}\begin{verbatim} + (6) + 2 1 2 1 1 2 1 2 + Ä (7) + Ä (5 1 ) + Ä (4 2 1) + Ä (3 1) + ÄÄ (3 2 ) + 7 5 4 9 12 + + + 1 4 1 2 3 1 7 + ÄÄ (3 1 ) + ÄÄ (2 1 ) + ÄÄÄÄ (1 ) + 36 24 2520 + Type: SymmetricPolynomial Fraction Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{CycleIndicatorsXmpPageEmpty7} +\begin{paste}{CycleIndicatorsXmpPageEmpty7}{CycleIndicatorsXmpPagePatch7} +\pastebutton{CycleIndicatorsXmpPageEmpty7}{\showpaste} +\tab{5}\spadcommand{alternating 7} +\end{paste}\end{patch} + +\begin{patch}{CycleIndicatorsXmpPagePatch8} +\begin{paste}{CycleIndicatorsXmpPageFull8}{CycleIndicatorsXmpPageEmpty8} +\pastebutton{CycleIndicatorsXmpPageFull8}{\hidepaste} +\tab{5}\spadcommand{cyclic 7} +\indentrel{3}\begin{verbatim} + 6 1 7 + (7) Ä (7) + Ä (1 ) + 7 7 + Type: SymmetricPolynomial Fraction Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{CycleIndicatorsXmpPageEmpty8} +\begin{paste}{CycleIndicatorsXmpPageEmpty8}{CycleIndicatorsXmpPagePatch8} +\pastebutton{CycleIndicatorsXmpPageEmpty8}{\showpaste} +\tab{5}\spadcommand{cyclic 7} +\end{paste}\end{patch} + +\begin{patch}{CycleIndicatorsXmpPagePatch9} +\begin{paste}{CycleIndicatorsXmpPageFull9}{CycleIndicatorsXmpPageEmpty9} +\pastebutton{CycleIndicatorsXmpPageFull9}{\hidepaste} +\tab{5}\spadcommand{dihedral 7} +\indentrel{3}\begin{verbatim} + 3 1 3 1 7 + (8) Ä (7) + Ä (2 1) + ÄÄ (1 ) + 7 2 14 + Type: SymmetricPolynomial Fraction Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{CycleIndicatorsXmpPageEmpty9} +\begin{paste}{CycleIndicatorsXmpPageEmpty9}{CycleIndicatorsXmpPagePatch9} +\pastebutton{CycleIndicatorsXmpPageEmpty9}{\showpaste} +\tab{5}\spadcommand{dihedral 7} +\end{paste}\end{patch} + +\begin{patch}{CycleIndicatorsXmpPagePatch10} +\begin{paste}{CycleIndicatorsXmpPageFull10}{CycleIndicatorsXmpPageEmpty10} +\pastebutton{CycleIndicatorsXmpPageFull10}{\hidepaste} +\tab{5}\spadcommand{graphs 5} +\indentrel{3}\begin{verbatim} + (9) + 1 1 2 1 2 1 3 1 4 2 + Ä (6 3 1) + Ä (5 ) + Ä (4 2) + Ä (3 1) + Ä (2 1 ) + 6 5 4 6 8 + + + 1 3 4 1 10 + ÄÄ (2 1 ) + ÄÄÄ (1 ) + 12 120 + Type: SymmetricPolynomial Fraction Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{CycleIndicatorsXmpPageEmpty10} +\begin{paste}{CycleIndicatorsXmpPageEmpty10}{CycleIndicatorsXmpPagePatch10} +\pastebutton{CycleIndicatorsXmpPageEmpty10}{\showpaste} +\tab{5}\spadcommand{graphs 5} +\end{paste}\end{patch} + +\begin{patch}{CycleIndicatorsXmpPagePatch11} +\begin{paste}{CycleIndicatorsXmpPageFull11}{CycleIndicatorsXmpPageEmpty11} +\pastebutton{CycleIndicatorsXmpPageFull11}{\hidepaste} +\tab{5}\spadcommand{cap(complete 2**2, complete 2*complete 1**2)} +\indentrel{3}\begin{verbatim} + (10) 4 + Type: Fraction Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{CycleIndicatorsXmpPageEmpty11} +\begin{paste}{CycleIndicatorsXmpPageEmpty11}{CycleIndicatorsXmpPagePatch11} +\pastebutton{CycleIndicatorsXmpPageEmpty11}{\showpaste} +\tab{5}\spadcommand{cap(complete 2**2, complete 2*complete 1**2)} +\end{paste}\end{patch} + +\begin{patch}{CycleIndicatorsXmpPagePatch12} +\begin{paste}{CycleIndicatorsXmpPageFull12}{CycleIndicatorsXmpPageEmpty12} +\pastebutton{CycleIndicatorsXmpPageFull12}{\hidepaste} +\tab{5}\spadcommand{cap(elementary 2**2, complete 2*complete 1**2)} +\indentrel{3}\begin{verbatim} + (11) 2 + Type: Fraction Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{CycleIndicatorsXmpPageEmpty12} +\begin{paste}{CycleIndicatorsXmpPageEmpty12}{CycleIndicatorsXmpPagePatch12} +\pastebutton{CycleIndicatorsXmpPageEmpty12}{\showpaste} +\tab{5}\spadcommand{cap(elementary 2**2, complete 2*complete 1**2)} +\end{paste}\end{patch} + +\begin{patch}{CycleIndicatorsXmpPagePatch13} +\begin{paste}{CycleIndicatorsXmpPageFull13}{CycleIndicatorsXmpPageEmpty13} +\pastebutton{CycleIndicatorsXmpPageFull13}{\hidepaste} +\tab{5}\spadcommand{ +cap(complete 3*complete 2*complete 1,complete 2**2*complete 1**2)} +\indentrel{3}\begin{verbatim} + (12) 24 + Type: Fraction Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{CycleIndicatorsXmpPageEmpty13} +\begin{paste}{CycleIndicatorsXmpPageEmpty13}{CycleIndicatorsXmpPagePatch13} +\pastebutton{CycleIndicatorsXmpPageEmpty13}{\showpaste} +\tab{5}\spadcommand{ +cap(complete 3*complete 2*complete 1,complete 2**2*complete 1**2)} +\end{paste}\end{patch} + +\begin{patch}{CycleIndicatorsXmpPagePatch14} +\begin{paste}{CycleIndicatorsXmpPageFull14}{CycleIndicatorsXmpPageEmpty14} +\pastebutton{CycleIndicatorsXmpPageFull14}{\hidepaste} +\tab{5}\spadcommand{ +cap(elementary 3*elementary 2*elementary 1,complete 2**2*complete 1**2)} +\indentrel{3}\begin{verbatim} + (13) 8 + Type: Fraction Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{CycleIndicatorsXmpPageEmpty14} +\begin{paste}{CycleIndicatorsXmpPageEmpty14}{CycleIndicatorsXmpPagePatch14} +\pastebutton{CycleIndicatorsXmpPageEmpty14}{\showpaste} +\tab{5}\spadcommand{ +cap(elementary 3*elementary 2*elementary 1,complete 2**2*complete 1**2)} +\end{paste}\end{patch} + +\begin{patch}{CycleIndicatorsXmpPagePatch15} +\begin{paste}{CycleIndicatorsXmpPageFull15}{CycleIndicatorsXmpPageEmpty15} +\pastebutton{CycleIndicatorsXmpPageFull15}{\hidepaste} +\tab{5}\spadcommand{ +cap(complete 3*complete 2*complete 1,elementary 2**2*elementary 1**2)} +\indentrel{3}\begin{verbatim} + (14) 8 + Type: Fraction Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{CycleIndicatorsXmpPageEmpty15} +\begin{paste}{CycleIndicatorsXmpPageEmpty15}{CycleIndicatorsXmpPagePatch15} +\pastebutton{CycleIndicatorsXmpPageEmpty15}{\showpaste} +\tab{5}\spadcommand{ +cap(complete 3*complete 2*complete 1,elementary 2**2*elementary 1**2)} +\end{paste}\end{patch} + +\begin{patch}{CycleIndicatorsXmpPagePatch16} +\begin{paste}{CycleIndicatorsXmpPageFull16}{CycleIndicatorsXmpPageEmpty16} +\pastebutton{CycleIndicatorsXmpPageFull16}{\hidepaste} +\tab{5}\spadcommand{ +eval(cup(complete 3*complete 2*complete 1, _ + cup(complete 2**2*complete 1**2,complete 2**3)))} +\indentrel{3}\begin{verbatim} + (15) 1500 + Type: Fraction Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{CycleIndicatorsXmpPageEmpty16} +\begin{paste}{CycleIndicatorsXmpPageEmpty16}{CycleIndicatorsXmpPagePatch16} +\pastebutton{CycleIndicatorsXmpPageEmpty16}{\showpaste} +\tab{5}\spadcommand{ +eval(cup(complete 3*complete 2*complete 1, _ + cup(complete 2**2*complete 1**2,complete 2**3)))} +\end{paste}\end{patch} + +\begin{patch}{CycleIndicatorsXmpPagePatch17} +\begin{paste}{CycleIndicatorsXmpPageFull17}{CycleIndicatorsXmpPageEmpty17} +\pastebutton{CycleIndicatorsXmpPageFull17}{\hidepaste} +\tab{5}\spadcommand{square:=dihedral 4} +\indentrel{3}\begin{verbatim} + 1 3 2 1 2 1 4 + (16) Ä (4) + Ä (2 ) + Ä (2 1 ) + Ä (1 ) + 4 8 4 8 + Type: SymmetricPolynomial Fraction Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{CycleIndicatorsXmpPageEmpty17} +\begin{paste}{CycleIndicatorsXmpPageEmpty17}{CycleIndicatorsXmpPagePatch17} +\pastebutton{CycleIndicatorsXmpPageEmpty17}{\showpaste} +\tab{5}\spadcommand{square:=dihedral 4} +\end{paste}\end{patch} + +\begin{patch}{CycleIndicatorsXmpPagePatch18} +\begin{paste}{CycleIndicatorsXmpPageFull18}{CycleIndicatorsXmpPageEmpty18} +\pastebutton{CycleIndicatorsXmpPageFull18}{\hidepaste} +\tab{5}\spadcommand{cap(complete 2**2,square)} +\indentrel{3}\begin{verbatim} + (17) 2 + Type: Fraction Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{CycleIndicatorsXmpPageEmpty18} +\begin{paste}{CycleIndicatorsXmpPageEmpty18}{CycleIndicatorsXmpPagePatch18} +\pastebutton{CycleIndicatorsXmpPageEmpty18}{\showpaste} +\tab{5}\spadcommand{cap(complete 2**2,square)} +\end{paste}\end{patch} + +\begin{patch}{CycleIndicatorsXmpPagePatch19} +\begin{paste}{CycleIndicatorsXmpPageFull19}{CycleIndicatorsXmpPageEmpty19} +\pastebutton{CycleIndicatorsXmpPageFull19}{\hidepaste} +\tab{5}\spadcommand{cap(complete 3*complete 2**2,dihedral 7)} +\indentrel{3}\begin{verbatim} + (18) 18 + Type: Fraction Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{CycleIndicatorsXmpPageEmpty19} +\begin{paste}{CycleIndicatorsXmpPageEmpty19}{CycleIndicatorsXmpPagePatch19} +\pastebutton{CycleIndicatorsXmpPageEmpty19}{\showpaste} +\tab{5}\spadcommand{cap(complete 3*complete 2**2,dihedral 7)} +\end{paste}\end{patch} + +\begin{patch}{CycleIndicatorsXmpPagePatch20} +\begin{paste}{CycleIndicatorsXmpPageFull20}{CycleIndicatorsXmpPageEmpty20} +\pastebutton{CycleIndicatorsXmpPageFull20}{\hidepaste} +\tab{5}\spadcommand{cap(graphs 5,complete 7*complete 3)} +\indentrel{3}\begin{verbatim} + (19) 4 + Type: Fraction Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{CycleIndicatorsXmpPageEmpty20} +\begin{paste}{CycleIndicatorsXmpPageEmpty20}{CycleIndicatorsXmpPagePatch20} +\pastebutton{CycleIndicatorsXmpPageEmpty20}{\showpaste} +\tab{5}\spadcommand{cap(graphs 5,complete 7*complete 3)} +\end{paste}\end{patch} + +\begin{patch}{CycleIndicatorsXmpPagePatch21} +\begin{paste}{CycleIndicatorsXmpPageFull21}{CycleIndicatorsXmpPageEmpty21} +\pastebutton{CycleIndicatorsXmpPageFull21}{\hidepaste} +\tab{5}\spadcommand{s(x) == powerSum(x)} +\indentrel{3}\begin{verbatim} + Type: Void +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{CycleIndicatorsXmpPageEmpty21} +\begin{paste}{CycleIndicatorsXmpPageEmpty21}{CycleIndicatorsXmpPagePatch21} +\pastebutton{CycleIndicatorsXmpPageEmpty21}{\showpaste} +\tab{5}\spadcommand{s(x) == powerSum(x)} +\end{paste}\end{patch} + +\begin{patch}{CycleIndicatorsXmpPagePatch22} +\begin{paste}{CycleIndicatorsXmpPageFull22}{CycleIndicatorsXmpPageEmpty22} +\pastebutton{CycleIndicatorsXmpPageFull22}{\hidepaste} +\tab{5}\spadcommand{ +cube:=(1/24)*(s 1**8+9*s 2**4 + 8*s 3**2*s 1**2+6*s 4**2)} +\indentrel{3}\begin{verbatim} + 1 2 1 2 2 3 4 1 8 + (21) Ä (4 ) + Ä (3 1 ) + Ä (2 ) + ÄÄ (1 ) + 4 3 8 24 + Type: SymmetricPolynomial Fraction Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{CycleIndicatorsXmpPageEmpty22} +\begin{paste}{CycleIndicatorsXmpPageEmpty22}{CycleIndicatorsXmpPagePatch22} +\pastebutton{CycleIndicatorsXmpPageEmpty22}{\showpaste} +\tab{5}\spadcommand{ +cube:=(1/24)*(s 1**8+9*s 2**4 + 8*s 3**2*s 1**2+6*s 4**2)} +\end{paste}\end{patch} + +\begin{patch}{CycleIndicatorsXmpPagePatch23} +\begin{paste}{CycleIndicatorsXmpPageFull23}{CycleIndicatorsXmpPageEmpty23} +\pastebutton{CycleIndicatorsXmpPageFull23}{\hidepaste} +\tab{5}\spadcommand{cap(complete 4**2,cube)} +\indentrel{3}\begin{verbatim} + (22) 7 + Type: Fraction Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{CycleIndicatorsXmpPageEmpty23} +\begin{paste}{CycleIndicatorsXmpPageEmpty23}{CycleIndicatorsXmpPagePatch23} +\pastebutton{CycleIndicatorsXmpPageEmpty23}{\showpaste} +\tab{5}\spadcommand{cap(complete 4**2,cube)} +\end{paste}\end{patch} + +\begin{patch}{CycleIndicatorsXmpPagePatch24} +\begin{paste}{CycleIndicatorsXmpPageFull24}{CycleIndicatorsXmpPageEmpty24} +\pastebutton{CycleIndicatorsXmpPageFull24}{\hidepaste} +\tab{5}\spadcommand{ +cap(complete 2**3*complete 1**2,wreath(elementary 4,elementary 2))} +\indentrel{3}\begin{verbatim} + (23) 7 + Type: Fraction Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{CycleIndicatorsXmpPageEmpty24} +\begin{paste}{CycleIndicatorsXmpPageEmpty24}{CycleIndicatorsXmpPagePatch24} +\pastebutton{CycleIndicatorsXmpPageEmpty24}{\showpaste} +\tab{5}\spadcommand{ +cap(complete 2**3*complete 1**2,wreath(elementary 4,elementary 2))} +\end{paste}\end{patch} + +\begin{patch}{CycleIndicatorsXmpPagePatch25} +\begin{paste}{CycleIndicatorsXmpPageFull25}{CycleIndicatorsXmpPageEmpty25} +\pastebutton{CycleIndicatorsXmpPageFull25}{\hidepaste} +\tab{5}\spadcommand{ +cap(complete 2**3*complete 1**2,wreath(elementary 4,complete 2))} +\indentrel{3}\begin{verbatim} + (24) 17 + Type: Fraction Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{CycleIndicatorsXmpPageEmpty25} +\begin{paste}{CycleIndicatorsXmpPageEmpty25}{CycleIndicatorsXmpPagePatch25} +\pastebutton{CycleIndicatorsXmpPageEmpty25}{\showpaste} +\tab{5}\spadcommand{ +cap(complete 2**3*complete 1**2,wreath(elementary 4,complete 2))} +\end{paste}\end{patch} + +\begin{patch}{CycleIndicatorsXmpPagePatch26} +\begin{paste}{CycleIndicatorsXmpPageFull26}{CycleIndicatorsXmpPageEmpty26} +\pastebutton{CycleIndicatorsXmpPageFull26}{\hidepaste} +\tab{5}\spadcommand{ +cap(complete 2**3*complete 1**2,wreath(complete 4,elementary 2))} +\indentrel{3}\begin{verbatim} + (25) 10 + Type: Fraction Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{CycleIndicatorsXmpPageEmpty26} +\begin{paste}{CycleIndicatorsXmpPageEmpty26}{CycleIndicatorsXmpPagePatch26} +\pastebutton{CycleIndicatorsXmpPageEmpty26}{\showpaste} +\tab{5}\spadcommand{ +cap(complete 2**3*complete 1**2,wreath(complete 4,elementary 2))} +\end{paste}\end{patch} + +\begin{patch}{CycleIndicatorsXmpPagePatch27} +\begin{paste}{CycleIndicatorsXmpPageFull27}{CycleIndicatorsXmpPageEmpty27} +\pastebutton{CycleIndicatorsXmpPageFull27}{\hidepaste} +\tab{5}\spadcommand{ +cap(complete 2**3*complete 1**2,wreath(complete 4,complete 2))} +\indentrel{3}\begin{verbatim} + (26) 23 + Type: Fraction Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{CycleIndicatorsXmpPageEmpty27} +\begin{paste}{CycleIndicatorsXmpPageEmpty27}{CycleIndicatorsXmpPagePatch27} +\pastebutton{CycleIndicatorsXmpPageEmpty27}{\showpaste} +\tab{5}\spadcommand{ +cap(complete 2**3*complete 1**2,wreath(complete 4,complete 2))} +\end{paste}\end{patch} + +\begin{patch}{CycleIndicatorsXmpPagePatch28} +\begin{paste}{CycleIndicatorsXmpPageFull28}{CycleIndicatorsXmpPageEmpty28} +\pastebutton{CycleIndicatorsXmpPageFull28}{\hidepaste} +\tab{5}\spadcommand{x: ULS(FRAC INT,'x,0) := 'x\bound{x }} +\indentrel{3}\begin{verbatim} + (27) x + Type: UnivariateLaurentSeries(Fraction Integer,x,0) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{CycleIndicatorsXmpPageEmpty28} +\begin{paste}{CycleIndicatorsXmpPageEmpty28}{CycleIndicatorsXmpPagePatch28} +\pastebutton{CycleIndicatorsXmpPageEmpty28}{\showpaste} +\tab{5}\spadcommand{x: ULS(FRAC INT,'x,0) := 'x\bound{x }} +\end{paste}\end{patch} + +\begin{patch}{CycleIndicatorsXmpPagePatch29} +\begin{paste}{CycleIndicatorsXmpPageFull29}{CycleIndicatorsXmpPageEmpty29} +\pastebutton{CycleIndicatorsXmpPageFull29}{\hidepaste} +\tab{5}\spadcommand{ZeroOrOne: INT -> ULS(FRAC INT, 'x, 0)\bound{zodec }} +\indentrel{3}\begin{verbatim} + Type: Void +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{CycleIndicatorsXmpPageEmpty29} +\begin{paste}{CycleIndicatorsXmpPageEmpty29}{CycleIndicatorsXmpPagePatch29} +\pastebutton{CycleIndicatorsXmpPageEmpty29}{\showpaste} +\tab{5}\spadcommand{ZeroOrOne: INT -> ULS(FRAC INT, 'x, 0)\bound{zodec }} +\end{paste}\end{patch} + +\begin{patch}{CycleIndicatorsXmpPagePatch30} +\begin{paste}{CycleIndicatorsXmpPageFull30}{CycleIndicatorsXmpPageEmpty30} +\pastebutton{CycleIndicatorsXmpPageFull30}{\hidepaste} +\tab{5}\spadcommand{Integers: INT -> ULS(FRAC INT, 'x, 0)\bound{idec }} +\indentrel{3}\begin{verbatim} + Type: Void +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{CycleIndicatorsXmpPageEmpty30} +\begin{paste}{CycleIndicatorsXmpPageEmpty30}{CycleIndicatorsXmpPagePatch30} +\pastebutton{CycleIndicatorsXmpPageEmpty30}{\showpaste} +\tab{5}\spadcommand{Integers: INT -> ULS(FRAC INT, 'x, 0)\bound{idec }} +\end{paste}\end{patch} + +\begin{patch}{CycleIndicatorsXmpPagePatch31} +\begin{paste}{CycleIndicatorsXmpPageFull31}{CycleIndicatorsXmpPageEmpty31} +\pastebutton{CycleIndicatorsXmpPageFull31}{\hidepaste} +\tab{5}\spadcommand{ZeroOrOne n == 1+x**n\free{x zodec }\bound{zo }} +\indentrel{3}\begin{verbatim} + Type: Void +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{CycleIndicatorsXmpPageEmpty31} +\begin{paste}{CycleIndicatorsXmpPageEmpty31}{CycleIndicatorsXmpPagePatch31} +\pastebutton{CycleIndicatorsXmpPageEmpty31}{\showpaste} +\tab{5}\spadcommand{ZeroOrOne n == 1+x**n\free{x zodec }\bound{zo }} +\end{paste}\end{patch} + +\begin{patch}{CycleIndicatorsXmpPagePatch32} +\begin{paste}{CycleIndicatorsXmpPageFull32}{CycleIndicatorsXmpPageEmpty32} +\pastebutton{CycleIndicatorsXmpPageFull32}{\hidepaste} +\tab{5}\spadcommand{ZeroOrOne 5\free{zo }} +\indentrel{3}\begin{verbatim} + 5 + (31) 1 + x + Type: UnivariateLaurentSeries(Fraction Integer,x,0) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{CycleIndicatorsXmpPageEmpty32} +\begin{paste}{CycleIndicatorsXmpPageEmpty32}{CycleIndicatorsXmpPagePatch32} +\pastebutton{CycleIndicatorsXmpPageEmpty32}{\showpaste} +\tab{5}\spadcommand{ZeroOrOne 5\free{zo }} +\end{paste}\end{patch} + +\begin{patch}{CycleIndicatorsXmpPagePatch33} +\begin{paste}{CycleIndicatorsXmpPageFull33}{CycleIndicatorsXmpPageEmpty33} +\pastebutton{CycleIndicatorsXmpPageFull33}{\hidepaste} +\tab{5}\spadcommand{Integers n == 1/(1-x**n)\free{x idec }\bound{i }} +\indentrel{3}\begin{verbatim} + Type: Void +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{CycleIndicatorsXmpPageEmpty33} +\begin{paste}{CycleIndicatorsXmpPageEmpty33}{CycleIndicatorsXmpPagePatch33} +\pastebutton{CycleIndicatorsXmpPageEmpty33}{\showpaste} +\tab{5}\spadcommand{Integers n == 1/(1-x**n)\free{x idec }\bound{i }} +\end{paste}\end{patch} + +\begin{patch}{CycleIndicatorsXmpPagePatch34} +\begin{paste}{CycleIndicatorsXmpPageFull34}{CycleIndicatorsXmpPageEmpty34} +\pastebutton{CycleIndicatorsXmpPageFull34}{\hidepaste} +\tab{5}\spadcommand{Integers 5\free{i }} +\indentrel{3}\begin{verbatim} + 5 10 11 + (33) 1 + x + x + O(x ) + Type: UnivariateLaurentSeries(Fraction Integer,x,0) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{CycleIndicatorsXmpPageEmpty34} +\begin{paste}{CycleIndicatorsXmpPageEmpty34}{CycleIndicatorsXmpPagePatch34} +\pastebutton{CycleIndicatorsXmpPageEmpty34}{\showpaste} +\tab{5}\spadcommand{Integers 5\free{i }} +\end{paste}\end{patch} + +\begin{patch}{CycleIndicatorsXmpPagePatch35} +\begin{paste}{CycleIndicatorsXmpPageFull35}{CycleIndicatorsXmpPageEmpty35} +\pastebutton{CycleIndicatorsXmpPageFull35}{\hidepaste} +\tab{5}\spadcommand{eval(ZeroOrOne, graphs 5)\free{zo }} +\indentrel{3}\begin{verbatim} + (34) + 2 3 4 5 6 7 8 9 + 1 + x + 2x + 4x + 6x + 6x + 6x + 4x + 2x + x + + + 10 11 + x + O(x ) + Type: UnivariateLaurentSeries(Fraction Integer,x,0) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{CycleIndicatorsXmpPageEmpty35} +\begin{paste}{CycleIndicatorsXmpPageEmpty35}{CycleIndicatorsXmpPagePatch35} +\pastebutton{CycleIndicatorsXmpPageEmpty35}{\showpaste} +\tab{5}\spadcommand{eval(ZeroOrOne, graphs 5)\free{zo }} +\end{paste}\end{patch} + +\begin{patch}{CycleIndicatorsXmpPagePatch36} +\begin{paste}{CycleIndicatorsXmpPageFull36}{CycleIndicatorsXmpPageEmpty36} +\pastebutton{CycleIndicatorsXmpPageFull36}{\hidepaste} +\tab{5}\spadcommand{eval(ZeroOrOne,dihedral 8)\free{zo }} +\indentrel{3}\begin{verbatim} + 2 3 4 5 6 7 8 + (35) 1 + x + 4x + 5x + 8x + 5x + 4x + x + x + Type: UnivariateLaurentSeries(Fraction Integer,x,0) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{CycleIndicatorsXmpPageEmpty36} +\begin{paste}{CycleIndicatorsXmpPageEmpty36}{CycleIndicatorsXmpPagePatch36} +\pastebutton{CycleIndicatorsXmpPageEmpty36}{\showpaste} +\tab{5}\spadcommand{eval(ZeroOrOne,dihedral 8)\free{zo }} +\end{paste}\end{patch} + +\begin{patch}{CycleIndicatorsXmpPagePatch37} +\begin{paste}{CycleIndicatorsXmpPageFull37}{CycleIndicatorsXmpPageEmpty37} +\pastebutton{CycleIndicatorsXmpPageFull37}{\hidepaste} +\tab{5}\spadcommand{eval(Integers,complete 4)\free{i }} +\indentrel{3}\begin{verbatim} + (36) + 2 3 4 5 6 7 8 + 1 + x + 2x + 3x + 5x + 6x + 9x + 11x + 15x + + + 9 10 11 + 18x + 23x + O(x ) + Type: UnivariateLaurentSeries(Fraction Integer,x,0) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{CycleIndicatorsXmpPageEmpty37} +\begin{paste}{CycleIndicatorsXmpPageEmpty37}{CycleIndicatorsXmpPagePatch37} +\pastebutton{CycleIndicatorsXmpPageEmpty37}{\showpaste} +\tab{5}\spadcommand{eval(Integers,complete 4)\free{i }} +\end{paste}\end{patch} + +\begin{patch}{CycleIndicatorsXmpPagePatch38} +\begin{paste}{CycleIndicatorsXmpPageFull38}{CycleIndicatorsXmpPageEmpty38} +\pastebutton{CycleIndicatorsXmpPageFull38}{\hidepaste} +\tab{5}\spadcommand{eval(Integers,elementary 4)\free{i }} +\indentrel{3}\begin{verbatim} + (37) + 6 7 8 9 10 11 12 13 + x + x + 2x + 3x + 5x + 6x + 9x + 11x + + + 14 15 16 17 + 15x + 18x + 23x + O(x ) + Type: UnivariateLaurentSeries(Fraction Integer,x,0) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{CycleIndicatorsXmpPageEmpty38} +\begin{paste}{CycleIndicatorsXmpPageEmpty38}{CycleIndicatorsXmpPagePatch38} +\pastebutton{CycleIndicatorsXmpPageEmpty38}{\showpaste} +\tab{5}\spadcommand{eval(Integers,elementary 4)\free{i }} +\end{paste}\end{patch} + +\begin{patch}{CycleIndicatorsXmpPagePatch39} +\begin{paste}{CycleIndicatorsXmpPageFull39}{CycleIndicatorsXmpPageEmpty39} +\pastebutton{CycleIndicatorsXmpPageFull39}{\hidepaste} +\tab{5}\spadcommand{eval(ZeroOrOne,cube)\free{zo }} +\indentrel{3}\begin{verbatim} + 2 3 4 5 6 7 8 + (38) 1 + x + 3x + 3x + 7x + 3x + 3x + x + x + Type: UnivariateLaurentSeries(Fraction Integer,x,0) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{CycleIndicatorsXmpPageEmpty39} +\begin{paste}{CycleIndicatorsXmpPageEmpty39}{CycleIndicatorsXmpPagePatch39} +\pastebutton{CycleIndicatorsXmpPageEmpty39}{\showpaste} +\tab{5}\spadcommand{eval(ZeroOrOne,cube)\free{zo }} +\end{paste}\end{patch} + +\begin{patch}{CycleIndicatorsXmpPagePatch40} +\begin{paste}{CycleIndicatorsXmpPageFull40}{CycleIndicatorsXmpPageEmpty40} +\pastebutton{CycleIndicatorsXmpPageFull40}{\hidepaste} +\tab{5}\spadcommand{eval(Integers,cube)\free{i }} +\indentrel{3}\begin{verbatim} + (39) + 2 3 4 5 6 7 + 1 + x + 4x + 7x + 21x + 37x + 85x + 151x + + + 8 9 10 11 + 292x + 490x + 848x + O(x ) + Type: UnivariateLaurentSeries(Fraction Integer,x,0) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{CycleIndicatorsXmpPageEmpty40} +\begin{paste}{CycleIndicatorsXmpPageEmpty40}{CycleIndicatorsXmpPagePatch40} +\pastebutton{CycleIndicatorsXmpPageEmpty40}{\showpaste} +\tab{5}\spadcommand{eval(Integers,cube)\free{i }} +\end{paste}\end{patch} + +\begin{patch}{CycleIndicatorsXmpPagePatch41} +\begin{paste}{CycleIndicatorsXmpPageFull41}{CycleIndicatorsXmpPageEmpty41} +\pastebutton{CycleIndicatorsXmpPageFull41}{\hidepaste} +\tab{5}\spadcommand{eval(Integers,graphs 5)\free{i }} +\indentrel{3}\begin{verbatim} + (40) + 2 3 4 5 6 7 + 1 + x + 3x + 7x + 17x + 35x + 76x + 149x + + + 8 9 10 11 + 291x + 539x + 974x + O(x ) + Type: UnivariateLaurentSeries(Fraction Integer,x,0) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{CycleIndicatorsXmpPageEmpty41} +\begin{paste}{CycleIndicatorsXmpPageEmpty41}{CycleIndicatorsXmpPagePatch41} +\pastebutton{CycleIndicatorsXmpPageEmpty41}{\showpaste} +\tab{5}\spadcommand{eval(Integers,graphs 5)\free{i }} +\end{paste}\end{patch} + +\begin{patch}{CycleIndicatorsXmpPagePatch42} +\begin{paste}{CycleIndicatorsXmpPageFull42}{CycleIndicatorsXmpPageEmpty42} +\pastebutton{CycleIndicatorsXmpPageFull42}{\hidepaste} +\tab{5}\spadcommand{eval(ZeroOrOne ,graphs 15)\free{zo }} +\indentrel{3}\begin{verbatim} + (41) + 2 3 4 5 6 7 + 1 + x + 2x + 5x + 11x + 26x + 68x + 177x + + + 8 9 10 11 + 496x + 1471x + 4583x + O(x ) + Type: UnivariateLaurentSeries(Fraction Integer,x,0) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{CycleIndicatorsXmpPageEmpty42} +\begin{paste}{CycleIndicatorsXmpPageEmpty42}{CycleIndicatorsXmpPagePatch42} +\pastebutton{CycleIndicatorsXmpPageEmpty42}{\showpaste} +\tab{5}\spadcommand{eval(ZeroOrOne ,graphs 15)\free{zo }} +\end{paste}\end{patch} + +\begin{patch}{CycleIndicatorsXmpPagePatch43} +\begin{paste}{CycleIndicatorsXmpPageFull43}{CycleIndicatorsXmpPageEmpty43} +\pastebutton{CycleIndicatorsXmpPageFull43}{\hidepaste} +\tab{5}\spadcommand{cap(dihedral 30,complete 7*complete 8*complete 5*complete 10)} +\indentrel{3}\begin{verbatim} + (42) 49958972383320 + Type: Fraction Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{CycleIndicatorsXmpPageEmpty43} +\begin{paste}{CycleIndicatorsXmpPageEmpty43}{CycleIndicatorsXmpPagePatch43} +\pastebutton{CycleIndicatorsXmpPageEmpty43}{\showpaste} +\tab{5}\spadcommand{ +cap(dihedral 30,complete 7*complete 8*complete 5*complete 10)} +\end{paste}\end{patch} + +\begin{patch}{CycleIndicatorsXmpPagePatch44} +\begin{paste}{CycleIndicatorsXmpPageFull44}{CycleIndicatorsXmpPageEmpty44} +\pastebutton{CycleIndicatorsXmpPageFull44}{\hidepaste} +\tab{5}\spadcommand{sf3221:= SFunction [3,2,2,1]\bound{sf3221 }} +\indentrel{3}\begin{verbatim} + (43) + 1 1 2 1 2 1 + ÄÄ (6 2) - ÄÄ (6 1 ) - ÄÄ (4 ) + ÄÄ (4 3 1) + 12 12 16 12 + + + 1 4 1 2 1 2 2 1 2 + ÄÄ (4 1 ) - ÄÄ (3 2) + ÄÄ (3 1 ) - ÄÄ (3 2 1) + 24 36 36 24 + + + 1 3 1 5 1 4 1 3 2 + - ÄÄ (3 2 1 ) - ÄÄ (3 1 ) - ÄÄÄ (2 ) + ÄÄ (2 1 ) + 36 72 192 48 + + + 1 2 4 1 6 1 8 + ÄÄ (2 1 ) - ÄÄÄ (2 1 ) + ÄÄÄ (1 ) + 96 144 576 + Type: SymmetricPolynomial Fraction Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{CycleIndicatorsXmpPageEmpty44} +\begin{paste}{CycleIndicatorsXmpPageEmpty44}{CycleIndicatorsXmpPagePatch44} +\pastebutton{CycleIndicatorsXmpPageEmpty44}{\showpaste} +\tab{5}\spadcommand{sf3221:= SFunction [3,2,2,1]\bound{sf3221 }} +\end{paste}\end{patch} + +\begin{patch}{CycleIndicatorsXmpPagePatch45} +\begin{paste}{CycleIndicatorsXmpPageFull45}{CycleIndicatorsXmpPageEmpty45} +\pastebutton{CycleIndicatorsXmpPageFull45}{\hidepaste} +\tab{5}\spadcommand{cap(sf3221,complete 2**4)\free{sf3221 }} +\indentrel{3}\begin{verbatim} + (44) 3 + Type: Fraction Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{CycleIndicatorsXmpPageEmpty45} +\begin{paste}{CycleIndicatorsXmpPageEmpty45}{CycleIndicatorsXmpPagePatch45} +\pastebutton{CycleIndicatorsXmpPageEmpty45}{\showpaste} +\tab{5}\spadcommand{cap(sf3221,complete 2**4)\free{sf3221 }} +\end{paste}\end{patch} + +\begin{patch}{CycleIndicatorsXmpPagePatch46} +\begin{paste}{CycleIndicatorsXmpPageFull46}{CycleIndicatorsXmpPageEmpty46} +\pastebutton{CycleIndicatorsXmpPageFull46}{\hidepaste} +\tab{5}\spadcommand{cap(sf3221, powerSum 1**8)\free{sf3221 }} +\indentrel{3}\begin{verbatim} + (45) 70 + Type: Fraction Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{CycleIndicatorsXmpPageEmpty46} +\begin{paste}{CycleIndicatorsXmpPageEmpty46}{CycleIndicatorsXmpPagePatch46} +\pastebutton{CycleIndicatorsXmpPageEmpty46}{\showpaste} +\tab{5}\spadcommand{cap(sf3221, powerSum 1**8)\free{sf3221 }} +\end{paste}\end{patch} + +\begin{patch}{CycleIndicatorsXmpPagePatch47} +\begin{paste}{CycleIndicatorsXmpPageFull47}{CycleIndicatorsXmpPageEmpty47} +\pastebutton{CycleIndicatorsXmpPageFull47}{\hidepaste} +\tab{5}\spadcommand{eval(Integers, sf3221)\free{i sf3221 }} +\indentrel{3}\begin{verbatim} + (46) + 9 10 11 12 13 14 15 + x + 3x + 7x + 14x + 27x + 47x + 79x + + + 16 17 18 19 20 + 126x + 196x + 294x + 432x + O(x ) + Type: UnivariateLaurentSeries(Fraction Integer,x,0) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{CycleIndicatorsXmpPageEmpty47} +\begin{paste}{CycleIndicatorsXmpPageEmpty47}{CycleIndicatorsXmpPagePatch47} +\pastebutton{CycleIndicatorsXmpPageEmpty47}{\showpaste} +\tab{5}\spadcommand{eval(Integers, sf3221)\free{i sf3221 }} +\end{paste}\end{patch} + @ \section{coverex.ht} \pagehead{ExampleCoverPage}{coverex.ht}{Examples Of Axiom Commands} @@ -4866,7 +10441,205 @@ The smallest is \spadpaste{f := integrate(sqrt(1 + t**3),t) \bound{f}} \spadpaste{differentiate(f,t) \free{f}} \spadpaste{differentiate(f * t**2,t) \free{f}} -\endmenu\endscroll\end{page} +\endmenu\endscroll +\end{page} + +\begin{patch}{MenuexdiffPatch1} +\begin{paste}{MenuexdiffFull1}{MenuexdiffEmpty1} +\pastebutton{MenuexdiffFull1}{\hidepaste} +\tab{5}\spadcommand{differentiate(sin(x) * exp(x**2),x)} +\indentrel{3}\begin{verbatim} + 2 2 + x x + (1) 2x %e sin(x) + cos(x)%e + Type: Expression Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{MenuexdiffEmpty1} +\begin{paste}{MenuexdiffEmpty1}{MenuexdiffPatch1} +\pastebutton{MenuexdiffEmpty1}{\showpaste} +\tab{5}\spadcommand{differentiate(sin(x) * exp(x**2),x)} +\end{paste}\end{patch} + +\begin{patch}{MenuexdiffPatch2} +\begin{paste}{MenuexdiffFull2}{MenuexdiffEmpty2} +\pastebutton{MenuexdiffFull2}{\hidepaste} +\tab{5}\spadcommand{differentiate(sin(x) * tan(y)/(x**2 + y**2),x)} +\indentrel{3}\begin{verbatim} + 2 2 + (- 2x sin(x) + (y + x )cos(x))tan(y) + (2) ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ + 4 2 2 4 + y + 2x y + x + Type: Expression Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{MenuexdiffEmpty2} +\begin{paste}{MenuexdiffEmpty2}{MenuexdiffPatch2} +\pastebutton{MenuexdiffEmpty2}{\showpaste} +\tab{5}\spadcommand{differentiate(sin(x) * tan(y)/(x**2 + y**2),x)} +\end{paste}\end{patch} + +\begin{patch}{MenuexdiffPatch3} +\begin{paste}{MenuexdiffFull3}{MenuexdiffEmpty3} +\pastebutton{MenuexdiffFull3}{\hidepaste} +\tab{5}\spadcommand{differentiate(sin(x) * tan(y)/(x**2 + y**2),y)} +\indentrel{3}\begin{verbatim} + (3) + 2 2 2 + (y + x )sin(x)tan(y) - 2y sin(x)tan(y) + + + 2 2 + (y + x )sin(x) + / + 4 2 2 4 + y + 2x y + x + Type: Expression Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{MenuexdiffEmpty3} +\begin{paste}{MenuexdiffEmpty3}{MenuexdiffPatch3} +\pastebutton{MenuexdiffEmpty3}{\showpaste} +\tab{5}\spadcommand{differentiate(sin(x) * tan(y)/(x**2 + y**2),y)} +\end{paste}\end{patch} + +\begin{patch}{MenuexdiffPatch4} +\begin{paste}{MenuexdiffFull4}{MenuexdiffEmpty4} +\pastebutton{MenuexdiffFull4}{\hidepaste} +\tab{5}\spadcommand{differentiate(exp(x**2),x,4)} +\indentrel{3}\begin{verbatim} + 2 + 4 2 x + (4) (16x + 48x + 12)%e + Type: Expression Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{MenuexdiffEmpty4} +\begin{paste}{MenuexdiffEmpty4}{MenuexdiffPatch4} +\pastebutton{MenuexdiffEmpty4}{\showpaste} +\tab{5}\spadcommand{differentiate(exp(x**2),x,4)} +\end{paste}\end{patch} + +\begin{patch}{MenuexdiffPatch5} +\begin{paste}{MenuexdiffFull5}{MenuexdiffEmpty5} +\pastebutton{MenuexdiffFull5}{\hidepaste} +\tab{5}\spadcommand{differentiate(sin(x)/(x**2 + y**2),[x,y])} +\indentrel{3}\begin{verbatim} + 3 2 + 8x y sin(x) + (- 2y - 2x y)cos(x) + (5) ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ + 6 2 4 4 2 6 + y + 3x y + 3x y + x + Type: Expression Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{MenuexdiffEmpty5} +\begin{paste}{MenuexdiffEmpty5}{MenuexdiffPatch5} +\pastebutton{MenuexdiffEmpty5}{\showpaste} +\tab{5}\spadcommand{differentiate(sin(x)/(x**2 + y**2),[x,y])} +\end{paste}\end{patch} + +\begin{patch}{MenuexdiffPatch6} +\begin{paste}{MenuexdiffFull6}{MenuexdiffEmpty6} +\pastebutton{MenuexdiffFull6}{\hidepaste} +\tab{5}\spadcommand{differentiate(sin(x)/(x**2 + y**2),[x,y,y])} +\indentrel{3}\begin{verbatim} + (6) + 2 3 4 2 2 4 + (- 40x y + 8x )sin(x) + (6y + 4x y - 2x )cos(x) + ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ + 8 2 6 4 4 6 2 8 + y + 4x y + 6x y + 4x y + x + Type: Expression Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{MenuexdiffEmpty6} +\begin{paste}{MenuexdiffEmpty6}{MenuexdiffPatch6} +\pastebutton{MenuexdiffEmpty6}{\showpaste} +\tab{5}\spadcommand{differentiate(sin(x)/(x**2 + y**2),[x,y,y])} +\end{paste}\end{patch} + +\begin{patch}{MenuexdiffPatch7} +\begin{paste}{MenuexdiffFull7}{MenuexdiffEmpty7} +\pastebutton{MenuexdiffFull7}{\hidepaste} +\tab{5}\spadcommand{differentiate(cos(z)/(x**2 + y**3),[x,y,z],[1,2,3])} +\indentrel{3}\begin{verbatim} + 4 3 + (- 84x y + 24x y)sin(z) + (7) ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ + 12 2 9 4 6 6 3 8 + y + 4x y + 6x y + 4x y + x + Type: Expression Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{MenuexdiffEmpty7} +\begin{paste}{MenuexdiffEmpty7}{MenuexdiffPatch7} +\pastebutton{MenuexdiffEmpty7}{\showpaste} +\tab{5}\spadcommand{differentiate(cos(z)/(x**2 + y**3),[x,y,z],[1,2,3])} +\end{paste}\end{patch} + +\begin{patch}{MenuexdiffPatch8} +\begin{paste}{MenuexdiffFull8}{MenuexdiffEmpty8} +\pastebutton{MenuexdiffFull8}{\hidepaste} +\tab{5}\spadcommand{f := integrate(sqrt(1 + t**3),t)\bound{f }} +\indentrel{3}\begin{verbatim} + t ÚÄÄÄÄÄÄÄ¿ + Ú¿ ³ 3 + (8) ³ \³%N + 1 d%N + ÀÙ + Type: Union(Expression Integer,...) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{MenuexdiffEmpty8} +\begin{paste}{MenuexdiffEmpty8}{MenuexdiffPatch8} +\pastebutton{MenuexdiffEmpty8}{\showpaste} +\tab{5}\spadcommand{f := integrate(sqrt(1 + t**3),t)\bound{f }} +\end{paste}\end{patch} + +\begin{patch}{MenuexdiffPatch9} +\begin{paste}{MenuexdiffFull9}{MenuexdiffEmpty9} +\pastebutton{MenuexdiffFull9}{\hidepaste} +\tab{5}\spadcommand{differentiate(f,t)\free{f }} +\indentrel{3}\begin{verbatim} + ÚÄÄÄÄÄÄ¿ + ³ 3 + (9) \³t + 1 + Type: Expression Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{MenuexdiffEmpty9} +\begin{paste}{MenuexdiffEmpty9}{MenuexdiffPatch9} +\pastebutton{MenuexdiffEmpty9}{\showpaste} +\tab{5}\spadcommand{differentiate(f,t)\free{f }} +\end{paste}\end{patch} + +\begin{patch}{MenuexdiffPatch10} +\begin{paste}{MenuexdiffFull10}{MenuexdiffEmpty10} +\pastebutton{MenuexdiffFull10}{\hidepaste} +\tab{5}\spadcommand{differentiate(f * t**2,t)\free{f }} +\indentrel{3}\begin{verbatim} + t ÚÄÄÄÄÄÄÄ¿ ÚÄÄÄÄÄÄ¿ + Ú¿ ³ 3 2 ³ 3 + (10) 2t ³ \³%N + 1 d%N + t \³t + 1 + ÀÙ + Type: Expression Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{MenuexdiffEmpty10} +\begin{paste}{MenuexdiffEmpty10}{MenuexdiffPatch10} +\pastebutton{MenuexdiffEmpty10}{\showpaste} +\tab{5}\spadcommand{differentiate(f * t**2,t)\free{f }} +\end{paste}\end{patch} @ \pagehead{Menuexint}{coverex.ht}{Integration} @@ -4920,7 +10693,312 @@ The smallest is \menudownlink{An Integral of a Non-elementary Function}{ExIntNonElementary} \spadpaste{integrate(exp(-x**2) * erf(x) / (erf(x)**3 - erf(x)**2 - erf(x) + 1),x)} -\endmenu\endscroll\end{page} +\endmenu\endscroll +\end{page} + +\begin{patch}{MenuexintPatch1} +\begin{paste}{MenuexintFull1}{MenuexintEmpty1} +\pastebutton{MenuexintFull1}{\hidepaste} +\tab{5}\spadcommand{integrate((x**2+2*x+1)/((x+1)**6+1),x)} +\indentrel{3}\begin{verbatim} + 3 2 + atan(x + 3x + 3x + 1) + (1) ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ + 3 + Type: Union(Expression Integer,...) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{MenuexintEmpty1} +\begin{paste}{MenuexintEmpty1}{MenuexintPatch1} +\pastebutton{MenuexintEmpty1}{\showpaste} +\tab{5}\spadcommand{integrate((x**2+2*x+1)/((x+1)**6+1),x)} +\end{paste}\end{patch} + +\begin{patch}{MenuexintPatch2} +\begin{paste}{MenuexintFull2}{MenuexintEmpty2} +\pastebutton{MenuexintFull2}{\hidepaste} +\tab{5}\spadcommand{integrate(1/(x**3+x+1),x)\bound{i }} +\indentrel{3}\begin{verbatim} + (2) + ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿ + ³ 2 + ³- 93%%CE0 + 12 + ( ³ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ - %%CE0) + \³ 31 + * + log + ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿ + ³ 2 + ³- 93%%CE0 + 12 2 + (62%%CE0 + 31) ³ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ + 62%%CE0 + \³ 31 + + + - 31%%CE0 + 18x - 4 + + + ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿ + ³ 2 + ³- 93%%CE0 + 12 + (- ³ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ - %%CE0) + \³ 31 + * + log + ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿ + ³ 2 + ³- 93%%CE0 + 12 + (- 62%%CE0 - 31) ³ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ + \³ 31 + + + 2 + 62%%CE0 - 31%%CE0 + 18x - 4 + + + 2 + 2%%CE0 log(- 62%%CE0 + 31%%CE0 + 9x + 4) + / + 2 + Type: Union(Expression Integer,...) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{MenuexintEmpty2} +\begin{paste}{MenuexintEmpty2}{MenuexintPatch2} +\pastebutton{MenuexintEmpty2}{\showpaste} +\tab{5}\spadcommand{integrate(1/(x**3+x+1),x)\bound{i }} +\end{paste}\end{patch} + +\begin{patch}{MenuexintPatch3} +\begin{paste}{MenuexintFull3}{MenuexintEmpty3} +\pastebutton{MenuexintFull3}{\hidepaste} +\tab{5}\spadcommand{definingPolynomial(tower(\%).2::EXPR INT)\free{i }} +\indentrel{3}\begin{verbatim} + 3 + 31%%CE0 - 3%%CE0 - 1 + (3) ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ + 31 + Type: Expression Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{MenuexintEmpty3} +\begin{paste}{MenuexintEmpty3}{MenuexintPatch3} +\pastebutton{MenuexintEmpty3}{\showpaste} +\tab{5}\spadcommand{definingPolynomial(tower(\%).2::EXPR INT)\free{i }} +\end{paste}\end{patch} + +\begin{patch}{MenuexintPatch4} +\begin{paste}{MenuexintFull4}{MenuexintEmpty4} +\pastebutton{MenuexintFull4}{\hidepaste} +\tab{5}\spadcommand{integrate(1/(x**2 + a),x)} +\indentrel{3}\begin{verbatim} + 2 ÚÄÄÄ¿ + (x - a)\³- a + 2a x ÚÄ¿ + log(ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ) x\³a + 2 atan(ÄÄÄÄÄ) + x + a a + (4) [ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ,ÄÄÄÄÄÄÄÄÄÄÄ] + ÚÄÄÄ¿ ÚÄ¿ + 2\³- a \³a + Type: Union(List Expression Integer,...) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{MenuexintEmpty4} +\begin{paste}{MenuexintEmpty4}{MenuexintPatch4} +\pastebutton{MenuexintEmpty4}{\showpaste} +\tab{5}\spadcommand{integrate(1/(x**2 + a),x)} +\end{paste}\end{patch} + +\begin{patch}{MenuexintPatch5} +\begin{paste}{MenuexintFull5}{MenuexintEmpty5} +\pastebutton{MenuexintFull5}{\hidepaste} +\tab{5}\spadcommand{complexIntegrate(1/(x**2 + a),x)} +\indentrel{3}\begin{verbatim} + ÚÄÄÄ¿ ÚÄÄÄ¿ + x\³- a + a x\³- a - a + log(ÄÄÄÄÄÄÄÄÄÄÄ) - log(ÄÄÄÄÄÄÄÄÄÄÄ) + ÚÄÄÄ¿ ÚÄÄÄ¿ + \³- a \³- a + (5) ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ + ÚÄÄÄ¿ + 2\³- a + Type: Expression Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{MenuexintEmpty5} +\begin{paste}{MenuexintEmpty5}{MenuexintPatch5} +\pastebutton{MenuexintEmpty5}{\showpaste} +\tab{5}\spadcommand{complexIntegrate(1/(x**2 + a),x)} +\end{paste}\end{patch} + +\begin{patch}{MenuexintPatch6} +\begin{paste}{MenuexintFull6}{MenuexintEmpty6} +\pastebutton{MenuexintFull6}{\hidepaste} +\tab{5}\spadcommand{integrate(x**3 / (a+b*x)**(1/3),x)} +\indentrel{3}\begin{verbatim} + (6) + 3 3 2 2 2 3 3ÚÄÄÄÄÄÄÄ¿2 + (120b x - 135a b x + 162a b x - 243a )\³b x + a + ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ + 4 + 440b + Type: Union(Expression Integer,...) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{MenuexintEmpty6} +\begin{paste}{MenuexintEmpty6}{MenuexintPatch6} +\pastebutton{MenuexintEmpty6}{\showpaste} +\tab{5}\spadcommand{integrate(x**3 / (a+b*x)**(1/3),x)} +\end{paste}\end{patch} + +\begin{patch}{MenuexintPatch7} +\begin{paste}{MenuexintFull7}{MenuexintEmpty7} +\pastebutton{MenuexintFull7}{\hidepaste} +\tab{5}\spadcommand{integrate(1 / (x**3 * (a+b*x)**(1/3)),x)} +\indentrel{3}\begin{verbatim} + (7) + - + 2 2 ÚÄ¿ + 2b x \³3 + * + 3ÚÄ¿3ÚÄÄÄÄÄÄÄ¿2 3ÚÄ¿2 3ÚÄÄÄÄÄÄÄ¿ + log(\³a \³b x + a + \³a \³b x + a + a) + + + 2 2 ÚÄ¿ 3ÚÄ¿2 3ÚÄÄÄÄÄÄÄ¿ + 4b x \³3 log(\³a \³b x + a - a) + + + ÚÄ¿3ÚÄ¿2 3ÚÄÄÄÄÄÄÄ¿ ÚÄ¿ + 2 2 2\³3 \³a \³b x + a + a\³3 + 12b x atan(ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ) + 3a + + + ÚÄ¿3ÚÄ¿3ÚÄÄÄÄÄÄÄ¿2 + (12b x - 9a)\³3 \³a \³b x + a + / + 2 2 ÚÄ¿3ÚÄ¿ + 18a x \³3 \³a + Type: Union(Expression Integer,...) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{MenuexintEmpty7} +\begin{paste}{MenuexintEmpty7}{MenuexintPatch7} +\pastebutton{MenuexintEmpty7}{\showpaste} +\tab{5}\spadcommand{integrate(1 / (x**3 * (a+b*x)**(1/3)),x)} +\end{paste}\end{patch} + +\begin{patch}{MenuexintPatch8} +\begin{paste}{MenuexintFull8}{MenuexintEmpty8} +\pastebutton{MenuexintFull8}{\hidepaste} +\tab{5}\spadcommand{integrate(log(1 + sqrt(a*x + b)) / x,x)} +\indentrel{3}\begin{verbatim} + x ÚÄÄÄÄÄÄÄÄ¿ + Ú¿ log(\³b + %N a + 1) + (8) ³ ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ d%N + ÀÙ %N + Type: Union(Expression Integer,...) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{MenuexintEmpty8} +\begin{paste}{MenuexintEmpty8}{MenuexintPatch8} +\pastebutton{MenuexintEmpty8}{\showpaste} +\tab{5}\spadcommand{integrate(log(1 + sqrt(a*x + b)) / x,x)} +\end{paste}\end{patch} + +\begin{patch}{MenuexintPatch9} +\begin{paste}{MenuexintFull9}{MenuexintEmpty9} +\pastebutton{MenuexintFull9}{\hidepaste} +\tab{5}\spadcommand{ +integrate((sinh(1+sqrt(x+b))+2*sqrt(x+b))/_ + (sqrt(x+b)*(x+cosh(1+sqrt(x+b)))),x)} +\indentrel{3}\begin{verbatim} + (9) + ÚÄÄÄÄÄ¿ + - 2cosh(\³x + b + 1) - 2x + 2log(ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ) + ÚÄÄÄÄÄ¿ ÚÄÄÄÄÄ¿ + sinh(\³x + b + 1) - cosh(\³x + b + 1) + + + ÚÄÄÄÄÄ¿ + - 2\³x + b + Type: Union(Expression Integer,...) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{MenuexintEmpty9} +\begin{paste}{MenuexintEmpty9}{MenuexintPatch9} +\pastebutton{MenuexintEmpty9}{\showpaste} +\tab{5}\spadcommand{ +integrate((sinh(1+sqrt(x+b))+2*sqrt(x+b))/_ + (sqrt(x+b)*(x+cosh(1+sqrt(x+b)))),x)} +\end{paste}\end{patch} + +\begin{patch}{MenuexintPatch10} +\begin{paste}{MenuexintFull10}{MenuexintEmpty10} +\pastebutton{MenuexintFull10}{\hidepaste} +\tab{5}\spadcommand{integrate(tan(atan(x)/3),x)} +\indentrel{3}\begin{verbatim} + (10) + atan(x) 2 atan(x) 2 + 8log(3tan(ÄÄÄÄÄÄÄ) - 1) - 3tan(ÄÄÄÄÄÄÄ) + 3 3 + + + atan(x) + 18x tan(ÄÄÄÄÄÄÄ) + 3 + / + 18 + Type: Union(Expression Integer,...) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{MenuexintEmpty10} +\begin{paste}{MenuexintEmpty10}{MenuexintPatch10} +\pastebutton{MenuexintEmpty10}{\showpaste} +\tab{5}\spadcommand{integrate(tan(atan(x)/3),x)} +\end{paste}\end{patch} + +\begin{patch}{MenuexintPatch11} +\begin{paste}{MenuexintFull11}{MenuexintEmpty11} +\pastebutton{MenuexintFull11}{\hidepaste} +\tab{5}\spadcommand{integrate((x + 1) / (x * (x + log x)**(3/2)),x)} +\indentrel{3}\begin{verbatim} + ÚÄÄÄÄÄÄÄÄÄÄ¿ + 2\³log(x) + x + (11) - ÄÄÄÄÄÄÄÄÄÄÄÄÄÄ + log(x) + x + Type: Union(Expression Integer,...) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{MenuexintEmpty11} +\begin{paste}{MenuexintEmpty11}{MenuexintPatch11} +\pastebutton{MenuexintEmpty11}{\showpaste} +\tab{5}\spadcommand{integrate((x + 1) / (x * (x + log x)**(3/2)),x)} +\end{paste}\end{patch} + +\begin{patch}{MenuexintPatch12} +\begin{paste}{MenuexintFull12}{MenuexintEmpty12} +\pastebutton{MenuexintFull12}{\hidepaste} +\tab{5}\spadcommand{integrate(exp(-x**2) * erf(x) / (erf(x)**3 - erf(x)**2 - erf(x) + 1),x)} +\indentrel{3}\begin{verbatim} + ÚÄÄÄ¿ erf(x) - 1 ÚÄÄÄ¿ + (erf(x) - 1)\³%pi log(ÄÄÄÄÄÄÄÄÄÄ) - 2\³%pi + erf(x) + 1 + (12) ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ + 8erf(x) - 8 + Type: Union(Expression Integer,...) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{MenuexintEmpty12} +\begin{paste}{MenuexintEmpty12}{MenuexintPatch12} +\pastebutton{MenuexintEmpty12}{\showpaste} +\tab{5}\spadcommand{integrate(exp(-x**2) * erf(x) / + (erf(x)**3 - erf(x)**2 - erf(x) + 1),x)} +\end{paste}\end{patch} @ \pagehead{Menuexlap}{coverex.ht}{Laplace Transforms} @@ -4949,7 +11027,122 @@ The smallest is \spadpaste{laplace(exp(a*t+b)*Ei(c*t), t, s)} \menudownlink{Laplace transform of special functions}{ExLapSpecial2} \spadpaste{laplace(a*Ci(b*t) + c*Si(d*t), t, s)} -\endmenu\endscroll\end{page} +\endmenu\endscroll +\end{page} + +\begin{patch}{MenuexlapPatch1} +\begin{paste}{MenuexlapFull1}{MenuexlapEmpty1} +\pastebutton{MenuexlapFull1}{\hidepaste} +\tab{5}\spadcommand{laplace(t**4 * exp(-a*t) / factorial(4), t, s)} +\indentrel{3}\begin{verbatim} + 1 + (1) ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ + 5 4 2 3 3 2 4 5 + s + 5a s + 10a s + 10a s + 5a s + a + Type: Expression Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{MenuexlapEmpty1} +\begin{paste}{MenuexlapEmpty1}{MenuexlapPatch1} +\pastebutton{MenuexlapEmpty1}{\showpaste} +\tab{5}\spadcommand{laplace(t**4 * exp(-a*t) / factorial(4), t, s)} +\end{paste}\end{patch} + +\begin{patch}{MenuexlapPatch2} +\begin{paste}{MenuexlapFull2}{MenuexlapEmpty2} +\pastebutton{MenuexlapFull2}{\hidepaste} +\tab{5}\spadcommand{laplace(sin(a*t) * cosh(a*t) - cos(a*t) * sinh(a*t), t, s)} +\indentrel{3}\begin{verbatim} + 3 + 4a + (2) ÄÄÄÄÄÄÄÄ + 4 4 + s + 4a + Type: Expression Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{MenuexlapEmpty2} +\begin{paste}{MenuexlapEmpty2}{MenuexlapPatch2} +\pastebutton{MenuexlapEmpty2}{\showpaste} +\tab{5}\spadcommand{laplace(sin(a*t) * cosh(a*t) - cos(a*t) * sinh(a*t), t, s)} +\end{paste}\end{patch} + +\begin{patch}{MenuexlapPatch3} +\begin{paste}{MenuexlapFull3}{MenuexlapEmpty3} +\pastebutton{MenuexlapFull3}{\hidepaste} +\tab{5}\spadcommand{laplace(2/t * (1 - cos(a*t)), t, s)} +\indentrel{3}\begin{verbatim} + 2 2 + (3) log(s + a ) - 2log(s) + Type: Expression Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{MenuexlapEmpty3} +\begin{paste}{MenuexlapEmpty3}{MenuexlapPatch3} +\pastebutton{MenuexlapEmpty3}{\showpaste} +\tab{5}\spadcommand{laplace(2/t * (1 - cos(a*t)), t, s)} +\end{paste}\end{patch} + +\begin{patch}{MenuexlapPatch4} +\begin{paste}{MenuexlapFull4}{MenuexlapEmpty4} +\pastebutton{MenuexlapFull4}{\hidepaste} +\tab{5}\spadcommand{laplace((exp(a*t) - exp(b*t))/t, t, s)} +\indentrel{3}\begin{verbatim} + (4) - log(s - a) + log(s - b) + Type: Expression Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{MenuexlapEmpty4} +\begin{paste}{MenuexlapEmpty4}{MenuexlapPatch4} +\pastebutton{MenuexlapEmpty4}{\showpaste} +\tab{5}\spadcommand{laplace((exp(a*t) - exp(b*t))/t, t, s)} +\end{paste}\end{patch} + +\begin{patch}{MenuexlapPatch5} +\begin{paste}{MenuexlapFull5}{MenuexlapEmpty5} +\pastebutton{MenuexlapFull5}{\hidepaste} +\tab{5}\spadcommand{laplace(exp(a*t+b)*Ei(c*t), t, s)} +\indentrel{3}\begin{verbatim} + b s + c - a + %e log(ÄÄÄÄÄÄÄÄÄ) + c + (5) ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ + s - a + Type: Expression Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{MenuexlapEmpty5} +\begin{paste}{MenuexlapEmpty5}{MenuexlapPatch5} +\pastebutton{MenuexlapEmpty5}{\showpaste} +\tab{5}\spadcommand{laplace(exp(a*t+b)*Ei(c*t), t, s)} +\end{paste}\end{patch} + +\begin{patch}{MenuexlapPatch6} +\begin{paste}{MenuexlapFull6}{MenuexlapEmpty6} +\pastebutton{MenuexlapFull6}{\hidepaste} +\tab{5}\spadcommand{laplace(a*Ci(b*t) + c*Si(d*t), t, s)} +\indentrel{3}\begin{verbatim} + 2 2 + s + b d + a log(ÄÄÄÄÄÄÄ) + 2c atan(Ä) + 2 s + b + (6) ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ + 2s + Type: Expression Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{MenuexlapEmpty6} +\begin{paste}{MenuexlapEmpty6}{MenuexlapPatch6} +\pastebutton{MenuexlapEmpty6}{\showpaste} +\tab{5}\spadcommand{laplace(a*Ci(b*t) + c*Si(d*t), t, s)} +\end{paste}\end{patch} @ \pagehead{Menuexlimit}{coverex.ht}{Limits} @@ -4983,7 +11176,229 @@ The smallest is \spadpaste{complexLimit((2 + z)/(1 - z),z = \%infinity)} \spadpaste{limit(sin(x)/x,x = \%plusInfinity)} \spadpaste{complexLimit(sin(x)/x,x = \%infinity)} -\endmenu\endscroll\end{page} +\endmenu\endscroll +\end{page} + +\begin{patch}{MenuexlimitPatch1} +\begin{paste}{MenuexlimitFull1}{MenuexlimitEmpty1} +\pastebutton{MenuexlimitFull1}{\hidepaste} +\tab{5}\spadcommand{limit((x**2 - 3*x + 2)/(x**2 - 1),x = 1)} +\indentrel{3}\begin{verbatim} + 1 + (1) - Ä + 2 +Type: Union(OrderedCompletion Fraction Polynomial Integer,...) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{MenuexlimitEmpty1} +\begin{paste}{MenuexlimitEmpty1}{MenuexlimitPatch1} +\pastebutton{MenuexlimitEmpty1}{\showpaste} +\tab{5}\spadcommand{limit((x**2 - 3*x + 2)/(x**2 - 1),x = 1)} +\end{paste}\end{patch} + +\begin{patch}{MenuexlimitPatch2} +\begin{paste}{MenuexlimitFull2}{MenuexlimitEmpty2} +\pastebutton{MenuexlimitFull2}{\hidepaste} +\tab{5}\spadcommand{limit(sinh(a*x)/tan(b*x),x = 0)} +\indentrel{3}\begin{verbatim} + a + (2) Ä + b + Type: Union(OrderedCompletion Expression Integer,...) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{MenuexlimitEmpty2} +\begin{paste}{MenuexlimitEmpty2}{MenuexlimitPatch2} +\pastebutton{MenuexlimitEmpty2}{\showpaste} +\tab{5}\spadcommand{limit(sinh(a*x)/tan(b*x),x = 0)} +\end{paste}\end{patch} + +\begin{patch}{MenuexlimitPatch3} +\begin{paste}{MenuexlimitFull3}{MenuexlimitEmpty3} +\pastebutton{MenuexlimitFull3}{\hidepaste} +\tab{5}\spadcommand{limit(x * log(x),x = 0,"right")} +\indentrel{3}\begin{verbatim} + (3) 0 + Type: Union(OrderedCompletion Expression Integer,...) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{MenuexlimitEmpty3} +\begin{paste}{MenuexlimitEmpty3}{MenuexlimitPatch3} +\pastebutton{MenuexlimitEmpty3}{\showpaste} +\tab{5}\spadcommand{limit(x * log(x),x = 0,"right")} +\end{paste}\end{patch} + +\begin{patch}{MenuexlimitPatch4} +\begin{paste}{MenuexlimitFull4}{MenuexlimitEmpty4} +\pastebutton{MenuexlimitFull4}{\hidepaste} +\tab{5}\spadcommand{limit(x * log(x),x = 0)} +\indentrel{3}\begin{verbatim} + (4) [leftHandLimit= "failed",rightHandLimit= 0] +Type: Union(Record(leftHandLimit: Union(OrderedCompletion Expression Integer,"failed"),rightHandLimit: Union(OrderedCompletion Expression Integer,"failed")),...) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{MenuexlimitEmpty4} +\begin{paste}{MenuexlimitEmpty4}{MenuexlimitPatch4} +\pastebutton{MenuexlimitEmpty4}{\showpaste} +\tab{5}\spadcommand{limit(x * log(x),x = 0)} +\end{paste}\end{patch} + +\begin{patch}{MenuexlimitPatch5} +\begin{paste}{MenuexlimitFull5}{MenuexlimitEmpty5} +\pastebutton{MenuexlimitFull5}{\hidepaste} +\tab{5}\spadcommand{limit(sqrt(y**2)/y,y = 0)} +\indentrel{3}\begin{verbatim} + (5) [leftHandLimit= - 1,rightHandLimit= 1] +Type: Union(Record(leftHandLimit: Union(OrderedCompletion Expression Integer,"failed"),rightHandLimit: Union(OrderedCompletion Expression Integer,"failed")),...) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{MenuexlimitEmpty5} +\begin{paste}{MenuexlimitEmpty5}{MenuexlimitPatch5} +\pastebutton{MenuexlimitEmpty5}{\showpaste} +\tab{5}\spadcommand{limit(sqrt(y**2)/y,y = 0)} +\end{paste}\end{patch} + +\begin{patch}{MenuexlimitPatch6} +\begin{paste}{MenuexlimitFull6}{MenuexlimitEmpty6} +\pastebutton{MenuexlimitFull6}{\hidepaste} +\tab{5}\spadcommand{limit(sqrt(1 - cos(t))/t,t = 0)} +\indentrel{3}\begin{verbatim} + 1 1 + (6) [leftHandLimit= - ÄÄÄÄ,rightHandLimit= ÄÄÄÄ] + ÚÄ¿ ÚÄ¿ + \³2 \³2 +Type: Union(Record(leftHandLimit: Union(OrderedCompletion Expression Integer,"failed"),rightHandLimit: Union(OrderedCompletion Expression Integer,"failed")),...) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{MenuexlimitEmpty6} +\begin{paste}{MenuexlimitEmpty6}{MenuexlimitPatch6} +\pastebutton{MenuexlimitEmpty6}{\showpaste} +\tab{5}\spadcommand{limit(sqrt(1 - cos(t))/t,t = 0)} +\end{paste}\end{patch} + +\begin{patch}{MenuexlimitPatch7} +\begin{paste}{MenuexlimitFull7}{MenuexlimitEmpty7} +\pastebutton{MenuexlimitFull7}{\hidepaste} +\tab{5}\spadcommand{limit(sqrt(3*x**2 + 1)/(5*x),x = \%plusInfinity)} +\indentrel{3}\begin{verbatim} + ÚÄ¿ + \³3 + (7) ÄÄÄÄ + 5 + Type: Union(OrderedCompletion Expression Integer,...) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{MenuexlimitEmpty7} +\begin{paste}{MenuexlimitEmpty7}{MenuexlimitPatch7} +\pastebutton{MenuexlimitEmpty7}{\showpaste} +\tab{5}\spadcommand{limit(sqrt(3*x**2 + 1)/(5*x),x = \%plusInfinity)} +\end{paste}\end{patch} + +\begin{patch}{MenuexlimitPatch8} +\begin{paste}{MenuexlimitFull8}{MenuexlimitEmpty8} +\pastebutton{MenuexlimitFull8}{\hidepaste} +\tab{5}\spadcommand{limit(sqrt(3*x**2 + 1)/(5*x),x = \%minusInfinity)} +\indentrel{3}\begin{verbatim} + ÚÄ¿ + \³3 + (8) - ÄÄÄÄ + 5 + Type: Union(OrderedCompletion Expression Integer,...) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{MenuexlimitEmpty8} +\begin{paste}{MenuexlimitEmpty8}{MenuexlimitPatch8} +\pastebutton{MenuexlimitEmpty8}{\showpaste} +\tab{5}\spadcommand{limit(sqrt(3*x**2 + 1)/(5*x),x = \%minusInfinity)} +\end{paste}\end{patch} + +\begin{patch}{MenuexlimitPatch9} +\begin{paste}{MenuexlimitFull9}{MenuexlimitEmpty9} +\pastebutton{MenuexlimitFull9}{\hidepaste} +\tab{5}\spadcommand{limit(z * sin(1/z),z = 0)} +\indentrel{3}\begin{verbatim} + (9) 0 + Type: Union(OrderedCompletion Expression Integer,...) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{MenuexlimitEmpty9} +\begin{paste}{MenuexlimitEmpty9}{MenuexlimitPatch9} +\pastebutton{MenuexlimitEmpty9}{\showpaste} +\tab{5}\spadcommand{limit(z * sin(1/z),z = 0)} +\end{paste}\end{patch} + +\begin{patch}{MenuexlimitPatch10} +\begin{paste}{MenuexlimitFull10}{MenuexlimitEmpty10} +\pastebutton{MenuexlimitFull10}{\hidepaste} +\tab{5}\spadcommand{complexLimit(z * sin(1/z),z = 0)} +\indentrel{3}\begin{verbatim} + (10) "failed" + Type: Union("failed",...) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{MenuexlimitEmpty10} +\begin{paste}{MenuexlimitEmpty10}{MenuexlimitPatch10} +\pastebutton{MenuexlimitEmpty10}{\showpaste} +\tab{5}\spadcommand{complexLimit(z * sin(1/z),z = 0)} +\end{paste}\end{patch} + +\begin{patch}{MenuexlimitPatch11} +\begin{paste}{MenuexlimitFull11}{MenuexlimitEmpty11} +\pastebutton{MenuexlimitFull11}{\hidepaste} +\tab{5}\spadcommand{complexLimit((2 + z)/(1 - z),z = \%infinity)} +\indentrel{3}\begin{verbatim} + (11) - 1 + Type: OnePointCompletion Fraction Polynomial Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{MenuexlimitEmpty11} +\begin{paste}{MenuexlimitEmpty11}{MenuexlimitPatch11} +\pastebutton{MenuexlimitEmpty11}{\showpaste} +\tab{5}\spadcommand{complexLimit((2 + z)/(1 - z),z = \%infinity)} +\end{paste}\end{patch} + +\begin{patch}{MenuexlimitPatch12} +\begin{paste}{MenuexlimitFull12}{MenuexlimitEmpty12} +\pastebutton{MenuexlimitFull12}{\hidepaste} +\tab{5}\spadcommand{limit(sin(x)/x,x = \%plusInfinity)} +\indentrel{3}\begin{verbatim} + (12) 0 + Type: Union(OrderedCompletion Expression Integer,...) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{MenuexlimitEmpty12} +\begin{paste}{MenuexlimitEmpty12}{MenuexlimitPatch12} +\pastebutton{MenuexlimitEmpty12}{\showpaste} +\tab{5}\spadcommand{limit(sin(x)/x,x = \%plusInfinity)} +\end{paste}\end{patch} + +\begin{patch}{MenuexlimitPatch13} +\begin{paste}{MenuexlimitFull13}{MenuexlimitEmpty13} +\pastebutton{MenuexlimitFull13}{\hidepaste} +\tab{5}\spadcommand{complexLimit(sin(x)/x,x = \%infinity)} +\indentrel{3}\begin{verbatim} + (13) "failed" + Type: Union("failed",...) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{MenuexlimitEmpty13} +\begin{paste}{MenuexlimitEmpty13}{MenuexlimitPatch13} +\pastebutton{MenuexlimitEmpty13}{\showpaste} +\tab{5}\spadcommand{complexLimit(sin(x)/x,x = \%infinity)} +\end{paste}\end{patch} @ \pagehead{Menuexmatrix}{coverex.ht}{Matrices} @@ -5028,7 +11443,349 @@ determinant(matrix([[1,2,3,4],[2,3,2,5],[3,4,5,6],[4,1,6,7]]))} \spadpaste{inverse(matrix([[1,2,1],[-2,3,4],[-1,5,6]])) } \menudownlink{Rank of a Matrix}{ExRankMatrix} \spadpaste{rank(matrix([[0,4,1],[5,3,-7],[-5,5,9]]))} -\endmenu\endscroll\end{page} +\endmenu\endscroll +\end{page} + +\begin{patch}{MenuexmatrixPatch1} +\begin{paste}{MenuexmatrixFull1}{MenuexmatrixEmpty1} +\pastebutton{MenuexmatrixFull1}{\hidepaste} +\tab{5}\spadcommand{m1 := matrix([[1,-2,1],[4,2,-4]])\bound{m1 }} +\indentrel{3}\begin{verbatim} + Ú1 - 2 1 ¿ + (1) ³ ³ + À4 2 - 4Ù + Type: Matrix Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{MenuexmatrixEmpty1} +\begin{paste}{MenuexmatrixEmpty1}{MenuexmatrixPatch1} +\pastebutton{MenuexmatrixEmpty1}{\showpaste} +\tab{5}\spadcommand{m1 := matrix([[1,-2,1],[4,2,-4]])\bound{m1 }} +\end{paste}\end{patch} + +\begin{patch}{MenuexmatrixPatch2} +\begin{paste}{MenuexmatrixFull2}{MenuexmatrixEmpty2} +\pastebutton{MenuexmatrixFull2}{\hidepaste} +\tab{5}\spadcommand{m2 := matrix([[1,0,2],[20,30,10],[0,200,100]])\bound{m2 }} +\indentrel{3}\begin{verbatim} + Ú1 0 2 ¿ + ³ ³ + (2) ³20 30 10 ³ + ³ ³ + À0 200 100Ù + Type: Matrix Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{MenuexmatrixEmpty2} +\begin{paste}{MenuexmatrixEmpty2}{MenuexmatrixPatch2} +\pastebutton{MenuexmatrixEmpty2}{\showpaste} +\tab{5}\spadcommand{m2 := matrix([[1,0,2],[20,30,10],[0,200,100]])\bound{m2 }} +\end{paste}\end{patch} + +\begin{patch}{MenuexmatrixPatch3} +\begin{paste}{MenuexmatrixFull3}{MenuexmatrixEmpty3} +\pastebutton{MenuexmatrixFull3}{\hidepaste} +\tab{5}\spadcommand{m3 := matrix([[1,2,3],[2,4,6]])\bound{m3 }} +\indentrel{3}\begin{verbatim} + Ú1 2 3¿ + (3) ³ ³ + À2 4 6Ù + Type: Matrix Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{MenuexmatrixEmpty3} +\begin{paste}{MenuexmatrixEmpty3}{MenuexmatrixPatch3} +\pastebutton{MenuexmatrixEmpty3}{\showpaste} +\tab{5}\spadcommand{m3 := matrix([[1,2,3],[2,4,6]])\bound{m3 }} +\end{paste}\end{patch} + +\begin{patch}{MenuexmatrixPatch4} +\begin{paste}{MenuexmatrixFull4}{MenuexmatrixEmpty4} +\pastebutton{MenuexmatrixFull4}{\hidepaste} +\tab{5}\spadcommand{m1 + m3\free{m1 }\free{m3 }} +\indentrel{3}\begin{verbatim} + Ú2 0 4¿ + (4) ³ ³ + À6 6 2Ù + Type: Matrix Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{MenuexmatrixEmpty4} +\begin{paste}{MenuexmatrixEmpty4}{MenuexmatrixPatch4} +\pastebutton{MenuexmatrixEmpty4}{\showpaste} +\tab{5}\spadcommand{m1 + m3\free{m1 }\free{m3 }} +\end{paste}\end{patch} + +\begin{patch}{MenuexmatrixPatch5} +\begin{paste}{MenuexmatrixFull5}{MenuexmatrixEmpty5} +\pastebutton{MenuexmatrixFull5}{\hidepaste} +\tab{5}\spadcommand{100 * m1\free{m1 }} +\indentrel{3}\begin{verbatim} + Ú100 - 200 100 ¿ + (5) ³ ³ + À400 200 - 400Ù + Type: Matrix Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{MenuexmatrixEmpty5} +\begin{paste}{MenuexmatrixEmpty5}{MenuexmatrixPatch5} +\pastebutton{MenuexmatrixEmpty5}{\showpaste} +\tab{5}\spadcommand{100 * m1\free{m1 }} +\end{paste}\end{patch} + +\begin{patch}{MenuexmatrixPatch6} +\begin{paste}{MenuexmatrixFull6}{MenuexmatrixEmpty6} +\pastebutton{MenuexmatrixFull6}{\hidepaste} +\tab{5}\spadcommand{m1 * m2\free{m1 }\free{m2 }} +\indentrel{3}\begin{verbatim} + Ú- 39 140 82 ¿ + (6) ³ ³ + À 44 - 740 - 372Ù + Type: Matrix Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{MenuexmatrixEmpty6} +\begin{paste}{MenuexmatrixEmpty6}{MenuexmatrixPatch6} +\pastebutton{MenuexmatrixEmpty6}{\showpaste} +\tab{5}\spadcommand{m1 * m2\free{m1 }\free{m2 }} +\end{paste}\end{patch} + +\begin{patch}{MenuexmatrixPatch7} +\begin{paste}{MenuexmatrixFull7}{MenuexmatrixEmpty7} +\pastebutton{MenuexmatrixFull7}{\hidepaste} +\tab{5}\spadcommand{-m1 + m3 * m2\free{m1 }\free{m2 }\free{m3 }} +\indentrel{3}\begin{verbatim} + Ú40 662 321¿ + (7) ³ ³ + À78 1318 648Ù + Type: Matrix Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{MenuexmatrixEmpty7} +\begin{paste}{MenuexmatrixEmpty7}{MenuexmatrixPatch7} +\pastebutton{MenuexmatrixEmpty7}{\showpaste} +\tab{5}\spadcommand{-m1 + m3 * m2\free{m1 }\free{m2 }\free{m3 }} +\end{paste}\end{patch} + +\begin{patch}{MenuexmatrixPatch8} +\begin{paste}{MenuexmatrixFull8}{MenuexmatrixEmpty8} +\pastebutton{MenuexmatrixFull8}{\hidepaste} +\tab{5}\spadcommand{m3 *vector([1,0,1])\free{m3 }} +\indentrel{3}\begin{verbatim} + (8) [4,8] + Type: Vector Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{MenuexmatrixEmpty8} +\begin{paste}{MenuexmatrixEmpty8}{MenuexmatrixPatch8} +\pastebutton{MenuexmatrixEmpty8}{\showpaste} +\tab{5}\spadcommand{m3 *vector([1,0,1])\free{m3 }} +\end{paste}\end{patch} + +\begin{patch}{MenuexmatrixPatch9} +\begin{paste}{MenuexmatrixFull9}{MenuexmatrixEmpty9} +\pastebutton{MenuexmatrixFull9}{\hidepaste} +\tab{5}\spadcommand{diagonalMatrix([1,2,3,2,1])} +\indentrel{3}\begin{verbatim} + Ú1 0 0 0 0¿ + ³ ³ + ³0 2 0 0 0³ + ³ ³ + (9) ³0 0 3 0 0³ + ³ ³ + ³0 0 0 2 0³ + ³ ³ + À0 0 0 0 1Ù + Type: Matrix Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{MenuexmatrixEmpty9} +\begin{paste}{MenuexmatrixEmpty9}{MenuexmatrixPatch9} +\pastebutton{MenuexmatrixEmpty9}{\showpaste} +\tab{5}\spadcommand{diagonalMatrix([1,2,3,2,1])} +\end{paste}\end{patch} + +\begin{patch}{MenuexmatrixPatch10} +\begin{paste}{MenuexmatrixFull10}{MenuexmatrixEmpty10} +\pastebutton{MenuexmatrixFull10}{\hidepaste} +\tab{5}\spadcommand{subMatrix(matrix([[0,1,2,3,4],[5,6,7,8,9],[10,11,12,13,14]]), 1,3,2,4)} +\indentrel{3}\begin{verbatim} + Ú1 2 3 ¿ + ³ ³ + (10) ³6 7 8 ³ + ³ ³ + À11 12 13Ù + Type: Matrix Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{MenuexmatrixEmpty10} +\begin{paste}{MenuexmatrixEmpty10}{MenuexmatrixPatch10} +\pastebutton{MenuexmatrixEmpty10}{\showpaste} +\tab{5}\spadcommand{subMatrix(matrix([[0,1,2,3,4],[5,6,7,8,9],[10,11,12,13,14]]), 1,3,2,4)} +\end{paste}\end{patch} + +\begin{patch}{MenuexmatrixPatch11} +\begin{paste}{MenuexmatrixFull11}{MenuexmatrixEmpty11} +\pastebutton{MenuexmatrixFull11}{\hidepaste} +\tab{5}\spadcommand{horizConcat(matrix([[1,2,3],[6,7,8]]),matrix([[11,12,13],[55,77,88]]))} +\indentrel{3}\begin{verbatim} + Ú1 2 3 11 12 13¿ + (11) ³ ³ + À6 7 8 55 77 88Ù + Type: Matrix Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{MenuexmatrixEmpty11} +\begin{paste}{MenuexmatrixEmpty11}{MenuexmatrixPatch11} +\pastebutton{MenuexmatrixEmpty11}{\showpaste} +\tab{5}\spadcommand{horizConcat(matrix([[1,2,3],[6,7,8]]),matrix([[11,12,13],[55,77,88]]))} +\end{paste}\end{patch} + +\begin{patch}{MenuexmatrixPatch12} +\begin{paste}{MenuexmatrixFull12}{MenuexmatrixEmpty12} +\pastebutton{MenuexmatrixFull12}{\hidepaste} +\tab{5}\spadcommand{vertConcat(matrix([[1,2,3],[6,7,8]]),matrix([[11,12,13],[55,77,88]]))} +\indentrel{3}\begin{verbatim} + Ú1 2 3 ¿ + ³ ³ + ³6 7 8 ³ + (12) ³ ³ + ³11 12 13³ + ³ ³ + À55 77 88Ù + Type: Matrix Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{MenuexmatrixEmpty12} +\begin{paste}{MenuexmatrixEmpty12}{MenuexmatrixPatch12} +\pastebutton{MenuexmatrixEmpty12}{\showpaste} +\tab{5}\spadcommand{vertConcat(matrix([[1,2,3],[6,7,8]]),matrix([[11,12,13],[55,77,88]]))} +\end{paste}\end{patch} + +\begin{patch}{MenuexmatrixPatch13} +\begin{paste}{MenuexmatrixFull13}{MenuexmatrixEmpty13} +\pastebutton{MenuexmatrixFull13}{\hidepaste} +\tab{5}\spadcommand{b:=matrix([[0,1,2,3,4],[5,6,7,8,9],[10,11,12,13,14]])\bound{b }} +\indentrel{3}\begin{verbatim} + Ú0 1 2 3 4 ¿ + ³ ³ + (13) ³5 6 7 8 9 ³ + ³ ³ + À10 11 12 13 14Ù + Type: Matrix Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{MenuexmatrixEmpty13} +\begin{paste}{MenuexmatrixEmpty13}{MenuexmatrixPatch13} +\pastebutton{MenuexmatrixEmpty13}{\showpaste} +\tab{5}\spadcommand{b:=matrix([[0,1,2,3,4],[5,6,7,8,9],[10,11,12,13,14]])\bound{b }} +\end{paste}\end{patch} + +\begin{patch}{MenuexmatrixPatch14} +\begin{paste}{MenuexmatrixFull14}{MenuexmatrixEmpty14} +\pastebutton{MenuexmatrixFull14}{\hidepaste} +\tab{5}\spadcommand{setsubMatrix!(b,1,1,transpose(subMatrix(b,1,3,1,3)))\free{b }} +\indentrel{3}\begin{verbatim} + Ú0 5 10 3 4 ¿ + ³ ³ + (14) ³1 6 11 8 9 ³ + ³ ³ + À2 7 12 13 14Ù + Type: Matrix Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{MenuexmatrixEmpty14} +\begin{paste}{MenuexmatrixEmpty14}{MenuexmatrixPatch14} +\pastebutton{MenuexmatrixEmpty14}{\showpaste} +\tab{5}\spadcommand{setsubMatrix!(b,1,1,transpose(subMatrix(b,1,3,1,3)))\free{b }} +\end{paste}\end{patch} + +\begin{patch}{MenuexmatrixPatch15} +\begin{paste}{MenuexmatrixFull15}{MenuexmatrixEmpty15} +\pastebutton{MenuexmatrixFull15}{\hidepaste} +\tab{5}\spadcommand{trace( matrix([[1,x,x**2,x**3],[1,y,y**2,y**3],[1,z,z**2,z**3],[1,u,u**2,u**3]]) )} +\indentrel{3}\begin{verbatim} + 2 3 + (15) z + y + u + 1 + Type: Polynomial Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{MenuexmatrixEmpty15} +\begin{paste}{MenuexmatrixEmpty15}{MenuexmatrixPatch15} +\pastebutton{MenuexmatrixEmpty15}{\showpaste} +\tab{5}\spadcommand{trace( matrix([[1,x,x**2,x**3],[1,y,y**2,y**3],[1,z,z**2,z**3],[1,u,u**2,u**3]]) )} +\end{paste}\end{patch} + +\begin{patch}{MenuexmatrixPatch16} +\begin{paste}{MenuexmatrixFull16}{MenuexmatrixEmpty16} +\pastebutton{MenuexmatrixFull16}{\hidepaste} +\tab{5}\spadcommand{determinant(matrix([[1,2,3,4],[2,3,2,5],[3,4,5,6],[4,1,6,7]]))} +\indentrel{3}\begin{verbatim} + (16) - 48 + Type: Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{MenuexmatrixEmpty16} +\begin{paste}{MenuexmatrixEmpty16}{MenuexmatrixPatch16} +\pastebutton{MenuexmatrixEmpty16}{\showpaste} +\tab{5}\spadcommand{determinant(matrix([[1,2,3,4],[2,3,2,5],[3,4,5,6],[4,1,6,7]]))} +\end{paste}\end{patch} + +\begin{patch}{MenuexmatrixPatch17} +\begin{paste}{MenuexmatrixFull17}{MenuexmatrixEmpty17} +\pastebutton{MenuexmatrixFull17}{\hidepaste} +\tab{5}\spadcommand{inverse(matrix([[1,2,1],[-2,3,4],[-1,5,6]]))} +\indentrel{3}\begin{verbatim} + Ú 2 5 ¿ + ³- Ä - 1 Ä ³ + ³ 7 7 ³ + ³ ³ + (17) ³ 8 6³ + ³ Ä 1 - ij + ³ 7 7³ + ³ ³ + À- 1 - 1 1 Ù + Type: Union(Matrix Fraction Integer,...) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{MenuexmatrixEmpty17} +\begin{paste}{MenuexmatrixEmpty17}{MenuexmatrixPatch17} +\pastebutton{MenuexmatrixEmpty17}{\showpaste} +\tab{5}\spadcommand{inverse(matrix([[1,2,1],[-2,3,4],[-1,5,6]]))} +\end{paste}\end{patch} + +\begin{patch}{MenuexmatrixPatch18} +\begin{paste}{MenuexmatrixFull18}{MenuexmatrixEmpty18} +\pastebutton{MenuexmatrixFull18}{\hidepaste} +\tab{5}\spadcommand{rank(matrix([[0,4,1],[5,3,-7],[-5,5,9]]))} +\indentrel{3}\begin{verbatim} + (18) 2 + Type: PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{MenuexmatrixEmpty18} +\begin{paste}{MenuexmatrixEmpty18}{MenuexmatrixPatch18} +\pastebutton{MenuexmatrixEmpty18}{\showpaste} +\tab{5}\spadcommand{rank(matrix([[0,4,1],[5,3,-7],[-5,5,9]]))} +\end{paste}\end{patch} @ \pagehead{Menuexplot2d}{coverex.ht}{2-D Graphics} @@ -5047,7 +11804,60 @@ determinant(matrix([[1,2,3,4],[2,3,2,5],[3,4,5,6],[4,1,6,7]]))} \graphpaste{draw(sin(4*t/7),t = 0..14*\%pi,coordinates == polar)} \menudownlink{Plotting Plane Algebraic Curves}{ExPlot2DAlgebraic} \graphpaste{draw(y**2 + y - (x**3 - x) = 0, x, y, range == [-2..2,-2..1])} -\endmenu\endscroll\end{page} +\endmenu\endscroll +\end{page} + +\begin{patch}{Menuexplot2dPatch1} +\begin{paste}{Menuexplot2dFull1}{Menuexplot2dEmpty1} +\pastebutton{Menuexplot2dFull1}{\hidepaste} +\tab{5}\spadgraph{draw(sin(tan(x)) - tan(sin(x)),x = 0..6)} +\center{\unixcommand{\inputimage{\env{AXIOM}/doc/viewports/menuexplot2d1.view/image}}{viewalone\space{1} \env{AXIOM}/doc/viewports/menuexplot2d1}} +\end{paste}\end{patch} + +\begin{patch}{Menuexplot2dEmpty1} +\begin{paste}{Menuexplot2dEmpty1}{Menuexplot2dPatch1} +\pastebutton{Menuexplot2dEmpty1}{\showpaste} +\tab{5}\spadgraph{draw(sin(tan(x)) - tan(sin(x)),x = 0..6)} +\end{paste}\end{patch} + +\begin{patch}{Menuexplot2dPatch2} +\begin{paste}{Menuexplot2dFull2}{Menuexplot2dEmpty2} +\pastebutton{Menuexplot2dFull2}{\hidepaste} +\tab{5}\spadgraph{draw(curve(9 * sin(3*t/4),8 * sin(t)),t = -4*\%pi..4*\%pi)} +\center{\unixcommand{\inputimage{\env{AXIOM}/doc/viewports/menuexplot2d2.view/image}}{viewalone\space{1} \env{AXIOM}/doc/viewports/menuexplot2d2}} +\end{paste}\end{patch} + +\begin{patch}{Menuexplot2dEmpty2} +\begin{paste}{Menuexplot2dEmpty2}{Menuexplot2dPatch2} +\pastebutton{Menuexplot2dEmpty2}{\showpaste} +\tab{5}\spadgraph{draw(curve(9 * sin(3*t/4),8 * sin(t)),t = -4*\%pi..4*\%pi)} +\end{paste}\end{patch} + +\begin{patch}{Menuexplot2dPatch3} +\begin{paste}{Menuexplot2dFull3}{Menuexplot2dEmpty3} +\pastebutton{Menuexplot2dFull3}{\hidepaste} +\tab{5}\spadgraph{draw(sin(4*t/7),t = 0..14*\%pi,coordinates == polar)} +\center{\unixcommand{\inputimage{\env{AXIOM}/doc/viewports/menuexplot2d3.view/image}}{viewalone\space{1} \env{AXIOM}/doc/viewports/menuexplot2d3}} +\end{paste}\end{patch} + +\begin{patch}{Menuexplot2dEmpty3} +\begin{paste}{Menuexplot2dEmpty3}{Menuexplot2dPatch3} +\pastebutton{Menuexplot2dEmpty3}{\showpaste} +\tab{5}\spadgraph{draw(sin(4*t/7),t = 0..14*\%pi,coordinates == polar)} +\end{paste}\end{patch} + +\begin{patch}{Menuexplot2dPatch4} +\begin{paste}{Menuexplot2dFull4}{Menuexplot2dEmpty4} +\pastebutton{Menuexplot2dFull4}{\hidepaste} +\tab{5}\spadgraph{draw(y**2 + y - (x**3 - x) = 0, x, y, range == [-2..2,-2..1])} +\center{\unixcommand{\inputimage{\env{AXIOM}/doc/viewports/menuexplot2d4.view/image}}{viewalone\space{1} \env{AXIOM}/doc/viewports/menuexplot2d4}} +\end{paste}\end{patch} + +\begin{patch}{Menuexplot2dEmpty4} +\begin{paste}{Menuexplot2dEmpty4}{Menuexplot2dPatch4} +\pastebutton{Menuexplot2dEmpty4}{\showpaste} +\tab{5}\spadgraph{draw(y**2 + y - (x**3 - x) = 0, x, y, range == [-2..2,-2..1])} +\end{paste}\end{patch} @ \pagehead{Menuexplot3d}{coverex.ht}{3-D Graphics} @@ -5066,7 +11876,73 @@ u=0..\%pi,v=0..2*\%pi)} \menudownlink{Plotting Parametric Curves}{ExPlot3DParametricCurve} \graphpaste{draw(curve(cos(t),sin(t),t),t=0..6)} \graphpaste{draw(curve(t,t**2,t**3),t=-3..3)} -\endmenu\endscroll\end{page} +\endmenu\endscroll +\end{page} + +\begin{patch}{Menuexplot3dPatch1} +\begin{paste}{Menuexplot3dFull1}{Menuexplot3dEmpty1} +\pastebutton{Menuexplot3dFull1}{\hidepaste} +\tab{5}\spadgraph{draw(cos(x*y),x = -3..3,y = -3..3)} +\center{\unixcommand{\inputimage{\env{AXIOM}/doc/viewports/menuexplot3d1.view/image}}{viewalone\space{1} \env{AXIOM}/doc/viewports/menuexplot3d1}} +\end{paste}\end{patch} + +\begin{patch}{Menuexplot3dEmpty1} +\begin{paste}{Menuexplot3dEmpty1}{Menuexplot3dPatch1} +\pastebutton{Menuexplot3dEmpty1}{\showpaste} +\tab{5}\spadgraph{draw(cos(x*y),x = -3..3,y = -3..3)} +\end{paste}\end{patch} + +\begin{patch}{Menuexplot3dPatch2} +\begin{paste}{Menuexplot3dFull2}{Menuexplot3dEmpty2} +\pastebutton{Menuexplot3dFull2}{\hidepaste} +\tab{5}\spadgraph{draw(surface(5*sin(u)*cos(v),4*sin(u)*sin(v),3*cos(u)),u=0..\%pi,v=0..2*\%pi)} +\center{\unixcommand{\inputimage{\env{AXIOM}/doc/viewports/menuexplot3d2.view/image}}{viewalone\space{1} \env{AXIOM}/doc/viewports/menuexplot3d2}} +\end{paste}\end{patch} + +\begin{patch}{Menuexplot3dEmpty2} +\begin{paste}{Menuexplot3dEmpty2}{Menuexplot3dPatch2} +\pastebutton{Menuexplot3dEmpty2}{\showpaste} +\tab{5}\spadgraph{draw(surface(5*sin(u)*cos(v),4*sin(u)*sin(v),3*cos(u)),u=0..\%pi,v=0..2*\%pi)} +\end{paste}\end{patch} + +\begin{patch}{Menuexplot3dPatch3} +\begin{paste}{Menuexplot3dFull3}{Menuexplot3dEmpty3} +\pastebutton{Menuexplot3dFull3}{\hidepaste} +\tab{5}\spadgraph{draw(surface(u*cos(v),u*sin(v),u),u=0..4,v=0..2*\%pi)} +\center{\unixcommand{\inputimage{\env{AXIOM}/doc/viewports/menuexplot3d3.view/image}}{viewalone\space{1} \env{AXIOM}/doc/viewports/menuexplot3d3}} +\end{paste}\end{patch} + +\begin{patch}{Menuexplot3dEmpty3} +\begin{paste}{Menuexplot3dEmpty3}{Menuexplot3dPatch3} +\pastebutton{Menuexplot3dEmpty3}{\showpaste} +\tab{5}\spadgraph{draw(surface(u*cos(v),u*sin(v),u),u=0..4,v=0..2*\%pi)} +\end{paste}\end{patch} + +\begin{patch}{Menuexplot3dPatch4} +\begin{paste}{Menuexplot3dFull4}{Menuexplot3dEmpty4} +\pastebutton{Menuexplot3dFull4}{\hidepaste} +\tab{5}\spadgraph{draw(curve(cos(t),sin(t),t),t=0..6)} +\center{\unixcommand{\inputimage{\env{AXIOM}/doc/viewports/menuexplot3d4.view/image}}{viewalone\space{1} \env{AXIOM}/doc/viewports/menuexplot3d4}} +\end{paste}\end{patch} + +\begin{patch}{Menuexplot3dEmpty4} +\begin{paste}{Menuexplot3dEmpty4}{Menuexplot3dPatch4} +\pastebutton{Menuexplot3dEmpty4}{\showpaste} +\tab{5}\spadgraph{draw(curve(cos(t),sin(t),t),t=0..6)} +\end{paste}\end{patch} + +\begin{patch}{Menuexplot3dPatch5} +\begin{paste}{Menuexplot3dFull5}{Menuexplot3dEmpty5} +\pastebutton{Menuexplot3dFull5}{\hidepaste} +\tab{5}\spadgraph{draw(curve(t,t**2,t**3),t=-3..3)} +\center{\unixcommand{\inputimage{\env{AXIOM}/doc/viewports/menuexplot3d5.view/image}}{viewalone\space{1} \env{AXIOM}/doc/viewports/menuexplot3d5}} +\end{paste}\end{patch} + +\begin{patch}{Menuexplot3dEmpty5} +\begin{paste}{Menuexplot3dEmpty5}{Menuexplot3dPatch5} +\pastebutton{Menuexplot3dEmpty5}{\showpaste} +\tab{5}\spadgraph{draw(curve(t,t**2,t**3),t=-3..3)} +\end{paste}\end{patch} @ \pagehead{Menuexseries}{coverex.ht}{Series} @@ -5092,7 +11968,232 @@ u=0..\%pi,v=0..2*\%pi)} {ExSeriesSubstitution} \spadpaste{f := taylor(exp(x)) \bound{f2}} \spadpaste{eval(f,1.0) \free{f2}} -\endmenu\endscroll\end{page} +\endmenu\endscroll +\end{page} + +\begin{patch}{MenuexseriesPatch1} +\begin{paste}{MenuexseriesFull1}{MenuexseriesEmpty1} +\pastebutton{MenuexseriesFull1}{\hidepaste} +\tab{5}\spadcommand{series(sin(a*x),x = 0)} +\indentrel{3}\begin{verbatim} + (1) + 3 5 7 9 + a 3 a 5 a 7 a 9 + a x - ÄÄ x + ÄÄÄ x - ÄÄÄÄ x + ÄÄÄÄÄÄ x + 6 120 5040 362880 + + + 11 + a 11 12 + - ÄÄÄÄÄÄÄÄ x + O(x ) + 39916800 + Type: UnivariatePuiseuxSeries(Expression Integer,x,0) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{MenuexseriesEmpty1} +\begin{paste}{MenuexseriesEmpty1}{MenuexseriesPatch1} +\pastebutton{MenuexseriesEmpty1}{\showpaste} +\tab{5}\spadcommand{series(sin(a*x),x = 0)} +\end{paste}\end{patch} + +\begin{patch}{MenuexseriesPatch2} +\begin{paste}{MenuexseriesFull2}{MenuexseriesEmpty2} +\pastebutton{MenuexseriesFull2}{\hidepaste} +\tab{5}\spadcommand{series(sin(a*x),a = \%pi/4)} +\indentrel{3}\begin{verbatim} + (2) + %pi x %pi x %pi + sin(ÄÄÄÄÄ) + x cos(ÄÄÄÄÄ)(a - ÄÄÄ) + 4 4 4 + + + 2 %pi x 3 %pi x + x sin(ÄÄÄÄÄ) x cos(ÄÄÄÄÄ) + 4 %pi 2 4 %pi 3 + - ÄÄÄÄÄÄÄÄÄÄÄÄ (a - ÄÄÄ) - ÄÄÄÄÄÄÄÄÄÄÄÄ (a - ÄÄÄ) + 2 4 6 4 + + + 4 %pi x 5 %pi x + x sin(ÄÄÄÄÄ) x cos(ÄÄÄÄÄ) + 4 %pi 4 4 %pi 5 + ÄÄÄÄÄÄÄÄÄÄÄÄ (a - ÄÄÄ) + ÄÄÄÄÄÄÄÄÄÄÄÄ (a - ÄÄÄ) + 24 4 120 4 + + + 6 %pi x 7 %pi x + x sin(ÄÄÄÄÄ) x cos(ÄÄÄÄÄ) + 4 %pi 6 4 %pi 7 + - ÄÄÄÄÄÄÄÄÄÄÄÄ (a - ÄÄÄ) - ÄÄÄÄÄÄÄÄÄÄÄÄ (a - ÄÄÄ) + 720 4 5040 4 + + + 8 %pi x 9 %pi x + x sin(ÄÄÄÄÄ) x cos(ÄÄÄÄÄ) + 4 %pi 8 4 %pi 9 + ÄÄÄÄÄÄÄÄÄÄÄÄ (a - ÄÄÄ) + ÄÄÄÄÄÄÄÄÄÄÄÄ (a - ÄÄÄ) + 40320 4 362880 4 + + + 10 %pi x + x sin(ÄÄÄÄÄ) + 4 %pi 10 %pi 11 + - ÄÄÄÄÄÄÄÄÄÄÄÄÄ (a - ÄÄÄ) + O((a - ÄÄÄ) ) + 3628800 4 4 +Type: UnivariatePuiseuxSeries(Expression Integer,a,pi/4) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{MenuexseriesEmpty2} +\begin{paste}{MenuexseriesEmpty2}{MenuexseriesPatch2} +\pastebutton{MenuexseriesEmpty2}{\showpaste} +\tab{5}\spadcommand{series(sin(a*x),a = \%pi/4)} +\end{paste}\end{patch} + +\begin{patch}{MenuexseriesPatch3} +\begin{paste}{MenuexseriesFull3}{MenuexseriesEmpty3} +\pastebutton{MenuexseriesFull3}{\hidepaste} +\tab{5}\spadcommand{f := series(1/(1-x),x = 0)\bound{f }} +\indentrel{3}\begin{verbatim} + (3) + 2 3 4 5 6 7 8 9 10 + 1 + x + x + x + x + x + x + x + x + x + x + + + 11 + O(x ) + Type: UnivariatePuiseuxSeries(Expression Integer,x,0) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{MenuexseriesEmpty3} +\begin{paste}{MenuexseriesEmpty3}{MenuexseriesPatch3} +\pastebutton{MenuexseriesEmpty3}{\showpaste} +\tab{5}\spadcommand{f := series(1/(1-x),x = 0)\bound{f }} +\end{paste}\end{patch} + +\begin{patch}{MenuexseriesPatch4} +\begin{paste}{MenuexseriesFull4}{MenuexseriesEmpty4} +\pastebutton{MenuexseriesFull4}{\hidepaste} +\tab{5}\spadcommand{f ** 2\free{f }} +\indentrel{3}\begin{verbatim} + (4) + 2 3 4 5 6 7 8 + 1 + 2x + 3x + 4x + 5x + 6x + 7x + 8x + 9x + + + 9 10 11 + 10x + 11x + O(x ) + Type: UnivariatePuiseuxSeries(Expression Integer,x,0) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{MenuexseriesEmpty4} +\begin{paste}{MenuexseriesEmpty4}{MenuexseriesPatch4} +\pastebutton{MenuexseriesEmpty4}{\showpaste} +\tab{5}\spadcommand{f ** 2\free{f }} +\end{paste}\end{patch} + +\begin{patch}{MenuexseriesPatch5} +\begin{paste}{MenuexseriesFull5}{MenuexseriesEmpty5} +\pastebutton{MenuexseriesFull5}{\hidepaste} +\tab{5}\spadcommand{f := series(1/(1-x),x = 0)\bound{f1 }} +\indentrel{3}\begin{verbatim} + (5) + 2 3 4 5 6 7 8 9 10 + 1 + x + x + x + x + x + x + x + x + x + x + + + 11 + O(x ) + Type: UnivariatePuiseuxSeries(Expression Integer,x,0) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{MenuexseriesEmpty5} +\begin{paste}{MenuexseriesEmpty5}{MenuexseriesPatch5} +\pastebutton{MenuexseriesEmpty5}{\showpaste} +\tab{5}\spadcommand{f := series(1/(1-x),x = 0)\bound{f1 }} +\end{paste}\end{patch} + +\begin{patch}{MenuexseriesPatch6} +\begin{paste}{MenuexseriesFull6}{MenuexseriesEmpty6} +\pastebutton{MenuexseriesFull6}{\hidepaste} +\tab{5}\spadcommand{g := log(f)\free{f1 }\bound{g }} +\indentrel{3}\begin{verbatim} + (6) + 1 2 1 3 1 4 1 5 1 6 1 7 1 8 + x + Ä x + Ä x + Ä x + Ä x + Ä x + Ä x + Ä x + 2 3 4 5 6 7 8 + + + 1 9 1 10 1 11 12 + Ä x + ÄÄ x + ÄÄ x + O(x ) + 9 10 11 + Type: UnivariatePuiseuxSeries(Expression Integer,x,0) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{MenuexseriesEmpty6} +\begin{paste}{MenuexseriesEmpty6}{MenuexseriesPatch6} +\pastebutton{MenuexseriesEmpty6}{\showpaste} +\tab{5}\spadcommand{g := log(f)\free{f1 }\bound{g }} +\end{paste}\end{patch} + +\begin{patch}{MenuexseriesPatch7} +\begin{paste}{MenuexseriesFull7}{MenuexseriesEmpty7} +\pastebutton{MenuexseriesFull7}{\hidepaste} +\tab{5}\spadcommand{exp(g)\free{g }} +\indentrel{3}\begin{verbatim} + (7) + 2 3 4 5 6 7 8 9 10 + 1 + x + x + x + x + x + x + x + x + x + x + + + 11 + O(x ) + Type: UnivariatePuiseuxSeries(Expression Integer,x,0) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{MenuexseriesEmpty7} +\begin{paste}{MenuexseriesEmpty7}{MenuexseriesPatch7} +\pastebutton{MenuexseriesEmpty7}{\showpaste} +\tab{5}\spadcommand{exp(g)\free{g }} +\end{paste}\end{patch} + +\begin{patch}{MenuexseriesPatch8} +\begin{paste}{MenuexseriesFull8}{MenuexseriesEmpty8} +\pastebutton{MenuexseriesFull8}{\hidepaste} +\tab{5}\spadcommand{f := taylor(exp(x))\bound{f2 }} +\indentrel{3}\begin{verbatim} + (8) + 1 2 1 3 1 4 1 5 1 6 + 1 + x + Ä x + Ä x + ÄÄ x + ÄÄÄ x + ÄÄÄ x + 2 6 24 120 720 + + + 1 7 1 8 1 9 1 10 11 + ÄÄÄÄ x + ÄÄÄÄÄ x + ÄÄÄÄÄÄ x + ÄÄÄÄÄÄÄ x + O(x ) + 5040 40320 362880 3628800 + Type: UnivariateTaylorSeries(Expression Integer,x,0) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{MenuexseriesEmpty8} +\begin{paste}{MenuexseriesEmpty8}{MenuexseriesPatch8} +\pastebutton{MenuexseriesEmpty8}{\showpaste} +\tab{5}\spadcommand{f := taylor(exp(x))\bound{f2 }} +\end{paste}\end{patch} + +\begin{patch}{MenuexseriesPatch9} +\begin{paste}{MenuexseriesFull9}{MenuexseriesEmpty9} +\pastebutton{MenuexseriesFull9}{\hidepaste} +\tab{5}\spadcommand{eval(f,1.0)\free{f2 }} +\indentrel{3}\begin{verbatim} + (9) + [1.0, 2.0, 2.5, 2.6666666666 666666667, + 2.7083333333 333333333, 2.7166666666 666666667, + 2.7180555555 555555556, 2.7182539682 53968254, + 2.7182787698 412698413, 2.7182815255 731922399, ...] + Type: Stream Expression Float +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{MenuexseriesEmpty9} +\begin{paste}{MenuexseriesEmpty9}{MenuexseriesPatch9} +\pastebutton{MenuexseriesEmpty9}{\showpaste} +\tab{5}\spadcommand{eval(f,1.0)\free{f2 }} +\end{paste}\end{patch} @ \pagehead{Menuexsum}{coverex.ht}{Summations} @@ -5128,7 +12229,243 @@ u=0..\%pi,v=0..2*\%pi)} \spadpaste{sum(k * x**k,k = 1..n)} \menudownlink{Infinite Sums}{ExSumInfinite} \spadpaste{limit( sum(1/(k * (k + 2)),k = 1..n) ,n = \%plusInfinity)} -\endmenu\endscroll\end{page} +\endmenu\endscroll +\end{page} + +\begin{patch}{MenuexsumPatch1} +\begin{paste}{MenuexsumFull1}{MenuexsumEmpty1} +\pastebutton{MenuexsumFull1}{\hidepaste} +\tab{5}\spadcommand{[i for i in 1..15]} +\indentrel{3}\begin{verbatim} + (1) [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15] + Type: List PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{MenuexsumEmpty1} +\begin{paste}{MenuexsumEmpty1}{MenuexsumPatch1} +\pastebutton{MenuexsumEmpty1}{\showpaste} +\tab{5}\spadcommand{[i for i in 1..15]} +\end{paste}\end{patch} + +\begin{patch}{MenuexsumPatch2} +\begin{paste}{MenuexsumFull2}{MenuexsumEmpty2} +\pastebutton{MenuexsumFull2}{\hidepaste} +\tab{5}\spadcommand{reduce(+,[i for i in 1..15])} +\indentrel{3}\begin{verbatim} + (2) 120 + Type: PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{MenuexsumEmpty2} +\begin{paste}{MenuexsumEmpty2}{MenuexsumPatch2} +\pastebutton{MenuexsumEmpty2}{\showpaste} +\tab{5}\spadcommand{reduce(+,[i for i in 1..15])} +\end{paste}\end{patch} + +\begin{patch}{MenuexsumPatch3} +\begin{paste}{MenuexsumFull3}{MenuexsumEmpty3} +\pastebutton{MenuexsumFull3}{\hidepaste} +\tab{5}\spadcommand{[n**2 for n in 5..20]} +\indentrel{3}\begin{verbatim} + (3) + [25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, + 256, 289, 324, 361, 400] + Type: List PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{MenuexsumEmpty3} +\begin{paste}{MenuexsumEmpty3}{MenuexsumPatch3} +\pastebutton{MenuexsumEmpty3}{\showpaste} +\tab{5}\spadcommand{[n**2 for n in 5..20]} +\end{paste}\end{patch} + +\begin{patch}{MenuexsumPatch4} +\begin{paste}{MenuexsumFull4}{MenuexsumEmpty4} +\pastebutton{MenuexsumFull4}{\hidepaste} +\tab{5}\spadcommand{reduce(+,[n**2 for n in 5..20])} +\indentrel{3}\begin{verbatim} + (4) 2840 + Type: PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{MenuexsumEmpty4} +\begin{paste}{MenuexsumEmpty4}{MenuexsumPatch4} +\pastebutton{MenuexsumEmpty4}{\showpaste} +\tab{5}\spadcommand{reduce(+,[n**2 for n in 5..20])} +\end{paste}\end{patch} + +\begin{patch}{MenuexsumPatch5} +\begin{paste}{MenuexsumFull5}{MenuexsumEmpty5} +\pastebutton{MenuexsumFull5}{\hidepaste} +\tab{5}\spadcommand{reduce(+,[1.0/factorial(n) for n in 0..20])} +\indentrel{3}\begin{verbatim} + (5) 2.7182818284 590452354 + Type: Float +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{MenuexsumEmpty5} +\begin{paste}{MenuexsumEmpty5}{MenuexsumPatch5} +\pastebutton{MenuexsumEmpty5}{\showpaste} +\tab{5}\spadcommand{reduce(+,[1.0/factorial(n) for n in 0..20])} +\end{paste}\end{patch} + +\begin{patch}{MenuexsumPatch6} +\begin{paste}{MenuexsumFull6}{MenuexsumEmpty6} +\pastebutton{MenuexsumFull6}{\hidepaste} +\tab{5}\spadcommand{s := sum(k**2,k = a..b)\bound{s }} +\indentrel{3}\begin{verbatim} + 3 2 3 2 + 2b + 3b + b - 2a + 3a - a + (6) ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ + 6 + Type: Fraction Polynomial Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{MenuexsumEmpty6} +\begin{paste}{MenuexsumEmpty6}{MenuexsumPatch6} +\pastebutton{MenuexsumEmpty6}{\showpaste} +\tab{5}\spadcommand{s := sum(k**2,k = a..b)\bound{s }} +\end{paste}\end{patch} + +\begin{patch}{MenuexsumPatch7} +\begin{paste}{MenuexsumFull7}{MenuexsumEmpty7} +\pastebutton{MenuexsumFull7}{\hidepaste} +\tab{5}\spadcommand{eval(s,[a,b],[1,25])\free{s }} +\indentrel{3}\begin{verbatim} + (7) 5525 + Type: Fraction Polynomial Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{MenuexsumEmpty7} +\begin{paste}{MenuexsumEmpty7}{MenuexsumPatch7} +\pastebutton{MenuexsumEmpty7}{\showpaste} +\tab{5}\spadcommand{eval(s,[a,b],[1,25])\free{s }} +\end{paste}\end{patch} + +\begin{patch}{MenuexsumPatch8} +\begin{paste}{MenuexsumFull8}{MenuexsumEmpty8} +\pastebutton{MenuexsumFull8}{\hidepaste} +\tab{5}\spadcommand{reduce(+,[i**2 for i in 1..25])} +\indentrel{3}\begin{verbatim} + (8) 5525 + Type: PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{MenuexsumEmpty8} +\begin{paste}{MenuexsumEmpty8}{MenuexsumPatch8} +\pastebutton{MenuexsumEmpty8}{\showpaste} +\tab{5}\spadcommand{reduce(+,[i**2 for i in 1..25])} +\end{paste}\end{patch} + +\begin{patch}{MenuexsumPatch9} +\begin{paste}{MenuexsumFull9}{MenuexsumEmpty9} +\pastebutton{MenuexsumFull9}{\hidepaste} +\tab{5}\spadcommand{sum(k**3,k = 1..n)} +\indentrel{3}\begin{verbatim} + 4 3 2 + n + 2n + n + (9) ÄÄÄÄÄÄÄÄÄÄÄÄÄ + 4 + Type: Fraction Polynomial Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{MenuexsumEmpty9} +\begin{paste}{MenuexsumEmpty9}{MenuexsumPatch9} +\pastebutton{MenuexsumEmpty9}{\showpaste} +\tab{5}\spadcommand{sum(k**3,k = 1..n)} +\end{paste}\end{patch} + +\begin{patch}{MenuexsumPatch10} +\begin{paste}{MenuexsumFull10}{MenuexsumEmpty10} +\pastebutton{MenuexsumFull10}{\hidepaste} +\tab{5}\spadcommand{sum(k,k = 1..n) ** 2} +\indentrel{3}\begin{verbatim} + 4 3 2 + n + 2n + n + (10) ÄÄÄÄÄÄÄÄÄÄÄÄÄ + 4 + Type: Fraction Polynomial Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{MenuexsumEmpty10} +\begin{paste}{MenuexsumEmpty10}{MenuexsumPatch10} +\pastebutton{MenuexsumEmpty10}{\showpaste} +\tab{5}\spadcommand{sum(k,k = 1..n) ** 2} +\end{paste}\end{patch} + +\begin{patch}{MenuexsumPatch11} +\begin{paste}{MenuexsumFull11}{MenuexsumEmpty11} +\pastebutton{MenuexsumFull11}{\hidepaste} +\tab{5}\spadcommand{sum(3*k**2/(c**2 + 1) + 12*k/d,k = (3*a)..(4*b))} +\indentrel{3}\begin{verbatim} + (11) + 3 2 3 2 + (128b + 48b + 4b - 54a + 27a - 3a)d + + + 2 2 2 2 2 + (192b + 48b - 108a + 36a)c + 192b + 48b - 108a + + + 36a + / + 2 + (2c + 2)d + Type: Union(Fraction Polynomial Integer,...) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{MenuexsumEmpty11} +\begin{paste}{MenuexsumEmpty11}{MenuexsumPatch11} +\pastebutton{MenuexsumEmpty11}{\showpaste} +\tab{5}\spadcommand{sum(3*k**2/(c**2 + 1) + 12*k/d,k = (3*a)..(4*b))} +\end{paste}\end{patch} + +\begin{patch}{MenuexsumPatch12} +\begin{paste}{MenuexsumFull12}{MenuexsumEmpty12} +\pastebutton{MenuexsumFull12}{\hidepaste} +\tab{5}\spadcommand{sum(k * x**k,k = 1..n)} +\indentrel{3}\begin{verbatim} + 2 n + (n x + (- n - 1)x)x + x + (12) ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ + 2 + x - 2x + 1 + Type: Expression Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{MenuexsumEmpty12} +\begin{paste}{MenuexsumEmpty12}{MenuexsumPatch12} +\pastebutton{MenuexsumEmpty12}{\showpaste} +\tab{5}\spadcommand{sum(k * x**k,k = 1..n)} +\end{paste}\end{patch} + +\begin{patch}{MenuexsumPatch13} +\begin{paste}{MenuexsumFull13}{MenuexsumEmpty13} +\pastebutton{MenuexsumFull13}{\hidepaste} +\tab{5}\spadcommand{limit( sum(1/(k * (k + 2)),k = 1..n) ,n = \%plusInfinity)} +\indentrel{3}\begin{verbatim} + 3 + (13) Ä + 4 +Type: Union(OrderedCompletion Fraction Polynomial Integer,...) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{MenuexsumEmpty13} +\begin{paste}{MenuexsumEmpty13}{MenuexsumPatch13} +\pastebutton{MenuexsumEmpty13}{\showpaste} +\tab{5}\spadcommand{limit( sum(1/(k * (k + 2)),k = 1..n) ,n = \%plusInfinity)} +\end{paste}\end{patch} @ \section{decimal.ht} @@ -5192,6 +12529,142 @@ These numbers are bona fide algebraic objects. \autobuttons \end{page} +\begin{patch}{DecimalExpansionXmpPagePatch1} +\begin{paste}{DecimalExpansionXmpPageFull1}{DecimalExpansionXmpPageEmpty1} +\pastebutton{DecimalExpansionXmpPageFull1}{\hidepaste} +\tab{5}\spadcommand{r := decimal(22/7)\bound{r }} +\indentrel{3}\begin{verbatim} + ______ + (1) 3.142857 + Type: DecimalExpansion +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{DecimalExpansionXmpPageEmpty1} +\begin{paste}{DecimalExpansionXmpPageEmpty1}{DecimalExpansionXmpPagePatch1} +\pastebutton{DecimalExpansionXmpPageEmpty1}{\showpaste} +\tab{5}\spadcommand{r := decimal(22/7)\bound{r }} +\end{paste}\end{patch} + +\begin{patch}{DecimalExpansionXmpPagePatch2} +\begin{paste}{DecimalExpansionXmpPageFull2}{DecimalExpansionXmpPageEmpty2} +\pastebutton{DecimalExpansionXmpPageFull2}{\hidepaste} +\tab{5}\spadcommand{r + decimal(6/7)\free{r }} +\indentrel{3}\begin{verbatim} + (2) 4 + Type: DecimalExpansion +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{DecimalExpansionXmpPageEmpty2} +\begin{paste}{DecimalExpansionXmpPageEmpty2}{DecimalExpansionXmpPagePatch2} +\pastebutton{DecimalExpansionXmpPageEmpty2}{\showpaste} +\tab{5}\spadcommand{r + decimal(6/7)\free{r }} +\end{paste}\end{patch} + +\begin{patch}{DecimalExpansionXmpPagePatch3} +\begin{paste}{DecimalExpansionXmpPageFull3}{DecimalExpansionXmpPageEmpty3} +\pastebutton{DecimalExpansionXmpPageFull3}{\hidepaste} +\tab{5}\spadcommand{[decimal(1/i) for i in 350..354]} +\indentrel{3}\begin{verbatim} + (3) + ______ ______ __ + [0.00285714, 0.002849, 0.0028409, + ________________________________ + 0.00283286118980169971671388101983, + + 0.0 + OVERBAR + 02824858757062146892655367231638418079096045197 + 74011299435 + ] + Type: List DecimalExpansion +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{DecimalExpansionXmpPageEmpty3} +\begin{paste}{DecimalExpansionXmpPageEmpty3}{DecimalExpansionXmpPagePatch3} +\pastebutton{DecimalExpansionXmpPageEmpty3}{\showpaste} +\tab{5}\spadcommand{[decimal(1/i) for i in 350..354]} +\end{paste}\end{patch} + +\begin{patch}{DecimalExpansionXmpPagePatch4} +\begin{paste}{DecimalExpansionXmpPageFull4}{DecimalExpansionXmpPageEmpty4} +\pastebutton{DecimalExpansionXmpPageFull4}{\hidepaste} +\tab{5}\spadcommand{decimal(1/2049)} +\indentrel{3}\begin{verbatim} + (4) + 0. + OVERBAR + 0004880429477794045876037091264031234748657881893 + 60663738408979990239141044411908247925817471937 + 53050268423621278672523182040019521717911176183 + 50414836505612493899463152757442654953635919960 + 95656417764763299170326988775012201073694485114 + 69009272816007808687164470473401659346022449975 + 59785261102977061981454367984382625671059053196 + 6813079551 + Type: DecimalExpansion +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{DecimalExpansionXmpPageEmpty4} +\begin{paste}{DecimalExpansionXmpPageEmpty4}{DecimalExpansionXmpPagePatch4} +\pastebutton{DecimalExpansionXmpPageEmpty4}{\showpaste} +\tab{5}\spadcommand{decimal(1/2049)} +\end{paste}\end{patch} + +\begin{patch}{DecimalExpansionXmpPagePatch5} +\begin{paste}{DecimalExpansionXmpPageFull5}{DecimalExpansionXmpPageEmpty5} +\pastebutton{DecimalExpansionXmpPageFull5}{\hidepaste} +\tab{5}\spadcommand{p := decimal(1/4)*x**2 + decimal(2/3)*x + decimal(4/9)\bound{p }} +\indentrel{3}\begin{verbatim} + 2 _ _ + (5) 0.25x + 0.6x + 0.4 + Type: Polynomial DecimalExpansion +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{DecimalExpansionXmpPageEmpty5} +\begin{paste}{DecimalExpansionXmpPageEmpty5}{DecimalExpansionXmpPagePatch5} +\pastebutton{DecimalExpansionXmpPageEmpty5}{\showpaste} +\tab{5}\spadcommand{p := decimal(1/4)*x**2 + decimal(2/3)*x + decimal(4/9)\bound{p }} +\end{paste}\end{patch} + +\begin{patch}{DecimalExpansionXmpPagePatch6} +\begin{paste}{DecimalExpansionXmpPageFull6}{DecimalExpansionXmpPageEmpty6} +\pastebutton{DecimalExpansionXmpPageFull6}{\hidepaste} +\tab{5}\spadcommand{q := differentiate(p, x)\free{p }\bound{q }} +\indentrel{3}\begin{verbatim} + _ + (6) 0.5x + 0.6 + Type: Polynomial DecimalExpansion +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{DecimalExpansionXmpPageEmpty6} +\begin{paste}{DecimalExpansionXmpPageEmpty6}{DecimalExpansionXmpPagePatch6} +\pastebutton{DecimalExpansionXmpPageEmpty6}{\showpaste} +\tab{5}\spadcommand{q := differentiate(p, x)\free{p }\bound{q }} +\end{paste}\end{patch} + +\begin{patch}{DecimalExpansionXmpPagePatch7} +\begin{paste}{DecimalExpansionXmpPageFull7}{DecimalExpansionXmpPageEmpty7} +\pastebutton{DecimalExpansionXmpPageFull7}{\hidepaste} +\tab{5}\spadcommand{g := gcd(p, q)\free{p q }\bound{g }} +\indentrel{3}\begin{verbatim} + _ + (7) x + 1.3 + Type: Polynomial DecimalExpansion +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{DecimalExpansionXmpPageEmpty7} +\begin{paste}{DecimalExpansionXmpPageEmpty7}{DecimalExpansionXmpPagePatch7} +\pastebutton{DecimalExpansionXmpPageEmpty7}{\showpaste} +\tab{5}\spadcommand{g := gcd(p, q)\free{p q }\bound{g }} +\end{paste}\end{patch} + @ \section{derham.ht} \pagehead{DeRhamComplexXmpPage}{derham.ht}{DeRhamComplex} @@ -5405,6 +12878,597 @@ consists of the eight forms: \spad{1}, \spad{dx}, \spad{dy}, \spad{dz}, \autobuttons \end{page} +\begin{patch}{DeRhamComplexXmpPagePatch1} +\begin{paste}{DeRhamComplexXmpPageFull1}{DeRhamComplexXmpPageEmpty1} +\pastebutton{DeRhamComplexXmpPageFull1}{\hidepaste} +\tab{5}\spadcommand{coefRing := Integer\bound{coefRing }} +\indentrel{3}\begin{verbatim} + (1) Integer + Type: Domain +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{DeRhamComplexXmpPageEmpty1} +\begin{paste}{DeRhamComplexXmpPageEmpty1}{DeRhamComplexXmpPagePatch1} +\pastebutton{DeRhamComplexXmpPageEmpty1}{\showpaste} +\tab{5}\spadcommand{coefRing := Integer\bound{coefRing }} +\end{paste}\end{patch} + +\begin{patch}{DeRhamComplexXmpPagePatch2} +\begin{paste}{DeRhamComplexXmpPageFull2}{DeRhamComplexXmpPageEmpty2} +\pastebutton{DeRhamComplexXmpPageFull2}{\hidepaste} +\tab{5}\spadcommand{lv : List Symbol := [x,y,z]\bound{lv }} +\indentrel{3}\begin{verbatim} + (2) [x,y,z] + Type: List Symbol +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{DeRhamComplexXmpPageEmpty2} +\begin{paste}{DeRhamComplexXmpPageEmpty2}{DeRhamComplexXmpPagePatch2} +\pastebutton{DeRhamComplexXmpPageEmpty2}{\showpaste} +\tab{5}\spadcommand{lv : List Symbol := [x,y,z]\bound{lv }} +\end{paste}\end{patch} + +\begin{patch}{DeRhamComplexXmpPagePatch3} +\begin{paste}{DeRhamComplexXmpPageFull3}{DeRhamComplexXmpPageEmpty3} +\pastebutton{DeRhamComplexXmpPageFull3}{\hidepaste} +\tab{5}\spadcommand{der := DERHAM(coefRing,lv)\free{coefRing }\free{lv }\bound{der }} +\indentrel{3}\begin{verbatim} + (3) DeRhamComplex(Integer,[x,y,z]) + Type: Domain +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{DeRhamComplexXmpPageEmpty3} +\begin{paste}{DeRhamComplexXmpPageEmpty3}{DeRhamComplexXmpPagePatch3} +\pastebutton{DeRhamComplexXmpPageEmpty3}{\showpaste} +\tab{5}\spadcommand{der := DERHAM(coefRing,lv)\free{coefRing }\free{lv }\bound{der }} +\end{paste}\end{patch} + +\begin{patch}{DeRhamComplexXmpPagePatch4} +\begin{paste}{DeRhamComplexXmpPageFull4}{DeRhamComplexXmpPageEmpty4} +\pastebutton{DeRhamComplexXmpPageFull4}{\hidepaste} +\tab{5}\spadcommand{R := Expression coefRing\free{coefRing }\bound{R }} +\indentrel{3}\begin{verbatim} + (4) Expression Integer + Type: Domain +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{DeRhamComplexXmpPageEmpty4} +\begin{paste}{DeRhamComplexXmpPageEmpty4}{DeRhamComplexXmpPagePatch4} +\pastebutton{DeRhamComplexXmpPageEmpty4}{\showpaste} +\tab{5}\spadcommand{R := Expression coefRing\free{coefRing }\bound{R }} +\end{paste}\end{patch} + +\begin{patch}{DeRhamComplexXmpPagePatch5} +\begin{paste}{DeRhamComplexXmpPageFull5}{DeRhamComplexXmpPageEmpty5} +\pastebutton{DeRhamComplexXmpPageFull5}{\hidepaste} +\tab{5}\spadcommand{f : R := x**2*y*z-5*x**3*y**2*z**5\free{R }\bound{f }} +\indentrel{3}\begin{verbatim} + 3 2 5 2 + (5) - 5x y z + x y z + Type: Expression Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{DeRhamComplexXmpPageEmpty5} +\begin{paste}{DeRhamComplexXmpPageEmpty5}{DeRhamComplexXmpPagePatch5} +\pastebutton{DeRhamComplexXmpPageEmpty5}{\showpaste} +\tab{5}\spadcommand{f : R := x**2*y*z-5*x**3*y**2*z**5\free{R }\bound{f }} +\end{paste}\end{patch} + +\begin{patch}{DeRhamComplexXmpPagePatch6} +\begin{paste}{DeRhamComplexXmpPageFull6}{DeRhamComplexXmpPageEmpty6} +\pastebutton{DeRhamComplexXmpPageFull6}{\hidepaste} +\tab{5}\spadcommand{g : R := z**2*y*cos(z)-7*sin(x**3*y**2)*z**2\free{R }\bound{g }} +\indentrel{3}\begin{verbatim} + 2 3 2 2 + (6) - 7z sin(x y ) + y z cos(z) + Type: Expression Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{DeRhamComplexXmpPageEmpty6} +\begin{paste}{DeRhamComplexXmpPageEmpty6}{DeRhamComplexXmpPagePatch6} +\pastebutton{DeRhamComplexXmpPageEmpty6}{\showpaste} +\tab{5}\spadcommand{g : R := z**2*y*cos(z)-7*sin(x**3*y**2)*z**2\free{R }\bound{g }} +\end{paste}\end{patch} + +\begin{patch}{DeRhamComplexXmpPagePatch7} +\begin{paste}{DeRhamComplexXmpPageFull7}{DeRhamComplexXmpPageEmpty7} +\pastebutton{DeRhamComplexXmpPageFull7}{\hidepaste} +\tab{5}\spadcommand{h : R :=x*y*z-2*x**3*y*z**2\free{R }\bound{h }} +\indentrel{3}\begin{verbatim} + 3 2 + (7) - 2x y z + x y z + Type: Expression Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{DeRhamComplexXmpPageEmpty7} +\begin{paste}{DeRhamComplexXmpPageEmpty7}{DeRhamComplexXmpPagePatch7} +\pastebutton{DeRhamComplexXmpPageEmpty7}{\showpaste} +\tab{5}\spadcommand{h : R :=x*y*z-2*x**3*y*z**2\free{R }\bound{h }} +\end{paste}\end{patch} + +\begin{patch}{DeRhamComplexXmpPagePatch8} +\begin{paste}{DeRhamComplexXmpPageFull8}{DeRhamComplexXmpPageEmpty8} +\pastebutton{DeRhamComplexXmpPageFull8}{\hidepaste} +\tab{5}\spadcommand{dx : der := generator(1)\free{der }\bound{dx }} +\indentrel{3}\begin{verbatim} + (8) dx + Type: DeRhamComplex(Integer,[x,y,z]) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{DeRhamComplexXmpPageEmpty8} +\begin{paste}{DeRhamComplexXmpPageEmpty8}{DeRhamComplexXmpPagePatch8} +\pastebutton{DeRhamComplexXmpPageEmpty8}{\showpaste} +\tab{5}\spadcommand{dx : der := generator(1)\free{der }\bound{dx }} +\end{paste}\end{patch} + +\begin{patch}{DeRhamComplexXmpPagePatch9} +\begin{paste}{DeRhamComplexXmpPageFull9}{DeRhamComplexXmpPageEmpty9} +\pastebutton{DeRhamComplexXmpPageFull9}{\hidepaste} +\tab{5}\spadcommand{dy : der := generator(2)\free{der }\bound{dy }} +\indentrel{3}\begin{verbatim} + (9) dy + Type: DeRhamComplex(Integer,[x,y,z]) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{DeRhamComplexXmpPageEmpty9} +\begin{paste}{DeRhamComplexXmpPageEmpty9}{DeRhamComplexXmpPagePatch9} +\pastebutton{DeRhamComplexXmpPageEmpty9}{\showpaste} +\tab{5}\spadcommand{dy : der := generator(2)\free{der }\bound{dy }} +\end{paste}\end{patch} + +\begin{patch}{DeRhamComplexXmpPagePatch10} +\begin{paste}{DeRhamComplexXmpPageFull10}{DeRhamComplexXmpPageEmpty10} +\pastebutton{DeRhamComplexXmpPageFull10}{\hidepaste} +\tab{5}\spadcommand{dz : der := generator(3)\free{der }\bound{dz }} +\indentrel{3}\begin{verbatim} + (10) dz + Type: DeRhamComplex(Integer,[x,y,z]) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{DeRhamComplexXmpPageEmpty10} +\begin{paste}{DeRhamComplexXmpPageEmpty10}{DeRhamComplexXmpPagePatch10} +\pastebutton{DeRhamComplexXmpPageEmpty10}{\showpaste} +\tab{5}\spadcommand{dz : der := generator(3)\free{der }\bound{dz }} +\end{paste}\end{patch} + +\begin{patch}{DeRhamComplexXmpPagePatch11} +\begin{paste}{DeRhamComplexXmpPageFull11}{DeRhamComplexXmpPageEmpty11} +\pastebutton{DeRhamComplexXmpPageFull11}{\hidepaste} +\tab{5}\spadcommand{[dx,dy,dz] := [generator(i)$der for i in 1..3]\free{der }\bound{dxyz }} +\indentrel{3}\begin{verbatim} + (11) [dx,dy,dz] + Type: List DeRhamComplex(Integer,[x,y,z]) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{DeRhamComplexXmpPageEmpty11} +\begin{paste}{DeRhamComplexXmpPageEmpty11}{DeRhamComplexXmpPagePatch11} +\pastebutton{DeRhamComplexXmpPageEmpty11}{\showpaste} +\tab{5}\spadcommand{[dx,dy,dz] := [generator(i)$der for i in 1..3]\free{der }\bound{dxyz }} +\end{paste}\end{patch} + +\begin{patch}{DeRhamComplexXmpPagePatch12} +\begin{paste}{DeRhamComplexXmpPageFull12}{DeRhamComplexXmpPageEmpty12} +\pastebutton{DeRhamComplexXmpPageFull12}{\hidepaste} +\tab{5}\spadcommand{alpha : der := f*dx + g*dy + h*dz\bound{alpha }\free{der f g h dxyz }} +\indentrel{3}\begin{verbatim} + (12) + 3 2 + (- 2x y z + x y z)dz + + + 2 3 2 2 3 2 5 2 + (- 7z sin(x y ) + y z cos(z))dy + (- 5x y z + x y z)dx + Type: DeRhamComplex(Integer,[x,y,z]) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{DeRhamComplexXmpPageEmpty12} +\begin{paste}{DeRhamComplexXmpPageEmpty12}{DeRhamComplexXmpPagePatch12} +\pastebutton{DeRhamComplexXmpPageEmpty12}{\showpaste} +\tab{5}\spadcommand{alpha : der := f*dx + g*dy + h*dz\bound{alpha }\free{der f g h dxyz }} +\end{paste}\end{patch} + +\begin{patch}{DeRhamComplexXmpPagePatch13} +\begin{paste}{DeRhamComplexXmpPageFull13}{DeRhamComplexXmpPageEmpty13} +\pastebutton{DeRhamComplexXmpPageFull13}{\hidepaste} +\tab{5}\spadcommand{beta : der := cos(tan(x*y*z)+x*y*z)*dx + x*dy\bound{beta }\free{der f g h dxyz }} +\indentrel{3}\begin{verbatim} + (13) x dy + cos(tan(x y z) + x y z)dx + Type: DeRhamComplex(Integer,[x,y,z]) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{DeRhamComplexXmpPageEmpty13} +\begin{paste}{DeRhamComplexXmpPageEmpty13}{DeRhamComplexXmpPagePatch13} +\pastebutton{DeRhamComplexXmpPageEmpty13}{\showpaste} +\tab{5}\spadcommand{beta : der := cos(tan(x*y*z)+x*y*z)*dx + x*dy\bound{beta }\free{der f g h dxyz }} +\end{paste}\end{patch} + +\begin{patch}{DeRhamComplexXmpPagePatch14} +\begin{paste}{DeRhamComplexXmpPageFull14}{DeRhamComplexXmpPageEmpty14} +\pastebutton{DeRhamComplexXmpPageFull14}{\hidepaste} +\tab{5}\spadcommand{exteriorDifferential alpha;\free{alpha }\bound{ed }} +\indentrel{3}\begin{verbatim} + Type: DeRhamComplex(Integer,[x,y,z]) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{DeRhamComplexXmpPageEmpty14} +\begin{paste}{DeRhamComplexXmpPageEmpty14}{DeRhamComplexXmpPagePatch14} +\pastebutton{DeRhamComplexXmpPageEmpty14}{\showpaste} +\tab{5}\spadcommand{exteriorDifferential alpha;\free{alpha }\bound{ed }} +\end{paste}\end{patch} + +\begin{patch}{DeRhamComplexXmpPagePatch15} +\begin{paste}{DeRhamComplexXmpPageFull15}{DeRhamComplexXmpPageEmpty15} +\pastebutton{DeRhamComplexXmpPageFull15}{\hidepaste} +\tab{5}\spadcommand{exteriorDifferential \%\free{ed }} +\indentrel{3}\begin{verbatim} + (15) 0 + Type: DeRhamComplex(Integer,[x,y,z]) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{DeRhamComplexXmpPageEmpty15} +\begin{paste}{DeRhamComplexXmpPageEmpty15}{DeRhamComplexXmpPagePatch15} +\pastebutton{DeRhamComplexXmpPageEmpty15}{\showpaste} +\tab{5}\spadcommand{exteriorDifferential \%\free{ed }} +\end{paste}\end{patch} + +\begin{patch}{DeRhamComplexXmpPagePatch16} +\begin{paste}{DeRhamComplexXmpPageFull16}{DeRhamComplexXmpPageEmpty16} +\pastebutton{DeRhamComplexXmpPageFull16}{\hidepaste} +\tab{5}\spadcommand{gamma := alpha * beta\bound{gamma }\free{alpha }\free{beta }} +\indentrel{3}\begin{verbatim} + (16) + 4 2 2 + (2x y z - x y z)dy dz + + + 3 2 + (2x y z - x y z)cos(tan(x y z) + x y z)dx dz + + + 2 3 2 2 + (7z sin(x y ) - y z cos(z)) + * + cos(tan(x y z) + x y z) + + + 4 2 5 3 + - 5x y z + x y z + * + dx dy + Type: DeRhamComplex(Integer,[x,y,z]) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{DeRhamComplexXmpPageEmpty16} +\begin{paste}{DeRhamComplexXmpPageEmpty16}{DeRhamComplexXmpPagePatch16} +\pastebutton{DeRhamComplexXmpPageEmpty16}{\showpaste} +\tab{5}\spadcommand{gamma := alpha * beta\bound{gamma }\free{alpha }\free{beta }} +\end{paste}\end{patch} + +\begin{patch}{DeRhamComplexXmpPagePatch17} +\begin{paste}{DeRhamComplexXmpPageFull17}{DeRhamComplexXmpPageEmpty17} +\pastebutton{DeRhamComplexXmpPageFull17}{\hidepaste} +\tab{5}\spadcommand{exteriorDifferential(gamma) - (exteriorDifferential(alpha)*beta - alpha * exteriorDifferential(beta))\free{alpha beta gamma }} +\indentrel{3}\begin{verbatim} + (17) 0 + Type: DeRhamComplex(Integer,[x,y,z]) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{DeRhamComplexXmpPageEmpty17} +\begin{paste}{DeRhamComplexXmpPageEmpty17}{DeRhamComplexXmpPagePatch17} +\pastebutton{DeRhamComplexXmpPageEmpty17}{\showpaste} +\tab{5}\spadcommand{exteriorDifferential(gamma) - (exteriorDifferential(alpha)*beta - alpha * exteriorDifferential(beta))\free{alpha beta gamma }} +\end{paste}\end{patch} + +\begin{patch}{DeRhamComplexXmpPagePatch18} +\begin{paste}{DeRhamComplexXmpPageFull18}{DeRhamComplexXmpPageEmpty18} +\pastebutton{DeRhamComplexXmpPageFull18}{\hidepaste} +\tab{5}\spadcommand{a : BOP := operator('a)\bound{ao }} +\indentrel{3}\begin{verbatim} + (18) a + Type: BasicOperator +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{DeRhamComplexXmpPageEmpty18} +\begin{paste}{DeRhamComplexXmpPageEmpty18}{DeRhamComplexXmpPagePatch18} +\pastebutton{DeRhamComplexXmpPageEmpty18}{\showpaste} +\tab{5}\spadcommand{a : BOP := operator('a)\bound{ao }} +\end{paste}\end{patch} + +\begin{patch}{DeRhamComplexXmpPagePatch19} +\begin{paste}{DeRhamComplexXmpPageFull19}{DeRhamComplexXmpPageEmpty19} +\pastebutton{DeRhamComplexXmpPageFull19}{\hidepaste} +\tab{5}\spadcommand{b : BOP := operator('b)\bound{bo }} +\indentrel{3}\begin{verbatim} + (19) b + Type: BasicOperator +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{DeRhamComplexXmpPageEmpty19} +\begin{paste}{DeRhamComplexXmpPageEmpty19}{DeRhamComplexXmpPagePatch19} +\pastebutton{DeRhamComplexXmpPageEmpty19}{\showpaste} +\tab{5}\spadcommand{b : BOP := operator('b)\bound{bo }} +\end{paste}\end{patch} + +\begin{patch}{DeRhamComplexXmpPagePatch20} +\begin{paste}{DeRhamComplexXmpPageFull20}{DeRhamComplexXmpPageEmpty20} +\pastebutton{DeRhamComplexXmpPageFull20}{\hidepaste} +\tab{5}\spadcommand{c : BOP := operator('c)\bound{co }} +\indentrel{3}\begin{verbatim} + (20) c + Type: BasicOperator +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{DeRhamComplexXmpPageEmpty20} +\begin{paste}{DeRhamComplexXmpPageEmpty20}{DeRhamComplexXmpPagePatch20} +\pastebutton{DeRhamComplexXmpPageEmpty20}{\showpaste} +\tab{5}\spadcommand{c : BOP := operator('c)\bound{co }} +\end{paste}\end{patch} + +\begin{patch}{DeRhamComplexXmpPagePatch21} +\begin{paste}{DeRhamComplexXmpPageFull21}{DeRhamComplexXmpPageEmpty21} +\pastebutton{DeRhamComplexXmpPageFull21}{\hidepaste} +\tab{5}\spadcommand{sigma := a(x,y,z) * dx + b(x,y,z) * dy + c(x,y,z) * dz\bound{sigma }\free{ao bo co dxyz }} +\indentrel{3}\begin{verbatim} + (21) c(x,y,z)dz + b(x,y,z)dy + a(x,y,z)dx + Type: DeRhamComplex(Integer,[x,y,z]) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{DeRhamComplexXmpPageEmpty21} +\begin{paste}{DeRhamComplexXmpPageEmpty21}{DeRhamComplexXmpPagePatch21} +\pastebutton{DeRhamComplexXmpPageEmpty21}{\showpaste} +\tab{5}\spadcommand{sigma := a(x,y,z) * dx + b(x,y,z) * dy + c(x,y,z) * dz\bound{sigma }\free{ao bo co dxyz }} +\end{paste}\end{patch} + +\begin{patch}{DeRhamComplexXmpPagePatch22} +\begin{paste}{DeRhamComplexXmpPageFull22}{DeRhamComplexXmpPageEmpty22} +\pastebutton{DeRhamComplexXmpPageFull22}{\hidepaste} +\tab{5}\spadcommand{theta := a(x,y,z) * dx * dy + b(x,y,z) * dx * dz + c(x,y,z) * dy * dz\bound{theta }\free{ao bo co dxyz }} +\indentrel{3}\begin{verbatim} + (22) c(x,y,z)dy dz + b(x,y,z)dx dz + a(x,y,z)dx dy + Type: DeRhamComplex(Integer,[x,y,z]) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{DeRhamComplexXmpPageEmpty22} +\begin{paste}{DeRhamComplexXmpPageEmpty22}{DeRhamComplexXmpPagePatch22} +\pastebutton{DeRhamComplexXmpPageEmpty22}{\showpaste} +\tab{5}\spadcommand{theta := a(x,y,z) * dx * dy + b(x,y,z) * dx * dz + c(x,y,z) * dy * dz\bound{theta }\free{ao bo co dxyz }} +\end{paste}\end{patch} + +\begin{patch}{DeRhamComplexXmpPagePatch23} +\begin{paste}{DeRhamComplexXmpPageFull23}{DeRhamComplexXmpPageEmpty23} +\pastebutton{DeRhamComplexXmpPageFull23}{\hidepaste} +\tab{5}\spadcommand{totalDifferential(a(x,y,z))$der\free{ao der }} +\indentrel{3}\begin{verbatim} + (23) a (x,y,z)dz + a (x,y,z)dy + a (x,y,z)dx + ,3 ,2 ,1 + Type: DeRhamComplex(Integer,[x,y,z]) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{DeRhamComplexXmpPageEmpty23} +\begin{paste}{DeRhamComplexXmpPageEmpty23}{DeRhamComplexXmpPagePatch23} +\pastebutton{DeRhamComplexXmpPageEmpty23}{\showpaste} +\tab{5}\spadcommand{totalDifferential(a(x,y,z))$der\free{ao der }} +\end{paste}\end{patch} + +\begin{patch}{DeRhamComplexXmpPagePatch24} +\begin{paste}{DeRhamComplexXmpPageFull24}{DeRhamComplexXmpPageEmpty24} +\pastebutton{DeRhamComplexXmpPageFull24}{\hidepaste} +\tab{5}\spadcommand{exteriorDifferential sigma\free{sigma }} +\indentrel{3}\begin{verbatim} + (24) + (c (x,y,z) - b (x,y,z))dy dz + ,2 ,3 + + + (c (x,y,z) - a (x,y,z))dx dz + ,1 ,3 + + + (b (x,y,z) - a (x,y,z))dx dy + ,1 ,2 + Type: DeRhamComplex(Integer,[x,y,z]) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{DeRhamComplexXmpPageEmpty24} +\begin{paste}{DeRhamComplexXmpPageEmpty24}{DeRhamComplexXmpPagePatch24} +\pastebutton{DeRhamComplexXmpPageEmpty24}{\showpaste} +\tab{5}\spadcommand{exteriorDifferential sigma\free{sigma }} +\end{paste}\end{patch} + +\begin{patch}{DeRhamComplexXmpPagePatch25} +\begin{paste}{DeRhamComplexXmpPageFull25}{DeRhamComplexXmpPageEmpty25} +\pastebutton{DeRhamComplexXmpPageFull25}{\hidepaste} +\tab{5}\spadcommand{exteriorDifferential theta\free{theta }} +\indentrel{3}\begin{verbatim} + (25) (c (x,y,z) - b (x,y,z) + a (x,y,z))dx dy dz + ,1 ,2 ,3 + Type: DeRhamComplex(Integer,[x,y,z]) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{DeRhamComplexXmpPageEmpty25} +\begin{paste}{DeRhamComplexXmpPageEmpty25}{DeRhamComplexXmpPagePatch25} +\pastebutton{DeRhamComplexXmpPageEmpty25}{\showpaste} +\tab{5}\spadcommand{exteriorDifferential theta\free{theta }} +\end{paste}\end{patch} + +\begin{patch}{DeRhamComplexXmpPagePatch26} +\begin{paste}{DeRhamComplexXmpPageFull26}{DeRhamComplexXmpPageEmpty26} +\pastebutton{DeRhamComplexXmpPageFull26}{\hidepaste} +\tab{5}\spadcommand{one : der := 1\bound{one }\free{der }} +\indentrel{3}\begin{verbatim} + (26) 1 + Type: DeRhamComplex(Integer,[x,y,z]) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{DeRhamComplexXmpPageEmpty26} +\begin{paste}{DeRhamComplexXmpPageEmpty26}{DeRhamComplexXmpPagePatch26} +\pastebutton{DeRhamComplexXmpPageEmpty26}{\showpaste} +\tab{5}\spadcommand{one : der := 1\bound{one }\free{der }} +\end{paste}\end{patch} + +\begin{patch}{DeRhamComplexXmpPagePatch27} +\begin{paste}{DeRhamComplexXmpPageFull27}{DeRhamComplexXmpPageEmpty27} +\pastebutton{DeRhamComplexXmpPageFull27}{\hidepaste} +\tab{5}\spadcommand{g1 : der := a([x,t,y,u,v,z,e]) * one\free{der one ao }\bound{g1 }} +\indentrel{3}\begin{verbatim} + (27) a(x,t,y,u,v,z,e) + Type: DeRhamComplex(Integer,[x,y,z]) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{DeRhamComplexXmpPageEmpty27} +\begin{paste}{DeRhamComplexXmpPageEmpty27}{DeRhamComplexXmpPagePatch27} +\pastebutton{DeRhamComplexXmpPageEmpty27}{\showpaste} +\tab{5}\spadcommand{g1 : der := a([x,t,y,u,v,z,e]) * one\free{der one ao }\bound{g1 }} +\end{paste}\end{patch} + +\begin{patch}{DeRhamComplexXmpPagePatch28} +\begin{paste}{DeRhamComplexXmpPageFull28}{DeRhamComplexXmpPageEmpty28} +\pastebutton{DeRhamComplexXmpPageFull28}{\hidepaste} +\tab{5}\spadcommand{h1 : der := a([x,y,x,t,x,z,y,r,u,x]) * one\free{der one ao }\bound{h1 }} +\indentrel{3}\begin{verbatim} + (28) a(x,y,x,t,x,z,y,r,u,x) + Type: DeRhamComplex(Integer,[x,y,z]) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{DeRhamComplexXmpPageEmpty28} +\begin{paste}{DeRhamComplexXmpPageEmpty28}{DeRhamComplexXmpPagePatch28} +\pastebutton{DeRhamComplexXmpPageEmpty28}{\showpaste} +\tab{5}\spadcommand{h1 : der := a([x,y,x,t,x,z,y,r,u,x]) * one\free{der one ao }\bound{h1 }} +\end{paste}\end{patch} + +\begin{patch}{DeRhamComplexXmpPagePatch29} +\begin{paste}{DeRhamComplexXmpPageFull29}{DeRhamComplexXmpPageEmpty29} +\pastebutton{DeRhamComplexXmpPageFull29}{\hidepaste} +\tab{5}\spadcommand{exteriorDifferential g1\free{g1 }} +\indentrel{3}\begin{verbatim} + (29) + a (x,t,y,u,v,z,e)dz + a (x,t,y,u,v,z,e)dy + ,6 ,3 + + + a (x,t,y,u,v,z,e)dx + ,1 + Type: DeRhamComplex(Integer,[x,y,z]) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{DeRhamComplexXmpPageEmpty29} +\begin{paste}{DeRhamComplexXmpPageEmpty29}{DeRhamComplexXmpPagePatch29} +\pastebutton{DeRhamComplexXmpPageEmpty29}{\showpaste} +\tab{5}\spadcommand{exteriorDifferential g1\free{g1 }} +\end{paste}\end{patch} + +\begin{patch}{DeRhamComplexXmpPagePatch30} +\begin{paste}{DeRhamComplexXmpPageFull30}{DeRhamComplexXmpPageEmpty30} +\pastebutton{DeRhamComplexXmpPageFull30}{\hidepaste} +\tab{5}\spadcommand{exteriorDifferential h1\free{h1 }} +\indentrel{3}\begin{verbatim} + (30) + a (x,y,x,t,x,z,y,r,u,x)dz + ,6 + + + a (x,y,x,t,x,z,y,r,u,x) + ,7 + + + a (x,y,x,t,x,z,y,r,u,x) + ,2 + * + dy + + + a (x,y,x,t,x,z,y,r,u,x) + ,10 + + + a (x,y,x,t,x,z,y,r,u,x) + ,5 + + + a (x,y,x,t,x,z,y,r,u,x) + a (x,y,x,t,x,z,y,r,u,x) + ,3 ,1 + * + dx + Type: DeRhamComplex(Integer,[x,y,z]) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{DeRhamComplexXmpPageEmpty30} +\begin{paste}{DeRhamComplexXmpPageEmpty30}{DeRhamComplexXmpPagePatch30} +\pastebutton{DeRhamComplexXmpPageEmpty30}{\showpaste} +\tab{5}\spadcommand{exteriorDifferential h1\free{h1 }} +\end{paste}\end{patch} + +\begin{patch}{DeRhamComplexXmpPagePatch31} +\begin{paste}{DeRhamComplexXmpPageFull31}{DeRhamComplexXmpPageEmpty31} +\pastebutton{DeRhamComplexXmpPageFull31}{\hidepaste} +\tab{5}\spadcommand{coefficient(gamma, dx*dy)\free{gamma dxyz }} +\indentrel{3}\begin{verbatim} + (31) + 2 3 2 2 + (7z sin(x y ) - y z cos(z))cos(tan(x y z) + x y z) + + + 4 2 5 3 + - 5x y z + x y z + Type: Expression Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{DeRhamComplexXmpPageEmpty31} +\begin{paste}{DeRhamComplexXmpPageEmpty31}{DeRhamComplexXmpPagePatch31} +\pastebutton{DeRhamComplexXmpPageEmpty31}{\showpaste} +\tab{5}\spadcommand{coefficient(gamma, dx*dy)\free{gamma dxyz }} +\end{paste}\end{patch} + +\begin{patch}{DeRhamComplexXmpPagePatch32} +\begin{paste}{DeRhamComplexXmpPageFull32}{DeRhamComplexXmpPageEmpty32} +\pastebutton{DeRhamComplexXmpPageFull32}{\hidepaste} +\tab{5}\spadcommand{coefficient(gamma, one)\free{gamma one }} +\indentrel{3}\begin{verbatim} + (32) 0 + Type: Expression Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{DeRhamComplexXmpPageEmpty32} +\begin{paste}{DeRhamComplexXmpPageEmpty32}{DeRhamComplexXmpPagePatch32} +\pastebutton{DeRhamComplexXmpPageEmpty32}{\showpaste} +\tab{5}\spadcommand{coefficient(gamma, one)\free{gamma one }} +\end{paste}\end{patch} + +\begin{patch}{DeRhamComplexXmpPagePatch33} +\begin{paste}{DeRhamComplexXmpPageFull33}{DeRhamComplexXmpPageEmpty33} +\pastebutton{DeRhamComplexXmpPageFull33}{\hidepaste} +\tab{5}\spadcommand{coefficient(g1,one)\free{g1 one }} +\indentrel{3}\begin{verbatim} + (33) a(x,t,y,u,v,z,e) + Type: Expression Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{DeRhamComplexXmpPageEmpty33} +\begin{paste}{DeRhamComplexXmpPageEmpty33}{DeRhamComplexXmpPagePatch33} +\pastebutton{DeRhamComplexXmpPageEmpty33}{\showpaste} +\tab{5}\spadcommand{coefficient(g1,one)\free{g1 one }} +\end{paste}\end{patch} + @ \section{dfloat.ht} \pagehead{DoubleFloatXmpPage}{dfloat.ht}{DoubleFloat} @@ -5516,6 +13580,170 @@ Section 8.1\ignore{ugProblemNumeric}, and \autobuttons \end{page} +\begin{patch}{DoubleFloatXmpPagePatch1} +\begin{paste}{DoubleFloatXmpPageFull1}{DoubleFloatXmpPageEmpty1} +\pastebutton{DoubleFloatXmpPageFull1}{\hidepaste} +\tab{5}\spadcommand{2.71828} +\indentrel{3}\begin{verbatim} + (1) 2.71828 + Type: Float +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{DoubleFloatXmpPageEmpty1} +\begin{paste}{DoubleFloatXmpPageEmpty1}{DoubleFloatXmpPagePatch1} +\pastebutton{DoubleFloatXmpPageEmpty1}{\showpaste} +\tab{5}\spadcommand{2.71828} +\end{paste}\end{patch} + +\begin{patch}{DoubleFloatXmpPagePatch2} +\begin{paste}{DoubleFloatXmpPageFull2}{DoubleFloatXmpPageEmpty2} +\pastebutton{DoubleFloatXmpPageFull2}{\hidepaste} +\tab{5}\spadcommand{2.71828@DoubleFloat} +\indentrel{3}\begin{verbatim} + (2) 2.71828 + Type: DoubleFloat +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{DoubleFloatXmpPageEmpty2} +\begin{paste}{DoubleFloatXmpPageEmpty2}{DoubleFloatXmpPagePatch2} +\pastebutton{DoubleFloatXmpPageEmpty2}{\showpaste} +\tab{5}\spadcommand{2.71828@DoubleFloat} +\end{paste}\end{patch} + +\begin{patch}{DoubleFloatXmpPagePatch3} +\begin{paste}{DoubleFloatXmpPageFull3}{DoubleFloatXmpPageEmpty3} +\pastebutton{DoubleFloatXmpPageFull3}{\hidepaste} +\tab{5}\spadcommand{2.71828 :: DoubleFloat} +\indentrel{3}\begin{verbatim} + (3) 2.71828 + Type: DoubleFloat +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{DoubleFloatXmpPageEmpty3} +\begin{paste}{DoubleFloatXmpPageEmpty3}{DoubleFloatXmpPagePatch3} +\pastebutton{DoubleFloatXmpPageEmpty3}{\showpaste} +\tab{5}\spadcommand{2.71828 :: DoubleFloat} +\end{paste}\end{patch} + +\begin{patch}{DoubleFloatXmpPagePatch4} +\begin{paste}{DoubleFloatXmpPageFull4}{DoubleFloatXmpPageEmpty4} +\pastebutton{DoubleFloatXmpPageFull4}{\hidepaste} +\tab{5}\spadcommand{eApprox : DoubleFloat := 2.71828\bound{eApprox }} +\indentrel{3}\begin{verbatim} + (4) 2.71828 + Type: DoubleFloat +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{DoubleFloatXmpPageEmpty4} +\begin{paste}{DoubleFloatXmpPageEmpty4}{DoubleFloatXmpPagePatch4} +\pastebutton{DoubleFloatXmpPageEmpty4}{\showpaste} +\tab{5}\spadcommand{eApprox : DoubleFloat := 2.71828\bound{eApprox }} +\end{paste}\end{patch} + +\begin{patch}{DoubleFloatXmpPagePatch5} +\begin{paste}{DoubleFloatXmpPageFull5}{DoubleFloatXmpPageEmpty5} +\pastebutton{DoubleFloatXmpPageFull5}{\hidepaste} +\tab{5}\spadcommand{avg : List DoubleFloat -> DoubleFloat\bound{avgDec }} +\indentrel{3}\begin{verbatim} + Type: Void +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{DoubleFloatXmpPageEmpty5} +\begin{paste}{DoubleFloatXmpPageEmpty5}{DoubleFloatXmpPagePatch5} +\pastebutton{DoubleFloatXmpPageEmpty5}{\showpaste} +\tab{5}\spadcommand{avg : List DoubleFloat -> DoubleFloat\bound{avgDec }} +\end{paste}\end{patch} + +\begin{patch}{DoubleFloatXmpPagePatch6} +\begin{paste}{DoubleFloatXmpPageFull6}{DoubleFloatXmpPageEmpty6} +\pastebutton{DoubleFloatXmpPageFull6}{\hidepaste} +\tab{5}\spadcommand{avg l == + empty? l => 0 :: DoubleFloat + reduce(_+,l) / \#l +\bound{avg }\free{avgDec }} +\indentrel{3}\begin{verbatim} + Type: Void +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{DoubleFloatXmpPageEmpty6} +\begin{paste}{DoubleFloatXmpPageEmpty6}{DoubleFloatXmpPagePatch6} +\pastebutton{DoubleFloatXmpPageEmpty6}{\showpaste} +\tab{5}\spadcommand{avg l == + empty? l => 0 :: DoubleFloat + reduce(_+,l) / \#l +\bound{avg }\free{avgDec }} +\end{paste}\end{patch} + +\begin{patch}{DoubleFloatXmpPagePatch7} +\begin{paste}{DoubleFloatXmpPageFull7}{DoubleFloatXmpPageEmpty7} +\pastebutton{DoubleFloatXmpPageFull7}{\hidepaste} +\tab{5}\spadcommand{avg []\free{avg }} +\indentrel{3}\begin{verbatim} + (7) 0.0 + Type: DoubleFloat +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{DoubleFloatXmpPageEmpty7} +\begin{paste}{DoubleFloatXmpPageEmpty7}{DoubleFloatXmpPagePatch7} +\pastebutton{DoubleFloatXmpPageEmpty7}{\showpaste} +\tab{5}\spadcommand{avg []\free{avg }} +\end{paste}\end{patch} + +\begin{patch}{DoubleFloatXmpPagePatch8} +\begin{paste}{DoubleFloatXmpPageFull8}{DoubleFloatXmpPageEmpty8} +\pastebutton{DoubleFloatXmpPageFull8}{\hidepaste} +\tab{5}\spadcommand{avg [3.4,9.7,-6.8]\free{avg }} +\indentrel{3}\begin{verbatim} + (8) 2.1 + Type: DoubleFloat +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{DoubleFloatXmpPageEmpty8} +\begin{paste}{DoubleFloatXmpPageEmpty8}{DoubleFloatXmpPagePatch8} +\pastebutton{DoubleFloatXmpPageEmpty8}{\showpaste} +\tab{5}\spadcommand{avg [3.4,9.7,-6.8]\free{avg }} +\end{paste}\end{patch} + +\begin{patch}{DoubleFloatXmpPagePatch9} +\begin{paste}{DoubleFloatXmpPageFull9}{DoubleFloatXmpPageEmpty9} +\pastebutton{DoubleFloatXmpPageFull9}{\hidepaste} +\tab{5}\spadcommand{cos(3.1415926)$DoubleFloat} +\indentrel{3}\begin{verbatim} + (9) - 0.999999999999999 + Type: DoubleFloat +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{DoubleFloatXmpPageEmpty9} +\begin{paste}{DoubleFloatXmpPageEmpty9}{DoubleFloatXmpPagePatch9} +\pastebutton{DoubleFloatXmpPageEmpty9}{\showpaste} +\tab{5}\spadcommand{cos(3.1415926)$DoubleFloat} +\end{paste}\end{patch} + +\begin{patch}{DoubleFloatXmpPagePatch10} +\begin{paste}{DoubleFloatXmpPageFull10}{DoubleFloatXmpPageEmpty10} +\pastebutton{DoubleFloatXmpPageFull10}{\hidepaste} +\tab{5}\spadcommand{cos(3.1415926 :: DoubleFloat)} +\indentrel{3}\begin{verbatim} + (10) - 0.999999999999999 + Type: DoubleFloat +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{DoubleFloatXmpPageEmpty10} +\begin{paste}{DoubleFloatXmpPageEmpty10}{DoubleFloatXmpPagePatch10} +\pastebutton{DoubleFloatXmpPageEmpty10}{\showpaste} +\tab{5}\spadcommand{cos(3.1415926 :: DoubleFloat)} +\end{paste}\end{patch} + @ \section{dmp.ht} \pagehead{DistributedMultivariatePolyXmpPage}{dmp.ht} @@ -5606,7 +13834,169 @@ in Section 2.7\ignore{ugTypesConvert}, \endscroll \autobuttons \end{page} -% + +\begin{patch}{DistributedMultivariatePolynomialXmpPagePatch1} +\begin{paste}{DistributedMultivariatePolynomialXmpPageFull1}{DistributedMultivariatePolynomialXmpPageEmpty1} +\pastebutton{DistributedMultivariatePolynomialXmpPageFull1}{\hidepaste} +\tab{5}\spadcommand{(d1,d2,d3) : DMP([z,y,x],FRAC INT)\bound{d1dec d2dec d3dec }} +\indentrel{3}\begin{verbatim} + Type: Void +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{DistributedMultivariatePolynomialXmpPageEmpty1} +\begin{paste}{DistributedMultivariatePolynomialXmpPageEmpty1}{DistributedMultivariatePolynomialXmpPagePatch1} +\pastebutton{DistributedMultivariatePolynomialXmpPageEmpty1}{\showpaste} +\tab{5}\spadcommand{(d1,d2,d3) : DMP([z,y,x],FRAC INT)\bound{d1dec d2dec d3dec }} +\end{paste}\end{patch} + +\begin{patch}{DistributedMultivariatePolynomialXmpPagePatch2} +\begin{paste}{DistributedMultivariatePolynomialXmpPageFull2}{DistributedMultivariatePolynomialXmpPageEmpty2} +\pastebutton{DistributedMultivariatePolynomialXmpPageFull2}{\hidepaste} +\tab{5}\spadcommand{d1 := -4*z + 4*y**2*x + 16*x**2 + 1\bound{d1 }\free{d1dec }} +\indentrel{3}\begin{verbatim} + 2 2 + (2) - 4z + 4y x + 16x + 1 +Type: DistributedMultivariatePolynomial([z,y,x],Fraction Integer) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{DistributedMultivariatePolynomialXmpPageEmpty2} +\begin{paste}{DistributedMultivariatePolynomialXmpPageEmpty2}{DistributedMultivariatePolynomialXmpPagePatch2} +\pastebutton{DistributedMultivariatePolynomialXmpPageEmpty2}{\showpaste} +\tab{5}\spadcommand{d1 := -4*z + 4*y**2*x + 16*x**2 + 1\bound{d1 }\free{d1dec }} +\end{paste}\end{patch} + +\begin{patch}{DistributedMultivariatePolynomialXmpPagePatch3} +\begin{paste}{DistributedMultivariatePolynomialXmpPageFull3}{DistributedMultivariatePolynomialXmpPageEmpty3} +\pastebutton{DistributedMultivariatePolynomialXmpPageFull3}{\hidepaste} +\tab{5}\spadcommand{d2 := 2*z*y**2 + 4*x + 1\bound{d2 }\free{d2dec }} +\indentrel{3}\begin{verbatim} + 2 + (3) 2z y + 4x + 1 +Type: DistributedMultivariatePolynomial([z,y,x],Fraction Integer) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{DistributedMultivariatePolynomialXmpPageEmpty3} +\begin{paste}{DistributedMultivariatePolynomialXmpPageEmpty3}{DistributedMultivariatePolynomialXmpPagePatch3} +\pastebutton{DistributedMultivariatePolynomialXmpPageEmpty3}{\showpaste} +\tab{5}\spadcommand{d2 := 2*z*y**2 + 4*x + 1\bound{d2 }\free{d2dec }} +\end{paste}\end{patch} + +\begin{patch}{DistributedMultivariatePolynomialXmpPagePatch4} +\begin{paste}{DistributedMultivariatePolynomialXmpPageFull4}{DistributedMultivariatePolynomialXmpPageEmpty4} +\pastebutton{DistributedMultivariatePolynomialXmpPageFull4}{\hidepaste} +\tab{5}\spadcommand{d3 := 2*z*x**2 - 2*y**2 - x\bound{d3 }\free{d3dec }} +\indentrel{3}\begin{verbatim} + 2 2 + (4) 2z x - 2y - x +Type: DistributedMultivariatePolynomial([z,y,x],Fraction Integer) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{DistributedMultivariatePolynomialXmpPageEmpty4} +\begin{paste}{DistributedMultivariatePolynomialXmpPageEmpty4}{DistributedMultivariatePolynomialXmpPagePatch4} +\pastebutton{DistributedMultivariatePolynomialXmpPageEmpty4}{\showpaste} +\tab{5}\spadcommand{d3 := 2*z*x**2 - 2*y**2 - x\bound{d3 }\free{d3dec }} +\end{paste}\end{patch} + +\begin{patch}{DistributedMultivariatePolynomialXmpPagePatch5} +\begin{paste}{DistributedMultivariatePolynomialXmpPageFull5}{DistributedMultivariatePolynomialXmpPageEmpty5} +\pastebutton{DistributedMultivariatePolynomialXmpPageFull5}{\hidepaste} +\tab{5}\spadcommand{groebner [d1,d2,d3]\free{d1 d2 d3 }} +\indentrel{3}\begin{verbatim} + (5) + [ + 1568 6 1264 5 6 4 182 3 2047 2 + z - ÄÄÄÄ x - ÄÄÄÄ x + ÄÄÄ x + ÄÄÄ x - ÄÄÄÄ x + 2745 305 305 549 610 + + + 103 2857 + - ÄÄÄÄ x - ÄÄÄÄÄ + 2745 10980 + , + + 2 112 6 84 5 1264 4 13 3 84 2 + y + ÄÄÄÄ x - ÄÄÄ x - ÄÄÄÄ x - ÄÄÄ x + ÄÄÄ x + 2745 305 305 549 305 + + + 1772 2 + ÄÄÄÄ x + ÄÄÄÄ + 2745 2745 + , + 7 29 6 17 4 11 3 1 2 15 1 + x + ÄÄ x - ÄÄ x - ÄÄ x + ÄÄ x + ÄÄ x + Ä] + 4 16 8 32 16 4 +Type: List DistributedMultivariatePolynomial([z,y,x],Fraction Integer) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{DistributedMultivariatePolynomialXmpPageEmpty5} +\begin{paste}{DistributedMultivariatePolynomialXmpPageEmpty5}{DistributedMultivariatePolynomialXmpPagePatch5} +\pastebutton{DistributedMultivariatePolynomialXmpPageEmpty5}{\showpaste} +\tab{5}\spadcommand{groebner [d1,d2,d3]\free{d1 d2 d3 }} +\end{paste}\end{patch} + +\begin{patch}{DistributedMultivariatePolynomialXmpPagePatch6} +\begin{paste}{DistributedMultivariatePolynomialXmpPageFull6}{DistributedMultivariatePolynomialXmpPageEmpty6} +\pastebutton{DistributedMultivariatePolynomialXmpPageFull6}{\hidepaste} +\tab{5}\spadcommand{(n1,n2,n3) : HDMP([z,y,x],FRAC INT)\bound{ndec }} +\indentrel{3}\begin{verbatim} + Type: Void +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{DistributedMultivariatePolynomialXmpPageEmpty6} +\begin{paste}{DistributedMultivariatePolynomialXmpPageEmpty6}{DistributedMultivariatePolynomialXmpPagePatch6} +\pastebutton{DistributedMultivariatePolynomialXmpPageEmpty6}{\showpaste} +\tab{5}\spadcommand{(n1,n2,n3) : HDMP([z,y,x],FRAC INT)\bound{ndec }} +\end{paste}\end{patch} + +\begin{patch}{DistributedMultivariatePolynomialXmpPagePatch7} +\begin{paste}{DistributedMultivariatePolynomialXmpPageFull7}{DistributedMultivariatePolynomialXmpPageEmpty7} +\pastebutton{DistributedMultivariatePolynomialXmpPageFull7}{\hidepaste} +\tab{5}\spadcommand{(n1,n2,n3) := (d1,d2,d3)\free{ndec }\bound{n }\free{d1 d2 d3 }} +\indentrel{3}\begin{verbatim} + 2 2 + (7) 2z x - 2y - x +Type: HomogeneousDistributedMultivariatePolynomial([z,y,x],Fraction Integer) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{DistributedMultivariatePolynomialXmpPageEmpty7} +\begin{paste}{DistributedMultivariatePolynomialXmpPageEmpty7}{DistributedMultivariatePolynomialXmpPagePatch7} +\pastebutton{DistributedMultivariatePolynomialXmpPageEmpty7}{\showpaste} +\tab{5}\spadcommand{(n1,n2,n3) := (d1,d2,d3)\free{ndec }\bound{n }\free{d1 d2 d3 }} +\end{paste}\end{patch} + +\begin{patch}{DistributedMultivariatePolynomialXmpPagePatch8} +\begin{paste}{DistributedMultivariatePolynomialXmpPageFull8}{DistributedMultivariatePolynomialXmpPageEmpty8} +\pastebutton{DistributedMultivariatePolynomialXmpPageFull8}{\hidepaste} +\tab{5}\spadcommand{groebner [n1,n2,n3]\free{n }} +\indentrel{3}\begin{verbatim} + (8) + 4 3 3 2 1 1 + [y + 2x - Ä x + Ä z - Ä, + 2 2 8 + 4 29 3 1 2 7 9 1 2 1 + x + ÄÄ x - Ä y - Ä z x - ÄÄ x - Ä, z y + 2x + Ä, + 4 8 4 16 4 2 + 2 2 1 2 2 1 + y x + 4x - z + Ä, z x - y - Ä x, + 4 2 + 2 2 2 1 3 + z - 4y + 2x - Ä z - Ä x] + 4 2 +Type: List HomogeneousDistributedMultivariatePolynomial([z,y,x],Fraction Integer) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{DistributedMultivariatePolynomialXmpPageEmpty8} +\begin{paste}{DistributedMultivariatePolynomialXmpPageEmpty8}{DistributedMultivariatePolynomialXmpPagePatch8} +\pastebutton{DistributedMultivariatePolynomialXmpPageEmpty8}{\showpaste} +\tab{5}\spadcommand{groebner [n1,n2,n3]\free{n }} +\end{paste}\end{patch} @ \section{eq.ht} @@ -5689,6 +14079,200 @@ all one has to do is ask! \autobuttons \end{page} +\begin{patch}{EquationXmpPagePatch1} +\begin{paste}{EquationXmpPageFull1}{EquationXmpPageEmpty1} +\pastebutton{EquationXmpPageFull1}{\hidepaste} +\tab{5}\spadcommand{eq1 := 3*x + 4*y = 5\bound{eq1 }} +\indentrel{3}\begin{verbatim} + (1) 4y + 3x= 5 + Type: Equation Polynomial Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{EquationXmpPageEmpty1} +\begin{paste}{EquationXmpPageEmpty1}{EquationXmpPagePatch1} +\pastebutton{EquationXmpPageEmpty1}{\showpaste} +\tab{5}\spadcommand{eq1 := 3*x + 4*y = 5\bound{eq1 }} +\end{paste}\end{patch} + +\begin{patch}{EquationXmpPagePatch2} +\begin{paste}{EquationXmpPageFull2}{EquationXmpPageEmpty2} +\pastebutton{EquationXmpPageFull2}{\hidepaste} +\tab{5}\spadcommand{eq2 := 2*x + 2*y = 3\bound{eq2 }} +\indentrel{3}\begin{verbatim} + (2) 2y + 2x= 3 + Type: Equation Polynomial Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{EquationXmpPageEmpty2} +\begin{paste}{EquationXmpPageEmpty2}{EquationXmpPagePatch2} +\pastebutton{EquationXmpPageEmpty2}{\showpaste} +\tab{5}\spadcommand{eq2 := 2*x + 2*y = 3\bound{eq2 }} +\end{paste}\end{patch} + +\begin{patch}{EquationXmpPagePatch3} +\begin{paste}{EquationXmpPageFull3}{EquationXmpPageEmpty3} +\pastebutton{EquationXmpPageFull3}{\hidepaste} +\tab{5}\spadcommand{lhs eq1\free{eq1 }} +\indentrel{3}\begin{verbatim} + (3) 4y + 3x + Type: Polynomial Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{EquationXmpPageEmpty3} +\begin{paste}{EquationXmpPageEmpty3}{EquationXmpPagePatch3} +\pastebutton{EquationXmpPageEmpty3}{\showpaste} +\tab{5}\spadcommand{lhs eq1\free{eq1 }} +\end{paste}\end{patch} + +\begin{patch}{EquationXmpPagePatch4} +\begin{paste}{EquationXmpPageFull4}{EquationXmpPageEmpty4} +\pastebutton{EquationXmpPageFull4}{\hidepaste} +\tab{5}\spadcommand{rhs eq1\free{eq1 }} +\indentrel{3}\begin{verbatim} + (4) 5 + Type: Polynomial Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{EquationXmpPageEmpty4} +\begin{paste}{EquationXmpPageEmpty4}{EquationXmpPagePatch4} +\pastebutton{EquationXmpPageEmpty4}{\showpaste} +\tab{5}\spadcommand{rhs eq1\free{eq1 }} +\end{paste}\end{patch} + +\begin{patch}{EquationXmpPagePatch5} +\begin{paste}{EquationXmpPageFull5}{EquationXmpPageEmpty5} +\pastebutton{EquationXmpPageFull5}{\hidepaste} +\tab{5}\spadcommand{eq1 + eq2\free{eq1 eq2 }} +\indentrel{3}\begin{verbatim} + (5) 6y + 5x= 8 + Type: Equation Polynomial Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{EquationXmpPageEmpty5} +\begin{paste}{EquationXmpPageEmpty5}{EquationXmpPagePatch5} +\pastebutton{EquationXmpPageEmpty5}{\showpaste} +\tab{5}\spadcommand{eq1 + eq2\free{eq1 eq2 }} +\end{paste}\end{patch} + +\begin{patch}{EquationXmpPagePatch6} +\begin{paste}{EquationXmpPageFull6}{EquationXmpPageEmpty6} +\pastebutton{EquationXmpPageFull6}{\hidepaste} +\tab{5}\spadcommand{eq1 * eq2\free{eq1 eq2 }} +\indentrel{3}\begin{verbatim} + 2 2 + (6) 8y + 14x y + 6x = 15 + Type: Equation Polynomial Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{EquationXmpPageEmpty6} +\begin{paste}{EquationXmpPageEmpty6}{EquationXmpPagePatch6} +\pastebutton{EquationXmpPageEmpty6}{\showpaste} +\tab{5}\spadcommand{eq1 * eq2\free{eq1 eq2 }} +\end{paste}\end{patch} + +\begin{patch}{EquationXmpPagePatch7} +\begin{paste}{EquationXmpPageFull7}{EquationXmpPageEmpty7} +\pastebutton{EquationXmpPageFull7}{\hidepaste} +\tab{5}\spadcommand{2*eq2 - eq1\free{eq1 eq2 }} +\indentrel{3}\begin{verbatim} + (7) x= 1 + Type: Equation Polynomial Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{EquationXmpPageEmpty7} +\begin{paste}{EquationXmpPageEmpty7}{EquationXmpPagePatch7} +\pastebutton{EquationXmpPageEmpty7}{\showpaste} +\tab{5}\spadcommand{2*eq2 - eq1\free{eq1 eq2 }} +\end{paste}\end{patch} + +\begin{patch}{EquationXmpPagePatch8} +\begin{paste}{EquationXmpPageFull8}{EquationXmpPageEmpty8} +\pastebutton{EquationXmpPageFull8}{\hidepaste} +\tab{5}\spadcommand{eq1**2\free{eq1 }} +\indentrel{3}\begin{verbatim} + 2 2 + (8) 16y + 24x y + 9x = 25 + Type: Equation Polynomial Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{EquationXmpPageEmpty8} +\begin{paste}{EquationXmpPageEmpty8}{EquationXmpPagePatch8} +\pastebutton{EquationXmpPageEmpty8}{\showpaste} +\tab{5}\spadcommand{eq1**2\free{eq1 }} +\end{paste}\end{patch} + +\begin{patch}{EquationXmpPagePatch9} +\begin{paste}{EquationXmpPageFull9}{EquationXmpPageEmpty9} +\pastebutton{EquationXmpPageFull9}{\hidepaste} +\tab{5}\spadcommand{if x+1 = y then "equal" else "unequal"} +\indentrel{3}\begin{verbatim} + (9) "unequal" + Type: String +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{EquationXmpPageEmpty9} +\begin{paste}{EquationXmpPageEmpty9}{EquationXmpPagePatch9} +\pastebutton{EquationXmpPageEmpty9}{\showpaste} +\tab{5}\spadcommand{if x+1 = y then "equal" else "unequal"} +\end{paste}\end{patch} + +\begin{patch}{EquationXmpPagePatch10} +\begin{paste}{EquationXmpPageFull10}{EquationXmpPageEmpty10} +\pastebutton{EquationXmpPageFull10}{\hidepaste} +\tab{5}\spadcommand{eqpol := x+1 = y\bound{eqpol }} +\indentrel{3}\begin{verbatim} + (10) x + 1= y + Type: Equation Polynomial Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{EquationXmpPageEmpty10} +\begin{paste}{EquationXmpPageEmpty10}{EquationXmpPagePatch10} +\pastebutton{EquationXmpPageEmpty10}{\showpaste} +\tab{5}\spadcommand{eqpol := x+1 = y\bound{eqpol }} +\end{paste}\end{patch} + +\begin{patch}{EquationXmpPagePatch11} +\begin{paste}{EquationXmpPageFull11}{EquationXmpPageEmpty11} +\pastebutton{EquationXmpPageFull11}{\hidepaste} +\tab{5}\spadcommand{if eqpol then "equal" else "unequal"\free{eqpol }} +\indentrel{3}\begin{verbatim} + (11) "unequal" + Type: String +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{EquationXmpPageEmpty11} +\begin{paste}{EquationXmpPageEmpty11}{EquationXmpPagePatch11} +\pastebutton{EquationXmpPageEmpty11}{\showpaste} +\tab{5}\spadcommand{if eqpol then "equal" else "unequal"\free{eqpol }} +\end{paste}\end{patch} + +\begin{patch}{EquationXmpPagePatch12} +\begin{paste}{EquationXmpPageFull12}{EquationXmpPageEmpty12} +\pastebutton{EquationXmpPageFull12}{\hidepaste} +\tab{5}\spadcommand{eqpol::Boolean\free{eqpol }} +\indentrel{3}\begin{verbatim} + (12) false + Type: Boolean +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{EquationXmpPageEmpty12} +\begin{paste}{EquationXmpPageEmpty12}{EquationXmpPagePatch12} +\pastebutton{EquationXmpPageEmpty12}{\showpaste} +\tab{5}\spadcommand{eqpol::Boolean\free{eqpol }} +\end{paste}\end{patch} + @ \section{eqtbl.ht} \pagehead{EqTableXmpPage}{eqtbl.ht}{EqTable} @@ -5741,6 +14325,102 @@ can be stored under each. \autobuttons \end{page} +\begin{patch}{EqTableXmpPagePatch1} +\begin{paste}{EqTableXmpPageFull1}{EqTableXmpPageEmpty1} +\pastebutton{EqTableXmpPageFull1}{\hidepaste} +\tab{5}\spadcommand{e: EqTable(List Integer, Integer) := table()\bound{e }} +\indentrel{3}\begin{verbatim} + (1) table() + Type: EqTable(List Integer,Integer) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{EqTableXmpPageEmpty1} +\begin{paste}{EqTableXmpPageEmpty1}{EqTableXmpPagePatch1} +\pastebutton{EqTableXmpPageEmpty1}{\showpaste} +\tab{5}\spadcommand{e: EqTable(List Integer, Integer) := table()\bound{e }} +\end{paste}\end{patch} + +\begin{patch}{EqTableXmpPagePatch2} +\begin{paste}{EqTableXmpPageFull2}{EqTableXmpPageEmpty2} +\pastebutton{EqTableXmpPageFull2}{\hidepaste} +\tab{5}\spadcommand{l1 := [1,2,3]\bound{l1 }} +\indentrel{3}\begin{verbatim} + (2) [1,2,3] + Type: List PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{EqTableXmpPageEmpty2} +\begin{paste}{EqTableXmpPageEmpty2}{EqTableXmpPagePatch2} +\pastebutton{EqTableXmpPageEmpty2}{\showpaste} +\tab{5}\spadcommand{l1 := [1,2,3]\bound{l1 }} +\end{paste}\end{patch} + +\begin{patch}{EqTableXmpPagePatch3} +\begin{paste}{EqTableXmpPageFull3}{EqTableXmpPageEmpty3} +\pastebutton{EqTableXmpPageFull3}{\hidepaste} +\tab{5}\spadcommand{l2 := [1,2,3]\bound{l2 }} +\indentrel{3}\begin{verbatim} + (3) [1,2,3] + Type: List PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{EqTableXmpPageEmpty3} +\begin{paste}{EqTableXmpPageEmpty3}{EqTableXmpPagePatch3} +\pastebutton{EqTableXmpPageEmpty3}{\showpaste} +\tab{5}\spadcommand{l2 := [1,2,3]\bound{l2 }} +\end{paste}\end{patch} + +\begin{patch}{EqTableXmpPagePatch4} +\begin{paste}{EqTableXmpPageFull4}{EqTableXmpPageEmpty4} +\pastebutton{EqTableXmpPageFull4}{\hidepaste} +\tab{5}\spadcommand{e.l1 := 111\free{e l1 }\bound{e1 }} +\indentrel{3}\begin{verbatim} + (4) 111 + Type: PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{EqTableXmpPageEmpty4} +\begin{paste}{EqTableXmpPageEmpty4}{EqTableXmpPagePatch4} +\pastebutton{EqTableXmpPageEmpty4}{\showpaste} +\tab{5}\spadcommand{e.l1 := 111\free{e l1 }\bound{e1 }} +\end{paste}\end{patch} + +\begin{patch}{EqTableXmpPagePatch5} +\begin{paste}{EqTableXmpPageFull5}{EqTableXmpPageEmpty5} +\pastebutton{EqTableXmpPageFull5}{\hidepaste} +\tab{5}\spadcommand{e.l2 := 222\free{e1 l2 }\bound{e2 }} +\indentrel{3}\begin{verbatim} + (5) 222 + Type: PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{EqTableXmpPageEmpty5} +\begin{paste}{EqTableXmpPageEmpty5}{EqTableXmpPagePatch5} +\pastebutton{EqTableXmpPageEmpty5}{\showpaste} +\tab{5}\spadcommand{e.l2 := 222\free{e1 l2 }\bound{e2 }} +\end{paste}\end{patch} + +\begin{patch}{EqTableXmpPagePatch6} +\begin{paste}{EqTableXmpPageFull6}{EqTableXmpPageEmpty6} +\pastebutton{EqTableXmpPageFull6}{\hidepaste} +\tab{5}\spadcommand{e.l1\free{e2 l1 }} +\indentrel{3}\begin{verbatim} + (6) 111 + Type: PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{EqTableXmpPageEmpty6} +\begin{paste}{EqTableXmpPageEmpty6}{EqTableXmpPagePatch6} +\pastebutton{EqTableXmpPageEmpty6}{\showpaste} +\tab{5}\spadcommand{e.l1\free{e2 l1 }} +\end{paste}\end{patch} + @ \section{evalex.ht} \pagehead{PrefixEval}{evalex.ht}{Example of Standard Evaluation} @@ -5778,7 +14458,24 @@ for {\em op a}. Try it: \example{cos(2)} \endscroll -\autobuttons\end{page} +\autobuttons +\end{page} + +\begin{patch}{PrefixEvalPatch1} +\begin{paste}{PrefixEvalFull1}{PrefixEvalEmpty1} +\pastebutton{PrefixEvalFull1}{\hidepaste} +\tab{5}\spadcommand{cos(2)} +\indentrel{3}\begin{verbatim} + (1) cos(2) + Type: Expression Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{PrefixEvalEmpty1} +\begin{paste}{PrefixEvalEmpty1}{PrefixEvalPatch1} +\pastebutton{PrefixEvalEmpty1}{\showpaste} +\tab{5}\spadcommand{cos(2)} +\end{paste}\end{patch} @ \pagehead{InfixEval}{evalex.ht}{Example of Standard Evaluation} @@ -5820,7 +14517,24 @@ produce {\em 5.4}. Try it: \example{2 + 3.4} \endscroll -\autobuttons\end{page} +\autobuttons +\end{page} + +\begin{patch}{InfixEvalPatch1} +\begin{paste}{InfixEvalFull1}{InfixEvalEmpty1} +\pastebutton{InfixEvalFull1}{\hidepaste} +\tab{5}\spadcommand{2 + 3.4} +\indentrel{3}\begin{verbatim} + (1) 5.4 + Type: Float +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{InfixEvalEmpty1} +\begin{paste}{InfixEvalEmpty1}{InfixEvalPatch1} +\pastebutton{InfixEvalEmpty1}{\showpaste} +\tab{5}\spadcommand{2 + 3.4} +\end{paste}\end{patch} @ \section{exdiff.ht} @@ -5834,7 +14548,26 @@ For example, to compute the derivative of {\em sin(x) * exp(x**2)} with respect to the variable {\em x}, issue the following command: \spadpaste{differentiate(sin(x) * exp(x**2),x)} \endscroll -\autobuttons\end{page} +\autobuttons +\end{page} + +\begin{patch}{ExDiffBasicPatch1} +\begin{paste}{ExDiffBasicFull1}{ExDiffBasicEmpty1} +\pastebutton{ExDiffBasicFull1}{\hidepaste} +\tab{5}\spadcommand{differentiate(sin(x) * exp(x**2),x)} +\indentrel{3}\begin{verbatim} + 2 2 + x x + (1) 2x %e sin(x) + cos(x)%e + Type: Expression Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ExDiffBasicEmpty1} +\begin{paste}{ExDiffBasicEmpty1}{ExDiffBasicPatch1} +\pastebutton{ExDiffBasicEmpty1}{\showpaste} +\tab{5}\spadcommand{differentiate(sin(x) * exp(x**2),x)} +\end{paste}\end{patch} @ \pagehead{ExDiffSeveralVariables}{exdiff.ht} @@ -5849,7 +14582,52 @@ For example: \spadpaste{differentiate(sin(x) * tan(y)/(x**2 + y**2),x)} \spadpaste{differentiate(sin(x) * tan(y)/(x**2 + y**2),y)} \endscroll -\autobuttons\end{page} +\autobuttons +\end{page} + +\begin{patch}{ExDiffSeveralVariablesPatch1} +\begin{paste}{ExDiffSeveralVariablesFull1}{ExDiffSeveralVariablesEmpty1} +\pastebutton{ExDiffSeveralVariablesFull1}{\hidepaste} +\tab{5}\spadcommand{differentiate(sin(x) * tan(y)/(x**2 + y**2),x)} +\indentrel{3}\begin{verbatim} + 2 2 + (- 2x sin(x) + (y + x )cos(x))tan(y) + (1) ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ + 4 2 2 4 + y + 2x y + x + Type: Expression Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ExDiffSeveralVariablesEmpty1} +\begin{paste}{ExDiffSeveralVariablesEmpty1}{ExDiffSeveralVariablesPatch1} +\pastebutton{ExDiffSeveralVariablesEmpty1}{\showpaste} +\tab{5}\spadcommand{differentiate(sin(x) * tan(y)/(x**2 + y**2),x)} +\end{paste}\end{patch} + +\begin{patch}{ExDiffSeveralVariablesPatch2} +\begin{paste}{ExDiffSeveralVariablesFull2}{ExDiffSeveralVariablesEmpty2} +\pastebutton{ExDiffSeveralVariablesFull2}{\hidepaste} +\tab{5}\spadcommand{differentiate(sin(x) * tan(y)/(x**2 + y**2),y)} +\indentrel{3}\begin{verbatim} + (2) + 2 2 2 + (y + x )sin(x)tan(y) - 2y sin(x)tan(y) + + + 2 2 + (y + x )sin(x) + / + 4 2 2 4 + y + 2x y + x + Type: Expression Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ExDiffSeveralVariablesEmpty2} +\begin{paste}{ExDiffSeveralVariablesEmpty2}{ExDiffSeveralVariablesPatch2} +\pastebutton{ExDiffSeveralVariablesEmpty2}{\showpaste} +\tab{5}\spadcommand{differentiate(sin(x) * tan(y)/(x**2 + y**2),y)} +\end{paste}\end{patch} @ \pagehead{ExDiffHigherOrder}{exdiff.ht}{Derivatives of Higher Order} @@ -5862,7 +14640,26 @@ For example, to compute the fourth derivative of {\em exp(x**2)}, issue the following command: \spadpaste{differentiate(exp(x**2),x,4)} \endscroll -\autobuttons\end{page} +\autobuttons +\end{page} + +\begin{patch}{ExDiffHigherOrderPatch1} +\begin{paste}{ExDiffHigherOrderFull1}{ExDiffHigherOrderEmpty1} +\pastebutton{ExDiffHigherOrderFull1}{\hidepaste} +\tab{5}\spadcommand{differentiate(exp(x**2),x,4)} +\indentrel{3}\begin{verbatim} + 2 + 4 2 x + (1) (16x + 48x + 12)%e + Type: Expression Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ExDiffHigherOrderEmpty1} +\begin{paste}{ExDiffHigherOrderEmpty1}{ExDiffHigherOrderPatch1} +\pastebutton{ExDiffHigherOrderEmpty1}{\showpaste} +\tab{5}\spadcommand{differentiate(exp(x**2),x,4)} +\end{paste}\end{patch} @ \pagehead{ExDiffMultipleI}{exdiff.ht}{Multiple Derivatives I} @@ -5882,7 +14679,49 @@ For example, the following command differentiates the same function with respect to {\em x} and then twice with respect to {\em y}. \spadpaste{differentiate(sin(x)/(x**2 + y**2),[x,y,y])} \endscroll -\autobuttons\end{page} +\autobuttons +\end{page} + +\begin{patch}{ExDiffMultipleIPatch1} +\begin{paste}{ExDiffMultipleIFull1}{ExDiffMultipleIEmpty1} +\pastebutton{ExDiffMultipleIFull1}{\hidepaste} +\tab{5}\spadcommand{differentiate(sin(x)/(x**2 + y**2),[x,y])} +\indentrel{3}\begin{verbatim} + 3 2 + 8x y sin(x) + (- 2y - 2x y)cos(x) + (1) ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ + 6 2 4 4 2 6 + y + 3x y + 3x y + x + Type: Expression Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ExDiffMultipleIEmpty1} +\begin{paste}{ExDiffMultipleIEmpty1}{ExDiffMultipleIPatch1} +\pastebutton{ExDiffMultipleIEmpty1}{\showpaste} +\tab{5}\spadcommand{differentiate(sin(x)/(x**2 + y**2),[x,y])} +\end{paste}\end{patch} + +\begin{patch}{ExDiffMultipleIPatch2} +\begin{paste}{ExDiffMultipleIFull2}{ExDiffMultipleIEmpty2} +\pastebutton{ExDiffMultipleIFull2}{\hidepaste} +\tab{5}\spadcommand{differentiate(sin(x)/(x**2 + y**2),[x,y,y])} +\indentrel{3}\begin{verbatim} + (2) + 2 3 4 2 2 4 + (- 40x y + 8x )sin(x) + (6y + 4x y - 2x )cos(x) + ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ + 8 2 6 4 4 6 2 8 + y + 4x y + 6x y + 4x y + x + Type: Expression Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ExDiffMultipleIEmpty2} +\begin{paste}{ExDiffMultipleIEmpty2}{ExDiffMultipleIPatch2} +\pastebutton{ExDiffMultipleIEmpty2}{\showpaste} +\tab{5}\spadcommand{differentiate(sin(x)/(x**2 + y**2),[x,y,y])} +\end{paste}\end{patch} @ \pagehead{ExDiffMultipleII}{exdiff.ht}{Multiple Derivatives II} @@ -5897,7 +14736,28 @@ then three times with respect to {\em z}, issue the following command: \spadpaste{differentiate(cos(z)/(x**2 + y**3),[x,y,z],[1,2,3])} \endscroll -\autobuttons\end{page} +\autobuttons +\end{page} + +\begin{patch}{ExDiffMultipleIIPatch1} +\begin{paste}{ExDiffMultipleIIFull1}{ExDiffMultipleIIEmpty1} +\pastebutton{ExDiffMultipleIIFull1}{\hidepaste} +\tab{5}\spadcommand{differentiate(cos(z)/(x**2 + y**3),[x,y,z],[1,2,3])} +\indentrel{3}\begin{verbatim} + 4 3 + (- 84x y + 24x y)sin(z) + (1) ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ + 12 2 9 4 6 6 3 8 + y + 4x y + 6x y + 4x y + x + Type: Expression Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ExDiffMultipleIIEmpty1} +\begin{paste}{ExDiffMultipleIIEmpty1}{ExDiffMultipleIIPatch1} +\pastebutton{ExDiffMultipleIIEmpty1}{\showpaste} +\tab{5}\spadcommand{differentiate(cos(z)/(x**2 + y**3),[x,y,z],[1,2,3])} +\end{paste}\end{patch} @ \pagehead{ExDiffFormalIntegral}{exdiff.ht} @@ -5915,7 +14775,64 @@ combination with other functions: \spadpaste{differentiate(f,t) \free{f}} \spadpaste{differentiate(f * t**2,t) \free{f}} \endscroll -\autobuttons\end{page} +\autobuttons +\end{page} + +\begin{patch}{ExDiffFormalIntegralPatch1} +\begin{paste}{ExDiffFormalIntegralFull1}{ExDiffFormalIntegralEmpty1} +\pastebutton{ExDiffFormalIntegralFull1}{\hidepaste} +\tab{5}\spadcommand{f := integrate(sqrt(1 + t**3),t)\bound{f }} +\indentrel{3}\begin{verbatim} + t ÚÄÄÄÄÄÄÄ¿ + Ú¿ ³ 3 + (1) ³ \³%N + 1 d%N + ÀÙ + Type: Union(Expression Integer,...) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ExDiffFormalIntegralEmpty1} +\begin{paste}{ExDiffFormalIntegralEmpty1}{ExDiffFormalIntegralPatch1} +\pastebutton{ExDiffFormalIntegralEmpty1}{\showpaste} +\tab{5}\spadcommand{f := integrate(sqrt(1 + t**3),t)\bound{f }} +\end{paste}\end{patch} + +\begin{patch}{ExDiffFormalIntegralPatch2} +\begin{paste}{ExDiffFormalIntegralFull2}{ExDiffFormalIntegralEmpty2} +\pastebutton{ExDiffFormalIntegralFull2}{\hidepaste} +\tab{5}\spadcommand{differentiate(f,t)\free{f }} +\indentrel{3}\begin{verbatim} + ÚÄÄÄÄÄÄ¿ + ³ 3 + (2) \³t + 1 + Type: Expression Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ExDiffFormalIntegralEmpty2} +\begin{paste}{ExDiffFormalIntegralEmpty2}{ExDiffFormalIntegralPatch2} +\pastebutton{ExDiffFormalIntegralEmpty2}{\showpaste} +\tab{5}\spadcommand{differentiate(f,t)\free{f }} +\end{paste}\end{patch} + +\begin{patch}{ExDiffFormalIntegralPatch3} +\begin{paste}{ExDiffFormalIntegralFull3}{ExDiffFormalIntegralEmpty3} +\pastebutton{ExDiffFormalIntegralFull3}{\hidepaste} +\tab{5}\spadcommand{differentiate(f * t**2,t)\free{f }} +\indentrel{3}\begin{verbatim} + t ÚÄÄÄÄÄÄÄ¿ ÚÄÄÄÄÄÄ¿ + Ú¿ ³ 3 2 ³ 3 + (3) 2t ³ \³%N + 1 d%N + t \³t + 1 + ÀÙ + Type: Expression Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ExDiffFormalIntegralEmpty3} +\begin{paste}{ExDiffFormalIntegralEmpty3}{ExDiffFormalIntegralPatch3} +\pastebutton{ExDiffFormalIntegralEmpty3}{\showpaste} +\tab{5}\spadcommand{differentiate(f * t**2,t)\free{f }} +\end{paste}\end{patch} @ \pagehead{ExitXmpPage}{exit.ht}{Exit} @@ -5979,6 +14896,112 @@ See \downlink{``User-Defined Functions, Macros and Rules''} \autobuttons \end{page} +\begin{patch}{ExitXmpPagePatch1} +\begin{paste}{ExitXmpPageFull1}{ExitXmpPageEmpty1} +\pastebutton{ExitXmpPageFull1}{\hidepaste} +\tab{5}\spadcommand{n := 0\bound{n }} +\indentrel{3}\begin{verbatim} + (1) 0 + Type: NonNegativeInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ExitXmpPageEmpty1} +\begin{paste}{ExitXmpPageEmpty1}{ExitXmpPagePatch1} +\pastebutton{ExitXmpPageEmpty1}{\showpaste} +\tab{5}\spadcommand{n := 0\bound{n }} +\end{paste}\end{patch} + +\begin{patch}{ExitXmpPagePatch2} +\begin{paste}{ExitXmpPageFull2}{ExitXmpPageEmpty2} +\pastebutton{ExitXmpPageFull2}{\hidepaste} +\tab{5}\spadcommand{gasp(): Exit == + free n + n := n + 1 + error "Oh no!" +\bound{gasp }\free{n }} +\indentrel{3}\begin{verbatim} + Type: Void +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ExitXmpPageEmpty2} +\begin{paste}{ExitXmpPageEmpty2}{ExitXmpPagePatch2} +\pastebutton{ExitXmpPageEmpty2}{\showpaste} +\tab{5}\spadcommand{gasp(): Exit == + free n + n := n + 1 + error "Oh no!" +\bound{gasp }\free{n }} +\end{paste}\end{patch} + +\begin{patch}{ExitXmpPagePatch3} +\begin{paste}{ExitXmpPageFull3}{ExitXmpPageEmpty3} +\pastebutton{ExitXmpPageFull3}{\hidepaste} +\tab{5}\spadcommand{half(k) == + if odd? k then gasp() + else k quo 2 +\bound{half }\free{gasp }} +\indentrel{3}\begin{verbatim} + Type: Void +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ExitXmpPageEmpty3} +\begin{paste}{ExitXmpPageEmpty3}{ExitXmpPagePatch3} +\pastebutton{ExitXmpPageEmpty3}{\showpaste} +\tab{5}\spadcommand{half(k) == + if odd? k then gasp() + else k quo 2 +\bound{half }\free{gasp }} +\end{paste}\end{patch} + +\begin{patch}{ExitXmpPagePatch4} +\begin{paste}{ExitXmpPageFull4}{ExitXmpPageEmpty4} +\pastebutton{ExitXmpPageFull4}{\hidepaste} +\tab{5}\spadcommand{half 4\free{half }\bound{app1 }} +\indentrel{3}\begin{verbatim} + (4) 2 + Type: PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ExitXmpPageEmpty4} +\begin{paste}{ExitXmpPageEmpty4}{ExitXmpPagePatch4} +\pastebutton{ExitXmpPageEmpty4}{\showpaste} +\tab{5}\spadcommand{half 4\free{half }\bound{app1 }} +\end{paste}\end{patch} + +\begin{patch}{ExitXmpPagePatch5} +\begin{paste}{ExitXmpPageFull5}{ExitXmpPageEmpty5} +\pastebutton{ExitXmpPageFull5}{\hidepaste} +\tab{5}\spadcommand{half 3\free{half app1 }\bound{app2 }} +\indentrel{3}\begin{verbatim} +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ExitXmpPageEmpty5} +\begin{paste}{ExitXmpPageEmpty5}{ExitXmpPagePatch5} +\pastebutton{ExitXmpPageEmpty5}{\showpaste} +\tab{5}\spadcommand{half 3\free{half app1 }\bound{app2 }} +\end{paste}\end{patch} + +\begin{patch}{ExitXmpPagePatch6} +\begin{paste}{ExitXmpPageFull6}{ExitXmpPageEmpty6} +\pastebutton{ExitXmpPageFull6}{\hidepaste} +\tab{5}\spadcommand{n\free{app2 }} +\indentrel{3}\begin{verbatim} + (5) 1 + Type: NonNegativeInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ExitXmpPageEmpty6} +\begin{paste}{ExitXmpPageEmpty6}{ExitXmpPagePatch6} +\pastebutton{ExitXmpPageEmpty6}{\showpaste} +\tab{5}\spadcommand{n\free{app2 }} +\end{paste}\end{patch} + @ \section{exlap.ht} \pagehead{ExLapSimplePole}{exlap.ht}{Laplace transform with a single pole} @@ -5992,6 +15015,25 @@ answer. \endscroll \autobuttons\end{page} +\begin{patch}{ExLapSimplePolePatch1} +\begin{paste}{ExLapSimplePoleFull1}{ExLapSimplePoleEmpty1} +\pastebutton{ExLapSimplePoleFull1}{\hidepaste} +\tab{5}\spadcommand{laplace(t**4 * exp(-a*t) / factorial(4), t, s)} +\indentrel{3}\begin{verbatim} + 1 + (1) ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ + 5 4 2 3 3 2 4 5 + s + 5a s + 10a s + 10a s + 5a s + a + Type: Expression Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ExLapSimplePoleEmpty1} +\begin{paste}{ExLapSimplePoleEmpty1}{ExLapSimplePolePatch1} +\pastebutton{ExLapSimplePoleEmpty1}{\showpaste} +\tab{5}\spadcommand{laplace(t**4 * exp(-a*t) / factorial(4), t, s)} +\end{paste}\end{patch} + @ \pagehead{ExLapTrigTrigh}{exlap.ht} {Laplace transform of a trigonometric function} @@ -6005,6 +15047,26 @@ logarithms. \endscroll \autobuttons\end{page} +\begin{patch}{ExLapTrigTrighPatch1} +\begin{paste}{ExLapTrigTrighFull1}{ExLapTrigTrighEmpty1} +\pastebutton{ExLapTrigTrighFull1}{\hidepaste} +\tab{5}\spadcommand{laplace(sin(a*t) * cosh(a*t) - cos(a*t) * sinh(a*t), t, s)} +\indentrel{3}\begin{verbatim} + 3 + 4a + (1) ÄÄÄÄÄÄÄÄ + 4 4 + s + 4a + Type: Expression Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ExLapTrigTrighEmpty1} +\begin{paste}{ExLapTrigTrighEmpty1}{ExLapTrigTrighPatch1} +\pastebutton{ExLapTrigTrighEmpty1}{\showpaste} +\tab{5}\spadcommand{laplace(sin(a*t) * cosh(a*t) - cos(a*t) * sinh(a*t), t, s)} +\end{paste}\end{patch} + @ \pagehead{ExLapDefInt}{exlap.ht} {Laplace transform requiring a definite integration} @@ -6018,7 +15080,25 @@ transform between a symbol and infinity. We use the full power of Axiom's integrator in such cases. \spadpaste{laplace(2/t * (1 - cos(a*t)), t, s)} \endscroll -\autobuttons\end{page} +\autobuttons +\end{page} + +\begin{patch}{ExLapDefIntPatch1} +\begin{paste}{ExLapDefIntFull1}{ExLapDefIntEmpty1} +\pastebutton{ExLapDefIntFull1}{\hidepaste} +\tab{5}\spadcommand{laplace(2/t * (1 - cos(a*t)), t, s)} +\indentrel{3}\begin{verbatim} + 2 2 + (1) log(s + a ) - 2log(s) + Type: Expression Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ExLapDefIntEmpty1} +\begin{paste}{ExLapDefIntEmpty1}{ExLapDefIntPatch1} +\pastebutton{ExLapDefIntEmpty1}{\showpaste} +\tab{5}\spadcommand{laplace(2/t * (1 - cos(a*t)), t, s)} +\end{paste}\end{patch} @ \pagehead{ExLapExpExp}{exlap.ht}{Laplace transform of exponentials} @@ -6029,7 +15109,24 @@ This is another example where it is necessary to integrate the result of another laplace transform. \spadpaste{laplace((exp(a*t) - exp(b*t))/t, t, s)} \endscroll -\autobuttons\end{page} +\autobuttons +\end{page} + +\begin{patch}{ExLapExpExpPatch1} +\begin{paste}{ExLapExpExpFull1}{ExLapExpExpEmpty1} +\pastebutton{ExLapExpExpFull1}{\hidepaste} +\tab{5}\spadcommand{laplace((exp(a*t) - exp(b*t))/t, t, s)} +\indentrel{3}\begin{verbatim} + (1) - log(s - a) + log(s - b) + Type: Expression Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ExLapExpExpEmpty1} +\begin{paste}{ExLapExpExpEmpty1}{ExLapExpExpPatch1} +\pastebutton{ExLapExpExpEmpty1}{\showpaste} +\tab{5}\spadcommand{laplace((exp(a*t) - exp(b*t))/t, t, s)} +\end{paste}\end{patch} @ \pagehead{ExLapSpecial1}{exlap.ht} @@ -6042,7 +15139,50 @@ linear exponential integrals among them. \beginscroll \spadpaste{laplace(exp(a*t+b)*Ei(c*t), t, s)} \endscroll -\autobuttons\end{page} +\autobuttons +\end{page} + +\begin{patch}{ExLapSpecial1Patch1} +\begin{paste}{ExLapSpecial1Full1}{ExLapSpecial1Empty1} +\pastebutton{ExLapSpecial1Full1}{\hidepaste} +\tab{5}\spadcommand{laplace(exp(a*t+b)*Ei(c*t), t, s)} +\indentrel{3}\begin{verbatim} + b s + c - a + %e log(ÄÄÄÄÄÄÄÄÄ) + c + (1) ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ + s - a + Type: Expression Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ExLapSpecial1Empty1} +\begin{paste}{ExLapSpecial1Empty1}{ExLapSpecial1Patch1} +\pastebutton{ExLapSpecial1Empty1}{\showpaste} +\tab{5}\spadcommand{laplace(exp(a*t+b)*Ei(c*t), t, s)} +\end{paste}\end{patch} + +\begin{patch}{ExLapSpecial2Patch1} +\begin{paste}{ExLapSpecial2Full1}{ExLapSpecial2Empty1} +\pastebutton{ExLapSpecial2Full1}{\hidepaste} +\tab{5}\spadcommand{laplace(a*Ci(b*t) + c*Si(d*t), t, s)} +\indentrel{3}\begin{verbatim} + 2 2 + s + b d + a log(ÄÄÄÄÄÄÄ) + 2c atan(Ä) + 2 s + b + (1) ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ + 2s + Type: Expression Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ExLapSpecial2Empty1} +\begin{paste}{ExLapSpecial2Empty1}{ExLapSpecial2Patch1} +\pastebutton{ExLapSpecial2Empty1}{\showpaste} +\tab{5}\spadcommand{laplace(a*Ci(b*t) + c*Si(d*t), t, s)} +\end{paste}\end{patch} @ \pagehead{ExLapSpecial2}{exlap.ht}{Laplace transform of special functions} @@ -6080,7 +15220,96 @@ algebraic number from the expression and displays its defining polynomial. \spadpaste{definingPolynomial(tower(\%).2::EXPR INT) \free{i}} \endscroll -\autobuttons\end{page} +\autobuttons +\end{page} + +\begin{patch}{ExIntRationalFunctionPatch1} +\begin{paste}{ExIntRationalFunctionFull1}{ExIntRationalFunctionEmpty1} +\pastebutton{ExIntRationalFunctionFull1}{\hidepaste} +\tab{5}\spadcommand{integrate((x**2+2*x+1)/((x+1)**6+1),x)} +\indentrel{3}\begin{verbatim} + 3 2 + atan(x + 3x + 3x + 1) + (1) ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ + 3 + Type: Union(Expression Integer,...) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ExIntRationalFunctionEmpty1} +\begin{paste}{ExIntRationalFunctionEmpty1}{ExIntRationalFunctionPatch1} +\pastebutton{ExIntRationalFunctionEmpty1}{\showpaste} +\tab{5}\spadcommand{integrate((x**2+2*x+1)/((x+1)**6+1),x)} +\end{paste}\end{patch} + +\begin{patch}{ExIntRationalFunctionPatch2} +\begin{paste}{ExIntRationalFunctionFull2}{ExIntRationalFunctionEmpty2} +\pastebutton{ExIntRationalFunctionFull2}{\hidepaste} +\tab{5}\spadcommand{integrate(1/(x**3+x+1),x)\bound{i }} +\indentrel{3}\begin{verbatim} + (2) + ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿ + ³ 2 + ³- 93%%H0 + 12 + ( ³ÄÄÄÄÄÄÄÄÄÄÄÄÄÄ - %%H0) + \³ 31 + * + log + ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿ + ³ 2 + ³- 93%%H0 + 12 2 + (62%%H0 + 31) ³ÄÄÄÄÄÄÄÄÄÄÄÄÄÄ + 62%%H0 + \³ 31 + + + - 31%%H0 + 18x - 4 + + + ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿ + ³ 2 + ³- 93%%H0 + 12 + (- ³ÄÄÄÄÄÄÄÄÄÄÄÄÄÄ - %%H0) + \³ 31 + * + log + ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿ + ³ 2 + ³- 93%%H0 + 12 2 + (- 62%%H0 - 31) ³ÄÄÄÄÄÄÄÄÄÄÄÄÄÄ + 62%%H0 + \³ 31 + + + - 31%%H0 + 18x - 4 + + + 2 + 2%%H0 log(- 62%%H0 + 31%%H0 + 9x + 4) + / + 2 + Type: Union(Expression Integer,...) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ExIntRationalFunctionEmpty2} +\begin{paste}{ExIntRationalFunctionEmpty2}{ExIntRationalFunctionPatch2} +\pastebutton{ExIntRationalFunctionEmpty2}{\showpaste} +\tab{5}\spadcommand{integrate(1/(x**3+x+1),x)\bound{i }} +\end{paste}\end{patch} + +\begin{patch}{ExIntRationalFunctionPatch3} +\begin{paste}{ExIntRationalFunctionFull3}{ExIntRationalFunctionEmpty3} +\pastebutton{ExIntRationalFunctionFull3}{\hidepaste} +\tab{5}\spadcommand{definingPolynomial(tower(\%).2::EXPR INT)\free{i }} +\indentrel{3}\begin{verbatim} + 3 + 31%%H0 - 3%%H0 - 1 + (3) ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ + 31 + Type: Expression Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ExIntRationalFunctionEmpty3} +\begin{paste}{ExIntRationalFunctionEmpty3}{ExIntRationalFunctionPatch3} +\pastebutton{ExIntRationalFunctionEmpty3}{\showpaste} +\tab{5}\spadcommand{definingPolynomial(tower(\%).2::EXPR INT)\free{i }} +\end{paste}\end{patch} @ \pagehead{ExIntRationalWithRealParameter}{exint.ht} @@ -6095,7 +15324,31 @@ sign assumptions, Axiom returns all possible answers. \spadpaste{integrate(1/(x**2 + a),x)} The integrate command generally assumes that all parameters are real. \endscroll -\autobuttons\end{page} +\autobuttons +\end{page} + +\begin{patch}{ExIntRationalWithRealParameterPatch1} +\begin{paste}{ExIntRationalWithRealParameterFull1}{ExIntRationalWithRealParameterEmpty1} +\pastebutton{ExIntRationalWithRealParameterFull1}{\hidepaste} +\tab{5}\spadcommand{integrate(1/(x**2 + a),x)} +\indentrel{3}\begin{verbatim} + 2 ÚÄÄÄ¿ + (x - a)\³- a + 2a x ÚÄ¿ + log(ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ) x\³a + 2 atan(ÄÄÄÄÄ) + x + a a + (1) [ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ,ÄÄÄÄÄÄÄÄÄÄÄ] + ÚÄÄÄ¿ ÚÄ¿ + 2\³- a \³a + Type: Union(List Expression Integer,...) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ExIntRationalWithRealParameterEmpty1} +\begin{paste}{ExIntRationalWithRealParameterEmpty1}{ExIntRationalWithRealParameterPatch1} +\pastebutton{ExIntRationalWithRealParameterEmpty1}{\showpaste} +\tab{5}\spadcommand{integrate(1/(x**2 + a),x)} +\end{paste}\end{patch} @ \pagehead{ExIntRationalWithComplexParameter}{exint.ht} @@ -6110,7 +15363,31 @@ You can request this answer by prepending the word `complex' to the command name: \spadpaste{complexIntegrate(1/(x**2 + a),x)} \endscroll -\autobuttons\end{page} +\autobuttons +\end{page} + +\begin{patch}{ExIntRationalWithComplexParameterPatch1} +\begin{paste}{ExIntRationalWithComplexParameterFull1}{ExIntRationalWithComplexParameterEmpty1} +\pastebutton{ExIntRationalWithComplexParameterFull1}{\hidepaste} +\tab{5}\spadcommand{complexIntegrate(1/(x**2 + a),x)} +\indentrel{3}\begin{verbatim} + ÚÄÄÄ¿ ÚÄÄÄ¿ + x\³- a + a x\³- a - a + log(ÄÄÄÄÄÄÄÄÄÄÄ) - log(ÄÄÄÄÄÄÄÄÄÄÄ) + ÚÄÄÄ¿ ÚÄÄÄ¿ + \³- a \³- a + (1) ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ + ÚÄÄÄ¿ + 2\³- a + Type: Expression Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ExIntRationalWithComplexParameterEmpty1} +\begin{paste}{ExIntRationalWithComplexParameterEmpty1}{ExIntRationalWithComplexParameterPatch1} +\pastebutton{ExIntRationalWithComplexParameterEmpty1}{\showpaste} +\tab{5}\spadcommand{complexIntegrate(1/(x**2 + a),x)} +\end{paste}\end{patch} @ \pagehead{ExIntTwoSimilarIntegrands}{exint.ht} @@ -6130,7 +15407,65 @@ is guaranteed to find what new constants must be added in order to find a solution: \spadpaste{integrate(1 / (x**3 * (a+b*x)**(1/3)),x)} \endscroll -\autobuttons\end{page} +\autobuttons +\end{page} + +\begin{patch}{ExIntTwoSimilarIntegrandsPatch1} +\begin{paste}{ExIntTwoSimilarIntegrandsFull1}{ExIntTwoSimilarIntegrandsEmpty1} +\pastebutton{ExIntTwoSimilarIntegrandsFull1}{\hidepaste} +\tab{5}\spadcommand{integrate(x**3 / (a+b*x)**(1/3),x)} +\indentrel{3}\begin{verbatim} + (1) + 3 3 2 2 2 3 3ÚÄÄÄÄÄÄÄ¿2 + (120b x - 135a b x + 162a b x - 243a )\³b x + a + ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ + 4 + 440b + Type: Union(Expression Integer,...) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ExIntTwoSimilarIntegrandsEmpty1} +\begin{paste}{ExIntTwoSimilarIntegrandsEmpty1}{ExIntTwoSimilarIntegrandsPatch1} +\pastebutton{ExIntTwoSimilarIntegrandsEmpty1}{\showpaste} +\tab{5}\spadcommand{integrate(x**3 / (a+b*x)**(1/3),x)} +\end{paste}\end{patch} + +\begin{patch}{ExIntTwoSimilarIntegrandsPatch2} +\begin{paste}{ExIntTwoSimilarIntegrandsFull2}{ExIntTwoSimilarIntegrandsEmpty2} +\pastebutton{ExIntTwoSimilarIntegrandsFull2}{\hidepaste} +\tab{5}\spadcommand{integrate(1 / (x**3 * (a+b*x)**(1/3)),x)} +\indentrel{3}\begin{verbatim} + (2) + - + 2 2 ÚÄ¿ + 2b x \³3 + * + 3ÚÄ¿3ÚÄÄÄÄÄÄÄ¿2 3ÚÄ¿2 3ÚÄÄÄÄÄÄÄ¿ + log(\³a \³b x + a + \³a \³b x + a + a) + + + 2 2 ÚÄ¿ 3ÚÄ¿2 3ÚÄÄÄÄÄÄÄ¿ + 4b x \³3 log(\³a \³b x + a - a) + + + ÚÄ¿3ÚÄ¿2 3ÚÄÄÄÄÄÄÄ¿ ÚÄ¿ + 2 2 2\³3 \³a \³b x + a + a\³3 + 12b x atan(ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ) + 3a + + + ÚÄ¿3ÚÄ¿3ÚÄÄÄÄÄÄÄ¿2 + (12b x - 9a)\³3 \³a \³b x + a + / + 2 2 ÚÄ¿3ÚÄ¿ + 18a x \³3 \³a + Type: Union(Expression Integer,...) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ExIntTwoSimilarIntegrandsEmpty2} +\begin{paste}{ExIntTwoSimilarIntegrandsEmpty2}{ExIntTwoSimilarIntegrandsPatch2} +\pastebutton{ExIntTwoSimilarIntegrandsEmpty2}{\showpaste} +\tab{5}\spadcommand{integrate(1 / (x**3 * (a+b*x)**(1/3)),x)} +\end{paste}\end{patch} @ \pagehead{ExIntNoSolution}{exint.ht}{An Integral Which Does Not Exist} @@ -6147,7 +15482,27 @@ When Axiom returns an integral sign, it has proved that no answer exists as an elementary function. \spadpaste{integrate(log(1 + sqrt(a*x + b)) / x,x)} \endscroll -\autobuttons\end{page} +\autobuttons +\end{page} + +\begin{patch}{ExIntNoSolutionPatch1} +\begin{paste}{ExIntNoSolutionFull1}{ExIntNoSolutionEmpty1} +\pastebutton{ExIntNoSolutionFull1}{\hidepaste} +\tab{5}\spadcommand{integrate(log(1 + sqrt(a*x + b)) / x,x)} +\indentrel{3}\begin{verbatim} + x ÚÄÄÄÄÄÄÄÄ¿ + Ú¿ log(\³b + %T a + 1) + (1) ³ ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ d%T + ÀÙ %T + Type: Union(Expression Integer,...) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ExIntNoSolutionEmpty1} +\begin{paste}{ExIntNoSolutionEmpty1}{ExIntNoSolutionPatch1} +\pastebutton{ExIntNoSolutionEmpty1}{\showpaste} +\tab{5}\spadcommand{integrate(log(1 + sqrt(a*x + b)) / x,x)} +\end{paste}\end{patch} @ \begin{verbatim} @@ -6175,7 +15530,33 @@ find in tables: Whenever possible, Axiom tries to express the answer using the functions present in the integrand. \endscroll -\autobuttons\end{page} +\autobuttons +\end{page} + +\begin{patch}{ExIntTrigPatch1} +\begin{paste}{ExIntTrigFull1}{ExIntTrigEmpty1} +\pastebutton{ExIntTrigFull1}{\hidepaste} +\tab{5}\spadcommand{integrate((sinh(1+sqrt(x+b))+2*sqrt(x+b))/(sqrt(x+b)*(x+cosh(1+sqrt(x+b)))),x)} +\indentrel{3}\begin{verbatim} + (1) + ÚÄÄÄÄÄ¿ + - 2cosh(\³x + b + 1) - 2x + 2log(ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ) + ÚÄÄÄÄÄ¿ ÚÄÄÄÄÄ¿ + sinh(\³x + b + 1) - cosh(\³x + b + 1) + + + ÚÄÄÄÄÄ¿ + - 2\³x + b + Type: Union(Expression Integer,...) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ExIntTrigEmpty1} +\begin{paste}{ExIntTrigEmpty1}{ExIntTrigPatch1} +\pastebutton{ExIntTrigEmpty1}{\showpaste} +\tab{5}\spadcommand{integrate((sinh(1+sqrt(x+b))+2*sqrt(x+b))/(sqrt(x+b)*(x+cosh(1+sqrt(x+b)))),x)} +\end{paste} +\end{patch} @ \pagehead{ExIntAlgebraicRelation}{exint.ht} @@ -6192,7 +15573,33 @@ The discovery of this algebraic relationship is necessary for correctly integrating this function. \downlink{Details.}{ExIntAlgebraicRelationExplain} \space{1} \endscroll -\autobuttons\end{page} +\autobuttons +\end{page} + +\begin{patch}{ExIntAlgebraicRelationPatch1} +\begin{paste}{ExIntAlgebraicRelationFull1}{ExIntAlgebraicRelationEmpty1} +\pastebutton{ExIntAlgebraicRelationFull1}{\hidepaste} +\tab{5}\spadcommand{integrate(tan(atan(x)/3),x)} +\indentrel{3}\begin{verbatim} + (1) + atan(x) 2 atan(x) 2 + 8log(3tan(ÄÄÄÄÄÄÄ) - 1) - 3tan(ÄÄÄÄÄÄÄ) + 3 3 + + + atan(x) + 18x tan(ÄÄÄÄÄÄÄ) + 3 + / + 18 + Type: Union(Expression Integer,...) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ExIntAlgebraicRelationEmpty1} +\begin{paste}{ExIntAlgebraicRelationEmpty1}{ExIntAlgebraicRelationPatch1} +\pastebutton{ExIntAlgebraicRelationEmpty1}{\showpaste} +\tab{5}\spadcommand{integrate(tan(atan(x)/3),x)} +\end{paste}\end{patch} @ \pagehead{ExIntAlgebraicRelationExplain}{exint.ht} @@ -6234,7 +15641,27 @@ This is an example of a mixed function where the algebraic layer is over the transcendental one. \spadpaste{integrate((x + 1) / (x * (x + log x)**(3/2)),x)} \endscroll -\autobuttons\end{page} +\autobuttons +\end{page} + +\begin{patch}{ExIntRadicalOfTranscendentalPatch1} +\begin{paste}{ExIntRadicalOfTranscendentalFull1}{ExIntRadicalOfTranscendentalEmpty1} +\pastebutton{ExIntRadicalOfTranscendentalFull1}{\hidepaste} +\tab{5}\spadcommand{integrate((x + 1) / (x * (x + log x)**(3/2)),x)} +\indentrel{3}\begin{verbatim} + ÚÄÄÄÄÄÄÄÄÄÄ¿ + 2\³log(x) + x + (1) - ÄÄÄÄÄÄÄÄÄÄÄÄÄÄ + log(x) + x + Type: Union(Expression Integer,...) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ExIntRadicalOfTranscendentalEmpty1} +\begin{paste}{ExIntRadicalOfTranscendentalEmpty1}{ExIntRadicalOfTranscendentalPatch1} +\pastebutton{ExIntRadicalOfTranscendentalEmpty1}{\showpaste} +\tab{5}\spadcommand{integrate((x + 1) / (x * (x + log x)**(3/2)),x)} +\end{paste}\end{patch} @ \pagehead{ExIntNonElementary}{exint.ht} @@ -6247,7 +15674,28 @@ handle some of them: \spadpaste{integrate(exp(-x**2) * erf(x) / (erf(x)**3 - erf(x)**2 - erf(x) + 1),x)} \endscroll -\autobuttons\end{page} +\autobuttons +\end{page} + +\begin{patch}{ExIntNonElementaryPatch1} +\begin{paste}{ExIntNonElementaryFull1}{ExIntNonElementaryEmpty1} +\pastebutton{ExIntNonElementaryFull1}{\hidepaste} +\tab{5}\spadcommand{integrate(exp(-x**2) * erf(x) / (erf(x)**3 - erf(x)**2 - erf(x) + 1),x)} +\indentrel{3}\begin{verbatim} + ÚÄÄÄ¿ erf(x) - 1 ÚÄÄÄ¿ + (erf(x) - 1)\³%pi log(ÄÄÄÄÄÄÄÄÄÄ) - 2\³%pi + erf(x) + 1 + (1) ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ + 8erf(x) - 8 + Type: Union(Expression Integer,...) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ExIntNonElementaryEmpty1} +\begin{paste}{ExIntNonElementaryEmpty1}{ExIntNonElementaryPatch1} +\pastebutton{ExIntNonElementaryEmpty1}{\showpaste} +\tab{5}\spadcommand{integrate(exp(-x**2) * erf(x) / (erf(x)**3 - erf(x)**2 - erf(x) + 1),x)} +\end{paste}\end{patch} @ \section{exlimit.ht} @@ -6270,7 +15718,26 @@ the left is different from the limit from the right. wish to ask for a one-sided limit. \downlink{How. }{ExLimitOneSided} \endscroll -\autobuttons\end{page} +\autobuttons +\end{page} + +\begin{patch}{ExLimitBasicPatch1} +\begin{paste}{ExLimitBasicFull1}{ExLimitBasicEmpty1} +\pastebutton{ExLimitBasicFull1}{\hidepaste} +\tab{5}\spadcommand{limit((x**2 - 3*x + 2)/(x**2 - 1),x = 1)} +\indentrel{3}\begin{verbatim} + 1 + (1) - Ä + 2 +Type: Union(OrderedCompletion Fraction Polynomial Integer,...) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ExLimitBasicEmpty1} +\begin{paste}{ExLimitBasicEmpty1}{ExLimitBasicPatch1} +\pastebutton{ExLimitBasicEmpty1}{\showpaste} +\tab{5}\spadcommand{limit((x**2 - 3*x + 2)/(x**2 - 1),x = 1)} +\end{paste}\end{patch} @ \pagehead{ExLimitParameter}{exlimit.ht}{Limits of Functions with Parameters} @@ -6283,7 +15750,26 @@ Here's an example: \spadpaste{limit(sinh(a*x)/tan(b*x),x = 0)} % answer := a/b \endscroll -\autobuttons\end{page} +\autobuttons +\end{page} + +\begin{patch}{ExLimitParameterPatch1} +\begin{paste}{ExLimitParameterFull1}{ExLimitParameterEmpty1} +\pastebutton{ExLimitParameterFull1}{\hidepaste} +\tab{5}\spadcommand{limit(sinh(a*x)/tan(b*x),x = 0)} +\indentrel{3}\begin{verbatim} + a + (1) Ä + b + Type: Union(OrderedCompletion Expression Integer,...) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ExLimitParameterEmpty1} +\begin{paste}{ExLimitParameterEmpty1}{ExLimitParameterPatch1} +\pastebutton{ExLimitParameterEmpty1}{\showpaste} +\tab{5}\spadcommand{limit(sinh(a*x)/tan(b*x),x = 0)} +\end{paste}\end{patch} @ \pagehead{ExLimitOneSided}{exlimit.ht}{One-sided Limits} @@ -6306,7 +15792,40 @@ will indicate when you try to take a two-sided limit: \spadpaste{limit(x * log(x),x = 0)} % answer := [left = "failed",right = 0] \endscroll -\autobuttons\end{page} +\autobuttons +\end{page} + +\begin{patch}{ExLimitOneSidedPatch1} +\begin{paste}{ExLimitOneSidedFull1}{ExLimitOneSidedEmpty1} +\pastebutton{ExLimitOneSidedFull1}{\hidepaste} +\tab{5}\spadcommand{limit(x * log(x),x = 0,"right")} +\indentrel{3}\begin{verbatim} + (1) 0 + Type: Union(OrderedCompletion Expression Integer,...) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ExLimitOneSidedEmpty1} +\begin{paste}{ExLimitOneSidedEmpty1}{ExLimitOneSidedPatch1} +\pastebutton{ExLimitOneSidedEmpty1}{\showpaste} +\tab{5}\spadcommand{limit(x * log(x),x = 0,"right")} +\end{paste}\end{patch} + +\begin{patch}{ExLimitOneSidedPatch2} +\begin{paste}{ExLimitOneSidedFull2}{ExLimitOneSidedEmpty2} +\pastebutton{ExLimitOneSidedFull2}{\hidepaste} +\tab{5}\spadcommand{limit(x * log(x),x = 0)} +\indentrel{3}\begin{verbatim} + (2) [leftHandLimit= "failed",rightHandLimit= 0] +Type: Union(Record(leftHandLimit: Union(OrderedCompletion Expression Integer,"failed"),rightHandLimit: Union(OrderedCompletion Expression Integer,"failed")),...) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ExLimitOneSidedEmpty2} +\begin{paste}{ExLimitOneSidedEmpty2}{ExLimitOneSidedPatch2} +\pastebutton{ExLimitOneSidedEmpty2}{\showpaste} +\tab{5}\spadcommand{limit(x * log(x),x = 0)} +\end{paste}\end{patch} @ \pagehead{ExLimitTwoSided}{exlimit.ht}{Two-sided Limits} @@ -6331,7 +15850,43 @@ Here's another example, this time using a more complicated function: \spadpaste{limit(sqrt(1 - cos(t))/t,t = 0)} % answer := [left = -sqrt(1/2),right = sqrt(1/2)] \endscroll -\autobuttons\end{page} +\autobuttons +\end{page} + +\begin{patch}{ExLimitTwoSidedPatch1} +\begin{paste}{ExLimitTwoSidedFull1}{ExLimitTwoSidedEmpty1} +\pastebutton{ExLimitTwoSidedFull1}{\hidepaste} +\tab{5}\spadcommand{limit(sqrt(y**2)/y,y = 0)} +\indentrel{3}\begin{verbatim} + (1) [leftHandLimit= - 1,rightHandLimit= 1] +Type: Union(Record(leftHandLimit: Union(OrderedCompletion Expression Integer,"failed"),rightHandLimit: Union(OrderedCompletion Expression Integer,"failed")),...) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ExLimitTwoSidedEmpty1} +\begin{paste}{ExLimitTwoSidedEmpty1}{ExLimitTwoSidedPatch1} +\pastebutton{ExLimitTwoSidedEmpty1}{\showpaste} +\tab{5}\spadcommand{limit(sqrt(y**2)/y,y = 0)} +\end{paste}\end{patch} + +\begin{patch}{ExLimitTwoSidedPatch2} +\begin{paste}{ExLimitTwoSidedFull2}{ExLimitTwoSidedEmpty2} +\pastebutton{ExLimitTwoSidedFull2}{\hidepaste} +\tab{5}\spadcommand{limit(sqrt(1 - cos(t))/t,t = 0)} +\indentrel{3}\begin{verbatim} + 1 1 + (2) [leftHandLimit= - ÄÄÄÄ,rightHandLimit= ÄÄÄÄ] + ÚÄ¿ ÚÄ¿ + \³2 \³2 +Type: Union(Record(leftHandLimit: Union(OrderedCompletion Expression Integer,"failed"),rightHandLimit: Union(OrderedCompletion Expression Integer,"failed")),...) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ExLimitTwoSidedEmpty2} +\begin{paste}{ExLimitTwoSidedEmpty2}{ExLimitTwoSidedPatch2} +\pastebutton{ExLimitTwoSidedEmpty2}{\showpaste} +\tab{5}\spadcommand{limit(sqrt(1 - cos(t))/t,t = 0)} +\end{paste}\end{patch} @ \pagehead{ExLimitInfinite}{exlimit.ht}{Limits at Infinity} @@ -6345,7 +15900,46 @@ To do this, use the constants \spad{\%plusInfinity} and \spadpaste{limit(sqrt(3*x**2 + 1)/(5*x),x = \%plusInfinity)} \spadpaste{limit(sqrt(3*x**2 + 1)/(5*x),x = \%minusInfinity)} \endscroll -\autobuttons\end{page} +\autobuttons +\end{page} + +\begin{patch}{ExLimitInfinitePatch1} +\begin{paste}{ExLimitInfiniteFull1}{ExLimitInfiniteEmpty1} +\pastebutton{ExLimitInfiniteFull1}{\hidepaste} +\tab{5}\spadcommand{limit(sqrt(3*x**2 + 1)/(5*x),x = \%plusInfinity)} +\indentrel{3}\begin{verbatim} + ÚÄ¿ + \³3 + (1) ÄÄÄÄ + 5 + Type: Union(OrderedCompletion Expression Integer,...) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ExLimitInfiniteEmpty1} +\begin{paste}{ExLimitInfiniteEmpty1}{ExLimitInfinitePatch1} +\pastebutton{ExLimitInfiniteEmpty1}{\showpaste} +\tab{5}\spadcommand{limit(sqrt(3*x**2 + 1)/(5*x),x = \%plusInfinity)} +\end{paste}\end{patch} + +\begin{patch}{ExLimitInfinitePatch2} +\begin{paste}{ExLimitInfiniteFull2}{ExLimitInfiniteEmpty2} +\pastebutton{ExLimitInfiniteFull2}{\hidepaste} +\tab{5}\spadcommand{limit(sqrt(3*x**2 + 1)/(5*x),x = \%minusInfinity)} +\indentrel{3}\begin{verbatim} + ÚÄ¿ + \³3 + (2) - ÄÄÄÄ + 5 + Type: Union(OrderedCompletion Expression Integer,...) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ExLimitInfiniteEmpty2} +\begin{paste}{ExLimitInfiniteEmpty2}{ExLimitInfinitePatch2} +\pastebutton{ExLimitInfiniteEmpty2}{\showpaste} +\tab{5}\spadcommand{limit(sqrt(3*x**2 + 1)/(5*x),x = \%minusInfinity)} +\end{paste}\end{patch} @ \pagehead{ExLimitRealComplex}{exlimit.ht}{Real Limits vs. Complex Limits} @@ -6367,7 +15961,41 @@ does not approach any limit as \spad{z} tends to \spad{0} in the complex plane. Axiom indicates this when we call the function \spadfun{complexLimit}: \spadpaste{complexLimit(z * sin(1/z),z = 0)} \endscroll -\autobuttons\end{page} +\autobuttons +\end{page} + +\begin{patch}{ExLimitRealComplexPatch1} +\begin{paste}{ExLimitRealComplexFull1}{ExLimitRealComplexEmpty1} +\pastebutton{ExLimitRealComplexFull1}{\hidepaste} +\tab{5}\spadcommand{limit(z * sin(1/z),z = 0)} +\indentrel{3}\begin{verbatim} + (1) 0 + Type: Union(OrderedCompletion Expression Integer,...) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ExLimitRealComplexEmpty1} +\begin{paste}{ExLimitRealComplexEmpty1}{ExLimitRealComplexPatch1} +\pastebutton{ExLimitRealComplexEmpty1}{\showpaste} +\tab{5}\spadcommand{limit(z * sin(1/z),z = 0)} +\end{paste}\end{patch} + +\begin{patch}{ExLimitRealComplexPatch2} +\begin{paste}{ExLimitRealComplexFull2}{ExLimitRealComplexEmpty2} +\pastebutton{ExLimitRealComplexFull2}{\hidepaste} +\tab{5}\spadcommand{complexLimit(z * sin(1/z),z = 0)} +\indentrel{3}\begin{verbatim} + (2) "failed" + Type: Union("failed",...) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ExLimitRealComplexEmpty2} +\begin{paste}{ExLimitRealComplexEmpty2}{ExLimitRealComplexPatch2} +\pastebutton{ExLimitRealComplexEmpty2}{\showpaste} +\tab{5}\spadcommand{complexLimit(z * sin(1/z),z = 0)} +\end{paste} +\end{patch} @ \pagehead{ExLimitComplexInfinite}{exlimit.ht}{Complex Limits at Infinity} @@ -6387,7 +16015,56 @@ For example: \spadpaste{limit(sin(x)/x,x = \%plusInfinity)} \spadpaste{complexLimit(sin(x)/x,x = \%infinity)} \endscroll -\autobuttons\end{page} +\autobuttons +\end{page} + +\begin{patch}{ExLimitComplexInfinitePatch1} +\begin{paste}{ExLimitComplexInfiniteFull1}{ExLimitComplexInfiniteEmpty1} +\pastebutton{ExLimitComplexInfiniteFull1}{\hidepaste} +\tab{5}\spadcommand{complexLimit((2 + z)/(1 - z),z = \%infinity)} +\indentrel{3}\begin{verbatim} + (1) - 1 + Type: OnePointCompletion Fraction Polynomial Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ExLimitComplexInfiniteEmpty1} +\begin{paste}{ExLimitComplexInfiniteEmpty1}{ExLimitComplexInfinitePatch1} +\pastebutton{ExLimitComplexInfiniteEmpty1}{\showpaste} +\tab{5}\spadcommand{complexLimit((2 + z)/(1 - z),z = \%infinity)} +\end{paste}\end{patch} + +\begin{patch}{ExLimitComplexInfinitePatch2} +\begin{paste}{ExLimitComplexInfiniteFull2}{ExLimitComplexInfiniteEmpty2} +\pastebutton{ExLimitComplexInfiniteFull2}{\hidepaste} +\tab{5}\spadcommand{limit(sin(x)/x,x = \%plusInfinity)} +\indentrel{3}\begin{verbatim} + (2) 0 + Type: Union(OrderedCompletion Expression Integer,...) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ExLimitComplexInfiniteEmpty2} +\begin{paste}{ExLimitComplexInfiniteEmpty2}{ExLimitComplexInfinitePatch2} +\pastebutton{ExLimitComplexInfiniteEmpty2}{\showpaste} +\tab{5}\spadcommand{limit(sin(x)/x,x = \%plusInfinity)} +\end{paste}\end{patch} + +\begin{patch}{ExLimitComplexInfinitePatch3} +\begin{paste}{ExLimitComplexInfiniteFull3}{ExLimitComplexInfiniteEmpty3} +\pastebutton{ExLimitComplexInfiniteFull3}{\hidepaste} +\tab{5}\spadcommand{complexLimit(sin(x)/x,x = \%infinity)} +\indentrel{3}\begin{verbatim} + (3) "failed" + Type: Union("failed",...) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ExLimitComplexInfiniteEmpty3} +\begin{paste}{ExLimitComplexInfiniteEmpty3}{ExLimitComplexInfinitePatch3} +\pastebutton{ExLimitComplexInfiniteEmpty3}{\showpaste} +\tab{5}\spadcommand{complexLimit(sin(x)/x,x = \%infinity)} +\end{paste}\end{patch} @ \section{exmatrix.ht} @@ -6415,7 +16092,153 @@ that the matrix and vector have compatible dimensions. However, the dimensions of the matrices must be compatible in order for Axiom to perform an operation - otherwise an error message will occur. \endscroll -\autobuttons\end{page} +\autobuttons +\end{page} + +\begin{patch}{ExMatrixBasicFunctionPatch1} +\begin{paste}{ExMatrixBasicFunctionFull1}{ExMatrixBasicFunctionEmpty1} +\pastebutton{ExMatrixBasicFunctionFull1}{\hidepaste} +\tab{5}\spadcommand{m1 := matrix([[1,-2,1],[4,2,-4]])\bound{m1 }} +\indentrel{3}\begin{verbatim} + Ú1 - 2 1 ¿ + (1) ³ ³ + À4 2 - 4Ù + Type: Matrix Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ExMatrixBasicFunctionEmpty1} +\begin{paste}{ExMatrixBasicFunctionEmpty1}{ExMatrixBasicFunctionPatch1} +\pastebutton{ExMatrixBasicFunctionEmpty1}{\showpaste} +\tab{5}\spadcommand{m1 := matrix([[1,-2,1],[4,2,-4]])\bound{m1 }} +\end{paste}\end{patch} + +\begin{patch}{ExMatrixBasicFunctionPatch2} +\begin{paste}{ExMatrixBasicFunctionFull2}{ExMatrixBasicFunctionEmpty2} +\pastebutton{ExMatrixBasicFunctionFull2}{\hidepaste} +\tab{5}\spadcommand{m2 := matrix([[1,0,2],[20,30,10],[0,200,100]])\bound{m2 }} +\indentrel{3}\begin{verbatim} + Ú1 0 2 ¿ + ³ ³ + (2) ³20 30 10 ³ + ³ ³ + À0 200 100Ù + Type: Matrix Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ExMatrixBasicFunctionEmpty2} +\begin{paste}{ExMatrixBasicFunctionEmpty2}{ExMatrixBasicFunctionPatch2} +\pastebutton{ExMatrixBasicFunctionEmpty2}{\showpaste} +\tab{5}\spadcommand{m2 := matrix([[1,0,2],[20,30,10],[0,200,100]])\bound{m2 }} +\end{paste}\end{patch} + +\begin{patch}{ExMatrixBasicFunctionPatch3} +\begin{paste}{ExMatrixBasicFunctionFull3}{ExMatrixBasicFunctionEmpty3} +\pastebutton{ExMatrixBasicFunctionFull3}{\hidepaste} +\tab{5}\spadcommand{m3 := matrix([[1,2,3],[2,4,6]])\bound{m3 }} +\indentrel{3}\begin{verbatim} + Ú1 2 3¿ + (3) ³ ³ + À2 4 6Ù + Type: Matrix Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ExMatrixBasicFunctionEmpty3} +\begin{paste}{ExMatrixBasicFunctionEmpty3}{ExMatrixBasicFunctionPatch3} +\pastebutton{ExMatrixBasicFunctionEmpty3}{\showpaste} +\tab{5}\spadcommand{m3 := matrix([[1,2,3],[2,4,6]])\bound{m3 }} +\end{paste}\end{patch} + +\begin{patch}{ExMatrixBasicFunctionPatch4} +\begin{paste}{ExMatrixBasicFunctionFull4}{ExMatrixBasicFunctionEmpty4} +\pastebutton{ExMatrixBasicFunctionFull4}{\hidepaste} +\tab{5}\spadcommand{m1 + m3\free{m1 }\free{m3 }} +\indentrel{3}\begin{verbatim} + Ú2 0 4¿ + (4) ³ ³ + À6 6 2Ù + Type: Matrix Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ExMatrixBasicFunctionEmpty4} +\begin{paste}{ExMatrixBasicFunctionEmpty4}{ExMatrixBasicFunctionPatch4} +\pastebutton{ExMatrixBasicFunctionEmpty4}{\showpaste} +\tab{5}\spadcommand{m1 + m3\free{m1 }\free{m3 }} +\end{paste}\end{patch} + +\begin{patch}{ExMatrixBasicFunctionPatch5} +\begin{paste}{ExMatrixBasicFunctionFull5}{ExMatrixBasicFunctionEmpty5} +\pastebutton{ExMatrixBasicFunctionFull5}{\hidepaste} +\tab{5}\spadcommand{100 * m1\free{m1 }} +\indentrel{3}\begin{verbatim} + Ú100 - 200 100 ¿ + (5) ³ ³ + À400 200 - 400Ù + Type: Matrix Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ExMatrixBasicFunctionEmpty5} +\begin{paste}{ExMatrixBasicFunctionEmpty5}{ExMatrixBasicFunctionPatch5} +\pastebutton{ExMatrixBasicFunctionEmpty5}{\showpaste} +\tab{5}\spadcommand{100 * m1\free{m1 }} +\end{paste}\end{patch} + +\begin{patch}{ExMatrixBasicFunctionPatch6} +\begin{paste}{ExMatrixBasicFunctionFull6}{ExMatrixBasicFunctionEmpty6} +\pastebutton{ExMatrixBasicFunctionFull6}{\hidepaste} +\tab{5}\spadcommand{m1 * m2\free{m1 }\free{m2 }} +\indentrel{3}\begin{verbatim} + Ú- 39 140 82 ¿ + (6) ³ ³ + À 44 - 740 - 372Ù + Type: Matrix Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ExMatrixBasicFunctionEmpty6} +\begin{paste}{ExMatrixBasicFunctionEmpty6}{ExMatrixBasicFunctionPatch6} +\pastebutton{ExMatrixBasicFunctionEmpty6}{\showpaste} +\tab{5}\spadcommand{m1 * m2\free{m1 }\free{m2 }} +\end{paste}\end{patch} + +\begin{patch}{ExMatrixBasicFunctionPatch7} +\begin{paste}{ExMatrixBasicFunctionFull7}{ExMatrixBasicFunctionEmpty7} +\pastebutton{ExMatrixBasicFunctionFull7}{\hidepaste} +\tab{5}\spadcommand{-m1 + m3 * m2\free{m1 }\free{m2 }\free{m3 }} +\indentrel{3}\begin{verbatim} + Ú40 662 321¿ + (7) ³ ³ + À78 1318 648Ù + Type: Matrix Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ExMatrixBasicFunctionEmpty7} +\begin{paste}{ExMatrixBasicFunctionEmpty7}{ExMatrixBasicFunctionPatch7} +\pastebutton{ExMatrixBasicFunctionEmpty7}{\showpaste} +\tab{5}\spadcommand{-m1 + m3 * m2\free{m1 }\free{m2 }\free{m3 }} +\end{paste}\end{patch} + +\begin{patch}{ExMatrixBasicFunctionPatch8} +\begin{paste}{ExMatrixBasicFunctionFull8}{ExMatrixBasicFunctionEmpty8} +\pastebutton{ExMatrixBasicFunctionFull8}{\hidepaste} +\tab{5}\spadcommand{m3 *vector([1,0,1])\free{m3 }} +\indentrel{3}\begin{verbatim} + (8) [4,8] + Type: Vector Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ExMatrixBasicFunctionEmpty8} +\begin{paste}{ExMatrixBasicFunctionEmpty8}{ExMatrixBasicFunctionPatch8} +\pastebutton{ExMatrixBasicFunctionEmpty8}{\showpaste} +\tab{5}\spadcommand{m3 *vector([1,0,1])\free{m3 }} +\end{paste} +\end{patch} @ \pagehead{ExConstructMatrix}{exmatrix.ht}{Constructing new Matrices} @@ -6457,7 +16280,132 @@ matrix i\spad{b}. changes the submatrix of \spad{b} consisting of the first 3 rows and columns to its transpose. \endscroll -\autobuttons\end{page} +\autobuttons +\end{page} + +\begin{patch}{ExConstructMatrixPatch1} +\begin{paste}{ExConstructMatrixFull1}{ExConstructMatrixEmpty1} +\pastebutton{ExConstructMatrixFull1}{\hidepaste} +\tab{5}\spadcommand{diagonalMatrix([1,2,3,2,1])} +\indentrel{3}\begin{verbatim} + Ú1 0 0 0 0¿ + ³ ³ + ³0 2 0 0 0³ + ³ ³ + (1) ³0 0 3 0 0³ + ³ ³ + ³0 0 0 2 0³ + ³ ³ + À0 0 0 0 1Ù + Type: Matrix Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ExConstructMatrixEmpty1} +\begin{paste}{ExConstructMatrixEmpty1}{ExConstructMatrixPatch1} +\pastebutton{ExConstructMatrixEmpty1}{\showpaste} +\tab{5}\spadcommand{diagonalMatrix([1,2,3,2,1])} +\end{paste}\end{patch} + +\begin{patch}{ExConstructMatrixPatch2} +\begin{paste}{ExConstructMatrixFull2}{ExConstructMatrixEmpty2} +\pastebutton{ExConstructMatrixFull2}{\hidepaste} +\tab{5}\spadcommand{subMatrix(matrix([[0,1,2,3,4],[5,6,7,8,9],[10,11,12,13,14]]), 1,3,2,4)} +\indentrel{3}\begin{verbatim} + Ú1 2 3 ¿ + ³ ³ + (2) ³6 7 8 ³ + ³ ³ + À11 12 13Ù + Type: Matrix Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ExConstructMatrixEmpty2} +\begin{paste}{ExConstructMatrixEmpty2}{ExConstructMatrixPatch2} +\pastebutton{ExConstructMatrixEmpty2}{\showpaste} +\tab{5}\spadcommand{subMatrix(matrix([[0,1,2,3,4],[5,6,7,8,9],[10,11,12,13,14]]), 1,3,2,4)} +\end{paste}\end{patch} + +\begin{patch}{ExConstructMatrixPatch3} +\begin{paste}{ExConstructMatrixFull3}{ExConstructMatrixEmpty3} +\pastebutton{ExConstructMatrixFull3}{\hidepaste} +\tab{5}\spadcommand{horizConcat(matrix([[1,2,3],[6,7,8]]),matrix([[11,12,13],[55,77,88]]))} +\indentrel{3}\begin{verbatim} + Ú1 2 3 11 12 13¿ + (3) ³ ³ + À6 7 8 55 77 88Ù + Type: Matrix Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ExConstructMatrixEmpty3} +\begin{paste}{ExConstructMatrixEmpty3}{ExConstructMatrixPatch3} +\pastebutton{ExConstructMatrixEmpty3}{\showpaste} +\tab{5}\spadcommand{horizConcat(matrix([[1,2,3],[6,7,8]]),matrix([[11,12,13],[55,77,88]]))} +\end{paste}\end{patch} + +\begin{patch}{ExConstructMatrixPatch4} +\begin{paste}{ExConstructMatrixFull4}{ExConstructMatrixEmpty4} +\pastebutton{ExConstructMatrixFull4}{\hidepaste} +\tab{5}\spadcommand{vertConcat(matrix([[1,2,3],[6,7,8]]),matrix([[11,12,13],[55,77,88]]))} +\indentrel{3}\begin{verbatim} + Ú1 2 3 ¿ + ³ ³ + ³6 7 8 ³ + (4) ³ ³ + ³11 12 13³ + ³ ³ + À55 77 88Ù + Type: Matrix Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ExConstructMatrixEmpty4} +\begin{paste}{ExConstructMatrixEmpty4}{ExConstructMatrixPatch4} +\pastebutton{ExConstructMatrixEmpty4}{\showpaste} +\tab{5}\spadcommand{vertConcat(matrix([[1,2,3],[6,7,8]]),matrix([[11,12,13],[55,77,88]]))} +\end{paste}\end{patch} + +\begin{patch}{ExConstructMatrixPatch5} +\begin{paste}{ExConstructMatrixFull5}{ExConstructMatrixEmpty5} +\pastebutton{ExConstructMatrixFull5}{\hidepaste} +\tab{5}\spadcommand{b:=matrix([[0,1,2,3,4],[5,6,7,8,9],[10,11,12,13,14]])\bound{b }} +\indentrel{3}\begin{verbatim} + Ú0 1 2 3 4 ¿ + ³ ³ + (5) ³5 6 7 8 9 ³ + ³ ³ + À10 11 12 13 14Ù + Type: Matrix Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ExConstructMatrixEmpty5} +\begin{paste}{ExConstructMatrixEmpty5}{ExConstructMatrixPatch5} +\pastebutton{ExConstructMatrixEmpty5}{\showpaste} +\tab{5}\spadcommand{b:=matrix([[0,1,2,3,4],[5,6,7,8,9],[10,11,12,13,14]])\bound{b }} +\end{paste}\end{patch} + +\begin{patch}{ExConstructMatrixPatch6} +\begin{paste}{ExConstructMatrixFull6}{ExConstructMatrixEmpty6} +\pastebutton{ExConstructMatrixFull6}{\hidepaste} +\tab{5}\spadcommand{setsubMatrix!(b,1,1,transpose(subMatrix(b,1,3,1,3)))\free{b }} +\indentrel{3}\begin{verbatim} + Ú0 5 10 3 4 ¿ + ³ ³ + (6) ³1 6 11 8 9 ³ + ³ ³ + À2 7 12 13 14Ù + Type: Matrix Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ExConstructMatrixEmpty6} +\begin{paste}{ExConstructMatrixEmpty6}{ExConstructMatrixPatch6} +\pastebutton{ExConstructMatrixEmpty6}{\showpaste} +\tab{5}\spadcommand{setsubMatrix!(b,1,1,transpose(subMatrix(b,1,3,1,3)))\free{b }} +\end{paste}\end{patch} @ \pagehead{ExTraceMatrix}{exmatrix.ht}{Trace of a Matrix} @@ -6471,7 +16419,25 @@ For example `trace' for a four by four Vandermonde matrix. \spadpaste{trace( matrix([[1,x,x**2,x**3],[1,y,y**2,y**3], [1,z,z**2,z**3],[1,u,u**2,u**3]]) )} \endscroll -\autobuttons\end{page} +\autobuttons +\end{page} + +\begin{patch}{ExTraceMatrixPatch1} +\begin{paste}{ExTraceMatrixFull1}{ExTraceMatrixEmpty1} +\pastebutton{ExTraceMatrixFull1}{\hidepaste} +\tab{5}\spadcommand{trace( matrix([[1,x,x**2,x**3],[1,y,y**2,y**3],[1,z,z**2,z**3],[1,u,u**2,u**3]]) )} +\indentrel{3}\begin{verbatim} + 2 3 + (1) z + y + u + 1 + Type: Polynomial Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ExTraceMatrixEmpty1} +\begin{paste}{ExTraceMatrixEmpty1}{ExTraceMatrixPatch1} +\pastebutton{ExTraceMatrixEmpty1}{\showpaste} +\tab{5}\spadcommand{trace( matrix([[1,x,x**2,x**3],[1,y,y**2,y**3],[1,z,z**2,z**3],[1,u,u**2,u**3]]) )} +\end{paste}\end{patch} @ \pagehead{ExDeterminantMatrix}{exmatrix.ht}{Determinant of a Matrix} @@ -6483,7 +16449,25 @@ over a commutative ring, that is a ring whose multiplication is commutative. \spadpaste{determinant(matrix([[1,2,3,4],[2,3,2,5],[3,4,5,6],[4,1,6,7]]))} \endscroll -\autobuttons\end{page} +\autobuttons +\end{page} + +\begin{patch}{ExDeterminantMatrixPatch1} +\begin{paste}{ExDeterminantMatrixFull1}{ExDeterminantMatrixEmpty1} +\pastebutton{ExDeterminantMatrixFull1}{\hidepaste} +\tab{5}\spadcommand{determinant(matrix([[1,2,3,4],[2,3,2,5],[3,4,5,6],[4,1,6,7]]))} +\indentrel{3}\begin{verbatim} + (1) - 48 + Type: Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ExDeterminantMatrixEmpty1} +\begin{paste}{ExDeterminantMatrixEmpty1}{ExDeterminantMatrixPatch1} +\pastebutton{ExDeterminantMatrixEmpty1}{\showpaste} +\tab{5}\spadcommand{determinant(matrix([[1,2,3,4],[2,3,2,5],[3,4,5,6],[4,1,6,7]]))} +\end{paste} +\end{patch} @ \pagehead{ExInverseMatrix}{exmatrix.ht}{Inverse of a Matrix} @@ -6494,7 +16478,32 @@ The function \spadfun{inverse} computes the inverse of a square matrix. \spadpaste{inverse(matrix([[1,2,1],[-2,3,4],[-1,5,6]])) } (If the inverse doesn't exist, then Axiom returns `failed'.) \endscroll -\autobuttons\end{page} +\autobuttons +\end{page} + +\begin{patch}{ExInverseMatrixPatch1} +\begin{paste}{ExInverseMatrixFull1}{ExInverseMatrixEmpty1} +\pastebutton{ExInverseMatrixFull1}{\hidepaste} +\tab{5}\spadcommand{inverse(matrix([[1,2,1],[-2,3,4],[-1,5,6]]))} +\indentrel{3}\begin{verbatim} + Ú 2 5 ¿ + ³- Ä - 1 Ä ³ + ³ 7 7 ³ + ³ ³ + (1) ³ 8 6³ + ³ Ä 1 - ij + ³ 7 7³ + ³ ³ + À- 1 - 1 1 Ù + Type: Union(Matrix Fraction Integer,...) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ExInverseMatrixEmpty1} +\begin{paste}{ExInverseMatrixEmpty1}{ExInverseMatrixPatch1} +\pastebutton{ExInverseMatrixEmpty1}{\showpaste} +\tab{5}\spadcommand{inverse(matrix([[1,2,1],[-2,3,4],[-1,5,6]]))} +\end{paste}\end{patch} @ \pagehead{ExRankMatrix}{exmatrix.ht}{Rank of a Matrix} @@ -6504,7 +16513,24 @@ The function \spadfun{inverse} computes the inverse of a square matrix. The function \spadfun{rank} gives you the rank of a matrix: \spadpaste{rank(matrix([[0,4,1],[5,3,-7],[-5,5,9]]))} \endscroll -\autobuttons\end{page} +\autobuttons +\end{page} + +\begin{patch}{ExRankMatrixPatch1} +\begin{paste}{ExRankMatrixFull1}{ExRankMatrixEmpty1} +\pastebutton{ExRankMatrixFull1}{\hidepaste} +\tab{5}\spadcommand{rank(matrix([[0,4,1],[5,3,-7],[-5,5,9]]))} +\indentrel{3}\begin{verbatim} + (1) 2 + Type: PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ExRankMatrixEmpty1} +\begin{paste}{ExRankMatrixEmpty1}{ExRankMatrixPatch1} +\pastebutton{ExRankMatrixEmpty1}{\showpaste} +\tab{5}\spadcommand{rank(matrix([[0,4,1],[5,3,-7],[-5,5,9]]))} +\end{paste}\end{patch} @ \section{expr.ht} @@ -6719,6 +16745,429 @@ rewrite rules for expressions. \autobuttons \end{page} +\begin{patch}{ExpressionXmpPagePatch1} +\begin{paste}{ExpressionXmpPageFull1}{ExpressionXmpPageEmpty1} +\pastebutton{ExpressionXmpPageFull1}{\hidepaste} +\tab{5}\spadcommand{sin(x) + 3*cos(x)**2} +\indentrel{3}\begin{verbatim} + 2 + (1) sin(x) + 3cos(x) + Type: Expression Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ExpressionXmpPageEmpty1} +\begin{paste}{ExpressionXmpPageEmpty1}{ExpressionXmpPagePatch1} +\pastebutton{ExpressionXmpPageEmpty1}{\showpaste} +\tab{5}\spadcommand{sin(x) + 3*cos(x)**2} +\end{paste}\end{patch} + +\begin{patch}{ExpressionXmpPagePatch2} +\begin{paste}{ExpressionXmpPageFull2}{ExpressionXmpPageEmpty2} +\pastebutton{ExpressionXmpPageFull2}{\hidepaste} +\tab{5}\spadcommand{tan(x) - 3.45*x} +\indentrel{3}\begin{verbatim} + (2) tan(x) - 3.45 x + Type: Expression Float +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ExpressionXmpPageEmpty2} +\begin{paste}{ExpressionXmpPageEmpty2}{ExpressionXmpPagePatch2} +\pastebutton{ExpressionXmpPageEmpty2}{\showpaste} +\tab{5}\spadcommand{tan(x) - 3.45*x} +\end{paste}\end{patch} + +\begin{patch}{ExpressionXmpPagePatch3} +\begin{paste}{ExpressionXmpPageFull3}{ExpressionXmpPageEmpty3} +\pastebutton{ExpressionXmpPageFull3}{\hidepaste} +\tab{5}\spadcommand{(tan sqrt 7 - sin sqrt 11)**2 / (4 - cos(x - y))} +\indentrel{3}\begin{verbatim} + (3) + ÚÄ¿ 2 ÚÄÄ¿ ÚÄ¿ ÚÄÄ¿ 2 + - tan(\³7 ) + 2sin(\³11 )tan(\³7 ) - sin(\³11 ) + ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ + cos(y - x) - 4 + Type: Expression Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ExpressionXmpPageEmpty3} +\begin{paste}{ExpressionXmpPageEmpty3}{ExpressionXmpPagePatch3} +\pastebutton{ExpressionXmpPageEmpty3}{\showpaste} +\tab{5}\spadcommand{(tan sqrt 7 - sin sqrt 11)**2 / (4 - cos(x - y))} +\end{paste}\end{patch} + +\begin{patch}{ExpressionXmpPagePatch4} +\begin{paste}{ExpressionXmpPageFull4}{ExpressionXmpPageEmpty4} +\pastebutton{ExpressionXmpPageFull4}{\hidepaste} +\tab{5}\spadcommand{log(exp x)@Expression(Integer)} +\indentrel{3}\begin{verbatim} + (4) x + Type: Expression Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ExpressionXmpPageEmpty4} +\begin{paste}{ExpressionXmpPageEmpty4}{ExpressionXmpPagePatch4} +\pastebutton{ExpressionXmpPageEmpty4}{\showpaste} +\tab{5}\spadcommand{log(exp x)@Expression(Integer)} +\end{paste}\end{patch} + +\begin{patch}{ExpressionXmpPagePatch5} +\begin{paste}{ExpressionXmpPageFull5}{ExpressionXmpPageEmpty5} +\pastebutton{ExpressionXmpPageFull5}{\hidepaste} +\tab{5}\spadcommand{log(exp x)@Expression(Complex Integer)} +\indentrel{3}\begin{verbatim} + x + (5) log(%e ) + Type: Expression Complex Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ExpressionXmpPageEmpty5} +\begin{paste}{ExpressionXmpPageEmpty5}{ExpressionXmpPagePatch5} +\pastebutton{ExpressionXmpPageEmpty5}{\showpaste} +\tab{5}\spadcommand{log(exp x)@Expression(Complex Integer)} +\end{paste}\end{patch} + +\begin{patch}{ExpressionXmpPagePatch6} +\begin{paste}{ExpressionXmpPageFull6}{ExpressionXmpPageEmpty6} +\pastebutton{ExpressionXmpPageFull6}{\hidepaste} +\tab{5}\spadcommand{sqrt 3 + sqrt(2 + sqrt(-5))\bound{algnum1 }} +\indentrel{3}\begin{verbatim} + ÚÄÄÄÄÄÄÄÄÄÄ¿ + ³ ÚÄÄÄ¿ ÚÄ¿ + (6) \³\³- 5 + 2 + \³3 + Type: AlgebraicNumber +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ExpressionXmpPageEmpty6} +\begin{paste}{ExpressionXmpPageEmpty6}{ExpressionXmpPagePatch6} +\pastebutton{ExpressionXmpPageEmpty6}{\showpaste} +\tab{5}\spadcommand{sqrt 3 + sqrt(2 + sqrt(-5))\bound{algnum1 }} +\end{paste}\end{patch} + +\begin{patch}{ExpressionXmpPagePatch7} +\begin{paste}{ExpressionXmpPageFull7}{ExpressionXmpPageEmpty7} +\pastebutton{ExpressionXmpPageFull7}{\hidepaste} +\tab{5}\spadcommand{\% :: Expression Integer\free{algnum1 }} +\indentrel{3}\begin{verbatim} + ÚÄÄÄÄÄÄÄÄÄÄ¿ + ³ ÚÄÄÄ¿ ÚÄ¿ + (7) \³\³- 5 + 2 + \³3 + Type: Expression Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ExpressionXmpPageEmpty7} +\begin{paste}{ExpressionXmpPageEmpty7}{ExpressionXmpPagePatch7} +\pastebutton{ExpressionXmpPageEmpty7}{\showpaste} +\tab{5}\spadcommand{\% :: Expression Integer\free{algnum1 }} +\end{paste}\end{patch} + +\begin{patch}{ExpressionXmpPagePatch8} +\begin{paste}{ExpressionXmpPageFull8}{ExpressionXmpPageEmpty8} +\pastebutton{ExpressionXmpPageFull8}{\hidepaste} +\tab{5}\spadcommand{height mainKernel sin(x + 4)} +\indentrel{3}\begin{verbatim} + (8) 2 + Type: PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ExpressionXmpPageEmpty8} +\begin{paste}{ExpressionXmpPageEmpty8}{ExpressionXmpPagePatch8} +\pastebutton{ExpressionXmpPageEmpty8}{\showpaste} +\tab{5}\spadcommand{height mainKernel sin(x + 4)} +\end{paste}\end{patch} + +\begin{patch}{ExpressionXmpPagePatch9} +\begin{paste}{ExpressionXmpPageFull9}{ExpressionXmpPageEmpty9} +\pastebutton{ExpressionXmpPageFull9}{\hidepaste} +\tab{5}\spadcommand{e := (sin(x) - 4)**2 / ( 1 - 2*y*sqrt(- y) )\bound{e }} +\indentrel{3}\begin{verbatim} + 2 + - sin(x) + 8sin(x) - 16 + (9) ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ + ÚÄÄÄ¿ + 2y\³- y - 1 + Type: Expression Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ExpressionXmpPageEmpty9} +\begin{paste}{ExpressionXmpPageEmpty9}{ExpressionXmpPagePatch9} +\pastebutton{ExpressionXmpPageEmpty9}{\showpaste} +\tab{5}\spadcommand{e := (sin(x) - 4)**2 / ( 1 - 2*y*sqrt(- y) )\bound{e }} +\end{paste}\end{patch} + +\begin{patch}{ExpressionXmpPagePatch10} +\begin{paste}{ExpressionXmpPageFull10}{ExpressionXmpPageEmpty10} +\pastebutton{ExpressionXmpPageFull10}{\hidepaste} +\tab{5}\spadcommand{numer e\free{e }} +\indentrel{3}\begin{verbatim} + 2 + (10) - sin(x) + 8sin(x) - 16 +Type: SparseMultivariatePolynomial(Integer,Kernel Expression Integer) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ExpressionXmpPageEmpty10} +\begin{paste}{ExpressionXmpPageEmpty10}{ExpressionXmpPagePatch10} +\pastebutton{ExpressionXmpPageEmpty10}{\showpaste} +\tab{5}\spadcommand{numer e\free{e }} +\end{paste}\end{patch} + +\begin{patch}{ExpressionXmpPagePatch11} +\begin{paste}{ExpressionXmpPageFull11}{ExpressionXmpPageEmpty11} +\pastebutton{ExpressionXmpPageFull11}{\hidepaste} +\tab{5}\spadcommand{denom e\free{e }} +\indentrel{3}\begin{verbatim} + ÚÄÄÄ¿ + (11) 2y\³- y - 1 +Type: SparseMultivariatePolynomial(Integer,Kernel Expression Integer) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ExpressionXmpPageEmpty11} +\begin{paste}{ExpressionXmpPageEmpty11}{ExpressionXmpPagePatch11} +\pastebutton{ExpressionXmpPageEmpty11}{\showpaste} +\tab{5}\spadcommand{denom e\free{e }} +\end{paste}\end{patch} + +\begin{patch}{ExpressionXmpPagePatch12} +\begin{paste}{ExpressionXmpPageFull12}{ExpressionXmpPageEmpty12} +\pastebutton{ExpressionXmpPageFull12}{\hidepaste} +\tab{5}\spadcommand{D(e, x)\free{e }} +\indentrel{3}\begin{verbatim} + (12) + ÚÄÄÄ¿ + (4y cos(x)sin(x) - 16y cos(x))\³- y + + + - 2cos(x)sin(x) + 8cos(x) + / + ÚÄÄÄ¿ 3 + 4y\³- y + 4y - 1 + Type: Expression Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ExpressionXmpPageEmpty12} +\begin{paste}{ExpressionXmpPageEmpty12}{ExpressionXmpPagePatch12} +\pastebutton{ExpressionXmpPageEmpty12}{\showpaste} +\tab{5}\spadcommand{D(e, x)\free{e }} +\end{paste}\end{patch} + +\begin{patch}{ExpressionXmpPagePatch13} +\begin{paste}{ExpressionXmpPageFull13}{ExpressionXmpPageEmpty13} +\pastebutton{ExpressionXmpPageFull13}{\hidepaste} +\tab{5}\spadcommand{D(e, [x, y], [1, 2])\free{e }} +\indentrel{3}\begin{verbatim} + (13) + 7 4 + (- 2304y + 960y )cos(x)sin(x) + + + 7 4 + (9216y - 3840y )cos(x) + * + ÚÄÄÄ¿ + \³- y + + + 9 6 3 + (- 960y + 2160y - 180y - 3)cos(x)sin(x) + + + 9 6 3 + (3840y - 8640y + 720y + 12)cos(x) + / + 12 9 6 3 ÚÄÄÄ¿ + (256y - 1792y + 1120y - 112y + 1)\³- y + + + 11 8 5 2 + - 1024y + 1792y - 448y + 16y + Type: Expression Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ExpressionXmpPageEmpty13} +\begin{paste}{ExpressionXmpPageEmpty13}{ExpressionXmpPagePatch13} +\pastebutton{ExpressionXmpPageEmpty13}{\showpaste} +\tab{5}\spadcommand{D(e, [x, y], [1, 2])\free{e }} +\end{paste}\end{patch} + +\begin{patch}{ExpressionXmpPagePatch14} +\begin{paste}{ExpressionXmpPageFull14}{ExpressionXmpPageEmpty14} +\pastebutton{ExpressionXmpPageFull14}{\hidepaste} +\tab{5}\spadcommand{complexNumeric(cos(2 - 3*\%i))} +\indentrel{3}\begin{verbatim} + (14) + - 4.1896256909 688072301 + 9.1092278937 55336598 %i + Type: Complex Float +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ExpressionXmpPageEmpty14} +\begin{paste}{ExpressionXmpPageEmpty14}{ExpressionXmpPagePatch14} +\pastebutton{ExpressionXmpPageEmpty14}{\showpaste} +\tab{5}\spadcommand{complexNumeric(cos(2 - 3*\%i))} +\end{paste}\end{patch} + +\begin{patch}{ExpressionXmpPagePatch15} +\begin{paste}{ExpressionXmpPageFull15}{ExpressionXmpPageEmpty15} +\pastebutton{ExpressionXmpPageFull15}{\hidepaste} +\tab{5}\spadcommand{numeric(tan 3.8)} +\indentrel{3}\begin{verbatim} + (15) 0.7735560905 0312607286 + Type: Float +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ExpressionXmpPageEmpty15} +\begin{paste}{ExpressionXmpPageEmpty15}{ExpressionXmpPagePatch15} +\pastebutton{ExpressionXmpPageEmpty15}{\showpaste} +\tab{5}\spadcommand{numeric(tan 3.8)} +\end{paste}\end{patch} + +\begin{patch}{ExpressionXmpPagePatch16} +\begin{paste}{ExpressionXmpPageFull16}{ExpressionXmpPageEmpty16} +\pastebutton{ExpressionXmpPageFull16}{\hidepaste} +\tab{5}\spadcommand{e2 := cos(x**2 - y + 3)\bound{e2 }} +\indentrel{3}\begin{verbatim} + 2 + (16) cos(y - x - 3) + Type: Expression Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ExpressionXmpPageEmpty16} +\begin{paste}{ExpressionXmpPageEmpty16}{ExpressionXmpPagePatch16} +\pastebutton{ExpressionXmpPageEmpty16}{\showpaste} +\tab{5}\spadcommand{e2 := cos(x**2 - y + 3)\bound{e2 }} +\end{paste}\end{patch} + +\begin{patch}{ExpressionXmpPagePatch17} +\begin{paste}{ExpressionXmpPageFull17}{ExpressionXmpPageEmpty17} +\pastebutton{ExpressionXmpPageFull17}{\hidepaste} +\tab{5}\spadcommand{e3 := asin(e2) - \%pi/2\free{e2 }\bound{e3 }} +\indentrel{3}\begin{verbatim} + 2 + (17) - y + x + 3 + Type: Expression Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ExpressionXmpPageEmpty17} +\begin{paste}{ExpressionXmpPageEmpty17}{ExpressionXmpPagePatch17} +\pastebutton{ExpressionXmpPageEmpty17}{\showpaste} +\tab{5}\spadcommand{e3 := asin(e2) - \%pi/2\free{e2 }\bound{e3 }} +\end{paste}\end{patch} + +\begin{patch}{ExpressionXmpPagePatch18} +\begin{paste}{ExpressionXmpPageFull18}{ExpressionXmpPageEmpty18} +\pastebutton{ExpressionXmpPageFull18}{\hidepaste} +\tab{5}\spadcommand{e3 :: Polynomial Integer\free{e3 }} +\indentrel{3}\begin{verbatim} + 2 + (18) - y + x + 3 + Type: Polynomial Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ExpressionXmpPageEmpty18} +\begin{paste}{ExpressionXmpPageEmpty18}{ExpressionXmpPagePatch18} +\pastebutton{ExpressionXmpPageEmpty18}{\showpaste} +\tab{5}\spadcommand{e3 :: Polynomial Integer\free{e3 }} +\end{paste}\end{patch} + +\begin{patch}{ExpressionXmpPagePatch19} +\begin{paste}{ExpressionXmpPageFull19}{ExpressionXmpPageEmpty19} +\pastebutton{ExpressionXmpPageFull19}{\hidepaste} +\tab{5}\spadcommand{e3 :: DMP([x, y], Integer)\free{e3 }} +\indentrel{3}\begin{verbatim} + 2 + (19) x - y + 3 + Type: DistributedMultivariatePolynomial([x,y],Integer) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ExpressionXmpPageEmpty19} +\begin{paste}{ExpressionXmpPageEmpty19}{ExpressionXmpPagePatch19} +\pastebutton{ExpressionXmpPageEmpty19}{\showpaste} +\tab{5}\spadcommand{e3 :: DMP([x, y], Integer)\free{e3 }} +\end{paste}\end{patch} + +\begin{patch}{ExpressionXmpPagePatch20} +\begin{paste}{ExpressionXmpPageFull20}{ExpressionXmpPageEmpty20} +\pastebutton{ExpressionXmpPageFull20}{\hidepaste} +\tab{5}\spadcommand{sin \%pi} +\indentrel{3}\begin{verbatim} + (20) 0 + Type: Expression Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ExpressionXmpPageEmpty20} +\begin{paste}{ExpressionXmpPageEmpty20}{ExpressionXmpPagePatch20} +\pastebutton{ExpressionXmpPageEmpty20}{\showpaste} +\tab{5}\spadcommand{sin \%pi} +\end{paste}\end{patch} + +\begin{patch}{ExpressionXmpPagePatch21} +\begin{paste}{ExpressionXmpPageFull21}{ExpressionXmpPageEmpty21} +\pastebutton{ExpressionXmpPageFull21}{\hidepaste} +\tab{5}\spadcommand{cos(\%pi / 4)} +\indentrel{3}\begin{verbatim} + ÚÄ¿ + \³2 + (21) ÄÄÄÄ + 2 + Type: Expression Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ExpressionXmpPageEmpty21} +\begin{paste}{ExpressionXmpPageEmpty21}{ExpressionXmpPagePatch21} +\pastebutton{ExpressionXmpPageEmpty21}{\showpaste} +\tab{5}\spadcommand{cos(\%pi / 4)} +\end{paste}\end{patch} + +\begin{patch}{ExpressionXmpPagePatch22} +\begin{paste}{ExpressionXmpPageFull22}{ExpressionXmpPageEmpty22} +\pastebutton{ExpressionXmpPageFull22}{\hidepaste} +\tab{5}\spadcommand{tan(x)**6 + 3*tan(x)**4 + 3*tan(x)**2 + 1\bound{tan6 }} +\indentrel{3}\begin{verbatim} + 6 4 2 + (22) tan(x) + 3tan(x) + 3tan(x) + 1 + Type: Expression Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ExpressionXmpPageEmpty22} +\begin{paste}{ExpressionXmpPageEmpty22}{ExpressionXmpPagePatch22} +\pastebutton{ExpressionXmpPageEmpty22}{\showpaste} +\tab{5}\spadcommand{tan(x)**6 + 3*tan(x)**4 + 3*tan(x)**2 + 1\bound{tan6 }} +\end{paste}\end{patch} + +\begin{patch}{ExpressionXmpPagePatch23} +\begin{paste}{ExpressionXmpPageFull23}{ExpressionXmpPageEmpty23} +\pastebutton{ExpressionXmpPageFull23}{\hidepaste} +\tab{5}\spadcommand{simplify \%\free{tan6 }} +\indentrel{3}\begin{verbatim} + 1 + (23) ÄÄÄÄÄÄÄ + 6 + cos(x) + Type: Expression Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ExpressionXmpPageEmpty23} +\begin{paste}{ExpressionXmpPageEmpty23}{ExpressionXmpPagePatch23} +\pastebutton{ExpressionXmpPageEmpty23}{\showpaste} +\tab{5}\spadcommand{simplify \%\free{tan6 }} +\end{paste}\end{patch} + @ \section{explot2d.ht} \pagehead{ExPlot2DFunctions}{explot2d.ht}{Plotting Functions of One Variable} @@ -6729,7 +17178,21 @@ To plot a function {\em y = f(x)}, you need only specify the function and the interval on which it is to be plotted. \graphpaste{draw(sin(tan(x)) - tan(sin(x)),x = 0..6)} \endscroll -\autobuttons\end{page} +\autobuttons +\end{page} + +\begin{patch}{ExPlot2DFunctionsPatch1} +\begin{paste}{ExPlot2DFunctionsFull1}{ExPlot2DFunctionsEmpty1} +\pastebutton{ExPlot2DFunctionsFull1}{\hidepaste} +\tab{5}\spadgraph{draw(sin(tan(x)) - tan(sin(x)),x = 0..6)} +\center{\unixcommand{\inputimage{\env{AXIOM}/doc/viewports/explot2dfunctions1.view/image}}{viewalone\space{1} \env{AXIOM}/doc/viewports/explot2dfunctions1}} +\end{paste}\end{patch} + +\begin{patch}{ExPlot2DFunctionsEmpty1} +\begin{paste}{ExPlot2DFunctionsEmpty1}{ExPlot2DFunctionsPatch1} +\pastebutton{ExPlot2DFunctionsEmpty1}{\showpaste} +\tab{5}\spadgraph{draw(sin(tan(x)) - tan(sin(x)),x = 0..6)} +\end{paste}\end{patch} @ \pagehead{ExPlot2DParametric}{explot2d.ht}{Plotting Parametric Curves} @@ -6743,7 +17206,22 @@ as arguments of the function `curve', then give the interval over which {\em t} is to range. \graphpaste{draw(curve(9 * sin(3*t/4),8 * sin(t)),t = -4*\%pi..4*\%pi)} \endscroll -\autobuttons\end{page} +\autobuttons +\end{page} + +\begin{patch}{ExPlot2DParametricPatch1} +\begin{paste}{ExPlot2DParametricFull1}{ExPlot2DParametricEmpty1} +\pastebutton{ExPlot2DParametricFull1}{\hidepaste} +\tab{5}\spadgraph{draw(curve(9 * sin(3*t/4),8 * sin(t)),t = -4*\%pi..4*\%pi)} +\center{\unixcommand{\inputimage{\env{AXIOM}/doc/viewports/explot2dparametric1.view/image}}{viewalone\space{1} \env{AXIOM}/doc/viewports/explot2dparametric1}} +\end{paste}\end{patch} + +\begin{patch}{ExPlot2DParametricEmpty1} +\begin{paste}{ExPlot2DParametricEmpty1}{ExPlot2DParametricPatch1} +\pastebutton{ExPlot2DParametricEmpty1}{\showpaste} +\tab{5}\spadgraph{draw(curve(9 * sin(3*t/4),8 * sin(t)),t = -4*\%pi..4*\%pi)} +\end{paste} +\end{patch} @ \pagehead{ExPlot2DPolar}{explot2d.ht}{Plotting Using Polar Coordinates} @@ -6757,7 +17235,21 @@ call the function 'draw' and specify the function {\em f(theta)} and the interval over which {\em theta} is to range. \graphpaste{draw(sin(4*t/7),t = 0..14*\%pi,coordinates == polar)} \endscroll -\autobuttons\end{page} +\autobuttons +\end{page} + +\begin{patch}{ExPlot2DPolarPatch1} +\begin{paste}{ExPlot2DPolarFull1}{ExPlot2DPolarEmpty1} +\pastebutton{ExPlot2DPolarFull1}{\hidepaste} +\tab{5}\spadgraph{draw(sin(4*t/7),t = 0..14*\%pi,coordinates == polar)} +\center{\unixcommand{\inputimage{\env{AXIOM}/doc/viewports/explot2dpolar1.view/image}}{viewalone\space{1} \env{AXIOM}/doc/viewports/explot2dpolar1}} +\end{paste}\end{patch} + +\begin{patch}{ExPlot2DPolarEmpty1} +\begin{paste}{ExPlot2DPolarEmpty1}{ExPlot2DPolarPatch1} +\pastebutton{ExPlot2DPolarEmpty1}{\showpaste} +\tab{5}\spadgraph{draw(sin(4*t/7),t = 0..14*\%pi,coordinates == polar)} +\end{paste}\end{patch} @ \pagehead{ExPlot2DAlgebraic}{explot2d.ht}{Plotting Plane Algebraic Curves} @@ -6771,7 +17263,21 @@ Here's an example: \graphpaste{draw(y**2 + y - (x**3 - x) = 0, x, y, range == [-2..2,-2..1])} Here the region of the sketch is {\em -2 <= x <= 2, -2 <= y <= 1}. \endscroll -\autobuttons\end{page} +\autobuttons +\end{page} + +\begin{patch}{ExPlot2DAlgebraicPatch1} +\begin{paste}{ExPlot2DAlgebraicFull1}{ExPlot2DAlgebraicEmpty1} +\pastebutton{ExPlot2DAlgebraicFull1}{\hidepaste} +\tab{5}\spadgraph{draw(y**2 + y - (x**3 - x) = 0, x, y, range == [-2..2,-2..1])} +\center{\unixcommand{\inputimage{\env{AXIOM}/doc/viewports/explot2dalgebraic1.view/image}}{viewalone\space{1} \env{AXIOM}/doc/viewports/explot2dalgebraic1}} +\end{paste}\end{patch} + +\begin{patch}{ExPlot2DAlgebraicEmpty1} +\begin{paste}{ExPlot2DAlgebraicEmpty1}{ExPlot2DAlgebraicPatch1} +\pastebutton{ExPlot2DAlgebraicEmpty1}{\showpaste} +\tab{5}\spadgraph{draw(y**2 + y - (x**3 - x) = 0, x, y, range == [-2..2,-2..1])} +\end{paste}\end{patch} @ \section{explot3d.ht} @@ -6785,8 +17291,23 @@ For example, here's how you plot the function {\em z = cos(x*y)} as the variables {\em x} and {\em y} both range between -3 and 3: \graphpaste{draw(cos(x*y),x = -3..3,y = -3..3)} \endscroll -\autobuttons\end{page} +\autobuttons +\end{page} +\begin{patch}{ExPlot3DFunctionsPatch1} +\begin{paste}{ExPlot3DFunctionsFull1}{ExPlot3DFunctionsEmpty1} +\pastebutton{ExPlot3DFunctionsFull1}{\hidepaste} +\tab{5}\spadgraph{draw(cos(x*y),x = -3..3,y = -3..3)} +\center{\unixcommand{\inputimage{\env{AXIOM}/doc/viewports/explot3dfunctions1.view/image}}{viewalone\space{1} \env{AXIOM}/doc/viewports/explot3dfunctions1}} +\end{paste}\end{patch} + +\begin{patch}{ExPlot3DFunctionsEmpty1} +\begin{paste}{ExPlot3DFunctionsEmpty1}{ExPlot3DFunctionsPatch1} +\pastebutton{ExPlot3DFunctionsEmpty1}{\showpaste} +\tab{5}\spadgraph{draw(cos(x*y),x = -3..3,y = -3..3)} +\end{paste} +\end{patch} + @ \pagehead{ExPlot3DParametricSurface}{explot3d.ht} {Plotting Parametric Surfaces} @@ -6805,8 +17326,35 @@ u=0..\%pi,v=0..2*\%pi)} Here's a cone: \graphpaste{draw(surface(u*cos(v),u*sin(v),u),u=0..4,v=0..2*\%pi)} \endscroll -\autobuttons\end{page} +\autobuttons +\end{page} +\begin{patch}{ExPlot3DParametricSurfacePatch1} +\begin{paste}{ExPlot3DParametricSurfaceFull1}{ExPlot3DParametricSurfaceEmpty1} +\pastebutton{ExPlot3DParametricSurfaceFull1}{\hidepaste} +\tab{5}\spadgraph{draw(surface(5*sin(u)*cos(v),4*sin(u)*sin(v),3*cos(u)),u=0..\%pi,v=0..2*\%pi)} +\center{\unixcommand{\inputimage{\env{AXIOM}/doc/viewports/explot3dparametricsurface1.view/image}}{viewalone\space{1} \env{AXIOM}/doc/viewports/explot3dparametricsurface1}} +\end{paste}\end{patch} + +\begin{patch}{ExPlot3DParametricSurfaceEmpty1} +\begin{paste}{ExPlot3DParametricSurfaceEmpty1}{ExPlot3DParametricSurfacePatch1} +\pastebutton{ExPlot3DParametricSurfaceEmpty1}{\showpaste} +\tab{5}\spadgraph{draw(surface(5*sin(u)*cos(v),4*sin(u)*sin(v),3*cos(u)),u=0..\%pi,v=0..2*\%pi)} +\end{paste}\end{patch} + +\begin{patch}{ExPlot3DParametricSurfacePatch2} +\begin{paste}{ExPlot3DParametricSurfaceFull2}{ExPlot3DParametricSurfaceEmpty2} +\pastebutton{ExPlot3DParametricSurfaceFull2}{\hidepaste} +\tab{5}\spadgraph{draw(surface(u*cos(v),u*sin(v),u),u=0..4,v=0..2*\%pi)} +\center{\unixcommand{\inputimage{\env{AXIOM}/doc/viewports/explot3dparametricsurface2.view/image}}{viewalone\space{1} \env{AXIOM}/doc/viewports/explot3dparametricsurface2}} +\end{paste}\end{patch} + +\begin{patch}{ExPlot3DParametricSurfaceEmpty2} +\begin{paste}{ExPlot3DParametricSurfaceEmpty2}{ExPlot3DParametricSurfacePatch2} +\pastebutton{ExPlot3DParametricSurfaceEmpty2}{\showpaste} +\tab{5}\spadgraph{draw(surface(u*cos(v),u*sin(v),u),u=0..4,v=0..2*\%pi)} +\end{paste}\end{patch} + @ \pagehead{ExPlot3DParametricCurve}{explot3d.ht}{Plotting Parametric Curves} <>= @@ -6822,7 +17370,35 @@ Here is a spiral: Here is the {\em twisted cubic curve}: \graphpaste{draw(curve(t,t**2,t**3),t=-3..3)} \endscroll -\autobuttons\end{page} +\autobuttons +\end{page} + +\begin{patch}{ExPlot3DParametricCurvePatch1} +\begin{paste}{ExPlot3DParametricCurveFull1}{ExPlot3DParametricCurveEmpty1} +\pastebutton{ExPlot3DParametricCurveFull1}{\hidepaste} +\tab{5}\spadgraph{draw(curve(cos(t),sin(t),t),t=0..6)} +\center{\unixcommand{\inputimage{\env{AXIOM}/doc/viewports/explot3dparametriccurve1.view/image}}{viewalone\space{1} \env{AXIOM}/doc/viewports/explot3dparametriccurve1}} +\end{paste}\end{patch} + +\begin{patch}{ExPlot3DParametricCurveEmpty1} +\begin{paste}{ExPlot3DParametricCurveEmpty1}{ExPlot3DParametricCurvePatch1} +\pastebutton{ExPlot3DParametricCurveEmpty1}{\showpaste} +\tab{5}\spadgraph{draw(curve(cos(t),sin(t),t),t=0..6)} +\end{paste}\end{patch} + +\begin{patch}{ExPlot3DParametricCurvePatch2} +\begin{paste}{ExPlot3DParametricCurveFull2}{ExPlot3DParametricCurveEmpty2} +\pastebutton{ExPlot3DParametricCurveFull2}{\hidepaste} +\tab{5}\spadgraph{draw(curve(t,t**2,t**3),t=-3..3)} +\center{\unixcommand{\inputimage{\env{AXIOM}/doc/viewports/explot3dparametriccurve2.view/image}}{viewalone\space{1} \env{AXIOM}/doc/viewports/explot3dparametriccurve2}} +\end{paste}\end{patch} + +\begin{patch}{ExPlot3DParametricCurveEmpty2} +\begin{paste}{ExPlot3DParametricCurveEmpty2}{ExPlot3DParametricCurvePatch2} +\pastebutton{ExPlot3DParametricCurveEmpty2}{\showpaste} +\tab{5}\spadgraph{draw(curve(t,t**2,t**3),t=-3..3)} +\end{paste} +\end{patch} @ \section{expose.ht} @@ -6972,8 +17548,83 @@ You can have {\em sin(a*x)} expanded in powers of {\em (a - \%pi/4)} by issuing the following command: \spadpaste{series(sin(a*x),a = \%pi/4)} \endscroll -\autobuttons\end{page} +\autobuttons +\end{page} +\begin{patch}{ExSeriesConvertPatch1} +\begin{paste}{ExSeriesConvertFull1}{ExSeriesConvertEmpty1} +\pastebutton{ExSeriesConvertFull1}{\hidepaste} +\tab{5}\spadcommand{series(sin(a*x),x = 0)} +\indentrel{3}\begin{verbatim} + (1) + 3 5 7 9 + a 3 a 5 a 7 a 9 + a x - ÄÄ x + ÄÄÄ x - ÄÄÄÄ x + ÄÄÄÄÄÄ x + 6 120 5040 362880 + + + 11 + a 11 12 + - ÄÄÄÄÄÄÄÄ x + O(x ) + 39916800 + Type: UnivariatePuiseuxSeries(Expression Integer,x,0) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ExSeriesConvertEmpty1} +\begin{paste}{ExSeriesConvertEmpty1}{ExSeriesConvertPatch1} +\pastebutton{ExSeriesConvertEmpty1}{\showpaste} +\tab{5}\spadcommand{series(sin(a*x),x = 0)} +\end{paste}\end{patch} + +\begin{patch}{ExSeriesConvertPatch2} +\begin{paste}{ExSeriesConvertFull2}{ExSeriesConvertEmpty2} +\pastebutton{ExSeriesConvertFull2}{\hidepaste} +\tab{5}\spadcommand{series(sin(a*x),a = \%pi/4)} +\indentrel{3}\begin{verbatim} + (2) + %pi x %pi x %pi + sin(ÄÄÄÄÄ) + x cos(ÄÄÄÄÄ)(a - ÄÄÄ) + 4 4 4 + + + 2 %pi x 3 %pi x + x sin(ÄÄÄÄÄ) x cos(ÄÄÄÄÄ) + 4 %pi 2 4 %pi 3 + - ÄÄÄÄÄÄÄÄÄÄÄÄ (a - ÄÄÄ) - ÄÄÄÄÄÄÄÄÄÄÄÄ (a - ÄÄÄ) + 2 4 6 4 + + + 4 %pi x 5 %pi x + x sin(ÄÄÄÄÄ) x cos(ÄÄÄÄÄ) + 4 %pi 4 4 %pi 5 + ÄÄÄÄÄÄÄÄÄÄÄÄ (a - ÄÄÄ) + ÄÄÄÄÄÄÄÄÄÄÄÄ (a - ÄÄÄ) + 24 4 120 4 + + + 6 %pi x 7 %pi x + x sin(ÄÄÄÄÄ) x cos(ÄÄÄÄÄ) + 4 %pi 6 4 %pi 7 + - ÄÄÄÄÄÄÄÄÄÄÄÄ (a - ÄÄÄ) - ÄÄÄÄÄÄÄÄÄÄÄÄ (a - ÄÄÄ) + 720 4 5040 4 + + + 8 %pi x 9 %pi x + x sin(ÄÄÄÄÄ) x cos(ÄÄÄÄÄ) + 4 %pi 8 4 %pi 9 + ÄÄÄÄÄÄÄÄÄÄÄÄ (a - ÄÄÄ) + ÄÄÄÄÄÄÄÄÄÄÄÄ (a - ÄÄÄ) + 40320 4 362880 4 + + + 10 %pi x + x sin(ÄÄÄÄÄ) + 4 %pi 10 %pi 11 + - ÄÄÄÄÄÄÄÄÄÄÄÄÄ (a - ÄÄÄ) + O((a - ÄÄÄ) ) + 3628800 4 4 +Type: UnivariatePuiseuxSeries(Expression Integer,a,pi/4) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ExSeriesConvertEmpty2} +\begin{paste}{ExSeriesConvertEmpty2}{ExSeriesConvertPatch2} +\pastebutton{ExSeriesConvertEmpty2}{\showpaste} +\tab{5}\spadcommand{series(sin(a*x),a = \%pi/4)} +\end{paste}\end{patch} + @ \pagehead{ExSeriesManipulate}{exseries.ht}{Manipulating Power Series} <>= @@ -6987,8 +17638,52 @@ Now compute the square of that series: \spadpaste{f ** 2 \free{f}} It's as easy as 1, 2, 3,... \endscroll -\autobuttons\end{page} +\autobuttons +\end{page} +\begin{patch}{ExSeriesManipulatePatch1} +\begin{paste}{ExSeriesManipulateFull1}{ExSeriesManipulateEmpty1} +\pastebutton{ExSeriesManipulateFull1}{\hidepaste} +\tab{5}\spadcommand{f := series(1/(1-x),x = 0)\bound{f }} +\indentrel{3}\begin{verbatim} + (1) + 2 3 4 5 6 7 8 9 10 + 1 + x + x + x + x + x + x + x + x + x + x + + + 11 + O(x ) + Type: UnivariatePuiseuxSeries(Expression Integer,x,0) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ExSeriesManipulateEmpty1} +\begin{paste}{ExSeriesManipulateEmpty1}{ExSeriesManipulatePatch1} +\pastebutton{ExSeriesManipulateEmpty1}{\showpaste} +\tab{5}\spadcommand{f := series(1/(1-x),x = 0)\bound{f }} +\end{paste}\end{patch} + +\begin{patch}{ExSeriesManipulatePatch2} +\begin{paste}{ExSeriesManipulateFull2}{ExSeriesManipulateEmpty2} +\pastebutton{ExSeriesManipulateFull2}{\hidepaste} +\tab{5}\spadcommand{f ** 2\free{f }} +\indentrel{3}\begin{verbatim} + (2) + 2 3 4 5 6 7 8 + 1 + 2x + 3x + 4x + 5x + 6x + 7x + 8x + 9x + + + 9 10 11 + 10x + 11x + O(x ) + Type: UnivariatePuiseuxSeries(Expression Integer,x,0) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ExSeriesManipulateEmpty2} +\begin{paste}{ExSeriesManipulateEmpty2}{ExSeriesManipulatePatch2} +\pastebutton{ExSeriesManipulateEmpty2}{\showpaste} +\tab{5}\spadcommand{f ** 2\free{f }} +\end{paste} +\end{patch} + @ \pagehead{ExSeriesFunctions}{exseries.ht}{Functions on Power Series} <>= @@ -7005,8 +17700,74 @@ and then apply these functions to the series: \spadpaste{g := log(f) \free{f1} \bound{g}} \spadpaste{exp(g) \free{g}} \endscroll -\autobuttons\end{page} +\autobuttons +\end{page} +\begin{patch}{ExSeriesFunctionsPatch1} +\begin{paste}{ExSeriesFunctionsFull1}{ExSeriesFunctionsEmpty1} +\pastebutton{ExSeriesFunctionsFull1}{\hidepaste} +\tab{5}\spadcommand{f := series(1/(1-x),x = 0)\bound{f1 }} +\indentrel{3}\begin{verbatim} + (1) + 2 3 4 5 6 7 8 9 10 + 1 + x + x + x + x + x + x + x + x + x + x + + + 11 + O(x ) + Type: UnivariatePuiseuxSeries(Expression Integer,x,0) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ExSeriesFunctionsEmpty1} +\begin{paste}{ExSeriesFunctionsEmpty1}{ExSeriesFunctionsPatch1} +\pastebutton{ExSeriesFunctionsEmpty1}{\showpaste} +\tab{5}\spadcommand{f := series(1/(1-x),x = 0)\bound{f1 }} +\end{paste}\end{patch} + +\begin{patch}{ExSeriesFunctionsPatch2} +\begin{paste}{ExSeriesFunctionsFull2}{ExSeriesFunctionsEmpty2} +\pastebutton{ExSeriesFunctionsFull2}{\hidepaste} +\tab{5}\spadcommand{g := log(f)\free{f1 }\bound{g }} +\indentrel{3}\begin{verbatim} + (2) + 1 2 1 3 1 4 1 5 1 6 1 7 1 8 + x + Ä x + Ä x + Ä x + Ä x + Ä x + Ä x + Ä x + 2 3 4 5 6 7 8 + + + 1 9 1 10 1 11 12 + Ä x + ÄÄ x + ÄÄ x + O(x ) + 9 10 11 + Type: UnivariatePuiseuxSeries(Expression Integer,x,0) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ExSeriesFunctionsEmpty2} +\begin{paste}{ExSeriesFunctionsEmpty2}{ExSeriesFunctionsPatch2} +\pastebutton{ExSeriesFunctionsEmpty2}{\showpaste} +\tab{5}\spadcommand{g := log(f)\free{f1 }\bound{g }} +\end{paste}\end{patch} + +\begin{patch}{ExSeriesFunctionsPatch3} +\begin{paste}{ExSeriesFunctionsFull3}{ExSeriesFunctionsEmpty3} +\pastebutton{ExSeriesFunctionsFull3}{\hidepaste} +\tab{5}\spadcommand{exp(g)\free{g }} +\indentrel{3}\begin{verbatim} + (3) + 2 3 4 5 6 7 8 9 10 + 1 + x + x + x + x + x + x + x + x + x + x + + + 11 + O(x ) + Type: UnivariatePuiseuxSeries(Expression Integer,x,0) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ExSeriesFunctionsEmpty3} +\begin{paste}{ExSeriesFunctionsEmpty3}{ExSeriesFunctionsPatch3} +\pastebutton{ExSeriesFunctionsEmpty3}{\showpaste} +\tab{5}\spadcommand{exp(g)\free{g }} +\end{paste}\end{patch} + @ \pagehead{ExSeriesSubstitution}{exseries.ht} {Substituting Numerical Values in Power Series} @@ -7024,7 +17785,51 @@ Now you evaluate the series at the value {\em 1.0}: \spadpaste{eval(f,1.0) \free{f2}} You get a sequence of partial sums. \endscroll -\autobuttons\end{page} +\autobuttons +\end{page} + +\begin{patch}{ExSeriesSubstitutionPatch1} +\begin{paste}{ExSeriesSubstitutionFull1}{ExSeriesSubstitutionEmpty1} +\pastebutton{ExSeriesSubstitutionFull1}{\hidepaste} +\tab{5}\spadcommand{f := taylor(exp(x))\bound{f2 }} +\indentrel{3}\begin{verbatim} + (1) + 1 2 1 3 1 4 1 5 1 6 + 1 + x + Ä x + Ä x + ÄÄ x + ÄÄÄ x + ÄÄÄ x + 2 6 24 120 720 + + + 1 7 1 8 1 9 1 10 11 + ÄÄÄÄ x + ÄÄÄÄÄ x + ÄÄÄÄÄÄ x + ÄÄÄÄÄÄÄ x + O(x ) + 5040 40320 362880 3628800 + Type: UnivariateTaylorSeries(Expression Integer,x,0) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ExSeriesSubstitutionEmpty1} +\begin{paste}{ExSeriesSubstitutionEmpty1}{ExSeriesSubstitutionPatch1} +\pastebutton{ExSeriesSubstitutionEmpty1}{\showpaste} +\tab{5}\spadcommand{f := taylor(exp(x))\bound{f2 }} +\end{paste}\end{patch} + +\begin{patch}{ExSeriesSubstitutionPatch2} +\begin{paste}{ExSeriesSubstitutionFull2}{ExSeriesSubstitutionEmpty2} +\pastebutton{ExSeriesSubstitutionFull2}{\hidepaste} +\tab{5}\spadcommand{eval(f,1.0)\free{f2 }} +\indentrel{3}\begin{verbatim} + (2) + [1.0, 2.0, 2.5, 2.6666666666 666666667, + 2.7083333333 333333333, 2.7166666666 666666667, + 2.7180555555 555555556, 2.7182539682 53968254, + 2.7182787698 412698413, 2.7182815255 731922399, ...] + Type: Stream Expression Float +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ExSeriesSubstitutionEmpty2} +\begin{paste}{ExSeriesSubstitutionEmpty2}{ExSeriesSubstitutionPatch2} +\pastebutton{ExSeriesSubstitutionEmpty2}{\showpaste} +\tab{5}\spadcommand{eval(f,1.0)\free{f2 }} +\end{paste}\end{patch} @ \section{exsum.ht} @@ -7040,7 +17845,40 @@ To sum the entries of a list, simply put {\em +/} in front of the list. For example, the following command will sum the integers from 1 to 15: \spadpaste{reduce(+,[i for i in 1..15])} \endscroll -\autobuttons\end{page} +\autobuttons +\end{page} + +\begin{patch}{ExSumListEntriesIPatch1} +\begin{paste}{ExSumListEntriesIFull1}{ExSumListEntriesIEmpty1} +\pastebutton{ExSumListEntriesIFull1}{\hidepaste} +\tab{5}\spadcommand{[i for i in 1..15]} +\indentrel{3}\begin{verbatim} + (1) [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15] + Type: List PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ExSumListEntriesIEmpty1} +\begin{paste}{ExSumListEntriesIEmpty1}{ExSumListEntriesIPatch1} +\pastebutton{ExSumListEntriesIEmpty1}{\showpaste} +\tab{5}\spadcommand{[i for i in 1..15]} +\end{paste}\end{patch} + +\begin{patch}{ExSumListEntriesIPatch2} +\begin{paste}{ExSumListEntriesIFull2}{ExSumListEntriesIEmpty2} +\pastebutton{ExSumListEntriesIFull2}{\hidepaste} +\tab{5}\spadcommand{reduce(+,[i for i in 1..15])} +\indentrel{3}\begin{verbatim} + (2) 120 + Type: PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ExSumListEntriesIEmpty2} +\begin{paste}{ExSumListEntriesIEmpty2}{ExSumListEntriesIPatch2} +\pastebutton{ExSumListEntriesIEmpty2}{\showpaste} +\tab{5}\spadcommand{reduce(+,[i for i in 1..15])} +\end{paste}\end{patch} @ \pagehead{ExSumListEntriesII}{exsum.ht}{Summing the Entries of a List II} @@ -7055,7 +17893,42 @@ the integers between {\em 5} and {\em 20}: You can also compute the sum of the entries of this list: \spadpaste{reduce(+,[n**2 for n in 5..20])} \endscroll -\autobuttons\end{page} +\autobuttons +\end{page} + +\begin{patch}{ExSumListEntriesIIPatch1} +\begin{paste}{ExSumListEntriesIIFull1}{ExSumListEntriesIIEmpty1} +\pastebutton{ExSumListEntriesIIFull1}{\hidepaste} +\tab{5}\spadcommand{[n**2 for n in 5..20]} +\indentrel{3}\begin{verbatim} + (1) + [25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, + 256, 289, 324, 361, 400] + Type: List PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ExSumListEntriesIIEmpty1} +\begin{paste}{ExSumListEntriesIIEmpty1}{ExSumListEntriesIIPatch1} +\pastebutton{ExSumListEntriesIIEmpty1}{\showpaste} +\tab{5}\spadcommand{[n**2 for n in 5..20]} +\end{paste}\end{patch} + +\begin{patch}{ExSumListEntriesIIPatch2} +\begin{paste}{ExSumListEntriesIIFull2}{ExSumListEntriesIIEmpty2} +\pastebutton{ExSumListEntriesIIFull2}{\hidepaste} +\tab{5}\spadcommand{reduce(+,[n**2 for n in 5..20])} +\indentrel{3}\begin{verbatim} + (2) 2840 + Type: PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ExSumListEntriesIIEmpty2} +\begin{paste}{ExSumListEntriesIIEmpty2}{ExSumListEntriesIIPatch2} +\pastebutton{ExSumListEntriesIIEmpty2}{\showpaste} +\tab{5}\spadcommand{reduce(+,[n**2 for n in 5..20])} +\end{paste}\end{patch} @ \pagehead{ExSumApproximateE}{exsum.ht}{Approximating $e$} @@ -7066,7 +17939,24 @@ You can obtain a numerical approximation of the number {\em e} by summing the entries of the following list: \spadpaste{reduce(+,[1.0/factorial(n) for n in 0..20])} \endscroll -\autobuttons\end{page} +\autobuttons +\end{page} + +\begin{patch}{ExSumApproximateEPatch1} +\begin{paste}{ExSumApproximateEFull1}{ExSumApproximateEEmpty1} +\pastebutton{ExSumApproximateEFull1}{\hidepaste} +\tab{5}\spadcommand{reduce(+,[1.0/factorial(n) for n in 0..20])} +\indentrel{3}\begin{verbatim} + (1) 2.7182818284 590452354 + Type: Float +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ExSumApproximateEEmpty1} +\begin{paste}{ExSumApproximateEEmpty1}{ExSumApproximateEPatch1} +\pastebutton{ExSumApproximateEEmpty1}{\showpaste} +\tab{5}\spadcommand{reduce(+,[1.0/factorial(n) for n in 0..20])} +\end{paste}\end{patch} @ \pagehead{ExSumClosedForm}{exsum.ht}{Closed Form Summations} @@ -7088,7 +17978,59 @@ for {\em a} and {\em b} in our formula: \spadpaste{eval(s,[a,b],[1,25]) \free{s}} \spadpaste{reduce(+,[i**2 for i in 1..25])} \endscroll -\autobuttons\end{page} +\autobuttons +\end{page} + +\begin{patch}{ExSumClosedFormPatch1} +\begin{paste}{ExSumClosedFormFull1}{ExSumClosedFormEmpty1} +\pastebutton{ExSumClosedFormFull1}{\hidepaste} +\tab{5}\spadcommand{s := sum(k**2,k = a..b)\bound{s }} +\indentrel{3}\begin{verbatim} + 3 2 3 2 + 2b + 3b + b - 2a + 3a - a + (1) ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ + 6 + Type: Fraction Polynomial Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ExSumClosedFormEmpty1} +\begin{paste}{ExSumClosedFormEmpty1}{ExSumClosedFormPatch1} +\pastebutton{ExSumClosedFormEmpty1}{\showpaste} +\tab{5}\spadcommand{s := sum(k**2,k = a..b)\bound{s }} +\end{paste}\end{patch} + +\begin{patch}{ExSumClosedFormPatch2} +\begin{paste}{ExSumClosedFormFull2}{ExSumClosedFormEmpty2} +\pastebutton{ExSumClosedFormFull2}{\hidepaste} +\tab{5}\spadcommand{eval(s,[a,b],[1,25])\free{s }} +\indentrel{3}\begin{verbatim} + (2) 5525 + Type: Fraction Polynomial Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ExSumClosedFormEmpty2} +\begin{paste}{ExSumClosedFormEmpty2}{ExSumClosedFormPatch2} +\pastebutton{ExSumClosedFormEmpty2}{\showpaste} +\tab{5}\spadcommand{eval(s,[a,b],[1,25])\free{s }} +\end{paste}\end{patch} + +\begin{patch}{ExSumClosedFormPatch3} +\begin{paste}{ExSumClosedFormFull3}{ExSumClosedFormEmpty3} +\pastebutton{ExSumClosedFormFull3}{\hidepaste} +\tab{5}\spadcommand{reduce(+,[i**2 for i in 1..25])} +\indentrel{3}\begin{verbatim} + (3) 5525 + Type: PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ExSumClosedFormEmpty3} +\begin{paste}{ExSumClosedFormEmpty3}{ExSumClosedFormPatch3} +\pastebutton{ExSumClosedFormEmpty3}{\showpaste} +\tab{5}\spadcommand{reduce(+,[i**2 for i in 1..25])} +\end{paste}\end{patch} @ \pagehead{ExSumCubes}{exsum.ht}{Sums of Cubes} @@ -7102,7 +18044,46 @@ Then compute the square of the sum of the integers from {\em 1} to {\em n}: \spadpaste{sum(k,k = 1..n) ** 2} The answers are the same. \endscroll -\autobuttons\end{page} +\autobuttons +\end{page} + +\begin{patch}{ExSumCubesPatch1} +\begin{paste}{ExSumCubesFull1}{ExSumCubesEmpty1} +\pastebutton{ExSumCubesFull1}{\hidepaste} +\tab{5}\spadcommand{sum(k**3,k = 1..n)} +\indentrel{3}\begin{verbatim} + 4 3 2 + n + 2n + n + (1) ÄÄÄÄÄÄÄÄÄÄÄÄÄ + 4 + Type: Fraction Polynomial Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ExSumCubesEmpty1} +\begin{paste}{ExSumCubesEmpty1}{ExSumCubesPatch1} +\pastebutton{ExSumCubesEmpty1}{\showpaste} +\tab{5}\spadcommand{sum(k**3,k = 1..n)} +\end{paste}\end{patch} + +\begin{patch}{ExSumCubesPatch2} +\begin{paste}{ExSumCubesFull2}{ExSumCubesEmpty2} +\pastebutton{ExSumCubesFull2}{\hidepaste} +\tab{5}\spadcommand{sum(k,k = 1..n) ** 2} +\indentrel{3}\begin{verbatim} + 4 3 2 + n + 2n + n + (2) ÄÄÄÄÄÄÄÄÄÄÄÄÄ + 4 + Type: Fraction Polynomial Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ExSumCubesEmpty2} +\begin{paste}{ExSumCubesEmpty2}{ExSumCubesPatch2} +\pastebutton{ExSumCubesEmpty2}{\showpaste} +\tab{5}\spadcommand{sum(k,k = 1..n) ** 2} +\end{paste}\end{patch} @ \pagehead{ExSumPolynomial}{exsum.ht}{Sums of Polynomials} @@ -7114,7 +18095,34 @@ when {\em f} is any polynomial in {\em k}, even one with parameters. \spadpaste{sum(3*k**2/(c**2 + 1) + 12*k/d,k = (3*a)..(4*b))} \endscroll -\autobuttons\end{page} +\autobuttons +\end{page} + +\begin{patch}{ExSumPolynomialPatch1} +\begin{paste}{ExSumPolynomialFull1}{ExSumPolynomialEmpty1} +\pastebutton{ExSumPolynomialFull1}{\hidepaste} +\tab{5}\spadcommand{sum(3*k**2/(c**2 + 1) + 12*k/d,k = (3*a)..(4*b))} +\indentrel{3}\begin{verbatim} + (1) + 3 2 3 2 + (128b + 48b + 4b - 54a + 27a - 3a)d + + + 2 2 2 2 2 + (192b + 48b - 108a + 36a)c + 192b + 48b - 108a + + + 36a + / + 2 + (2c + 2)d + Type: Union(Fraction Polynomial Integer,...) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ExSumPolynomialEmpty1} +\begin{paste}{ExSumPolynomialEmpty1}{ExSumPolynomialPatch1} +\pastebutton{ExSumPolynomialEmpty1}{\showpaste} +\tab{5}\spadcommand{sum(3*k**2/(c**2 + 1) + 12*k/d,k = (3*a)..(4*b))} +\end{paste}\end{patch} @ \begin{verbatim} @@ -7141,7 +18149,28 @@ f which are not rational functions in {\em k}. Here's an example: \spadpaste{sum(k * x**k,k = 1..n)} \endscroll -\autobuttons\end{page} +\autobuttons +\end{page} + +\begin{patch}{ExSumGeneralFunctionPatch1} +\begin{paste}{ExSumGeneralFunctionFull1}{ExSumGeneralFunctionEmpty1} +\pastebutton{ExSumGeneralFunctionFull1}{\hidepaste} +\tab{5}\spadcommand{sum(k * x**k,k = 1..n)} +\indentrel{3}\begin{verbatim} + 2 n + (n x + (- n - 1)x)x + x + (1) ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ + 2 + x - 2x + 1 + Type: Expression Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ExSumGeneralFunctionEmpty1} +\begin{paste}{ExSumGeneralFunctionEmpty1}{ExSumGeneralFunctionPatch1} +\pastebutton{ExSumGeneralFunctionEmpty1}{\showpaste} +\tab{5}\spadcommand{sum(k * x**k,k = 1..n)} +\end{paste}\end{patch} @ \pagehead{ExSumInfinite}{exsum.ht}{Infinite Sums} @@ -7157,7 +18186,26 @@ ranges from Use {\em \%plusInfinity} to denote `plus infinity'. \spadpaste{limit( sum(1/(k * (k + 2)),k = 1..n) ,n = \%plusInfinity)} \endscroll -\autobuttons\end{page} +\autobuttons +\end{page} + +\begin{patch}{ExSumInfinitePatch1} +\begin{paste}{ExSumInfiniteFull1}{ExSumInfiniteEmpty1} +\pastebutton{ExSumInfiniteFull1}{\hidepaste} +\tab{5}\spadcommand{limit( sum(1/(k * (k + 2)),k = 1..n) ,n = \%plusInfinity)} +\indentrel{3}\begin{verbatim} + 3 + (1) Ä + 4 +Type: Union(OrderedCompletion Fraction Polynomial Integer,...) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ExSumInfiniteEmpty1} +\begin{paste}{ExSumInfiniteEmpty1}{ExSumInfinitePatch1} +\pastebutton{ExSumInfiniteEmpty1}{\showpaste} +\tab{5}\spadcommand{limit( sum(1/(k * (k + 2)),k = 1..n) ,n = \%plusInfinity)} +\end{paste}\end{patch} @ \section{farray.ht} @@ -7284,7 +18332,264 @@ The previous value is returned. \endscroll \autobuttons \end{page} -% + +\begin{patch}{FlexibleArrayXmpPagePatch1} +\begin{paste}{FlexibleArrayXmpPageFull1}{FlexibleArrayXmpPageEmpty1} +\pastebutton{FlexibleArrayXmpPageFull1}{\hidepaste} +\tab{5}\spadcommand{flexibleArray [i for i in 1..6]} +\indentrel{3}\begin{verbatim} + (1) [1,2,3,4,5,6] + Type: FlexibleArray PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{FlexibleArrayXmpPageEmpty1} +\begin{paste}{FlexibleArrayXmpPageEmpty1}{FlexibleArrayXmpPagePatch1} +\pastebutton{FlexibleArrayXmpPageEmpty1}{\showpaste} +\tab{5}\spadcommand{flexibleArray [i for i in 1..6]} +\end{paste}\end{patch} + +\begin{patch}{FlexibleArrayXmpPagePatch2} +\begin{paste}{FlexibleArrayXmpPageFull2}{FlexibleArrayXmpPageEmpty2} +\pastebutton{FlexibleArrayXmpPageFull2}{\hidepaste} +\tab{5}\spadcommand{f : FARRAY INT := new(6,0)\bound{f }} +\indentrel{3}\begin{verbatim} + (2) [0,0,0,0,0,0] + Type: FlexibleArray Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{FlexibleArrayXmpPageEmpty2} +\begin{paste}{FlexibleArrayXmpPageEmpty2}{FlexibleArrayXmpPagePatch2} +\pastebutton{FlexibleArrayXmpPageEmpty2}{\showpaste} +\tab{5}\spadcommand{f : FARRAY INT := new(6,0)\bound{f }} +\end{paste}\end{patch} + +\begin{patch}{FlexibleArrayXmpPagePatch3} +\begin{paste}{FlexibleArrayXmpPageFull3}{FlexibleArrayXmpPageEmpty3} +\pastebutton{FlexibleArrayXmpPageFull3}{\hidepaste} +\tab{5}\spadcommand{for i in 1..6 repeat f.i := i; f\bound{f1 }\free{f }} +\indentrel{3}\begin{verbatim} + (3) [1,2,3,4,5,6] + Type: FlexibleArray Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{FlexibleArrayXmpPageEmpty3} +\begin{paste}{FlexibleArrayXmpPageEmpty3}{FlexibleArrayXmpPagePatch3} +\pastebutton{FlexibleArrayXmpPageEmpty3}{\showpaste} +\tab{5}\spadcommand{for i in 1..6 repeat f.i := i; f\bound{f1 }\free{f }} +\end{paste}\end{patch} + +\begin{patch}{FlexibleArrayXmpPagePatch4} +\begin{paste}{FlexibleArrayXmpPageFull4}{FlexibleArrayXmpPageEmpty4} +\pastebutton{FlexibleArrayXmpPageFull4}{\hidepaste} +\tab{5}\spadcommand{physicalLength f\free{f1 }} +\indentrel{3}\begin{verbatim} + (4) 6 + Type: PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{FlexibleArrayXmpPageEmpty4} +\begin{paste}{FlexibleArrayXmpPageEmpty4}{FlexibleArrayXmpPagePatch4} +\pastebutton{FlexibleArrayXmpPageEmpty4}{\showpaste} +\tab{5}\spadcommand{physicalLength f\free{f1 }} +\end{paste}\end{patch} + +\begin{patch}{FlexibleArrayXmpPagePatch5} +\begin{paste}{FlexibleArrayXmpPageFull5}{FlexibleArrayXmpPageEmpty5} +\pastebutton{FlexibleArrayXmpPageFull5}{\hidepaste} +\tab{5}\spadcommand{concat!(f,11)\bound{f2 }\free{f1 }} +\indentrel{3}\begin{verbatim} + (5) [1,2,3,4,5,6,11] + Type: FlexibleArray Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{FlexibleArrayXmpPageEmpty5} +\begin{paste}{FlexibleArrayXmpPageEmpty5}{FlexibleArrayXmpPagePatch5} +\pastebutton{FlexibleArrayXmpPageEmpty5}{\showpaste} +\tab{5}\spadcommand{concat!(f,11)\bound{f2 }\free{f1 }} +\end{paste}\end{patch} + +\begin{patch}{FlexibleArrayXmpPagePatch6} +\begin{paste}{FlexibleArrayXmpPageFull6}{FlexibleArrayXmpPageEmpty6} +\pastebutton{FlexibleArrayXmpPageFull6}{\hidepaste} +\tab{5}\spadcommand{physicalLength f\free{f2 }} +\indentrel{3}\begin{verbatim} + (6) 10 + Type: PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{FlexibleArrayXmpPageEmpty6} +\begin{paste}{FlexibleArrayXmpPageEmpty6}{FlexibleArrayXmpPagePatch6} +\pastebutton{FlexibleArrayXmpPageEmpty6}{\showpaste} +\tab{5}\spadcommand{physicalLength f\free{f2 }} +\end{paste}\end{patch} + +\begin{patch}{FlexibleArrayXmpPagePatch7} +\begin{paste}{FlexibleArrayXmpPageFull7}{FlexibleArrayXmpPageEmpty7} +\pastebutton{FlexibleArrayXmpPageFull7}{\hidepaste} +\tab{5}\spadcommand{physicalLength!(f,15)\bound{f3 }\free{f2 }} +\indentrel{3}\begin{verbatim} + (7) [1,2,3,4,5,6,11] + Type: FlexibleArray Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{FlexibleArrayXmpPageEmpty7} +\begin{paste}{FlexibleArrayXmpPageEmpty7}{FlexibleArrayXmpPagePatch7} +\pastebutton{FlexibleArrayXmpPageEmpty7}{\showpaste} +\tab{5}\spadcommand{physicalLength!(f,15)\bound{f3 }\free{f2 }} +\end{paste}\end{patch} + +\begin{patch}{FlexibleArrayXmpPagePatch8} +\begin{paste}{FlexibleArrayXmpPageFull8}{FlexibleArrayXmpPageEmpty8} +\pastebutton{FlexibleArrayXmpPageFull8}{\hidepaste} +\tab{5}\spadcommand{concat!(f,f)\bound{f4 }\free{f3 }} +\indentrel{3}\begin{verbatim} + (8) [1,2,3,4,5,6,11,1,2,3,4,5,6,11] + Type: FlexibleArray Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{FlexibleArrayXmpPageEmpty8} +\begin{paste}{FlexibleArrayXmpPageEmpty8}{FlexibleArrayXmpPagePatch8} +\pastebutton{FlexibleArrayXmpPageEmpty8}{\showpaste} +\tab{5}\spadcommand{concat!(f,f)\bound{f4 }\free{f3 }} +\end{paste}\end{patch} + +\begin{patch}{FlexibleArrayXmpPagePatch9} +\begin{paste}{FlexibleArrayXmpPageFull9}{FlexibleArrayXmpPageEmpty9} +\pastebutton{FlexibleArrayXmpPageFull9}{\hidepaste} +\tab{5}\spadcommand{insert!(22,f,1)\bound{f5 }\free{f4 }} +\indentrel{3}\begin{verbatim} + (9) [22,1,2,3,4,5,6,11,1,2,3,4,5,6,11] + Type: FlexibleArray Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{FlexibleArrayXmpPageEmpty9} +\begin{paste}{FlexibleArrayXmpPageEmpty9}{FlexibleArrayXmpPagePatch9} +\pastebutton{FlexibleArrayXmpPageEmpty9}{\showpaste} +\tab{5}\spadcommand{insert!(22,f,1)\bound{f5 }\free{f4 }} +\end{paste}\end{patch} + +\begin{patch}{FlexibleArrayXmpPagePatch10} +\begin{paste}{FlexibleArrayXmpPageFull10}{FlexibleArrayXmpPageEmpty10} +\pastebutton{FlexibleArrayXmpPageFull10}{\hidepaste} +\tab{5}\spadcommand{g := f(10..)\bound{g }\free{f5 }} +\indentrel{3}\begin{verbatim} + (10) [2,3,4,5,6,11] + Type: FlexibleArray Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{FlexibleArrayXmpPageEmpty10} +\begin{paste}{FlexibleArrayXmpPageEmpty10}{FlexibleArrayXmpPagePatch10} +\pastebutton{FlexibleArrayXmpPageEmpty10}{\showpaste} +\tab{5}\spadcommand{g := f(10..)\bound{g }\free{f5 }} +\end{paste}\end{patch} + +\begin{patch}{FlexibleArrayXmpPagePatch11} +\begin{paste}{FlexibleArrayXmpPageFull11}{FlexibleArrayXmpPageEmpty11} +\pastebutton{FlexibleArrayXmpPageFull11}{\hidepaste} +\tab{5}\spadcommand{insert!(g,f,1)\bound{g1 }\free{g f5 }} +\indentrel{3}\begin{verbatim} + (11) [2,3,4,5,6,11,22,1,2,3,4,5,6,11,1,2,3,4,5,6,11] + Type: FlexibleArray Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{FlexibleArrayXmpPageEmpty11} +\begin{paste}{FlexibleArrayXmpPageEmpty11}{FlexibleArrayXmpPagePatch11} +\pastebutton{FlexibleArrayXmpPageEmpty11}{\showpaste} +\tab{5}\spadcommand{insert!(g,f,1)\bound{g1 }\free{g f5 }} +\end{paste}\end{patch} + +\begin{patch}{FlexibleArrayXmpPagePatch12} +\begin{paste}{FlexibleArrayXmpPageFull12}{FlexibleArrayXmpPageEmpty12} +\pastebutton{FlexibleArrayXmpPageFull12}{\hidepaste} +\tab{5}\spadcommand{merge!(sort! f, sort! g)\bound{f6 }\free{g f5 }} +\indentrel{3}\begin{verbatim} + (12) + [1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, + 6, 6, 6, 6, 11, 11, 11, 11, 22] + Type: FlexibleArray Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{FlexibleArrayXmpPageEmpty12} +\begin{paste}{FlexibleArrayXmpPageEmpty12}{FlexibleArrayXmpPagePatch12} +\pastebutton{FlexibleArrayXmpPageEmpty12}{\showpaste} +\tab{5}\spadcommand{merge!(sort! f, sort! g)\bound{f6 }\free{g f5 }} +\end{paste}\end{patch} + +\begin{patch}{FlexibleArrayXmpPagePatch13} +\begin{paste}{FlexibleArrayXmpPageFull13}{FlexibleArrayXmpPageEmpty13} +\pastebutton{FlexibleArrayXmpPageFull13}{\hidepaste} +\tab{5}\spadcommand{removeDuplicates! f\bound{f7 }\free{f6 }} +\indentrel{3}\begin{verbatim} + (13) [1,2,3,4,5,6,11,22] + Type: FlexibleArray Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{FlexibleArrayXmpPageEmpty13} +\begin{paste}{FlexibleArrayXmpPageEmpty13}{FlexibleArrayXmpPagePatch13} +\pastebutton{FlexibleArrayXmpPageEmpty13}{\showpaste} +\tab{5}\spadcommand{removeDuplicates! f\bound{f7 }\free{f6 }} +\end{paste}\end{patch} + +\begin{patch}{FlexibleArrayXmpPagePatch14} +\begin{paste}{FlexibleArrayXmpPageFull14}{FlexibleArrayXmpPageEmpty14} +\pastebutton{FlexibleArrayXmpPageFull14}{\hidepaste} +\tab{5}\spadcommand{select!(i +-> even? i,f)\bound{f8 }\free{f7 }} +\indentrel{3}\begin{verbatim} + (14) [2,4,6,22] + Type: FlexibleArray Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{FlexibleArrayXmpPageEmpty14} +\begin{paste}{FlexibleArrayXmpPageEmpty14}{FlexibleArrayXmpPagePatch14} +\pastebutton{FlexibleArrayXmpPageEmpty14}{\showpaste} +\tab{5}\spadcommand{select!(i +-> even? i,f)\bound{f8 }\free{f7 }} +\end{paste}\end{patch} + +\begin{patch}{FlexibleArrayXmpPagePatch15} +\begin{paste}{FlexibleArrayXmpPageFull15}{FlexibleArrayXmpPageEmpty15} +\pastebutton{FlexibleArrayXmpPageFull15}{\hidepaste} +\tab{5}\spadcommand{physicalLength f\free{b8 }} +\indentrel{3}\begin{verbatim} + (15) 8 + Type: PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{FlexibleArrayXmpPageEmpty15} +\begin{paste}{FlexibleArrayXmpPageEmpty15}{FlexibleArrayXmpPagePatch15} +\pastebutton{FlexibleArrayXmpPageEmpty15}{\showpaste} +\tab{5}\spadcommand{physicalLength f\free{b8 }} +\end{paste}\end{patch} + +\begin{patch}{FlexibleArrayXmpPagePatch16} +\begin{paste}{FlexibleArrayXmpPageFull16}{FlexibleArrayXmpPageEmpty16} +\pastebutton{FlexibleArrayXmpPageFull16}{\hidepaste} +\tab{5}\spadcommand{shrinkable(false)$FlexibleArray(Integer)} +\indentrel{3}\begin{verbatim} + (16) true + Type: Boolean +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{FlexibleArrayXmpPageEmpty16} +\begin{paste}{FlexibleArrayXmpPageEmpty16}{FlexibleArrayXmpPagePatch16} +\pastebutton{FlexibleArrayXmpPageEmpty16}{\showpaste} +\tab{5}\spadcommand{shrinkable(false)$FlexibleArray(Integer)} +\end{paste}\end{patch} @ \section{file.ht} @@ -7392,6 +18697,212 @@ For more information on related topics, see \autobuttons \end{page} +\begin{patch}{FileXmpPagePatch1} +\begin{paste}{FileXmpPageFull1}{FileXmpPageEmpty1} +\pastebutton{FileXmpPageFull1}{\hidepaste} +\tab{5}\spadcommand{ifile:File List Integer:=open("/tmp/jazz1","output")\bound{ifile }} +\indentrel{3}\begin{verbatim} + (1) "/tmp/jazz1" + Type: File List Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{FileXmpPageEmpty1} +\begin{paste}{FileXmpPageEmpty1}{FileXmpPagePatch1} +\pastebutton{FileXmpPageEmpty1}{\showpaste} +\tab{5}\spadcommand{ifile:File List Integer:=open("/tmp/jazz1","output")\bound{ifile }} +\end{paste}\end{patch} + +\begin{patch}{FileXmpPagePatch2} +\begin{paste}{FileXmpPageFull2}{FileXmpPageEmpty2} +\pastebutton{FileXmpPageFull2}{\hidepaste} +\tab{5}\spadcommand{write!(ifile, [-1,2,3])\free{ifile }\bound{ifile1 }} +\indentrel{3}\begin{verbatim} + (2) [- 1,2,3] + Type: List Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{FileXmpPageEmpty2} +\begin{paste}{FileXmpPageEmpty2}{FileXmpPagePatch2} +\pastebutton{FileXmpPageEmpty2}{\showpaste} +\tab{5}\spadcommand{write!(ifile, [-1,2,3])\free{ifile }\bound{ifile1 }} +\end{paste}\end{patch} + +\begin{patch}{FileXmpPagePatch3} +\begin{paste}{FileXmpPageFull3}{FileXmpPageEmpty3} +\pastebutton{FileXmpPageFull3}{\hidepaste} +\tab{5}\spadcommand{write!(ifile, [10,-10,0,111])\free{ifile1 }\bound{ifile2 }} +\indentrel{3}\begin{verbatim} + (3) [10,- 10,0,111] + Type: List Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{FileXmpPageEmpty3} +\begin{paste}{FileXmpPageEmpty3}{FileXmpPagePatch3} +\pastebutton{FileXmpPageEmpty3}{\showpaste} +\tab{5}\spadcommand{write!(ifile, [10,-10,0,111])\free{ifile1 }\bound{ifile2 }} +\end{paste}\end{patch} + +\begin{patch}{FileXmpPagePatch4} +\begin{paste}{FileXmpPageFull4}{FileXmpPageEmpty4} +\pastebutton{FileXmpPageFull4}{\hidepaste} +\tab{5}\spadcommand{write!(ifile, [7])\free{ifile2 }\bound{ifile3 }} +\indentrel{3}\begin{verbatim} + (4) [7] + Type: List Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{FileXmpPageEmpty4} +\begin{paste}{FileXmpPageEmpty4}{FileXmpPagePatch4} +\pastebutton{FileXmpPageEmpty4}{\showpaste} +\tab{5}\spadcommand{write!(ifile, [7])\free{ifile2 }\bound{ifile3 }} +\end{paste}\end{patch} + +\begin{patch}{FileXmpPagePatch5} +\begin{paste}{FileXmpPageFull5}{FileXmpPageEmpty5} +\pastebutton{FileXmpPageFull5}{\hidepaste} +\tab{5}\spadcommand{reopen!(ifile, "input")\free{ifile3 }\bound{ifile4 }} +\indentrel{3}\begin{verbatim} + (5) "/tmp/jazz1" + Type: File List Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{FileXmpPageEmpty5} +\begin{paste}{FileXmpPageEmpty5}{FileXmpPagePatch5} +\pastebutton{FileXmpPageEmpty5}{\showpaste} +\tab{5}\spadcommand{reopen!(ifile, "input")\free{ifile3 }\bound{ifile4 }} +\end{paste}\end{patch} + +\begin{patch}{FileXmpPagePatch6} +\begin{paste}{FileXmpPageFull6}{FileXmpPageEmpty6} +\pastebutton{FileXmpPageFull6}{\hidepaste} +\tab{5}\spadcommand{read! ifile\free{ifile4 }\bound{ifile5 }} +\indentrel{3}\begin{verbatim} + (6) [- 1,2,3] + Type: List Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{FileXmpPageEmpty6} +\begin{paste}{FileXmpPageEmpty6}{FileXmpPagePatch6} +\pastebutton{FileXmpPageEmpty6}{\showpaste} +\tab{5}\spadcommand{read! ifile\free{ifile4 }\bound{ifile5 }} +\end{paste}\end{patch} + +\begin{patch}{FileXmpPagePatch7} +\begin{paste}{FileXmpPageFull7}{FileXmpPageEmpty7} +\pastebutton{FileXmpPageFull7}{\hidepaste} +\tab{5}\spadcommand{read! ifile\free{ifile5 }\bound{ifile6 }} +\indentrel{3}\begin{verbatim} + (7) [10,- 10,0,111] + Type: List Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{FileXmpPageEmpty7} +\begin{paste}{FileXmpPageEmpty7}{FileXmpPagePatch7} +\pastebutton{FileXmpPageEmpty7}{\showpaste} +\tab{5}\spadcommand{read! ifile\free{ifile5 }\bound{ifile6 }} +\end{paste}\end{patch} + +\begin{patch}{FileXmpPagePatch8} +\begin{paste}{FileXmpPageFull8}{FileXmpPageEmpty8} +\pastebutton{FileXmpPageFull8}{\hidepaste} +\tab{5}\spadcommand{readIfCan! ifile\free{ifile6 }\bound{ifile7 }} +\indentrel{3}\begin{verbatim} + (8) [7] + Type: Union(List Integer,...) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{FileXmpPageEmpty8} +\begin{paste}{FileXmpPageEmpty8}{FileXmpPagePatch8} +\pastebutton{FileXmpPageEmpty8}{\showpaste} +\tab{5}\spadcommand{readIfCan! ifile\free{ifile6 }\bound{ifile7 }} +\end{paste}\end{patch} + +\begin{patch}{FileXmpPagePatch9} +\begin{paste}{FileXmpPageFull9}{FileXmpPageEmpty9} +\pastebutton{FileXmpPageFull9}{\hidepaste} +\tab{5}\spadcommand{readIfCan! ifile\free{ifile7 }\bound{ifile8 }} +\indentrel{3}\begin{verbatim} + (9) "failed" + Type: Union("failed",...) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{FileXmpPageEmpty9} +\begin{paste}{FileXmpPageEmpty9}{FileXmpPagePatch9} +\pastebutton{FileXmpPageEmpty9}{\showpaste} +\tab{5}\spadcommand{readIfCan! ifile\free{ifile7 }\bound{ifile8 }} +\end{paste}\end{patch} + +\begin{patch}{FileXmpPagePatch10} +\begin{paste}{FileXmpPageFull10}{FileXmpPageEmpty10} +\pastebutton{FileXmpPageFull10}{\hidepaste} +\tab{5}\spadcommand{iomode ifile\free{ifile }} +\indentrel{3}\begin{verbatim} + (10) "input" + Type: String +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{FileXmpPageEmpty10} +\begin{paste}{FileXmpPageEmpty10}{FileXmpPagePatch10} +\pastebutton{FileXmpPageEmpty10}{\showpaste} +\tab{5}\spadcommand{iomode ifile\free{ifile }} +\end{paste}\end{patch} + +\begin{patch}{FileXmpPagePatch11} +\begin{paste}{FileXmpPageFull11}{FileXmpPageEmpty11} +\pastebutton{FileXmpPageFull11}{\hidepaste} +\tab{5}\spadcommand{name ifile\free{ifile }} +\indentrel{3}\begin{verbatim} + (11) "/tmp/jazz1" + Type: FileName +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{FileXmpPageEmpty11} +\begin{paste}{FileXmpPageEmpty11}{FileXmpPagePatch11} +\pastebutton{FileXmpPageEmpty11}{\showpaste} +\tab{5}\spadcommand{name ifile\free{ifile }} +\end{paste}\end{patch} + +\begin{patch}{FileXmpPagePatch12} +\begin{paste}{FileXmpPageFull12}{FileXmpPageEmpty12} +\pastebutton{FileXmpPageFull12}{\hidepaste} +\tab{5}\spadcommand{close! ifile\free{ifile }\bound{ifileA }} +\indentrel{3}\begin{verbatim} + (12) "/tmp/jazz1" + Type: File List Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{FileXmpPageEmpty12} +\begin{paste}{FileXmpPageEmpty12}{FileXmpPagePatch12} +\pastebutton{FileXmpPageEmpty12}{\showpaste} +\tab{5}\spadcommand{close! ifile\free{ifile }\bound{ifileA }} +\end{paste}\end{patch} + +\begin{patch}{FileXmpPagePatch13} +\begin{paste}{FileXmpPageFull13}{FileXmpPageEmpty13} +\pastebutton{FileXmpPageFull13}{\hidepaste} +\tab{5}\spadcommand{)system rm /tmp/jazz1\free{ifileA }} +\indentrel{3}\begin{verbatim} +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{FileXmpPageEmpty13} +\begin{paste}{FileXmpPageEmpty13}{FileXmpPagePatch13} +\pastebutton{FileXmpPageEmpty13}{\showpaste} +\tab{5}\spadcommand{)system rm /tmp/jazz1\free{ifileA }} +\end{paste}\end{patch} + @ \section{float.ht} \pagehead{FloatXmpPage}{float.ht}{Float} @@ -7479,6 +18990,54 @@ numbers. \autobuttons \end{page} +\begin{patch}{ugxFloatIntroPagePatch1} +\begin{paste}{ugxFloatIntroPageFull1}{ugxFloatIntroPageEmpty1} +\pastebutton{ugxFloatIntroPageFull1}{\hidepaste} +\tab{5}\spadcommand{1.234} +\indentrel{3}\begin{verbatim} + (1) 1.234 + Type: Float +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxFloatIntroPageEmpty1} +\begin{paste}{ugxFloatIntroPageEmpty1}{ugxFloatIntroPagePatch1} +\pastebutton{ugxFloatIntroPageEmpty1}{\showpaste} +\tab{5}\spadcommand{1.234} +\end{paste}\end{patch} + +\begin{patch}{ugxFloatIntroPagePatch2} +\begin{paste}{ugxFloatIntroPageFull2}{ugxFloatIntroPageEmpty2} +\pastebutton{ugxFloatIntroPageFull2}{\hidepaste} +\tab{5}\spadcommand{1.234E2} +\indentrel{3}\begin{verbatim} + (2) 123.4 + Type: Float +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxFloatIntroPageEmpty2} +\begin{paste}{ugxFloatIntroPageEmpty2}{ugxFloatIntroPagePatch2} +\pastebutton{ugxFloatIntroPageEmpty2}{\showpaste} +\tab{5}\spadcommand{1.234E2} +\end{paste}\end{patch} + +\begin{patch}{ugxFloatIntroPagePatch3} +\begin{paste}{ugxFloatIntroPageFull3}{ugxFloatIntroPageEmpty3} +\pastebutton{ugxFloatIntroPageFull3}{\hidepaste} +\tab{5}\spadcommand{sqrt(1.2 + 2.3 / 3.4 ** 4.5)} +\indentrel{3}\begin{verbatim} + (3) 1.0996972790 671286226 + Type: Float +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxFloatIntroPageEmpty3} +\begin{paste}{ugxFloatIntroPageEmpty3}{ugxFloatIntroPagePatch3} +\pastebutton{ugxFloatIntroPageEmpty3}{\showpaste} +\tab{5}\spadcommand{sqrt(1.2 + 2.3 / 3.4 ** 4.5)} +\end{paste}\end{patch} + @ \pagehead{ugxFloatConvertPage}{float.ht}{Conversion Functions} \pageto{notitle}{ugTypesConvertPage} @@ -7590,6 +19149,292 @@ general, be represented exactly. \autobuttons \end{page} +\begin{patch}{ugxFloatConvertPagePatch1} +\begin{paste}{ugxFloatConvertPageFull1}{ugxFloatConvertPageEmpty1} +\pastebutton{ugxFloatConvertPageFull1}{\hidepaste} +\tab{5}\spadcommand{i := 3 :: Float\bound{i }} +\indentrel{3}\begin{verbatim} + (1) 3.0 + Type: Float +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxFloatConvertPageEmpty1} +\begin{paste}{ugxFloatConvertPageEmpty1}{ugxFloatConvertPagePatch1} +\pastebutton{ugxFloatConvertPageEmpty1}{\showpaste} +\tab{5}\spadcommand{i := 3 :: Float\bound{i }} +\end{paste}\end{patch} + +\begin{patch}{ugxFloatConvertPagePatch2} +\begin{paste}{ugxFloatConvertPageFull2}{ugxFloatConvertPageEmpty2} +\pastebutton{ugxFloatConvertPageFull2}{\hidepaste} +\tab{5}\spadcommand{i :: Integer\free{i }} +\indentrel{3}\begin{verbatim} + (2) 3 + Type: Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxFloatConvertPageEmpty2} +\begin{paste}{ugxFloatConvertPageEmpty2}{ugxFloatConvertPagePatch2} +\pastebutton{ugxFloatConvertPageEmpty2}{\showpaste} +\tab{5}\spadcommand{i :: Integer\free{i }} +\end{paste}\end{patch} + +\begin{patch}{ugxFloatConvertPagePatch3} +\begin{paste}{ugxFloatConvertPageFull3}{ugxFloatConvertPageEmpty3} +\pastebutton{ugxFloatConvertPageFull3}{\hidepaste} +\tab{5}\spadcommand{i :: Fraction Integer\free{i }} +\indentrel{3}\begin{verbatim} + (3) 3 + Type: Fraction Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxFloatConvertPageEmpty3} +\begin{paste}{ugxFloatConvertPageEmpty3}{ugxFloatConvertPagePatch3} +\pastebutton{ugxFloatConvertPageEmpty3}{\showpaste} +\tab{5}\spadcommand{i :: Fraction Integer\free{i }} +\end{paste}\end{patch} + +\begin{patch}{ugxFloatConvertPagePatch4} +\begin{paste}{ugxFloatConvertPageFull4}{ugxFloatConvertPageEmpty4} +\pastebutton{ugxFloatConvertPageFull4}{\hidepaste} +\tab{5}\spadcommand{r := 3/7 :: Float\bound{r }} +\indentrel{3}\begin{verbatim} + (4) 0.42857 14285 71428 57143 + Type: Float +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxFloatConvertPageEmpty4} +\begin{paste}{ugxFloatConvertPageEmpty4}{ugxFloatConvertPagePatch4} +\pastebutton{ugxFloatConvertPageEmpty4}{\showpaste} +\tab{5}\spadcommand{r := 3/7 :: Float\bound{r }} +\end{paste}\end{patch} + +\begin{patch}{ugxFloatConvertPagePatch5} +\begin{paste}{ugxFloatConvertPageFull5}{ugxFloatConvertPageEmpty5} +\pastebutton{ugxFloatConvertPageFull5}{\hidepaste} +\tab{5}\spadcommand{r :: Fraction Integer\free{r }} +\indentrel{3}\begin{verbatim} + 3 + (5) Ä + 7 + Type: Fraction Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxFloatConvertPageEmpty5} +\begin{paste}{ugxFloatConvertPageEmpty5}{ugxFloatConvertPagePatch5} +\pastebutton{ugxFloatConvertPageEmpty5}{\showpaste} +\tab{5}\spadcommand{r :: Fraction Integer\free{r }} +\end{paste}\end{patch} + +\begin{patch}{ugxFloatConvertPagePatch6} +\begin{paste}{ugxFloatConvertPageFull6}{ugxFloatConvertPageEmpty6} +\pastebutton{ugxFloatConvertPageFull6}{\hidepaste} +\tab{5}\spadcommand{r :: Integer\free{r }} +\indentrel{3}\begin{verbatim} + 0.42857 14285 71428 57143 +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxFloatConvertPageEmpty6} +\begin{paste}{ugxFloatConvertPageEmpty6}{ugxFloatConvertPagePatch6} +\pastebutton{ugxFloatConvertPageEmpty6}{\showpaste} +\tab{5}\spadcommand{r :: Integer\free{r }} +\end{paste}\end{patch} + +\begin{patch}{ugxFloatConvertPagePatch7} +\begin{paste}{ugxFloatConvertPageFull7}{ugxFloatConvertPageEmpty7} +\pastebutton{ugxFloatConvertPageFull7}{\hidepaste} +\tab{5}\spadcommand{truncate 3.6} +\indentrel{3}\begin{verbatim} + (6) 3.0 + Type: Float +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxFloatConvertPageEmpty7} +\begin{paste}{ugxFloatConvertPageEmpty7}{ugxFloatConvertPagePatch7} +\pastebutton{ugxFloatConvertPageEmpty7}{\showpaste} +\tab{5}\spadcommand{truncate 3.6} +\end{paste}\end{patch} + +\begin{patch}{ugxFloatConvertPagePatch8} +\begin{paste}{ugxFloatConvertPageFull8}{ugxFloatConvertPageEmpty8} +\pastebutton{ugxFloatConvertPageFull8}{\hidepaste} +\tab{5}\spadcommand{round 3.6} +\indentrel{3}\begin{verbatim} + (7) 4.0 + Type: Float +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxFloatConvertPageEmpty8} +\begin{paste}{ugxFloatConvertPageEmpty8}{ugxFloatConvertPagePatch8} +\pastebutton{ugxFloatConvertPageEmpty8}{\showpaste} +\tab{5}\spadcommand{round 3.6} +\end{paste}\end{patch} + +\begin{patch}{ugxFloatConvertPagePatch9} +\begin{paste}{ugxFloatConvertPageFull9}{ugxFloatConvertPageEmpty9} +\pastebutton{ugxFloatConvertPageFull9}{\hidepaste} +\tab{5}\spadcommand{truncate(-3.6)} +\indentrel{3}\begin{verbatim} + (8) - 3.0 + Type: Float +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxFloatConvertPageEmpty9} +\begin{paste}{ugxFloatConvertPageEmpty9}{ugxFloatConvertPagePatch9} +\pastebutton{ugxFloatConvertPageEmpty9}{\showpaste} +\tab{5}\spadcommand{truncate(-3.6)} +\end{paste}\end{patch} + +\begin{patch}{ugxFloatConvertPagePatch10} +\begin{paste}{ugxFloatConvertPageFull10}{ugxFloatConvertPageEmpty10} +\pastebutton{ugxFloatConvertPageFull10}{\hidepaste} +\tab{5}\spadcommand{round(-3.6)} +\indentrel{3}\begin{verbatim} + (9) - 4.0 + Type: Float +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxFloatConvertPageEmpty10} +\begin{paste}{ugxFloatConvertPageEmpty10}{ugxFloatConvertPagePatch10} +\pastebutton{ugxFloatConvertPageEmpty10}{\showpaste} +\tab{5}\spadcommand{round(-3.6)} +\end{paste}\end{patch} + +\begin{patch}{ugxFloatConvertPagePatch11} +\begin{paste}{ugxFloatConvertPageFull11}{ugxFloatConvertPageEmpty11} +\pastebutton{ugxFloatConvertPageFull11}{\hidepaste} +\tab{5}\spadcommand{fractionPart 3.6} +\indentrel{3}\begin{verbatim} + (10) 0.6 + Type: Float +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxFloatConvertPageEmpty11} +\begin{paste}{ugxFloatConvertPageEmpty11}{ugxFloatConvertPagePatch11} +\pastebutton{ugxFloatConvertPageEmpty11}{\showpaste} +\tab{5}\spadcommand{fractionPart 3.6} +\end{paste}\end{patch} + +\begin{patch}{ugxFloatConvertPagePatch12} +\begin{paste}{ugxFloatConvertPageFull12}{ugxFloatConvertPageEmpty12} +\pastebutton{ugxFloatConvertPageFull12}{\hidepaste} +\tab{5}\spadcommand{digits 40\bound{d40 }} +\indentrel{3}\begin{verbatim} + (11) 20 + Type: PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxFloatConvertPageEmpty12} +\begin{paste}{ugxFloatConvertPageEmpty12}{ugxFloatConvertPagePatch12} +\pastebutton{ugxFloatConvertPageEmpty12}{\showpaste} +\tab{5}\spadcommand{digits 40\bound{d40 }} +\end{paste}\end{patch} + +\begin{patch}{ugxFloatConvertPagePatch13} +\begin{paste}{ugxFloatConvertPageFull13}{ugxFloatConvertPageEmpty13} +\pastebutton{ugxFloatConvertPageFull13}{\hidepaste} +\tab{5}\spadcommand{sqrt 0.2} +\indentrel{3}\begin{verbatim} + (12) + 0.44721 35954 99957 93928 18347 33746 25524 70881 + Type: Float +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxFloatConvertPageEmpty13} +\begin{paste}{ugxFloatConvertPageEmpty13}{ugxFloatConvertPagePatch13} +\pastebutton{ugxFloatConvertPageEmpty13}{\showpaste} +\tab{5}\spadcommand{sqrt 0.2} +\end{paste}\end{patch} + +\begin{patch}{ugxFloatConvertPagePatch14} +\begin{paste}{ugxFloatConvertPageFull14}{ugxFloatConvertPageEmpty14} +\pastebutton{ugxFloatConvertPageFull14}{\hidepaste} +\tab{5}\spadcommand{pi()$Float\free{d40 }} +\indentrel{3}\begin{verbatim} + (13) + 3.14159 26535 89793 23846 26433 83279 50288 4197 + Type: Float +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxFloatConvertPageEmpty14} +\begin{paste}{ugxFloatConvertPageEmpty14}{ugxFloatConvertPagePatch14} +\pastebutton{ugxFloatConvertPageEmpty14}{\showpaste} +\tab{5}\spadcommand{pi()$Float\free{d40 }} +\end{paste}\end{patch} + +\begin{patch}{ugxFloatConvertPagePatch15} +\begin{paste}{ugxFloatConvertPageFull15}{ugxFloatConvertPageEmpty15} +\pastebutton{ugxFloatConvertPageFull15}{\hidepaste} +\tab{5}\spadcommand{digits 500\bound{d1000 }} +\indentrel{3}\begin{verbatim} + (14) 40 + Type: PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxFloatConvertPageEmpty15} +\begin{paste}{ugxFloatConvertPageEmpty15}{ugxFloatConvertPagePatch15} +\pastebutton{ugxFloatConvertPageEmpty15}{\showpaste} +\tab{5}\spadcommand{digits 500\bound{d1000 }} +\end{paste}\end{patch} + +\begin{patch}{ugxFloatConvertPagePatch16} +\begin{paste}{ugxFloatConvertPageFull16}{ugxFloatConvertPageEmpty16} +\pastebutton{ugxFloatConvertPageFull16}{\hidepaste} +\tab{5}\spadcommand{pi()$Float\free{d1000 }} +\indentrel{3}\begin{verbatim} + (15) + 3.14159 26535 89793 23846 26433 83279 50288 41971 69399 + 37510 58209 74944 59230 78164 06286 20899 86280 34825 + 34211 70679 82148 08651 32823 06647 09384 46095 50582 2 + 3172 53594 08128 48111 74502 84102 70193 85211 05559 64 + 462 29489 54930 38196 44288 10975 66593 34461 28475 648 + 23 37867 83165 27120 19091 45648 56692 34603 48610 4543 + 2 66482 13393 60726 02491 41273 72458 70066 06315 58817 + 48815 20920 96282 92540 91715 36436 78925 90360 01133 + 05305 48820 46652 13841 46951 94151 16094 33057 27036 5 + 7595 91953 09218 61173 81932 61179 31051 18548 07446 23 + 799 62749 56735 18857 52724 89122 79381 83011 9491 + Type: Float +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxFloatConvertPageEmpty16} +\begin{paste}{ugxFloatConvertPageEmpty16}{ugxFloatConvertPagePatch16} +\pastebutton{ugxFloatConvertPageEmpty16}{\showpaste} +\tab{5}\spadcommand{pi()$Float\free{d1000 }} +\end{paste}\end{patch} + +\begin{patch}{ugxFloatConvertPagePatch17} +\begin{paste}{ugxFloatConvertPageFull17}{ugxFloatConvertPageEmpty17} +\pastebutton{ugxFloatConvertPageFull17}{\hidepaste} +\tab{5}\spadcommand{digits 20} +\indentrel{3}\begin{verbatim} + (16) 500 + Type: PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxFloatConvertPageEmpty17} +\begin{paste}{ugxFloatConvertPageEmpty17}{ugxFloatConvertPagePatch17} +\pastebutton{ugxFloatConvertPageEmpty17}{\showpaste} +\tab{5}\spadcommand{digits 20} +\end{paste}\end{patch} + @ \pagehead{ugxFloatOutputPage}{float.ht}{Output Functions} <>= @@ -7654,6 +19499,133 @@ This resets the output printing to the default behavior. \autobuttons \end{page} +\begin{patch}{ugxFloatOutputPagePatch1} +\begin{paste}{ugxFloatOutputPageFull1}{ugxFloatOutputPageEmpty1} +\pastebutton{ugxFloatOutputPageFull1}{\hidepaste} +\tab{5}\spadcommand{outputSpacing 0; x := sqrt 0.2\bound{x }\bound{os0 }} +\indentrel{3}\begin{verbatim} + (1) 0.44721359549995793928 + Type: Float +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxFloatOutputPageEmpty1} +\begin{paste}{ugxFloatOutputPageEmpty1}{ugxFloatOutputPagePatch1} +\pastebutton{ugxFloatOutputPageEmpty1}{\showpaste} +\tab{5}\spadcommand{outputSpacing 0; x := sqrt 0.2\bound{x }\bound{os0 }} +\end{paste}\end{patch} + +\begin{patch}{ugxFloatOutputPagePatch2} +\begin{paste}{ugxFloatOutputPageFull2}{ugxFloatOutputPageEmpty2} +\pastebutton{ugxFloatOutputPageFull2}{\hidepaste} +\tab{5}\spadcommand{outputSpacing 5; x\bound{os5 }\free{x }} +\indentrel{3}\begin{verbatim} + (2) 0.44721 35954 99957 93928 + Type: Float +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxFloatOutputPageEmpty2} +\begin{paste}{ugxFloatOutputPageEmpty2}{ugxFloatOutputPagePatch2} +\pastebutton{ugxFloatOutputPageEmpty2}{\showpaste} +\tab{5}\spadcommand{outputSpacing 5; x\bound{os5 }\free{x }} +\end{paste}\end{patch} + +\begin{patch}{ugxFloatOutputPagePatch3} +\begin{paste}{ugxFloatOutputPageFull3}{ugxFloatOutputPageEmpty3} +\pastebutton{ugxFloatOutputPageFull3}{\hidepaste} +\tab{5}\spadcommand{y := x/10**10\bound{y }\free{x os5 }} +\indentrel{3}\begin{verbatim} + (3) 0.44721 35954 99957 93928 E -10 + Type: Float +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxFloatOutputPageEmpty3} +\begin{paste}{ugxFloatOutputPageEmpty3}{ugxFloatOutputPagePatch3} +\pastebutton{ugxFloatOutputPageEmpty3}{\showpaste} +\tab{5}\spadcommand{y := x/10**10\bound{y }\free{x os5 }} +\end{paste}\end{patch} + +\begin{patch}{ugxFloatOutputPagePatch4} +\begin{paste}{ugxFloatOutputPageFull4}{ugxFloatOutputPageEmpty4} +\pastebutton{ugxFloatOutputPageFull4}{\hidepaste} +\tab{5}\spadcommand{outputFloating(); x\bound{of }\free{os5 x }} +\indentrel{3}\begin{verbatim} + (4) 0.44721 35954 99957 93928 E 0 + Type: Float +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxFloatOutputPageEmpty4} +\begin{paste}{ugxFloatOutputPageEmpty4}{ugxFloatOutputPagePatch4} +\pastebutton{ugxFloatOutputPageEmpty4}{\showpaste} +\tab{5}\spadcommand{outputFloating(); x\bound{of }\free{os5 x }} +\end{paste}\end{patch} + +\begin{patch}{ugxFloatOutputPagePatch5} +\begin{paste}{ugxFloatOutputPageFull5}{ugxFloatOutputPageEmpty5} +\pastebutton{ugxFloatOutputPageFull5}{\hidepaste} +\tab{5}\spadcommand{outputFixed(); y\bound{ox }\free{os5 y }} +\indentrel{3}\begin{verbatim} + (5) 0.00000 00000 44721 35954 99957 93928 + Type: Float +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxFloatOutputPageEmpty5} +\begin{paste}{ugxFloatOutputPageEmpty5}{ugxFloatOutputPagePatch5} +\pastebutton{ugxFloatOutputPageEmpty5}{\showpaste} +\tab{5}\spadcommand{outputFixed(); y\bound{ox }\free{os5 y }} +\end{paste}\end{patch} + +\begin{patch}{ugxFloatOutputPagePatch6} +\begin{paste}{ugxFloatOutputPageFull6}{ugxFloatOutputPageEmpty6} +\pastebutton{ugxFloatOutputPageFull6}{\hidepaste} +\tab{5}\spadcommand{outputFloating 2; y\bound{of2 }\free{os5 y }} +\indentrel{3}\begin{verbatim} + (6) 0.45 E -10 + Type: Float +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxFloatOutputPageEmpty6} +\begin{paste}{ugxFloatOutputPageEmpty6}{ugxFloatOutputPagePatch6} +\pastebutton{ugxFloatOutputPageEmpty6}{\showpaste} +\tab{5}\spadcommand{outputFloating 2; y\bound{of2 }\free{os5 y }} +\end{paste}\end{patch} + +\begin{patch}{ugxFloatOutputPagePatch7} +\begin{paste}{ugxFloatOutputPageFull7}{ugxFloatOutputPageEmpty7} +\pastebutton{ugxFloatOutputPageFull7}{\hidepaste} +\tab{5}\spadcommand{outputFixed 2; x\bound{ox2 }\free{os5 x }} +\indentrel{3}\begin{verbatim} + (7) 0.45 + Type: Float +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxFloatOutputPageEmpty7} +\begin{paste}{ugxFloatOutputPageEmpty7}{ugxFloatOutputPagePatch7} +\pastebutton{ugxFloatOutputPageEmpty7}{\showpaste} +\tab{5}\spadcommand{outputFixed 2; x\bound{ox2 }\free{os5 x }} +\end{paste}\end{patch} + +\begin{patch}{ugxFloatOutputPagePatch8} +\begin{paste}{ugxFloatOutputPageFull8}{ugxFloatOutputPageEmpty8} +\pastebutton{ugxFloatOutputPageFull8}{\hidepaste} +\tab{5}\spadcommand{outputGeneral()} +\indentrel{3}\begin{verbatim} + Type: Void +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxFloatOutputPageEmpty8} +\begin{paste}{ugxFloatOutputPageEmpty8}{ugxFloatOutputPagePatch8} +\pastebutton{ugxFloatOutputPageEmpty8}{\showpaste} +\tab{5}\spadcommand{outputGeneral()} +\end{paste}\end{patch} + @ \pagehead{ugxFloatHilbertPage}{float.ht} {An Example: Determinant of a Hilbert Matrix} @@ -7724,7 +19696,191 @@ Reset \spadfunFrom{digits}{Float} to its default value. \autobuttons \end{page} -@ +\begin{patch}{ugxFloatHilbertPagePatch1} +\begin{paste}{ugxFloatHilbertPageFull1}{ugxFloatHilbertPageEmpty1} +\pastebutton{ugxFloatHilbertPageFull1}{\hidepaste} +\tab{5}\spadcommand{a: Matrix Fraction Integer := matrix [[1/(i+j+1) for j in 0..9] for i in 0..9]\bound{a }} +\indentrel{3}\begin{verbatim} + Ú 1 1 1 1 1 1 1 1 1¿ + ³1 Ä Ä Ä Ä Ä Ä Ä Ä Äij + ³ 2 3 4 5 6 7 8 9 10³ + ³ ³ + ³1 1 1 1 1 1 1 1 1 1³ + ³Ä Ä Ä Ä Ä Ä Ä Ä ÄÄ Äij + ³2 3 4 5 6 7 8 9 10 11³ + ³ ³ + ³1 1 1 1 1 1 1 1 1 1³ + ³Ä Ä Ä Ä Ä Ä Ä ÄÄ ÄÄ Äij + ³3 4 5 6 7 8 9 10 11 12³ + ³ ³ + ³1 1 1 1 1 1 1 1 1 1³ + ³Ä Ä Ä Ä Ä Ä ÄÄ ÄÄ ÄÄ Äij + ³4 5 6 7 8 9 10 11 12 13³ + ³ ³ + ³1 1 1 1 1 1 1 1 1 1³ + ³Ä Ä Ä Ä Ä ÄÄ ÄÄ ÄÄ ÄÄ Äij + ³5 6 7 8 9 10 11 12 13 14³ + (1) ³ ³ + ³1 1 1 1 1 1 1 1 1 1³ + ³Ä Ä Ä Ä ÄÄ ÄÄ ÄÄ ÄÄ ÄÄ Äij + ³6 7 8 9 10 11 12 13 14 15³ + ³ ³ + ³1 1 1 1 1 1 1 1 1 1³ + ³Ä Ä Ä ÄÄ ÄÄ ÄÄ ÄÄ ÄÄ ÄÄ Äij + ³7 8 9 10 11 12 13 14 15 16³ + ³ ³ + ³1 1 1 1 1 1 1 1 1 1³ + ³Ä Ä ÄÄ ÄÄ ÄÄ ÄÄ ÄÄ ÄÄ ÄÄ Äij + ³8 9 10 11 12 13 14 15 16 17³ + ³ ³ + ³1 1 1 1 1 1 1 1 1 1³ + ³Ä ÄÄ ÄÄ ÄÄ ÄÄ ÄÄ ÄÄ ÄÄ ÄÄ Äij + ³9 10 11 12 13 14 15 16 17 18³ + ³ ³ + ³ 1 1 1 1 1 1 1 1 1 1³ + ³ÄÄ ÄÄ ÄÄ ÄÄ ÄÄ ÄÄ ÄÄ ÄÄ ÄÄ Äij + À10 11 12 13 14 15 16 17 18 19Ù + Type: Matrix Fraction Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxFloatHilbertPageEmpty1} +\begin{paste}{ugxFloatHilbertPageEmpty1}{ugxFloatHilbertPagePatch1} +\pastebutton{ugxFloatHilbertPageEmpty1}{\showpaste} +\tab{5}\spadcommand{a: Matrix Fraction Integer := matrix [[1/(i+j+1) for j in 0..9] for i in 0..9]\bound{a }} +\end{paste}\end{patch} + +\begin{patch}{ugxFloatHilbertPagePatch2} +\begin{paste}{ugxFloatHilbertPageFull2}{ugxFloatHilbertPageEmpty2} +\pastebutton{ugxFloatHilbertPageFull2}{\hidepaste} +\tab{5}\spadcommand{d:= determinant a\free{a }\bound{d }} +\indentrel{3}\begin{verbatim} + (2) + 1 + ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ + 46206893947914691316295628839036278726983680000000000 + Type: Fraction Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxFloatHilbertPageEmpty2} +\begin{paste}{ugxFloatHilbertPageEmpty2}{ugxFloatHilbertPagePatch2} +\pastebutton{ugxFloatHilbertPageEmpty2}{\showpaste} +\tab{5}\spadcommand{d:= determinant a\free{a }\bound{d }} +\end{paste}\end{patch} + +\begin{patch}{ugxFloatHilbertPagePatch3} +\begin{paste}{ugxFloatHilbertPageFull3}{ugxFloatHilbertPageEmpty3} +\pastebutton{ugxFloatHilbertPageFull3}{\hidepaste} +\tab{5}\spadcommand{d :: Float\free{d }} +\indentrel{3}\begin{verbatim} + (3) 0.21641 79226 43149 18691 E -52 + Type: Float +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxFloatHilbertPageEmpty3} +\begin{paste}{ugxFloatHilbertPageEmpty3}{ugxFloatHilbertPagePatch3} +\pastebutton{ugxFloatHilbertPageEmpty3}{\showpaste} +\tab{5}\spadcommand{d :: Float\free{d }} +\end{paste}\end{patch} + +\begin{patch}{ugxFloatHilbertPagePatch4} +\begin{paste}{ugxFloatHilbertPageFull4}{ugxFloatHilbertPageEmpty4} +\pastebutton{ugxFloatHilbertPageFull4}{\hidepaste} +\tab{5}\spadcommand{b: Matrix DoubleFloat := matrix [[1/(i+j+1$DoubleFloat) for j in 0..9] for i in 0..9];\bound{b }} +\indentrel{3}\begin{verbatim} + Type: Matrix DoubleFloat +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxFloatHilbertPageEmpty4} +\begin{paste}{ugxFloatHilbertPageEmpty4}{ugxFloatHilbertPagePatch4} +\pastebutton{ugxFloatHilbertPageEmpty4}{\showpaste} +\tab{5}\spadcommand{b: Matrix DoubleFloat := matrix [[1/(i+j+1$DoubleFloat) for j in 0..9] for i in 0..9];\bound{b }} +\end{paste}\end{patch} + +\begin{patch}{ugxFloatHilbertPagePatch5} +\begin{paste}{ugxFloatHilbertPageFull5}{ugxFloatHilbertPageEmpty5} +\pastebutton{ugxFloatHilbertPageFull5}{\hidepaste} +\tab{5}\spadcommand{determinant b\free{b }} +\indentrel{3}\begin{verbatim} + (5) 2.1643677945721411e-53 + Type: DoubleFloat +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxFloatHilbertPageEmpty5} +\begin{paste}{ugxFloatHilbertPageEmpty5}{ugxFloatHilbertPagePatch5} +\pastebutton{ugxFloatHilbertPageEmpty5}{\showpaste} +\tab{5}\spadcommand{determinant b\free{b }} +\end{paste}\end{patch} + +\begin{patch}{ugxFloatHilbertPagePatch6} +\begin{paste}{ugxFloatHilbertPageFull6}{ugxFloatHilbertPageEmpty6} +\pastebutton{ugxFloatHilbertPageFull6}{\hidepaste} +\tab{5}\spadcommand{digits 40\bound{d40 }} +\indentrel{3}\begin{verbatim} + (6) 20 + Type: PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxFloatHilbertPageEmpty6} +\begin{paste}{ugxFloatHilbertPageEmpty6}{ugxFloatHilbertPagePatch6} +\pastebutton{ugxFloatHilbertPageEmpty6}{\showpaste} +\tab{5}\spadcommand{digits 40\bound{d40 }} +\end{paste}\end{patch} + +\begin{patch}{ugxFloatHilbertPagePatch7} +\begin{paste}{ugxFloatHilbertPageFull7}{ugxFloatHilbertPageEmpty7} +\pastebutton{ugxFloatHilbertPageFull7}{\hidepaste} +\tab{5}\spadcommand{c: Matrix Float := matrix [[1/(i+j+1$Float) for j in 0..9] for i in 0..9];\free{d40 }\bound{c }} +\indentrel{3}\begin{verbatim} + Type: Matrix Float +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxFloatHilbertPageEmpty7} +\begin{paste}{ugxFloatHilbertPageEmpty7}{ugxFloatHilbertPagePatch7} +\pastebutton{ugxFloatHilbertPageEmpty7}{\showpaste} +\tab{5}\spadcommand{c: Matrix Float := matrix [[1/(i+j+1$Float) for j in 0..9] for i in 0..9];\free{d40 }\bound{c }} +\end{paste}\end{patch} + +\begin{patch}{ugxFloatHilbertPagePatch8} +\begin{paste}{ugxFloatHilbertPageFull8}{ugxFloatHilbertPageEmpty8} +\pastebutton{ugxFloatHilbertPageFull8}{\hidepaste} +\tab{5}\spadcommand{determinant c\free{c }} +\indentrel{3}\begin{verbatim} + (8) + 0.21641 79226 43149 18690 60594 98362 26174 36159 E -52 + Type: Float +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxFloatHilbertPageEmpty8} +\begin{paste}{ugxFloatHilbertPageEmpty8}{ugxFloatHilbertPagePatch8} +\pastebutton{ugxFloatHilbertPageEmpty8}{\showpaste} +\tab{5}\spadcommand{determinant c\free{c }} +\end{paste}\end{patch} + +\begin{patch}{ugxFloatHilbertPagePatch9} +\begin{paste}{ugxFloatHilbertPageFull9}{ugxFloatHilbertPageEmpty9} +\pastebutton{ugxFloatHilbertPageFull9}{\hidepaste} +\tab{5}\spadcommand{digits 20} +\indentrel{3}\begin{verbatim} + (9) 40 + Type: PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxFloatHilbertPageEmpty9} +\begin{paste}{ugxFloatHilbertPageEmpty9}{ugxFloatHilbertPagePatch9} +\pastebutton{ugxFloatHilbertPageEmpty9}{\showpaste} +\tab{5}\spadcommand{digits 20} +\end{paste}\end{patch} + +f@ \section{fname.ht} \pagehead{FileNameXmpPage}{fname.ht}{FileName} <>= @@ -7855,6 +20011,293 @@ with the given extension, and the same defaults are used. \autobuttons \end{page} +\begin{patch}{FileNameXmpPagePatch1} +\begin{paste}{FileNameXmpPageFull1}{FileNameXmpPageEmpty1} +\pastebutton{FileNameXmpPageFull1}{\hidepaste} +\tab{5}\spadcommand{fn: FileName\bound{fndecl }} +\indentrel{3}\begin{verbatim} + Type: Void +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{FileNameXmpPageEmpty1} +\begin{paste}{FileNameXmpPageEmpty1}{FileNameXmpPagePatch1} +\pastebutton{FileNameXmpPageEmpty1}{\showpaste} +\tab{5}\spadcommand{fn: FileName\bound{fndecl }} +\end{paste}\end{patch} + +\begin{patch}{FileNameXmpPagePatch2} +\begin{paste}{FileNameXmpPageFull2}{FileNameXmpPageEmpty2} +\pastebutton{FileNameXmpPageFull2}{\hidepaste} +\tab{5}\spadcommand{fn := "/spad/src/input/fname.input"\free{fndecl }\bound{fn }} +\indentrel{3}\begin{verbatim} + (2) "/spad/src/input/fname.input" + Type: FileName +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{FileNameXmpPageEmpty2} +\begin{paste}{FileNameXmpPageEmpty2}{FileNameXmpPagePatch2} +\pastebutton{FileNameXmpPageEmpty2}{\showpaste} +\tab{5}\spadcommand{fn := "/spad/src/input/fname.input"\free{fndecl }\bound{fn }} +\end{paste}\end{patch} + +\begin{patch}{FileNameXmpPagePatch3} +\begin{paste}{FileNameXmpPageFull3}{FileNameXmpPageEmpty3} +\pastebutton{FileNameXmpPageFull3}{\hidepaste} +\tab{5}\spadcommand{directory fn\free{fn }} +\indentrel{3}\begin{verbatim} + (3) "/spad/src/input" + Type: String +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{FileNameXmpPageEmpty3} +\begin{paste}{FileNameXmpPageEmpty3}{FileNameXmpPagePatch3} +\pastebutton{FileNameXmpPageEmpty3}{\showpaste} +\tab{5}\spadcommand{directory fn\free{fn }} +\end{paste}\end{patch} + +\begin{patch}{FileNameXmpPagePatch4} +\begin{paste}{FileNameXmpPageFull4}{FileNameXmpPageEmpty4} +\pastebutton{FileNameXmpPageFull4}{\hidepaste} +\tab{5}\spadcommand{name fn\free{fn }} +\indentrel{3}\begin{verbatim} + (4) "fname" + Type: String +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{FileNameXmpPageEmpty4} +\begin{paste}{FileNameXmpPageEmpty4}{FileNameXmpPagePatch4} +\pastebutton{FileNameXmpPageEmpty4}{\showpaste} +\tab{5}\spadcommand{name fn\free{fn }} +\end{paste}\end{patch} + +\begin{patch}{FileNameXmpPagePatch5} +\begin{paste}{FileNameXmpPageFull5}{FileNameXmpPageEmpty5} +\pastebutton{FileNameXmpPageFull5}{\hidepaste} +\tab{5}\spadcommand{extension fn\free{fn }} +\indentrel{3}\begin{verbatim} + (5) "input" + Type: String +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{FileNameXmpPageEmpty5} +\begin{paste}{FileNameXmpPageEmpty5}{FileNameXmpPagePatch5} +\pastebutton{FileNameXmpPageEmpty5}{\showpaste} +\tab{5}\spadcommand{extension fn\free{fn }} +\end{paste}\end{patch} + +\begin{patch}{FileNameXmpPagePatch6} +\begin{paste}{FileNameXmpPageFull6}{FileNameXmpPageEmpty6} +\pastebutton{FileNameXmpPageFull6}{\hidepaste} +\tab{5}\spadcommand{fn := filename("/u/smwatt/work", "fname", "input")\free{fndecl }\bound{fn1 }} +\indentrel{3}\begin{verbatim} + (6) "/u/smwatt/work/fname.input" + Type: FileName +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{FileNameXmpPageEmpty6} +\begin{paste}{FileNameXmpPageEmpty6}{FileNameXmpPagePatch6} +\pastebutton{FileNameXmpPageEmpty6}{\showpaste} +\tab{5}\spadcommand{fn := filename("/u/smwatt/work", "fname", "input")\free{fndecl }\bound{fn1 }} +\end{paste}\end{patch} + +\begin{patch}{FileNameXmpPagePatch7} +\begin{paste}{FileNameXmpPageFull7}{FileNameXmpPageEmpty7} +\pastebutton{FileNameXmpPageFull7}{\hidepaste} +\tab{5}\spadcommand{objdir := "/tmp"\bound{objdir }} +\indentrel{3}\begin{verbatim} + (7) "/tmp" + Type: String +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{FileNameXmpPageEmpty7} +\begin{paste}{FileNameXmpPageEmpty7}{FileNameXmpPagePatch7} +\pastebutton{FileNameXmpPageEmpty7}{\showpaste} +\tab{5}\spadcommand{objdir := "/tmp"\bound{objdir }} +\end{paste}\end{patch} + +\begin{patch}{FileNameXmpPagePatch8} +\begin{paste}{FileNameXmpPageFull8}{FileNameXmpPageEmpty8} +\pastebutton{FileNameXmpPageFull8}{\hidepaste} +\tab{5}\spadcommand{fn := filename(objdir, "table", "spad")\free{fndecl objdir }\bound{fn2 }} +\indentrel{3}\begin{verbatim} + (8) "/tmp/table.spad" + Type: FileName +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{FileNameXmpPageEmpty8} +\begin{paste}{FileNameXmpPageEmpty8}{FileNameXmpPagePatch8} +\pastebutton{FileNameXmpPageEmpty8}{\showpaste} +\tab{5}\spadcommand{fn := filename(objdir, "table", "spad")\free{fndecl objdir }\bound{fn2 }} +\end{paste}\end{patch} + +\begin{patch}{FileNameXmpPagePatch9} +\begin{paste}{FileNameXmpPageFull9}{FileNameXmpPageEmpty9} +\pastebutton{FileNameXmpPageFull9}{\hidepaste} +\tab{5}\spadcommand{fn := filename("", "letter", "")\free{fndecl }\bound{fn3 }} +\indentrel{3}\begin{verbatim} + (9) "letter" + Type: FileName +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{FileNameXmpPageEmpty9} +\begin{paste}{FileNameXmpPageEmpty9}{FileNameXmpPagePatch9} +\pastebutton{FileNameXmpPageEmpty9}{\showpaste} +\tab{5}\spadcommand{fn := filename("", "letter", "")\free{fndecl }\bound{fn3 }} +\end{paste}\end{patch} + +\begin{patch}{FileNameXmpPagePatch10} +\begin{paste}{FileNameXmpPageFull10}{FileNameXmpPageEmpty10} +\pastebutton{FileNameXmpPageFull10}{\hidepaste} +\tab{5}\spadcommand{exists? "/etc/passwd"} +\indentrel{3}\begin{verbatim} + (10) true + Type: Boolean +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{FileNameXmpPageEmpty10} +\begin{paste}{FileNameXmpPageEmpty10}{FileNameXmpPagePatch10} +\pastebutton{FileNameXmpPageEmpty10}{\showpaste} +\tab{5}\spadcommand{exists? "/etc/passwd"} +\end{paste}\end{patch} + +\begin{patch}{FileNameXmpPagePatch11} +\begin{paste}{FileNameXmpPageFull11}{FileNameXmpPageEmpty11} +\pastebutton{FileNameXmpPageFull11}{\hidepaste} +\tab{5}\spadcommand{readable? "/etc/passwd"} +\indentrel{3}\begin{verbatim} + (11) true + Type: Boolean +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{FileNameXmpPageEmpty11} +\begin{paste}{FileNameXmpPageEmpty11}{FileNameXmpPagePatch11} +\pastebutton{FileNameXmpPageEmpty11}{\showpaste} +\tab{5}\spadcommand{readable? "/etc/passwd"} +\end{paste}\end{patch} + +\begin{patch}{FileNameXmpPagePatch12} +\begin{paste}{FileNameXmpPageFull12}{FileNameXmpPageEmpty12} +\pastebutton{FileNameXmpPageFull12}{\hidepaste} +\tab{5}\spadcommand{readable? "/etc/security/passwd"} +\indentrel{3}\begin{verbatim} + (12) false + Type: Boolean +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{FileNameXmpPageEmpty12} +\begin{paste}{FileNameXmpPageEmpty12}{FileNameXmpPagePatch12} +\pastebutton{FileNameXmpPageEmpty12}{\showpaste} +\tab{5}\spadcommand{readable? "/etc/security/passwd"} +\end{paste}\end{patch} + +\begin{patch}{FileNameXmpPagePatch13} +\begin{paste}{FileNameXmpPageFull13}{FileNameXmpPageEmpty13} +\pastebutton{FileNameXmpPageFull13}{\hidepaste} +\tab{5}\spadcommand{readable? "/ect/passwd"} +\indentrel{3}\begin{verbatim} + (13) false + Type: Boolean +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{FileNameXmpPageEmpty13} +\begin{paste}{FileNameXmpPageEmpty13}{FileNameXmpPagePatch13} +\pastebutton{FileNameXmpPageEmpty13}{\showpaste} +\tab{5}\spadcommand{readable? "/ect/passwd"} +\end{paste}\end{patch} + +\begin{patch}{FileNameXmpPagePatch14} +\begin{paste}{FileNameXmpPageFull14}{FileNameXmpPageEmpty14} +\pastebutton{FileNameXmpPageFull14}{\hidepaste} +\tab{5}\spadcommand{writable? "/etc/passwd"} +\indentrel{3}\begin{verbatim} + (14) false + Type: Boolean +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{FileNameXmpPageEmpty14} +\begin{paste}{FileNameXmpPageEmpty14}{FileNameXmpPagePatch14} +\pastebutton{FileNameXmpPageEmpty14}{\showpaste} +\tab{5}\spadcommand{writable? "/etc/passwd"} +\end{paste}\end{patch} + +\begin{patch}{FileNameXmpPagePatch15} +\begin{paste}{FileNameXmpPageFull15}{FileNameXmpPageEmpty15} +\pastebutton{FileNameXmpPageFull15}{\hidepaste} +\tab{5}\spadcommand{writable? "/dev/null"} +\indentrel{3}\begin{verbatim} + (15) true + Type: Boolean +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{FileNameXmpPageEmpty15} +\begin{paste}{FileNameXmpPageEmpty15}{FileNameXmpPagePatch15} +\pastebutton{FileNameXmpPageEmpty15}{\showpaste} +\tab{5}\spadcommand{writable? "/dev/null"} +\end{paste}\end{patch} + +\begin{patch}{FileNameXmpPagePatch16} +\begin{paste}{FileNameXmpPageFull16}{FileNameXmpPageEmpty16} +\pastebutton{FileNameXmpPageFull16}{\hidepaste} +\tab{5}\spadcommand{writable? "/etc/DoesNotExist"} +\indentrel{3}\begin{verbatim} + (16) false + Type: Boolean +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{FileNameXmpPageEmpty16} +\begin{paste}{FileNameXmpPageEmpty16}{FileNameXmpPagePatch16} +\pastebutton{FileNameXmpPageEmpty16}{\showpaste} +\tab{5}\spadcommand{writable? "/etc/DoesNotExist"} +\end{paste}\end{patch} + +\begin{patch}{FileNameXmpPagePatch17} +\begin{paste}{FileNameXmpPageFull17}{FileNameXmpPageEmpty17} +\pastebutton{FileNameXmpPageFull17}{\hidepaste} +\tab{5}\spadcommand{writable? "/tmp/DoesNotExist"} +\indentrel{3}\begin{verbatim} + (17) true + Type: Boolean +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{FileNameXmpPageEmpty17} +\begin{paste}{FileNameXmpPageEmpty17}{FileNameXmpPagePatch17} +\pastebutton{FileNameXmpPageEmpty17}{\showpaste} +\tab{5}\spadcommand{writable? "/tmp/DoesNotExist"} +\end{paste}\end{patch} + +\begin{patch}{FileNameXmpPagePatch18} +\begin{paste}{FileNameXmpPageFull18}{FileNameXmpPageEmpty18} +\pastebutton{FileNameXmpPageFull18}{\hidepaste} +\tab{5}\spadcommand{fn := new(objdir, "xxx", "yy")\free{objdir fndecl }\bound{fn4 }} +\indentrel{3}\begin{verbatim} + (18) "/tmp/xxx82222.yy" + Type: FileName +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{FileNameXmpPageEmpty18} +\begin{paste}{FileNameXmpPageEmpty18}{FileNameXmpPagePatch18} +\pastebutton{FileNameXmpPageEmpty18}{\showpaste} +\tab{5}\spadcommand{fn := new(objdir, "xxx", "yy")\free{objdir fndecl }\bound{fn4 }} +\end{paste}\end{patch} + @ \section{fr.ht} \pagehead{FactoredXmpPage}{fr.ht}{Factored} @@ -7970,6 +20413,156 @@ Neither of these operations returns the unit. \autobuttons \end{page} +\begin{patch}{ugxFactoredDecompPagePatch1} +\begin{paste}{ugxFactoredDecompPageFull1}{ugxFactoredDecompPageEmpty1} +\pastebutton{ugxFactoredDecompPageFull1}{\hidepaste} +\tab{5}\spadcommand{g := factor(4312)\bound{g }} +\indentrel{3}\begin{verbatim} + 3 2 + (1) 2 7 11 + Type: Factored Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxFactoredDecompPageEmpty1} +\begin{paste}{ugxFactoredDecompPageEmpty1}{ugxFactoredDecompPagePatch1} +\pastebutton{ugxFactoredDecompPageEmpty1}{\showpaste} +\tab{5}\spadcommand{g := factor(4312)\bound{g }} +\end{paste}\end{patch} + +\begin{patch}{ugxFactoredDecompPagePatch2} +\begin{paste}{ugxFactoredDecompPageFull2}{ugxFactoredDecompPageEmpty2} +\pastebutton{ugxFactoredDecompPageFull2}{\hidepaste} +\tab{5}\spadcommand{unit(g)\free{g }} +\indentrel{3}\begin{verbatim} + (2) 1 + Type: PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxFactoredDecompPageEmpty2} +\begin{paste}{ugxFactoredDecompPageEmpty2}{ugxFactoredDecompPagePatch2} +\pastebutton{ugxFactoredDecompPageEmpty2}{\showpaste} +\tab{5}\spadcommand{unit(g)\free{g }} +\end{paste}\end{patch} + +\begin{patch}{ugxFactoredDecompPagePatch3} +\begin{paste}{ugxFactoredDecompPageFull3}{ugxFactoredDecompPageEmpty3} +\pastebutton{ugxFactoredDecompPageFull3}{\hidepaste} +\tab{5}\spadcommand{numberOfFactors(g)\free{g }} +\indentrel{3}\begin{verbatim} + (3) 3 + Type: PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxFactoredDecompPageEmpty3} +\begin{paste}{ugxFactoredDecompPageEmpty3}{ugxFactoredDecompPagePatch3} +\pastebutton{ugxFactoredDecompPageEmpty3}{\showpaste} +\tab{5}\spadcommand{numberOfFactors(g)\free{g }} +\end{paste}\end{patch} + +\begin{patch}{ugxFactoredDecompPagePatch4} +\begin{paste}{ugxFactoredDecompPageFull4}{ugxFactoredDecompPageEmpty4} +\pastebutton{ugxFactoredDecompPageFull4}{\hidepaste} +\tab{5}\spadcommand{[nthFactor(g,i) for i in 1..numberOfFactors(g)]\free{g }} +\indentrel{3}\begin{verbatim} + (4) [2,7,11] + Type: List Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxFactoredDecompPageEmpty4} +\begin{paste}{ugxFactoredDecompPageEmpty4}{ugxFactoredDecompPagePatch4} +\pastebutton{ugxFactoredDecompPageEmpty4}{\showpaste} +\tab{5}\spadcommand{[nthFactor(g,i) for i in 1..numberOfFactors(g)]\free{g }} +\end{paste}\end{patch} + +\begin{patch}{ugxFactoredDecompPagePatch5} +\begin{paste}{ugxFactoredDecompPageFull5}{ugxFactoredDecompPageEmpty5} +\pastebutton{ugxFactoredDecompPageFull5}{\hidepaste} +\tab{5}\spadcommand{[nthExponent(g,i) for i in 1..numberOfFactors(g)]\free{g }} +\indentrel{3}\begin{verbatim} + (5) [3,2,1] + Type: List Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxFactoredDecompPageEmpty5} +\begin{paste}{ugxFactoredDecompPageEmpty5}{ugxFactoredDecompPagePatch5} +\pastebutton{ugxFactoredDecompPageEmpty5}{\showpaste} +\tab{5}\spadcommand{[nthExponent(g,i) for i in 1..numberOfFactors(g)]\free{g }} +\end{paste}\end{patch} + +\begin{patch}{ugxFactoredDecompPagePatch6} +\begin{paste}{ugxFactoredDecompPageFull6}{ugxFactoredDecompPageEmpty6} +\pastebutton{ugxFactoredDecompPageFull6}{\hidepaste} +\tab{5}\spadcommand{[nthFlag(g,i) for i in 1..numberOfFactors(g)]\free{g }} +\indentrel{3}\begin{verbatim} + (6) ["prime","prime","prime"] + Type: List Union("nil","sqfr","irred","prime") +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxFactoredDecompPageEmpty6} +\begin{paste}{ugxFactoredDecompPageEmpty6}{ugxFactoredDecompPagePatch6} +\pastebutton{ugxFactoredDecompPageEmpty6}{\showpaste} +\tab{5}\spadcommand{[nthFlag(g,i) for i in 1..numberOfFactors(g)]\free{g }} +\end{paste}\end{patch} + +\begin{patch}{ugxFactoredDecompPagePatch7} +\begin{paste}{ugxFactoredDecompPageFull7}{ugxFactoredDecompPageEmpty7} +\pastebutton{ugxFactoredDecompPageFull7}{\hidepaste} +\tab{5}\spadcommand{factorList(g)\free{g }} +\indentrel{3}\begin{verbatim} + (7) + [[flg= "prime",fctr= 2,xpnt= 3], + [flg= "prime",fctr= 7,xpnt= 2], + [flg= "prime",fctr= 11,xpnt= 1]] +Type: List Record(flg: Union("nil","sqfr","irred","prime"),fctr: Integer,xpnt: Integer) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxFactoredDecompPageEmpty7} +\begin{paste}{ugxFactoredDecompPageEmpty7}{ugxFactoredDecompPagePatch7} +\pastebutton{ugxFactoredDecompPageEmpty7}{\showpaste} +\tab{5}\spadcommand{factorList(g)\free{g }} +\end{paste}\end{patch} + +\begin{patch}{ugxFactoredDecompPagePatch8} +\begin{paste}{ugxFactoredDecompPageFull8}{ugxFactoredDecompPageEmpty8} +\pastebutton{ugxFactoredDecompPageFull8}{\hidepaste} +\tab{5}\spadcommand{factors(g)\free{g }\bound{prev1 }} +\indentrel{3}\begin{verbatim} + (8) + [[factor= 2,exponent= 3], [factor= 7,exponent= 2], + [factor= 11,exponent= 1]] + Type: List Record(factor: Integer,exponent: Integer) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxFactoredDecompPageEmpty8} +\begin{paste}{ugxFactoredDecompPageEmpty8}{ugxFactoredDecompPagePatch8} +\pastebutton{ugxFactoredDecompPageEmpty8}{\showpaste} +\tab{5}\spadcommand{factors(g)\free{g }\bound{prev1 }} +\end{paste}\end{patch} + +\begin{patch}{ugxFactoredDecompPagePatch9} +\begin{paste}{ugxFactoredDecompPageFull9}{ugxFactoredDecompPageEmpty9} +\pastebutton{ugxFactoredDecompPageFull9}{\hidepaste} +\tab{5}\spadcommand{first(\%).factor\free{prev1 }} +\indentrel{3}\begin{verbatim} + (9) 2 + Type: PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxFactoredDecompPageEmpty9} +\begin{paste}{ugxFactoredDecompPageEmpty9}{ugxFactoredDecompPagePatch9} +\pastebutton{ugxFactoredDecompPageEmpty9}{\showpaste} +\tab{5}\spadcommand{first(\%).factor\free{prev1 }} +\end{paste}\end{patch} + @ \pagehead{ugxFactoredExpandPage}{fr.ht}{Expanding Factored Objects} \pagepic{ps/v71ugxfactoredexpandpage.eps}{ugxFactoredExpandPage} @@ -8001,6 +20594,55 @@ but with multiplicity one, you could do it this way. \autobuttons \end{page} +\begin{patch}{ugxFactoredExpandPagePatch1} +\begin{paste}{ugxFactoredExpandPageFull1}{ugxFactoredExpandPageEmpty1} +\pastebutton{ugxFactoredExpandPageFull1}{\hidepaste} +\tab{5}\spadcommand{g := factor(4312)\bound{g }} +\indentrel{3}\begin{verbatim} + 3 2 + (1) 2 7 11 + Type: Factored Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxFactoredExpandPageEmpty1} +\begin{paste}{ugxFactoredExpandPageEmpty1}{ugxFactoredExpandPagePatch1} +\pastebutton{ugxFactoredExpandPageEmpty1}{\showpaste} +\tab{5}\spadcommand{g := factor(4312)\bound{g }} +\end{paste}\end{patch} + +\begin{patch}{ugxFactoredExpandPagePatch2} +\begin{paste}{ugxFactoredExpandPageFull2}{ugxFactoredExpandPageEmpty2} +\pastebutton{ugxFactoredExpandPageFull2}{\hidepaste} +\tab{5}\spadcommand{expand(g)\free{g }} +\indentrel{3}\begin{verbatim} + (2) 4312 + Type: PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxFactoredExpandPageEmpty2} +\begin{paste}{ugxFactoredExpandPageEmpty2}{ugxFactoredExpandPagePatch2} +\pastebutton{ugxFactoredExpandPageEmpty2}{\showpaste} +\tab{5}\spadcommand{expand(g)\free{g }} +\end{paste}\end{patch} + +\begin{patch}{ugxFactoredExpandPagePatch3} +\begin{paste}{ugxFactoredExpandPageFull3}{ugxFactoredExpandPageEmpty3} +\pastebutton{ugxFactoredExpandPageFull3}{\hidepaste} +\tab{5}\spadcommand{reduce(*,[t.factor for t in factors(g)])\free{g }} +\indentrel{3}\begin{verbatim} + (3) 154 + Type: PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxFactoredExpandPageEmpty3} +\begin{paste}{ugxFactoredExpandPageEmpty3}{ugxFactoredExpandPagePatch3} +\pastebutton{ugxFactoredExpandPageEmpty3}{\showpaste} +\tab{5}\spadcommand{reduce(*,[t.factor for t in factors(g)])\free{g }} +\end{paste}\end{patch} + @ \pagehead{ugxFactoredArithPage}{fr.ht}{Arithmetic with Factored Objects} \pagepic{ps/v71ugxfactoredarithpage.eps}{ugxFactoredArithPage} @@ -8084,6 +20726,238 @@ package calling \autobuttons \end{page} +\begin{patch}{ugxFactoredArithPagePatch1} +\begin{paste}{ugxFactoredArithPageFull1}{ugxFactoredArithPageEmpty1} +\pastebutton{ugxFactoredArithPageFull1}{\hidepaste} +\tab{5}\spadcommand{g := factor(4312)\bound{g }} +\indentrel{3}\begin{verbatim} + 3 2 + (1) 2 7 11 + Type: Factored Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxFactoredArithPageEmpty1} +\begin{paste}{ugxFactoredArithPageEmpty1}{ugxFactoredArithPagePatch1} +\pastebutton{ugxFactoredArithPageEmpty1}{\showpaste} +\tab{5}\spadcommand{g := factor(4312)\bound{g }} +\end{paste}\end{patch} + +\begin{patch}{ugxFactoredArithPagePatch2} +\begin{paste}{ugxFactoredArithPageFull2}{ugxFactoredArithPageEmpty2} +\pastebutton{ugxFactoredArithPageFull2}{\hidepaste} +\tab{5}\spadcommand{f := factor(246960)\bound{f }} +\indentrel{3}\begin{verbatim} + 4 2 3 + (2) 2 3 5 7 + Type: Factored Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxFactoredArithPageEmpty2} +\begin{paste}{ugxFactoredArithPageEmpty2}{ugxFactoredArithPagePatch2} +\pastebutton{ugxFactoredArithPageEmpty2}{\showpaste} +\tab{5}\spadcommand{f := factor(246960)\bound{f }} +\end{paste}\end{patch} + +\begin{patch}{ugxFactoredArithPagePatch3} +\begin{paste}{ugxFactoredArithPageFull3}{ugxFactoredArithPageEmpty3} +\pastebutton{ugxFactoredArithPageFull3}{\hidepaste} +\tab{5}\spadcommand{f * g\free{f g }} +\indentrel{3}\begin{verbatim} + 7 2 5 + (3) 2 3 5 7 11 + Type: Factored Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxFactoredArithPageEmpty3} +\begin{paste}{ugxFactoredArithPageEmpty3}{ugxFactoredArithPagePatch3} +\pastebutton{ugxFactoredArithPageEmpty3}{\showpaste} +\tab{5}\spadcommand{f * g\free{f g }} +\end{paste}\end{patch} + +\begin{patch}{ugxFactoredArithPagePatch4} +\begin{paste}{ugxFactoredArithPageFull4}{ugxFactoredArithPageEmpty4} +\pastebutton{ugxFactoredArithPageFull4}{\hidepaste} +\tab{5}\spadcommand{f**500\free{f }} +\indentrel{3}\begin{verbatim} + 2000 1000 500 1500 + (4) 2 3 5 7 + Type: Factored Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxFactoredArithPageEmpty4} +\begin{paste}{ugxFactoredArithPageEmpty4}{ugxFactoredArithPagePatch4} +\pastebutton{ugxFactoredArithPageEmpty4}{\showpaste} +\tab{5}\spadcommand{f**500\free{f }} +\end{paste}\end{patch} + +\begin{patch}{ugxFactoredArithPagePatch5} +\begin{paste}{ugxFactoredArithPageFull5}{ugxFactoredArithPageEmpty5} +\pastebutton{ugxFactoredArithPageFull5}{\hidepaste} +\tab{5}\spadcommand{gcd(f,g)\free{f g }} +\indentrel{3}\begin{verbatim} + 3 2 + (5) 2 7 + Type: Factored Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxFactoredArithPageEmpty5} +\begin{paste}{ugxFactoredArithPageEmpty5}{ugxFactoredArithPagePatch5} +\pastebutton{ugxFactoredArithPageEmpty5}{\showpaste} +\tab{5}\spadcommand{gcd(f,g)\free{f g }} +\end{paste}\end{patch} + +\begin{patch}{ugxFactoredArithPagePatch6} +\begin{paste}{ugxFactoredArithPageFull6}{ugxFactoredArithPageEmpty6} +\pastebutton{ugxFactoredArithPageFull6}{\hidepaste} +\tab{5}\spadcommand{lcm(f,g)\free{f g }} +\indentrel{3}\begin{verbatim} + 4 2 3 + (6) 2 3 5 7 11 + Type: Factored Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxFactoredArithPageEmpty6} +\begin{paste}{ugxFactoredArithPageEmpty6}{ugxFactoredArithPagePatch6} +\pastebutton{ugxFactoredArithPageEmpty6}{\showpaste} +\tab{5}\spadcommand{lcm(f,g)\free{f g }} +\end{paste}\end{patch} + +\begin{patch}{ugxFactoredArithPagePatch7} +\begin{paste}{ugxFactoredArithPageFull7}{ugxFactoredArithPageEmpty7} +\pastebutton{ugxFactoredArithPageFull7}{\hidepaste} +\tab{5}\spadcommand{f + g\free{f g }} +\indentrel{3}\begin{verbatim} + 3 2 + (7) 2 7 641 + Type: Factored Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxFactoredArithPageEmpty7} +\begin{paste}{ugxFactoredArithPageEmpty7}{ugxFactoredArithPagePatch7} +\pastebutton{ugxFactoredArithPageEmpty7}{\showpaste} +\tab{5}\spadcommand{f + g\free{f g }} +\end{paste}\end{patch} + +\begin{patch}{ugxFactoredArithPagePatch8} +\begin{paste}{ugxFactoredArithPageFull8}{ugxFactoredArithPageEmpty8} +\pastebutton{ugxFactoredArithPageFull8}{\hidepaste} +\tab{5}\spadcommand{f - g\free{f g }} +\indentrel{3}\begin{verbatim} + 3 2 + (8) 2 7 619 + Type: Factored Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxFactoredArithPageEmpty8} +\begin{paste}{ugxFactoredArithPageEmpty8}{ugxFactoredArithPagePatch8} +\pastebutton{ugxFactoredArithPageEmpty8}{\showpaste} +\tab{5}\spadcommand{f - g\free{f g }} +\end{paste}\end{patch} + +\begin{patch}{ugxFactoredArithPagePatch9} +\begin{paste}{ugxFactoredArithPageFull9}{ugxFactoredArithPageEmpty9} +\pastebutton{ugxFactoredArithPageFull9}{\hidepaste} +\tab{5}\spadcommand{zero?(factor(0))} +\indentrel{3}\begin{verbatim} + (9) true + Type: Boolean +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxFactoredArithPageEmpty9} +\begin{paste}{ugxFactoredArithPageEmpty9}{ugxFactoredArithPagePatch9} +\pastebutton{ugxFactoredArithPageEmpty9}{\showpaste} +\tab{5}\spadcommand{zero?(factor(0))} +\end{paste}\end{patch} + +\begin{patch}{ugxFactoredArithPagePatch10} +\begin{paste}{ugxFactoredArithPageFull10}{ugxFactoredArithPageEmpty10} +\pastebutton{ugxFactoredArithPageFull10}{\hidepaste} +\tab{5}\spadcommand{zero?(g)\free{g }} +\indentrel{3}\begin{verbatim} + (10) false + Type: Boolean +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxFactoredArithPageEmpty10} +\begin{paste}{ugxFactoredArithPageEmpty10}{ugxFactoredArithPagePatch10} +\pastebutton{ugxFactoredArithPageEmpty10}{\showpaste} +\tab{5}\spadcommand{zero?(g)\free{g }} +\end{paste}\end{patch} + +\begin{patch}{ugxFactoredArithPagePatch11} +\begin{paste}{ugxFactoredArithPageFull11}{ugxFactoredArithPageEmpty11} +\pastebutton{ugxFactoredArithPageFull11}{\hidepaste} +\tab{5}\spadcommand{one?(factor(1))} +\indentrel{3}\begin{verbatim} + (11) true + Type: Boolean +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxFactoredArithPageEmpty11} +\begin{paste}{ugxFactoredArithPageEmpty11}{ugxFactoredArithPagePatch11} +\pastebutton{ugxFactoredArithPageEmpty11}{\showpaste} +\tab{5}\spadcommand{one?(factor(1))} +\end{paste}\end{patch} + +\begin{patch}{ugxFactoredArithPagePatch12} +\begin{paste}{ugxFactoredArithPageFull12}{ugxFactoredArithPageEmpty12} +\pastebutton{ugxFactoredArithPageFull12}{\hidepaste} +\tab{5}\spadcommand{one?(f)\free{f }} +\indentrel{3}\begin{verbatim} + (12) false + Type: Boolean +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxFactoredArithPageEmpty12} +\begin{paste}{ugxFactoredArithPageEmpty12}{ugxFactoredArithPagePatch12} +\pastebutton{ugxFactoredArithPageEmpty12}{\showpaste} +\tab{5}\spadcommand{one?(f)\free{f }} +\end{paste}\end{patch} + +\begin{patch}{ugxFactoredArithPagePatch13} +\begin{paste}{ugxFactoredArithPageFull13}{ugxFactoredArithPageEmpty13} +\pastebutton{ugxFactoredArithPageFull13}{\hidepaste} +\tab{5}\spadcommand{0$Factored(Integer)} +\indentrel{3}\begin{verbatim} + (13) 0 + Type: Factored Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxFactoredArithPageEmpty13} +\begin{paste}{ugxFactoredArithPageEmpty13}{ugxFactoredArithPagePatch13} +\pastebutton{ugxFactoredArithPageEmpty13}{\showpaste} +\tab{5}\spadcommand{0$Factored(Integer)} +\end{paste}\end{patch} + +\begin{patch}{ugxFactoredArithPagePatch14} +\begin{paste}{ugxFactoredArithPageFull14}{ugxFactoredArithPageEmpty14} +\pastebutton{ugxFactoredArithPageFull14}{\hidepaste} +\tab{5}\spadcommand{1$Factored(Integer)} +\indentrel{3}\begin{verbatim} + (14) 1 + Type: Factored Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxFactoredArithPageEmpty14} +\begin{paste}{ugxFactoredArithPageEmpty14}{ugxFactoredArithPagePatch14} +\pastebutton{ugxFactoredArithPageEmpty14}{\showpaste} +\tab{5}\spadcommand{1$Factored(Integer)} +\end{paste}\end{patch} + @ \pagehead{ugxFactoredNewPage}{fr.ht}{Creating New Factored Objects} \pagepic{ps/v71ugxfactorednewpage.eps}{ugxFactoredNewPage} @@ -8145,6 +21019,123 @@ returned by \spadfunFrom{factorList}{Factored}. \autobuttons \end{page} +\begin{patch}{ugxFactoredNewPagePatch1} +\begin{paste}{ugxFactoredNewPageFull1}{ugxFactoredNewPageEmpty1} +\pastebutton{ugxFactoredNewPageFull1}{\hidepaste} +\tab{5}\spadcommand{nilFactor(24,2)\bound{prev2 }} +\indentrel{3}\begin{verbatim} + 2 + (1) 24 + Type: Factored Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxFactoredNewPageEmpty1} +\begin{paste}{ugxFactoredNewPageEmpty1}{ugxFactoredNewPagePatch1} +\pastebutton{ugxFactoredNewPageEmpty1}{\showpaste} +\tab{5}\spadcommand{nilFactor(24,2)\bound{prev2 }} +\end{paste}\end{patch} + +\begin{patch}{ugxFactoredNewPagePatch2} +\begin{paste}{ugxFactoredNewPageFull2}{ugxFactoredNewPageEmpty2} +\pastebutton{ugxFactoredNewPageFull2}{\hidepaste} +\tab{5}\spadcommand{nthFlag(\%,1)\free{prev2 }} +\indentrel{3}\begin{verbatim} + (2) "nil" + Type: Union("nil",...) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxFactoredNewPageEmpty2} +\begin{paste}{ugxFactoredNewPageEmpty2}{ugxFactoredNewPagePatch2} +\pastebutton{ugxFactoredNewPageEmpty2}{\showpaste} +\tab{5}\spadcommand{nthFlag(\%,1)\free{prev2 }} +\end{paste}\end{patch} + +\begin{patch}{ugxFactoredNewPagePatch3} +\begin{paste}{ugxFactoredNewPageFull3}{ugxFactoredNewPageEmpty3} +\pastebutton{ugxFactoredNewPageFull3}{\hidepaste} +\tab{5}\spadcommand{sqfrFactor(30,2)\bound{prev3 }} +\indentrel{3}\begin{verbatim} + 2 + (3) 30 + Type: Factored Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxFactoredNewPageEmpty3} +\begin{paste}{ugxFactoredNewPageEmpty3}{ugxFactoredNewPagePatch3} +\pastebutton{ugxFactoredNewPageEmpty3}{\showpaste} +\tab{5}\spadcommand{sqfrFactor(30,2)\bound{prev3 }} +\end{paste}\end{patch} + +\begin{patch}{ugxFactoredNewPagePatch4} +\begin{paste}{ugxFactoredNewPageFull4}{ugxFactoredNewPageEmpty4} +\pastebutton{ugxFactoredNewPageFull4}{\hidepaste} +\tab{5}\spadcommand{irreducibleFactor(13,10)\bound{prev4 }} +\indentrel{3}\begin{verbatim} + 10 + (4) 13 + Type: Factored Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxFactoredNewPageEmpty4} +\begin{paste}{ugxFactoredNewPageEmpty4}{ugxFactoredNewPagePatch4} +\pastebutton{ugxFactoredNewPageEmpty4}{\showpaste} +\tab{5}\spadcommand{irreducibleFactor(13,10)\bound{prev4 }} +\end{paste}\end{patch} + +\begin{patch}{ugxFactoredNewPagePatch5} +\begin{paste}{ugxFactoredNewPageFull5}{ugxFactoredNewPageEmpty5} +\pastebutton{ugxFactoredNewPageFull5}{\hidepaste} +\tab{5}\spadcommand{primeFactor(11,5)\bound{prev5 }} +\indentrel{3}\begin{verbatim} + 5 + (5) 11 + Type: Factored Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxFactoredNewPageEmpty5} +\begin{paste}{ugxFactoredNewPageEmpty5}{ugxFactoredNewPagePatch5} +\pastebutton{ugxFactoredNewPageEmpty5}{\showpaste} +\tab{5}\spadcommand{primeFactor(11,5)\bound{prev5 }} +\end{paste}\end{patch} + +\begin{patch}{ugxFactoredNewPagePatch6} +\begin{paste}{ugxFactoredNewPageFull6}{ugxFactoredNewPageEmpty6} +\pastebutton{ugxFactoredNewPageFull6}{\hidepaste} +\tab{5}\spadcommand{h := factor(-720)\bound{h }} +\indentrel{3}\begin{verbatim} + 4 2 + (6) - 2 3 5 + Type: Factored Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxFactoredNewPageEmpty6} +\begin{paste}{ugxFactoredNewPageEmpty6}{ugxFactoredNewPagePatch6} +\pastebutton{ugxFactoredNewPageEmpty6}{\showpaste} +\tab{5}\spadcommand{h := factor(-720)\bound{h }} +\end{paste}\end{patch} + +\begin{patch}{ugxFactoredNewPagePatch7} +\begin{paste}{ugxFactoredNewPageFull7}{ugxFactoredNewPageEmpty7} +\pastebutton{ugxFactoredNewPageFull7}{\hidepaste} +\tab{5}\spadcommand{h - makeFR(unit(h),factorList(h))\free{h }} +\indentrel{3}\begin{verbatim} + (7) 0 + Type: Factored Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxFactoredNewPageEmpty7} +\begin{paste}{ugxFactoredNewPageEmpty7}{ugxFactoredNewPagePatch7} +\pastebutton{ugxFactoredNewPageEmpty7}{\showpaste} +\tab{5}\spadcommand{h - makeFR(unit(h),factorList(h))\free{h }} +\end{paste}\end{patch} + @ \pagehead{ugxFactoredVarPage}{fr.ht}{Factored Objects with Variables} \pagepic{ps/v71ugxfactoredvarpage.eps}{ugxFactoredVarPage} @@ -8182,6 +21173,91 @@ You can differentiate with respect to a variable. \autobuttons \end{page} +\begin{patch}{ugxFactoredVarPagePatch1} +\begin{paste}{ugxFactoredVarPageFull1}{ugxFactoredVarPageEmpty1} +\pastebutton{ugxFactoredVarPageFull1}{\hidepaste} +\tab{5}\spadcommand{p := (4*x*x-12*x+9)*y*y + (4*x*x-12*x+9)*y + 28*x*x - 84*x + 63\bound{p }} +\indentrel{3}\begin{verbatim} + (1) + 2 2 2 2 + (4x - 12x + 9)y + (4x - 12x + 9)y + 28x - 84x + 63 + Type: Polynomial Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxFactoredVarPageEmpty1} +\begin{paste}{ugxFactoredVarPageEmpty1}{ugxFactoredVarPagePatch1} +\pastebutton{ugxFactoredVarPageEmpty1}{\showpaste} +\tab{5}\spadcommand{p := (4*x*x-12*x+9)*y*y + (4*x*x-12*x+9)*y + 28*x*x - 84*x + 63\bound{p }} +\end{paste}\end{patch} + +\begin{patch}{ugxFactoredVarPagePatch2} +\begin{paste}{ugxFactoredVarPageFull2}{ugxFactoredVarPageEmpty2} +\pastebutton{ugxFactoredVarPageFull2}{\hidepaste} +\tab{5}\spadcommand{fp := factor(p)\free{p }\bound{fp }} +\indentrel{3}\begin{verbatim} + 2 2 + (2) (2x - 3) (y + y + 7) + Type: Factored Polynomial Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxFactoredVarPageEmpty2} +\begin{paste}{ugxFactoredVarPageEmpty2}{ugxFactoredVarPagePatch2} +\pastebutton{ugxFactoredVarPageEmpty2}{\showpaste} +\tab{5}\spadcommand{fp := factor(p)\free{p }\bound{fp }} +\end{paste}\end{patch} + +\begin{patch}{ugxFactoredVarPagePatch3} +\begin{paste}{ugxFactoredVarPageFull3}{ugxFactoredVarPageEmpty3} +\pastebutton{ugxFactoredVarPageFull3}{\hidepaste} +\tab{5}\spadcommand{D(p,x)\free{p }} +\indentrel{3}\begin{verbatim} + 2 + (3) (8x - 12)y + (8x - 12)y + 56x - 84 + Type: Polynomial Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxFactoredVarPageEmpty3} +\begin{paste}{ugxFactoredVarPageEmpty3}{ugxFactoredVarPagePatch3} +\pastebutton{ugxFactoredVarPageEmpty3}{\showpaste} +\tab{5}\spadcommand{D(p,x)\free{p }} +\end{paste}\end{patch} + +\begin{patch}{ugxFactoredVarPagePatch4} +\begin{paste}{ugxFactoredVarPageFull4}{ugxFactoredVarPageEmpty4} +\pastebutton{ugxFactoredVarPageFull4}{\hidepaste} +\tab{5}\spadcommand{D(fp,x)\free{fp }\bound{prev1 }} +\indentrel{3}\begin{verbatim} + 2 + (4) 4(2x - 3)(y + y + 7) + Type: Factored Polynomial Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxFactoredVarPageEmpty4} +\begin{paste}{ugxFactoredVarPageEmpty4}{ugxFactoredVarPagePatch4} +\pastebutton{ugxFactoredVarPageEmpty4}{\showpaste} +\tab{5}\spadcommand{D(fp,x)\free{fp }\bound{prev1 }} +\end{paste}\end{patch} + +\begin{patch}{ugxFactoredVarPagePatch5} +\begin{paste}{ugxFactoredVarPageFull5}{ugxFactoredVarPageEmpty5} +\pastebutton{ugxFactoredVarPageFull5}{\hidepaste} +\tab{5}\spadcommand{numberOfFactors(\%)\free{prev1 }} +\indentrel{3}\begin{verbatim} + (5) 3 + Type: PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxFactoredVarPageEmpty5} +\begin{paste}{ugxFactoredVarPageEmpty5}{ugxFactoredVarPagePatch5} +\pastebutton{ugxFactoredVarPageEmpty5}{\showpaste} +\tab{5}\spadcommand{numberOfFactors(\%)\free{prev1 }} +\end{paste}\end{patch} + @ \section{fr2.ht} \pagehead{FactoredFnsTwoXmpPage}{fr2.ht}{FactoredFunctions2} @@ -8245,6 +21321,103 @@ Section 8.13\ignore{ugProblemGalois}. \autobuttons \end{page} +\begin{patch}{FactoredFnsTwoXmpPagePatch1} +\begin{paste}{FactoredFnsTwoXmpPageFull1}{FactoredFnsTwoXmpPageEmpty1} +\pastebutton{FactoredFnsTwoXmpPageFull1}{\hidepaste} +\tab{5}\spadcommand{double(x) == x + x\bound{double }} +\indentrel{3}\begin{verbatim} + Type: Void +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{FactoredFnsTwoXmpPageEmpty1} +\begin{paste}{FactoredFnsTwoXmpPageEmpty1}{FactoredFnsTwoXmpPagePatch1} +\pastebutton{FactoredFnsTwoXmpPageEmpty1}{\showpaste} +\tab{5}\spadcommand{double(x) == x + x\bound{double }} +\end{paste}\end{patch} + +\begin{patch}{FactoredFnsTwoXmpPagePatch2} +\begin{paste}{FactoredFnsTwoXmpPageFull2}{FactoredFnsTwoXmpPageEmpty2} +\pastebutton{FactoredFnsTwoXmpPageFull2}{\hidepaste} +\tab{5}\spadcommand{f := factor(720)\bound{f }} +\indentrel{3}\begin{verbatim} + 4 2 + (2) 2 3 5 + Type: Factored Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{FactoredFnsTwoXmpPageEmpty2} +\begin{paste}{FactoredFnsTwoXmpPageEmpty2}{FactoredFnsTwoXmpPagePatch2} +\pastebutton{FactoredFnsTwoXmpPageEmpty2}{\showpaste} +\tab{5}\spadcommand{f := factor(720)\bound{f }} +\end{paste}\end{patch} + +\begin{patch}{FactoredFnsTwoXmpPagePatch3} +\begin{paste}{FactoredFnsTwoXmpPageFull3}{FactoredFnsTwoXmpPageEmpty3} +\pastebutton{FactoredFnsTwoXmpPageFull3}{\hidepaste} +\tab{5}\spadcommand{map(double,f)\free{f }\free{double }} +\indentrel{3}\begin{verbatim} + 4 2 + (3) 2 4 6 10 + Type: Factored Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{FactoredFnsTwoXmpPageEmpty3} +\begin{paste}{FactoredFnsTwoXmpPageEmpty3}{FactoredFnsTwoXmpPagePatch3} +\pastebutton{FactoredFnsTwoXmpPageEmpty3}{\showpaste} +\tab{5}\spadcommand{map(double,f)\free{f }\free{double }} +\end{paste}\end{patch} + +\begin{patch}{FactoredFnsTwoXmpPagePatch4} +\begin{paste}{FactoredFnsTwoXmpPageFull4}{FactoredFnsTwoXmpPageEmpty4} +\pastebutton{FactoredFnsTwoXmpPageFull4}{\hidepaste} +\tab{5}\spadcommand{makePoly(b) == x + b\bound{makePoly }} +\indentrel{3}\begin{verbatim} + Type: Void +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{FactoredFnsTwoXmpPageEmpty4} +\begin{paste}{FactoredFnsTwoXmpPageEmpty4}{FactoredFnsTwoXmpPagePatch4} +\pastebutton{FactoredFnsTwoXmpPageEmpty4}{\showpaste} +\tab{5}\spadcommand{makePoly(b) == x + b\bound{makePoly }} +\end{paste}\end{patch} + +\begin{patch}{FactoredFnsTwoXmpPagePatch5} +\begin{paste}{FactoredFnsTwoXmpPageFull5}{FactoredFnsTwoXmpPageEmpty5} +\pastebutton{FactoredFnsTwoXmpPageFull5}{\hidepaste} +\tab{5}\spadcommand{g := map(makePoly,f)\free{f }\free{makePoly }\bound{g }} +\indentrel{3}\begin{verbatim} + 4 2 + (5) (x + 1)(x + 2) (x + 3) (x + 5) + Type: Factored Polynomial Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{FactoredFnsTwoXmpPageEmpty5} +\begin{paste}{FactoredFnsTwoXmpPageEmpty5}{FactoredFnsTwoXmpPagePatch5} +\pastebutton{FactoredFnsTwoXmpPageEmpty5}{\showpaste} +\tab{5}\spadcommand{g := map(makePoly,f)\free{f }\free{makePoly }\bound{g }} +\end{paste}\end{patch} + +\begin{patch}{FactoredFnsTwoXmpPagePatch6} +\begin{paste}{FactoredFnsTwoXmpPageFull6}{FactoredFnsTwoXmpPageEmpty6} +\pastebutton{FactoredFnsTwoXmpPageFull6}{\hidepaste} +\tab{5}\spadcommand{nthFlag(g,1)\free{g }} +\indentrel{3}\begin{verbatim} + (6) "nil" + Type: Union("nil",...) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{FactoredFnsTwoXmpPageEmpty6} +\begin{paste}{FactoredFnsTwoXmpPageEmpty6}{FactoredFnsTwoXmpPagePatch6} +\pastebutton{FactoredFnsTwoXmpPageEmpty6}{\showpaste} +\tab{5}\spadcommand{nthFlag(g,1)\free{g }} +\end{paste}\end{patch} + @ \section{frac.ht} \pagehead{FractionXmpPage}{frac.ht}{Fraction} @@ -8348,6 +21521,225 @@ in Section 2.7\ignore{ugTypesConvert}. \autobuttons \end{page} +\begin{patch}{FractionXmpPagePatch1} +\begin{paste}{FractionXmpPageFull1}{FractionXmpPageEmpty1} +\pastebutton{FractionXmpPageFull1}{\hidepaste} +\tab{5}\spadcommand{a := 11/12\bound{a }} +\indentrel{3}\begin{verbatim} + 11 + (1) ÄÄ + 12 + Type: Fraction Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{FractionXmpPageEmpty1} +\begin{paste}{FractionXmpPageEmpty1}{FractionXmpPagePatch1} +\pastebutton{FractionXmpPageEmpty1}{\showpaste} +\tab{5}\spadcommand{a := 11/12\bound{a }} +\end{paste}\end{patch} + +\begin{patch}{FractionXmpPagePatch2} +\begin{paste}{FractionXmpPageFull2}{FractionXmpPageEmpty2} +\pastebutton{FractionXmpPageFull2}{\hidepaste} +\tab{5}\spadcommand{b := 23/24\bound{b }} +\indentrel{3}\begin{verbatim} + 23 + (2) ÄÄ + 24 + Type: Fraction Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{FractionXmpPageEmpty2} +\begin{paste}{FractionXmpPageEmpty2}{FractionXmpPagePatch2} +\pastebutton{FractionXmpPageEmpty2}{\showpaste} +\tab{5}\spadcommand{b := 23/24\bound{b }} +\end{paste}\end{patch} + +\begin{patch}{FractionXmpPagePatch3} +\begin{paste}{FractionXmpPageFull3}{FractionXmpPageEmpty3} +\pastebutton{FractionXmpPageFull3}{\hidepaste} +\tab{5}\spadcommand{3 - a*b**2 + a + b/a\free{a }\free{b }} +\indentrel{3}\begin{verbatim} + 313271 + (3) ÄÄÄÄÄÄ + 76032 + Type: Fraction Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{FractionXmpPageEmpty3} +\begin{paste}{FractionXmpPageEmpty3}{FractionXmpPagePatch3} +\pastebutton{FractionXmpPageEmpty3}{\showpaste} +\tab{5}\spadcommand{3 - a*b**2 + a + b/a\free{a }\free{b }} +\end{paste}\end{patch} + +\begin{patch}{FractionXmpPagePatch4} +\begin{paste}{FractionXmpPageFull4}{FractionXmpPageEmpty4} +\pastebutton{FractionXmpPageFull4}{\hidepaste} +\tab{5}\spadcommand{numer(a)\free{a }} +\indentrel{3}\begin{verbatim} + (4) 11 + Type: PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{FractionXmpPageEmpty4} +\begin{paste}{FractionXmpPageEmpty4}{FractionXmpPagePatch4} +\pastebutton{FractionXmpPageEmpty4}{\showpaste} +\tab{5}\spadcommand{numer(a)\free{a }} +\end{paste}\end{patch} + +\begin{patch}{FractionXmpPagePatch5} +\begin{paste}{FractionXmpPageFull5}{FractionXmpPageEmpty5} +\pastebutton{FractionXmpPageFull5}{\hidepaste} +\tab{5}\spadcommand{denom(b)\free{b }} +\indentrel{3}\begin{verbatim} + (5) 24 + Type: PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{FractionXmpPageEmpty5} +\begin{paste}{FractionXmpPageEmpty5}{FractionXmpPagePatch5} +\pastebutton{FractionXmpPageEmpty5}{\showpaste} +\tab{5}\spadcommand{denom(b)\free{b }} +\end{paste}\end{patch} + +\begin{patch}{FractionXmpPagePatch6} +\begin{paste}{FractionXmpPageFull6}{FractionXmpPageEmpty6} +\pastebutton{FractionXmpPageFull6}{\hidepaste} +\tab{5}\spadcommand{r := (x**2 + 2*x + 1)/(x**2 - 2*x + 1)\bound{r }} +\indentrel{3}\begin{verbatim} + 2 + x + 2x + 1 + (6) ÄÄÄÄÄÄÄÄÄÄÄ + 2 + x - 2x + 1 + Type: Fraction Polynomial Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{FractionXmpPageEmpty6} +\begin{paste}{FractionXmpPageEmpty6}{FractionXmpPagePatch6} +\pastebutton{FractionXmpPageEmpty6}{\showpaste} +\tab{5}\spadcommand{r := (x**2 + 2*x + 1)/(x**2 - 2*x + 1)\bound{r }} +\end{paste}\end{patch} + +\begin{patch}{FractionXmpPagePatch7} +\begin{paste}{FractionXmpPageFull7}{FractionXmpPageEmpty7} +\pastebutton{FractionXmpPageFull7}{\hidepaste} +\tab{5}\spadcommand{factor(r)\free{r }} +\indentrel{3}\begin{verbatim} + 2 + x + 2x + 1 + (7) ÄÄÄÄÄÄÄÄÄÄÄ + 2 + x - 2x + 1 + Type: Factored Fraction Polynomial Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{FractionXmpPageEmpty7} +\begin{paste}{FractionXmpPageEmpty7}{FractionXmpPagePatch7} +\pastebutton{FractionXmpPageEmpty7}{\showpaste} +\tab{5}\spadcommand{factor(r)\free{r }} +\end{paste}\end{patch} + +\begin{patch}{FractionXmpPagePatch8} +\begin{paste}{FractionXmpPageFull8}{FractionXmpPageEmpty8} +\pastebutton{FractionXmpPageFull8}{\hidepaste} +\tab{5}\spadcommand{map(factor,r)\free{r }} +\indentrel{3}\begin{verbatim} + 2 + (x + 1) + (8) ÄÄÄÄÄÄÄÄ + 2 + (x - 1) + Type: Fraction Factored Polynomial Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{FractionXmpPageEmpty8} +\begin{paste}{FractionXmpPageEmpty8}{FractionXmpPagePatch8} +\pastebutton{FractionXmpPageEmpty8}{\showpaste} +\tab{5}\spadcommand{map(factor,r)\free{r }} +\end{paste}\end{patch} + +\begin{patch}{FractionXmpPagePatch9} +\begin{paste}{FractionXmpPageFull9}{FractionXmpPageEmpty9} +\pastebutton{FractionXmpPageFull9}{\hidepaste} +\tab{5}\spadcommand{continuedFraction(7/12)} +\indentrel{3}\begin{verbatim} + 1 ³ 1 ³ 1 ³ 1 ³ + (9) ÚÄÄÄÙ + ÚÄÄÄÙ + ÚÄÄÄÙ + ÚÄÄÄÙ + ³ 1 ³ 1 ³ 2 ³ 2 + Type: ContinuedFraction Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{FractionXmpPageEmpty9} +\begin{paste}{FractionXmpPageEmpty9}{FractionXmpPagePatch9} +\pastebutton{FractionXmpPageEmpty9}{\showpaste} +\tab{5}\spadcommand{continuedFraction(7/12)} +\end{paste}\end{patch} + +\begin{patch}{FractionXmpPagePatch10} +\begin{paste}{FractionXmpPageFull10}{FractionXmpPageEmpty10} +\pastebutton{FractionXmpPageFull10}{\hidepaste} +\tab{5}\spadcommand{partialFraction(7,12)} +\indentrel{3}\begin{verbatim} + 3 1 + (10) 1 - ÄÄ + Ä + 2 3 + 2 + Type: PartialFraction Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{FractionXmpPageEmpty10} +\begin{paste}{FractionXmpPageEmpty10}{FractionXmpPagePatch10} +\pastebutton{FractionXmpPageEmpty10}{\showpaste} +\tab{5}\spadcommand{partialFraction(7,12)} +\end{paste}\end{patch} + +\begin{patch}{FractionXmpPagePatch11} +\begin{paste}{FractionXmpPageFull11}{FractionXmpPageEmpty11} +\pastebutton{FractionXmpPageFull11}{\hidepaste} +\tab{5}\spadcommand{g := 2/3 + 4/5*\%i\bound{g }} +\indentrel{3}\begin{verbatim} + 2 4 + (11) Ä + Ä %i + 3 5 + Type: Complex Fraction Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{FractionXmpPageEmpty11} +\begin{paste}{FractionXmpPageEmpty11}{FractionXmpPagePatch11} +\pastebutton{FractionXmpPageEmpty11}{\showpaste} +\tab{5}\spadcommand{g := 2/3 + 4/5*\%i\bound{g }} +\end{paste}\end{patch} + +\begin{patch}{FractionXmpPagePatch12} +\begin{paste}{FractionXmpPageFull12}{FractionXmpPageEmpty12} +\pastebutton{FractionXmpPageFull12}{\hidepaste} +\tab{5}\spadcommand{g :: FRAC COMPLEX INT\free{g }} +\indentrel{3}\begin{verbatim} + 10 + 12%i + (12) ÄÄÄÄÄÄÄÄÄ + 15 + Type: Fraction Complex Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{FractionXmpPageEmpty12} +\begin{paste}{FractionXmpPageEmpty12}{FractionXmpPagePatch12} +\pastebutton{FractionXmpPageEmpty12}{\showpaste} +\tab{5}\spadcommand{g :: FRAC COMPLEX INT\free{g }} +\end{paste}\end{patch} + @ \section{fparfrac.ht} \pagehead{FullPartialFracExpansionXmpPage}{fparfrac.ht} @@ -8455,6 +21847,417 @@ decompositions. \autobuttons \end{page} +\begin{patch}{FullPartialFractionExpansionXmpPagePatch1} +\begin{paste}{FullPartialFractionExpansionXmpPageFull1}{FullPartialFractionExpansionXmpPageEmpty1} +\pastebutton{FullPartialFractionExpansionXmpPageFull1}{\hidepaste} +\tab{5}\spadcommand{Fx := FRAC UP(x, FRAC INT)\bound{Fx }} +\indentrel{3}\begin{verbatim} + (1) + Fraction UnivariatePolynomial(x,Fraction Integer) + Type: Domain +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{FullPartialFractionExpansionXmpPageEmpty1} +\begin{paste}{FullPartialFractionExpansionXmpPageEmpty1}{FullPartialFractionExpansionXmpPagePatch1} +\pastebutton{FullPartialFractionExpansionXmpPageEmpty1}{\showpaste} +\tab{5}\spadcommand{Fx := FRAC UP(x, FRAC INT)\bound{Fx }} +\end{paste}\end{patch} + +\begin{patch}{FullPartialFractionExpansionXmpPagePatch2} +\begin{paste}{FullPartialFractionExpansionXmpPageFull2}{FullPartialFractionExpansionXmpPageEmpty2} +\pastebutton{FullPartialFractionExpansionXmpPageFull2}{\hidepaste} +\tab{5}\spadcommand{f : Fx := 36 / (x**5-2*x**4-2*x**3+4*x**2+x-2)\bound{f }\free{Fx }} +\indentrel{3}\begin{verbatim} + 36 + (2) ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ + 5 4 3 2 + x - 2x - 2x + 4x + x - 2 +Type: Fraction UnivariatePolynomial(x,Fraction Integer) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{FullPartialFractionExpansionXmpPageEmpty2} +\begin{paste}{FullPartialFractionExpansionXmpPageEmpty2}{FullPartialFractionExpansionXmpPagePatch2} +\pastebutton{FullPartialFractionExpansionXmpPageEmpty2}{\showpaste} +\tab{5}\spadcommand{f : Fx := 36 / (x**5-2*x**4-2*x**3+4*x**2+x-2)\bound{f }\free{Fx }} +\end{paste}\end{patch} + +\begin{patch}{FullPartialFractionExpansionXmpPagePatch3} +\begin{paste}{FullPartialFractionExpansionXmpPageFull3}{FullPartialFractionExpansionXmpPageEmpty3} +\pastebutton{FullPartialFractionExpansionXmpPageFull3}{\hidepaste} +\tab{5}\spadcommand{g := fullPartialFraction f\bound{g }\free{f }} +\indentrel{3}\begin{verbatim} + 4 4 ÄÄ¿ - 3%A - 6 + (3) ÄÄÄÄÄ - ÄÄÄÄÄ + > ÄÄÄÄÄÄÄÄÄ + x - 2 x + 1 ÄÄÙ 2 + 2 (x - %A) + %A - 1= 0 +Type: FullPartialFractionExpansion(Fraction Integer,UnivariatePolynomial(x,Fraction Integer)) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{FullPartialFractionExpansionXmpPageEmpty3} +\begin{paste}{FullPartialFractionExpansionXmpPageEmpty3}{FullPartialFractionExpansionXmpPagePatch3} +\pastebutton{FullPartialFractionExpansionXmpPageEmpty3}{\showpaste} +\tab{5}\spadcommand{g := fullPartialFraction f\bound{g }\free{f }} +\end{paste}\end{patch} + +\begin{patch}{FullPartialFractionExpansionXmpPagePatch4} +\begin{paste}{FullPartialFractionExpansionXmpPageFull4}{FullPartialFractionExpansionXmpPageEmpty4} +\pastebutton{FullPartialFractionExpansionXmpPageFull4}{\hidepaste} +\tab{5}\spadcommand{g :: Fx\free{g }} +\indentrel{3}\begin{verbatim} + 36 + (4) ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ + 5 4 3 2 + x - 2x - 2x + 4x + x - 2 +Type: Fraction UnivariatePolynomial(x,Fraction Integer) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{FullPartialFractionExpansionXmpPageEmpty4} +\begin{paste}{FullPartialFractionExpansionXmpPageEmpty4}{FullPartialFractionExpansionXmpPagePatch4} +\pastebutton{FullPartialFractionExpansionXmpPageEmpty4}{\showpaste} +\tab{5}\spadcommand{g :: Fx\free{g }} +\end{paste}\end{patch} + +\begin{patch}{FullPartialFractionExpansionXmpPagePatch5} +\begin{paste}{FullPartialFractionExpansionXmpPageFull5}{FullPartialFractionExpansionXmpPageEmpty5} +\pastebutton{FullPartialFractionExpansionXmpPageFull5}{\hidepaste} +\tab{5}\spadcommand{g5 := D(g, 5)\free{g }\bound{g5 }} +\indentrel{3}\begin{verbatim} + (5) + 480 480 ÄÄ¿ 2160%A + 4320 + - ÄÄÄÄÄÄÄÄ + ÄÄÄÄÄÄÄÄ + > ÄÄÄÄÄÄÄÄÄÄÄÄÄ + 6 6 ÄÄÙ 7 + (x - 2) (x + 1) 2 (x - %A) + %A - 1= 0 +Type: FullPartialFractionExpansion(Fraction Integer,UnivariatePolynomial(x,Fraction Integer)) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{FullPartialFractionExpansionXmpPageEmpty5} +\begin{paste}{FullPartialFractionExpansionXmpPageEmpty5}{FullPartialFractionExpansionXmpPagePatch5} +\pastebutton{FullPartialFractionExpansionXmpPageEmpty5}{\showpaste} +\tab{5}\spadcommand{g5 := D(g, 5)\free{g }\bound{g5 }} +\end{paste}\end{patch} + +\begin{patch}{FullPartialFractionExpansionXmpPagePatch6} +\begin{paste}{FullPartialFractionExpansionXmpPageFull6}{FullPartialFractionExpansionXmpPageEmpty6} +\pastebutton{FullPartialFractionExpansionXmpPageFull6}{\hidepaste} +\tab{5}\spadcommand{f5 := D(f, 5)\free{f }\bound{f5 }} +\indentrel{3}\begin{verbatim} + (6) + 10 9 8 7 + - 544320x + 4354560x - 14696640x + 28615680x + + + 6 5 4 3 + - 40085280x + 46656000x - 39411360x + 18247680x + + + 2 + - 5870880x + 3317760x + 246240 + / + 20 19 18 17 16 15 + x - 12x + 53x - 76x - 159x + 676x + + + 14 13 12 11 10 + - 391x - 1596x + 2527x + 1148x - 4977x + + + 9 8 7 6 5 4 + 1372x + 4907x - 3444x - 2381x + 2924x + 276x + + + 3 2 + - 1184x + 208x + 192x - 64 +Type: Fraction UnivariatePolynomial(x,Fraction Integer) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{FullPartialFractionExpansionXmpPageEmpty6} +\begin{paste}{FullPartialFractionExpansionXmpPageEmpty6}{FullPartialFractionExpansionXmpPagePatch6} +\pastebutton{FullPartialFractionExpansionXmpPageEmpty6}{\showpaste} +\tab{5}\spadcommand{f5 := D(f, 5)\free{f }\bound{f5 }} +\end{paste}\end{patch} + +\begin{patch}{FullPartialFractionExpansionXmpPagePatch7} +\begin{paste}{FullPartialFractionExpansionXmpPageFull7}{FullPartialFractionExpansionXmpPageEmpty7} +\pastebutton{FullPartialFractionExpansionXmpPageFull7}{\hidepaste} +\tab{5}\spadcommand{g5::Fx - f5\free{Fx g5 f5 }} +\indentrel{3}\begin{verbatim} + (7) 0 +Type: Fraction UnivariatePolynomial(x,Fraction Integer) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{FullPartialFractionExpansionXmpPageEmpty7} +\begin{paste}{FullPartialFractionExpansionXmpPageEmpty7}{FullPartialFractionExpansionXmpPagePatch7} +\pastebutton{FullPartialFractionExpansionXmpPageEmpty7}{\showpaste} +\tab{5}\spadcommand{g5::Fx - f5\free{Fx g5 f5 }} +\end{paste}\end{patch} + +\begin{patch}{FullPartialFractionExpansionXmpPagePatch8} +\begin{paste}{FullPartialFractionExpansionXmpPageFull8}{FullPartialFractionExpansionXmpPageEmpty8} +\pastebutton{FullPartialFractionExpansionXmpPageFull8}{\hidepaste} +\tab{5}\spadcommand{f : Fx := (x**5 * (x-1)) / ((x**2 + x + 1)**2 * (x-2)**3)\free{Fx }\bound{f2 }} +\indentrel{3}\begin{verbatim} + 6 5 + x - x + (8) ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ + 7 6 5 3 2 + x - 4x + 3x + 9x - 6x - 4x - 8 +Type: Fraction UnivariatePolynomial(x,Fraction Integer) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{FullPartialFractionExpansionXmpPageEmpty8} +\begin{paste}{FullPartialFractionExpansionXmpPageEmpty8}{FullPartialFractionExpansionXmpPagePatch8} +\pastebutton{FullPartialFractionExpansionXmpPageEmpty8}{\showpaste} +\tab{5}\spadcommand{f : Fx := (x**5 * (x-1)) / ((x**2 + x + 1)**2 * (x-2)**3)\free{Fx }\bound{f2 }} +\end{paste}\end{patch} + +\begin{patch}{FullPartialFractionExpansionXmpPagePatch9} +\begin{paste}{FullPartialFractionExpansionXmpPageFull9}{FullPartialFractionExpansionXmpPageEmpty9} +\pastebutton{FullPartialFractionExpansionXmpPageFull9}{\hidepaste} +\tab{5}\spadcommand{g := fullPartialFraction f\free{f2 }\bound{g2 }} +\indentrel{3}\begin{verbatim} + (9) + 1952 464 32 + ÄÄÄÄ ÄÄÄ ÄÄ + 2401 343 49 + ÄÄÄÄÄÄ + ÄÄÄÄÄÄÄÄ + ÄÄÄÄÄÄÄÄ + x - 2 2 3 + (x - 2) (x - 2) + + + 179 135 + - ÄÄÄÄ %A + ÄÄÄÄ + ÄÄ¿ 2401 2401 + > ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ + ÄÄÙ x - %A + 2 + %A + %A + 1= 0 + + + 37 20 + ÄÄÄÄ %A + ÄÄÄÄ + ÄÄ¿ 1029 1029 + > ÄÄÄÄÄÄÄÄÄÄÄÄÄÄ + ÄÄÙ 2 + 2 (x - %A) + %A + %A + 1= 0 +Type: FullPartialFractionExpansion(Fraction Integer,UnivariatePolynomial(x,Fraction Integer)) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{FullPartialFractionExpansionXmpPageEmpty9} +\begin{paste}{FullPartialFractionExpansionXmpPageEmpty9}{FullPartialFractionExpansionXmpPagePatch9} +\pastebutton{FullPartialFractionExpansionXmpPageEmpty9}{\showpaste} +\tab{5}\spadcommand{g := fullPartialFraction f\free{f2 }\bound{g2 }} +\end{paste}\end{patch} + +\begin{patch}{FullPartialFractionExpansionXmpPagePatch10} +\begin{paste}{FullPartialFractionExpansionXmpPageFull10}{FullPartialFractionExpansionXmpPageEmpty10} +\pastebutton{FullPartialFractionExpansionXmpPageFull10}{\hidepaste} +\tab{5}\spadcommand{g :: Fx - f\free{f2 g2 Fx }} +\indentrel{3}\begin{verbatim} + (10) 0 +Type: Fraction UnivariatePolynomial(x,Fraction Integer) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{FullPartialFractionExpansionXmpPageEmpty10} +\begin{paste}{FullPartialFractionExpansionXmpPageEmpty10}{FullPartialFractionExpansionXmpPagePatch10} +\pastebutton{FullPartialFractionExpansionXmpPageEmpty10}{\showpaste} +\tab{5}\spadcommand{g :: Fx - f\free{f2 g2 Fx }} +\end{paste}\end{patch} + +\begin{patch}{FullPartialFractionExpansionXmpPagePatch11} +\begin{paste}{FullPartialFractionExpansionXmpPageFull11}{FullPartialFractionExpansionXmpPageEmpty11} +\pastebutton{FullPartialFractionExpansionXmpPageFull11}{\hidepaste} +\tab{5}\spadcommand{f : Fx := (2*x**7-7*x**5+26*x**3+8*x) / (x**8-5*x**6+6*x**4+4*x**2-8)\free{Fx }\bound{f3 }} +\indentrel{3}\begin{verbatim} + 7 5 3 + 2x - 7x + 26x + 8x + (11) ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ + 8 6 4 2 + x - 5x + 6x + 4x - 8 +Type: Fraction UnivariatePolynomial(x,Fraction Integer) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{FullPartialFractionExpansionXmpPageEmpty11} +\begin{paste}{FullPartialFractionExpansionXmpPageEmpty11}{FullPartialFractionExpansionXmpPagePatch11} +\pastebutton{FullPartialFractionExpansionXmpPageEmpty11}{\showpaste} +\tab{5}\spadcommand{f : Fx := (2*x**7-7*x**5+26*x**3+8*x) / (x**8-5*x**6+6*x**4+4*x**2-8)\free{Fx }\bound{f3 }} +\end{paste}\end{patch} + +\begin{patch}{FullPartialFractionExpansionXmpPagePatch12} +\begin{paste}{FullPartialFractionExpansionXmpPageFull12}{FullPartialFractionExpansionXmpPageEmpty12} +\pastebutton{FullPartialFractionExpansionXmpPageFull12}{\hidepaste} +\tab{5}\spadcommand{g := fullPartialFraction f\free{f3 }\bound{g3 }} +\indentrel{3}\begin{verbatim} + (12) + 1 + Ä + ÄÄ¿ 2 ÄÄ¿ 1 + > ÄÄÄÄÄÄ + > ÄÄÄÄÄÄÄÄÄ + ÄÄÙ x - %A ÄÄÙ 3 + 2 2 (x - %A) + %A - 2= 0 %A - 2= 0 + + + 1 + Ä + ÄÄ¿ 2 + > ÄÄÄÄÄÄ + ÄÄÙ x - %A + 2 + %A + 1= 0 +Type: FullPartialFractionExpansion(Fraction Integer,UnivariatePolynomial(x,Fraction Integer)) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{FullPartialFractionExpansionXmpPageEmpty12} +\begin{paste}{FullPartialFractionExpansionXmpPageEmpty12}{FullPartialFractionExpansionXmpPagePatch12} +\pastebutton{FullPartialFractionExpansionXmpPageEmpty12}{\showpaste} +\tab{5}\spadcommand{g := fullPartialFraction f\free{f3 }\bound{g3 }} +\end{paste}\end{patch} + +\begin{patch}{FullPartialFractionExpansionXmpPagePatch13} +\begin{paste}{FullPartialFractionExpansionXmpPageFull13}{FullPartialFractionExpansionXmpPageEmpty13} +\pastebutton{FullPartialFractionExpansionXmpPageFull13}{\hidepaste} +\tab{5}\spadcommand{g :: Fx - f\free{f3 g3 Fx }} +\indentrel{3}\begin{verbatim} + (13) 0 +Type: Fraction UnivariatePolynomial(x,Fraction Integer) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{FullPartialFractionExpansionXmpPageEmpty13} +\begin{paste}{FullPartialFractionExpansionXmpPageEmpty13}{FullPartialFractionExpansionXmpPagePatch13} +\pastebutton{FullPartialFractionExpansionXmpPageEmpty13}{\showpaste} +\tab{5}\spadcommand{g :: Fx - f\free{f3 g3 Fx }} +\end{paste}\end{patch} + +\begin{patch}{FullPartialFractionExpansionXmpPagePatch14} +\begin{paste}{FullPartialFractionExpansionXmpPageFull14}{FullPartialFractionExpansionXmpPageEmpty14} +\pastebutton{FullPartialFractionExpansionXmpPageFull14}{\hidepaste} +\tab{5}\spadcommand{f:Fx := x**3 / (x**21 + 2*x**20 + 4*x**19 + 7*x**18 + 10*x**17 + 17*x**16 + 22*x**15 + 30*x**14 + 36*x**13 + 40*x**12 + 47*x**11 + 46*x**10 + 49*x**9 + 43*x**8 + 38*x**7 + 32*x**6 + 23*x**5 + 19*x**4 + 10*x**3 + 7*x**2 + 2*x + 1)\free{Fx }\bound{f4 }} +\indentrel{3}\begin{verbatim} + (14) + 3 + x + / + 21 20 19 18 17 16 15 + x + 2x + 4x + 7x + 10x + 17x + 22x + + + 14 13 12 11 10 9 8 + 30x + 36x + 40x + 47x + 46x + 49x + 43x + + + 7 6 5 4 3 2 + 38x + 32x + 23x + 19x + 10x + 7x + 2x + 1 +Type: Fraction UnivariatePolynomial(x,Fraction Integer) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{FullPartialFractionExpansionXmpPageEmpty14} +\begin{paste}{FullPartialFractionExpansionXmpPageEmpty14}{FullPartialFractionExpansionXmpPagePatch14} +\pastebutton{FullPartialFractionExpansionXmpPageEmpty14}{\showpaste} +\tab{5}\spadcommand{f:Fx := x**3 / (x**21 + 2*x**20 + 4*x**19 + 7*x**18 + 10*x**17 + 17*x**16 + 22*x**15 + 30*x**14 + 36*x**13 + 40*x**12 + 47*x**11 + 46*x**10 + 49*x**9 + 43*x**8 + 38*x**7 + 32*x**6 + 23*x**5 + 19*x**4 + 10*x**3 + 7*x**2 + 2*x + 1)\free{Fx }\bound{f4 }} +\end{paste}\end{patch} + +\begin{patch}{FullPartialFractionExpansionXmpPagePatch15} +\begin{paste}{FullPartialFractionExpansionXmpPageFull15}{FullPartialFractionExpansionXmpPageEmpty15} +\pastebutton{FullPartialFractionExpansionXmpPageFull15}{\hidepaste} +\tab{5}\spadcommand{g := fullPartialFraction f\free{f4 }\bound{g4 }} +\indentrel{3}\begin{verbatim} + (15) + 1 1 19 + Ä %A Ä %A - ÄÄ + ÄÄ¿ 2 ÄÄ¿ 9 27 + > ÄÄÄÄÄÄ + > ÄÄÄÄÄÄÄÄÄ + ÄÄÙ x - %A ÄÄÙ x - %A + 2 2 + %A + 1= 0 %A + %A + 1= 0 + + + 1 1 + ÄÄ %A - ÄÄ + ÄÄ¿ 27 27 + > ÄÄÄÄÄÄÄÄÄÄ + ÄÄÙ 2 + 2 (x - %A) + %A + %A + 1= 0 + + + SIGMA + 5 2 + %A + %A + 1= 0 + , + 96556567040 4 420961732891 3 + - ÄÄÄÄÄÄÄÄÄÄÄÄ %A + ÄÄÄÄÄÄÄÄÄÄÄÄ %A + 912390759099 912390759099 + + + 59101056149 2 373545875923 + - ÄÄÄÄÄÄÄÄÄÄÄÄ %A - ÄÄÄÄÄÄÄÄÄÄÄÄ %A + 912390759099 912390759099 + + + 529673492498 + ÄÄÄÄÄÄÄÄÄÄÄÄ + 912390759099 + / + x - %A + + + SIGMA + 5 2 + %A + %A + 1= 0 + , + 5580868 4 2024443 3 4321919 2 + - ÄÄÄÄÄÄÄÄ %A - ÄÄÄÄÄÄÄÄ %A + ÄÄÄÄÄÄÄÄ %A + 94070601 94070601 94070601 + + + 84614 5070620 + - ÄÄÄÄÄÄÄ %A - ÄÄÄÄÄÄÄÄ + 1542141 94070601 + / + 2 + (x - %A) + + + SIGMA + 5 2 + %A + %A + 1= 0 + , + 1610957 4 2763014 3 2016775 2 + ÄÄÄÄÄÄÄÄ %A + ÄÄÄÄÄÄÄÄ %A - ÄÄÄÄÄÄÄÄ %A + 94070601 94070601 94070601 + + + 266953 4529359 + ÄÄÄÄÄÄÄÄ %A + ÄÄÄÄÄÄÄÄ + 94070601 94070601 + / + 3 + (x - %A) +Type: FullPartialFractionExpansion(Fraction Integer,UnivariatePolynomial(x,Fraction Integer)) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{FullPartialFractionExpansionXmpPageEmpty15} +\begin{paste}{FullPartialFractionExpansionXmpPageEmpty15}{FullPartialFractionExpansionXmpPagePatch15} +\pastebutton{FullPartialFractionExpansionXmpPageEmpty15}{\showpaste} +\tab{5}\spadcommand{g := fullPartialFraction f\free{f4 }\bound{g4 }} +\end{paste}\end{patch} + +\begin{patch}{FullPartialFractionExpansionXmpPagePatch16} +\begin{paste}{FullPartialFractionExpansionXmpPageFull16}{FullPartialFractionExpansionXmpPageEmpty16} +\pastebutton{FullPartialFractionExpansionXmpPageFull16}{\hidepaste} +\tab{5}\spadcommand{g :: Fx - f\free{f4 g4 Fx }} +\indentrel{3}\begin{verbatim} + (16) 0 +Type: Fraction UnivariatePolynomial(x,Fraction Integer) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{FullPartialFractionExpansionXmpPageEmpty16} +\begin{paste}{FullPartialFractionExpansionXmpPageEmpty16}{FullPartialFractionExpansionXmpPagePatch16} +\pastebutton{FullPartialFractionExpansionXmpPageEmpty16}{\showpaste} +\tab{5}\spadcommand{g :: Fx - f\free{f4 g4 Fx }} +\end{paste}\end{patch} + @ \section{function.ht} \pagehead{FunctionPage}{function.ht}{Functions in Axiom} @@ -8528,6 +22331,92 @@ similar to the one for polynomials: \autobuttons \end{page} +\begin{patch}{RationatFunctionPagePatch1} +\begin{paste}{RationatFunctionPageFull1}{RationatFunctionPageEmpty1} +\pastebutton{RationatFunctionPageFull1}{\hidepaste} +\tab{5}\spadcommand{f := (x - y) / (x + y)\bound{f }} +\indentrel{3}\begin{verbatim} + - y + x + (1) ÄÄÄÄÄÄÄ + y + x + Type: Fraction Polynomial Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{RationatFunctionPageEmpty1} +\begin{paste}{RationatFunctionPageEmpty1}{RationatFunctionPagePatch1} +\pastebutton{RationatFunctionPageEmpty1}{\showpaste} +\tab{5}\spadcommand{f := (x - y) / (x + y)\bound{f }} +\end{paste}\end{patch} + +\begin{patch}{RationatFunctionPagePatch2} +\begin{paste}{RationatFunctionPageFull2}{RationatFunctionPageEmpty2} +\pastebutton{RationatFunctionPageFull2}{\hidepaste} +\tab{5}\spadcommand{numer f\free{f }} +\indentrel{3}\begin{verbatim} + (2) - y + x + Type: Polynomial Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{RationatFunctionPageEmpty2} +\begin{paste}{RationatFunctionPageEmpty2}{RationatFunctionPagePatch2} +\pastebutton{RationatFunctionPageEmpty2}{\showpaste} +\tab{5}\spadcommand{numer f\free{f }} +\end{paste}\end{patch} + +\begin{patch}{RationatFunctionPagePatch3} +\begin{paste}{RationatFunctionPageFull3}{RationatFunctionPageEmpty3} +\pastebutton{RationatFunctionPageFull3}{\hidepaste} +\tab{5}\spadcommand{denom f\free{f }} +\indentrel{3}\begin{verbatim} + (3) y + x + Type: Polynomial Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{RationatFunctionPageEmpty3} +\begin{paste}{RationatFunctionPageEmpty3}{RationatFunctionPagePatch3} +\pastebutton{RationatFunctionPageEmpty3}{\showpaste} +\tab{5}\spadcommand{denom f\free{f }} +\end{paste}\end{patch} + +\begin{patch}{RationatFunctionPagePatch4} +\begin{paste}{RationatFunctionPageFull4}{RationatFunctionPageEmpty4} +\pastebutton{RationatFunctionPageFull4}{\hidepaste} +\tab{5}\spadcommand{eval(f, x = 1/x)\free{f }} +\indentrel{3}\begin{verbatim} + - x y + 1 + (4) ÄÄÄÄÄÄÄÄÄ + x y + 1 + Type: Fraction Polynomial Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{RationatFunctionPageEmpty4} +\begin{paste}{RationatFunctionPageEmpty4}{RationatFunctionPagePatch4} +\pastebutton{RationatFunctionPageEmpty4}{\showpaste} +\tab{5}\spadcommand{eval(f, x = 1/x)\free{f }} +\end{paste}\end{patch} + +\begin{patch}{RationatFunctionPagePatch5} +\begin{paste}{RationatFunctionPageFull5}{RationatFunctionPageEmpty5} +\pastebutton{RationatFunctionPageFull5}{\hidepaste} +\tab{5}\spadcommand{eval(f, [x = y, y = x])\free{f }} +\indentrel{3}\begin{verbatim} + y - x + (5) ÄÄÄÄÄ + y + x + Type: Fraction Polynomial Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{RationatFunctionPageEmpty5} +\begin{paste}{RationatFunctionPageEmpty5}{RationatFunctionPagePatch5} +\pastebutton{RationatFunctionPageEmpty5}{\showpaste} +\tab{5}\spadcommand{eval(f, [x = y, y = x])\free{f }} +\end{paste}\end{patch} + @ \pagehead{AlgebraicFunctionPage}{function.ht}{Algebraic Functions} <>= @@ -8556,7 +22445,119 @@ Use \spadfun{ratDenom} to remove the algebraic quantities from the denominator: \spadpaste{ratDenom g\free{g}} \endscroll -\autobuttons \end{page} +\autobuttons +\end{page} + +\begin{patch}{AlgebraicFunctionPagePatch1} +\begin{paste}{AlgebraicFunctionPageFull1}{AlgebraicFunctionPageEmpty1} +\pastebutton{AlgebraicFunctionPageFull1}{\hidepaste} +\tab{5}\spadcommand{f := sqrt(1 + x ** (1/3))\bound{f }} +\indentrel{3}\begin{verbatim} + ÚÄÄÄÄÄÄÄÄ¿ + ³3ÚÄ¿ + (1) \³\³x + 1 + Type: Expression Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{AlgebraicFunctionPageEmpty1} +\begin{paste}{AlgebraicFunctionPageEmpty1}{AlgebraicFunctionPagePatch1} +\pastebutton{AlgebraicFunctionPageEmpty1}{\showpaste} +\tab{5}\spadcommand{f := sqrt(1 + x ** (1/3))\bound{f }} +\end{paste}\end{patch} + +\begin{patch}{AlgebraicFunctionPagePatch2} +\begin{paste}{AlgebraicFunctionPageFull2}{AlgebraicFunctionPageEmpty2} +\pastebutton{AlgebraicFunctionPageFull2}{\hidepaste} +\tab{5}\spadcommand{y := rootOf(y**3 + y**2 - x*y + x**3 - 1, y)\bound{y }} +\indentrel{3}\begin{verbatim} + (2) y + Type: Expression Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{AlgebraicFunctionPageEmpty2} +\begin{paste}{AlgebraicFunctionPageEmpty2}{AlgebraicFunctionPagePatch2} +\pastebutton{AlgebraicFunctionPageEmpty2}{\showpaste} +\tab{5}\spadcommand{y := rootOf(y**3 + y**2 - x*y + x**3 - 1, y)\bound{y }} +\end{paste}\end{patch} + +\begin{patch}{AlgebraicFunctionPagePatch3} +\begin{paste}{AlgebraicFunctionPageFull3}{AlgebraicFunctionPageEmpty3} +\pastebutton{AlgebraicFunctionPageFull3}{\hidepaste} +\tab{5}\spadcommand{differentiate(y, x)\free{y }} +\indentrel{3}\begin{verbatim} + 2 + y - 3x + (3) ÄÄÄÄÄÄÄÄÄÄÄÄ + 2 + 3y + 2y - x + Type: Expression Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{AlgebraicFunctionPageEmpty3} +\begin{paste}{AlgebraicFunctionPageEmpty3}{AlgebraicFunctionPagePatch3} +\pastebutton{AlgebraicFunctionPageEmpty3}{\showpaste} +\tab{5}\spadcommand{differentiate(y, x)\free{y }} +\end{paste}\end{patch} + +\begin{patch}{AlgebraicFunctionPagePatch4} +\begin{paste}{AlgebraicFunctionPageFull4}{AlgebraicFunctionPageEmpty4} +\pastebutton{AlgebraicFunctionPageFull4}{\hidepaste} +\tab{5}\spadcommand{(y + 1) ** 3\free{y }} +\indentrel{3}\begin{verbatim} + 2 3 + (4) 2y + (x + 3)y - x + 2 + Type: Expression Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{AlgebraicFunctionPageEmpty4} +\begin{paste}{AlgebraicFunctionPageEmpty4}{AlgebraicFunctionPagePatch4} +\pastebutton{AlgebraicFunctionPageEmpty4}{\showpaste} +\tab{5}\spadcommand{(y + 1) ** 3\free{y }} +\end{paste}\end{patch} + +\begin{patch}{AlgebraicFunctionPagePatch5} +\begin{paste}{AlgebraicFunctionPageFull5}{AlgebraicFunctionPageEmpty5} +\pastebutton{AlgebraicFunctionPageFull5}{\hidepaste} +\tab{5}\spadcommand{g := inv f\bound{g }\free{y }} +\indentrel{3}\begin{verbatim} + 1 + (5) ÄÄÄÄÄÄÄÄÄÄÄ + ÚÄÄÄÄÄÄÄÄ¿ + ³3ÚÄ¿ + \³\³x + 1 + Type: Expression Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{AlgebraicFunctionPageEmpty5} +\begin{paste}{AlgebraicFunctionPageEmpty5}{AlgebraicFunctionPagePatch5} +\pastebutton{AlgebraicFunctionPageEmpty5}{\showpaste} +\tab{5}\spadcommand{g := inv f\bound{g }\free{y }} +\end{paste}\end{patch} + +\begin{patch}{AlgebraicFunctionPagePatch6} +\begin{paste}{AlgebraicFunctionPageFull6}{AlgebraicFunctionPageEmpty6} +\pastebutton{AlgebraicFunctionPageFull6}{\hidepaste} +\tab{5}\spadcommand{ratDenom g\free{g }} +\indentrel{3}\begin{verbatim} + ÚÄÄÄÄÄÄÄÄ¿ + 3ÚÄ¿2 3ÚÄ¿ ³3ÚÄ¿ + (\³x - \³x + 1)\³\³x + 1 + (6) ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ + x + 1 + Type: Expression Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{AlgebraicFunctionPageEmpty6} +\begin{paste}{AlgebraicFunctionPageEmpty6}{AlgebraicFunctionPagePatch6} +\pastebutton{AlgebraicFunctionPageEmpty6}{\showpaste} +\tab{5}\spadcommand{ratDenom g\free{g }} +\end{paste}\end{patch} @ \pagehead{ElementaryFunctionPage}{function.ht}{Elementary Functions} @@ -8573,7 +22574,62 @@ case of polynomials. It's also possible to substitute expressions for kernels instead of variables: \spadpaste{eval(f, log y = acosh(x + sqrt y))\free{f}} \endscroll -\autobuttons \end{page} +\autobuttons +\end{page} + +\begin{patch}{ElementaryFunctionPagePatch1} +\begin{paste}{ElementaryFunctionPageFull1}{ElementaryFunctionPageEmpty1} +\pastebutton{ElementaryFunctionPageFull1}{\hidepaste} +\tab{5}\spadcommand{f := x * log y * sin(1/(x+y))\bound{f }} +\indentrel{3}\begin{verbatim} + 1 + (1) x log(y)sin(ÄÄÄÄÄ) + y + x + Type: Expression Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ElementaryFunctionPageEmpty1} +\begin{paste}{ElementaryFunctionPageEmpty1}{ElementaryFunctionPagePatch1} +\pastebutton{ElementaryFunctionPageEmpty1}{\showpaste} +\tab{5}\spadcommand{f := x * log y * sin(1/(x+y))\bound{f }} +\end{paste}\end{patch} + +\begin{patch}{ElementaryFunctionPagePatch2} +\begin{paste}{ElementaryFunctionPageFull2}{ElementaryFunctionPageEmpty2} +\pastebutton{ElementaryFunctionPageFull2}{\hidepaste} +\tab{5}\spadcommand{eval(f, [x = y, y = x])\free{f }} +\indentrel{3}\begin{verbatim} + 1 + (2) y log(x)sin(ÄÄÄÄÄ) + y + x + Type: Expression Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ElementaryFunctionPageEmpty2} +\begin{paste}{ElementaryFunctionPageEmpty2}{ElementaryFunctionPagePatch2} +\pastebutton{ElementaryFunctionPageEmpty2}{\showpaste} +\tab{5}\spadcommand{eval(f, [x = y, y = x])\free{f }} +\end{paste}\end{patch} + +\begin{patch}{ElementaryFunctionPagePatch3} +\begin{paste}{ElementaryFunctionPageFull3}{ElementaryFunctionPageEmpty3} +\pastebutton{ElementaryFunctionPageFull3}{\hidepaste} +\tab{5}\spadcommand{eval(f, log y = acosh(x + sqrt y))\free{f }} +\indentrel{3}\begin{verbatim} + 1 ÚÄ¿ + (3) x sin(ÄÄÄÄÄ)acosh(\³y + x) + y + x + Type: Expression Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ElementaryFunctionPageEmpty3} +\begin{paste}{ElementaryFunctionPageEmpty3}{ElementaryFunctionPagePatch3} +\pastebutton{ElementaryFunctionPageEmpty3}{\showpaste} +\tab{5}\spadcommand{eval(f, log y = acosh(x + sqrt y))\free{f }} +\end{paste}\end{patch} @ \pagehead{FunctionSimplificationPage}{function.ht}{Simplification} @@ -8636,6 +22692,262 @@ matcher}{ugUserRulesPage}. \autobuttons \end{page} +\begin{patch}{FunctionSimplificationPagePatch1} +\begin{paste}{FunctionSimplificationPageFull1}{FunctionSimplificationPageEmpty1} +\pastebutton{FunctionSimplificationPageFull1}{\hidepaste} +\tab{5}\spadcommand{f := cos(x)/sec(x) * log(sin(x)**2/(cos(x)**2+sin(x)**2))\bound{f }} +\indentrel{3}\begin{verbatim} + 2 + sin(x) + cos(x)log(ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ) + 2 2 + sin(x) + cos(x) + (1) ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ + sec(x) + Type: Expression Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{FunctionSimplificationPageEmpty1} +\begin{paste}{FunctionSimplificationPageEmpty1}{FunctionSimplificationPagePatch1} +\pastebutton{FunctionSimplificationPageEmpty1}{\showpaste} +\tab{5}\spadcommand{f := cos(x)/sec(x) * log(sin(x)**2/(cos(x)**2+sin(x)**2))\bound{f }} +\end{paste}\end{patch} + +\begin{patch}{FunctionSimplificationPagePatch2} +\begin{paste}{FunctionSimplificationPageFull2}{FunctionSimplificationPageEmpty2} +\pastebutton{FunctionSimplificationPageFull2}{\hidepaste} +\tab{5}\spadcommand{g := simplify f\bound{g }\free{f }} +\indentrel{3}\begin{verbatim} + 2 2 + (2) cos(x) log(- cos(x) + 1) + Type: Expression Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{FunctionSimplificationPageEmpty2} +\begin{paste}{FunctionSimplificationPageEmpty2}{FunctionSimplificationPagePatch2} +\pastebutton{FunctionSimplificationPageEmpty2}{\showpaste} +\tab{5}\spadcommand{g := simplify f\bound{g }\free{f }} +\end{paste}\end{patch} + +\begin{patch}{FunctionSimplificationPagePatch3} +\begin{paste}{FunctionSimplificationPageFull3}{FunctionSimplificationPageEmpty3} +\pastebutton{FunctionSimplificationPageFull3}{\hidepaste} +\tab{5}\spadcommand{h := sin2csc cos2sec g\bound{h }\free{g }} +\indentrel{3}\begin{verbatim} + 2 + sec(x) - 1 + log(ÄÄÄÄÄÄÄÄÄÄÄ) + 2 + sec(x) + (3) ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ + 2 + sec(x) + Type: Expression Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{FunctionSimplificationPageEmpty3} +\begin{paste}{FunctionSimplificationPageEmpty3}{FunctionSimplificationPagePatch3} +\pastebutton{FunctionSimplificationPageEmpty3}{\showpaste} +\tab{5}\spadcommand{h := sin2csc cos2sec g\bound{h }\free{g }} +\end{paste}\end{patch} + +\begin{patch}{FunctionSimplificationPagePatch4} +\begin{paste}{FunctionSimplificationPageFull4}{FunctionSimplificationPageEmpty4} +\pastebutton{FunctionSimplificationPageFull4}{\hidepaste} +\tab{5}\spadcommand{expandLog h\free{h }} +\indentrel{3}\begin{verbatim} + 2 + log(sec(x) - 1) - 2log(sec(x)) + (4) ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ + 2 + sec(x) + Type: Expression Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{FunctionSimplificationPageEmpty4} +\begin{paste}{FunctionSimplificationPageEmpty4}{FunctionSimplificationPagePatch4} +\pastebutton{FunctionSimplificationPageEmpty4}{\showpaste} +\tab{5}\spadcommand{expandLog h\free{h }} +\end{paste}\end{patch} + +\begin{patch}{FunctionSimplificationPagePatch5} +\begin{paste}{FunctionSimplificationPageFull5}{FunctionSimplificationPageEmpty5} +\pastebutton{FunctionSimplificationPageFull5}{\hidepaste} +\tab{5}\spadcommand{f1 := sqrt((x+1)**3)\bound{f1 }} +\indentrel{3}\begin{verbatim} + ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿ + ³ 3 2 + (5) \³x + 3x + 3x + 1 + Type: Expression Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{FunctionSimplificationPageEmpty5} +\begin{paste}{FunctionSimplificationPageEmpty5}{FunctionSimplificationPagePatch5} +\pastebutton{FunctionSimplificationPageEmpty5}{\showpaste} +\tab{5}\spadcommand{f1 := sqrt((x+1)**3)\bound{f1 }} +\end{paste}\end{patch} + +\begin{patch}{FunctionSimplificationPagePatch6} +\begin{paste}{FunctionSimplificationPageFull6}{FunctionSimplificationPageEmpty6} +\pastebutton{FunctionSimplificationPageFull6}{\hidepaste} +\tab{5}\spadcommand{rootSimp f1\free{f1 }} +\indentrel{3}\begin{verbatim} + ÚÄÄÄÄÄ¿ + (6) (x + 1)\³x + 1 + Type: Expression Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{FunctionSimplificationPageEmpty6} +\begin{paste}{FunctionSimplificationPageEmpty6}{FunctionSimplificationPagePatch6} +\pastebutton{FunctionSimplificationPageEmpty6}{\showpaste} +\tab{5}\spadcommand{rootSimp f1\free{f1 }} +\end{paste}\end{patch} + +\begin{patch}{FunctionSimplificationPagePatch7} +\begin{paste}{FunctionSimplificationPageFull7}{FunctionSimplificationPageEmpty7} +\pastebutton{FunctionSimplificationPageFull7}{\hidepaste} +\tab{5}\spadcommand{g1 := sin(x + cos x)\bound{g1 }} +\indentrel{3}\begin{verbatim} + (7) sin(cos(x) + x) + Type: Expression Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{FunctionSimplificationPageEmpty7} +\begin{paste}{FunctionSimplificationPageEmpty7}{FunctionSimplificationPagePatch7} +\pastebutton{FunctionSimplificationPageEmpty7}{\showpaste} +\tab{5}\spadcommand{g1 := sin(x + cos x)\bound{g1 }} +\end{paste}\end{patch} + +\begin{patch}{FunctionSimplificationPagePatch8} +\begin{paste}{FunctionSimplificationPageFull8}{FunctionSimplificationPageEmpty8} +\pastebutton{FunctionSimplificationPageFull8}{\hidepaste} +\tab{5}\spadcommand{g2 := complexElementary g1\bound{g2 }\free{g1 }} +\indentrel{3}\begin{verbatim} + (8) + - + ÚÄÄÄ¿ + \³- 1 + * + %e + ** + ÚÄÄÄ¿ 2 ÚÄÄÄ¿ + ÚÄÄÄ¿ x\³- 1 ÚÄÄÄ¿ x\³- 1 + \³- 1 (%e ) + 2x\³- 1 %e + + + ÚÄÄÄ¿ + \³- 1 + / + ÚÄÄÄ¿ + x\³- 1 + 2%e + ** + 2 + + + ÚÄÄÄ¿ + \³- 1 + / + ÚÄÄÄ¿ 2 ÚÄÄÄ¿ + ÚÄÄÄ¿ x\³- 1 ÚÄÄÄ¿ x\³- 1 ÚÄÄÄ¿ + \³- 1 (%e ) + 2x\³- 1 %e + \³- 1 + ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ + ÚÄÄÄ¿ + x\³- 1 + 2%e + 2%e + Type: Expression Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{FunctionSimplificationPageEmpty8} +\begin{paste}{FunctionSimplificationPageEmpty8}{FunctionSimplificationPagePatch8} +\pastebutton{FunctionSimplificationPageEmpty8}{\showpaste} +\tab{5}\spadcommand{g2 := complexElementary g1\bound{g2 }\free{g1 }} +\end{paste}\end{patch} + +\begin{patch}{FunctionSimplificationPagePatch9} +\begin{paste}{FunctionSimplificationPageFull9}{FunctionSimplificationPageEmpty9} +\pastebutton{FunctionSimplificationPageFull9}{\hidepaste} +\tab{5}\spadcommand{trigs g2\free{g2 }} +\indentrel{3}\begin{verbatim} + (9) sin(cos(x) + x) + Type: Expression Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{FunctionSimplificationPageEmpty9} +\begin{paste}{FunctionSimplificationPageEmpty9}{FunctionSimplificationPagePatch9} +\pastebutton{FunctionSimplificationPageEmpty9}{\showpaste} +\tab{5}\spadcommand{trigs g2\free{g2 }} +\end{paste}\end{patch} + +\begin{patch}{FunctionSimplificationPagePatch10} +\begin{paste}{FunctionSimplificationPageFull10}{FunctionSimplificationPageEmpty10} +\pastebutton{FunctionSimplificationPageFull10}{\hidepaste} +\tab{5}\spadcommand{h1 := sinh(x + cosh x)\bound{h1 }} +\indentrel{3}\begin{verbatim} + (10) sinh(cosh(x) + x) + Type: Expression Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{FunctionSimplificationPageEmpty10} +\begin{paste}{FunctionSimplificationPageEmpty10}{FunctionSimplificationPagePatch10} +\pastebutton{FunctionSimplificationPageEmpty10}{\showpaste} +\tab{5}\spadcommand{h1 := sinh(x + cosh x)\bound{h1 }} +\end{paste}\end{patch} + +\begin{patch}{FunctionSimplificationPagePatch11} +\begin{paste}{FunctionSimplificationPageFull11}{FunctionSimplificationPageEmpty11} +\pastebutton{FunctionSimplificationPageFull11}{\hidepaste} +\tab{5}\spadcommand{h2 := realElementary h1\bound{h2 }\free{h1 }} +\indentrel{3}\begin{verbatim} + x 2 x 2 + (%e ) + 2x %e + 1 + ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ + x + 2%e + (%e ) - 1 + (11) ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ + x 2 x + (%e ) + 2x %e + 1 + ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ + x + 2%e + 2%e + Type: Expression Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{FunctionSimplificationPageEmpty11} +\begin{paste}{FunctionSimplificationPageEmpty11}{FunctionSimplificationPagePatch11} +\pastebutton{FunctionSimplificationPageEmpty11}{\showpaste} +\tab{5}\spadcommand{h2 := realElementary h1\bound{h2 }\free{h1 }} +\end{paste}\end{patch} + +\begin{patch}{FunctionSimplificationPagePatch12} +\begin{paste}{FunctionSimplificationPageFull12}{FunctionSimplificationPageEmpty12} +\pastebutton{FunctionSimplificationPageFull12}{\hidepaste} +\tab{5}\spadcommand{htrigs h2\free{h2 }} +\indentrel{3}\begin{verbatim} + (12) sinh(cosh(x) + x) + Type: Expression Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{FunctionSimplificationPageEmpty12} +\begin{paste}{FunctionSimplificationPageEmpty12}{FunctionSimplificationPagePatch12} +\pastebutton{FunctionSimplificationPageEmpty12}{\showpaste} +\tab{5}\spadcommand{htrigs h2\free{h2 }} +\end{paste} +\end{patch} + @ \section{gbf.ht} \pagehead{GroebnerFactorizationPkgXmpPage}{gbf.ht} @@ -8733,6 +23045,116 @@ used. \autobuttons \end{page} +\begin{patch}{GroebnerFactorizationPackageXmpPagePatch1} +\begin{paste}{GroebnerFactorizationPackageXmpPageFull1}{GroebnerFactorizationPackageXmpPageEmpty1} +\pastebutton{GroebnerFactorizationPackageXmpPageFull1}{\hidepaste} +\tab{5}\spadcommand{mfzn : SQMATRIX(6,DMP([x,y,z],Fraction INT)) := [[0,1,1,1,1,1], [1,0,1,8/3,x,8/3], [1,1,0,1,8/3,y], [1,8/3,1,0,1,8/3], [1,x,8/3,1,0,1], [1,8/3,y,8/3,1,0]]\bound{mfzn }} +\indentrel{3}\begin{verbatim} + Ú0 1 1 1 1 1¿ + ³ ³ + ³ 8 8³ + ³1 0 1 Ä x ij + ³ 3 3³ + ³ ³ + ³ 8 ³ + ³1 1 0 1 Ä y³ + ³ 3 ³ + ³ ³ + (1) ³ 8 8³ + ³1 Ä 1 0 1 ij + ³ 3 3³ + ³ ³ + ³ 8 ³ + ³1 x Ä 1 0 1³ + ³ 3 ³ + ³ ³ + ³ 8 8 ³ + ³1 Ä y Ä 1 0³ + À 3 3 Ù +Type: SquareMatrix(6,DistributedMultivariatePolynomial([x,y,z],Fraction Integer)) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{GroebnerFactorizationPackageXmpPageEmpty1} +\begin{paste}{GroebnerFactorizationPackageXmpPageEmpty1}{GroebnerFactorizationPackageXmpPagePatch1} +\pastebutton{GroebnerFactorizationPackageXmpPageEmpty1}{\showpaste} +\tab{5}\spadcommand{mfzn : SQMATRIX(6,DMP([x,y,z],Fraction INT)) := [[0,1,1,1,1,1], [1,0,1,8/3,x,8/3], [1,1,0,1,8/3,y], [1,8/3,1,0,1,8/3], [1,x,8/3,1,0,1], [1,8/3,y,8/3,1,0]]\bound{mfzn }} +\end{paste}\end{patch} + +\begin{patch}{GroebnerFactorizationPackageXmpPagePatch2} +\begin{paste}{GroebnerFactorizationPackageXmpPageFull2}{GroebnerFactorizationPackageXmpPageEmpty2} +\pastebutton{GroebnerFactorizationPackageXmpPageFull2}{\hidepaste} +\tab{5}\spadcommand{eq := determinant mfzn\free{mfzn }\bound{eq }} +\indentrel{3}\begin{verbatim} + (2) + 2 2 22 2 25 2 22 2 388 250 + - x y + ÄÄ x y - ÄÄ x + ÄÄ x y - ÄÄÄ x y - ÄÄÄ x + 3 9 3 9 27 + + + 25 2 250 14575 + - ÄÄ y - ÄÄÄ y + ÄÄÄÄÄ + 9 27 81 +Type: DistributedMultivariatePolynomial([x,y,z],Fraction Integer) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{GroebnerFactorizationPackageXmpPageEmpty2} +\begin{paste}{GroebnerFactorizationPackageXmpPageEmpty2}{GroebnerFactorizationPackageXmpPagePatch2} +\pastebutton{GroebnerFactorizationPackageXmpPageEmpty2}{\showpaste} +\tab{5}\spadcommand{eq := determinant mfzn\free{mfzn }\bound{eq }} +\end{paste}\end{patch} + +\begin{patch}{GroebnerFactorizationPackageXmpPagePatch3} +\begin{paste}{GroebnerFactorizationPackageXmpPageFull3}{GroebnerFactorizationPackageXmpPageEmpty3} +\pastebutton{GroebnerFactorizationPackageXmpPageFull3}{\hidepaste} +\tab{5}\spadcommand{groebnerFactorize [eq, eval(eq, [x,y,z], [y,z,x]), eval(eq, [x,y,z], [z,x,y])]\free{eq }} +\indentrel{3}\begin{verbatim} + (3) + [ + 22 22 22 121 + [x y + x z - ÄÄ x + y z - ÄÄ y - ÄÄ z + ÄÄÄ, + 3 3 3 3 + + 2 22 25 2 22 25 + x z - ÄÄ x z + ÄÄ x + y z - ÄÄ y z + ÄÄ y + 3 9 3 9 + + + 22 2 388 250 + - ÄÄ z + ÄÄÄ z + ÄÄÄ + 3 9 27 + , + + 2 2 22 2 25 2 22 2 388 250 + y z - ÄÄ y z + ÄÄ y - ÄÄ y z + ÄÄÄ y z + ÄÄÄ y + 3 9 3 9 27 + + + 25 2 250 14575 + ÄÄ z + ÄÄÄ z - ÄÄÄÄÄ + 9 27 81 + ] + , + 21994 2 21994 4427 463 + [x + y - ÄÄÄÄÄ,y - ÄÄÄÄÄ y + ÄÄÄÄ,z - ÄÄÄ], + 5625 5625 675 87 + 2 1 11 5 265 2 38 265 + [x - Ä x z - ÄÄ x - Ä z + ÄÄÄ,y - z,z - ÄÄ z + ÄÄÄ], + 2 2 6 18 3 9 + 25 11 11 11 11 11 + [x - ÄÄ,y - ÄÄ,z - ÄÄ], [x - ÄÄ,y - ÄÄ,z - ÄÄ], + 9 3 3 3 3 3 + 5 5 5 19 5 5 + [x + Ä,y + Ä,z + Ä], [x - ÄÄ,y + Ä,z + Ä]] + 3 3 3 3 3 3 +Type: List List DistributedMultivariatePolynomial([x,y,z],Fraction Integer) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{GroebnerFactorizationPackageXmpPageEmpty3} +\begin{paste}{GroebnerFactorizationPackageXmpPageEmpty3}{GroebnerFactorizationPackageXmpPagePatch3} +\pastebutton{GroebnerFactorizationPackageXmpPageEmpty3}{\showpaste} +\tab{5}\spadcommand{groebnerFactorize [eq, eval(eq, [x,y,z], [y,z,x]), eval(eq, [x,y,z], [z,x,y])]\free{eq }} +\end{paste}\end{patch} + @ \section{gloss.ht} \pagehead{GlossaryPage}{gloss.ht}{Glossary} @@ -9879,7 +24301,102 @@ Implicit curves: p(x,y) = 0. Run all examples. \spadpaste{All \free{example1 example2 example3 example4 example5 example6}} \endscroll -\autobuttons \end{page} +\autobuttons +\end{page} + +\begin{patch}{AssortedGraphicsExamplePagePatch1} +\begin{paste}{AssortedGraphicsExamplePageFull1}{AssortedGraphicsExamplePageEmpty1} +\pastebutton{AssortedGraphicsExamplePageFull1}{\hidepaste} +\tab{5}\spadgraph{draw(sin(x * y), x = -2.5..2.5, y = -2.5..2.5)\bound{example1 }} +\center{\unixcommand{\inputimage{\env{AXIOM}/doc/viewports/assortedgraphicsexamplepage1.view/image}}{viewalone\space{1} \env{AXIOM}/doc/viewports/assortedgraphicsexamplepage1}} +\end{paste}\end{patch} + +\begin{patch}{AssortedGraphicsExamplePageEmpty1} +\begin{paste}{AssortedGraphicsExamplePageEmpty1}{AssortedGraphicsExamplePagePatch1} +\pastebutton{AssortedGraphicsExamplePageEmpty1}{\showpaste} +\tab{5}\spadgraph{draw(sin(x * y), x = -2.5..2.5, y = -2.5..2.5)\bound{example1 }} +\end{paste}\end{patch} + +\begin{patch}{AssortedGraphicsExamplePagePatch2} +\begin{paste}{AssortedGraphicsExamplePageFull2}{AssortedGraphicsExamplePageEmpty2} +\pastebutton{AssortedGraphicsExamplePageFull2}{\hidepaste} +\tab{5}\spadgraph{draw(sin tan x - tan sin x,x = 0..6)\bound{example2 }} +\center{\unixcommand{\inputimage{\env{AXIOM}/doc/viewports/assortedgraphicsexamplepage2.view/image}}{viewalone\space{1} \env{AXIOM}/doc/viewports/assortedgraphicsexamplepage2}} +\end{paste}\end{patch} + +\begin{patch}{AssortedGraphicsExamplePageEmpty2} +\begin{paste}{AssortedGraphicsExamplePageEmpty2}{AssortedGraphicsExamplePagePatch2} +\pastebutton{AssortedGraphicsExamplePageEmpty2}{\showpaste} +\tab{5}\spadgraph{draw(sin tan x - tan sin x,x = 0..6)\bound{example2 }} +\end{paste}\end{patch} + +\begin{patch}{AssortedGraphicsExamplePagePatch3} +\begin{paste}{AssortedGraphicsExamplePageFull3}{AssortedGraphicsExamplePageEmpty3} +\pastebutton{AssortedGraphicsExamplePageFull3}{\hidepaste} +\tab{5}\spadgraph{draw(curve(sin(t)*sin(2*t), sin(3*t)*sin(4*t)), t = 0..2*\%pi)\bound{example3 }} +\center{\unixcommand{\inputimage{\env{AXIOM}/doc/viewports/assortedgraphicsexamplepage3.view/image}}{viewalone\space{1} \env{AXIOM}/doc/viewports/assortedgraphicsexamplepage3}} +\end{paste}\end{patch} + +\begin{patch}{AssortedGraphicsExamplePageEmpty3} +\begin{paste}{AssortedGraphicsExamplePageEmpty3}{AssortedGraphicsExamplePagePatch3} +\pastebutton{AssortedGraphicsExamplePageEmpty3}{\showpaste} +\tab{5}\spadgraph{draw(curve(sin(t)*sin(2*t), sin(3*t)*sin(4*t)), t = 0..2*\%pi)\bound{example3 }} +\end{paste}\end{patch} + +\begin{patch}{AssortedGraphicsExamplePagePatch4} +\begin{paste}{AssortedGraphicsExamplePageFull4}{AssortedGraphicsExamplePageEmpty4} +\pastebutton{AssortedGraphicsExamplePageFull4}{\hidepaste} +\tab{5}\spadgraph{draw(curve(sin(t)*sin(2*t), sin(3*t)*sin(4*t), sin(5*t)*sin(6*t)), t = 0..2*\%pi)\bound{example4 }} +\center{\unixcommand{\inputimage{\env{AXIOM}/doc/viewports/assortedgraphicsexamplepage4.view/image}}{viewalone\space{1} \env{AXIOM}/doc/viewports/assortedgraphicsexamplepage4}} +\end{paste}\end{patch} + +\begin{patch}{AssortedGraphicsExamplePageEmpty4} +\begin{paste}{AssortedGraphicsExamplePageEmpty4}{AssortedGraphicsExamplePagePatch4} +\pastebutton{AssortedGraphicsExamplePageEmpty4}{\showpaste} +\tab{5}\spadgraph{draw(curve(sin(t)*sin(2*t), sin(3*t)*sin(4*t), sin(5*t)*sin(6*t)), t = 0..2*\%pi)\bound{example4 }} +\end{paste}\end{patch} + +\begin{patch}{AssortedGraphicsExamplePagePatch5} +\begin{paste}{AssortedGraphicsExamplePageFull5}{AssortedGraphicsExamplePageEmpty5} +\pastebutton{AssortedGraphicsExamplePageFull5}{\hidepaste} +\tab{5}\spadgraph{draw(sin(17*t), t = 0..2*\%pi, coordinates == polar)\bound{example5 }} +\center{\unixcommand{\inputimage{\env{AXIOM}/doc/viewports/assortedgraphicsexamplepage5.view/image}}{viewalone\space{1} \env{AXIOM}/doc/viewports/assortedgraphicsexamplepage5}} +\end{paste}\end{patch} + +\begin{patch}{AssortedGraphicsExamplePageEmpty5} +\begin{paste}{AssortedGraphicsExamplePageEmpty5}{AssortedGraphicsExamplePagePatch5} +\pastebutton{AssortedGraphicsExamplePageEmpty5}{\showpaste} +\tab{5}\spadgraph{draw(sin(17*t), t = 0..2*\%pi, coordinates == polar)\bound{example5 }} +\end{paste}\end{patch} + +\begin{patch}{AssortedGraphicsExamplePagePatch6} +\begin{paste}{AssortedGraphicsExamplePageFull6}{AssortedGraphicsExamplePageEmpty6} +\pastebutton{AssortedGraphicsExamplePageFull6}{\hidepaste} +\tab{5}\spadgraph{draw(y**2 + y = x**3 - x, x, y,range == [-2..2,-2..1])\bound{example6 }} +\center{\unixcommand{\inputimage{\env{AXIOM}/doc/viewports/assortedgraphicsexamplepage6.view/image}}{viewalone\space{1} \env{AXIOM}/doc/viewports/assortedgraphicsexamplepage6}} +\end{paste}\end{patch} + +\begin{patch}{AssortedGraphicsExamplePageEmpty6} +\begin{paste}{AssortedGraphicsExamplePageEmpty6}{AssortedGraphicsExamplePagePatch6} +\pastebutton{AssortedGraphicsExamplePageEmpty6}{\showpaste} +\tab{5}\spadgraph{draw(y**2 + y = x**3 - x, x, y,range == [-2..2,-2..1])\bound{example6 }} +\end{paste}\end{patch} + +\begin{patch}{AssortedGraphicsExamplePagePatch7} +\begin{paste}{AssortedGraphicsExamplePageFull7}{AssortedGraphicsExamplePageEmpty7} +\pastebutton{AssortedGraphicsExamplePageFull7}{\hidepaste} +\tab{5}\spadcommand{All\free{example1 example2 example3 example4 example5 example6 }} +\indentrel{3}\begin{verbatim} + (7) All + Type: Variable All +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{AssortedGraphicsExamplePageEmpty7} +\begin{paste}{AssortedGraphicsExamplePageEmpty7}{AssortedGraphicsExamplePagePatch7} +\pastebutton{AssortedGraphicsExamplePageEmpty7}{\showpaste} +\tab{5}\spadcommand{All\free{example1 example2 example3 example4 example5 example6 }} +\end{paste}\end{patch} @ \pagehead{ThreeDimensionalGraphicsExamplePage}{graphics.ht} @@ -9928,7 +24445,188 @@ title=="Banchoff Klein Bottle") \free{f g h} \bound{example4}} \newline \spadpaste{All \free{example1 example2 example3 example4}} \endscroll -\autobuttons \end{page} +\autobuttons +\end{page} + +\begin{patch}{ThreeDimensionalGraphicsExamplePagePatch1} +\begin{paste}{ThreeDimensionalGraphicsExamplePageFull1}{ThreeDimensionalGraphicsExamplePageEmpty1} +\pastebutton{ThreeDimensionalGraphicsExamplePageFull1}{\hidepaste} +\tab{5}\spadgraph{draw(surface((1+exp(-100*u*u))*sin(\%pi*u)*sin(\%pi*v), (1+exp(-100*u*u))*sin(\%pi*u)*cos(\%pi*v), (1+exp(-100*u*u))*cos(\%pi*u)), u=0..1, v=0..2, title=="Pear")\bound{example1 }} +\center{\unixcommand{\inputimage{\env{AXIOM}/doc/viewports/threedimensionalgraphicsexamplepage1.view/image}}{viewalone\space{1} \env{AXIOM}/doc/viewports/threedimensionalgraphicsexamplepage1}} +\end{paste}\end{patch} + +\begin{patch}{ThreeDimensionalGraphicsExamplePageEmpty1} +\begin{paste}{ThreeDimensionalGraphicsExamplePageEmpty1}{ThreeDimensionalGraphicsExamplePagePatch1} +\pastebutton{ThreeDimensionalGraphicsExamplePageEmpty1}{\showpaste} +\tab{5}\spadgraph{draw(surface((1+exp(-100*u*u))*sin(\%pi*u)*sin(\%pi*v), (1+exp(-100*u*u))*sin(\%pi*u)*cos(\%pi*v), (1+exp(-100*u*u))*cos(\%pi*u)), u=0..1, v=0..2, title=="Pear")\bound{example1 }} +\end{paste}\end{patch} + +\begin{patch}{ThreeDimensionalGraphicsExamplePagePatch2} +\begin{paste}{ThreeDimensionalGraphicsExamplePageFull2}{ThreeDimensionalGraphicsExamplePageEmpty2} +\pastebutton{ThreeDimensionalGraphicsExamplePageFull2}{\hidepaste} +\tab{5}\spadgraph{draw(surface(x*cos(y),x*sin(y),y*cos(x)), x=-4..4, y=0..2*\%pi, var1Steps==40, var2Steps==40, title=="Trig Screw")\bound{example2 }} +\center{\unixcommand{\inputimage{\env{AXIOM}/doc/viewports/threedimensionalgraphicsexamplepage2.view/image}}{viewalone\space{1} \env{AXIOM}/doc/viewports/threedimensionalgraphicsexamplepage2}} +\end{paste}\end{patch} + +\begin{patch}{ThreeDimensionalGraphicsExamplePageEmpty2} +\begin{paste}{ThreeDimensionalGraphicsExamplePageEmpty2}{ThreeDimensionalGraphicsExamplePagePatch2} +\pastebutton{ThreeDimensionalGraphicsExamplePageEmpty2}{\showpaste} +\tab{5}\spadgraph{draw(surface(x*cos(y),x*sin(y),y*cos(x)), x=-4..4, y=0..2*\%pi, var1Steps==40, var2Steps==40, title=="Trig Screw")\bound{example2 }} +\end{paste}\end{patch} + +\begin{patch}{ThreeDimensionalGraphicsExamplePagePatch3} +\begin{paste}{ThreeDimensionalGraphicsExamplePageFull3}{ThreeDimensionalGraphicsExamplePageEmpty3} +\pastebutton{ThreeDimensionalGraphicsExamplePageFull3}{\hidepaste} +\tab{5}\spadcommand{a := 1.3 * cos(2*x) * cos(y) + sin(y) * cos(x)\bound{a }} +\indentrel{3}\begin{verbatim} + (3) cos(x)sin(y) + 1.3 cos(2.0 x)cos(y) + Type: Expression Float +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ThreeDimensionalGraphicsExamplePageEmpty3} +\begin{paste}{ThreeDimensionalGraphicsExamplePageEmpty3}{ThreeDimensionalGraphicsExamplePagePatch3} +\pastebutton{ThreeDimensionalGraphicsExamplePageEmpty3}{\showpaste} +\tab{5}\spadcommand{a := 1.3 * cos(2*x) * cos(y) + sin(y) * cos(x)\bound{a }} +\end{paste}\end{patch} + +\begin{patch}{ThreeDimensionalGraphicsExamplePagePatch4} +\begin{paste}{ThreeDimensionalGraphicsExamplePageFull4}{ThreeDimensionalGraphicsExamplePageEmpty4} +\pastebutton{ThreeDimensionalGraphicsExamplePageFull4}{\hidepaste} +\tab{5}\spadcommand{b := 1.3 * sin(2*x) * cos(y) - sin(y) * sin(x)\bound{b }} +\indentrel{3}\begin{verbatim} + (4) - 1.0 sin(x)sin(y) + 1.3 cos(y)sin(2.0 x) + Type: Expression Float +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ThreeDimensionalGraphicsExamplePageEmpty4} +\begin{paste}{ThreeDimensionalGraphicsExamplePageEmpty4}{ThreeDimensionalGraphicsExamplePagePatch4} +\pastebutton{ThreeDimensionalGraphicsExamplePageEmpty4}{\showpaste} +\tab{5}\spadcommand{b := 1.3 * sin(2*x) * cos(y) - sin(y) * sin(x)\bound{b }} +\end{paste}\end{patch} + +\begin{patch}{ThreeDimensionalGraphicsExamplePagePatch5} +\begin{paste}{ThreeDimensionalGraphicsExamplePageFull5}{ThreeDimensionalGraphicsExamplePageEmpty5} +\pastebutton{ThreeDimensionalGraphicsExamplePageFull5}{\hidepaste} +\tab{5}\spadcommand{c := 2.5 * cos(y)\bound{c }} +\indentrel{3}\begin{verbatim} + (5) 2.5 cos(y) + Type: Expression Float +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ThreeDimensionalGraphicsExamplePageEmpty5} +\begin{paste}{ThreeDimensionalGraphicsExamplePageEmpty5}{ThreeDimensionalGraphicsExamplePagePatch5} +\pastebutton{ThreeDimensionalGraphicsExamplePageEmpty5}{\showpaste} +\tab{5}\spadcommand{c := 2.5 * cos(y)\bound{c }} +\end{paste}\end{patch} + +\begin{patch}{ThreeDimensionalGraphicsExamplePagePatch6} +\begin{paste}{ThreeDimensionalGraphicsExamplePageFull6}{ThreeDimensionalGraphicsExamplePageEmpty6} +\pastebutton{ThreeDimensionalGraphicsExamplePageFull6}{\hidepaste} +\tab{5}\spadgraph{draw(surface(a,b,c), x=0..\%pi, y=-\%pi..\%pi, var1Steps==40, var2Steps==40, title=="Etruscan Venus")\free{a b c }\bound{example3 }} +\center{\unixcommand{\inputimage{\env{AXIOM}/doc/viewports/threedimensionalgraphicsexamplepage6.view/image}}{viewalone\space{1} \env{AXIOM}/doc/viewports/threedimensionalgraphicsexamplepage6}} +\end{paste}\end{patch} + +\begin{patch}{ThreeDimensionalGraphicsExamplePageEmpty6} +\begin{paste}{ThreeDimensionalGraphicsExamplePageEmpty6}{ThreeDimensionalGraphicsExamplePagePatch6} +\pastebutton{ThreeDimensionalGraphicsExamplePageEmpty6}{\showpaste} +\tab{5}\spadgraph{draw(surface(a,b,c), x=0..\%pi, y=-\%pi..\%pi, var1Steps==40, var2Steps==40, title=="Etruscan Venus")\free{a b c }\bound{example3 }} +\end{paste}\end{patch} + +\begin{patch}{ThreeDimensionalGraphicsExamplePagePatch7} +\begin{paste}{ThreeDimensionalGraphicsExamplePageFull7}{ThreeDimensionalGraphicsExamplePageEmpty7} +\pastebutton{ThreeDimensionalGraphicsExamplePageFull7}{\hidepaste} +\tab{5}\spadcommand{f:=cos(x)*(cos(x/2)*(sqrt(2) + cos(y))+(sin(x/2)*sin(y)*cos(y)))\bound{f }} +\indentrel{3}\begin{verbatim} + (7) + x x + cos(x)cos(y)sin(Ä)sin(y) + cos(Ä)cos(x)cos(y) + 2 2 + + + ÚÄ¿ x + \³2 cos(Ä)cos(x) + 2 + Type: Expression Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ThreeDimensionalGraphicsExamplePageEmpty7} +\begin{paste}{ThreeDimensionalGraphicsExamplePageEmpty7}{ThreeDimensionalGraphicsExamplePagePatch7} +\pastebutton{ThreeDimensionalGraphicsExamplePageEmpty7}{\showpaste} +\tab{5}\spadcommand{f:=cos(x)*(cos(x/2)*(sqrt(2) + cos(y))+(sin(x/2)*sin(y)*cos(y)))\bound{f }} +\end{paste}\end{patch} + +\begin{patch}{ThreeDimensionalGraphicsExamplePagePatch8} +\begin{paste}{ThreeDimensionalGraphicsExamplePageFull8}{ThreeDimensionalGraphicsExamplePageEmpty8} +\pastebutton{ThreeDimensionalGraphicsExamplePageFull8}{\hidepaste} +\tab{5}\spadcommand{g:=sin(x)*(cos(x/2)*(sqrt(2) + cos(y))+(sin(x/2)*sin(y)*cos(y)))\bound{g }} +\indentrel{3}\begin{verbatim} + (8) + x + cos(y)sin(Ä)sin(x)sin(y) + 2 + + + x ÚÄ¿ x + (cos(Ä)cos(y) + \³2 cos(Ä))sin(x) + 2 2 + Type: Expression Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ThreeDimensionalGraphicsExamplePageEmpty8} +\begin{paste}{ThreeDimensionalGraphicsExamplePageEmpty8}{ThreeDimensionalGraphicsExamplePagePatch8} +\pastebutton{ThreeDimensionalGraphicsExamplePageEmpty8}{\showpaste} +\tab{5}\spadcommand{g:=sin(x)*(cos(x/2)*(sqrt(2) + cos(y))+(sin(x/2)*sin(y)*cos(y)))\bound{g }} +\end{paste}\end{patch} + +\begin{patch}{ThreeDimensionalGraphicsExamplePagePatch9} +\begin{paste}{ThreeDimensionalGraphicsExamplePageFull9}{ThreeDimensionalGraphicsExamplePageEmpty9} +\pastebutton{ThreeDimensionalGraphicsExamplePageFull9}{\hidepaste} +\tab{5}\spadcommand{h:=-sin(x/2)*(sqrt(2)+cos(y)) + cos(x/2)*sin(y)*cos(y)\bound{h }} +\indentrel{3}\begin{verbatim} + x ÚÄ¿ x + (9) cos(Ä)cos(y)sin(y) + (- cos(y) - \³2 )sin(Ä) + 2 2 + Type: Expression Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ThreeDimensionalGraphicsExamplePageEmpty9} +\begin{paste}{ThreeDimensionalGraphicsExamplePageEmpty9}{ThreeDimensionalGraphicsExamplePagePatch9} +\pastebutton{ThreeDimensionalGraphicsExamplePageEmpty9}{\showpaste} +\tab{5}\spadcommand{h:=-sin(x/2)*(sqrt(2)+cos(y)) + cos(x/2)*sin(y)*cos(y)\bound{h }} +\end{paste}\end{patch} + +\begin{patch}{ThreeDimensionalGraphicsExamplePagePatch10} +\begin{paste}{ThreeDimensionalGraphicsExamplePageFull10}{ThreeDimensionalGraphicsExamplePageEmpty10} +\pastebutton{ThreeDimensionalGraphicsExamplePageFull10}{\hidepaste} +\tab{5}\spadgraph{draw(surface(f,g,h), x=0..4*\%pi, y=0..2*\%pi, var1Steps==50, var2Steps==50, title=="Banchoff Klein Bottle")\free{f g h }\bound{example4 }} +\center{\unixcommand{\inputimage{\env{AXIOM}/doc/viewports/threedimensionalgraphicsexamplepage10.view/image}}{viewalone\space{1} \env{AXIOM}/doc/viewports/threedimensionalgraphicsexamplepage10}} +\end{paste}\end{patch} + +\begin{patch}{ThreeDimensionalGraphicsExamplePageEmpty10} +\begin{paste}{ThreeDimensionalGraphicsExamplePageEmpty10}{ThreeDimensionalGraphicsExamplePagePatch10} +\pastebutton{ThreeDimensionalGraphicsExamplePageEmpty10}{\showpaste} +\tab{5}\spadgraph{draw(surface(f,g,h), x=0..4*\%pi, y=0..2*\%pi, var1Steps==50, var2Steps==50, title=="Banchoff Klein Bottle")\free{f g h }\bound{example4 }} +\end{paste}\end{patch} + +\begin{patch}{ThreeDimensionalGraphicsExamplePagePatch11} +\begin{paste}{ThreeDimensionalGraphicsExamplePageFull11}{ThreeDimensionalGraphicsExamplePageEmpty11} +\pastebutton{ThreeDimensionalGraphicsExamplePageFull11}{\hidepaste} +\tab{5}\spadcommand{All\free{example1 example2 example3 example4 }} +\indentrel{3}\begin{verbatim} + (11) All + Type: Variable All +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ThreeDimensionalGraphicsExamplePageEmpty11} +\begin{paste}{ThreeDimensionalGraphicsExamplePageEmpty11}{ThreeDimensionalGraphicsExamplePagePatch11} +\pastebutton{ThreeDimensionalGraphicsExamplePageEmpty11}{\showpaste} +\tab{5}\spadcommand{All\free{example1 example2 example3 example4 }} +\end{paste}\end{patch} @ \pagehead{OneVariableGraphicsExamplePage}{graphics.ht} @@ -9948,7 +24646,76 @@ Choose a particular example or choose 'All' to see all the examples. \newline \spadpaste{All \free{example1 example2 example3 example4}} \endscroll -\autobuttons \end{page} +\autobuttons +\end{page} + +\begin{patch}{OneVariableGraphicsExamplePagePatch1} +\begin{paste}{OneVariableGraphicsExamplePageFull1}{OneVariableGraphicsExamplePageEmpty1} +\pastebutton{OneVariableGraphicsExamplePageFull1}{\hidepaste} +\tab{5}\spadgraph{draw(sin tan x - tan sin x, x = 0..6)\bound{example1 }} +\center{\unixcommand{\inputimage{\env{AXIOM}/doc/viewports/onevariablegraphicsexamplepage1.view/image}}{viewalone\space{1} \env{AXIOM}/doc/viewports/onevariablegraphicsexamplepage1}} +\end{paste}\end{patch} + +\begin{patch}{OneVariableGraphicsExamplePageEmpty1} +\begin{paste}{OneVariableGraphicsExamplePageEmpty1}{OneVariableGraphicsExamplePagePatch1} +\pastebutton{OneVariableGraphicsExamplePageEmpty1}{\showpaste} +\tab{5}\spadgraph{draw(sin tan x - tan sin x, x = 0..6)\bound{example1 }} +\end{paste}\end{patch} + +\begin{patch}{OneVariableGraphicsExamplePagePatch2} +\begin{paste}{OneVariableGraphicsExamplePageFull2}{OneVariableGraphicsExamplePageEmpty2} +\pastebutton{OneVariableGraphicsExamplePageFull2}{\hidepaste} +\tab{5}\spadgraph{draw(sin x + cos x, x = 0..2*\%pi)\bound{example2 }} +\center{\unixcommand{\inputimage{\env{AXIOM}/doc/viewports/onevariablegraphicsexamplepage2.view/image}}{viewalone\space{1} \env{AXIOM}/doc/viewports/onevariablegraphicsexamplepage2}} +\end{paste}\end{patch} + +\begin{patch}{OneVariableGraphicsExamplePageEmpty2} +\begin{paste}{OneVariableGraphicsExamplePageEmpty2}{OneVariableGraphicsExamplePagePatch2} +\pastebutton{OneVariableGraphicsExamplePageEmpty2}{\showpaste} +\tab{5}\spadgraph{draw(sin x + cos x, x = 0..2*\%pi)\bound{example2 }} +\end{paste}\end{patch} + +\begin{patch}{OneVariableGraphicsExamplePagePatch3} +\begin{paste}{OneVariableGraphicsExamplePageFull3}{OneVariableGraphicsExamplePageEmpty3} +\pastebutton{OneVariableGraphicsExamplePageFull3}{\hidepaste} +\tab{5}\spadgraph{draw(sin(1/x), x = -1..1)\bound{example3 }} +\center{\unixcommand{\inputimage{\env{AXIOM}/doc/viewports/onevariablegraphicsexamplepage3.view/image}}{viewalone\space{1} \env{AXIOM}/doc/viewports/onevariablegraphicsexamplepage3}} +\end{paste}\end{patch} + +\begin{patch}{OneVariableGraphicsExamplePageEmpty3} +\begin{paste}{OneVariableGraphicsExamplePageEmpty3}{OneVariableGraphicsExamplePagePatch3} +\pastebutton{OneVariableGraphicsExamplePageEmpty3}{\showpaste} +\tab{5}\spadgraph{draw(sin(1/x), x = -1..1)\bound{example3 }} +\end{paste}\end{patch} + +\begin{patch}{OneVariableGraphicsExamplePagePatch4} +\begin{paste}{OneVariableGraphicsExamplePageFull4}{OneVariableGraphicsExamplePageEmpty4} +\pastebutton{OneVariableGraphicsExamplePageFull4}{\hidepaste} +\tab{5}\spadgraph{draw(x * sin(1/x), x = -1..1)\bound{example4 }} +\center{\unixcommand{\inputimage{\env{AXIOM}/doc/viewports/onevariablegraphicsexamplepage4.view/image}}{viewalone\space{1} \env{AXIOM}/doc/viewports/onevariablegraphicsexamplepage4}} +\end{paste}\end{patch} + +\begin{patch}{OneVariableGraphicsExamplePageEmpty4} +\begin{paste}{OneVariableGraphicsExamplePageEmpty4}{OneVariableGraphicsExamplePagePatch4} +\pastebutton{OneVariableGraphicsExamplePageEmpty4}{\showpaste} +\tab{5}\spadgraph{draw(x * sin(1/x), x = -1..1)\bound{example4 }} +\end{paste}\end{patch} + +\begin{patch}{OneVariableGraphicsExamplePagePatch5} +\begin{paste}{OneVariableGraphicsExamplePageFull5}{OneVariableGraphicsExamplePageEmpty5} +\pastebutton{OneVariableGraphicsExamplePageFull5}{\hidepaste} +\tab{5}\spadcommand{All\free{example1 example2 example3 example4 }} +\indentrel{3}\begin{verbatim} + (5) All + Type: Variable All +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{OneVariableGraphicsExamplePageEmpty5} +\begin{paste}{OneVariableGraphicsExamplePageEmpty5}{OneVariableGraphicsExamplePagePatch5} +\pastebutton{OneVariableGraphicsExamplePageEmpty5}{\showpaste} +\tab{5}\spadcommand{All\free{example1 example2 example3 example4 }} +\end{paste}\end{patch} @ \pagehead{ParametricCurveGraphicsExamplePage}{graphics.ht} @@ -9974,7 +24741,76 @@ t = 0..2*\%pi) \bound{example4}} Run all examples on this page. \spadpaste{All \free{example1 example2 example3 example4}} \endscroll -\autobuttons \end{page} +\autobuttons +\end{page} + +\begin{patch}{ParametricCurveGraphicsExamplePagePatch1} +\begin{paste}{ParametricCurveGraphicsExamplePageFull1}{ParametricCurveGraphicsExamplePageEmpty1} +\pastebutton{ParametricCurveGraphicsExamplePageFull1}{\hidepaste} +\tab{5}\spadgraph{draw(curve(cos(t/(1+sin(t)**2)), sin(t)*cos(t)/(1+sin(t)**2)), t = -\%pi..\%pi)\bound{example1 }} +\center{\unixcommand{\inputimage{\env{AXIOM}/doc/viewports/parametriccurvegraphicsexamplepage1.view/image}}{viewalone\space{1} \env{AXIOM}/doc/viewports/parametriccurvegraphicsexamplepage1}} +\end{paste}\end{patch} + +\begin{patch}{ParametricCurveGraphicsExamplePageEmpty1} +\begin{paste}{ParametricCurveGraphicsExamplePageEmpty1}{ParametricCurveGraphicsExamplePagePatch1} +\pastebutton{ParametricCurveGraphicsExamplePageEmpty1}{\showpaste} +\tab{5}\spadgraph{draw(curve(cos(t/(1+sin(t)**2)), sin(t)*cos(t)/(1+sin(t)**2)), t = -\%pi..\%pi)\bound{example1 }} +\end{paste}\end{patch} + +\begin{patch}{ParametricCurveGraphicsExamplePagePatch2} +\begin{paste}{ParametricCurveGraphicsExamplePageFull2}{ParametricCurveGraphicsExamplePageEmpty2} +\pastebutton{ParametricCurveGraphicsExamplePageFull2}{\hidepaste} +\tab{5}\spadgraph{draw(curve(9*sin(3*t/4), 8*sin(t)), t = -4*\%pi..4*\%pi)\bound{example2 }} +\center{\unixcommand{\inputimage{\env{AXIOM}/doc/viewports/parametriccurvegraphicsexamplepage2.view/image}}{viewalone\space{1} \env{AXIOM}/doc/viewports/parametriccurvegraphicsexamplepage2}} +\end{paste}\end{patch} + +\begin{patch}{ParametricCurveGraphicsExamplePageEmpty2} +\begin{paste}{ParametricCurveGraphicsExamplePageEmpty2}{ParametricCurveGraphicsExamplePagePatch2} +\pastebutton{ParametricCurveGraphicsExamplePageEmpty2}{\showpaste} +\tab{5}\spadgraph{draw(curve(9*sin(3*t/4), 8*sin(t)), t = -4*\%pi..4*\%pi)\bound{example2 }} +\end{paste}\end{patch} + +\begin{patch}{ParametricCurveGraphicsExamplePagePatch3} +\begin{paste}{ParametricCurveGraphicsExamplePageFull3}{ParametricCurveGraphicsExamplePageEmpty3} +\pastebutton{ParametricCurveGraphicsExamplePageFull3}{\hidepaste} +\tab{5}\spadgraph{draw(curve(sin(t)*sin(2*t)*sin(3*t), sin(4*t)*sin(5*t)*sin(6*t)),t = 0..2*\%pi)\bound{example3 }} +\center{\unixcommand{\inputimage{\env{AXIOM}/doc/viewports/parametriccurvegraphicsexamplepage3.view/image}}{viewalone\space{1} \env{AXIOM}/doc/viewports/parametriccurvegraphicsexamplepage3}} +\end{paste}\end{patch} + +\begin{patch}{ParametricCurveGraphicsExamplePageEmpty3} +\begin{paste}{ParametricCurveGraphicsExamplePageEmpty3}{ParametricCurveGraphicsExamplePagePatch3} +\pastebutton{ParametricCurveGraphicsExamplePageEmpty3}{\showpaste} +\tab{5}\spadgraph{draw(curve(sin(t)*sin(2*t)*sin(3*t), sin(4*t)*sin(5*t)*sin(6*t)),t = 0..2*\%pi)\bound{example3 }} +\end{paste}\end{patch} + +\begin{patch}{ParametricCurveGraphicsExamplePagePatch4} +\begin{paste}{ParametricCurveGraphicsExamplePageFull4}{ParametricCurveGraphicsExamplePageEmpty4} +\pastebutton{ParametricCurveGraphicsExamplePageFull4}{\hidepaste} +\tab{5}\spadgraph{draw(curve(cos(4*t)*cos(7*t), cos(4*t)*sin(7*t)), t = 0..2*\%pi)\bound{example4 }} +\center{\unixcommand{\inputimage{\env{AXIOM}/doc/viewports/parametriccurvegraphicsexamplepage4.view/image}}{viewalone\space{1} \env{AXIOM}/doc/viewports/parametriccurvegraphicsexamplepage4}} +\end{paste}\end{patch} + +\begin{patch}{ParametricCurveGraphicsExamplePageEmpty4} +\begin{paste}{ParametricCurveGraphicsExamplePageEmpty4}{ParametricCurveGraphicsExamplePagePatch4} +\pastebutton{ParametricCurveGraphicsExamplePageEmpty4}{\showpaste} +\tab{5}\spadgraph{draw(curve(cos(4*t)*cos(7*t), cos(4*t)*sin(7*t)), t = 0..2*\%pi)\bound{example4 }} +\end{paste}\end{patch} + +\begin{patch}{ParametricCurveGraphicsExamplePagePatch5} +\begin{paste}{ParametricCurveGraphicsExamplePageFull5}{ParametricCurveGraphicsExamplePageEmpty5} +\pastebutton{ParametricCurveGraphicsExamplePageFull5}{\hidepaste} +\tab{5}\spadcommand{All\free{example1 example2 example3 example4 }} +\indentrel{3}\begin{verbatim} + (5) All + Type: Variable All +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ParametricCurveGraphicsExamplePageEmpty5} +\begin{paste}{ParametricCurveGraphicsExamplePageEmpty5}{ParametricCurveGraphicsExamplePagePatch5} +\pastebutton{ParametricCurveGraphicsExamplePageEmpty5}{\showpaste} +\tab{5}\spadcommand{All\free{example1 example2 example3 example4 }} +\end{paste}\end{patch} @ \pagehead{PolarGraphicsExamplePage}{graphics.ht}{Polar Coordinates} @@ -9998,7 +24834,76 @@ Run all examples on this page. %example1 example2 example3 example4}} \endscroll -\autobuttons \end{page} +\autobuttons +\end{page} + +\begin{patch}{PolarGraphicsExamplePagePatch1} +\begin{paste}{PolarGraphicsExamplePageFull1}{PolarGraphicsExamplePageEmpty1} +\pastebutton{PolarGraphicsExamplePageFull1}{\hidepaste} +\tab{5}\spadgraph{draw(1,t = 0..2*\%pi, coordinates == polar)\bound{example1 }} +\center{\unixcommand{\inputimage{\env{AXIOM}/doc/viewports/polargraphicsexamplepage1.view/image}}{viewalone\space{1} \env{AXIOM}/doc/viewports/polargraphicsexamplepage1}} +\end{paste}\end{patch} + +\begin{patch}{PolarGraphicsExamplePageEmpty1} +\begin{paste}{PolarGraphicsExamplePageEmpty1}{PolarGraphicsExamplePagePatch1} +\pastebutton{PolarGraphicsExamplePageEmpty1}{\showpaste} +\tab{5}\spadgraph{draw(1,t = 0..2*\%pi, coordinates == polar)\bound{example1 }} +\end{paste}\end{patch} + +\begin{patch}{PolarGraphicsExamplePagePatch2} +\begin{paste}{PolarGraphicsExamplePageFull2}{PolarGraphicsExamplePageEmpty2} +\pastebutton{PolarGraphicsExamplePageFull2}{\hidepaste} +\tab{5}\spadgraph{draw(t,t = 0..100, coordinates == polar)\bound{example2 }} +\center{\unixcommand{\inputimage{\env{AXIOM}/doc/viewports/polargraphicsexamplepage2.view/image}}{viewalone\space{1} \env{AXIOM}/doc/viewports/polargraphicsexamplepage2}} +\end{paste}\end{patch} + +\begin{patch}{PolarGraphicsExamplePageEmpty2} +\begin{paste}{PolarGraphicsExamplePageEmpty2}{PolarGraphicsExamplePagePatch2} +\pastebutton{PolarGraphicsExamplePageEmpty2}{\showpaste} +\tab{5}\spadgraph{draw(t,t = 0..100, coordinates == polar)\bound{example2 }} +\end{paste}\end{patch} + +\begin{patch}{PolarGraphicsExamplePagePatch3} +\begin{paste}{PolarGraphicsExamplePageFull3}{PolarGraphicsExamplePageEmpty3} +\pastebutton{PolarGraphicsExamplePageFull3}{\hidepaste} +\tab{5}\spadgraph{draw(sin(4*t), t = 0..2*\%pi, coordinates == polar)\bound{example3 }} +\center{\unixcommand{\inputimage{\env{AXIOM}/doc/viewports/polargraphicsexamplepage3.view/image}}{viewalone\space{1} \env{AXIOM}/doc/viewports/polargraphicsexamplepage3}} +\end{paste}\end{patch} + +\begin{patch}{PolarGraphicsExamplePageEmpty3} +\begin{paste}{PolarGraphicsExamplePageEmpty3}{PolarGraphicsExamplePagePatch3} +\pastebutton{PolarGraphicsExamplePageEmpty3}{\showpaste} +\tab{5}\spadgraph{draw(sin(4*t), t = 0..2*\%pi, coordinates == polar)\bound{example3 }} +\end{paste}\end{patch} + +\begin{patch}{PolarGraphicsExamplePagePatch4} +\begin{paste}{PolarGraphicsExamplePageFull4}{PolarGraphicsExamplePageEmpty4} +\pastebutton{PolarGraphicsExamplePageFull4}{\hidepaste} +\tab{5}\spadgraph{draw(2 + 3 * sin t, t = 0..2*\%pi, coordinates == polar)\bound{example4 }} +\center{\unixcommand{\inputimage{\env{AXIOM}/doc/viewports/polargraphicsexamplepage4.view/image}}{viewalone\space{1} \env{AXIOM}/doc/viewports/polargraphicsexamplepage4}} +\end{paste}\end{patch} + +\begin{patch}{PolarGraphicsExamplePageEmpty4} +\begin{paste}{PolarGraphicsExamplePageEmpty4}{PolarGraphicsExamplePagePatch4} +\pastebutton{PolarGraphicsExamplePageEmpty4}{\showpaste} +\tab{5}\spadgraph{draw(2 + 3 * sin t, t = 0..2*\%pi, coordinates == polar)\bound{example4 }} +\end{paste}\end{patch} + +\begin{patch}{PolarGraphicsExamplePagePatch5} +\begin{paste}{PolarGraphicsExamplePageFull5}{PolarGraphicsExamplePageEmpty5} +\pastebutton{PolarGraphicsExamplePageFull5}{\hidepaste} +\tab{5}\spadcommand{All\free{example2 example3 example4 }} +\indentrel{3}\begin{verbatim} + (5) All + Type: Variable All +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{PolarGraphicsExamplePageEmpty5} +\begin{paste}{PolarGraphicsExamplePageEmpty5}{PolarGraphicsExamplePagePatch5} +\pastebutton{PolarGraphicsExamplePageEmpty5}{\showpaste} +\tab{5}\spadcommand{All\free{example2 example3 example4 }} +\end{paste}\end{patch} @ \pagehead{ImplicitCurveGraphicsExamplePage}{graphics.ht}{Implicit Curves} @@ -10027,7 +24932,111 @@ title == "Cassinian oval with two loops") \free{q} \bound{example4} } Run all examples on this page. \spadpaste{All \free{example1 example2 example3 example4}} \endscroll -\autobuttons \end{page} +\autobuttons +\end{page} + +\begin{patch}{ImplicitCurveGraphicsExamplePagePatch1} +\begin{paste}{ImplicitCurveGraphicsExamplePageFull1}{ImplicitCurveGraphicsExamplePageEmpty1} +\pastebutton{ImplicitCurveGraphicsExamplePageFull1}{\hidepaste} +\tab{5}\spadgraph{draw(x * y = 1, x, y, range == [-3..3, -3..3])\bound{example1 }} +\center{\unixcommand{\inputimage{\env{AXIOM}/doc/viewports/implicitcurvegraphicsexamplepage1.view/image}}{viewalone\space{1} \env{AXIOM}/doc/viewports/implicitcurvegraphicsexamplepage1}} +\end{paste}\end{patch} + +\begin{patch}{ImplicitCurveGraphicsExamplePageEmpty1} +\begin{paste}{ImplicitCurveGraphicsExamplePageEmpty1}{ImplicitCurveGraphicsExamplePagePatch1} +\pastebutton{ImplicitCurveGraphicsExamplePageEmpty1}{\showpaste} +\tab{5}\spadgraph{draw(x * y = 1, x, y, range == [-3..3, -3..3])\bound{example1 }} +\end{paste}\end{patch} + +\begin{patch}{ImplicitCurveGraphicsExamplePagePatch2} +\begin{paste}{ImplicitCurveGraphicsExamplePageFull2}{ImplicitCurveGraphicsExamplePageEmpty2} +\pastebutton{ImplicitCurveGraphicsExamplePageFull2}{\hidepaste} +\tab{5}\spadgraph{draw(y**2 + y = x**3 - x, x, y, range == [-2..2, -2..1])\bound{example2 }} +\center{\unixcommand{\inputimage{\env{AXIOM}/doc/viewports/implicitcurvegraphicsexamplepage2.view/image}}{viewalone\space{1} \env{AXIOM}/doc/viewports/implicitcurvegraphicsexamplepage2}} +\end{paste}\end{patch} + +\begin{patch}{ImplicitCurveGraphicsExamplePageEmpty2} +\begin{paste}{ImplicitCurveGraphicsExamplePageEmpty2}{ImplicitCurveGraphicsExamplePagePatch2} +\pastebutton{ImplicitCurveGraphicsExamplePageEmpty2}{\showpaste} +\tab{5}\spadgraph{draw(y**2 + y = x**3 - x, x, y, range == [-2..2, -2..1])\bound{example2 }} +\end{paste}\end{patch} + +\begin{patch}{ImplicitCurveGraphicsExamplePagePatch3} +\begin{paste}{ImplicitCurveGraphicsExamplePageFull3}{ImplicitCurveGraphicsExamplePageEmpty3} +\pastebutton{ImplicitCurveGraphicsExamplePageFull3}{\hidepaste} +\tab{5}\spadcommand{p := ((x**2 + y**2 + 1) - 8*x)**2 - (8*(x**2 + y**2 + 1) - 4*x - 1)\bound{p }} +\indentrel{3}\begin{verbatim} + (3) + 4 2 2 4 3 2 + y + (2x - 16x - 6)y + x - 16x + 58x - 12x - 6 + Type: Polynomial Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ImplicitCurveGraphicsExamplePageEmpty3} +\begin{paste}{ImplicitCurveGraphicsExamplePageEmpty3}{ImplicitCurveGraphicsExamplePagePatch3} +\pastebutton{ImplicitCurveGraphicsExamplePageEmpty3}{\showpaste} +\tab{5}\spadcommand{p := ((x**2 + y**2 + 1) - 8*x)**2 - (8*(x**2 + y**2 + 1) - 4*x - 1)\bound{p }} +\end{paste}\end{patch} + +\begin{patch}{ImplicitCurveGraphicsExamplePagePatch4} +\begin{paste}{ImplicitCurveGraphicsExamplePageFull4}{ImplicitCurveGraphicsExamplePageEmpty4} +\pastebutton{ImplicitCurveGraphicsExamplePageFull4}{\hidepaste} +\tab{5}\spadgraph{draw(p = 0, x, y, range == [-1..11, -7..7], title == "Cartesian Ovals")\free{p }\bound{example3 }} +\center{\unixcommand{\inputimage{\env{AXIOM}/doc/viewports/implicitcurvegraphicsexamplepage4.view/image}}{viewalone\space{1} \env{AXIOM}/doc/viewports/implicitcurvegraphicsexamplepage4}} +\end{paste}\end{patch} + +\begin{patch}{ImplicitCurveGraphicsExamplePageEmpty4} +\begin{paste}{ImplicitCurveGraphicsExamplePageEmpty4}{ImplicitCurveGraphicsExamplePagePatch4} +\pastebutton{ImplicitCurveGraphicsExamplePageEmpty4}{\showpaste} +\tab{5}\spadgraph{draw(p = 0, x, y, range == [-1..11, -7..7], title == "Cartesian Ovals")\free{p }\bound{example3 }} +\end{paste}\end{patch} + +\begin{patch}{ImplicitCurveGraphicsExamplePagePatch5} +\begin{paste}{ImplicitCurveGraphicsExamplePageFull5}{ImplicitCurveGraphicsExamplePageEmpty5} +\pastebutton{ImplicitCurveGraphicsExamplePageFull5}{\hidepaste} +\tab{5}\spadcommand{q := (x**2 + y**2 + 7**2)**2 - (6**4 + 4*7**2*x**2)\bound{q }} +\indentrel{3}\begin{verbatim} + 4 2 2 4 2 + (5) y + (2x + 98)y + x - 98x + 1105 + Type: Polynomial Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ImplicitCurveGraphicsExamplePageEmpty5} +\begin{paste}{ImplicitCurveGraphicsExamplePageEmpty5}{ImplicitCurveGraphicsExamplePagePatch5} +\pastebutton{ImplicitCurveGraphicsExamplePageEmpty5}{\showpaste} +\tab{5}\spadcommand{q := (x**2 + y**2 + 7**2)**2 - (6**4 + 4*7**2*x**2)\bound{q }} +\end{paste}\end{patch} + +\begin{patch}{ImplicitCurveGraphicsExamplePagePatch6} +\begin{paste}{ImplicitCurveGraphicsExamplePageFull6}{ImplicitCurveGraphicsExamplePageEmpty6} +\pastebutton{ImplicitCurveGraphicsExamplePageFull6}{\hidepaste} +\tab{5}\spadgraph{draw(q = 0, x, y, range == [-10..10, -4..4], title == "Cassinian oval with two loops")\free{q }\bound{example4 }} +\center{\unixcommand{\inputimage{\env{AXIOM}/doc/viewports/implicitcurvegraphicsexamplepage6.view/image}}{viewalone\space{1} \env{AXIOM}/doc/viewports/implicitcurvegraphicsexamplepage6}} +\end{paste}\end{patch} + +\begin{patch}{ImplicitCurveGraphicsExamplePageEmpty6} +\begin{paste}{ImplicitCurveGraphicsExamplePageEmpty6}{ImplicitCurveGraphicsExamplePagePatch6} +\pastebutton{ImplicitCurveGraphicsExamplePageEmpty6}{\showpaste} +\tab{5}\spadgraph{draw(q = 0, x, y, range == [-10..10, -4..4], title == "Cassinian oval with two loops")\free{q }\bound{example4 }} +\end{paste}\end{patch} + +\begin{patch}{ImplicitCurveGraphicsExamplePagePatch7} +\begin{paste}{ImplicitCurveGraphicsExamplePageFull7}{ImplicitCurveGraphicsExamplePageEmpty7} +\pastebutton{ImplicitCurveGraphicsExamplePageFull7}{\hidepaste} +\tab{5}\spadcommand{All\free{example1 example2 example3 example4 }} +\indentrel{3}\begin{verbatim} + (7) All + Type: Variable All +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ImplicitCurveGraphicsExamplePageEmpty7} +\begin{paste}{ImplicitCurveGraphicsExamplePageEmpty7}{ImplicitCurveGraphicsExamplePagePatch7} +\pastebutton{ImplicitCurveGraphicsExamplePageEmpty7}{\showpaste} +\tab{5}\spadcommand{All\free{example1 example2 example3 example4 }} +\end{paste}\end{patch} @ \pagehead{ListPointsGraphicsExamplePage}{graphics.ht}{Lists of Points} @@ -10101,7 +25110,419 @@ The \spadfun{makeViewport2D} command takes a list of options as a parameter in this example. The string "Lines" is designated as the viewport's title. \endscroll -\autobuttons \end{page} +\autobuttons +\end{page} + +\begin{patch}{ListPointsGraphicsExamplePagePatch1} +\begin{paste}{ListPointsGraphicsExamplePageFull1}{ListPointsGraphicsExamplePageEmpty1} +\pastebutton{ListPointsGraphicsExamplePageFull1}{\hidepaste} +\tab{5}\spadcommand{p1 := point [1::SF,1::SF]$(Point SF)\bound{p1 }} +\indentrel{3}\begin{verbatim} + (1) [1.0,1.0] + Type: Point DoubleFloat +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ListPointsGraphicsExamplePageEmpty1} +\begin{paste}{ListPointsGraphicsExamplePageEmpty1}{ListPointsGraphicsExamplePagePatch1} +\pastebutton{ListPointsGraphicsExamplePageEmpty1}{\showpaste} +\tab{5}\spadcommand{p1 := point [1::SF,1::SF]$(Point SF)\bound{p1 }} +\end{paste}\end{patch} + +\begin{patch}{ListPointsGraphicsExamplePagePatch2} +\begin{paste}{ListPointsGraphicsExamplePageFull2}{ListPointsGraphicsExamplePageEmpty2} +\pastebutton{ListPointsGraphicsExamplePageFull2}{\hidepaste} +\tab{5}\spadcommand{p2 := point [0::SF,1::SF]$(Point SF)\bound{p2 }} +\indentrel{3}\begin{verbatim} + (2) [0.0,1.0] + Type: Point DoubleFloat +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ListPointsGraphicsExamplePageEmpty2} +\begin{paste}{ListPointsGraphicsExamplePageEmpty2}{ListPointsGraphicsExamplePagePatch2} +\pastebutton{ListPointsGraphicsExamplePageEmpty2}{\showpaste} +\tab{5}\spadcommand{p2 := point [0::SF,1::SF]$(Point SF)\bound{p2 }} +\end{paste}\end{patch} + +\begin{patch}{ListPointsGraphicsExamplePagePatch3} +\begin{paste}{ListPointsGraphicsExamplePageFull3}{ListPointsGraphicsExamplePageEmpty3} +\pastebutton{ListPointsGraphicsExamplePageFull3}{\hidepaste} +\tab{5}\spadcommand{p3 := point [0::SF,0::SF]$(Point SF)\bound{p3 }} +\indentrel{3}\begin{verbatim} + (3) [0.0,0.0] + Type: Point DoubleFloat +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ListPointsGraphicsExamplePageEmpty3} +\begin{paste}{ListPointsGraphicsExamplePageEmpty3}{ListPointsGraphicsExamplePagePatch3} +\pastebutton{ListPointsGraphicsExamplePageEmpty3}{\showpaste} +\tab{5}\spadcommand{p3 := point [0::SF,0::SF]$(Point SF)\bound{p3 }} +\end{paste}\end{patch} + +\begin{patch}{ListPointsGraphicsExamplePagePatch4} +\begin{paste}{ListPointsGraphicsExamplePageFull4}{ListPointsGraphicsExamplePageEmpty4} +\pastebutton{ListPointsGraphicsExamplePageFull4}{\hidepaste} +\tab{5}\spadcommand{p4 := point [1::SF,0::SF]$(Point SF)\bound{p4 }} +\indentrel{3}\begin{verbatim} + (4) [1.0,0.0] + Type: Point DoubleFloat +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ListPointsGraphicsExamplePageEmpty4} +\begin{paste}{ListPointsGraphicsExamplePageEmpty4}{ListPointsGraphicsExamplePagePatch4} +\pastebutton{ListPointsGraphicsExamplePageEmpty4}{\showpaste} +\tab{5}\spadcommand{p4 := point [1::SF,0::SF]$(Point SF)\bound{p4 }} +\end{paste}\end{patch} + +\begin{patch}{ListPointsGraphicsExamplePagePatch5} +\begin{paste}{ListPointsGraphicsExamplePageFull5}{ListPointsGraphicsExamplePageEmpty5} +\pastebutton{ListPointsGraphicsExamplePageFull5}{\hidepaste} +\tab{5}\spadcommand{p5 := point [1::SF,.5::SF]$(Point SF)\bound{p5 }} +\indentrel{3}\begin{verbatim} + (5) [1.0,0.5] + Type: Point DoubleFloat +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ListPointsGraphicsExamplePageEmpty5} +\begin{paste}{ListPointsGraphicsExamplePageEmpty5}{ListPointsGraphicsExamplePagePatch5} +\pastebutton{ListPointsGraphicsExamplePageEmpty5}{\showpaste} +\tab{5}\spadcommand{p5 := point [1::SF,.5::SF]$(Point SF)\bound{p5 }} +\end{paste}\end{patch} + +\begin{patch}{ListPointsGraphicsExamplePagePatch6} +\begin{paste}{ListPointsGraphicsExamplePageFull6}{ListPointsGraphicsExamplePageEmpty6} +\pastebutton{ListPointsGraphicsExamplePageFull6}{\hidepaste} +\tab{5}\spadcommand{p6 := point [.5::SF,0::SF]$(Point SF)\bound{p6 }} +\indentrel{3}\begin{verbatim} + (6) [0.5,0.0] + Type: Point DoubleFloat +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ListPointsGraphicsExamplePageEmpty6} +\begin{paste}{ListPointsGraphicsExamplePageEmpty6}{ListPointsGraphicsExamplePagePatch6} +\pastebutton{ListPointsGraphicsExamplePageEmpty6}{\showpaste} +\tab{5}\spadcommand{p6 := point [.5::SF,0::SF]$(Point SF)\bound{p6 }} +\end{paste}\end{patch} + +\begin{patch}{ListPointsGraphicsExamplePagePatch7} +\begin{paste}{ListPointsGraphicsExamplePageFull7}{ListPointsGraphicsExamplePageEmpty7} +\pastebutton{ListPointsGraphicsExamplePageFull7}{\hidepaste} +\tab{5}\spadcommand{p7 := point [0::SF,0.5::SF]$(Point SF)\bound{p7 }} +\indentrel{3}\begin{verbatim} + (7) [0.0,0.5] + Type: Point DoubleFloat +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ListPointsGraphicsExamplePageEmpty7} +\begin{paste}{ListPointsGraphicsExamplePageEmpty7}{ListPointsGraphicsExamplePagePatch7} +\pastebutton{ListPointsGraphicsExamplePageEmpty7}{\showpaste} +\tab{5}\spadcommand{p7 := point [0::SF,0.5::SF]$(Point SF)\bound{p7 }} +\end{paste}\end{patch} + +\begin{patch}{ListPointsGraphicsExamplePagePatch8} +\begin{paste}{ListPointsGraphicsExamplePageFull8}{ListPointsGraphicsExamplePageEmpty8} +\pastebutton{ListPointsGraphicsExamplePageFull8}{\hidepaste} +\tab{5}\spadcommand{p8 := point [.5::SF,1::SF]$(Point SF)\bound{p8 }} +\indentrel{3}\begin{verbatim} + (8) [0.5,1.0] + Type: Point DoubleFloat +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ListPointsGraphicsExamplePageEmpty8} +\begin{paste}{ListPointsGraphicsExamplePageEmpty8}{ListPointsGraphicsExamplePagePatch8} +\pastebutton{ListPointsGraphicsExamplePageEmpty8}{\showpaste} +\tab{5}\spadcommand{p8 := point [.5::SF,1::SF]$(Point SF)\bound{p8 }} +\end{paste}\end{patch} + +\begin{patch}{ListPointsGraphicsExamplePagePatch9} +\begin{paste}{ListPointsGraphicsExamplePageFull9}{ListPointsGraphicsExamplePageEmpty9} +\pastebutton{ListPointsGraphicsExamplePageFull9}{\hidepaste} +\tab{5}\spadcommand{p9 := point [.25::SF,.25::SF]$(Point SF)\bound{p9 }} +\indentrel{3}\begin{verbatim} + (9) [0.25,0.25] + Type: Point DoubleFloat +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ListPointsGraphicsExamplePageEmpty9} +\begin{paste}{ListPointsGraphicsExamplePageEmpty9}{ListPointsGraphicsExamplePagePatch9} +\pastebutton{ListPointsGraphicsExamplePageEmpty9}{\showpaste} +\tab{5}\spadcommand{p9 := point [.25::SF,.25::SF]$(Point SF)\bound{p9 }} +\end{paste}\end{patch} + +\begin{patch}{ListPointsGraphicsExamplePagePatch10} +\begin{paste}{ListPointsGraphicsExamplePageFull10}{ListPointsGraphicsExamplePageEmpty10} +\pastebutton{ListPointsGraphicsExamplePageFull10}{\hidepaste} +\tab{5}\spadcommand{p10 := point [.25::SF,.75::SF]$(Point SF)\bound{p10 }} +\indentrel{3}\begin{verbatim} + (10) [0.25,0.75] + Type: Point DoubleFloat +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ListPointsGraphicsExamplePageEmpty10} +\begin{paste}{ListPointsGraphicsExamplePageEmpty10}{ListPointsGraphicsExamplePagePatch10} +\pastebutton{ListPointsGraphicsExamplePageEmpty10}{\showpaste} +\tab{5}\spadcommand{p10 := point [.25::SF,.75::SF]$(Point SF)\bound{p10 }} +\end{paste}\end{patch} + +\begin{patch}{ListPointsGraphicsExamplePagePatch11} +\begin{paste}{ListPointsGraphicsExamplePageFull11}{ListPointsGraphicsExamplePageEmpty11} +\pastebutton{ListPointsGraphicsExamplePageFull11}{\hidepaste} +\tab{5}\spadcommand{p11 := point [.75::SF,.75::SF]$(Point SF)\bound{p11 }} +\indentrel{3}\begin{verbatim} + (11) [0.75,0.75] + Type: Point DoubleFloat +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ListPointsGraphicsExamplePageEmpty11} +\begin{paste}{ListPointsGraphicsExamplePageEmpty11}{ListPointsGraphicsExamplePagePatch11} +\pastebutton{ListPointsGraphicsExamplePageEmpty11}{\showpaste} +\tab{5}\spadcommand{p11 := point [.75::SF,.75::SF]$(Point SF)\bound{p11 }} +\end{paste}\end{patch} + +\begin{patch}{ListPointsGraphicsExamplePagePatch12} +\begin{paste}{ListPointsGraphicsExamplePageFull12}{ListPointsGraphicsExamplePageEmpty12} +\pastebutton{ListPointsGraphicsExamplePageFull12}{\hidepaste} +\tab{5}\spadcommand{p12 := point [.75::SF,.25::SF]$(Point SF)\bound{p12 }} +\indentrel{3}\begin{verbatim} + (12) [0.75,0.25] + Type: Point DoubleFloat +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ListPointsGraphicsExamplePageEmpty12} +\begin{paste}{ListPointsGraphicsExamplePageEmpty12}{ListPointsGraphicsExamplePagePatch12} +\pastebutton{ListPointsGraphicsExamplePageEmpty12}{\showpaste} +\tab{5}\spadcommand{p12 := point [.75::SF,.25::SF]$(Point SF)\bound{p12 }} +\end{paste}\end{patch} + +\begin{patch}{ListPointsGraphicsExamplePagePatch13} +\begin{paste}{ListPointsGraphicsExamplePageFull13}{ListPointsGraphicsExamplePageEmpty13} +\pastebutton{ListPointsGraphicsExamplePageFull13}{\hidepaste} +\tab{5}\spadcommand{llp := [[p1,p2],[p2,p3],[p3,p4],[p4,p1],[p5,p6],[p6,p7],[p7,p8],[p8,p5],[p9,p10],[p10,p11],[p11,p12],[p12,p9]]\bound{llp }\free{p1 p2 p3 p4 p5 p6 p7 p8 p9 p10 p11 p12 }} +\indentrel{3}\begin{verbatim} + (13) + [[[1.0,1.0],[0.0,1.0]], [[0.0,1.0],[0.0,0.0]], + [[0.0,0.0],[1.0,0.0]], [[1.0,0.0],[1.0,1.0]], + [[1.0,0.5],[0.5,0.0]], [[0.5,0.0],[0.0,0.5]], + [[0.0,0.5],[0.5,1.0]], [[0.5,1.0],[1.0,0.5]], + [[0.25,0.25],[0.25,0.75]], [[0.25,0.75],[0.75,0.75]], + [[0.75,0.75],[0.75,0.25]], [[0.75,0.25],[0.25,0.25]]] + Type: List List Point DoubleFloat +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ListPointsGraphicsExamplePageEmpty13} +\begin{paste}{ListPointsGraphicsExamplePageEmpty13}{ListPointsGraphicsExamplePagePatch13} +\pastebutton{ListPointsGraphicsExamplePageEmpty13}{\showpaste} +\tab{5}\spadcommand{llp := [[p1,p2],[p2,p3],[p3,p4],[p4,p1],[p5,p6],[p6,p7],[p7,p8],[p8,p5],[p9,p10],[p10,p11],[p11,p12],[p12,p9]]\bound{llp }\free{p1 p2 p3 p4 p5 p6 p7 p8 p9 p10 p11 p12 }} +\end{paste}\end{patch} + +\begin{patch}{ListPointsGraphicsExamplePagePatch14} +\begin{paste}{ListPointsGraphicsExamplePageFull14}{ListPointsGraphicsExamplePageEmpty14} +\pastebutton{ListPointsGraphicsExamplePageFull14}{\hidepaste} +\tab{5}\spadcommand{size1 := 6::PositiveInteger\bound{size1 }} +\indentrel{3}\begin{verbatim} + (14) 6 + Type: PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ListPointsGraphicsExamplePageEmpty14} +\begin{paste}{ListPointsGraphicsExamplePageEmpty14}{ListPointsGraphicsExamplePagePatch14} +\pastebutton{ListPointsGraphicsExamplePageEmpty14}{\showpaste} +\tab{5}\spadcommand{size1 := 6::PositiveInteger\bound{size1 }} +\end{paste}\end{patch} + +\begin{patch}{ListPointsGraphicsExamplePagePatch15} +\begin{paste}{ListPointsGraphicsExamplePageFull15}{ListPointsGraphicsExamplePageEmpty15} +\pastebutton{ListPointsGraphicsExamplePageFull15}{\hidepaste} +\tab{5}\spadcommand{size2 := 8::PositiveInteger\bound{size2 }} +\indentrel{3}\begin{verbatim} + (15) 8 + Type: PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ListPointsGraphicsExamplePageEmpty15} +\begin{paste}{ListPointsGraphicsExamplePageEmpty15}{ListPointsGraphicsExamplePagePatch15} +\pastebutton{ListPointsGraphicsExamplePageEmpty15}{\showpaste} +\tab{5}\spadcommand{size2 := 8::PositiveInteger\bound{size2 }} +\end{paste}\end{patch} + +\begin{patch}{ListPointsGraphicsExamplePagePatch16} +\begin{paste}{ListPointsGraphicsExamplePageFull16}{ListPointsGraphicsExamplePageEmpty16} +\pastebutton{ListPointsGraphicsExamplePageFull16}{\hidepaste} +\tab{5}\spadcommand{size3 := 10::PositiveInteger\bound{size3 }} +\indentrel{3}\begin{verbatim} + (16) 10 + Type: PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ListPointsGraphicsExamplePageEmpty16} +\begin{paste}{ListPointsGraphicsExamplePageEmpty16}{ListPointsGraphicsExamplePagePatch16} +\pastebutton{ListPointsGraphicsExamplePageEmpty16}{\showpaste} +\tab{5}\spadcommand{size3 := 10::PositiveInteger\bound{size3 }} +\end{paste}\end{patch} + +\begin{patch}{ListPointsGraphicsExamplePagePatch17} +\begin{paste}{ListPointsGraphicsExamplePageFull17}{ListPointsGraphicsExamplePageEmpty17} +\pastebutton{ListPointsGraphicsExamplePageFull17}{\hidepaste} +\tab{5}\spadcommand{lsize := [size1, size1, size1, size1, size2, size2, size2, size2, size3, size3, size3, size3]\bound{lsize }\free{size1 size2 size3 }} +\indentrel{3}\begin{verbatim} + (17) [6,6,6,6,8,8,8,8,10,10,10,10] + Type: List PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ListPointsGraphicsExamplePageEmpty17} +\begin{paste}{ListPointsGraphicsExamplePageEmpty17}{ListPointsGraphicsExamplePagePatch17} +\pastebutton{ListPointsGraphicsExamplePageEmpty17}{\showpaste} +\tab{5}\spadcommand{lsize := [size1, size1, size1, size1, size2, size2, size2, size2, size3, size3, size3, size3]\bound{lsize }\free{size1 size2 size3 }} +\end{paste}\end{patch} + +\begin{patch}{ListPointsGraphicsExamplePagePatch18} +\begin{paste}{ListPointsGraphicsExamplePageFull18}{ListPointsGraphicsExamplePageEmpty18} +\pastebutton{ListPointsGraphicsExamplePageFull18}{\hidepaste} +\tab{5}\spadcommand{pc1 := pastel red()\bound{pc1 }} +\indentrel{3}\begin{verbatim} + (18) [Hue: 1 Weight: 1.0] from the Pastel palette + Type: Palette +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ListPointsGraphicsExamplePageEmpty18} +\begin{paste}{ListPointsGraphicsExamplePageEmpty18}{ListPointsGraphicsExamplePagePatch18} +\pastebutton{ListPointsGraphicsExamplePageEmpty18}{\showpaste} +\tab{5}\spadcommand{pc1 := pastel red()\bound{pc1 }} +\end{paste}\end{patch} + +\begin{patch}{ListPointsGraphicsExamplePagePatch19} +\begin{paste}{ListPointsGraphicsExamplePageFull19}{ListPointsGraphicsExamplePageEmpty19} +\pastebutton{ListPointsGraphicsExamplePageFull19}{\hidepaste} +\tab{5}\spadcommand{pc2 := dim green()\bound{pc2 }} +\indentrel{3}\begin{verbatim} + (19) [Hue: 14 Weight: 1.0] from the Dim palette + Type: Palette +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ListPointsGraphicsExamplePageEmpty19} +\begin{paste}{ListPointsGraphicsExamplePageEmpty19}{ListPointsGraphicsExamplePagePatch19} +\pastebutton{ListPointsGraphicsExamplePageEmpty19}{\showpaste} +\tab{5}\spadcommand{pc2 := dim green()\bound{pc2 }} +\end{paste}\end{patch} + +\begin{patch}{ListPointsGraphicsExamplePagePatch20} +\begin{paste}{ListPointsGraphicsExamplePageFull20}{ListPointsGraphicsExamplePageEmpty20} +\pastebutton{ListPointsGraphicsExamplePageFull20}{\hidepaste} +\tab{5}\spadcommand{pc3 := pastel yellow()\bound{pc3 }} +\indentrel{3}\begin{verbatim} + (20) [Hue: 11 Weight: 1.0] from the Pastel palette + Type: Palette +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ListPointsGraphicsExamplePageEmpty20} +\begin{paste}{ListPointsGraphicsExamplePageEmpty20}{ListPointsGraphicsExamplePagePatch20} +\pastebutton{ListPointsGraphicsExamplePageEmpty20}{\showpaste} +\tab{5}\spadcommand{pc3 := pastel yellow()\bound{pc3 }} +\end{paste}\end{patch} + +\begin{patch}{ListPointsGraphicsExamplePagePatch21} +\begin{paste}{ListPointsGraphicsExamplePageFull21}{ListPointsGraphicsExamplePageEmpty21} +\pastebutton{ListPointsGraphicsExamplePageFull21}{\hidepaste} +\tab{5}\spadcommand{lpc := [pc1, pc1, pc1, pc1, pc2, pc2, pc2, pc2, pc3, pc3, pc3, pc3]\bound{lpc }\free{pc1 pc2 pc3 }} +\indentrel{3}\begin{verbatim} + (21) + [[Hue: 1 Weight: 1.0] from the Pastel palette, + [Hue: 1 Weight: 1.0] from the Pastel palette, + [Hue: 1 Weight: 1.0] from the Pastel palette, + [Hue: 1 Weight: 1.0] from the Pastel palette, + [Hue: 14 Weight: 1.0] from the Dim palette, + [Hue: 14 Weight: 1.0] from the Dim palette, + [Hue: 14 Weight: 1.0] from the Dim palette, + [Hue: 14 Weight: 1.0] from the Dim palette, + [Hue: 11 Weight: 1.0] from the Pastel palette, + [Hue: 11 Weight: 1.0] from the Pastel palette, + [Hue: 11 Weight: 1.0] from the Pastel palette, + [Hue: 11 Weight: 1.0] from the Pastel palette] + Type: List Palette +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ListPointsGraphicsExamplePageEmpty21} +\begin{paste}{ListPointsGraphicsExamplePageEmpty21}{ListPointsGraphicsExamplePagePatch21} +\pastebutton{ListPointsGraphicsExamplePageEmpty21}{\showpaste} +\tab{5}\spadcommand{lpc := [pc1, pc1, pc1, pc1, pc2, pc2, pc2, pc2, pc3, pc3, pc3, pc3]\bound{lpc }\free{pc1 pc2 pc3 }} +\end{paste}\end{patch} + +\begin{patch}{ListPointsGraphicsExamplePagePatch22} +\begin{paste}{ListPointsGraphicsExamplePageFull22}{ListPointsGraphicsExamplePageEmpty22} +\pastebutton{ListPointsGraphicsExamplePageFull22}{\hidepaste} +\tab{5}\spadcommand{lc := [pastel blue(), light yellow(), dim green(), bright red(), light green(), dim yellow(), bright blue(), dark red(), pastel red(), light blue(), dim green(), light yellow()]\bound{lc }} +\indentrel{3}\begin{verbatim} + (22) + [[Hue: 22 Weight: 1.0] from the Pastel palette, + [Hue: 11 Weight: 1.0] from the Light palette, + [Hue: 14 Weight: 1.0] from the Dim palette, + [Hue: 1 Weight: 1.0] from the Bright palette, + [Hue: 14 Weight: 1.0] from the Light palette, + [Hue: 11 Weight: 1.0] from the Dim palette, + [Hue: 22 Weight: 1.0] from the Bright palette, + [Hue: 1 Weight: 1.0] from the Dark palette, + [Hue: 1 Weight: 1.0] from the Pastel palette, + [Hue: 22 Weight: 1.0] from the Light palette, + [Hue: 14 Weight: 1.0] from the Dim palette, + [Hue: 11 Weight: 1.0] from the Light palette] + Type: List Palette +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ListPointsGraphicsExamplePageEmpty22} +\begin{paste}{ListPointsGraphicsExamplePageEmpty22}{ListPointsGraphicsExamplePagePatch22} +\pastebutton{ListPointsGraphicsExamplePageEmpty22}{\showpaste} +\tab{5}\spadcommand{lc := [pastel blue(), light yellow(), dim green(), bright red(), light green(), dim yellow(), bright blue(), dark red(), pastel red(), light blue(), dim green(), light yellow()]\bound{lc }} +\end{paste}\end{patch} + +\begin{patch}{ListPointsGraphicsExamplePagePatch23} +\begin{paste}{ListPointsGraphicsExamplePageFull23}{ListPointsGraphicsExamplePageEmpty23} +\pastebutton{ListPointsGraphicsExamplePageFull23}{\hidepaste} +\tab{5}\spadcommand{g := makeGraphImage(llp,lpc,lc,lsize)$GRIMAGE\bound{g }\free{llp lpc lc lsize }} +\indentrel{3}\begin{verbatim} + (23) Graph with 12 point lists + Type: GraphImage +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ListPointsGraphicsExamplePageEmpty23} +\begin{paste}{ListPointsGraphicsExamplePageEmpty23}{ListPointsGraphicsExamplePagePatch23} +\pastebutton{ListPointsGraphicsExamplePageEmpty23}{\showpaste} +\tab{5}\spadcommand{g := makeGraphImage(llp,lpc,lc,lsize)$GRIMAGE\bound{g }\free{llp lpc lc lsize }} +\end{paste}\end{patch} + +\begin{patch}{ListPointsGraphicsExamplePagePatch24} +\begin{paste}{ListPointsGraphicsExamplePageFull24}{ListPointsGraphicsExamplePageEmpty24} +\pastebutton{ListPointsGraphicsExamplePageFull24}{\hidepaste} +\tab{5}\spadgraph{makeViewport2D(g,[title("Lines")])$VIEW2D\free{g }} +\center{\unixcommand{\inputimage{\env{AXIOM}/doc/viewports/listpointsgraphicsexamplepage24.view/image}}{viewalone\space{1} \env{AXIOM}/doc/viewports/listpointsgraphicsexamplepage24}} +\end{paste}\end{patch} + +\begin{patch}{ListPointsGraphicsExamplePageEmpty24} +\begin{paste}{ListPointsGraphicsExamplePageEmpty24}{ListPointsGraphicsExamplePagePatch24} +\pastebutton{ListPointsGraphicsExamplePageEmpty24}{\showpaste} +\tab{5}\spadgraph{makeViewport2D(g,[title("Lines")])$VIEW2D\free{g }} +\end{paste}\end{patch} @ \pagehead{ThreeDimensionalGraphicsPage}{graphics.ht} @@ -10168,7 +25589,49 @@ which they are defined in the function specification. In this case the first range specifies the x-variable and the second range specifies the y-variable. \endscroll -\autobuttons \end{page} +\autobuttons +\end{page} + +\begin{patch}{TwoVariableGraphicsPagePatch1} +\begin{paste}{TwoVariableGraphicsPageFull1}{TwoVariableGraphicsPageEmpty1} +\pastebutton{TwoVariableGraphicsPageFull1}{\hidepaste} +\tab{5}\spadgraph{draw(cos(x*y),x=-3..3,y=-3..3)} +\center{\unixcommand{\inputimage{\env{AXIOM}/doc/viewports/twovariablegraphicspage1.view/image}}{viewalone\space{1} \env{AXIOM}/doc/viewports/twovariablegraphicspage1}} +\end{paste}\end{patch} + +\begin{patch}{TwoVariableGraphicsPageEmpty1} +\begin{paste}{TwoVariableGraphicsPageEmpty1}{TwoVariableGraphicsPagePatch1} +\pastebutton{TwoVariableGraphicsPageEmpty1}{\showpaste} +\tab{5}\spadgraph{draw(cos(x*y),x=-3..3,y=-3..3)} +\end{paste}\end{patch} + +\begin{patch}{TwoVariableGraphicsPagePatch2} +\begin{paste}{TwoVariableGraphicsPageFull2}{TwoVariableGraphicsPageEmpty2} +\pastebutton{TwoVariableGraphicsPageFull2}{\hidepaste} +\tab{5}\spadcommand{f(x:SF,y:SF):SF == sin(x)*cos(y)\bound{f }} +\indentrel{3}\begin{verbatim} + Type: Void +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{TwoVariableGraphicsPageEmpty2} +\begin{paste}{TwoVariableGraphicsPageEmpty2}{TwoVariableGraphicsPagePatch2} +\pastebutton{TwoVariableGraphicsPageEmpty2}{\showpaste} +\tab{5}\spadcommand{f(x:SF,y:SF):SF == sin(x)*cos(y)\bound{f }} +\end{paste}\end{patch} + +\begin{patch}{TwoVariableGraphicsPagePatch3} +\begin{paste}{TwoVariableGraphicsPageFull3}{TwoVariableGraphicsPageEmpty3} +\pastebutton{TwoVariableGraphicsPageFull3}{\hidepaste} +\tab{5}\spadgraph{draw(f,-\%pi..\%pi,-\%pi..\%pi)\free{f }} +\center{\unixcommand{\inputimage{\env{AXIOM}/doc/viewports/twovariablegraphicspage3.view/image}}{viewalone\space{1} \env{AXIOM}/doc/viewports/twovariablegraphicspage3}} +\end{paste}\end{patch} + +\begin{patch}{TwoVariableGraphicsPageEmpty3} +\begin{paste}{TwoVariableGraphicsPageEmpty3}{TwoVariableGraphicsPagePatch3} +\pastebutton{TwoVariableGraphicsPageEmpty3}{\showpaste} +\tab{5}\spadgraph{draw(f,-\%pi..\%pi,-\%pi..\%pi)\free{f }} +\end{paste}\end{patch} @ \pagehead{SpaceCurveGraphicsPage}{graphics.ht}{Parametric Space Curves} @@ -10209,7 +25672,79 @@ Note that the parameter range does not take the variable name as in the case of uncompiled functions. It is understood that the indicated range applies to the parameter of the functions, which in this case is t. \endscroll -\autobuttons \end{page} +\autobuttons +\end{page} + +\begin{patch}{SpaceCurveGraphicsPagePatch1} +\begin{paste}{SpaceCurveGraphicsPageFull1}{SpaceCurveGraphicsPageEmpty1} +\pastebutton{SpaceCurveGraphicsPageFull1}{\hidepaste} +\tab{5}\spadgraph{draw(curve(cos(t),sin(t),t), t=-12..12)} +\center{\unixcommand{\inputimage{\env{AXIOM}/doc/viewports/spacecurvegraphicspage1.view/image}}{viewalone\space{1} \env{AXIOM}/doc/viewports/spacecurvegraphicspage1}} +\end{paste}\end{patch} + +\begin{patch}{SpaceCurveGraphicsPageEmpty1} +\begin{paste}{SpaceCurveGraphicsPageEmpty1}{SpaceCurveGraphicsPagePatch1} +\pastebutton{SpaceCurveGraphicsPageEmpty1}{\showpaste} +\tab{5}\spadgraph{draw(curve(cos(t),sin(t),t), t=-12..12)} +\end{paste}\end{patch} + +\begin{patch}{SpaceCurveGraphicsPagePatch2} +\begin{paste}{SpaceCurveGraphicsPageFull2}{SpaceCurveGraphicsPageEmpty2} +\pastebutton{SpaceCurveGraphicsPageFull2}{\hidepaste} +\tab{5}\spadcommand{i1(t:SF):SF == sin(t)*cos(3*t/5)\bound{i1 }} +\indentrel{3}\begin{verbatim} + Type: Void +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{SpaceCurveGraphicsPageEmpty2} +\begin{paste}{SpaceCurveGraphicsPageEmpty2}{SpaceCurveGraphicsPagePatch2} +\pastebutton{SpaceCurveGraphicsPageEmpty2}{\showpaste} +\tab{5}\spadcommand{i1(t:SF):SF == sin(t)*cos(3*t/5)\bound{i1 }} +\end{paste}\end{patch} + +\begin{patch}{SpaceCurveGraphicsPagePatch3} +\begin{paste}{SpaceCurveGraphicsPageFull3}{SpaceCurveGraphicsPageEmpty3} +\pastebutton{SpaceCurveGraphicsPageFull3}{\hidepaste} +\tab{5}\spadcommand{i2(t:SF):SF == cos(t)*cos(3*t/5)\bound{i2 }} +\indentrel{3}\begin{verbatim} + Type: Void +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{SpaceCurveGraphicsPageEmpty3} +\begin{paste}{SpaceCurveGraphicsPageEmpty3}{SpaceCurveGraphicsPagePatch3} +\pastebutton{SpaceCurveGraphicsPageEmpty3}{\showpaste} +\tab{5}\spadcommand{i2(t:SF):SF == cos(t)*cos(3*t/5)\bound{i2 }} +\end{paste}\end{patch} + +\begin{patch}{SpaceCurveGraphicsPagePatch4} +\begin{paste}{SpaceCurveGraphicsPageFull4}{SpaceCurveGraphicsPageEmpty4} +\pastebutton{SpaceCurveGraphicsPageFull4}{\hidepaste} +\tab{5}\spadcommand{i3(t:SF):SF == cos(t)*sin(3*t/5)\bound{i3 }} +\indentrel{3}\begin{verbatim} + Type: Void +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{SpaceCurveGraphicsPageEmpty4} +\begin{paste}{SpaceCurveGraphicsPageEmpty4}{SpaceCurveGraphicsPagePatch4} +\pastebutton{SpaceCurveGraphicsPageEmpty4}{\showpaste} +\tab{5}\spadcommand{i3(t:SF):SF == cos(t)*sin(3*t/5)\bound{i3 }} +\end{paste}\end{patch} + +\begin{patch}{SpaceCurveGraphicsPagePatch5} +\begin{paste}{SpaceCurveGraphicsPageFull5}{SpaceCurveGraphicsPageEmpty5} +\pastebutton{SpaceCurveGraphicsPageFull5}{\hidepaste} +\tab{5}\spadgraph{draw(curve(i1,i2,i3),0..15*\%pi)\free{i1 i2 i3 }} +\center{\unixcommand{\inputimage{\env{AXIOM}/doc/viewports/spacecurvegraphicspage5.view/image}}{viewalone\space{1} \env{AXIOM}/doc/viewports/spacecurvegraphicspage5}} +\end{paste}\end{patch} + +\begin{patch}{SpaceCurveGraphicsPageEmpty5} +\begin{paste}{SpaceCurveGraphicsPageEmpty5}{SpaceCurveGraphicsPagePatch5} +\pastebutton{SpaceCurveGraphicsPageEmpty5}{\showpaste} +\tab{5}\spadgraph{draw(curve(i1,i2,i3),0..15*\%pi)\free{i1 i2 i3 }} +\end{paste}\end{patch} @ \pagehead{ParametricTubeGraphicsPage}{graphics.ht}{Parametric Tube Plots} @@ -10263,7 +25798,79 @@ t. Typically, the radius of the tube should be set between 0 and 1. A radius of less than 0 results in it's positive counterpart and a radius of greater than one causes self intersection. \endscroll -\autobuttons \end{page} +\autobuttons +\end{page} + +\begin{patch}{ParametricTubeGraphicsPagePatch1} +\begin{paste}{ParametricTubeGraphicsPageFull1}{ParametricTubeGraphicsPageEmpty1} +\pastebutton{ParametricTubeGraphicsPageFull1}{\hidepaste} +\tab{5}\spadgraph{draw(curve(sin(t)*cos(3*t/5), cos(t)*cos(3*t/5), cos(t)*sin(3*t/5)), t=0..15*\%pi,tubeRadius == .15)} +\center{\unixcommand{\inputimage{\env{AXIOM}/doc/viewports/parametrictubegraphicspage1.view/image}}{viewalone\space{1} \env{AXIOM}/doc/viewports/parametrictubegraphicspage1}} +\end{paste}\end{patch} + +\begin{patch}{ParametricTubeGraphicsPageEmpty1} +\begin{paste}{ParametricTubeGraphicsPageEmpty1}{ParametricTubeGraphicsPagePatch1} +\pastebutton{ParametricTubeGraphicsPageEmpty1}{\showpaste} +\tab{5}\spadgraph{draw(curve(sin(t)*cos(3*t/5), cos(t)*cos(3*t/5), cos(t)*sin(3*t/5)), t=0..15*\%pi,tubeRadius == .15)} +\end{paste}\end{patch} + +\begin{patch}{ParametricTubeGraphicsPagePatch2} +\begin{paste}{ParametricTubeGraphicsPageFull2}{ParametricTubeGraphicsPageEmpty2} +\pastebutton{ParametricTubeGraphicsPageFull2}{\hidepaste} +\tab{5}\spadcommand{t1(t:SF):SF == 4/(2-sin(3*t))*cos(2*t)\bound{t1 }} +\indentrel{3}\begin{verbatim} + Type: Void +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ParametricTubeGraphicsPageEmpty2} +\begin{paste}{ParametricTubeGraphicsPageEmpty2}{ParametricTubeGraphicsPagePatch2} +\pastebutton{ParametricTubeGraphicsPageEmpty2}{\showpaste} +\tab{5}\spadcommand{t1(t:SF):SF == 4/(2-sin(3*t))*cos(2*t)\bound{t1 }} +\end{paste}\end{patch} + +\begin{patch}{ParametricTubeGraphicsPagePatch3} +\begin{paste}{ParametricTubeGraphicsPageFull3}{ParametricTubeGraphicsPageEmpty3} +\pastebutton{ParametricTubeGraphicsPageFull3}{\hidepaste} +\tab{5}\spadcommand{t2(t:SF):SF == 4/(2-sin(3*t))*sin(2*t)\bound{t2 }} +\indentrel{3}\begin{verbatim} + Type: Void +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ParametricTubeGraphicsPageEmpty3} +\begin{paste}{ParametricTubeGraphicsPageEmpty3}{ParametricTubeGraphicsPagePatch3} +\pastebutton{ParametricTubeGraphicsPageEmpty3}{\showpaste} +\tab{5}\spadcommand{t2(t:SF):SF == 4/(2-sin(3*t))*sin(2*t)\bound{t2 }} +\end{paste}\end{patch} + +\begin{patch}{ParametricTubeGraphicsPagePatch4} +\begin{paste}{ParametricTubeGraphicsPageFull4}{ParametricTubeGraphicsPageEmpty4} +\pastebutton{ParametricTubeGraphicsPageFull4}{\hidepaste} +\tab{5}\spadcommand{t3(t:SF):SF == 4/(2-sin(3*t))*cos(3*t)\bound{t3 }} +\indentrel{3}\begin{verbatim} + Type: Void +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ParametricTubeGraphicsPageEmpty4} +\begin{paste}{ParametricTubeGraphicsPageEmpty4}{ParametricTubeGraphicsPagePatch4} +\pastebutton{ParametricTubeGraphicsPageEmpty4}{\showpaste} +\tab{5}\spadcommand{t3(t:SF):SF == 4/(2-sin(3*t))*cos(3*t)\bound{t3 }} +\end{paste}\end{patch} + +\begin{patch}{ParametricTubeGraphicsPagePatch5} +\begin{paste}{ParametricTubeGraphicsPageFull5}{ParametricTubeGraphicsPageEmpty5} +\pastebutton{ParametricTubeGraphicsPageFull5}{\hidepaste} +\tab{5}\spadgraph{draw(curve(t1,t2,t3),0..2*\%pi,tubeRadius == .2)\free{t1 t2 t3 }} +\center{\unixcommand{\inputimage{\env{AXIOM}/doc/viewports/parametrictubegraphicspage5.view/image}}{viewalone\space{1} \env{AXIOM}/doc/viewports/parametrictubegraphicspage5}} +\end{paste}\end{patch} + +\begin{patch}{ParametricTubeGraphicsPageEmpty5} +\begin{paste}{ParametricTubeGraphicsPageEmpty5}{ParametricTubeGraphicsPagePatch5} +\pastebutton{ParametricTubeGraphicsPageEmpty5}{\showpaste} +\tab{5}\spadgraph{draw(curve(t1,t2,t3),0..2*\%pi,tubeRadius == .2)\free{t1 t2 t3 }} +\end{paste}\end{patch} @ \pagehead{ParametricSurfaceGraphicsPage}{graphics.ht}{Parametric Surfaces} @@ -10314,7 +25921,79 @@ order in which they are defined in the function specification. In this case the first range specifies the u-variable and the second range specifies the v-variable. \endscroll -\autobuttons \end{page} +\autobuttons +\end{page} + +\begin{patch}{ParametricSurfaceGraphicsPagePatch1} +\begin{paste}{ParametricSurfaceGraphicsPageFull1}{ParametricSurfaceGraphicsPageEmpty1} +\pastebutton{ParametricSurfaceGraphicsPageFull1}{\hidepaste} +\tab{5}\spadgraph{draw(surface(u*cos(v), u*sin(v),v*cos(u)),u=-4..4,v=0..2*\%pi, coordinates== parabolicCylindrical)} +\center{\unixcommand{\inputimage{\env{AXIOM}/doc/viewports/parametricsurfacegraphicspage1.view/image}}{viewalone\space{1} \env{AXIOM}/doc/viewports/parametricsurfacegraphicspage1}} +\end{paste}\end{patch} + +\begin{patch}{ParametricSurfaceGraphicsPageEmpty1} +\begin{paste}{ParametricSurfaceGraphicsPageEmpty1}{ParametricSurfaceGraphicsPagePatch1} +\pastebutton{ParametricSurfaceGraphicsPageEmpty1}{\showpaste} +\tab{5}\spadgraph{draw(surface(u*cos(v), u*sin(v),v*cos(u)),u=-4..4,v=0..2*\%pi, coordinates== parabolicCylindrical)} +\end{paste}\end{patch} + +\begin{patch}{ParametricSurfaceGraphicsPagePatch2} +\begin{paste}{ParametricSurfaceGraphicsPageFull2}{ParametricSurfaceGraphicsPageEmpty2} +\pastebutton{ParametricSurfaceGraphicsPageFull2}{\hidepaste} +\tab{5}\spadcommand{n1(u:SF,v:SF):SF == u*cos(v)\bound{n1 }} +\indentrel{3}\begin{verbatim} + Type: Void +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ParametricSurfaceGraphicsPageEmpty2} +\begin{paste}{ParametricSurfaceGraphicsPageEmpty2}{ParametricSurfaceGraphicsPagePatch2} +\pastebutton{ParametricSurfaceGraphicsPageEmpty2}{\showpaste} +\tab{5}\spadcommand{n1(u:SF,v:SF):SF == u*cos(v)\bound{n1 }} +\end{paste}\end{patch} + +\begin{patch}{ParametricSurfaceGraphicsPagePatch3} +\begin{paste}{ParametricSurfaceGraphicsPageFull3}{ParametricSurfaceGraphicsPageEmpty3} +\pastebutton{ParametricSurfaceGraphicsPageFull3}{\hidepaste} +\tab{5}\spadcommand{n2(u:SF,v:SF):SF == u*sin(v)\bound{n2 }} +\indentrel{3}\begin{verbatim} + Type: Void +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ParametricSurfaceGraphicsPageEmpty3} +\begin{paste}{ParametricSurfaceGraphicsPageEmpty3}{ParametricSurfaceGraphicsPagePatch3} +\pastebutton{ParametricSurfaceGraphicsPageEmpty3}{\showpaste} +\tab{5}\spadcommand{n2(u:SF,v:SF):SF == u*sin(v)\bound{n2 }} +\end{paste}\end{patch} + +\begin{patch}{ParametricSurfaceGraphicsPagePatch4} +\begin{paste}{ParametricSurfaceGraphicsPageFull4}{ParametricSurfaceGraphicsPageEmpty4} +\pastebutton{ParametricSurfaceGraphicsPageFull4}{\hidepaste} +\tab{5}\spadcommand{n3(u:SF,v:SF):SF == u\bound{n3 }} +\indentrel{3}\begin{verbatim} + Type: Void +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ParametricSurfaceGraphicsPageEmpty4} +\begin{paste}{ParametricSurfaceGraphicsPageEmpty4}{ParametricSurfaceGraphicsPagePatch4} +\pastebutton{ParametricSurfaceGraphicsPageEmpty4}{\showpaste} +\tab{5}\spadcommand{n3(u:SF,v:SF):SF == u\bound{n3 }} +\end{paste}\end{patch} + +\begin{patch}{ParametricSurfaceGraphicsPagePatch5} +\begin{paste}{ParametricSurfaceGraphicsPageFull5}{ParametricSurfaceGraphicsPageEmpty5} +\pastebutton{ParametricSurfaceGraphicsPageFull5}{\hidepaste} +\tab{5}\spadgraph{draw(surface(n1,n2,n3), 1.0..4.0, 1.0..4*\%pi, coordinates == toroidal(1$SF))\free{n1 n2 n3 }} +\center{\unixcommand{\inputimage{\env{AXIOM}/doc/viewports/parametricsurfacegraphicspage5.view/image}}{viewalone\space{1} \env{AXIOM}/doc/viewports/parametricsurfacegraphicspage5}} +\end{paste}\end{patch} + +\begin{patch}{ParametricSurfaceGraphicsPageEmpty5} +\begin{paste}{ParametricSurfaceGraphicsPageEmpty5}{ParametricSurfaceGraphicsPagePatch5} +\pastebutton{ParametricSurfaceGraphicsPageEmpty5}{\showpaste} +\tab{5}\spadgraph{draw(surface(n1,n2,n3), 1.0..4.0, 1.0..4*\%pi, coordinates == toroidal(1$SF))\free{n1 n2 n3 }} +\end{paste}\end{patch} @ \pagehead{3DObjectGraphicsPage}{graphics.ht}{Building 3D Objects} @@ -10375,7 +26054,149 @@ The tailing string {\em \$VIEW3D} exposes the command \spadfun{makeViewport3D()} from the domain \spadtype{ThreeDimensionalViewport} if these commands are unexposed. \endscroll -\autobuttons \end{page} +\autobuttons +\end{page} + +\begin{patch}{3DObjectGraphicsPagePatch1} +\begin{paste}{3DObjectGraphicsPageFull1}{3DObjectGraphicsPageEmpty1} +\pastebutton{3DObjectGraphicsPageFull1}{\hidepaste} +\tab{5}\spadcommand{space := create3Space()$(ThreeSpace SF)\bound{space }} +\indentrel{3}\begin{verbatim} + (1) 3-Space with 0 components + Type: ThreeSpace DoubleFloat +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{3DObjectGraphicsPageEmpty1} +\begin{paste}{3DObjectGraphicsPageEmpty1}{3DObjectGraphicsPagePatch1} +\pastebutton{3DObjectGraphicsPageEmpty1}{\showpaste} +\tab{5}\spadcommand{space := create3Space()$(ThreeSpace SF)\bound{space }} +\end{paste}\end{patch} + +\begin{patch}{3DObjectGraphicsPagePatch2} +\begin{paste}{3DObjectGraphicsPageFull2}{3DObjectGraphicsPageEmpty2} +\pastebutton{3DObjectGraphicsPageFull2}{\hidepaste} +\tab{5}\spadcommand{curve(space,[[0,20,20],[0,20,30],[0,30,30],[0,30,100], [0,20,100],[0,20,110],[0,50,110],[0,50,100],[0,40,100], [0,40,30],[0,50,30],[0,50,20],[0,20,20]])\bound{curveI }} +\indentrel{3}\begin{verbatim} + (2) 3-Space with 1 component + Type: ThreeSpace DoubleFloat +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{3DObjectGraphicsPageEmpty2} +\begin{paste}{3DObjectGraphicsPageEmpty2}{3DObjectGraphicsPagePatch2} +\pastebutton{3DObjectGraphicsPageEmpty2}{\showpaste} +\tab{5}\spadcommand{curve(space,[[0,20,20],[0,20,30],[0,30,30],[0,30,100], [0,20,100],[0,20,110],[0,50,110],[0,50,100],[0,40,100], [0,40,30],[0,50,30],[0,50,20],[0,20,20]])\bound{curveI }} +\end{paste}\end{patch} + +\begin{patch}{3DObjectGraphicsPagePatch3} +\begin{paste}{3DObjectGraphicsPageFull3}{3DObjectGraphicsPageEmpty3} +\pastebutton{3DObjectGraphicsPageFull3}{\hidepaste} +\tab{5}\spadcommand{curve(space,[[0,80,20],[0,70,20],[0,70,110],[0,110,110], [0,120,100],[0,120,70],[0,115,65],[0,120,60],[0,120,30], [0,110,20],[0,80,20],[0,80,30],[0,105,30],[0,110,35]])\bound{curveB1 }} +\indentrel{3}\begin{verbatim} + (3) 3-Space with 2 components + Type: ThreeSpace DoubleFloat +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{3DObjectGraphicsPageEmpty3} +\begin{paste}{3DObjectGraphicsPageEmpty3}{3DObjectGraphicsPagePatch3} +\pastebutton{3DObjectGraphicsPageEmpty3}{\showpaste} +\tab{5}\spadcommand{curve(space,[[0,80,20],[0,70,20],[0,70,110],[0,110,110], [0,120,100],[0,120,70],[0,115,65],[0,120,60],[0,120,30], [0,110,20],[0,80,20],[0,80,30],[0,105,30],[0,110,35]])\bound{curveB1 }} +\end{paste}\end{patch} + +\begin{patch}{3DObjectGraphicsPagePatch4} +\begin{paste}{3DObjectGraphicsPageFull4}{3DObjectGraphicsPageEmpty4} +\pastebutton{3DObjectGraphicsPageFull4}{\hidepaste} +\tab{5}\spadcommand{curve(space,[[0,110,35],[0,110,55],[0,105,60],[0,80,60],[0,80,70], [0,105,70],[0,110,75],[0,110,95],[0,105,100],[0,80,100], [0,80,30]])\bound{curveB2 }} +\indentrel{3}\begin{verbatim} + (4) 3-Space with 3 components + Type: ThreeSpace DoubleFloat +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{3DObjectGraphicsPageEmpty4} +\begin{paste}{3DObjectGraphicsPageEmpty4}{3DObjectGraphicsPagePatch4} +\pastebutton{3DObjectGraphicsPageEmpty4}{\showpaste} +\tab{5}\spadcommand{curve(space,[[0,110,35],[0,110,55],[0,105,60],[0,80,60],[0,80,70], [0,105,70],[0,110,75],[0,110,95],[0,105,100],[0,80,100], [0,80,30]])\bound{curveB2 }} +\end{paste}\end{patch} + +\begin{patch}{3DObjectGraphicsPagePatch5} +\begin{paste}{3DObjectGraphicsPageFull5}{3DObjectGraphicsPageEmpty5} +\pastebutton{3DObjectGraphicsPageFull5}{\hidepaste} +\tab{5}\spadcommand{closedCurve(space,[[0,140,20],[0,140,110],[0,150,110],[0,170,50], [0,190,110],[0,200,110],[0,200,20],[0,190,20],[0,190,75], [0,175,35],[0,165,35],[0,150,75],[0,150,20]])\bound{curveM }} +\indentrel{3}\begin{verbatim} + (5) 3-Space with 4 components + Type: ThreeSpace DoubleFloat +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{3DObjectGraphicsPageEmpty5} +\begin{paste}{3DObjectGraphicsPageEmpty5}{3DObjectGraphicsPagePatch5} +\pastebutton{3DObjectGraphicsPageEmpty5}{\showpaste} +\tab{5}\spadcommand{closedCurve(space,[[0,140,20],[0,140,110],[0,150,110],[0,170,50], [0,190,110],[0,200,110],[0,200,20],[0,190,20],[0,190,75], [0,175,35],[0,165,35],[0,150,75],[0,150,20]])\bound{curveM }} +\end{paste}\end{patch} + +\begin{patch}{3DObjectGraphicsPagePatch6} +\begin{paste}{3DObjectGraphicsPageFull6}{3DObjectGraphicsPageEmpty6} +\pastebutton{3DObjectGraphicsPageFull6}{\hidepaste} +\tab{5}\spadcommand{closedCurve(space,[[200,0,20], [200,0,110], [185,0,110], [160,0,45], [160,0,110], [150,0,110], [150,0,20], [165,0,20], [190,0,85], [190,0,20]])\bound{curveN }} +\indentrel{3}\begin{verbatim} + (6) 3-Space with 5 components + Type: ThreeSpace DoubleFloat +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{3DObjectGraphicsPageEmpty6} +\begin{paste}{3DObjectGraphicsPageEmpty6}{3DObjectGraphicsPagePatch6} +\pastebutton{3DObjectGraphicsPageEmpty6}{\showpaste} +\tab{5}\spadcommand{closedCurve(space,[[200,0,20], [200,0,110], [185,0,110], [160,0,45], [160,0,110], [150,0,110], [150,0,20], [165,0,20], [190,0,85], [190,0,20]])\bound{curveN }} +\end{paste}\end{patch} + +\begin{patch}{3DObjectGraphicsPagePatch7} +\begin{paste}{3DObjectGraphicsPageFull7}{3DObjectGraphicsPageEmpty7} +\pastebutton{3DObjectGraphicsPageFull7}{\hidepaste} +\tab{5}\spadcommand{closedCurve(space,[[140,0,20], [120,0,110], [110,0,110], [90,0,20], [100,0,20], [108,0,50], [123,0,50], [121,0,60], [110,0,60], [115,0,90], [130,0,20]])\bound{curveA }} +\indentrel{3}\begin{verbatim} + (7) 3-Space with 6 components + Type: ThreeSpace DoubleFloat +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{3DObjectGraphicsPageEmpty7} +\begin{paste}{3DObjectGraphicsPageEmpty7}{3DObjectGraphicsPagePatch7} +\pastebutton{3DObjectGraphicsPageEmpty7}{\showpaste} +\tab{5}\spadcommand{closedCurve(space,[[140,0,20], [120,0,110], [110,0,110], [90,0,20], [100,0,20], [108,0,50], [123,0,50], [121,0,60], [110,0,60], [115,0,90], [130,0,20]])\bound{curveA }} +\end{paste}\end{patch} + +\begin{patch}{3DObjectGraphicsPagePatch8} +\begin{paste}{3DObjectGraphicsPageFull8}{3DObjectGraphicsPageEmpty8} +\pastebutton{3DObjectGraphicsPageFull8}{\hidepaste} +\tab{5}\spadcommand{closedCurve(space,[[80,0,30], [80,0,100], [70,0,110], [40,0,110], [30,0,100], [30,0,90], [40,0,90], [40,0,95], [45,0,100], [65,0,100], [70,0,95], [70,0,35], [65,0,30], [45,0,30], [40,0,35], [40,0,60], [50,0,60], [50,0,70], [30,0,70], [30,0,30], [40,0,20], [70,0,20]])\bound{curveG }} +\indentrel{3}\begin{verbatim} + (8) 3-Space with 7 components + Type: ThreeSpace DoubleFloat +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{3DObjectGraphicsPageEmpty8} +\begin{paste}{3DObjectGraphicsPageEmpty8}{3DObjectGraphicsPagePatch8} +\pastebutton{3DObjectGraphicsPageEmpty8}{\showpaste} +\tab{5}\spadcommand{closedCurve(space,[[80,0,30], [80,0,100], [70,0,110], [40,0,110], [30,0,100], [30,0,90], [40,0,90], [40,0,95], [45,0,100], [65,0,100], [70,0,95], [70,0,35], [65,0,30], [45,0,30], [40,0,35], [40,0,60], [50,0,60], [50,0,70], [30,0,70], [30,0,30], [40,0,20], [70,0,20]])\bound{curveG }} +\end{paste}\end{patch} + +\begin{patch}{3DObjectGraphicsPagePatch9} +\begin{paste}{3DObjectGraphicsPageFull9}{3DObjectGraphicsPageEmpty9} +\pastebutton{3DObjectGraphicsPageFull9}{\hidepaste} +\tab{5}\spadgraph{makeViewport3D(space,[title("Curves")])$VIEW3D\free{space curveI curveB1 curveB2 curveM curveN curveA curveG }} +\center{\unixcommand{\inputimage{\env{AXIOM}/doc/viewports/3dobjectgraphicspage9.view/image}}{viewalone\space{1} \env{AXIOM}/doc/viewports/3dobjectgraphicspage9}} +\end{paste}\end{patch} + +\begin{patch}{3DObjectGraphicsPageEmpty9} +\begin{paste}{3DObjectGraphicsPageEmpty9}{3DObjectGraphicsPagePatch9} +\pastebutton{3DObjectGraphicsPageEmpty9}{\showpaste} +\tab{5}\spadgraph{makeViewport3D(space,[title("Curves")])$VIEW3D\free{space curveI curveB1 curveB2 curveM curveN curveA curveG }} +\end{paste}\end{patch} @ \pagehead{TwoDimensionalGraphicsPage}{graphics.ht} @@ -10442,7 +26263,75 @@ Notice that our titles can be whatever we want, as long as they are enclosed by double quotes. However, a title which is too long to fit within the viewport title window will be clipped. \endscroll -\autobuttons \end{page} +\autobuttons +\end{page} + +\begin{patch}{OneVariableGraphicsPagePatch1} +\begin{paste}{OneVariableGraphicsPageFull1}{OneVariableGraphicsPageEmpty1} +\pastebutton{OneVariableGraphicsPageFull1}{\hidepaste} +\tab{5}\spadgraph{draw(sin(tan(x)) - tan(sin(x)),x = 0..6)} +\center{\unixcommand{\inputimage{\env{AXIOM}/doc/viewports/onevariablegraphicspage1.view/image}}{viewalone\space{1} \env{AXIOM}/doc/viewports/onevariablegraphicspage1}} +\end{paste}\end{patch} + +\begin{patch}{OneVariableGraphicsPageEmpty1} +\begin{paste}{OneVariableGraphicsPageEmpty1}{OneVariableGraphicsPagePatch1} +\pastebutton{OneVariableGraphicsPageEmpty1}{\showpaste} +\tab{5}\spadgraph{draw(sin(tan(x)) - tan(sin(x)),x = 0..6)} +\end{paste}\end{patch} + +\begin{patch}{OneVariableGraphicsPagePatch2} +\begin{paste}{OneVariableGraphicsPageFull2}{OneVariableGraphicsPageEmpty2} +\pastebutton{OneVariableGraphicsPageFull2}{\hidepaste} +\tab{5}\spadgraph{draw(sin(tan(x)) - tan(sin(x)),x = 10..16,title == "y = sin tan x - tan sin x")} +\center{\unixcommand{\inputimage{\env{AXIOM}/doc/viewports/onevariablegraphicspage2.view/image}}{viewalone\space{1} \env{AXIOM}/doc/viewports/onevariablegraphicspage2}} +\end{paste}\end{patch} + +\begin{patch}{OneVariableGraphicsPageEmpty2} +\begin{paste}{OneVariableGraphicsPageEmpty2}{OneVariableGraphicsPagePatch2} +\pastebutton{OneVariableGraphicsPageEmpty2}{\showpaste} +\tab{5}\spadgraph{draw(sin(tan(x)) - tan(sin(x)),x = 10..16,title == "y = sin tan x - tan sin x")} +\end{paste}\end{patch} + +\begin{patch}{OneVariableGraphicsPagePatch3} +\begin{paste}{OneVariableGraphicsPageFull3}{OneVariableGraphicsPageEmpty3} +\pastebutton{OneVariableGraphicsPageFull3}{\hidepaste} +\tab{5}\spadcommand{f(x) == (x-1)*(x-2)*(x-3)\bound{f }} +\indentrel{3}\begin{verbatim} + Type: Void +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{OneVariableGraphicsPageEmpty3} +\begin{paste}{OneVariableGraphicsPageEmpty3}{OneVariableGraphicsPagePatch3} +\pastebutton{OneVariableGraphicsPageEmpty3}{\showpaste} +\tab{5}\spadcommand{f(x) == (x-1)*(x-2)*(x-3)\bound{f }} +\end{paste}\end{patch} + +\begin{patch}{OneVariableGraphicsPagePatch4} +\begin{paste}{OneVariableGraphicsPageFull4}{OneVariableGraphicsPageEmpty4} +\pastebutton{OneVariableGraphicsPageFull4}{\hidepaste} +\tab{5}\spadgraph{draw(f, 0..2, title == "y = f(x) on [0,2]")\free{f }} +\center{\unixcommand{\inputimage{\env{AXIOM}/doc/viewports/OneVariableGraphicsPage4.view/image}}{viewalone\space{1} \env{AXIOM}/doc/viewports/OneVariableGraphicsPage4}} +\end{paste}\end{patch} + +\begin{patch}{OneVariableGraphicsPageEmpty4} +\begin{paste}{OneVariableGraphicsPageEmpty4}{OneVariableGraphicsPagePatch4} +\pastebutton{OneVariableGraphicsPageEmpty4}{\showpaste} +\tab{5}\spadgraph{draw(f, 0..2, title == "y = f(x) on [0,2]")\free{f }} +\end{paste}\end{patch} + +\begin{patch}{OneVariableGraphicsPagePatch5} +\begin{paste}{OneVariableGraphicsPageFull5}{OneVariableGraphicsPageEmpty5} +\pastebutton{OneVariableGraphicsPageFull5}{\hidepaste} +\tab{5}\spadgraph{draw(f, 0..4,title == "y = f(x) on [0,4]")\free{f }} +\center{\unixcommand{\inputimage{\env{AXIOM}/doc/viewports/OneVariableGraphicsPage5.view/image}}{viewalone\space{1} \env{AXIOM}/doc/viewports/OneVariableGraphicsPage5}} +\end{paste}\end{patch} + +\begin{patch}{OneVariableGraphicsPageEmpty5} +\begin{paste}{OneVariableGraphicsPageEmpty5}{OneVariableGraphicsPagePatch5} +\pastebutton{OneVariableGraphicsPageEmpty5}{\showpaste} +\tab{5}\spadgraph{draw(f, 0..4,title == "y = f(x) on [0,4]")\free{f }} +\end{paste}\end{patch} @ \pagehead{ParametricCurveGraphicsPage}{graphics.ht}{Parametric Curves} @@ -10480,7 +26369,103 @@ example: These examples show how the curve changes as the range of parameter t varies. \endscroll -\autobuttons \end{page} +\autobuttons +\end{page} + +\begin{patch}{ParametricCurveGraphicsPagePatch1} +\begin{paste}{ParametricCurveGraphicsPageFull1}{ParametricCurveGraphicsPageEmpty1} +\pastebutton{ParametricCurveGraphicsPageFull1}{\hidepaste} +\tab{5}\spadgraph{draw(curve(sin(t)*sin(2*t)*sin(3*t), sin(4*t)*sin(5*t)*sin(6*t)), t = 0..2*\%pi)} +\center{\unixcommand{\inputimage{\env{AXIOM}/doc/viewports/parametriccurvegraphicspage1.view/image}}{viewalone\space{1} \env{AXIOM}/doc/viewports/parametriccurvegraphicspage1}} +\end{paste}\end{patch} + +\begin{patch}{ParametricCurveGraphicsPageEmpty1} +\begin{paste}{ParametricCurveGraphicsPageEmpty1}{ParametricCurveGraphicsPagePatch1} +\pastebutton{ParametricCurveGraphicsPageEmpty1}{\showpaste} +\tab{5}\spadgraph{draw(curve(sin(t)*sin(2*t)*sin(3*t), sin(4*t)*sin(5*t)*sin(6*t)), t = 0..2*\%pi)} +\end{paste}\end{patch} + +\begin{patch}{ParametricCurveGraphicsPagePatch2} +\begin{paste}{ParametricCurveGraphicsPageFull2}{ParametricCurveGraphicsPageEmpty2} +\pastebutton{ParametricCurveGraphicsPageFull2}{\hidepaste} +\tab{5}\spadgraph{draw(curve(cos(t), sin(t)), t = 0..2*\%pi, title == "The Unit Circle")} +\center{\unixcommand{\inputimage{\env{AXIOM}/doc/viewports/parametriccurvegraphicspage2.view/image}}{viewalone\space{1} \env{AXIOM}/doc/viewports/parametriccurvegraphicspage2}} +\end{paste}\end{patch} + +\begin{patch}{ParametricCurveGraphicsPageEmpty2} +\begin{paste}{ParametricCurveGraphicsPageEmpty2}{ParametricCurveGraphicsPagePatch2} +\pastebutton{ParametricCurveGraphicsPageEmpty2}{\showpaste} +\tab{5}\spadgraph{draw(curve(cos(t), sin(t)), t = 0..2*\%pi, title == "The Unit Circle")} +\end{paste}\end{patch} + +\begin{patch}{ParametricCurveGraphicsPagePatch3} +\begin{paste}{ParametricCurveGraphicsPageFull3}{ParametricCurveGraphicsPageEmpty3} +\pastebutton{ParametricCurveGraphicsPageFull3}{\hidepaste} +\tab{5}\spadcommand{f(t:SF):SF == sin(3*t/4)\bound{f }} +\indentrel{3}\begin{verbatim} + Type: Void +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ParametricCurveGraphicsPageEmpty3} +\begin{paste}{ParametricCurveGraphicsPageEmpty3}{ParametricCurveGraphicsPagePatch3} +\pastebutton{ParametricCurveGraphicsPageEmpty3}{\showpaste} +\tab{5}\spadcommand{f(t:SF):SF == sin(3*t/4)\bound{f }} +\end{paste}\end{patch} + +\begin{patch}{ParametricCurveGraphicsPagePatch4} +\begin{paste}{ParametricCurveGraphicsPageFull4}{ParametricCurveGraphicsPageEmpty4} +\pastebutton{ParametricCurveGraphicsPageFull4}{\hidepaste} +\tab{5}\spadcommand{g(t:SF):SF == sin(t)\bound{g }} +\indentrel{3}\begin{verbatim} + Type: Void +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ParametricCurveGraphicsPageEmpty4} +\begin{paste}{ParametricCurveGraphicsPageEmpty4}{ParametricCurveGraphicsPagePatch4} +\pastebutton{ParametricCurveGraphicsPageEmpty4}{\showpaste} +\tab{5}\spadcommand{g(t:SF):SF == sin(t)\bound{g }} +\end{paste}\end{patch} + +\begin{patch}{ParametricCurveGraphicsPagePatch5} +\begin{paste}{ParametricCurveGraphicsPageFull5}{ParametricCurveGraphicsPageEmpty5} +\pastebutton{ParametricCurveGraphicsPageFull5}{\hidepaste} +\tab{5}\spadgraph{draw(curve(f,g), 0..\%pi)\free{f g }} +\center{\unixcommand{\inputimage{\env{AXIOM}/doc/viewports/parametriccurvegraphicspage5.view/image}}{viewalone\space{1} \env{AXIOM}/doc/viewports/parametriccurvegraphicspage5}} +\end{paste}\end{patch} + +\begin{patch}{ParametricCurveGraphicsPageEmpty5} +\begin{paste}{ParametricCurveGraphicsPageEmpty5}{ParametricCurveGraphicsPagePatch5} +\pastebutton{ParametricCurveGraphicsPageEmpty5}{\showpaste} +\tab{5}\spadgraph{draw(curve(f,g), 0..\%pi)\free{f g }} +\end{paste}\end{patch} + +\begin{patch}{ParametricCurveGraphicsPagePatch6} +\begin{paste}{ParametricCurveGraphicsPageFull6}{ParametricCurveGraphicsPageEmpty6} +\pastebutton{ParametricCurveGraphicsPageFull6}{\hidepaste} +\tab{5}\spadgraph{draw(curve(f,g) ,\%pi..2*\%pi)\free{f g }} +\center{\unixcommand{\inputimage{\env{AXIOM}/doc/viewports/parametriccurvegraphicspage6.view/image}}{viewalone\space{1} \env{AXIOM}/doc/viewports/parametriccurvegraphicspage6}} +\end{paste}\end{patch} + +\begin{patch}{ParametricCurveGraphicsPageEmpty6} +\begin{paste}{ParametricCurveGraphicsPageEmpty6}{ParametricCurveGraphicsPagePatch6} +\pastebutton{ParametricCurveGraphicsPageEmpty6}{\showpaste} +\tab{5}\spadgraph{draw(curve(f,g) ,\%pi..2*\%pi)\free{f g }} +\end{paste}\end{patch} + +\begin{patch}{ParametricCurveGraphicsPagePatch7} +\begin{paste}{ParametricCurveGraphicsPageFull7}{ParametricCurveGraphicsPageEmpty7} +\pastebutton{ParametricCurveGraphicsPageFull7}{\hidepaste} +\tab{5}\spadgraph{draw(curve(f,g), -4*\%pi..4*\%pi)\free{f g }} +\center{\unixcommand{\inputimage{\env{AXIOM}/doc/viewports/parametriccurvegraphicspage7.view/image}}{viewalone\space{1} \env{AXIOM}/doc/viewports/parametriccurvegraphicspage7}} +\end{paste}\end{patch} + +\begin{patch}{ParametricCurveGraphicsPageEmpty7} +\begin{paste}{ParametricCurveGraphicsPageEmpty7}{ParametricCurveGraphicsPagePatch7} +\pastebutton{ParametricCurveGraphicsPageEmpty7}{\showpaste} +\tab{5}\spadgraph{draw(curve(f,g), -4*\%pi..4*\%pi)\free{f g }} +\end{paste}\end{patch} @ \pagehead{PolarGraphicsPage}{graphics.ht}{Polar Coordinates} @@ -10511,7 +26496,75 @@ same curve as theta varies over several intervals. For information on plotting graphs in other coordinate systems see the pages for the \spadtype{CoordinateSystems} domain. \endscroll -\autobuttons \end{page} +\autobuttons +\end{page} + +\begin{patch}{PolarGraphicsPagePatch1} +\begin{paste}{PolarGraphicsPageFull1}{PolarGraphicsPageEmpty1} +\pastebutton{PolarGraphicsPageFull1}{\hidepaste} +\tab{5}\spadgraph{draw(1,t = 0..2*\%pi,coordinates == polar, title == "The Unit Circle")} +\center{\unixcommand{\inputimage{\env{AXIOM}/doc/viewports/polargraphicspage1.view/image}}{viewalone\space{1} \env{AXIOM}/doc/viewports/polargraphicspage1}} +\end{paste}\end{patch} + +\begin{patch}{PolarGraphicsPageEmpty1} +\begin{paste}{PolarGraphicsPageEmpty1}{PolarGraphicsPagePatch1} +\pastebutton{PolarGraphicsPageEmpty1}{\showpaste} +\tab{5}\spadgraph{draw(1,t = 0..2*\%pi,coordinates == polar, title == "The Unit Circle")} +\end{paste}\end{patch} + +\begin{patch}{PolarGraphicsPagePatch2} +\begin{paste}{PolarGraphicsPageFull2}{PolarGraphicsPageEmpty2} +\pastebutton{PolarGraphicsPageFull2}{\hidepaste} +\tab{5}\spadgraph{draw(sin(17*t), t = 0..2*\%pi, coordinates == polar, title == "A Petal Curve")} +\center{\unixcommand{\inputimage{\env{AXIOM}/doc/viewports/polargraphicspage2.view/image}}{viewalone\space{1} \env{AXIOM}/doc/viewports/polargraphicspage2}} +\end{paste}\end{patch} + +\begin{patch}{PolarGraphicsPageEmpty2} +\begin{paste}{PolarGraphicsPageEmpty2}{PolarGraphicsPagePatch2} +\pastebutton{PolarGraphicsPageEmpty2}{\showpaste} +\tab{5}\spadgraph{draw(sin(17*t), t = 0..2*\%pi, coordinates == polar, title == "A Petal Curve")} +\end{paste}\end{patch} + +\begin{patch}{PolarGraphicsPagePatch3} +\begin{paste}{PolarGraphicsPageFull3}{PolarGraphicsPageEmpty3} +\pastebutton{PolarGraphicsPageFull3}{\hidepaste} +\tab{5}\spadcommand{f(t) == cos(4*t/7)\bound{f }} +\indentrel{3}\begin{verbatim} + Type: Void +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{PolarGraphicsPageEmpty3} +\begin{paste}{PolarGraphicsPageEmpty3}{PolarGraphicsPagePatch3} +\pastebutton{PolarGraphicsPageEmpty3}{\showpaste} +\tab{5}\spadcommand{f(t) == cos(4*t/7)\bound{f }} +\end{paste}\end{patch} + +\begin{patch}{PolarGraphicsPagePatch4} +\begin{paste}{PolarGraphicsPageFull4}{PolarGraphicsPageEmpty4} +\pastebutton{PolarGraphicsPageFull4}{\hidepaste} +\tab{5}\spadgraph{draw(f, 0..2*\%pi, coordinates == polar)\free{f }} +\center{\unixcommand{\inputimage{\env{AXIOM}/doc/viewports/polargraphicspage4.view/image}}{viewalone\space{1} \env{AXIOM}/doc/viewports/polargraphicspage4}} +\end{paste}\end{patch} + +\begin{patch}{PolarGraphicsPageEmpty4} +\begin{paste}{PolarGraphicsPageEmpty4}{PolarGraphicsPagePatch4} +\pastebutton{PolarGraphicsPageEmpty4}{\showpaste} +\tab{5}\spadgraph{draw(f, 0..2*\%pi, coordinates == polar)\free{f }} +\end{paste}\end{patch} + +\begin{patch}{PolarGraphicsPagePatch5} +\begin{paste}{PolarGraphicsPageFull5}{PolarGraphicsPageEmpty5} +\pastebutton{PolarGraphicsPageFull5}{\hidepaste} +\tab{5}\spadgraph{draw(f, 0..14*\%pi, coordinates == polar)\free{f }} +\center{\unixcommand{\inputimage{\env{AXIOM}/doc/viewports/polargraphicspage5.view/image}}{viewalone\space{1} \env{AXIOM}/doc/viewports/polargraphicspage5}} +\end{paste}\end{patch} + +\begin{patch}{PolarGraphicsPageEmpty5} +\begin{paste}{PolarGraphicsPageEmpty5}{PolarGraphicsPagePatch5} +\pastebutton{PolarGraphicsPageEmpty5}{\showpaste} +\tab{5}\spadgraph{draw(f, 0..14*\%pi, coordinates == polar)\free{f }} +\end{paste}\end{patch} @ \pagehead{ImplicitCurveGraphicsPage}{graphics.ht}{Implicit Curves} @@ -10537,7 +26590,39 @@ title == "Cartesian Ovals") \free{p}} {\em A range must be declared for each variable specified in the algebraic curve equation}. \endscroll -\autobuttons \end{page} +\autobuttons +\end{page} + +\begin{patch}{ImplicitCurveGraphicsPagePatch1} +\begin{paste}{ImplicitCurveGraphicsPageFull1}{ImplicitCurveGraphicsPageEmpty1} +\pastebutton{ImplicitCurveGraphicsPageFull1}{\hidepaste} +\tab{5}\spadcommand{p := ((x**2 + y**2 + 1) - 8*x)**2 - (8*(x**2 + y**2 + 1) - 4*x - 1)\bound{p }} +\indentrel{3}\begin{verbatim} + (1) + 4 2 2 4 3 2 + y + (2x - 16x - 6)y + x - 16x + 58x - 12x - 6 + Type: Polynomial Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ImplicitCurveGraphicsPageEmpty1} +\begin{paste}{ImplicitCurveGraphicsPageEmpty1}{ImplicitCurveGraphicsPagePatch1} +\pastebutton{ImplicitCurveGraphicsPageEmpty1}{\showpaste} +\tab{5}\spadcommand{p := ((x**2 + y**2 + 1) - 8*x)**2 - (8*(x**2 + y**2 + 1) - 4*x - 1)\bound{p }} +\end{paste}\end{patch} + +\begin{patch}{ImplicitCurveGraphicsPagePatch2} +\begin{paste}{ImplicitCurveGraphicsPageFull2}{ImplicitCurveGraphicsPageEmpty2} +\pastebutton{ImplicitCurveGraphicsPageFull2}{\hidepaste} +\tab{5}\spadgraph{draw(p = 0, x, y, range == [-1..11, -7..7], title == "Cartesian Ovals")\free{p }} +\center{\unixcommand{\inputimage{\env{AXIOM}/doc/viewports/implicitcurvegraphicspage2.view/image}}{viewalone\space{1} \env{AXIOM}/doc/viewports/implicitcurvegraphicspage2}} +\end{paste}\end{patch} + +\begin{patch}{ImplicitCurveGraphicsPageEmpty2} +\begin{paste}{ImplicitCurveGraphicsPageEmpty2}{ImplicitCurveGraphicsPagePatch2} +\pastebutton{ImplicitCurveGraphicsPageEmpty2}{\showpaste} +\tab{5}\spadgraph{draw(p = 0, x, y, range == [-1..11, -7..7], title == "Cartesian Ovals")\free{p }} +\end{paste}\end{patch} @ \pagehead{ListPointsGraphicsPage}{graphics.ht}{Lists of Points} @@ -10623,7 +26708,419 @@ The \spadfun{makeViewport2D} command takes a list of options as a parameter. In this example the string "Lines" is designated as the viewport's title. \endscroll -\autobuttons \end{page} +\autobuttons +\end{page} + +\begin{patch}{ListPointsGraphicsPagePatch1} +\begin{paste}{ListPointsGraphicsPageFull1}{ListPointsGraphicsPageEmpty1} +\pastebutton{ListPointsGraphicsPageFull1}{\hidepaste} +\tab{5}\spadcommand{p1 := point [1::SF,1::SF]$(Point SF)\bound{p1 }} +\indentrel{3}\begin{verbatim} + (1) [1.0,1.0] + Type: Point DoubleFloat +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ListPointsGraphicsPageEmpty1} +\begin{paste}{ListPointsGraphicsPageEmpty1}{ListPointsGraphicsPagePatch1} +\pastebutton{ListPointsGraphicsPageEmpty1}{\showpaste} +\tab{5}\spadcommand{p1 := point [1::SF,1::SF]$(Point SF)\bound{p1 }} +\end{paste}\end{patch} + +\begin{patch}{ListPointsGraphicsPagePatch2} +\begin{paste}{ListPointsGraphicsPageFull2}{ListPointsGraphicsPageEmpty2} +\pastebutton{ListPointsGraphicsPageFull2}{\hidepaste} +\tab{5}\spadcommand{p2 := point [0::SF,1::SF]$(Point SF)\bound{p2 }} +\indentrel{3}\begin{verbatim} + (2) [0.0,1.0] + Type: Point DoubleFloat +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ListPointsGraphicsPageEmpty2} +\begin{paste}{ListPointsGraphicsPageEmpty2}{ListPointsGraphicsPagePatch2} +\pastebutton{ListPointsGraphicsPageEmpty2}{\showpaste} +\tab{5}\spadcommand{p2 := point [0::SF,1::SF]$(Point SF)\bound{p2 }} +\end{paste}\end{patch} + +\begin{patch}{ListPointsGraphicsPagePatch3} +\begin{paste}{ListPointsGraphicsPageFull3}{ListPointsGraphicsPageEmpty3} +\pastebutton{ListPointsGraphicsPageFull3}{\hidepaste} +\tab{5}\spadcommand{p3 := point [0::SF,0::SF]$(Point SF)\bound{p3 }} +\indentrel{3}\begin{verbatim} + (3) [0.0,0.0] + Type: Point DoubleFloat +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ListPointsGraphicsPageEmpty3} +\begin{paste}{ListPointsGraphicsPageEmpty3}{ListPointsGraphicsPagePatch3} +\pastebutton{ListPointsGraphicsPageEmpty3}{\showpaste} +\tab{5}\spadcommand{p3 := point [0::SF,0::SF]$(Point SF)\bound{p3 }} +\end{paste}\end{patch} + +\begin{patch}{ListPointsGraphicsPagePatch4} +\begin{paste}{ListPointsGraphicsPageFull4}{ListPointsGraphicsPageEmpty4} +\pastebutton{ListPointsGraphicsPageFull4}{\hidepaste} +\tab{5}\spadcommand{p4 := point [1::SF,0::SF]$(Point SF)\bound{p4 }} +\indentrel{3}\begin{verbatim} + (4) [1.0,0.0] + Type: Point DoubleFloat +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ListPointsGraphicsPageEmpty4} +\begin{paste}{ListPointsGraphicsPageEmpty4}{ListPointsGraphicsPagePatch4} +\pastebutton{ListPointsGraphicsPageEmpty4}{\showpaste} +\tab{5}\spadcommand{p4 := point [1::SF,0::SF]$(Point SF)\bound{p4 }} +\end{paste}\end{patch} + +\begin{patch}{ListPointsGraphicsPagePatch5} +\begin{paste}{ListPointsGraphicsPageFull5}{ListPointsGraphicsPageEmpty5} +\pastebutton{ListPointsGraphicsPageFull5}{\hidepaste} +\tab{5}\spadcommand{p5 := point [1::SF,.5::SF]$(Point SF)\bound{p5 }} +\indentrel{3}\begin{verbatim} + (5) [1.0,0.5] + Type: Point DoubleFloat +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ListPointsGraphicsPageEmpty5} +\begin{paste}{ListPointsGraphicsPageEmpty5}{ListPointsGraphicsPagePatch5} +\pastebutton{ListPointsGraphicsPageEmpty5}{\showpaste} +\tab{5}\spadcommand{p5 := point [1::SF,.5::SF]$(Point SF)\bound{p5 }} +\end{paste}\end{patch} + +\begin{patch}{ListPointsGraphicsPagePatch6} +\begin{paste}{ListPointsGraphicsPageFull6}{ListPointsGraphicsPageEmpty6} +\pastebutton{ListPointsGraphicsPageFull6}{\hidepaste} +\tab{5}\spadcommand{p6 := point [.5::SF,0::SF]$(Point SF)\bound{p6 }} +\indentrel{3}\begin{verbatim} + (6) [0.5,0.0] + Type: Point DoubleFloat +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ListPointsGraphicsPageEmpty6} +\begin{paste}{ListPointsGraphicsPageEmpty6}{ListPointsGraphicsPagePatch6} +\pastebutton{ListPointsGraphicsPageEmpty6}{\showpaste} +\tab{5}\spadcommand{p6 := point [.5::SF,0::SF]$(Point SF)\bound{p6 }} +\end{paste}\end{patch} + +\begin{patch}{ListPointsGraphicsPagePatch7} +\begin{paste}{ListPointsGraphicsPageFull7}{ListPointsGraphicsPageEmpty7} +\pastebutton{ListPointsGraphicsPageFull7}{\hidepaste} +\tab{5}\spadcommand{p7 := point [0::SF,0.5::SF]$(Point SF)\bound{p7 }} +\indentrel{3}\begin{verbatim} + (7) [0.0,0.5] + Type: Point DoubleFloat +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ListPointsGraphicsPageEmpty7} +\begin{paste}{ListPointsGraphicsPageEmpty7}{ListPointsGraphicsPagePatch7} +\pastebutton{ListPointsGraphicsPageEmpty7}{\showpaste} +\tab{5}\spadcommand{p7 := point [0::SF,0.5::SF]$(Point SF)\bound{p7 }} +\end{paste}\end{patch} + +\begin{patch}{ListPointsGraphicsPagePatch8} +\begin{paste}{ListPointsGraphicsPageFull8}{ListPointsGraphicsPageEmpty8} +\pastebutton{ListPointsGraphicsPageFull8}{\hidepaste} +\tab{5}\spadcommand{p8 := point [.5::SF,1::SF]$(Point SF)\bound{p8 }} +\indentrel{3}\begin{verbatim} + (8) [0.5,1.0] + Type: Point DoubleFloat +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ListPointsGraphicsPageEmpty8} +\begin{paste}{ListPointsGraphicsPageEmpty8}{ListPointsGraphicsPagePatch8} +\pastebutton{ListPointsGraphicsPageEmpty8}{\showpaste} +\tab{5}\spadcommand{p8 := point [.5::SF,1::SF]$(Point SF)\bound{p8 }} +\end{paste}\end{patch} + +\begin{patch}{ListPointsGraphicsPagePatch9} +\begin{paste}{ListPointsGraphicsPageFull9}{ListPointsGraphicsPageEmpty9} +\pastebutton{ListPointsGraphicsPageFull9}{\hidepaste} +\tab{5}\spadcommand{p9 := point [.25::SF,.25::SF]$(Point SF)\bound{p9 }} +\indentrel{3}\begin{verbatim} + (9) [0.25,0.25] + Type: Point DoubleFloat +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ListPointsGraphicsPageEmpty9} +\begin{paste}{ListPointsGraphicsPageEmpty9}{ListPointsGraphicsPagePatch9} +\pastebutton{ListPointsGraphicsPageEmpty9}{\showpaste} +\tab{5}\spadcommand{p9 := point [.25::SF,.25::SF]$(Point SF)\bound{p9 }} +\end{paste}\end{patch} + +\begin{patch}{ListPointsGraphicsPagePatch10} +\begin{paste}{ListPointsGraphicsPageFull10}{ListPointsGraphicsPageEmpty10} +\pastebutton{ListPointsGraphicsPageFull10}{\hidepaste} +\tab{5}\spadcommand{p10 := point [.25::SF,.75::SF]$(Point SF)\bound{p10 }} +\indentrel{3}\begin{verbatim} + (10) [0.25,0.75] + Type: Point DoubleFloat +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ListPointsGraphicsPageEmpty10} +\begin{paste}{ListPointsGraphicsPageEmpty10}{ListPointsGraphicsPagePatch10} +\pastebutton{ListPointsGraphicsPageEmpty10}{\showpaste} +\tab{5}\spadcommand{p10 := point [.25::SF,.75::SF]$(Point SF)\bound{p10 }} +\end{paste}\end{patch} + +\begin{patch}{ListPointsGraphicsPagePatch11} +\begin{paste}{ListPointsGraphicsPageFull11}{ListPointsGraphicsPageEmpty11} +\pastebutton{ListPointsGraphicsPageFull11}{\hidepaste} +\tab{5}\spadcommand{p11 := point [.75::SF,.75::SF]$(Point SF)\bound{p11 }} +\indentrel{3}\begin{verbatim} + (11) [0.75,0.75] + Type: Point DoubleFloat +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ListPointsGraphicsPageEmpty11} +\begin{paste}{ListPointsGraphicsPageEmpty11}{ListPointsGraphicsPagePatch11} +\pastebutton{ListPointsGraphicsPageEmpty11}{\showpaste} +\tab{5}\spadcommand{p11 := point [.75::SF,.75::SF]$(Point SF)\bound{p11 }} +\end{paste}\end{patch} + +\begin{patch}{ListPointsGraphicsPagePatch12} +\begin{paste}{ListPointsGraphicsPageFull12}{ListPointsGraphicsPageEmpty12} +\pastebutton{ListPointsGraphicsPageFull12}{\hidepaste} +\tab{5}\spadcommand{p12 := point [.75::SF,.25::SF]$(Point SF)\bound{p12 }} +\indentrel{3}\begin{verbatim} + (12) [0.75,0.25] + Type: Point DoubleFloat +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ListPointsGraphicsPageEmpty12} +\begin{paste}{ListPointsGraphicsPageEmpty12}{ListPointsGraphicsPagePatch12} +\pastebutton{ListPointsGraphicsPageEmpty12}{\showpaste} +\tab{5}\spadcommand{p12 := point [.75::SF,.25::SF]$(Point SF)\bound{p12 }} +\end{paste}\end{patch} + +\begin{patch}{ListPointsGraphicsPagePatch13} +\begin{paste}{ListPointsGraphicsPageFull13}{ListPointsGraphicsPageEmpty13} +\pastebutton{ListPointsGraphicsPageFull13}{\hidepaste} +\tab{5}\spadcommand{llp := [[p1,p2],[p2,p3],[p3,p4],[p4,p1],[p5,p6],[p6,p7],[p7,p8],[p8,p5],[p9,p10],[p10,p11],[p11,p12],[p12,p9]]\bound{llp }\free{p1 p2 p3 p4 p5 p6 p7 p8 p9 p10 p11 p12 }} +\indentrel{3}\begin{verbatim} + (13) + [[[1.0,1.0],[0.0,1.0]], [[0.0,1.0],[0.0,0.0]], + [[0.0,0.0],[1.0,0.0]], [[1.0,0.0],[1.0,1.0]], + [[1.0,0.5],[0.5,0.0]], [[0.5,0.0],[0.0,0.5]], + [[0.0,0.5],[0.5,1.0]], [[0.5,1.0],[1.0,0.5]], + [[0.25,0.25],[0.25,0.75]], [[0.25,0.75],[0.75,0.75]], + [[0.75,0.75],[0.75,0.25]], [[0.75,0.25],[0.25,0.25]]] + Type: List List Point DoubleFloat +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ListPointsGraphicsPageEmpty13} +\begin{paste}{ListPointsGraphicsPageEmpty13}{ListPointsGraphicsPagePatch13} +\pastebutton{ListPointsGraphicsPageEmpty13}{\showpaste} +\tab{5}\spadcommand{llp := [[p1,p2],[p2,p3],[p3,p4],[p4,p1],[p5,p6],[p6,p7],[p7,p8],[p8,p5],[p9,p10],[p10,p11],[p11,p12],[p12,p9]]\bound{llp }\free{p1 p2 p3 p4 p5 p6 p7 p8 p9 p10 p11 p12 }} +\end{paste}\end{patch} + +\begin{patch}{ListPointsGraphicsPagePatch14} +\begin{paste}{ListPointsGraphicsPageFull14}{ListPointsGraphicsPageEmpty14} +\pastebutton{ListPointsGraphicsPageFull14}{\hidepaste} +\tab{5}\spadcommand{size1 := 6::PositiveInteger\bound{size1 }} +\indentrel{3}\begin{verbatim} + (14) 6 + Type: PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ListPointsGraphicsPageEmpty14} +\begin{paste}{ListPointsGraphicsPageEmpty14}{ListPointsGraphicsPagePatch14} +\pastebutton{ListPointsGraphicsPageEmpty14}{\showpaste} +\tab{5}\spadcommand{size1 := 6::PositiveInteger\bound{size1 }} +\end{paste}\end{patch} + +\begin{patch}{ListPointsGraphicsPagePatch15} +\begin{paste}{ListPointsGraphicsPageFull15}{ListPointsGraphicsPageEmpty15} +\pastebutton{ListPointsGraphicsPageFull15}{\hidepaste} +\tab{5}\spadcommand{size2 := 8::PositiveInteger\bound{size2 }} +\indentrel{3}\begin{verbatim} + (15) 8 + Type: PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ListPointsGraphicsPageEmpty15} +\begin{paste}{ListPointsGraphicsPageEmpty15}{ListPointsGraphicsPagePatch15} +\pastebutton{ListPointsGraphicsPageEmpty15}{\showpaste} +\tab{5}\spadcommand{size2 := 8::PositiveInteger\bound{size2 }} +\end{paste}\end{patch} + +\begin{patch}{ListPointsGraphicsPagePatch16} +\begin{paste}{ListPointsGraphicsPageFull16}{ListPointsGraphicsPageEmpty16} +\pastebutton{ListPointsGraphicsPageFull16}{\hidepaste} +\tab{5}\spadcommand{size3 := 10::PositiveInteger\bound{size3 }} +\indentrel{3}\begin{verbatim} + (16) 10 + Type: PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ListPointsGraphicsPageEmpty16} +\begin{paste}{ListPointsGraphicsPageEmpty16}{ListPointsGraphicsPagePatch16} +\pastebutton{ListPointsGraphicsPageEmpty16}{\showpaste} +\tab{5}\spadcommand{size3 := 10::PositiveInteger\bound{size3 }} +\end{paste}\end{patch} + +\begin{patch}{ListPointsGraphicsPagePatch17} +\begin{paste}{ListPointsGraphicsPageFull17}{ListPointsGraphicsPageEmpty17} +\pastebutton{ListPointsGraphicsPageFull17}{\hidepaste} +\tab{5}\spadcommand{lsize := [size1, size1, size1, size1, size2, size2, size2, size2, size3, size3, size3, size3]\bound{lsize }\free{size1 size2 size3 }} +\indentrel{3}\begin{verbatim} + (17) [6,6,6,6,8,8,8,8,10,10,10,10] + Type: List PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ListPointsGraphicsPageEmpty17} +\begin{paste}{ListPointsGraphicsPageEmpty17}{ListPointsGraphicsPagePatch17} +\pastebutton{ListPointsGraphicsPageEmpty17}{\showpaste} +\tab{5}\spadcommand{lsize := [size1, size1, size1, size1, size2, size2, size2, size2, size3, size3, size3, size3]\bound{lsize }\free{size1 size2 size3 }} +\end{paste}\end{patch} + +\begin{patch}{ListPointsGraphicsPagePatch18} +\begin{paste}{ListPointsGraphicsPageFull18}{ListPointsGraphicsPageEmpty18} +\pastebutton{ListPointsGraphicsPageFull18}{\hidepaste} +\tab{5}\spadcommand{pc1 := pastel red()\bound{pc1 }} +\indentrel{3}\begin{verbatim} + (18) [Hue: 1 Weight: 1.0] from the Pastel palette + Type: Palette +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ListPointsGraphicsPageEmpty18} +\begin{paste}{ListPointsGraphicsPageEmpty18}{ListPointsGraphicsPagePatch18} +\pastebutton{ListPointsGraphicsPageEmpty18}{\showpaste} +\tab{5}\spadcommand{pc1 := pastel red()\bound{pc1 }} +\end{paste}\end{patch} + +\begin{patch}{ListPointsGraphicsPagePatch19} +\begin{paste}{ListPointsGraphicsPageFull19}{ListPointsGraphicsPageEmpty19} +\pastebutton{ListPointsGraphicsPageFull19}{\hidepaste} +\tab{5}\spadcommand{pc2 := dim green()\bound{pc2 }} +\indentrel{3}\begin{verbatim} + (19) [Hue: 14 Weight: 1.0] from the Dim palette + Type: Palette +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ListPointsGraphicsPageEmpty19} +\begin{paste}{ListPointsGraphicsPageEmpty19}{ListPointsGraphicsPagePatch19} +\pastebutton{ListPointsGraphicsPageEmpty19}{\showpaste} +\tab{5}\spadcommand{pc2 := dim green()\bound{pc2 }} +\end{paste}\end{patch} + +\begin{patch}{ListPointsGraphicsPagePatch20} +\begin{paste}{ListPointsGraphicsPageFull20}{ListPointsGraphicsPageEmpty20} +\pastebutton{ListPointsGraphicsPageFull20}{\hidepaste} +\tab{5}\spadcommand{pc3 := pastel yellow()\bound{pc3 }} +\indentrel{3}\begin{verbatim} + (20) [Hue: 11 Weight: 1.0] from the Pastel palette + Type: Palette +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ListPointsGraphicsPageEmpty20} +\begin{paste}{ListPointsGraphicsPageEmpty20}{ListPointsGraphicsPagePatch20} +\pastebutton{ListPointsGraphicsPageEmpty20}{\showpaste} +\tab{5}\spadcommand{pc3 := pastel yellow()\bound{pc3 }} +\end{paste}\end{patch} + +\begin{patch}{ListPointsGraphicsPagePatch21} +\begin{paste}{ListPointsGraphicsPageFull21}{ListPointsGraphicsPageEmpty21} +\pastebutton{ListPointsGraphicsPageFull21}{\hidepaste} +\tab{5}\spadcommand{lpc := [pc1, pc1, pc1, pc1, pc2, pc2, pc2, pc2, pc3, pc3, pc3, pc3]\bound{lpc }\free{pc1 pc2 pc3 }} +\indentrel{3}\begin{verbatim} + (21) + [[Hue: 1 Weight: 1.0] from the Pastel palette, + [Hue: 1 Weight: 1.0] from the Pastel palette, + [Hue: 1 Weight: 1.0] from the Pastel palette, + [Hue: 1 Weight: 1.0] from the Pastel palette, + [Hue: 14 Weight: 1.0] from the Dim palette, + [Hue: 14 Weight: 1.0] from the Dim palette, + [Hue: 14 Weight: 1.0] from the Dim palette, + [Hue: 14 Weight: 1.0] from the Dim palette, + [Hue: 11 Weight: 1.0] from the Pastel palette, + [Hue: 11 Weight: 1.0] from the Pastel palette, + [Hue: 11 Weight: 1.0] from the Pastel palette, + [Hue: 11 Weight: 1.0] from the Pastel palette] + Type: List Palette +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ListPointsGraphicsPageEmpty21} +\begin{paste}{ListPointsGraphicsPageEmpty21}{ListPointsGraphicsPagePatch21} +\pastebutton{ListPointsGraphicsPageEmpty21}{\showpaste} +\tab{5}\spadcommand{lpc := [pc1, pc1, pc1, pc1, pc2, pc2, pc2, pc2, pc3, pc3, pc3, pc3]\bound{lpc }\free{pc1 pc2 pc3 }} +\end{paste}\end{patch} + +\begin{patch}{ListPointsGraphicsPagePatch22} +\begin{paste}{ListPointsGraphicsPageFull22}{ListPointsGraphicsPageEmpty22} +\pastebutton{ListPointsGraphicsPageFull22}{\hidepaste} +\tab{5}\spadcommand{lc := [pastel blue(), light yellow(), dim green(), bright red(), light green(), dim yellow(), bright blue(), dark red(), pastel red(), light blue(), dim green(), light yellow()]\bound{lc }} +\indentrel{3}\begin{verbatim} + (22) + [[Hue: 22 Weight: 1.0] from the Pastel palette, + [Hue: 11 Weight: 1.0] from the Light palette, + [Hue: 14 Weight: 1.0] from the Dim palette, + [Hue: 1 Weight: 1.0] from the Bright palette, + [Hue: 14 Weight: 1.0] from the Light palette, + [Hue: 11 Weight: 1.0] from the Dim palette, + [Hue: 22 Weight: 1.0] from the Bright palette, + [Hue: 1 Weight: 1.0] from the Dark palette, + [Hue: 1 Weight: 1.0] from the Pastel palette, + [Hue: 22 Weight: 1.0] from the Light palette, + [Hue: 14 Weight: 1.0] from the Dim palette, + [Hue: 11 Weight: 1.0] from the Light palette] + Type: List Palette +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ListPointsGraphicsPageEmpty22} +\begin{paste}{ListPointsGraphicsPageEmpty22}{ListPointsGraphicsPagePatch22} +\pastebutton{ListPointsGraphicsPageEmpty22}{\showpaste} +\tab{5}\spadcommand{lc := [pastel blue(), light yellow(), dim green(), bright red(), light green(), dim yellow(), bright blue(), dark red(), pastel red(), light blue(), dim green(), light yellow()]\bound{lc }} +\end{paste}\end{patch} + +\begin{patch}{ListPointsGraphicsPagePatch23} +\begin{paste}{ListPointsGraphicsPageFull23}{ListPointsGraphicsPageEmpty23} +\pastebutton{ListPointsGraphicsPageFull23}{\hidepaste} +\tab{5}\spadcommand{g := makeGraphImage(llp,lpc,lc,lsize)$GRIMAGE\bound{g }\free{llp lpc lc lsize }} +\indentrel{3}\begin{verbatim} + (23) Graph with 12 point lists + Type: GraphImage +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ListPointsGraphicsPageEmpty23} +\begin{paste}{ListPointsGraphicsPageEmpty23}{ListPointsGraphicsPagePatch23} +\pastebutton{ListPointsGraphicsPageEmpty23}{\showpaste} +\tab{5}\spadcommand{g := makeGraphImage(llp,lpc,lc,lsize)$GRIMAGE\bound{g }\free{llp lpc lc lsize }} +\end{paste}\end{patch} + +\begin{patch}{ListPointsGraphicsPagePatch24} +\begin{paste}{ListPointsGraphicsPageFull24}{ListPointsGraphicsPageEmpty24} +\pastebutton{ListPointsGraphicsPageFull24}{\hidepaste} +\tab{5}\spadgraph{makeViewport2D(g,[title("Lines")])$VIEW2D\free{g }} +\center{\unixcommand{\inputimage{\env{AXIOM}/doc/viewports/listpointsgraphicspage24.view/image}}{viewalone\space{1} \env{AXIOM}/doc/viewports/listpointsgraphicspage24}} +\end{paste}\end{patch} + +\begin{patch}{ListPointsGraphicsPageEmpty24} +\begin{paste}{ListPointsGraphicsPageEmpty24}{ListPointsGraphicsPagePatch24} +\pastebutton{ListPointsGraphicsPageEmpty24}{\showpaste} +\tab{5}\spadgraph{makeViewport2D(g,[title("Lines")])$VIEW2D\free{g }} +\end{paste}\end{patch} @ \pagehead{ViewportPage}{graphics.ht}{Stand-alone Viewport} @@ -10709,7 +27206,37 @@ All these macros really do is include some path that indicates where Axiom stores the viewports. \newline \endscroll -\autobuttons \end{page} +\autobuttons +\end{page} + +\begin{patch}{ViewportPagePatch1} +\begin{paste}{ViewportPageFull1}{ViewportPageEmpty1} +\pastebutton{ViewportPageFull1}{\hidepaste} +\tab{5}\spadgraph{v := draw(x*x-y*y,x=-1..1,y=-1..1)\bound{v }} +\center{\unixcommand{\inputimage{\env{AXIOM}/doc/viewports/viewportpage1.view/image}}{viewalone\space{1} \env{AXIOM}/doc/viewports/viewportpage1}} +\end{paste}\end{patch} + +\begin{patch}{ViewportPageEmpty1} +\begin{paste}{ViewportPageEmpty1}{ViewportPagePatch1} +\pastebutton{ViewportPageEmpty1}{\showpaste} +\tab{5}\spadgraph{v := draw(x*x-y*y,x=-1..1,y=-1..1)\bound{v }} +\end{paste}\end{patch} + +\begin{patch}{ViewportPagePatch2} +\begin{paste}{ViewportPageFull2}{ViewportPageEmpty2} +\pastebutton{ViewportPageFull2}{\hidepaste} +\tab{5}\spadcommand{write(v,"saddle","pixmap")\free{v }} +\indentrel{3}\begin{verbatim} + (2) "NIL" + Type: String +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ViewportPageEmpty2} +\begin{paste}{ViewportPageEmpty2}{ViewportPagePatch2} +\pastebutton{ViewportPageEmpty2}{\showpaste} +\tab{5}\spadcommand{write(v,"saddle","pixmap")\free{v }} +\end{paste}\end{patch} @ \section{grpthry.ht} @@ -10837,7 +27364,874 @@ And here again is the irreducible, but not absolutely irreducible representations of \texht{$A_6$}{A6} over GF 2 \spadpaste{dA6d16 \free{dA6d16}} \endscroll -\autobuttons \end{page} +\autobuttons +\end{page} + +\begin{patch}{RepA6PagePatch1} +\begin{paste}{RepA6PageFull1}{RepA6PageEmpty1} +\pastebutton{RepA6PageFull1}{\hidepaste} +\tab{5}\spadcommand{genA6 : LIST PERM INT := [cycle [1,2,3],cycle [2,3,4,5,6]]\bound{genA6 }} +\indentrel{3}\begin{verbatim} + (1) [(1 2 3),(2 3 4 5 6)] + Type: List Permutation Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{RepA6PageEmpty1} +\begin{paste}{RepA6PageEmpty1}{RepA6PagePatch1} +\pastebutton{RepA6PageEmpty1}{\showpaste} +\tab{5}\spadcommand{genA6 : LIST PERM INT := [cycle [1,2,3],cycle [2,3,4,5,6]]\bound{genA6 }} +\end{paste}\end{patch} + +\begin{patch}{RepA6PagePatch2} +\begin{paste}{RepA6PageFull2}{RepA6PageEmpty2} +\pastebutton{RepA6PageFull2}{\hidepaste} +\tab{5}\spadcommand{pRA6 := permutationRepresentation (genA6, 6)\bound{pRA6 }\free{genA6 }} +\indentrel{3}\begin{verbatim} + Ú0 0 1 0 0 0¿ Ú1 0 0 0 0 0¿ + ³ ³ ³ ³ + ³1 0 0 0 0 0³ ³0 0 0 0 0 1³ + ³ ³ ³ ³ + ³0 1 0 0 0 0³ ³0 1 0 0 0 0³ + (2) [³ ³,³ ³] + ³0 0 0 1 0 0³ ³0 0 1 0 0 0³ + ³ ³ ³ ³ + ³0 0 0 0 1 0³ ³0 0 0 1 0 0³ + ³ ³ ³ ³ + À0 0 0 0 0 1Ù À0 0 0 0 1 0Ù + Type: List Matrix Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{RepA6PageEmpty2} +\begin{paste}{RepA6PageEmpty2}{RepA6PagePatch2} +\pastebutton{RepA6PageEmpty2}{\showpaste} +\tab{5}\spadcommand{pRA6 := permutationRepresentation (genA6, 6)\bound{pRA6 }\free{genA6 }} +\end{paste}\end{patch} + +\begin{patch}{RepA6PagePatch3} +\begin{paste}{RepA6PageFull3}{RepA6PageEmpty3} +\pastebutton{RepA6PageFull3}{\hidepaste} +\tab{5}\spadcommand{sp0 := meatAxe (pRA6::(LIST MATRIX PF 2))\free{pRA6 }\bound{sp0 }} +\indentrel{3}\begin{verbatim} + Fingerprint element in generated algebra is singular + A proper cyclic submodule is found. + Transition matrix computed + The inverse of the transition matrix computed + Now transform the matrices + Ú0 0 1 0 0¿ Ú1 0 0 0 0¿ + ³ ³ ³ ³ + ³1 0 0 0 0³ ³1 1 1 1 1³ + ³ ³ ³ ³ + (3) [[³0 1 0 0 0³,³0 1 0 0 0³],[[1],[1]]] + ³ ³ ³ ³ + ³0 0 0 1 0³ ³0 0 1 0 0³ + ³ ³ ³ ³ + À0 0 0 0 1Ù À0 0 0 1 0Ù + Type: List List Matrix PrimeField 2 +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{RepA6PageEmpty3} +\begin{paste}{RepA6PageEmpty3}{RepA6PagePatch3} +\pastebutton{RepA6PageEmpty3}{\showpaste} +\tab{5}\spadcommand{sp0 := meatAxe (pRA6::(LIST MATRIX PF 2))\free{pRA6 }\bound{sp0 }} +\end{paste}\end{patch} + +\begin{patch}{RepA6PagePatch4} +\begin{paste}{RepA6PageFull4}{RepA6PageEmpty4} +\pastebutton{RepA6PageFull4}{\hidepaste} +\tab{5}\spadcommand{sp1 := meatAxe sp0.1\bound{sp1 }} +\indentrel{3}\begin{verbatim} + Fingerprint element in generated algebra is singular + The generated cyclic submodule was not proper + The generated cyclic submodule was not proper + The generated cyclic submodule was not proper + We know that all the cyclic submodules generated by a + ll + non-trivial element of the singular matrix under vi + ew are + not proper, hence Norton's irreducibility test can + be done: + A proper cyclic submodule is found. + Transition matrix computed + The inverse of the transition matrix computed + Now transform the matrices + Representation is not irreducible and it will be spli + t: + Ú0 1 0 0¿ Ú0 1 1 1¿ + ³ ³ ³ ³ + ³0 0 1 0³ ³1 1 0 1³ + (4) [[[1],[1]],[³ ³,³ ³]] + ³1 0 0 0³ ³1 1 1 0³ + ³ ³ ³ ³ + À0 0 0 1Ù À1 1 1 1Ù + Type: List List Matrix PrimeField 2 +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{RepA6PageEmpty4} +\begin{paste}{RepA6PageEmpty4}{RepA6PagePatch4} +\pastebutton{RepA6PageEmpty4}{\showpaste} +\tab{5}\spadcommand{sp1 := meatAxe sp0.1\bound{sp1 }} +\end{paste}\end{patch} + +\begin{patch}{RepA6PagePatch5} +\begin{paste}{RepA6PageFull5}{RepA6PageEmpty5} +\pastebutton{RepA6PageFull5}{\hidepaste} +\tab{5}\spadcommand{isAbsolutelyIrreducible? sp1.2} +\indentrel{3}\begin{verbatim} + Random element in generated algebra does + not have a one-dimensional kernel + Random element in generated algebra does + not have a one-dimensional kernel + Random element in generated algebra has + one-dimensional kernel + We know that all the cyclic submodules generated by a + ll + non-trivial element of the singular matrix under vi + ew are + not proper, hence Norton's irreducibility test can + be done: + The generated cyclic submodule was not proper + Representation is absolutely irreducible + (5) true + Type: Boolean +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{RepA6PageEmpty5} +\begin{paste}{RepA6PageEmpty5}{RepA6PagePatch5} +\pastebutton{RepA6PageEmpty5}{\showpaste} +\tab{5}\spadcommand{isAbsolutelyIrreducible? sp1.2} +\end{paste}\end{patch} + +\begin{patch}{RepA6PagePatch6} +\begin{paste}{RepA6PageFull6}{RepA6PageEmpty6} +\pastebutton{RepA6PageFull6}{\hidepaste} +\tab{5}\spadcommand{d2211 := irreducibleRepresentation ([2,2,1,1],genA6)\bound{d2211 }} +\indentrel{3}\begin{verbatim} + (6) + Ú1 0 0 - 1 1 0 0 0 0 ¿ + ³ ³ + ³0 1 0 1 0 1 0 0 0 ³ + ³ ³ + ³0 0 1 0 1 - 1 0 0 0 ³ + ³ ³ + ³0 0 0 - 1 0 0 - 1 0 0 ³ + ³ ³ + [³0 0 0 0 - 1 0 0 - 1 0 ³, + ³ ³ + ³0 0 0 0 0 - 1 0 0 - 1³ + ³ ³ + ³0 0 0 1 0 0 0 0 0 ³ + ³ ³ + ³0 0 0 0 1 0 0 0 0 ³ + ³ ³ + À0 0 0 0 0 1 0 0 0 Ù + Ú 0 0 1 0 0 0 1 0 0¿ + ³ ³ + ³ 0 0 0 0 1 0 - 1 0 0³ + ³ ³ + ³ 0 0 0 0 0 1 1 0 0³ + ³ ³ + ³ 0 0 0 0 0 0 1 1 0³ + ³ ³ + ³ 0 0 0 0 0 0 - 1 0 1³] + ³ ³ + ³ 0 0 0 0 0 0 1 0 0³ + ³ ³ + ³- 1 0 0 0 0 0 - 1 0 0³ + ³ ³ + ³ 0 - 1 0 0 0 0 1 0 0³ + ³ ³ + À 0 0 0 - 1 0 0 - 1 0 0Ù + Type: List Matrix Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{RepA6PageEmpty6} +\begin{paste}{RepA6PageEmpty6}{RepA6PagePatch6} +\pastebutton{RepA6PageEmpty6}{\showpaste} +\tab{5}\spadcommand{d2211 := irreducibleRepresentation ([2,2,1,1],genA6)\bound{d2211 }} +\end{paste}\end{patch} + +\begin{patch}{RepA6PagePatch7} +\begin{paste}{RepA6PageFull7}{RepA6PageEmpty7} +\pastebutton{RepA6PageFull7}{\hidepaste} +\tab{5}\spadcommand{d2211m2 := d2211:: (LIST MATRIX PF 2); sp2 := meatAxe d2211m2\free{d2211 }\bound{sp2 }} +\indentrel{3}\begin{verbatim} + Fingerprint element in generated algebra is singular + A proper cyclic submodule is found. + Transition matrix computed + The inverse of the transition matrix computed + Now transform the matrices + (7) + Ú1 0 1 1¿ Ú0 0 1 0¿ + ³ ³ ³ ³ + ³0 1 0 1³ ³1 1 1 1³ + [[³ ³,³ ³], + ³1 1 0 0³ ³1 0 1 1³ + ³ ³ ³ ³ + À0 1 0 0Ù À0 1 0 1Ù + Ú1 0 0 0 0¿ Ú1 1 1 0 0¿ + ³ ³ ³ ³ + ³0 1 1 1 1³ ³0 0 1 1 1³ + ³ ³ ³ ³ + [³0 1 1 0 0³,³1 0 0 1 0³]] + ³ ³ ³ ³ + ³0 1 0 1 0³ ³0 0 1 0 1³ + ³ ³ ³ ³ + À0 1 1 1 0Ù À1 0 0 1 1Ù + Type: List List Matrix PrimeField 2 +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{RepA6PageEmpty7} +\begin{paste}{RepA6PageEmpty7}{RepA6PagePatch7} +\pastebutton{RepA6PageEmpty7}{\showpaste} +\tab{5}\spadcommand{d2211m2 := d2211:: (LIST MATRIX PF 2); sp2 := meatAxe d2211m2\free{d2211 }\bound{sp2 }} +\end{paste}\end{patch} + +\begin{patch}{RepA6PagePatch8} +\begin{paste}{RepA6PageFull8}{RepA6PageEmpty8} +\pastebutton{RepA6PageFull8}{\hidepaste} +\tab{5}\spadcommand{isAbsolutelyIrreducible? sp2.1} +\indentrel{3}\begin{verbatim} + Random element in generated algebra does + not have a one-dimensional kernel + Random element in generated algebra has + one-dimensional kernel + We know that all the cyclic submodules generated by a + ll + non-trivial element of the singular matrix under vi + ew are + not proper, hence Norton's irreducibility test can + be done: + The generated cyclic submodule was not proper + Representation is absolutely irreducible + (8) true + Type: Boolean +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{RepA6PageEmpty8} +\begin{paste}{RepA6PageEmpty8}{RepA6PagePatch8} +\pastebutton{RepA6PageEmpty8}{\showpaste} +\tab{5}\spadcommand{isAbsolutelyIrreducible? sp2.1} +\end{paste}\end{patch} + +\begin{patch}{RepA6PagePatch9} +\begin{paste}{RepA6PageFull9}{RepA6PageEmpty9} +\pastebutton{RepA6PageFull9}{\hidepaste} +\tab{5}\spadcommand{areEquivalent? (sp1.2, sp2.1)} +\indentrel{3}\begin{verbatim} + Random element in generated algebra does + not have a one-dimensional kernel + Random element in generated algebra does + not have a one-dimensional kernel + Random element in generated algebra has + one-dimensional kernel + There is no isomorphism, as the only possible one + fails to do the necessary base change + + Representations are not equivalent. + (9) [0] + Type: Matrix PrimeField 2 +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{RepA6PageEmpty9} +\begin{paste}{RepA6PageEmpty9}{RepA6PagePatch9} +\pastebutton{RepA6PageEmpty9}{\showpaste} +\tab{5}\spadcommand{areEquivalent? (sp1.2, sp2.1)} +\end{paste}\end{patch} + +\begin{patch}{RepA6PagePatch10} +\begin{paste}{RepA6PageFull10}{RepA6PageEmpty10} +\pastebutton{RepA6PageFull10}{\hidepaste} +\tab{5}\spadcommand{dA6d16 := tensorProduct(sp1.2,sp2.1); meatAxe dA6d16\bound{dA6d16 }} +\indentrel{3}\begin{verbatim} + Fingerprint element in generated algebra is non-singula + r + Fingerprint element in generated algebra is singular + The generated cyclic submodule was not proper + The generated cyclic submodule was not proper + The generated cyclic submodule was not proper + The generated cyclic submodule was not proper + The generated cyclic submodule was not proper + The generated cyclic submodule was not proper + The generated cyclic submodule was not proper + Fingerprint element in generated algebra is non-singula + r + Fingerprint element in generated algebra is singular + The generated cyclic submodule was not proper + The generated cyclic submodule was not proper + The generated cyclic submodule was not proper + The generated cyclic submodule was not proper + The generated cyclic submodule was not proper + The generated cyclic submodule was not proper + The generated cyclic submodule was not proper + Fingerprint element in generated algebra is singular + The generated cyclic submodule was not proper + The generated cyclic submodule was not proper + The generated cyclic submodule was not proper + We know that all the cyclic submodules generated by a + ll + non-trivial element of the singular matrix under vi + ew are + not proper, hence Norton's irreducibility test can + be done: + The generated cyclic submodule was not proper + Representation is irreducible, but we don't know + whether it is absolutely irreducible + (10) + [ + Ú0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0¿ + ³ ³ + ³0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0³ + ³ ³ + ³0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0³ + ³ ³ + ³0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0³ + ³ ³ + ³1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0³ + ³ ³ + ³0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0³ + ³ ³ + ³1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0³ + ³ ³ + ³1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0³ + [³ ³, + ³0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0³ + ³ ³ + ³0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0³ + ³ ³ + ³0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0³ + ³ ³ + ³0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0³ + ³ ³ + ³0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0³ + ³ ³ + ³0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1³ + ³ ³ + ³0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0³ + ³ ³ + À0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0Ù + Ú0 0 0 0 0 1 1 0 0 1 1 0 0 1 1 0¿ + ³ ³ + ³0 0 0 0 0 1 0 1 0 1 0 1 0 1 0 1³ + ³ ³ + ³0 0 0 0 1 1 1 0 1 1 1 0 1 1 1 0³ + ³ ³ + ³0 0 0 0 0 1 1 1 0 1 1 1 0 1 1 1³ + ³ ³ + ³0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0³ + ³ ³ + ³0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1³ + ³ ³ + ³1 1 1 0 1 1 1 0 1 1 1 0 1 1 1 0³ + ³ ³ + ³0 1 1 1 0 1 1 1 0 1 1 1 0 1 1 1³ + ³ ³] + ³0 1 1 0 0 0 0 0 0 1 1 0 0 1 1 0³ + ³ ³ + ³0 1 0 1 0 0 0 0 0 1 0 1 0 1 0 1³ + ³ ³ + ³1 1 1 0 0 0 0 0 1 1 1 0 1 1 1 0³ + ³ ³ + ³0 1 1 1 0 0 0 0 0 1 1 1 0 1 1 1³ + ³ ³ + ³0 1 1 0 0 1 1 0 0 0 0 0 0 1 1 0³ + ³ ³ + ³0 1 0 1 0 1 0 1 0 0 0 0 0 1 0 1³ + ³ ³ + ³1 1 1 0 1 1 1 0 0 0 0 0 1 1 1 0³ + ³ ³ + À0 1 1 1 0 1 1 1 0 0 0 0 0 1 1 1Ù + ] + Type: List List Matrix PrimeField 2 +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{RepA6PageEmpty10} +\begin{paste}{RepA6PageEmpty10}{RepA6PagePatch10} +\pastebutton{RepA6PageEmpty10}{\showpaste} +\tab{5}\spadcommand{dA6d16 := tensorProduct(sp1.2,sp2.1); meatAxe dA6d16\bound{dA6d16 }} +\end{paste}\end{patch} + +\begin{patch}{RepA6PagePatch11} +\begin{paste}{RepA6PageFull11}{RepA6PageEmpty11} +\pastebutton{RepA6PageFull11}{\hidepaste} +\tab{5}\spadcommand{isAbsolutelyIrreducible? dA6d16} +\indentrel{3}\begin{verbatim} + Random element in generated algebra does + not have a one-dimensional kernel + Random element in generated algebra does + not have a one-dimensional kernel + Random element in generated algebra does + not have a one-dimensional kernel + Random element in generated algebra does + not have a one-dimensional kernel + Random element in generated algebra does + not have a one-dimensional kernel + Random element in generated algebra does + not have a one-dimensional kernel + Random element in generated algebra does + not have a one-dimensional kernel + Random element in generated algebra does + not have a one-dimensional kernel + Random element in generated algebra does + not have a one-dimensional kernel + Random element in generated algebra does + not have a one-dimensional kernel + Random element in generated algebra does + not have a one-dimensional kernel + Random element in generated algebra does + not have a one-dimensional kernel + Random element in generated algebra does + not have a one-dimensional kernel + Random element in generated algebra does + not have a one-dimensional kernel + Random element in generated algebra does + not have a one-dimensional kernel + Random element in generated algebra does + not have a one-dimensional kernel + Random element in generated algebra does + not have a one-dimensional kernel + Random element in generated algebra does + not have a one-dimensional kernel + Random element in generated algebra does + not have a one-dimensional kernel + Random element in generated algebra does + not have a one-dimensional kernel + Random element in generated algebra does + not have a one-dimensional kernel + Random element in generated algebra does + not have a one-dimensional kernel + Random element in generated algebra does + not have a one-dimensional kernel + Random element in generated algebra does + not have a one-dimensional kernel + Random element in generated algebra does + not have a one-dimensional kernel + We have not found a one-dimensional kernel so far, + as we do a random search you could try again + (11) false + Type: Boolean +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{RepA6PageEmpty11} +\begin{paste}{RepA6PageEmpty11}{RepA6PagePatch11} +\pastebutton{RepA6PageEmpty11}{\showpaste} +\tab{5}\spadcommand{isAbsolutelyIrreducible? dA6d16} +\end{paste}\end{patch} + +\begin{patch}{RepA6PagePatch12} +\begin{paste}{RepA6PageFull12}{RepA6PageEmpty12} +\pastebutton{RepA6PageFull12}{\hidepaste} +\tab{5}\spadcommand{sp3 := meatAxe (dA6d16 :: (LIST MATRIX FF(2,2)))\bound{sp3 }} +\indentrel{3}\begin{verbatim} + Fingerprint element in generated algebra is non-singula + r + Fingerprint element in generated algebra is singular + The generated cyclic submodule was not proper + The generated cyclic submodule was not proper + The generated cyclic submodule was not proper + The generated cyclic submodule was not proper + The generated cyclic submodule was not proper + The generated cyclic submodule was not proper + The generated cyclic submodule was not proper + Fingerprint element in generated algebra is non-singula + r + Fingerprint element in generated algebra is singular + The generated cyclic submodule was not proper + The generated cyclic submodule was not proper + The generated cyclic submodule was not proper + The generated cyclic submodule was not proper + The generated cyclic submodule was not proper + The generated cyclic submodule was not proper + The generated cyclic submodule was not proper + Fingerprint element in generated algebra is singular + The generated cyclic submodule was not proper + The generated cyclic submodule was not proper + A proper cyclic submodule is found. + Transition matrix computed + The inverse of the transition matrix computed + Now transform the matrices + (12) + [ + [ + [[%A,%A + 1,0,%A,1,%A + 1,0,0], + [0,0,%A,%A + 1,%A,%A,0,0], + [%A,%A + 1,%A,1,%A + 1,0,0,0], + [%A,%A + 1,%A,1,%A,0,0,0], + [%A + 1,1,1,1,0,0,%A + 1,%A], + [0,0,%A + 1,1,0,0,%A,0], [1,0,1,1,0,0,0,0], + [1,1,0,0,0,0,0,0]] + , + + [[1,0,%A,0,1,1,%A,%A + 1], + [1,%A + 1,0,0,0,%A + 1,1,%A + 1], + [%A,1,%A + 1,%A + 1,%A + 1,1,%A,0], + [%A + 1,%A + 1,0,0,1,%A + 1,1,1], + [1,0,%A + 1,0,1,1,%A,%A], + [0,0,%A + 1,%A + 1,%A + 1,1,1,%A], [0,0,1,0,0,1,0,1], + [0,%A,0,%A,1,%A + 1,%A + 1,%A]] + ] + , + + Ú0 1 1 %A + 1 0 0 0 0¿ + ³ ³ + ³1 1 %A + 1 0 0 0 0 0³ + ³ ³ + ³%A 0 0 0 0 0 0 0³ + ³ ³ + ³1 %A 0 0 0 0 0 0³ + [³ ³, + ³%A %A + 1 1 1 1 0 1 1³ + ³ ³ + ³0 0 %A 1 0 1 0 1³ + ³ ³ + ³%A 1 0 1 1 1 0 0³ + ³ ³ + À1 %A %A + 1 %A 0 1 0 0Ù + + [[%A + 1,1,%A,0,0,%A + 1,0,1], + [0,%A,1,1,1,0,%A + 1,%A], + [0,%A + 1,0,%A + 1,%A + 1,1,%A + 1,%A], + [1,%A + 1,1,%A + 1,0,0,%A + 1,1], + [0,%A,0,%A + 1,%A + 1,0,0,%A + 1], + [%A + 1,0,%A + 1,%A,0,%A + 1,0,%A + 1], + [0,1,0,1,%A + 1,0,%A + 1,%A + 1], + [%A,%A,%A,1,%A,%A,1,%A + 1]] + ] + ] + Type: List List Matrix FiniteField(2,2) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{RepA6PageEmpty12} +\begin{paste}{RepA6PageEmpty12}{RepA6PagePatch12} +\pastebutton{RepA6PageEmpty12}{\showpaste} +\tab{5}\spadcommand{sp3 := meatAxe (dA6d16 :: (LIST MATRIX FF(2,2)))\bound{sp3 }} +\end{paste}\end{patch} + +\begin{patch}{RepA6PagePatch13} +\begin{paste}{RepA6PageFull13}{RepA6PageEmpty13} +\pastebutton{RepA6PageFull13}{\hidepaste} +\tab{5}\spadcommand{isAbsolutelyIrreducible? sp3.1} +\indentrel{3}\begin{verbatim} + Random element in generated algebra does + not have a one-dimensional kernel + Random element in generated algebra does + not have a one-dimensional kernel + Random element in generated algebra does + not have a one-dimensional kernel + Random element in generated algebra does + not have a one-dimensional kernel + Random element in generated algebra does + not have a one-dimensional kernel + Random element in generated algebra does + not have a one-dimensional kernel + Random element in generated algebra does + not have a one-dimensional kernel + Random element in generated algebra has + one-dimensional kernel + We know that all the cyclic submodules generated by a + ll + non-trivial element of the singular matrix under vi + ew are + not proper, hence Norton's irreducibility test can + be done: + The generated cyclic submodule was not proper + Representation is absolutely irreducible + (13) true + Type: Boolean +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{RepA6PageEmpty13} +\begin{paste}{RepA6PageEmpty13}{RepA6PagePatch13} +\pastebutton{RepA6PageEmpty13}{\showpaste} +\tab{5}\spadcommand{isAbsolutelyIrreducible? sp3.1} +\end{paste}\end{patch} + +\begin{patch}{RepA6PagePatch14} +\begin{paste}{RepA6PageFull14}{RepA6PageEmpty14} +\pastebutton{RepA6PageFull14}{\hidepaste} +\tab{5}\spadcommand{isAbsolutelyIrreducible? sp3.2} +\indentrel{3}\begin{verbatim} + Random element in generated algebra does + not have a one-dimensional kernel + Random element in generated algebra does + not have a one-dimensional kernel + Random element in generated algebra does + not have a one-dimensional kernel + Random element in generated algebra has + one-dimensional kernel + We know that all the cyclic submodules generated by a + ll + non-trivial element of the singular matrix under vi + ew are + not proper, hence Norton's irreducibility test can + be done: + The generated cyclic submodule was not proper + Representation is absolutely irreducible + (14) true + Type: Boolean +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{RepA6PageEmpty14} +\begin{paste}{RepA6PageEmpty14}{RepA6PagePatch14} +\pastebutton{RepA6PageEmpty14}{\showpaste} +\tab{5}\spadcommand{isAbsolutelyIrreducible? sp3.2} +\end{paste}\end{patch} + +\begin{patch}{RepA6PagePatch15} +\begin{paste}{RepA6PageFull15}{RepA6PageEmpty15} +\pastebutton{RepA6PageFull15}{\hidepaste} +\tab{5}\spadcommand{areEquivalent? (sp3.1,sp3.2)} +\indentrel{3}\begin{verbatim} + Random element in generated algebra does + not have a one-dimensional kernel + Random element in generated algebra does + not have a one-dimensional kernel + Random element in generated algebra does + not have a one-dimensional kernel + Random element in generated algebra does + not have a one-dimensional kernel + Random element in generated algebra has + one-dimensional kernel + There is no isomorphism, as the only possible one + fails to do the necessary base change + + Representations are not equivalent. + (15) [0] + Type: Matrix FiniteField(2,2) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{RepA6PageEmpty15} +\begin{paste}{RepA6PageEmpty15}{RepA6PagePatch15} +\pastebutton{RepA6PageEmpty15}{\showpaste} +\tab{5}\spadcommand{areEquivalent? (sp3.1,sp3.2)} +\end{paste}\end{patch} + +\begin{patch}{RepA6PagePatch16} +\begin{paste}{RepA6PageFull16}{RepA6PageEmpty16} +\pastebutton{RepA6PageFull16}{\hidepaste} +\tab{5}\spadcommand{sp0.2\free{sp0 }} +\indentrel{3}\begin{verbatim} + (16) [[1],[1]] + Type: List Matrix PrimeField 2 +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{RepA6PageEmpty16} +\begin{paste}{RepA6PageEmpty16}{RepA6PagePatch16} +\pastebutton{RepA6PageEmpty16}{\showpaste} +\tab{5}\spadcommand{sp0.2\free{sp0 }} +\end{paste}\end{patch} + +\begin{patch}{RepA6PagePatch17} +\begin{paste}{RepA6PageFull17}{RepA6PageEmpty17} +\pastebutton{RepA6PageFull17}{\hidepaste} +\tab{5}\spadcommand{sp1.2\free{sp1 }} +\indentrel{3}\begin{verbatim} + Ú0 1 0 0¿ Ú0 1 1 1¿ + ³ ³ ³ ³ + ³0 0 1 0³ ³1 1 0 1³ + (17) [³ ³,³ ³] + ³1 0 0 0³ ³1 1 1 0³ + ³ ³ ³ ³ + À0 0 0 1Ù À1 1 1 1Ù + Type: List Matrix PrimeField 2 +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{RepA6PageEmpty17} +\begin{paste}{RepA6PageEmpty17}{RepA6PagePatch17} +\pastebutton{RepA6PageEmpty17}{\showpaste} +\tab{5}\spadcommand{sp1.2\free{sp1 }} +\end{paste}\end{patch} + +\begin{patch}{RepA6PagePatch18} +\begin{paste}{RepA6PageFull18}{RepA6PageEmpty18} +\pastebutton{RepA6PageFull18}{\hidepaste} +\tab{5}\spadcommand{sp2.1\free{sp2 }} +\indentrel{3}\begin{verbatim} + Ú1 0 1 1¿ Ú0 0 1 0¿ + ³ ³ ³ ³ + ³0 1 0 1³ ³1 1 1 1³ + (18) [³ ³,³ ³] + ³1 1 0 0³ ³1 0 1 1³ + ³ ³ ³ ³ + À0 1 0 0Ù À0 1 0 1Ù + Type: List Matrix PrimeField 2 +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{RepA6PageEmpty18} +\begin{paste}{RepA6PageEmpty18}{RepA6PagePatch18} +\pastebutton{RepA6PageEmpty18}{\showpaste} +\tab{5}\spadcommand{sp2.1\free{sp2 }} +\end{paste}\end{patch} + +\begin{patch}{RepA6PagePatch19} +\begin{paste}{RepA6PageFull19}{RepA6PageEmpty19} +\pastebutton{RepA6PageFull19}{\hidepaste} +\tab{5}\spadcommand{sp3.1\free{sp3 }} +\indentrel{3}\begin{verbatim} + (19) + [ + [[%A,%A + 1,0,%A,1,%A + 1,0,0], + [0,0,%A,%A + 1,%A,%A,0,0], + [%A,%A + 1,%A,1,%A + 1,0,0,0], + [%A,%A + 1,%A,1,%A,0,0,0], + [%A + 1,1,1,1,0,0,%A + 1,%A], + [0,0,%A + 1,1,0,0,%A,0], [1,0,1,1,0,0,0,0], + [1,1,0,0,0,0,0,0]] + , + + [[1,0,%A,0,1,1,%A,%A + 1], + [1,%A + 1,0,0,0,%A + 1,1,%A + 1], + [%A,1,%A + 1,%A + 1,%A + 1,1,%A,0], + [%A + 1,%A + 1,0,0,1,%A + 1,1,1], + [1,0,%A + 1,0,1,1,%A,%A], + [0,0,%A + 1,%A + 1,%A + 1,1,1,%A], [0,0,1,0,0,1,0,1], + [0,%A,0,%A,1,%A + 1,%A + 1,%A]] + ] + Type: List Matrix FiniteField(2,2) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{RepA6PageEmpty19} +\begin{paste}{RepA6PageEmpty19}{RepA6PagePatch19} +\pastebutton{RepA6PageEmpty19}{\showpaste} +\tab{5}\spadcommand{sp3.1\free{sp3 }} +\end{paste}\end{patch} + +\begin{patch}{RepA6PagePatch20} +\begin{paste}{RepA6PageFull20}{RepA6PageEmpty20} +\pastebutton{RepA6PageFull20}{\hidepaste} +\tab{5}\spadcommand{sp3.2\free{sp3 }} +\indentrel{3}\begin{verbatim} + (20) + Ú0 1 1 %A + 1 0 0 0 0¿ + ³ ³ + ³1 1 %A + 1 0 0 0 0 0³ + ³ ³ + ³%A 0 0 0 0 0 0 0³ + ³ ³ + ³1 %A 0 0 0 0 0 0³ + [³ ³, + ³%A %A + 1 1 1 1 0 1 1³ + ³ ³ + ³0 0 %A 1 0 1 0 1³ + ³ ³ + ³%A 1 0 1 1 1 0 0³ + ³ ³ + À1 %A %A + 1 %A 0 1 0 0Ù + + [[%A + 1,1,%A,0,0,%A + 1,0,1], + [0,%A,1,1,1,0,%A + 1,%A], + [0,%A + 1,0,%A + 1,%A + 1,1,%A + 1,%A], + [1,%A + 1,1,%A + 1,0,0,%A + 1,1], + [0,%A,0,%A + 1,%A + 1,0,0,%A + 1], + [%A + 1,0,%A + 1,%A,0,%A + 1,0,%A + 1], + [0,1,0,1,%A + 1,0,%A + 1,%A + 1], + [%A,%A,%A,1,%A,%A,1,%A + 1]] + ] + Type: List Matrix FiniteField(2,2) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{RepA6PageEmpty20} +\begin{paste}{RepA6PageEmpty20}{RepA6PagePatch20} +\pastebutton{RepA6PageEmpty20}{\showpaste} +\tab{5}\spadcommand{sp3.2\free{sp3 }} +\end{paste}\end{patch} + +\begin{patch}{RepA6PagePatch21} +\begin{paste}{RepA6PageFull21}{RepA6PageEmpty21} +\pastebutton{RepA6PageFull21}{\hidepaste} +\tab{5}\spadcommand{dA6d16\free{dA6d16 }} +\indentrel{3}\begin{verbatim} + (21) + Ú0 0 0 0 1 0 1 1 0 0 0 0 0 0 0 0¿ + ³ ³ + ³0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0³ + ³ ³ + ³0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0³ + ³ ³ + ³0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0³ + ³ ³ + ³0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 0³ + ³ ³ + ³0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0³ + ³ ³ + ³0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0³ + ³ ³ + ³0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0³ + [³ ³, + ³1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0³ + ³ ³ + ³0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0³ + ³ ³ + ³1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0³ + ³ ³ + ³0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0³ + ³ ³ + ³0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1³ + ³ ³ + ³0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1³ + ³ ³ + ³0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0³ + ³ ³ + À0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0Ù + Ú0 0 0 0 0 0 1 0 0 0 1 0 0 0 1 0¿ + ³ ³ + ³0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1³ + ³ ³ + ³0 0 0 0 1 0 1 1 1 0 1 1 1 0 1 1³ + ³ ³ + ³0 0 0 0 0 1 0 1 0 1 0 1 0 1 0 1³ + ³ ³ + ³0 0 1 0 0 0 1 0 0 0 0 0 0 0 1 0³ + ³ ³ + ³1 1 1 1 1 1 1 1 0 0 0 0 1 1 1 1³ + ³ ³ + ³1 0 1 1 1 0 1 1 0 0 0 0 1 0 1 1³ + ³ ³ + ³0 1 0 1 0 1 0 1 0 0 0 0 0 1 0 1³ + ³ ³] + ³0 0 1 0 0 0 1 0 0 0 1 0 0 0 0 0³ + ³ ³ + ³1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0³ + ³ ³ + ³1 0 1 1 1 0 1 1 1 0 1 1 0 0 0 0³ + ³ ³ + ³0 1 0 1 0 1 0 1 0 1 0 1 0 0 0 0³ + ³ ³ + ³0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 0³ + ³ ³ + ³1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1³ + ³ ³ + ³1 0 1 1 1 0 1 1 1 0 1 1 1 0 1 1³ + ³ ³ + À0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1Ù + Type: List Matrix PrimeField 2 +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{RepA6PageEmpty21} +\begin{paste}{RepA6PageEmpty21}{RepA6PagePatch21} +\pastebutton{RepA6PageEmpty21}{\showpaste} +\tab{5}\spadcommand{dA6d16\free{dA6d16 }} +\end{paste}\end{patch} @ \pagehead{InfoRepTheoryPage}{grpthry.ht}{Representation Theory} @@ -10990,6 +28384,115 @@ So the project is cancelled and we can delete the data base: \autobuttons \end{page} +\begin{patch}{GeneralSparseTableXmpPagePatch1} +\begin{paste}{GeneralSparseTableXmpPageFull1}{GeneralSparseTableXmpPageEmpty1} +\pastebutton{GeneralSparseTableXmpPageFull1}{\hidepaste} +\tab{5}\spadcommand{patrons: GeneralSparseTable(String, Integer, KeyedAccessFile(Integer), 0) := table() ;\bound{patrons }} +\indentrel{3}\begin{verbatim} +Type: GeneralSparseTable(String,Integer,KeyedAccessFile Integer,0) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{GeneralSparseTableXmpPageEmpty1} +\begin{paste}{GeneralSparseTableXmpPageEmpty1}{GeneralSparseTableXmpPagePatch1} +\pastebutton{GeneralSparseTableXmpPageEmpty1}{\showpaste} +\tab{5}\spadcommand{patrons: GeneralSparseTable(String, Integer, KeyedAccessFile(Integer), 0) := table() ;\bound{patrons }} +\end{paste}\end{patch} + +\begin{patch}{GeneralSparseTableXmpPagePatch2} +\begin{paste}{GeneralSparseTableXmpPageFull2}{GeneralSparseTableXmpPageEmpty2} +\pastebutton{GeneralSparseTableXmpPageFull2}{\hidepaste} +\tab{5}\spadcommand{patrons."Smith" := 10500\free{patrons }\bound{smith }} +\indentrel{3}\begin{verbatim} + (2) 10500 + Type: PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{GeneralSparseTableXmpPageEmpty2} +\begin{paste}{GeneralSparseTableXmpPageEmpty2}{GeneralSparseTableXmpPagePatch2} +\pastebutton{GeneralSparseTableXmpPageEmpty2}{\showpaste} +\tab{5}\spadcommand{patrons."Smith" := 10500\free{patrons }\bound{smith }} +\end{paste}\end{patch} + +\begin{patch}{GeneralSparseTableXmpPagePatch3} +\begin{paste}{GeneralSparseTableXmpPageFull3}{GeneralSparseTableXmpPageEmpty3} +\pastebutton{GeneralSparseTableXmpPageFull3}{\hidepaste} +\tab{5}\spadcommand{patrons."Jones" := 22000\free{smith }\bound{jones }} +\indentrel{3}\begin{verbatim} + (3) 22000 + Type: PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{GeneralSparseTableXmpPageEmpty3} +\begin{paste}{GeneralSparseTableXmpPageEmpty3}{GeneralSparseTableXmpPagePatch3} +\pastebutton{GeneralSparseTableXmpPageEmpty3}{\showpaste} +\tab{5}\spadcommand{patrons."Jones" := 22000\free{smith }\bound{jones }} +\end{paste}\end{patch} + +\begin{patch}{GeneralSparseTableXmpPagePatch4} +\begin{paste}{GeneralSparseTableXmpPageFull4}{GeneralSparseTableXmpPageEmpty4} +\pastebutton{GeneralSparseTableXmpPageFull4}{\hidepaste} +\tab{5}\spadcommand{patrons."Jones"\free{jones }} +\indentrel{3}\begin{verbatim} + (4) 22000 + Type: PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{GeneralSparseTableXmpPageEmpty4} +\begin{paste}{GeneralSparseTableXmpPageEmpty4}{GeneralSparseTableXmpPagePatch4} +\pastebutton{GeneralSparseTableXmpPageEmpty4}{\showpaste} +\tab{5}\spadcommand{patrons."Jones"\free{jones }} +\end{paste}\end{patch} + +\begin{patch}{GeneralSparseTableXmpPagePatch5} +\begin{paste}{GeneralSparseTableXmpPageFull5}{GeneralSparseTableXmpPageEmpty5} +\pastebutton{GeneralSparseTableXmpPageFull5}{\hidepaste} +\tab{5}\spadcommand{patrons."Stingy"\free{jones }} +\indentrel{3}\begin{verbatim} + (5) 0 + Type: NonNegativeInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{GeneralSparseTableXmpPageEmpty5} +\begin{paste}{GeneralSparseTableXmpPageEmpty5}{GeneralSparseTableXmpPagePatch5} +\pastebutton{GeneralSparseTableXmpPageEmpty5}{\showpaste} +\tab{5}\spadcommand{patrons."Stingy"\free{jones }} +\end{paste}\end{patch} + +\begin{patch}{GeneralSparseTableXmpPagePatch6} +\begin{paste}{GeneralSparseTableXmpPageFull6}{GeneralSparseTableXmpPageEmpty6} +\pastebutton{GeneralSparseTableXmpPageFull6}{\hidepaste} +\tab{5}\spadcommand{reduce(+, entries patrons)\free{jones }} +\indentrel{3}\begin{verbatim} + (6) 32500 + Type: PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{GeneralSparseTableXmpPageEmpty6} +\begin{paste}{GeneralSparseTableXmpPageEmpty6}{GeneralSparseTableXmpPagePatch6} +\pastebutton{GeneralSparseTableXmpPageEmpty6}{\showpaste} +\tab{5}\spadcommand{reduce(+, entries patrons)\free{jones }} +\end{paste}\end{patch} + +\begin{patch}{GeneralSparseTableXmpPagePatch7} +\begin{paste}{GeneralSparseTableXmpPageFull7}{GeneralSparseTableXmpPageEmpty7} +\pastebutton{GeneralSparseTableXmpPageFull7}{\hidepaste} +\tab{5}\spadcommand{)system rm -r kaf*.sdata\free{patrons }} +\indentrel{3}\begin{verbatim} +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{GeneralSparseTableXmpPageEmpty7} +\begin{paste}{GeneralSparseTableXmpPageEmpty7}{GeneralSparseTableXmpPagePatch7} +\pastebutton{GeneralSparseTableXmpPageEmpty7}{\showpaste} +\tab{5}\spadcommand{)system rm -r kaf*.sdata\free{patrons }} +\end{paste}\end{patch} + @ \section{heap.ht} \pagehead{HeapXmpPage}{heap.ht}{Heap} @@ -11117,6 +28620,133 @@ These numbers are bona fide algebraic objects. \autobuttons \end{page} +\begin{patch}{HexExpansionXmpPagePatch1} +\begin{paste}{HexExpansionXmpPageFull1}{HexExpansionXmpPageEmpty1} +\pastebutton{HexExpansionXmpPageFull1}{\hidepaste} +\tab{5}\spadcommand{r := hex(22/7)\bound{r }} +\indentrel{3}\begin{verbatim} + ___ + (1) 3.249 + Type: HexadecimalExpansion +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{HexExpansionXmpPageEmpty1} +\begin{paste}{HexExpansionXmpPageEmpty1}{HexExpansionXmpPagePatch1} +\pastebutton{HexExpansionXmpPageEmpty1}{\showpaste} +\tab{5}\spadcommand{r := hex(22/7)\bound{r }} +\end{paste}\end{patch} + +\begin{patch}{HexExpansionXmpPagePatch2} +\begin{paste}{HexExpansionXmpPageFull2}{HexExpansionXmpPageEmpty2} +\pastebutton{HexExpansionXmpPageFull2}{\hidepaste} +\tab{5}\spadcommand{r + hex(6/7)\free{r }} +\indentrel{3}\begin{verbatim} + (2) 4 + Type: HexadecimalExpansion +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{HexExpansionXmpPageEmpty2} +\begin{paste}{HexExpansionXmpPageEmpty2}{HexExpansionXmpPagePatch2} +\pastebutton{HexExpansionXmpPageEmpty2}{\showpaste} +\tab{5}\spadcommand{r + hex(6/7)\free{r }} +\end{paste}\end{patch} + +\begin{patch}{HexExpansionXmpPagePatch3} +\begin{paste}{HexExpansionXmpPageFull3}{HexExpansionXmpPageEmpty3} +\pastebutton{HexExpansionXmpPageFull3}{\hidepaste} +\tab{5}\spadcommand{[hex(1/i) for i in 350..354]} +\indentrel{3}\begin{verbatim} + (3) + _______________ _________ _____ + [0.00BB3EE721A54D88, 0.00BAB6561, 0.00BA2E8, + ______________________ + 0.00B9A7862A0FF465879D5F, + _____________________________ + 0.00B92143FA36F5E02E4850FE8DBD78] + Type: List HexadecimalExpansion +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{HexExpansionXmpPageEmpty3} +\begin{paste}{HexExpansionXmpPageEmpty3}{HexExpansionXmpPagePatch3} +\pastebutton{HexExpansionXmpPageEmpty3}{\showpaste} +\tab{5}\spadcommand{[hex(1/i) for i in 350..354]} +\end{paste}\end{patch} + +\begin{patch}{HexExpansionXmpPagePatch4} +\begin{paste}{HexExpansionXmpPageFull4}{HexExpansionXmpPageEmpty4} +\pastebutton{HexExpansionXmpPageFull4}{\hidepaste} +\tab{5}\spadcommand{hex(1/1007)} +\indentrel{3}\begin{verbatim} + (4) + 0. + OVERBAR + 0041149783F0BF2C7D13933192AF6980619EE345E91EC2BB9 + D5CCA5C071E40926E54E8DDAE24196C0B2F8A0AAD60DBA5 + 7F5D4C8536262210C74F1 + Type: HexadecimalExpansion +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{HexExpansionXmpPageEmpty4} +\begin{paste}{HexExpansionXmpPageEmpty4}{HexExpansionXmpPagePatch4} +\pastebutton{HexExpansionXmpPageEmpty4}{\showpaste} +\tab{5}\spadcommand{hex(1/1007)} +\end{paste}\end{patch} + +\begin{patch}{HexExpansionXmpPagePatch5} +\begin{paste}{HexExpansionXmpPageFull5}{HexExpansionXmpPageEmpty5} +\pastebutton{HexExpansionXmpPageFull5}{\hidepaste} +\tab{5}\spadcommand{p := hex(1/4)*x**2 + hex(2/3)*x + hex(4/9)\bound{p }} +\indentrel{3}\begin{verbatim} + 2 _ ___ + (5) 0.4x + 0.Ax + 0.71C + Type: Polynomial HexadecimalExpansion +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{HexExpansionXmpPageEmpty5} +\begin{paste}{HexExpansionXmpPageEmpty5}{HexExpansionXmpPagePatch5} +\pastebutton{HexExpansionXmpPageEmpty5}{\showpaste} +\tab{5}\spadcommand{p := hex(1/4)*x**2 + hex(2/3)*x + hex(4/9)\bound{p }} +\end{paste}\end{patch} + +\begin{patch}{HexExpansionXmpPagePatch6} +\begin{paste}{HexExpansionXmpPageFull6}{HexExpansionXmpPageEmpty6} +\pastebutton{HexExpansionXmpPageFull6}{\hidepaste} +\tab{5}\spadcommand{q := D(p, x)\free{p }\bound{q }} +\indentrel{3}\begin{verbatim} + _ + (6) 0.8x + 0.A + Type: Polynomial HexadecimalExpansion +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{HexExpansionXmpPageEmpty6} +\begin{paste}{HexExpansionXmpPageEmpty6}{HexExpansionXmpPagePatch6} +\pastebutton{HexExpansionXmpPageEmpty6}{\showpaste} +\tab{5}\spadcommand{q := D(p, x)\free{p }\bound{q }} +\end{paste}\end{patch} + +\begin{patch}{HexExpansionXmpPagePatch7} +\begin{paste}{HexExpansionXmpPageFull7}{HexExpansionXmpPageEmpty7} +\pastebutton{HexExpansionXmpPageFull7}{\hidepaste} +\tab{5}\spadcommand{g := gcd(p, q)\free{p }\free{q }} +\indentrel{3}\begin{verbatim} + _ + (7) x + 1.5 + Type: Polynomial HexadecimalExpansion +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{HexExpansionXmpPageEmpty7} +\begin{paste}{HexExpansionXmpPageEmpty7}{HexExpansionXmpPagePatch7} +\pastebutton{HexExpansionXmpPageEmpty7}{\showpaste} +\tab{5}\spadcommand{g := gcd(p, q)\free{p }\free{q }} +\end{paste}\end{patch} + @ \section{int.ht} \pagehead{IntegerXmpPage}{int.ht}{Integer} @@ -11367,6 +28997,493 @@ Records are discussed in detail in \autobuttons \end{page} +\begin{patch}{ugxIntegerBasicPagePatch1} +\begin{paste}{ugxIntegerBasicPageFull1}{ugxIntegerBasicPageEmpty1} +\pastebutton{ugxIntegerBasicPageFull1}{\hidepaste} +\tab{5}\spadcommand{2**(5678 - 4856 + 2 * 17)} +\indentrel{3}\begin{verbatim} + (1) + 480481077043500814718154092512592439123952613987168226_ + 34738556100880842000763082930863425270914120837430745_ + 72278211496076276922026433435687527334980249539302425_ + 42523045817764949544214392905306388478705146745768073_ + 877141698859815495632935288783334250628775936 + Type: PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxIntegerBasicPageEmpty1} +\begin{paste}{ugxIntegerBasicPageEmpty1}{ugxIntegerBasicPagePatch1} +\pastebutton{ugxIntegerBasicPageEmpty1}{\showpaste} +\tab{5}\spadcommand{2**(5678 - 4856 + 2 * 17)} +\end{paste}\end{patch} + +\begin{patch}{ugxIntegerBasicPagePatch2} +\begin{paste}{ugxIntegerBasicPageFull2}{ugxIntegerBasicPageEmpty2} +\pastebutton{ugxIntegerBasicPageFull2}{\hidepaste} +\tab{5}\spadcommand{x := -101\bound{x }} +\indentrel{3}\begin{verbatim} + (2) - 101 + Type: Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxIntegerBasicPageEmpty2} +\begin{paste}{ugxIntegerBasicPageEmpty2}{ugxIntegerBasicPagePatch2} +\pastebutton{ugxIntegerBasicPageEmpty2}{\showpaste} +\tab{5}\spadcommand{x := -101\bound{x }} +\end{paste}\end{patch} + +\begin{patch}{ugxIntegerBasicPagePatch3} +\begin{paste}{ugxIntegerBasicPageFull3}{ugxIntegerBasicPageEmpty3} +\pastebutton{ugxIntegerBasicPageFull3}{\hidepaste} +\tab{5}\spadcommand{abs(x)\free{x }} +\indentrel{3}\begin{verbatim} + (3) 101 + Type: PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxIntegerBasicPageEmpty3} +\begin{paste}{ugxIntegerBasicPageEmpty3}{ugxIntegerBasicPagePatch3} +\pastebutton{ugxIntegerBasicPageEmpty3}{\showpaste} +\tab{5}\spadcommand{abs(x)\free{x }} +\end{paste}\end{patch} + +\begin{patch}{ugxIntegerBasicPagePatch4} +\begin{paste}{ugxIntegerBasicPageFull4}{ugxIntegerBasicPageEmpty4} +\pastebutton{ugxIntegerBasicPageFull4}{\hidepaste} +\tab{5}\spadcommand{sign(x)\free{x }} +\indentrel{3}\begin{verbatim} + (4) - 1 + Type: Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxIntegerBasicPageEmpty4} +\begin{paste}{ugxIntegerBasicPageEmpty4}{ugxIntegerBasicPagePatch4} +\pastebutton{ugxIntegerBasicPageEmpty4}{\showpaste} +\tab{5}\spadcommand{sign(x)\free{x }} +\end{paste}\end{patch} + +\begin{patch}{ugxIntegerBasicPagePatch5} +\begin{paste}{ugxIntegerBasicPageFull5}{ugxIntegerBasicPageEmpty5} +\pastebutton{ugxIntegerBasicPageFull5}{\hidepaste} +\tab{5}\spadcommand{x < 0\free{x }} +\indentrel{3}\begin{verbatim} + (5) true + Type: Boolean +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxIntegerBasicPageEmpty5} +\begin{paste}{ugxIntegerBasicPageEmpty5}{ugxIntegerBasicPagePatch5} +\pastebutton{ugxIntegerBasicPageEmpty5}{\showpaste} +\tab{5}\spadcommand{x < 0\free{x }} +\end{paste}\end{patch} + +\begin{patch}{ugxIntegerBasicPagePatch6} +\begin{paste}{ugxIntegerBasicPageFull6}{ugxIntegerBasicPageEmpty6} +\pastebutton{ugxIntegerBasicPageFull6}{\hidepaste} +\tab{5}\spadcommand{x <= -1\free{x }} +\indentrel{3}\begin{verbatim} + (6) true + Type: Boolean +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxIntegerBasicPageEmpty6} +\begin{paste}{ugxIntegerBasicPageEmpty6}{ugxIntegerBasicPagePatch6} +\pastebutton{ugxIntegerBasicPageEmpty6}{\showpaste} +\tab{5}\spadcommand{x <= -1\free{x }} +\end{paste}\end{patch} + +\begin{patch}{ugxIntegerBasicPagePatch7} +\begin{paste}{ugxIntegerBasicPageFull7}{ugxIntegerBasicPageEmpty7} +\pastebutton{ugxIntegerBasicPageFull7}{\hidepaste} +\tab{5}\spadcommand{negative?(x)\free{x }} +\indentrel{3}\begin{verbatim} + (7) true + Type: Boolean +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxIntegerBasicPageEmpty7} +\begin{paste}{ugxIntegerBasicPageEmpty7}{ugxIntegerBasicPagePatch7} +\pastebutton{ugxIntegerBasicPageEmpty7}{\showpaste} +\tab{5}\spadcommand{negative?(x)\free{x }} +\end{paste}\end{patch} + +\begin{patch}{ugxIntegerBasicPagePatch8} +\begin{paste}{ugxIntegerBasicPageFull8}{ugxIntegerBasicPageEmpty8} +\pastebutton{ugxIntegerBasicPageFull8}{\hidepaste} +\tab{5}\spadcommand{x > 0\free{x }} +\indentrel{3}\begin{verbatim} + (8) false + Type: Boolean +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxIntegerBasicPageEmpty8} +\begin{paste}{ugxIntegerBasicPageEmpty8}{ugxIntegerBasicPagePatch8} +\pastebutton{ugxIntegerBasicPageEmpty8}{\showpaste} +\tab{5}\spadcommand{x > 0\free{x }} +\end{paste}\end{patch} + +\begin{patch}{ugxIntegerBasicPagePatch9} +\begin{paste}{ugxIntegerBasicPageFull9}{ugxIntegerBasicPageEmpty9} +\pastebutton{ugxIntegerBasicPageFull9}{\hidepaste} +\tab{5}\spadcommand{x >= 1\free{x }} +\indentrel{3}\begin{verbatim} + (9) false + Type: Boolean +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxIntegerBasicPageEmpty9} +\begin{paste}{ugxIntegerBasicPageEmpty9}{ugxIntegerBasicPagePatch9} +\pastebutton{ugxIntegerBasicPageEmpty9}{\showpaste} +\tab{5}\spadcommand{x >= 1\free{x }} +\end{paste}\end{patch} + +\begin{patch}{ugxIntegerBasicPagePatch10} +\begin{paste}{ugxIntegerBasicPageFull10}{ugxIntegerBasicPageEmpty10} +\pastebutton{ugxIntegerBasicPageFull10}{\hidepaste} +\tab{5}\spadcommand{positive?(x)\free{x }} +\indentrel{3}\begin{verbatim} + (10) false + Type: Boolean +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxIntegerBasicPageEmpty10} +\begin{paste}{ugxIntegerBasicPageEmpty10}{ugxIntegerBasicPagePatch10} +\pastebutton{ugxIntegerBasicPageEmpty10}{\showpaste} +\tab{5}\spadcommand{positive?(x)\free{x }} +\end{paste}\end{patch} + +\begin{patch}{ugxIntegerBasicPagePatch11} +\begin{paste}{ugxIntegerBasicPageFull11}{ugxIntegerBasicPageEmpty11} +\pastebutton{ugxIntegerBasicPageFull11}{\hidepaste} +\tab{5}\spadcommand{zero?(x)\free{x }} +\indentrel{3}\begin{verbatim} + (11) false + Type: Boolean +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxIntegerBasicPageEmpty11} +\begin{paste}{ugxIntegerBasicPageEmpty11}{ugxIntegerBasicPagePatch11} +\pastebutton{ugxIntegerBasicPageEmpty11}{\showpaste} +\tab{5}\spadcommand{zero?(x)\free{x }} +\end{paste}\end{patch} + +\begin{patch}{ugxIntegerBasicPagePatch12} +\begin{paste}{ugxIntegerBasicPageFull12}{ugxIntegerBasicPageEmpty12} +\pastebutton{ugxIntegerBasicPageFull12}{\hidepaste} +\tab{5}\spadcommand{one?(x)\free{x }} +\indentrel{3}\begin{verbatim} + (12) false + Type: Boolean +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxIntegerBasicPageEmpty12} +\begin{paste}{ugxIntegerBasicPageEmpty12}{ugxIntegerBasicPagePatch12} +\pastebutton{ugxIntegerBasicPageEmpty12}{\showpaste} +\tab{5}\spadcommand{one?(x)\free{x }} +\end{paste}\end{patch} + +\begin{patch}{ugxIntegerBasicPagePatch13} +\begin{paste}{ugxIntegerBasicPageFull13}{ugxIntegerBasicPageEmpty13} +\pastebutton{ugxIntegerBasicPageFull13}{\hidepaste} +\tab{5}\spadcommand{(x = -101)@Boolean\free{x }} +\indentrel{3}\begin{verbatim} + (13) true + Type: Boolean +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxIntegerBasicPageEmpty13} +\begin{paste}{ugxIntegerBasicPageEmpty13}{ugxIntegerBasicPagePatch13} +\pastebutton{ugxIntegerBasicPageEmpty13}{\showpaste} +\tab{5}\spadcommand{(x = -101)@Boolean\free{x }} +\end{paste}\end{patch} + +\begin{patch}{ugxIntegerBasicPagePatch14} +\begin{paste}{ugxIntegerBasicPageFull14}{ugxIntegerBasicPageEmpty14} +\pastebutton{ugxIntegerBasicPageFull14}{\hidepaste} +\tab{5}\spadcommand{odd?(x)\free{x }} +\indentrel{3}\begin{verbatim} + (14) true + Type: Boolean +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxIntegerBasicPageEmpty14} +\begin{paste}{ugxIntegerBasicPageEmpty14}{ugxIntegerBasicPagePatch14} +\pastebutton{ugxIntegerBasicPageEmpty14}{\showpaste} +\tab{5}\spadcommand{odd?(x)\free{x }} +\end{paste}\end{patch} + +\begin{patch}{ugxIntegerBasicPagePatch15} +\begin{paste}{ugxIntegerBasicPageFull15}{ugxIntegerBasicPageEmpty15} +\pastebutton{ugxIntegerBasicPageFull15}{\hidepaste} +\tab{5}\spadcommand{even?(x)\free{x }} +\indentrel{3}\begin{verbatim} + (15) false + Type: Boolean +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxIntegerBasicPageEmpty15} +\begin{paste}{ugxIntegerBasicPageEmpty15}{ugxIntegerBasicPagePatch15} +\pastebutton{ugxIntegerBasicPageEmpty15}{\showpaste} +\tab{5}\spadcommand{even?(x)\free{x }} +\end{paste}\end{patch} + +\begin{patch}{ugxIntegerBasicPagePatch16} +\begin{paste}{ugxIntegerBasicPageFull16}{ugxIntegerBasicPageEmpty16} +\pastebutton{ugxIntegerBasicPageFull16}{\hidepaste} +\tab{5}\spadcommand{gcd(56788,43688)} +\indentrel{3}\begin{verbatim} + (16) 4 + Type: PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxIntegerBasicPageEmpty16} +\begin{paste}{ugxIntegerBasicPageEmpty16}{ugxIntegerBasicPagePatch16} +\pastebutton{ugxIntegerBasicPageEmpty16}{\showpaste} +\tab{5}\spadcommand{gcd(56788,43688)} +\end{paste}\end{patch} + +\begin{patch}{ugxIntegerBasicPagePatch17} +\begin{paste}{ugxIntegerBasicPageFull17}{ugxIntegerBasicPageEmpty17} +\pastebutton{ugxIntegerBasicPageFull17}{\hidepaste} +\tab{5}\spadcommand{lcm(56788,43688)} +\indentrel{3}\begin{verbatim} + (17) 620238536 + Type: PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxIntegerBasicPageEmpty17} +\begin{paste}{ugxIntegerBasicPageEmpty17}{ugxIntegerBasicPagePatch17} +\pastebutton{ugxIntegerBasicPageEmpty17}{\showpaste} +\tab{5}\spadcommand{lcm(56788,43688)} +\end{paste}\end{patch} + +\begin{patch}{ugxIntegerBasicPagePatch18} +\begin{paste}{ugxIntegerBasicPageFull18}{ugxIntegerBasicPageEmpty18} +\pastebutton{ugxIntegerBasicPageFull18}{\hidepaste} +\tab{5}\spadcommand{max(678,567)} +\indentrel{3}\begin{verbatim} + (18) 678 + Type: PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxIntegerBasicPageEmpty18} +\begin{paste}{ugxIntegerBasicPageEmpty18}{ugxIntegerBasicPagePatch18} +\pastebutton{ugxIntegerBasicPageEmpty18}{\showpaste} +\tab{5}\spadcommand{max(678,567)} +\end{paste}\end{patch} + +\begin{patch}{ugxIntegerBasicPagePatch19} +\begin{paste}{ugxIntegerBasicPageFull19}{ugxIntegerBasicPageEmpty19} +\pastebutton{ugxIntegerBasicPageFull19}{\hidepaste} +\tab{5}\spadcommand{min(678,567)} +\indentrel{3}\begin{verbatim} + (19) 567 + Type: PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxIntegerBasicPageEmpty19} +\begin{paste}{ugxIntegerBasicPageEmpty19}{ugxIntegerBasicPagePatch19} +\pastebutton{ugxIntegerBasicPageEmpty19}{\showpaste} +\tab{5}\spadcommand{min(678,567)} +\end{paste}\end{patch} + +\begin{patch}{ugxIntegerBasicPagePatch20} +\begin{paste}{ugxIntegerBasicPageFull20}{ugxIntegerBasicPageEmpty20} +\pastebutton{ugxIntegerBasicPageFull20}{\hidepaste} +\tab{5}\spadcommand{reduce(max,[2,45,-89,78,100,-45])} +\indentrel{3}\begin{verbatim} + (20) 100 + Type: PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxIntegerBasicPageEmpty20} +\begin{paste}{ugxIntegerBasicPageEmpty20}{ugxIntegerBasicPagePatch20} +\pastebutton{ugxIntegerBasicPageEmpty20}{\showpaste} +\tab{5}\spadcommand{reduce(max,[2,45,-89,78,100,-45])} +\end{paste}\end{patch} + +\begin{patch}{ugxIntegerBasicPagePatch21} +\begin{paste}{ugxIntegerBasicPageFull21}{ugxIntegerBasicPageEmpty21} +\pastebutton{ugxIntegerBasicPageFull21}{\hidepaste} +\tab{5}\spadcommand{reduce(min,[2,45,-89,78,100,-45])} +\indentrel{3}\begin{verbatim} + (21) - 89 + Type: Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxIntegerBasicPageEmpty21} +\begin{paste}{ugxIntegerBasicPageEmpty21}{ugxIntegerBasicPagePatch21} +\pastebutton{ugxIntegerBasicPageEmpty21}{\showpaste} +\tab{5}\spadcommand{reduce(min,[2,45,-89,78,100,-45])} +\end{paste}\end{patch} + +\begin{patch}{ugxIntegerBasicPagePatch22} +\begin{paste}{ugxIntegerBasicPageFull22}{ugxIntegerBasicPageEmpty22} +\pastebutton{ugxIntegerBasicPageFull22}{\hidepaste} +\tab{5}\spadcommand{reduce(gcd,[2,45,-89,78,100,-45])} +\indentrel{3}\begin{verbatim} + (22) 1 + Type: PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxIntegerBasicPageEmpty22} +\begin{paste}{ugxIntegerBasicPageEmpty22}{ugxIntegerBasicPagePatch22} +\pastebutton{ugxIntegerBasicPageEmpty22}{\showpaste} +\tab{5}\spadcommand{reduce(gcd,[2,45,-89,78,100,-45])} +\end{paste}\end{patch} + +\begin{patch}{ugxIntegerBasicPagePatch23} +\begin{paste}{ugxIntegerBasicPageFull23}{ugxIntegerBasicPageEmpty23} +\pastebutton{ugxIntegerBasicPageFull23}{\hidepaste} +\tab{5}\spadcommand{reduce(lcm,[2,45,-89,78,100,-45])} +\indentrel{3}\begin{verbatim} + (23) 1041300 + Type: PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxIntegerBasicPageEmpty23} +\begin{paste}{ugxIntegerBasicPageEmpty23}{ugxIntegerBasicPagePatch23} +\pastebutton{ugxIntegerBasicPageEmpty23}{\showpaste} +\tab{5}\spadcommand{reduce(lcm,[2,45,-89,78,100,-45])} +\end{paste}\end{patch} + +\begin{patch}{ugxIntegerBasicPagePatch24} +\begin{paste}{ugxIntegerBasicPageFull24}{ugxIntegerBasicPageEmpty24} +\pastebutton{ugxIntegerBasicPageFull24}{\hidepaste} +\tab{5}\spadcommand{13 / 4} +\indentrel{3}\begin{verbatim} + 13 + (24) ÄÄ + 4 + Type: Fraction Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxIntegerBasicPageEmpty24} +\begin{paste}{ugxIntegerBasicPageEmpty24}{ugxIntegerBasicPagePatch24} +\pastebutton{ugxIntegerBasicPageEmpty24}{\showpaste} +\tab{5}\spadcommand{13 / 4} +\end{paste}\end{patch} + +\begin{patch}{ugxIntegerBasicPagePatch25} +\begin{paste}{ugxIntegerBasicPageFull25}{ugxIntegerBasicPageEmpty25} +\pastebutton{ugxIntegerBasicPageFull25}{\hidepaste} +\tab{5}\spadcommand{13 quo 4} +\indentrel{3}\begin{verbatim} + (25) 3 + Type: PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxIntegerBasicPageEmpty25} +\begin{paste}{ugxIntegerBasicPageEmpty25}{ugxIntegerBasicPagePatch25} +\pastebutton{ugxIntegerBasicPageEmpty25}{\showpaste} +\tab{5}\spadcommand{13 quo 4} +\end{paste}\end{patch} + +\begin{patch}{ugxIntegerBasicPagePatch26} +\begin{paste}{ugxIntegerBasicPageFull26}{ugxIntegerBasicPageEmpty26} +\pastebutton{ugxIntegerBasicPageFull26}{\hidepaste} +\tab{5}\spadcommand{13 rem 4} +\indentrel{3}\begin{verbatim} + (26) 1 + Type: PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxIntegerBasicPageEmpty26} +\begin{paste}{ugxIntegerBasicPageEmpty26}{ugxIntegerBasicPagePatch26} +\pastebutton{ugxIntegerBasicPageEmpty26}{\showpaste} +\tab{5}\spadcommand{13 rem 4} +\end{paste}\end{patch} + +\begin{patch}{ugxIntegerBasicPagePatch27} +\begin{paste}{ugxIntegerBasicPageFull27}{ugxIntegerBasicPageEmpty27} +\pastebutton{ugxIntegerBasicPageFull27}{\hidepaste} +\tab{5}\spadcommand{zero?(167604736446952 rem 2003644)} +\indentrel{3}\begin{verbatim} + (27) true + Type: Boolean +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxIntegerBasicPageEmpty27} +\begin{paste}{ugxIntegerBasicPageEmpty27}{ugxIntegerBasicPagePatch27} +\pastebutton{ugxIntegerBasicPageEmpty27}{\showpaste} +\tab{5}\spadcommand{zero?(167604736446952 rem 2003644)} +\end{paste}\end{patch} + +\begin{patch}{ugxIntegerBasicPagePatch28} +\begin{paste}{ugxIntegerBasicPageFull28}{ugxIntegerBasicPageEmpty28} +\pastebutton{ugxIntegerBasicPageFull28}{\hidepaste} +\tab{5}\spadcommand{d := divide(13,4)\bound{d }} +\indentrel{3}\begin{verbatim} + (28) [quotient= 3,remainder= 1] + Type: Record(quotient: Integer,remainder: Integer) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxIntegerBasicPageEmpty28} +\begin{paste}{ugxIntegerBasicPageEmpty28}{ugxIntegerBasicPagePatch28} +\pastebutton{ugxIntegerBasicPageEmpty28}{\showpaste} +\tab{5}\spadcommand{d := divide(13,4)\bound{d }} +\end{paste}\end{patch} + +\begin{patch}{ugxIntegerBasicPagePatch29} +\begin{paste}{ugxIntegerBasicPageFull29}{ugxIntegerBasicPageEmpty29} +\pastebutton{ugxIntegerBasicPageFull29}{\hidepaste} +\tab{5}\spadcommand{d.quotient\free{d }} +\indentrel{3}\begin{verbatim} + (29) 3 + Type: PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxIntegerBasicPageEmpty29} +\begin{paste}{ugxIntegerBasicPageEmpty29}{ugxIntegerBasicPagePatch29} +\pastebutton{ugxIntegerBasicPageEmpty29}{\showpaste} +\tab{5}\spadcommand{d.quotient\free{d }} +\end{paste}\end{patch} + +\begin{patch}{ugxIntegerBasicPagePatch30} +\begin{paste}{ugxIntegerBasicPageFull30}{ugxIntegerBasicPageEmpty30} +\pastebutton{ugxIntegerBasicPageFull30}{\hidepaste} +\tab{5}\spadcommand{d.remainder\free{d }} +\indentrel{3}\begin{verbatim} + (30) 1 + Type: PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxIntegerBasicPageEmpty30} +\begin{paste}{ugxIntegerBasicPageEmpty30}{ugxIntegerBasicPagePatch30} +\pastebutton{ugxIntegerBasicPageEmpty30}{\showpaste} +\tab{5}\spadcommand{d.remainder\free{d }} +\end{paste}\end{patch} + @ \pagehead{ugxIntegerPrimesPage}{int.ht}{Primes and Factorization} \pagepic{ps/v71ugxintegerprimespage.eps}{ugxIntegerPrimesPage} @@ -11430,6 +29547,122 @@ See \downlink{`Complex'}{ComplexXmpPage}\ignore{Complex} for more details. \autobuttons \end{page} +\begin{patch}{ugxIntegerPrimesPagePatch1} +\begin{paste}{ugxIntegerPrimesPageFull1}{ugxIntegerPrimesPageEmpty1} +\pastebutton{ugxIntegerPrimesPageFull1}{\hidepaste} +\tab{5}\spadcommand{factor 102400} +\indentrel{3}\begin{verbatim} + 12 2 + (1) 2 5 + Type: Factored Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxIntegerPrimesPageEmpty1} +\begin{paste}{ugxIntegerPrimesPageEmpty1}{ugxIntegerPrimesPagePatch1} +\pastebutton{ugxIntegerPrimesPageEmpty1}{\showpaste} +\tab{5}\spadcommand{factor 102400} +\end{paste}\end{patch} + +\begin{patch}{ugxIntegerPrimesPagePatch2} +\begin{paste}{ugxIntegerPrimesPageFull2}{ugxIntegerPrimesPageEmpty2} +\pastebutton{ugxIntegerPrimesPageFull2}{\hidepaste} +\tab{5}\spadcommand{prime? 7} +\indentrel{3}\begin{verbatim} + (2) true + Type: Boolean +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxIntegerPrimesPageEmpty2} +\begin{paste}{ugxIntegerPrimesPageEmpty2}{ugxIntegerPrimesPagePatch2} +\pastebutton{ugxIntegerPrimesPageEmpty2}{\showpaste} +\tab{5}\spadcommand{prime? 7} +\end{paste}\end{patch} + +\begin{patch}{ugxIntegerPrimesPagePatch3} +\begin{paste}{ugxIntegerPrimesPageFull3}{ugxIntegerPrimesPageEmpty3} +\pastebutton{ugxIntegerPrimesPageFull3}{\hidepaste} +\tab{5}\spadcommand{prime? 8} +\indentrel{3}\begin{verbatim} + (3) false + Type: Boolean +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxIntegerPrimesPageEmpty3} +\begin{paste}{ugxIntegerPrimesPageEmpty3}{ugxIntegerPrimesPagePatch3} +\pastebutton{ugxIntegerPrimesPageEmpty3}{\showpaste} +\tab{5}\spadcommand{prime? 8} +\end{paste}\end{patch} + +\begin{patch}{ugxIntegerPrimesPagePatch4} +\begin{paste}{ugxIntegerPrimesPageFull4}{ugxIntegerPrimesPageEmpty4} +\pastebutton{ugxIntegerPrimesPageFull4}{\hidepaste} +\tab{5}\spadcommand{nextPrime 100} +\indentrel{3}\begin{verbatim} + (4) 101 + Type: PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxIntegerPrimesPageEmpty4} +\begin{paste}{ugxIntegerPrimesPageEmpty4}{ugxIntegerPrimesPagePatch4} +\pastebutton{ugxIntegerPrimesPageEmpty4}{\showpaste} +\tab{5}\spadcommand{nextPrime 100} +\end{paste}\end{patch} + +\begin{patch}{ugxIntegerPrimesPagePatch5} +\begin{paste}{ugxIntegerPrimesPageFull5}{ugxIntegerPrimesPageEmpty5} +\pastebutton{ugxIntegerPrimesPageFull5}{\hidepaste} +\tab{5}\spadcommand{prevPrime 100} +\indentrel{3}\begin{verbatim} + (5) 97 + Type: PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxIntegerPrimesPageEmpty5} +\begin{paste}{ugxIntegerPrimesPageEmpty5}{ugxIntegerPrimesPagePatch5} +\pastebutton{ugxIntegerPrimesPageEmpty5}{\showpaste} +\tab{5}\spadcommand{prevPrime 100} +\end{paste}\end{patch} + +\begin{patch}{ugxIntegerPrimesPagePatch6} +\begin{paste}{ugxIntegerPrimesPageFull6}{ugxIntegerPrimesPageEmpty6} +\pastebutton{ugxIntegerPrimesPageFull6}{\hidepaste} +\tab{5}\spadcommand{primes(100,175)} +\indentrel{3}\begin{verbatim} + (6) + [173, 167, 163, 157, 151, 149, 139, 137, 131, 127, + 113, 109, 107, 103, 101] + Type: List Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxIntegerPrimesPageEmpty6} +\begin{paste}{ugxIntegerPrimesPageEmpty6}{ugxIntegerPrimesPagePatch6} +\pastebutton{ugxIntegerPrimesPageEmpty6}{\showpaste} +\tab{5}\spadcommand{primes(100,175)} +\end{paste}\end{patch} + +\begin{patch}{ugxIntegerPrimesPagePatch7} +\begin{paste}{ugxIntegerPrimesPageFull7}{ugxIntegerPrimesPageEmpty7} +\pastebutton{ugxIntegerPrimesPageFull7}{\hidepaste} +\tab{5}\spadcommand{factor(2 :: Complex Integer)} +\indentrel{3}\begin{verbatim} + 2 + (7) - %i (1 + %i) + Type: Factored Complex Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxIntegerPrimesPageEmpty7} +\begin{paste}{ugxIntegerPrimesPageEmpty7}{ugxIntegerPrimesPagePatch7} +\pastebutton{ugxIntegerPrimesPageEmpty7}{\showpaste} +\tab{5}\spadcommand{factor(2 :: Complex Integer)} +\end{paste}\end{patch} + @ \pagehead{ugxIntegerNTPage}{int.ht}{Some Number Theoretic Functions} \pagepic{ps/v71ugxintegerntpage.eps}{ugxIntegerNTPage} @@ -11512,7 +29745,166 @@ Roman numerals. \endscroll \autobuttons \end{page} -% + +\begin{patch}{ugxIntegerNTPagePatch1} +\begin{paste}{ugxIntegerNTPageFull1}{ugxIntegerNTPageEmpty1} +\pastebutton{ugxIntegerNTPageFull1}{\hidepaste} +\tab{5}\spadcommand{[fibonacci(k) for k in 0..]} +\indentrel{3}\begin{verbatim} + (1) [0,1,1,2,3,5,8,13,21,34,...] + Type: Stream Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxIntegerNTPageEmpty1} +\begin{paste}{ugxIntegerNTPageEmpty1}{ugxIntegerNTPagePatch1} +\pastebutton{ugxIntegerNTPageEmpty1}{\showpaste} +\tab{5}\spadcommand{[fibonacci(k) for k in 0..]} +\end{paste}\end{patch} + +\begin{patch}{ugxIntegerNTPagePatch2} +\begin{paste}{ugxIntegerNTPageFull2}{ugxIntegerNTPageEmpty2} +\pastebutton{ugxIntegerNTPageFull2}{\hidepaste} +\tab{5}\spadcommand{[legendre(i,11) for i in 0..10]} +\indentrel{3}\begin{verbatim} + (2) [0,1,- 1,1,1,1,- 1,- 1,- 1,1,- 1] + Type: List Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxIntegerNTPageEmpty2} +\begin{paste}{ugxIntegerNTPageEmpty2}{ugxIntegerNTPagePatch2} +\pastebutton{ugxIntegerNTPageEmpty2}{\showpaste} +\tab{5}\spadcommand{[legendre(i,11) for i in 0..10]} +\end{paste}\end{patch} + +\begin{patch}{ugxIntegerNTPagePatch3} +\begin{paste}{ugxIntegerNTPageFull3}{ugxIntegerNTPageEmpty3} +\pastebutton{ugxIntegerNTPageFull3}{\hidepaste} +\tab{5}\spadcommand{[jacobi(i,15) for i in 0..9]} +\indentrel{3}\begin{verbatim} + (3) [0,1,1,0,1,0,0,- 1,1,0] + Type: List Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxIntegerNTPageEmpty3} +\begin{paste}{ugxIntegerNTPageEmpty3}{ugxIntegerNTPagePatch3} +\pastebutton{ugxIntegerNTPageEmpty3}{\showpaste} +\tab{5}\spadcommand{[jacobi(i,15) for i in 0..9]} +\end{paste}\end{patch} + +\begin{patch}{ugxIntegerNTPagePatch4} +\begin{paste}{ugxIntegerNTPageFull4}{ugxIntegerNTPageEmpty4} +\pastebutton{ugxIntegerNTPageFull4}{\hidepaste} +\tab{5}\spadcommand{[eulerPhi i for i in 1..]} +\indentrel{3}\begin{verbatim} + (4) [1,1,2,2,4,2,6,4,6,4,...] + Type: Stream Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxIntegerNTPageEmpty4} +\begin{paste}{ugxIntegerNTPageEmpty4}{ugxIntegerNTPagePatch4} +\pastebutton{ugxIntegerNTPageEmpty4}{\showpaste} +\tab{5}\spadcommand{[eulerPhi i for i in 1..]} +\end{paste}\end{patch} + +\begin{patch}{ugxIntegerNTPagePatch5} +\begin{paste}{ugxIntegerNTPageFull5}{ugxIntegerNTPageEmpty5} +\pastebutton{ugxIntegerNTPageFull5}{\hidepaste} +\tab{5}\spadcommand{[moebiusMu i for i in 1..]} +\indentrel{3}\begin{verbatim} + (5) [1,- 1,- 1,0,- 1,1,- 1,0,0,1,...] + Type: Stream Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxIntegerNTPageEmpty5} +\begin{paste}{ugxIntegerNTPageEmpty5}{ugxIntegerNTPagePatch5} +\pastebutton{ugxIntegerNTPageEmpty5}{\showpaste} +\tab{5}\spadcommand{[moebiusMu i for i in 1..]} +\end{paste}\end{patch} + +\begin{patch}{ugxIntegerNTPagePatch6} +\begin{paste}{ugxIntegerNTPageFull6}{ugxIntegerNTPageEmpty6} +\pastebutton{ugxIntegerNTPageFull6}{\hidepaste} +\tab{5}\spadcommand{a := roman(78)\bound{a }} +\indentrel{3}\begin{verbatim} + (6) LXXVIII + Type: RomanNumeral +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxIntegerNTPageEmpty6} +\begin{paste}{ugxIntegerNTPageEmpty6}{ugxIntegerNTPagePatch6} +\pastebutton{ugxIntegerNTPageEmpty6}{\showpaste} +\tab{5}\spadcommand{a := roman(78)\bound{a }} +\end{paste}\end{patch} + +\begin{patch}{ugxIntegerNTPagePatch7} +\begin{paste}{ugxIntegerNTPageFull7}{ugxIntegerNTPageEmpty7} +\pastebutton{ugxIntegerNTPageFull7}{\hidepaste} +\tab{5}\spadcommand{b := roman(87)\bound{b }} +\indentrel{3}\begin{verbatim} + (7) LXXXVII + Type: RomanNumeral +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxIntegerNTPageEmpty7} +\begin{paste}{ugxIntegerNTPageEmpty7}{ugxIntegerNTPagePatch7} +\pastebutton{ugxIntegerNTPageEmpty7}{\showpaste} +\tab{5}\spadcommand{b := roman(87)\bound{b }} +\end{paste}\end{patch} + +\begin{patch}{ugxIntegerNTPagePatch8} +\begin{paste}{ugxIntegerNTPageFull8}{ugxIntegerNTPageEmpty8} +\pastebutton{ugxIntegerNTPageFull8}{\hidepaste} +\tab{5}\spadcommand{a + b\free{a }\free{b }} +\indentrel{3}\begin{verbatim} + (8) CLXV + Type: RomanNumeral +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxIntegerNTPageEmpty8} +\begin{paste}{ugxIntegerNTPageEmpty8}{ugxIntegerNTPagePatch8} +\pastebutton{ugxIntegerNTPageEmpty8}{\showpaste} +\tab{5}\spadcommand{a + b\free{a }\free{b }} +\end{paste}\end{patch} + +\begin{patch}{ugxIntegerNTPagePatch9} +\begin{paste}{ugxIntegerNTPageFull9}{ugxIntegerNTPageEmpty9} +\pastebutton{ugxIntegerNTPageFull9}{\hidepaste} +\tab{5}\spadcommand{a * b\free{a }\free{b }} +\indentrel{3}\begin{verbatim} + (9) MMMMMMDCCLXXXVI + Type: RomanNumeral +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxIntegerNTPageEmpty9} +\begin{paste}{ugxIntegerNTPageEmpty9}{ugxIntegerNTPagePatch9} +\pastebutton{ugxIntegerNTPageEmpty9}{\showpaste} +\tab{5}\spadcommand{a * b\free{a }\free{b }} +\end{paste}\end{patch} + +\begin{patch}{ugxIntegerNTPagePatch10} +\begin{paste}{ugxIntegerNTPageFull10}{ugxIntegerNTPageEmpty10} +\pastebutton{ugxIntegerNTPageFull10}{\hidepaste} +\tab{5}\spadcommand{b rem a\free{a }\free{b }} +\indentrel{3}\begin{verbatim} + (10) IX + Type: RomanNumeral +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxIntegerNTPageEmpty10} +\begin{paste}{ugxIntegerNTPageEmpty10}{ugxIntegerNTPagePatch10} +\pastebutton{ugxIntegerNTPageEmpty10}{\showpaste} +\tab{5}\spadcommand{b rem a\free{a }\free{b }} +\end{paste}\end{patch} @ \section{intheory.ht} @@ -11737,6 +30129,354 @@ quadratic field with discriminant \spad{d}. \autobuttons \end{page} +\begin{patch}{IntNumberTheoryFnsXmpPagePatch1} +\begin{paste}{IntNumberTheoryFnsXmpPageFull1}{IntNumberTheoryFnsXmpPageEmpty1} +\pastebutton{IntNumberTheoryFnsXmpPageFull1}{\hidepaste} +\tab{5}\spadcommand{div144 := divisors(144)\bound{div144 }} +\indentrel{3}\begin{verbatim} + (1) [1,2,3,4,6,8,9,12,16,18,24,36,48,72,144] + Type: List Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{IntNumberTheoryFnsXmpPageEmpty1} +\begin{paste}{IntNumberTheoryFnsXmpPageEmpty1}{IntNumberTheoryFnsXmpPagePatch1} +\pastebutton{IntNumberTheoryFnsXmpPageEmpty1}{\showpaste} +\tab{5}\spadcommand{div144 := divisors(144)\bound{div144 }} +\end{paste}\end{patch} + +\begin{patch}{IntNumberTheoryFnsXmpPagePatch2} +\begin{paste}{IntNumberTheoryFnsXmpPageFull2}{IntNumberTheoryFnsXmpPageEmpty2} +\pastebutton{IntNumberTheoryFnsXmpPageFull2}{\hidepaste} +\tab{5}\spadcommand{\#(div144)\free{div144 }} +\indentrel{3}\begin{verbatim} + (2) 15 + Type: PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{IntNumberTheoryFnsXmpPageEmpty2} +\begin{paste}{IntNumberTheoryFnsXmpPageEmpty2}{IntNumberTheoryFnsXmpPagePatch2} +\pastebutton{IntNumberTheoryFnsXmpPageEmpty2}{\showpaste} +\tab{5}\spadcommand{\#(div144)\free{div144 }} +\end{paste}\end{patch} + +\begin{patch}{IntNumberTheoryFnsXmpPagePatch3} +\begin{paste}{IntNumberTheoryFnsXmpPageFull3}{IntNumberTheoryFnsXmpPageEmpty3} +\pastebutton{IntNumberTheoryFnsXmpPageFull3}{\hidepaste} +\tab{5}\spadcommand{reduce(+,div144)\free{div144 }} +\indentrel{3}\begin{verbatim} + (3) 403 + Type: PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{IntNumberTheoryFnsXmpPageEmpty3} +\begin{paste}{IntNumberTheoryFnsXmpPageEmpty3}{IntNumberTheoryFnsXmpPagePatch3} +\pastebutton{IntNumberTheoryFnsXmpPageEmpty3}{\showpaste} +\tab{5}\spadcommand{reduce(+,div144)\free{div144 }} +\end{paste}\end{patch} + +\begin{patch}{IntNumberTheoryFnsXmpPagePatch4} +\begin{paste}{IntNumberTheoryFnsXmpPageFull4}{IntNumberTheoryFnsXmpPageEmpty4} +\pastebutton{IntNumberTheoryFnsXmpPageFull4}{\hidepaste} +\tab{5}\spadcommand{numberOfDivisors(144)} +\indentrel{3}\begin{verbatim} + (4) 15 + Type: PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{IntNumberTheoryFnsXmpPageEmpty4} +\begin{paste}{IntNumberTheoryFnsXmpPageEmpty4}{IntNumberTheoryFnsXmpPagePatch4} +\pastebutton{IntNumberTheoryFnsXmpPageEmpty4}{\showpaste} +\tab{5}\spadcommand{numberOfDivisors(144)} +\end{paste}\end{patch} + +\begin{patch}{IntNumberTheoryFnsXmpPagePatch5} +\begin{paste}{IntNumberTheoryFnsXmpPageFull5}{IntNumberTheoryFnsXmpPageEmpty5} +\pastebutton{IntNumberTheoryFnsXmpPageFull5}{\hidepaste} +\tab{5}\spadcommand{sumOfDivisors(144)} +\indentrel{3}\begin{verbatim} + (5) 403 + Type: PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{IntNumberTheoryFnsXmpPageEmpty5} +\begin{paste}{IntNumberTheoryFnsXmpPageEmpty5}{IntNumberTheoryFnsXmpPagePatch5} +\pastebutton{IntNumberTheoryFnsXmpPageEmpty5}{\showpaste} +\tab{5}\spadcommand{sumOfDivisors(144)} +\end{paste}\end{patch} + +\begin{patch}{IntNumberTheoryFnsXmpPagePatch6} +\begin{paste}{IntNumberTheoryFnsXmpPageFull6}{IntNumberTheoryFnsXmpPageEmpty6} +\pastebutton{IntNumberTheoryFnsXmpPageFull6}{\hidepaste} +\tab{5}\spadcommand{f1(n) == reduce(+,[moebiusMu(d) * numberOfDivisors(quo(n,d)) for d in divisors(n)])\bound{f1 }} +\indentrel{3}\begin{verbatim} + Type: Void +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{IntNumberTheoryFnsXmpPageEmpty6} +\begin{paste}{IntNumberTheoryFnsXmpPageEmpty6}{IntNumberTheoryFnsXmpPagePatch6} +\pastebutton{IntNumberTheoryFnsXmpPageEmpty6}{\showpaste} +\tab{5}\spadcommand{f1(n) == reduce(+,[moebiusMu(d) * numberOfDivisors(quo(n,d)) for d in divisors(n)])\bound{f1 }} +\end{paste}\end{patch} + +\begin{patch}{IntNumberTheoryFnsXmpPagePatch7} +\begin{paste}{IntNumberTheoryFnsXmpPageFull7}{IntNumberTheoryFnsXmpPageEmpty7} +\pastebutton{IntNumberTheoryFnsXmpPageFull7}{\hidepaste} +\tab{5}\spadcommand{f1(200)\free{f1 }} +\indentrel{3}\begin{verbatim} + (7) 1 + Type: PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{IntNumberTheoryFnsXmpPageEmpty7} +\begin{paste}{IntNumberTheoryFnsXmpPageEmpty7}{IntNumberTheoryFnsXmpPagePatch7} +\pastebutton{IntNumberTheoryFnsXmpPageEmpty7}{\showpaste} +\tab{5}\spadcommand{f1(200)\free{f1 }} +\end{paste}\end{patch} + +\begin{patch}{IntNumberTheoryFnsXmpPagePatch8} +\begin{paste}{IntNumberTheoryFnsXmpPageFull8}{IntNumberTheoryFnsXmpPageEmpty8} +\pastebutton{IntNumberTheoryFnsXmpPageFull8}{\hidepaste} +\tab{5}\spadcommand{f1(846)\free{f1 }} +\indentrel{3}\begin{verbatim} + (8) 1 + Type: PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{IntNumberTheoryFnsXmpPageEmpty8} +\begin{paste}{IntNumberTheoryFnsXmpPageEmpty8}{IntNumberTheoryFnsXmpPagePatch8} +\pastebutton{IntNumberTheoryFnsXmpPageEmpty8}{\showpaste} +\tab{5}\spadcommand{f1(846)\free{f1 }} +\end{paste}\end{patch} + +\begin{patch}{IntNumberTheoryFnsXmpPagePatch9} +\begin{paste}{IntNumberTheoryFnsXmpPageFull9}{IntNumberTheoryFnsXmpPageEmpty9} +\pastebutton{IntNumberTheoryFnsXmpPageFull9}{\hidepaste} +\tab{5}\spadcommand{f2(n) == reduce(+,[moebiusMu(d) * sumOfDivisors(quo(n,d)) for d in divisors(n)])\bound{f2 }} +\indentrel{3}\begin{verbatim} + Type: Void +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{IntNumberTheoryFnsXmpPageEmpty9} +\begin{paste}{IntNumberTheoryFnsXmpPageEmpty9}{IntNumberTheoryFnsXmpPagePatch9} +\pastebutton{IntNumberTheoryFnsXmpPageEmpty9}{\showpaste} +\tab{5}\spadcommand{f2(n) == reduce(+,[moebiusMu(d) * sumOfDivisors(quo(n,d)) for d in divisors(n)])\bound{f2 }} +\end{paste}\end{patch} + +\begin{patch}{IntNumberTheoryFnsXmpPagePatch10} +\begin{paste}{IntNumberTheoryFnsXmpPageFull10}{IntNumberTheoryFnsXmpPageEmpty10} +\pastebutton{IntNumberTheoryFnsXmpPageFull10}{\hidepaste} +\tab{5}\spadcommand{f2(200)\free{f2 }} +\indentrel{3}\begin{verbatim} + (10) 200 + Type: PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{IntNumberTheoryFnsXmpPageEmpty10} +\begin{paste}{IntNumberTheoryFnsXmpPageEmpty10}{IntNumberTheoryFnsXmpPagePatch10} +\pastebutton{IntNumberTheoryFnsXmpPageEmpty10}{\showpaste} +\tab{5}\spadcommand{f2(200)\free{f2 }} +\end{paste}\end{patch} + +\begin{patch}{IntNumberTheoryFnsXmpPagePatch11} +\begin{paste}{IntNumberTheoryFnsXmpPageFull11}{IntNumberTheoryFnsXmpPageEmpty11} +\pastebutton{IntNumberTheoryFnsXmpPageFull11}{\hidepaste} +\tab{5}\spadcommand{f2(846)\free{f2 }} +\indentrel{3}\begin{verbatim} + (11) 846 + Type: PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{IntNumberTheoryFnsXmpPageEmpty11} +\begin{paste}{IntNumberTheoryFnsXmpPageEmpty11}{IntNumberTheoryFnsXmpPagePatch11} +\pastebutton{IntNumberTheoryFnsXmpPageEmpty11}{\showpaste} +\tab{5}\spadcommand{f2(846)\free{f2 }} +\end{paste}\end{patch} + +\begin{patch}{IntNumberTheoryFnsXmpPagePatch12} +\begin{paste}{IntNumberTheoryFnsXmpPageFull12}{IntNumberTheoryFnsXmpPageEmpty12} +\pastebutton{IntNumberTheoryFnsXmpPageFull12}{\hidepaste} +\tab{5}\spadcommand{fibonacci(25)} +\indentrel{3}\begin{verbatim} + (12) 75025 + Type: PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{IntNumberTheoryFnsXmpPageEmpty12} +\begin{paste}{IntNumberTheoryFnsXmpPageEmpty12}{IntNumberTheoryFnsXmpPagePatch12} +\pastebutton{IntNumberTheoryFnsXmpPageEmpty12}{\showpaste} +\tab{5}\spadcommand{fibonacci(25)} +\end{paste}\end{patch} + +\begin{patch}{IntNumberTheoryFnsXmpPagePatch13} +\begin{paste}{IntNumberTheoryFnsXmpPageFull13}{IntNumberTheoryFnsXmpPageEmpty13} +\pastebutton{IntNumberTheoryFnsXmpPageFull13}{\hidepaste} +\tab{5}\spadcommand{[fibonacci(n) for n in 1..15]} +\indentrel{3}\begin{verbatim} + (13) [1,1,2,3,5,8,13,21,34,55,89,144,233,377,610] + Type: List Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{IntNumberTheoryFnsXmpPageEmpty13} +\begin{paste}{IntNumberTheoryFnsXmpPageEmpty13}{IntNumberTheoryFnsXmpPagePatch13} +\pastebutton{IntNumberTheoryFnsXmpPageEmpty13}{\showpaste} +\tab{5}\spadcommand{[fibonacci(n) for n in 1..15]} +\end{paste}\end{patch} + +\begin{patch}{IntNumberTheoryFnsXmpPagePatch14} +\begin{paste}{IntNumberTheoryFnsXmpPageFull14}{IntNumberTheoryFnsXmpPageEmpty14} +\pastebutton{IntNumberTheoryFnsXmpPageFull14}{\hidepaste} +\tab{5}\spadcommand{fib(n) == reduce(+,[binomial(n-1-k,k) for k in 0..quo(n-1,2)])\bound{fib }} +\indentrel{3}\begin{verbatim} + Type: Void +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{IntNumberTheoryFnsXmpPageEmpty14} +\begin{paste}{IntNumberTheoryFnsXmpPageEmpty14}{IntNumberTheoryFnsXmpPagePatch14} +\pastebutton{IntNumberTheoryFnsXmpPageEmpty14}{\showpaste} +\tab{5}\spadcommand{fib(n) == reduce(+,[binomial(n-1-k,k) for k in 0..quo(n-1,2)])\bound{fib }} +\end{paste}\end{patch} + +\begin{patch}{IntNumberTheoryFnsXmpPagePatch15} +\begin{paste}{IntNumberTheoryFnsXmpPageFull15}{IntNumberTheoryFnsXmpPageEmpty15} +\pastebutton{IntNumberTheoryFnsXmpPageFull15}{\hidepaste} +\tab{5}\spadcommand{fib(25)\free{fib }} +\indentrel{3}\begin{verbatim} + (15) 75025 + Type: PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{IntNumberTheoryFnsXmpPageEmpty15} +\begin{paste}{IntNumberTheoryFnsXmpPageEmpty15}{IntNumberTheoryFnsXmpPagePatch15} +\pastebutton{IntNumberTheoryFnsXmpPageEmpty15}{\showpaste} +\tab{5}\spadcommand{fib(25)\free{fib }} +\end{paste}\end{patch} + +\begin{patch}{IntNumberTheoryFnsXmpPagePatch16} +\begin{paste}{IntNumberTheoryFnsXmpPageFull16}{IntNumberTheoryFnsXmpPageEmpty16} +\pastebutton{IntNumberTheoryFnsXmpPageFull16}{\hidepaste} +\tab{5}\spadcommand{[fib(n) for n in 1..15]\free{fib }} +\indentrel{3}\begin{verbatim} + (16) [1,1,2,3,5,8,13,21,34,55,89,144,233,377,610] + Type: List Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{IntNumberTheoryFnsXmpPageEmpty16} +\begin{paste}{IntNumberTheoryFnsXmpPageEmpty16}{IntNumberTheoryFnsXmpPagePatch16} +\pastebutton{IntNumberTheoryFnsXmpPageEmpty16}{\showpaste} +\tab{5}\spadcommand{[fib(n) for n in 1..15]\free{fib }} +\end{paste}\end{patch} + +\begin{patch}{IntNumberTheoryFnsXmpPagePatch17} +\begin{paste}{IntNumberTheoryFnsXmpPageFull17}{IntNumberTheoryFnsXmpPageEmpty17} +\pastebutton{IntNumberTheoryFnsXmpPageFull17}{\hidepaste} +\tab{5}\spadcommand{legendre(3,5)} +\indentrel{3}\begin{verbatim} + (17) - 1 + Type: Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{IntNumberTheoryFnsXmpPageEmpty17} +\begin{paste}{IntNumberTheoryFnsXmpPageEmpty17}{IntNumberTheoryFnsXmpPagePatch17} +\pastebutton{IntNumberTheoryFnsXmpPageEmpty17}{\showpaste} +\tab{5}\spadcommand{legendre(3,5)} +\end{paste}\end{patch} + +\begin{patch}{IntNumberTheoryFnsXmpPagePatch18} +\begin{paste}{IntNumberTheoryFnsXmpPageFull18}{IntNumberTheoryFnsXmpPageEmpty18} +\pastebutton{IntNumberTheoryFnsXmpPageFull18}{\hidepaste} +\tab{5}\spadcommand{legendre(23,691)} +\indentrel{3}\begin{verbatim} + (18) - 1 + Type: Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{IntNumberTheoryFnsXmpPageEmpty18} +\begin{paste}{IntNumberTheoryFnsXmpPageEmpty18}{IntNumberTheoryFnsXmpPagePatch18} +\pastebutton{IntNumberTheoryFnsXmpPageEmpty18}{\showpaste} +\tab{5}\spadcommand{legendre(23,691)} +\end{paste}\end{patch} + +\begin{patch}{IntNumberTheoryFnsXmpPagePatch19} +\begin{paste}{IntNumberTheoryFnsXmpPageFull19}{IntNumberTheoryFnsXmpPageEmpty19} +\pastebutton{IntNumberTheoryFnsXmpPageFull19}{\hidepaste} +\tab{5}\spadcommand{h(d) == quo(reduce(+, [jacobi(d,k) for k in 1..quo(-d, 2)]), 2 - jacobi(d,2))\bound{h }} +\indentrel{3}\begin{verbatim} + Type: Void +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{IntNumberTheoryFnsXmpPageEmpty19} +\begin{paste}{IntNumberTheoryFnsXmpPageEmpty19}{IntNumberTheoryFnsXmpPagePatch19} +\pastebutton{IntNumberTheoryFnsXmpPageEmpty19}{\showpaste} +\tab{5}\spadcommand{h(d) == quo(reduce(+, [jacobi(d,k) for k in 1..quo(-d, 2)]), 2 - jacobi(d,2))\bound{h }} +\end{paste}\end{patch} + +\begin{patch}{IntNumberTheoryFnsXmpPagePatch20} +\begin{paste}{IntNumberTheoryFnsXmpPageFull20}{IntNumberTheoryFnsXmpPageEmpty20} +\pastebutton{IntNumberTheoryFnsXmpPageFull20}{\hidepaste} +\tab{5}\spadcommand{h(-163)\free{h }} +\indentrel{3}\begin{verbatim} + (20) 1 + Type: PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{IntNumberTheoryFnsXmpPageEmpty20} +\begin{paste}{IntNumberTheoryFnsXmpPageEmpty20}{IntNumberTheoryFnsXmpPagePatch20} +\pastebutton{IntNumberTheoryFnsXmpPageEmpty20}{\showpaste} +\tab{5}\spadcommand{h(-163)\free{h }} +\end{paste}\end{patch} + +\begin{patch}{IntNumberTheoryFnsXmpPagePatch21} +\begin{paste}{IntNumberTheoryFnsXmpPageFull21}{IntNumberTheoryFnsXmpPageEmpty21} +\pastebutton{IntNumberTheoryFnsXmpPageFull21}{\hidepaste} +\tab{5}\spadcommand{h(-499)\free{h }} +\indentrel{3}\begin{verbatim} + (21) 3 + Type: PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{IntNumberTheoryFnsXmpPageEmpty21} +\begin{paste}{IntNumberTheoryFnsXmpPageEmpty21}{IntNumberTheoryFnsXmpPagePatch21} +\pastebutton{IntNumberTheoryFnsXmpPageEmpty21}{\showpaste} +\tab{5}\spadcommand{h(-499)\free{h }} +\end{paste}\end{patch} + +\begin{patch}{IntNumberTheoryFnsXmpPagePatch22} +\begin{paste}{IntNumberTheoryFnsXmpPageFull22}{IntNumberTheoryFnsXmpPageEmpty22} +\pastebutton{IntNumberTheoryFnsXmpPageFull22}{\hidepaste} +\tab{5}\spadcommand{h(-1832)\free{h }} +\indentrel{3}\begin{verbatim} + (22) 26 + Type: PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{IntNumberTheoryFnsXmpPageEmpty22} +\begin{paste}{IntNumberTheoryFnsXmpPageEmpty22}{IntNumberTheoryFnsXmpPagePatch22} +\pastebutton{IntNumberTheoryFnsXmpPageEmpty22}{\showpaste} +\tab{5}\spadcommand{h(-1832)\free{h }} +\end{paste}\end{patch} + @ \section{kafile.ht} \pagehead{KeyedAccessFileXmpPage}{kafile.ht}{KeyedAccessFile} @@ -11879,6 +30619,341 @@ For more information on related topics, see \autobuttons \end{page} +\begin{patch}{KeyedAccessFileXmpPagePatch1} +\begin{paste}{KeyedAccessFileXmpPageFull1}{KeyedAccessFileXmpPageEmpty1} +\pastebutton{KeyedAccessFileXmpPageFull1}{\hidepaste} +\tab{5}\spadcommand{ey: KeyedAccessFile(Integer) := open("/tmp/editor.year", "output")\bound{ey }} +\indentrel{3}\begin{verbatim} + (1) "/tmp/editor.year" + Type: KeyedAccessFile Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{KeyedAccessFileXmpPageEmpty1} +\begin{paste}{KeyedAccessFileXmpPageEmpty1}{KeyedAccessFileXmpPagePatch1} +\pastebutton{KeyedAccessFileXmpPageEmpty1}{\showpaste} +\tab{5}\spadcommand{ey: KeyedAccessFile(Integer) := open("/tmp/editor.year", "output")\bound{ey }} +\end{paste}\end{patch} + +\begin{patch}{KeyedAccessFileXmpPagePatch2} +\begin{paste}{KeyedAccessFileXmpPageFull2}{KeyedAccessFileXmpPageEmpty2} +\pastebutton{KeyedAccessFileXmpPageFull2}{\hidepaste} +\tab{5}\spadcommand{ey."Char" := 1986\free{ey }\bound{eya }} +\indentrel{3}\begin{verbatim} + (2) 1986 + Type: PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{KeyedAccessFileXmpPageEmpty2} +\begin{paste}{KeyedAccessFileXmpPageEmpty2}{KeyedAccessFileXmpPagePatch2} +\pastebutton{KeyedAccessFileXmpPageEmpty2}{\showpaste} +\tab{5}\spadcommand{ey."Char" := 1986\free{ey }\bound{eya }} +\end{paste}\end{patch} + +\begin{patch}{KeyedAccessFileXmpPagePatch3} +\begin{paste}{KeyedAccessFileXmpPageFull3}{KeyedAccessFileXmpPageEmpty3} +\pastebutton{KeyedAccessFileXmpPageFull3}{\hidepaste} +\tab{5}\spadcommand{ey."Caviness" := 1985\free{ey }\bound{eyb }} +\indentrel{3}\begin{verbatim} + (3) 1985 + Type: PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{KeyedAccessFileXmpPageEmpty3} +\begin{paste}{KeyedAccessFileXmpPageEmpty3}{KeyedAccessFileXmpPagePatch3} +\pastebutton{KeyedAccessFileXmpPageEmpty3}{\showpaste} +\tab{5}\spadcommand{ey."Caviness" := 1985\free{ey }\bound{eyb }} +\end{paste}\end{patch} + +\begin{patch}{KeyedAccessFileXmpPagePatch4} +\begin{paste}{KeyedAccessFileXmpPageFull4}{KeyedAccessFileXmpPageEmpty4} +\pastebutton{KeyedAccessFileXmpPageFull4}{\hidepaste} +\tab{5}\spadcommand{ey."Fitch" := 1984\free{ey }\bound{eyc }} +\indentrel{3}\begin{verbatim} + (4) 1984 + Type: PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{KeyedAccessFileXmpPageEmpty4} +\begin{paste}{KeyedAccessFileXmpPageEmpty4}{KeyedAccessFileXmpPagePatch4} +\pastebutton{KeyedAccessFileXmpPageEmpty4}{\showpaste} +\tab{5}\spadcommand{ey."Fitch" := 1984\free{ey }\bound{eyc }} +\end{paste}\end{patch} + +\begin{patch}{KeyedAccessFileXmpPagePatch5} +\begin{paste}{KeyedAccessFileXmpPageFull5}{KeyedAccessFileXmpPageEmpty5} +\pastebutton{KeyedAccessFileXmpPageFull5}{\hidepaste} +\tab{5}\spadcommand{ey."Char"\free{eya }} +\indentrel{3}\begin{verbatim} + (5) 1986 + Type: PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{KeyedAccessFileXmpPageEmpty5} +\begin{paste}{KeyedAccessFileXmpPageEmpty5}{KeyedAccessFileXmpPagePatch5} +\pastebutton{KeyedAccessFileXmpPageEmpty5}{\showpaste} +\tab{5}\spadcommand{ey."Char"\free{eya }} +\end{paste}\end{patch} + +\begin{patch}{KeyedAccessFileXmpPagePatch6} +\begin{paste}{KeyedAccessFileXmpPageFull6}{KeyedAccessFileXmpPageEmpty6} +\pastebutton{KeyedAccessFileXmpPageFull6}{\hidepaste} +\tab{5}\spadcommand{ey("Char")\free{eya }} +\indentrel{3}\begin{verbatim} + (6) 1986 + Type: PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{KeyedAccessFileXmpPageEmpty6} +\begin{paste}{KeyedAccessFileXmpPageEmpty6}{KeyedAccessFileXmpPagePatch6} +\pastebutton{KeyedAccessFileXmpPageEmpty6}{\showpaste} +\tab{5}\spadcommand{ey("Char")\free{eya }} +\end{paste}\end{patch} + +\begin{patch}{KeyedAccessFileXmpPagePatch7} +\begin{paste}{KeyedAccessFileXmpPageFull7}{KeyedAccessFileXmpPageEmpty7} +\pastebutton{KeyedAccessFileXmpPageFull7}{\hidepaste} +\tab{5}\spadcommand{ey "Char"\free{eya }} +\indentrel{3}\begin{verbatim} + (7) 1986 + Type: PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{KeyedAccessFileXmpPageEmpty7} +\begin{paste}{KeyedAccessFileXmpPageEmpty7}{KeyedAccessFileXmpPagePatch7} +\pastebutton{KeyedAccessFileXmpPageEmpty7}{\showpaste} +\tab{5}\spadcommand{ey "Char"\free{eya }} +\end{paste}\end{patch} + +\begin{patch}{KeyedAccessFileXmpPagePatch8} +\begin{paste}{KeyedAccessFileXmpPageFull8}{KeyedAccessFileXmpPageEmpty8} +\pastebutton{KeyedAccessFileXmpPageFull8}{\hidepaste} +\tab{5}\spadcommand{search("Char", ey)\free{eya eyb eyc }\bound{eyaa }} +\indentrel{3}\begin{verbatim} + (8) 1986 + Type: Union(Integer,...) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{KeyedAccessFileXmpPageEmpty8} +\begin{paste}{KeyedAccessFileXmpPageEmpty8}{KeyedAccessFileXmpPagePatch8} +\pastebutton{KeyedAccessFileXmpPageEmpty8}{\showpaste} +\tab{5}\spadcommand{search("Char", ey)\free{eya eyb eyc }\bound{eyaa }} +\end{paste}\end{patch} + +\begin{patch}{KeyedAccessFileXmpPagePatch9} +\begin{paste}{KeyedAccessFileXmpPageFull9}{KeyedAccessFileXmpPageEmpty9} +\pastebutton{KeyedAccessFileXmpPageFull9}{\hidepaste} +\tab{5}\spadcommand{search("Smith", ey)\free{eyaa }} +\indentrel{3}\begin{verbatim} + (9) "failed" + Type: Union("failed",...) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{KeyedAccessFileXmpPageEmpty9} +\begin{paste}{KeyedAccessFileXmpPageEmpty9}{KeyedAccessFileXmpPagePatch9} +\pastebutton{KeyedAccessFileXmpPageEmpty9}{\showpaste} +\tab{5}\spadcommand{search("Smith", ey)\free{eyaa }} +\end{paste}\end{patch} + +\begin{patch}{KeyedAccessFileXmpPagePatch10} +\begin{paste}{KeyedAccessFileXmpPageFull10}{KeyedAccessFileXmpPageEmpty10} +\pastebutton{KeyedAccessFileXmpPageFull10}{\hidepaste} +\tab{5}\spadcommand{remove!("Char", ey)\free{eyaa }\bound{eybb }} +\indentrel{3}\begin{verbatim} + (10) 1986 + Type: Union(Integer,...) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{KeyedAccessFileXmpPageEmpty10} +\begin{paste}{KeyedAccessFileXmpPageEmpty10}{KeyedAccessFileXmpPagePatch10} +\pastebutton{KeyedAccessFileXmpPageEmpty10}{\showpaste} +\tab{5}\spadcommand{remove!("Char", ey)\free{eyaa }\bound{eybb }} +\end{paste}\end{patch} + +\begin{patch}{KeyedAccessFileXmpPagePatch11} +\begin{paste}{KeyedAccessFileXmpPageFull11}{KeyedAccessFileXmpPageEmpty11} +\pastebutton{KeyedAccessFileXmpPageFull11}{\hidepaste} +\tab{5}\spadcommand{keys ey\free{eybb }} +\indentrel{3}\begin{verbatim} + (11) ["Fitch","Caviness"] + Type: List String +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{KeyedAccessFileXmpPageEmpty11} +\begin{paste}{KeyedAccessFileXmpPageEmpty11}{KeyedAccessFileXmpPagePatch11} +\pastebutton{KeyedAccessFileXmpPageEmpty11}{\showpaste} +\tab{5}\spadcommand{keys ey\free{eybb }} +\end{paste}\end{patch} + +\begin{patch}{KeyedAccessFileXmpPagePatch12} +\begin{paste}{KeyedAccessFileXmpPageFull12}{KeyedAccessFileXmpPageEmpty12} +\pastebutton{KeyedAccessFileXmpPageFull12}{\hidepaste} +\tab{5}\spadcommand{\#ey\free{eybb }} +\indentrel{3}\begin{verbatim} + (12) 2 + Type: PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{KeyedAccessFileXmpPageEmpty12} +\begin{paste}{KeyedAccessFileXmpPageEmpty12}{KeyedAccessFileXmpPagePatch12} +\pastebutton{KeyedAccessFileXmpPageEmpty12}{\showpaste} +\tab{5}\spadcommand{\#ey\free{eybb }} +\end{paste}\end{patch} + +\begin{patch}{KeyedAccessFileXmpPagePatch13} +\begin{paste}{KeyedAccessFileXmpPageFull13}{KeyedAccessFileXmpPageEmpty13} +\pastebutton{KeyedAccessFileXmpPageFull13}{\hidepaste} +\tab{5}\spadcommand{KE := Record(key: String, entry: Integer)\bound{KE }} +\indentrel{3}\begin{verbatim} + (13) Record(key: String,entry: Integer) + Type: Domain +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{KeyedAccessFileXmpPageEmpty13} +\begin{paste}{KeyedAccessFileXmpPageEmpty13}{KeyedAccessFileXmpPagePatch13} +\pastebutton{KeyedAccessFileXmpPageEmpty13}{\showpaste} +\tab{5}\spadcommand{KE := Record(key: String, entry: Integer)\bound{KE }} +\end{paste}\end{patch} + +\begin{patch}{KeyedAccessFileXmpPagePatch14} +\begin{paste}{KeyedAccessFileXmpPageFull14}{KeyedAccessFileXmpPageEmpty14} +\pastebutton{KeyedAccessFileXmpPageFull14}{\hidepaste} +\tab{5}\spadcommand{reopen!(ey, "output")\free{eybb KE }\bound{eycc }} +\indentrel{3}\begin{verbatim} + (14) "/tmp/editor.year" + Type: KeyedAccessFile Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{KeyedAccessFileXmpPageEmpty14} +\begin{paste}{KeyedAccessFileXmpPageEmpty14}{KeyedAccessFileXmpPagePatch14} +\pastebutton{KeyedAccessFileXmpPageEmpty14}{\showpaste} +\tab{5}\spadcommand{reopen!(ey, "output")\free{eybb KE }\bound{eycc }} +\end{paste}\end{patch} + +\begin{patch}{KeyedAccessFileXmpPagePatch15} +\begin{paste}{KeyedAccessFileXmpPageFull15}{KeyedAccessFileXmpPageEmpty15} +\pastebutton{KeyedAccessFileXmpPageFull15}{\hidepaste} +\tab{5}\spadcommand{write!(ey, ["van Hulzen", 1983]$KE)\bound{eyccA }\free{eycc }} +\indentrel{3}\begin{verbatim} + (15) [key= "van Hulzen",entry= 1983] + Type: Record(key: String,entry: Integer) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{KeyedAccessFileXmpPageEmpty15} +\begin{paste}{KeyedAccessFileXmpPageEmpty15}{KeyedAccessFileXmpPagePatch15} +\pastebutton{KeyedAccessFileXmpPageEmpty15}{\showpaste} +\tab{5}\spadcommand{write!(ey, ["van Hulzen", 1983]$KE)\bound{eyccA }\free{eycc }} +\end{paste}\end{patch} + +\begin{patch}{KeyedAccessFileXmpPagePatch16} +\begin{paste}{KeyedAccessFileXmpPageFull16}{KeyedAccessFileXmpPageEmpty16} +\pastebutton{KeyedAccessFileXmpPageFull16}{\hidepaste} +\tab{5}\spadcommand{write!(ey, ["Calmet", 1982]$KE)\bound{eyccB }\free{eycc }} +\indentrel{3}\begin{verbatim} + (16) [key= "Calmet",entry= 1982] + Type: Record(key: String,entry: Integer) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{KeyedAccessFileXmpPageEmpty16} +\begin{paste}{KeyedAccessFileXmpPageEmpty16}{KeyedAccessFileXmpPagePatch16} +\pastebutton{KeyedAccessFileXmpPageEmpty16}{\showpaste} +\tab{5}\spadcommand{write!(ey, ["Calmet", 1982]$KE)\bound{eyccB }\free{eycc }} +\end{paste}\end{patch} + +\begin{patch}{KeyedAccessFileXmpPagePatch17} +\begin{paste}{KeyedAccessFileXmpPageFull17}{KeyedAccessFileXmpPageEmpty17} +\pastebutton{KeyedAccessFileXmpPageFull17}{\hidepaste} +\tab{5}\spadcommand{write!(ey, ["Wang", 1981]$KE)\bound{eyccC }\free{eycc }} +\indentrel{3}\begin{verbatim} + (17) [key= "Wang",entry= 1981] + Type: Record(key: String,entry: Integer) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{KeyedAccessFileXmpPageEmpty17} +\begin{paste}{KeyedAccessFileXmpPageEmpty17}{KeyedAccessFileXmpPagePatch17} +\pastebutton{KeyedAccessFileXmpPageEmpty17}{\showpaste} +\tab{5}\spadcommand{write!(ey, ["Wang", 1981]$KE)\bound{eyccC }\free{eycc }} +\end{paste}\end{patch} + +\begin{patch}{KeyedAccessFileXmpPagePatch18} +\begin{paste}{KeyedAccessFileXmpPageFull18}{KeyedAccessFileXmpPageEmpty18} +\pastebutton{KeyedAccessFileXmpPageFull18}{\hidepaste} +\tab{5}\spadcommand{close! ey\free{eyccA eyccB eyccC }\bound{eydd }} +\indentrel{3}\begin{verbatim} + (18) "/tmp/editor.year" + Type: KeyedAccessFile Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{KeyedAccessFileXmpPageEmpty18} +\begin{paste}{KeyedAccessFileXmpPageEmpty18}{KeyedAccessFileXmpPagePatch18} +\pastebutton{KeyedAccessFileXmpPageEmpty18}{\showpaste} +\tab{5}\spadcommand{close! ey\free{eyccA eyccB eyccC }\bound{eydd }} +\end{paste}\end{patch} + +\begin{patch}{KeyedAccessFileXmpPagePatch19} +\begin{paste}{KeyedAccessFileXmpPageFull19}{KeyedAccessFileXmpPageEmpty19} +\pastebutton{KeyedAccessFileXmpPageFull19}{\hidepaste} +\tab{5}\spadcommand{keys ey\free{eydd }} +\indentrel{3}\begin{verbatim} + (19) + ["Wang","Calmet","van Hulzen","Fitch","Caviness"] + Type: List String +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{KeyedAccessFileXmpPageEmpty19} +\begin{paste}{KeyedAccessFileXmpPageEmpty19}{KeyedAccessFileXmpPagePatch19} +\pastebutton{KeyedAccessFileXmpPageEmpty19}{\showpaste} +\tab{5}\spadcommand{keys ey\free{eydd }} +\end{paste}\end{patch} + +\begin{patch}{KeyedAccessFileXmpPagePatch20} +\begin{paste}{KeyedAccessFileXmpPageFull20}{KeyedAccessFileXmpPageEmpty20} +\pastebutton{KeyedAccessFileXmpPageFull20}{\hidepaste} +\tab{5}\spadcommand{members ey\free{eydd }} +\indentrel{3}\begin{verbatim} + (20) [1981,1982,1983,1984,1985] + Type: List Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{KeyedAccessFileXmpPageEmpty20} +\begin{paste}{KeyedAccessFileXmpPageEmpty20}{KeyedAccessFileXmpPagePatch20} +\pastebutton{KeyedAccessFileXmpPageEmpty20}{\showpaste} +\tab{5}\spadcommand{members ey\free{eydd }} +\end{paste}\end{patch} + +\begin{patch}{KeyedAccessFileXmpPagePatch21} +\begin{paste}{KeyedAccessFileXmpPageFull21}{KeyedAccessFileXmpPageEmpty21} +\pastebutton{KeyedAccessFileXmpPageFull21}{\hidepaste} +\tab{5}\spadcommand{)system rm -r /tmp/editor.year\free{ey }} +\indentrel{3}\begin{verbatim} +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{KeyedAccessFileXmpPageEmpty21} +\begin{paste}{KeyedAccessFileXmpPageEmpty21}{KeyedAccessFileXmpPagePatch21} +\pastebutton{KeyedAccessFileXmpPageEmpty21}{\showpaste} +\tab{5}\spadcommand{)system rm -r /tmp/editor.year\free{ey }} +\end{paste}\end{patch} + @ \section{kernel.ht} \pagehead{KernelXmpPage}{kernel.ht}{Kernel} @@ -12023,6 +31098,311 @@ take apart expression objects. \autobuttons \end{page} +\begin{patch}{KernelXmpPagePatch1} +\begin{paste}{KernelXmpPageFull1}{KernelXmpPageEmpty1} +\pastebutton{KernelXmpPageFull1}{\hidepaste} +\tab{5}\spadcommand{x :: Expression Integer} +\indentrel{3}\begin{verbatim} + (1) x + Type: Expression Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{KernelXmpPageEmpty1} +\begin{paste}{KernelXmpPageEmpty1}{KernelXmpPagePatch1} +\pastebutton{KernelXmpPageEmpty1}{\showpaste} +\tab{5}\spadcommand{x :: Expression Integer} +\end{paste}\end{patch} + +\begin{patch}{KernelXmpPagePatch2} +\begin{paste}{KernelXmpPageFull2}{KernelXmpPageEmpty2} +\pastebutton{KernelXmpPageFull2}{\hidepaste} +\tab{5}\spadcommand{kernel x} +\indentrel{3}\begin{verbatim} + (2) x + Type: Kernel Expression Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{KernelXmpPageEmpty2} +\begin{paste}{KernelXmpPageEmpty2}{KernelXmpPagePatch2} +\pastebutton{KernelXmpPageEmpty2}{\showpaste} +\tab{5}\spadcommand{kernel x} +\end{paste}\end{patch} + +\begin{patch}{KernelXmpPagePatch3} +\begin{paste}{KernelXmpPageFull3}{KernelXmpPageEmpty3} +\pastebutton{KernelXmpPageFull3}{\hidepaste} +\tab{5}\spadcommand{sin(x) + cos(x)\bound{sincos }} +\indentrel{3}\begin{verbatim} + (3) sin(x) + cos(x) + Type: Expression Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{KernelXmpPageEmpty3} +\begin{paste}{KernelXmpPageEmpty3}{KernelXmpPagePatch3} +\pastebutton{KernelXmpPageEmpty3}{\showpaste} +\tab{5}\spadcommand{sin(x) + cos(x)\bound{sincos }} +\end{paste}\end{patch} + +\begin{patch}{KernelXmpPagePatch4} +\begin{paste}{KernelXmpPageFull4}{KernelXmpPageEmpty4} +\pastebutton{KernelXmpPageFull4}{\hidepaste} +\tab{5}\spadcommand{kernels \%\free{sincos }} +\indentrel{3}\begin{verbatim} + (4) [sin(x),cos(x)] + Type: List Kernel Expression Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{KernelXmpPageEmpty4} +\begin{paste}{KernelXmpPageEmpty4}{KernelXmpPagePatch4} +\pastebutton{KernelXmpPageEmpty4}{\showpaste} +\tab{5}\spadcommand{kernels \%\free{sincos }} +\end{paste}\end{patch} + +\begin{patch}{KernelXmpPagePatch5} +\begin{paste}{KernelXmpPageFull5}{KernelXmpPageEmpty5} +\pastebutton{KernelXmpPageFull5}{\hidepaste} +\tab{5}\spadcommand{sin(x)**2 + sin(x) + cos(x)\bound{sincos2 }} +\indentrel{3}\begin{verbatim} + 2 + (5) sin(x) + sin(x) + cos(x) + Type: Expression Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{KernelXmpPageEmpty5} +\begin{paste}{KernelXmpPageEmpty5}{KernelXmpPagePatch5} +\pastebutton{KernelXmpPageEmpty5}{\showpaste} +\tab{5}\spadcommand{sin(x)**2 + sin(x) + cos(x)\bound{sincos2 }} +\end{paste}\end{patch} + +\begin{patch}{KernelXmpPagePatch6} +\begin{paste}{KernelXmpPageFull6}{KernelXmpPageEmpty6} +\pastebutton{KernelXmpPageFull6}{\hidepaste} +\tab{5}\spadcommand{kernels \%\free{sincos2 }} +\indentrel{3}\begin{verbatim} + (6) [sin(x),cos(x)] + Type: List Kernel Expression Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{KernelXmpPageEmpty6} +\begin{paste}{KernelXmpPageEmpty6}{KernelXmpPagePatch6} +\pastebutton{KernelXmpPageEmpty6}{\showpaste} +\tab{5}\spadcommand{kernels \%\free{sincos2 }} +\end{paste}\end{patch} + +\begin{patch}{KernelXmpPagePatch7} +\begin{paste}{KernelXmpPageFull7}{KernelXmpPageEmpty7} +\pastebutton{KernelXmpPageFull7}{\hidepaste} +\tab{5}\spadcommand{kernels(1 :: Expression Integer)} +\indentrel{3}\begin{verbatim} + (7) [] + Type: List Kernel Expression Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{KernelXmpPageEmpty7} +\begin{paste}{KernelXmpPageEmpty7}{KernelXmpPagePatch7} +\pastebutton{KernelXmpPageEmpty7}{\showpaste} +\tab{5}\spadcommand{kernels(1 :: Expression Integer)} +\end{paste}\end{patch} + +\begin{patch}{KernelXmpPagePatch8} +\begin{paste}{KernelXmpPageFull8}{KernelXmpPageEmpty8} +\pastebutton{KernelXmpPageFull8}{\hidepaste} +\tab{5}\spadcommand{mainKernel(cos(x) + tan(x))} +\indentrel{3}\begin{verbatim} + (8) tan(x) + Type: Union(Kernel Expression Integer,...) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{KernelXmpPageEmpty8} +\begin{paste}{KernelXmpPageEmpty8}{KernelXmpPagePatch8} +\pastebutton{KernelXmpPageEmpty8}{\showpaste} +\tab{5}\spadcommand{mainKernel(cos(x) + tan(x))} +\end{paste}\end{patch} + +\begin{patch}{KernelXmpPagePatch9} +\begin{paste}{KernelXmpPageFull9}{KernelXmpPageEmpty9} +\pastebutton{KernelXmpPageFull9}{\hidepaste} +\tab{5}\spadcommand{height kernel x} +\indentrel{3}\begin{verbatim} + (9) 1 + Type: PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{KernelXmpPageEmpty9} +\begin{paste}{KernelXmpPageEmpty9}{KernelXmpPagePatch9} +\pastebutton{KernelXmpPageEmpty9}{\showpaste} +\tab{5}\spadcommand{height kernel x} +\end{paste}\end{patch} + +\begin{patch}{KernelXmpPagePatch10} +\begin{paste}{KernelXmpPageFull10}{KernelXmpPageEmpty10} +\pastebutton{KernelXmpPageFull10}{\hidepaste} +\tab{5}\spadcommand{height mainKernel(sin x)} +\indentrel{3}\begin{verbatim} + (10) 2 + Type: PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{KernelXmpPageEmpty10} +\begin{paste}{KernelXmpPageEmpty10}{KernelXmpPagePatch10} +\pastebutton{KernelXmpPageEmpty10}{\showpaste} +\tab{5}\spadcommand{height mainKernel(sin x)} +\end{paste}\end{patch} + +\begin{patch}{KernelXmpPagePatch11} +\begin{paste}{KernelXmpPageFull11}{KernelXmpPageEmpty11} +\pastebutton{KernelXmpPageFull11}{\hidepaste} +\tab{5}\spadcommand{height mainKernel(sin cos x)} +\indentrel{3}\begin{verbatim} + (11) 3 + Type: PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{KernelXmpPageEmpty11} +\begin{paste}{KernelXmpPageEmpty11}{KernelXmpPagePatch11} +\pastebutton{KernelXmpPageEmpty11}{\showpaste} +\tab{5}\spadcommand{height mainKernel(sin cos x)} +\end{paste}\end{patch} + +\begin{patch}{KernelXmpPagePatch12} +\begin{paste}{KernelXmpPageFull12}{KernelXmpPageEmpty12} +\pastebutton{KernelXmpPageFull12}{\hidepaste} +\tab{5}\spadcommand{height mainKernel(sin cos (tan x + sin x))} +\indentrel{3}\begin{verbatim} + (12) 4 + Type: PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{KernelXmpPageEmpty12} +\begin{paste}{KernelXmpPageEmpty12}{KernelXmpPagePatch12} +\pastebutton{KernelXmpPageEmpty12}{\showpaste} +\tab{5}\spadcommand{height mainKernel(sin cos (tan x + sin x))} +\end{paste}\end{patch} + +\begin{patch}{KernelXmpPagePatch13} +\begin{paste}{KernelXmpPageFull13}{KernelXmpPageEmpty13} +\pastebutton{KernelXmpPageFull13}{\hidepaste} +\tab{5}\spadcommand{operator mainKernel(sin cos (tan x + sin x))} +\indentrel{3}\begin{verbatim} + (13) sin + Type: BasicOperator +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{KernelXmpPageEmpty13} +\begin{paste}{KernelXmpPageEmpty13}{KernelXmpPagePatch13} +\pastebutton{KernelXmpPageEmpty13}{\showpaste} +\tab{5}\spadcommand{operator mainKernel(sin cos (tan x + sin x))} +\end{paste}\end{patch} + +\begin{patch}{KernelXmpPagePatch14} +\begin{paste}{KernelXmpPageFull14}{KernelXmpPageEmpty14} +\pastebutton{KernelXmpPageFull14}{\hidepaste} +\tab{5}\spadcommand{name mainKernel(sin cos (tan x + sin x))} +\indentrel{3}\begin{verbatim} + (14) sin + Type: Symbol +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{KernelXmpPageEmpty14} +\begin{paste}{KernelXmpPageEmpty14}{KernelXmpPagePatch14} +\pastebutton{KernelXmpPageEmpty14}{\showpaste} +\tab{5}\spadcommand{name mainKernel(sin cos (tan x + sin x))} +\end{paste}\end{patch} + +\begin{patch}{KernelXmpPagePatch15} +\begin{paste}{KernelXmpPageFull15}{KernelXmpPageEmpty15} +\pastebutton{KernelXmpPageFull15}{\hidepaste} +\tab{5}\spadcommand{f := operator 'f\bound{f }} +\indentrel{3}\begin{verbatim} + (15) f + Type: BasicOperator +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{KernelXmpPageEmpty15} +\begin{paste}{KernelXmpPageEmpty15}{KernelXmpPagePatch15} +\pastebutton{KernelXmpPageEmpty15}{\showpaste} +\tab{5}\spadcommand{f := operator 'f\bound{f }} +\end{paste}\end{patch} + +\begin{patch}{KernelXmpPagePatch16} +\begin{paste}{KernelXmpPageFull16}{KernelXmpPageEmpty16} +\pastebutton{KernelXmpPageFull16}{\hidepaste} +\tab{5}\spadcommand{e := f(x, y, 10)\free{f }\bound{e }} +\indentrel{3}\begin{verbatim} + (16) f(x,y,10) + Type: Expression Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{KernelXmpPageEmpty16} +\begin{paste}{KernelXmpPageEmpty16}{KernelXmpPagePatch16} +\pastebutton{KernelXmpPageEmpty16}{\showpaste} +\tab{5}\spadcommand{e := f(x, y, 10)\free{f }\bound{e }} +\end{paste}\end{patch} + +\begin{patch}{KernelXmpPagePatch17} +\begin{paste}{KernelXmpPageFull17}{KernelXmpPageEmpty17} +\pastebutton{KernelXmpPageFull17}{\hidepaste} +\tab{5}\spadcommand{is?(e, f)\free{f e }} +\indentrel{3}\begin{verbatim} + (17) true + Type: Boolean +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{KernelXmpPageEmpty17} +\begin{paste}{KernelXmpPageEmpty17}{KernelXmpPagePatch17} +\pastebutton{KernelXmpPageEmpty17}{\showpaste} +\tab{5}\spadcommand{is?(e, f)\free{f e }} +\end{paste}\end{patch} + +\begin{patch}{KernelXmpPagePatch18} +\begin{paste}{KernelXmpPageFull18}{KernelXmpPageEmpty18} +\pastebutton{KernelXmpPageFull18}{\hidepaste} +\tab{5}\spadcommand{is?(e, 'f)\free{e }} +\indentrel{3}\begin{verbatim} + (18) true + Type: Boolean +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{KernelXmpPageEmpty18} +\begin{paste}{KernelXmpPageEmpty18}{KernelXmpPagePatch18} +\pastebutton{KernelXmpPageEmpty18}{\showpaste} +\tab{5}\spadcommand{is?(e, 'f)\free{e }} +\end{paste}\end{patch} + +\begin{patch}{KernelXmpPagePatch19} +\begin{paste}{KernelXmpPageFull19}{KernelXmpPageEmpty19} +\pastebutton{KernelXmpPageFull19}{\hidepaste} +\tab{5}\spadcommand{argument mainKernel e\free{f }\free{e }} +\indentrel{3}\begin{verbatim} + (19) [x,y,10] + Type: List Expression Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{KernelXmpPageEmpty19} +\begin{paste}{KernelXmpPageEmpty19}{KernelXmpPagePatch19} +\pastebutton{KernelXmpPageEmpty19}{\showpaste} +\tab{5}\spadcommand{argument mainKernel e\free{f }\free{e }} +\end{paste}\end{patch} + @ \section{lazm3pk.ht} \pagehead{LazardSetSolvingPackageXmpPage}{lazm3pk.ht} @@ -12326,6 +31706,961 @@ components may be investigated further with the \autobuttons \end{page} +\begin{patch}{LazardSetSolvingPackageXmpPagePatch1} +\begin{paste}{LazardSetSolvingPackageXmpPageFull1}{LazardSetSolvingPackageXmpPageEmpty1} +\pastebutton{LazardSetSolvingPackageXmpPageFull1}{\hidepaste} +\tab{5}\spadcommand{R := Integer\bound{R }} +\indentrel{3}\begin{verbatim} + (1) Integer + Type: Domain +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{LazardSetSolvingPackageXmpPageEmpty1} +\begin{paste}{LazardSetSolvingPackageXmpPageEmpty1}{LazardSetSolvingPackageXmpPagePatch1} +\pastebutton{LazardSetSolvingPackageXmpPageEmpty1}{\showpaste} +\tab{5}\spadcommand{R := Integer\bound{R }} +\end{paste}\end{patch} + +\begin{patch}{LazardSetSolvingPackageXmpPagePatch2} +\begin{paste}{LazardSetSolvingPackageXmpPageFull2}{LazardSetSolvingPackageXmpPageEmpty2} +\pastebutton{LazardSetSolvingPackageXmpPageFull2}{\hidepaste} +\tab{5}\spadcommand{ls : List Symbol := [b1,x,y,z,t,v,u,w]\bound{ls }} +\indentrel{3}\begin{verbatim} + (2) [b1,x,y,z,t,v,u,w] + Type: List Symbol +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{LazardSetSolvingPackageXmpPageEmpty2} +\begin{paste}{LazardSetSolvingPackageXmpPageEmpty2}{LazardSetSolvingPackageXmpPagePatch2} +\pastebutton{LazardSetSolvingPackageXmpPageEmpty2}{\showpaste} +\tab{5}\spadcommand{ls : List Symbol := [b1,x,y,z,t,v,u,w]\bound{ls }} +\end{paste}\end{patch} + +\begin{patch}{LazardSetSolvingPackageXmpPagePatch3} +\begin{paste}{LazardSetSolvingPackageXmpPageFull3}{LazardSetSolvingPackageXmpPageEmpty3} +\pastebutton{LazardSetSolvingPackageXmpPageFull3}{\hidepaste} +\tab{5}\spadcommand{V := OVAR(ls)\free{ls }\bound{V }} +\indentrel{3}\begin{verbatim} + (3) OrderedVariableList [b1,x,y,z,t,v,u,w] + Type: Domain +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{LazardSetSolvingPackageXmpPageEmpty3} +\begin{paste}{LazardSetSolvingPackageXmpPageEmpty3}{LazardSetSolvingPackageXmpPagePatch3} +\pastebutton{LazardSetSolvingPackageXmpPageEmpty3}{\showpaste} +\tab{5}\spadcommand{V := OVAR(ls)\free{ls }\bound{V }} +\end{paste}\end{patch} + +\begin{patch}{LazardSetSolvingPackageXmpPagePatch4} +\begin{paste}{LazardSetSolvingPackageXmpPageFull4}{LazardSetSolvingPackageXmpPageEmpty4} +\pastebutton{LazardSetSolvingPackageXmpPageFull4}{\hidepaste} +\tab{5}\spadcommand{E := IndexedExponents V\free{V }\bound{E }} +\indentrel{3}\begin{verbatim} + (4) + IndexedExponents OrderedVariableList [b1,x,y,z,t,v,u,w] + Type: Domain +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{LazardSetSolvingPackageXmpPageEmpty4} +\begin{paste}{LazardSetSolvingPackageXmpPageEmpty4}{LazardSetSolvingPackageXmpPagePatch4} +\pastebutton{LazardSetSolvingPackageXmpPageEmpty4}{\showpaste} +\tab{5}\spadcommand{E := IndexedExponents V\free{V }\bound{E }} +\end{paste}\end{patch} + +\begin{patch}{LazardSetSolvingPackageXmpPagePatch5} +\begin{paste}{LazardSetSolvingPackageXmpPageFull5}{LazardSetSolvingPackageXmpPageEmpty5} +\pastebutton{LazardSetSolvingPackageXmpPageFull5}{\hidepaste} +\tab{5}\spadcommand{P := NSMP(R, V)\free{R }\free{V }\bound{P }} +\indentrel{3}\begin{verbatim} + (5) + NewSparseMultivariatePolynomial(Integer,OrderedVariable + List [b1,x,y,z,t,v,u,w]) + Type: Domain +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{LazardSetSolvingPackageXmpPageEmpty5} +\begin{paste}{LazardSetSolvingPackageXmpPageEmpty5}{LazardSetSolvingPackageXmpPagePatch5} +\pastebutton{LazardSetSolvingPackageXmpPageEmpty5}{\showpaste} +\tab{5}\spadcommand{P := NSMP(R, V)\free{R }\free{V }\bound{P }} +\end{paste}\end{patch} + +\begin{patch}{LazardSetSolvingPackageXmpPagePatch6} +\begin{paste}{LazardSetSolvingPackageXmpPageFull6}{LazardSetSolvingPackageXmpPageEmpty6} +\pastebutton{LazardSetSolvingPackageXmpPageFull6}{\hidepaste} +\tab{5}\spadcommand{b1: P := 'b1\free{P }\bound{b1 }} +\indentrel{3}\begin{verbatim} + (6) b1 +Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [b1,x,y,z,t,v,u,w]) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{LazardSetSolvingPackageXmpPageEmpty6} +\begin{paste}{LazardSetSolvingPackageXmpPageEmpty6}{LazardSetSolvingPackageXmpPagePatch6} +\pastebutton{LazardSetSolvingPackageXmpPageEmpty6}{\showpaste} +\tab{5}\spadcommand{b1: P := 'b1\free{P }\bound{b1 }} +\end{paste}\end{patch} + +\begin{patch}{LazardSetSolvingPackageXmpPagePatch7} +\begin{paste}{LazardSetSolvingPackageXmpPageFull7}{LazardSetSolvingPackageXmpPageEmpty7} +\pastebutton{LazardSetSolvingPackageXmpPageFull7}{\hidepaste} +\tab{5}\spadcommand{x: P := 'x\free{P }\bound{x }} +\indentrel{3}\begin{verbatim} + (7) x +Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [b1,x,y,z,t,v,u,w]) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{LazardSetSolvingPackageXmpPageEmpty7} +\begin{paste}{LazardSetSolvingPackageXmpPageEmpty7}{LazardSetSolvingPackageXmpPagePatch7} +\pastebutton{LazardSetSolvingPackageXmpPageEmpty7}{\showpaste} +\tab{5}\spadcommand{x: P := 'x\free{P }\bound{x }} +\end{paste}\end{patch} + +\begin{patch}{LazardSetSolvingPackageXmpPagePatch8} +\begin{paste}{LazardSetSolvingPackageXmpPageFull8}{LazardSetSolvingPackageXmpPageEmpty8} +\pastebutton{LazardSetSolvingPackageXmpPageFull8}{\hidepaste} +\tab{5}\spadcommand{y: P := 'y\free{P }\bound{y }} +\indentrel{3}\begin{verbatim} + (8) y +Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [b1,x,y,z,t,v,u,w]) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{LazardSetSolvingPackageXmpPageEmpty8} +\begin{paste}{LazardSetSolvingPackageXmpPageEmpty8}{LazardSetSolvingPackageXmpPagePatch8} +\pastebutton{LazardSetSolvingPackageXmpPageEmpty8}{\showpaste} +\tab{5}\spadcommand{y: P := 'y\free{P }\bound{y }} +\end{paste}\end{patch} + +\begin{patch}{LazardSetSolvingPackageXmpPagePatch9} +\begin{paste}{LazardSetSolvingPackageXmpPageFull9}{LazardSetSolvingPackageXmpPageEmpty9} +\pastebutton{LazardSetSolvingPackageXmpPageFull9}{\hidepaste} +\tab{5}\spadcommand{z: P := 'z\free{P }\bound{z }} +\indentrel{3}\begin{verbatim} + (9) z +Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [b1,x,y,z,t,v,u,w]) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{LazardSetSolvingPackageXmpPageEmpty9} +\begin{paste}{LazardSetSolvingPackageXmpPageEmpty9}{LazardSetSolvingPackageXmpPagePatch9} +\pastebutton{LazardSetSolvingPackageXmpPageEmpty9}{\showpaste} +\tab{5}\spadcommand{z: P := 'z\free{P }\bound{z }} +\end{paste}\end{patch} + +\begin{patch}{LazardSetSolvingPackageXmpPagePatch10} +\begin{paste}{LazardSetSolvingPackageXmpPageFull10}{LazardSetSolvingPackageXmpPageEmpty10} +\pastebutton{LazardSetSolvingPackageXmpPageFull10}{\hidepaste} +\tab{5}\spadcommand{t: P := 't\free{P }\bound{t }} +\indentrel{3}\begin{verbatim} + (10) t +Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [b1,x,y,z,t,v,u,w]) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{LazardSetSolvingPackageXmpPageEmpty10} +\begin{paste}{LazardSetSolvingPackageXmpPageEmpty10}{LazardSetSolvingPackageXmpPagePatch10} +\pastebutton{LazardSetSolvingPackageXmpPageEmpty10}{\showpaste} +\tab{5}\spadcommand{t: P := 't\free{P }\bound{t }} +\end{paste}\end{patch} + +\begin{patch}{LazardSetSolvingPackageXmpPagePatch11} +\begin{paste}{LazardSetSolvingPackageXmpPageFull11}{LazardSetSolvingPackageXmpPageEmpty11} +\pastebutton{LazardSetSolvingPackageXmpPageFull11}{\hidepaste} +\tab{5}\spadcommand{u: P := 'u\free{P }\bound{u }} +\indentrel{3}\begin{verbatim} + (11) u +Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [b1,x,y,z,t,v,u,w]) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{LazardSetSolvingPackageXmpPageEmpty11} +\begin{paste}{LazardSetSolvingPackageXmpPageEmpty11}{LazardSetSolvingPackageXmpPagePatch11} +\pastebutton{LazardSetSolvingPackageXmpPageEmpty11}{\showpaste} +\tab{5}\spadcommand{u: P := 'u\free{P }\bound{u }} +\end{paste}\end{patch} + +\begin{patch}{LazardSetSolvingPackageXmpPagePatch12} +\begin{paste}{LazardSetSolvingPackageXmpPageFull12}{LazardSetSolvingPackageXmpPageEmpty12} +\pastebutton{LazardSetSolvingPackageXmpPageFull12}{\hidepaste} +\tab{5}\spadcommand{v: P := 'v\free{P }\bound{v }} +\indentrel{3}\begin{verbatim} + (12) v +Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [b1,x,y,z,t,v,u,w]) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{LazardSetSolvingPackageXmpPageEmpty12} +\begin{paste}{LazardSetSolvingPackageXmpPageEmpty12}{LazardSetSolvingPackageXmpPagePatch12} +\pastebutton{LazardSetSolvingPackageXmpPageEmpty12}{\showpaste} +\tab{5}\spadcommand{v: P := 'v\free{P }\bound{v }} +\end{paste}\end{patch} + +\begin{patch}{LazardSetSolvingPackageXmpPagePatch13} +\begin{paste}{LazardSetSolvingPackageXmpPageFull13}{LazardSetSolvingPackageXmpPageEmpty13} +\pastebutton{LazardSetSolvingPackageXmpPageFull13}{\hidepaste} +\tab{5}\spadcommand{w: P := 'w\free{P }\bound{w }} +\indentrel{3}\begin{verbatim} + (13) w +Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [b1,x,y,z,t,v,u,w]) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{LazardSetSolvingPackageXmpPageEmpty13} +\begin{paste}{LazardSetSolvingPackageXmpPageEmpty13}{LazardSetSolvingPackageXmpPagePatch13} +\pastebutton{LazardSetSolvingPackageXmpPageEmpty13}{\showpaste} +\tab{5}\spadcommand{w: P := 'w\free{P }\bound{w }} +\end{paste}\end{patch} + +\begin{patch}{LazardSetSolvingPackageXmpPagePatch14} +\begin{paste}{LazardSetSolvingPackageXmpPageFull14}{LazardSetSolvingPackageXmpPageEmpty14} +\pastebutton{LazardSetSolvingPackageXmpPageFull14}{\hidepaste} +\tab{5}\spadcommand{T := REGSET(R,E,V,P)\free{R }\free{E }\free{V }\free{P }\bound{T }} +\indentrel{3}\begin{verbatim} + (14) + RegularTriangularSet(Integer,IndexedExponents OrderedVa + riableList [b1,x,y,z,t,v,u,w],OrderedVariableList [b1,x + ,y,z,t,v,u,w],NewSparseMultivariatePolynomial(Integer,O + rderedVariableList [b1,x,y,z,t,v,u,w])) + Type: Domain +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{LazardSetSolvingPackageXmpPageEmpty14} +\begin{paste}{LazardSetSolvingPackageXmpPageEmpty14}{LazardSetSolvingPackageXmpPagePatch14} +\pastebutton{LazardSetSolvingPackageXmpPageEmpty14}{\showpaste} +\tab{5}\spadcommand{T := REGSET(R,E,V,P)\free{R }\free{E }\free{V }\free{P }\bound{T }} +\end{paste}\end{patch} + +\begin{patch}{LazardSetSolvingPackageXmpPagePatch15} +\begin{paste}{LazardSetSolvingPackageXmpPageFull15}{LazardSetSolvingPackageXmpPageEmpty15} +\pastebutton{LazardSetSolvingPackageXmpPageFull15}{\hidepaste} +\tab{5}\spadcommand{p0 := b1 + y + z - t - w\free{b1 }\free{x }\free{y }\free{z }\free{t }\free{u }\free{v }\free{w }\bound{p0 }} +\indentrel{3}\begin{verbatim} + (15) b1 + y + z - t - w +Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [b1,x,y,z,t,v,u,w]) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{LazardSetSolvingPackageXmpPageEmpty15} +\begin{paste}{LazardSetSolvingPackageXmpPageEmpty15}{LazardSetSolvingPackageXmpPagePatch15} +\pastebutton{LazardSetSolvingPackageXmpPageEmpty15}{\showpaste} +\tab{5}\spadcommand{p0 := b1 + y + z - t - w\free{b1 }\free{x }\free{y }\free{z }\free{t }\free{u }\free{v }\free{w }\bound{p0 }} +\end{paste}\end{patch} + +\begin{patch}{LazardSetSolvingPackageXmpPagePatch16} +\begin{paste}{LazardSetSolvingPackageXmpPageFull16}{LazardSetSolvingPackageXmpPageEmpty16} +\pastebutton{LazardSetSolvingPackageXmpPageFull16}{\hidepaste} +\tab{5}\spadcommand{p1 := 2*z*u + 2*y*v + 2*t*w - 2*w**2 - w - 1\free{b1 }\free{x }\free{y }\free{z }\free{t }\free{u }\free{v }\free{w }\bound{p1 }} +\indentrel{3}\begin{verbatim} + 2 + (16) 2v y + 2u z + 2w t - 2w - w - 1 +Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [b1,x,y,z,t,v,u,w]) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{LazardSetSolvingPackageXmpPageEmpty16} +\begin{paste}{LazardSetSolvingPackageXmpPageEmpty16}{LazardSetSolvingPackageXmpPagePatch16} +\pastebutton{LazardSetSolvingPackageXmpPageEmpty16}{\showpaste} +\tab{5}\spadcommand{p1 := 2*z*u + 2*y*v + 2*t*w - 2*w**2 - w - 1\free{b1 }\free{x }\free{y }\free{z }\free{t }\free{u }\free{v }\free{w }\bound{p1 }} +\end{paste}\end{patch} + +\begin{patch}{LazardSetSolvingPackageXmpPagePatch17} +\begin{paste}{LazardSetSolvingPackageXmpPageFull17}{LazardSetSolvingPackageXmpPageEmpty17} +\pastebutton{LazardSetSolvingPackageXmpPageFull17}{\hidepaste} +\tab{5}\spadcommand{p2 := 3*z*u**2 + 3*y*v**2 - 3*t*w**2 + 3*w**3 + 3*w**2 - t + 4*w\free{b1 }\free{x }\free{y }\free{z }\free{t }\free{u }\free{v }\free{w }\bound{p2 }} +\indentrel{3}\begin{verbatim} + 2 2 2 3 2 + (17) 3v y + 3u z + (- 3w - 1)t + 3w + 3w + 4w +Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [b1,x,y,z,t,v,u,w]) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{LazardSetSolvingPackageXmpPageEmpty17} +\begin{paste}{LazardSetSolvingPackageXmpPageEmpty17}{LazardSetSolvingPackageXmpPagePatch17} +\pastebutton{LazardSetSolvingPackageXmpPageEmpty17}{\showpaste} +\tab{5}\spadcommand{p2 := 3*z*u**2 + 3*y*v**2 - 3*t*w**2 + 3*w**3 + 3*w**2 - t + 4*w\free{b1 }\free{x }\free{y }\free{z }\free{t }\free{u }\free{v }\free{w }\bound{p2 }} +\end{paste}\end{patch} + +\begin{patch}{LazardSetSolvingPackageXmpPagePatch18} +\begin{paste}{LazardSetSolvingPackageXmpPageFull18}{LazardSetSolvingPackageXmpPageEmpty18} +\pastebutton{LazardSetSolvingPackageXmpPageFull18}{\hidepaste} +\tab{5}\spadcommand{p3 := 6*x*z*v - 6*t*w**2 + 6*w**3 - 3*t*w + 6*w**2 - t + 4*w\free{b1 }\free{x }\free{y }\free{z }\free{t }\free{u }\free{v }\free{w }\bound{p3 }} +\indentrel{3}\begin{verbatim} + 2 3 2 + (18) 6v z x + (- 6w - 3w - 1)t + 6w + 6w + 4w +Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [b1,x,y,z,t,v,u,w]) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{LazardSetSolvingPackageXmpPageEmpty18} +\begin{paste}{LazardSetSolvingPackageXmpPageEmpty18}{LazardSetSolvingPackageXmpPagePatch18} +\pastebutton{LazardSetSolvingPackageXmpPageEmpty18}{\showpaste} +\tab{5}\spadcommand{p3 := 6*x*z*v - 6*t*w**2 + 6*w**3 - 3*t*w + 6*w**2 - t + 4*w\free{b1 }\free{x }\free{y }\free{z }\free{t }\free{u }\free{v }\free{w }\bound{p3 }} +\end{paste}\end{patch} + +\begin{patch}{LazardSetSolvingPackageXmpPagePatch19} +\begin{paste}{LazardSetSolvingPackageXmpPageFull19}{LazardSetSolvingPackageXmpPageEmpty19} +\pastebutton{LazardSetSolvingPackageXmpPageFull19}{\hidepaste} +\tab{5}\spadcommand{p4 := 4*z*u**3+ 4*y*v**3+ 4*t*w**3- 4*w**4 - 6*w**3+ 4*t*w- 10*w**2- w- 1\free{b1 }\free{x }\free{y }\free{z }\free{t }\free{u }\free{v }\free{w }\bound{p4 }} +\indentrel{3}\begin{verbatim} + (19) + 3 3 3 4 3 2 + 4v y + 4u z + (4w + 4w)t - 4w - 6w - 10w - w - 1 +Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [b1,x,y,z,t,v,u,w]) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{LazardSetSolvingPackageXmpPageEmpty19} +\begin{paste}{LazardSetSolvingPackageXmpPageEmpty19}{LazardSetSolvingPackageXmpPagePatch19} +\pastebutton{LazardSetSolvingPackageXmpPageEmpty19}{\showpaste} +\tab{5}\spadcommand{p4 := 4*z*u**3+ 4*y*v**3+ 4*t*w**3- 4*w**4 - 6*w**3+ 4*t*w- 10*w**2- w- 1\free{b1 }\free{x }\free{y }\free{z }\free{t }\free{u }\free{v }\free{w }\bound{p4 }} +\end{paste}\end{patch} + +\begin{patch}{LazardSetSolvingPackageXmpPagePatch20} +\begin{paste}{LazardSetSolvingPackageXmpPageFull20}{LazardSetSolvingPackageXmpPageEmpty20} +\pastebutton{LazardSetSolvingPackageXmpPageFull20}{\hidepaste} +\tab{5}\spadcommand{p5 := 8*x*z*u*v +8*t*w**3 -8*w**4 +4*t*w**2 -12*w**3 +4*t*w -14*w**2 -3*w -1\free{b1 }\free{x }\free{y }\free{z }\free{t }\free{u }\free{v }\free{w }\bound{p5 }} +\indentrel{3}\begin{verbatim} + (20) + 3 2 4 3 2 + 8u v z x + (8w + 4w + 4w)t - 8w - 12w - 14w - 3w + + + - 1 +Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [b1,x,y,z,t,v,u,w]) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{LazardSetSolvingPackageXmpPageEmpty20} +\begin{paste}{LazardSetSolvingPackageXmpPageEmpty20}{LazardSetSolvingPackageXmpPagePatch20} +\pastebutton{LazardSetSolvingPackageXmpPageEmpty20}{\showpaste} +\tab{5}\spadcommand{p5 := 8*x*z*u*v +8*t*w**3 -8*w**4 +4*t*w**2 -12*w**3 +4*t*w -14*w**2 -3*w -1\free{b1 }\free{x }\free{y }\free{z }\free{t }\free{u }\free{v }\free{w }\bound{p5 }} +\end{paste}\end{patch} + +\begin{patch}{LazardSetSolvingPackageXmpPagePatch21} +\begin{paste}{LazardSetSolvingPackageXmpPageFull21}{LazardSetSolvingPackageXmpPageEmpty21} +\pastebutton{LazardSetSolvingPackageXmpPageFull21}{\hidepaste} +\tab{5}\spadcommand{p6 := 12*x*z*v**2+12*t*w**3 -12*w**4 +12*t*w**2 -18*w**3 +8*t*w -14*w**2 -w -1\free{b1 }\free{x }\free{y }\free{z }\free{t }\free{u }\free{v }\free{w }\bound{p6 }} +\indentrel{3}\begin{verbatim} + (21) + 2 3 2 4 3 2 + 12v z x + (12w + 12w + 8w)t - 12w - 18w - 14w + + + - w - 1 +Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [b1,x,y,z,t,v,u,w]) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{LazardSetSolvingPackageXmpPageEmpty21} +\begin{paste}{LazardSetSolvingPackageXmpPageEmpty21}{LazardSetSolvingPackageXmpPagePatch21} +\pastebutton{LazardSetSolvingPackageXmpPageEmpty21}{\showpaste} +\tab{5}\spadcommand{p6 := 12*x*z*v**2+12*t*w**3 -12*w**4 +12*t*w**2 -18*w**3 +8*t*w -14*w**2 -w -1\free{b1 }\free{x }\free{y }\free{z }\free{t }\free{u }\free{v }\free{w }\bound{p6 }} +\end{paste}\end{patch} + +\begin{patch}{LazardSetSolvingPackageXmpPagePatch22} +\begin{paste}{LazardSetSolvingPackageXmpPageFull22}{LazardSetSolvingPackageXmpPageEmpty22} +\pastebutton{LazardSetSolvingPackageXmpPageFull22}{\hidepaste} +\tab{5}\spadcommand{p7 := -24*t*w**3 + 24*w**4 - 24*t*w**2 + 36*w**3 - 8*t*w + 26*w**2 + 7*w + 1\free{b1 }\free{x }\free{y }\free{z }\free{t }\free{u }\free{v }\free{w }\bound{p7 }} +\indentrel{3}\begin{verbatim} + (22) + 3 2 4 3 2 + (- 24w - 24w - 8w)t + 24w + 36w + 26w + 7w + 1 +Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [b1,x,y,z,t,v,u,w]) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{LazardSetSolvingPackageXmpPageEmpty22} +\begin{paste}{LazardSetSolvingPackageXmpPageEmpty22}{LazardSetSolvingPackageXmpPagePatch22} +\pastebutton{LazardSetSolvingPackageXmpPageEmpty22}{\showpaste} +\tab{5}\spadcommand{p7 := -24*t*w**3 + 24*w**4 - 24*t*w**2 + 36*w**3 - 8*t*w + 26*w**2 + 7*w + 1\free{b1 }\free{x }\free{y }\free{z }\free{t }\free{u }\free{v }\free{w }\bound{p7 }} +\end{paste}\end{patch} + +\begin{patch}{LazardSetSolvingPackageXmpPagePatch23} +\begin{paste}{LazardSetSolvingPackageXmpPageFull23}{LazardSetSolvingPackageXmpPageEmpty23} +\pastebutton{LazardSetSolvingPackageXmpPageFull23}{\hidepaste} +\tab{5}\spadcommand{lp := [p0, p1, p2, p3, p4, p5, p6, p7]\free{p0 }\free{p1 }\free{p2 }\free{p3 }\free{p4 }\free{p5 }\free{p6 }\free{p7 }\bound{lp }} +\indentrel{3}\begin{verbatim} + (23) + 2 + [b1 + y + z - t - w, 2v y + 2u z + 2w t - 2w - w - 1, + 2 2 2 3 2 + 3v y + 3u z + (- 3w - 1)t + 3w + 3w + 4w, + 2 3 2 + 6v z x + (- 6w - 3w - 1)t + 6w + 6w + 4w, + 3 3 3 4 3 2 + 4v y + 4u z + (4w + 4w)t - 4w - 6w - 10w - w - 1, + + 3 2 4 3 2 + 8u v z x + (8w + 4w + 4w)t - 8w - 12w - 14w + + + - 3w - 1 + , + + 2 3 2 4 3 2 + 12v z x + (12w + 12w + 8w)t - 12w - 18w - 14w + + + - w - 1 + , + 3 2 4 3 2 + (- 24w - 24w - 8w)t + 24w + 36w + 26w + 7w + 1] +Type: List NewSparseMultivariatePolynomial(Integer,OrderedVariableList [b1,x,y,z,t,v,u,w]) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{LazardSetSolvingPackageXmpPageEmpty23} +\begin{paste}{LazardSetSolvingPackageXmpPageEmpty23}{LazardSetSolvingPackageXmpPagePatch23} +\pastebutton{LazardSetSolvingPackageXmpPageEmpty23}{\showpaste} +\tab{5}\spadcommand{lp := [p0, p1, p2, p3, p4, p5, p6, p7]\free{p0 }\free{p1 }\free{p2 }\free{p3 }\free{p4 }\free{p5 }\free{p6 }\free{p7 }\bound{lp }} +\end{paste}\end{patch} + +\begin{patch}{LazardSetSolvingPackageXmpPagePatch24} +\begin{paste}{LazardSetSolvingPackageXmpPageFull24}{LazardSetSolvingPackageXmpPageEmpty24} +\pastebutton{LazardSetSolvingPackageXmpPageFull24}{\hidepaste} +\tab{5}\spadcommand{lts := zeroSetSplit(lp,false)$T\free{lp }\free{T }\bound{lts }} +\indentrel{3}\begin{verbatim} + (24) + [{w + 1,u,v,t + 1,b1 + y + z + 2}, + {w + 1,v,t + 1,z,b1 + y + 2}, + {w + 1,t + 1,z,y,b1 + 2}, + {w + 1,v - u,t + 1,y + z,x,b1 + 2}, + {w + 1,u,t + 1,y,x,b1 + z + 2}, + + 5 4 3 2 + {144w + 216w + 96w + 6w - 11w - 1, + 2 5 4 3 2 + (12w + 9w + 1)u - 72w - 108w - 42w - 9w - 3w, + 2 4 3 2 + (12w + 9w + 1)v + 36w + 54w + 18w , + 3 2 4 3 2 + (24w + 24w + 8w)t - 24w - 36w - 26w - 7w - 1, + + 2 2 + (12u v - 12u )z + (12w v + 12w + 4)t + (3w - 5)v + + + 4 3 2 + 36w + 42w + 6w - 16w + , + 2 + 2v y + 2u z + 2w t - 2w - w - 1, + 2 3 2 + 6v z x + (- 6w - 3w - 1)t + 6w + 6w + 4w, + b1 + y + z - t - w} + ] +Type: List RegularTriangularSet(Integer,IndexedExponents OrderedVariableList [b1,x,y,z,t,v,u,w],OrderedVariableList [b1,x,y,z,t,v,u,w],NewSparseMultivariatePolynomial(Integer,OrderedVariableList [b1,x,y,z,t,v,u,w])) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{LazardSetSolvingPackageXmpPageEmpty24} +\begin{paste}{LazardSetSolvingPackageXmpPageEmpty24}{LazardSetSolvingPackageXmpPagePatch24} +\pastebutton{LazardSetSolvingPackageXmpPageEmpty24}{\showpaste} +\tab{5}\spadcommand{lts := zeroSetSplit(lp,false)$T\free{lp }\free{T }\bound{lts }} +\end{paste}\end{patch} + +\begin{patch}{LazardSetSolvingPackageXmpPagePatch25} +\begin{paste}{LazardSetSolvingPackageXmpPageFull25}{LazardSetSolvingPackageXmpPageEmpty25} +\pastebutton{LazardSetSolvingPackageXmpPageFull25}{\hidepaste} +\tab{5}\spadcommand{[coHeight(ts) for ts in lts]\free{lts }} +\indentrel{3}\begin{verbatim} + (25) [3,3,3,2,2,0] + Type: List NonNegativeInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{LazardSetSolvingPackageXmpPageEmpty25} +\begin{paste}{LazardSetSolvingPackageXmpPageEmpty25}{LazardSetSolvingPackageXmpPagePatch25} +\pastebutton{LazardSetSolvingPackageXmpPageEmpty25}{\showpaste} +\tab{5}\spadcommand{[coHeight(ts) for ts in lts]\free{lts }} +\end{paste}\end{patch} + +\begin{patch}{LazardSetSolvingPackageXmpPagePatch26} +\begin{paste}{LazardSetSolvingPackageXmpPageFull26}{LazardSetSolvingPackageXmpPageEmpty26} +\pastebutton{LazardSetSolvingPackageXmpPageFull26}{\hidepaste} +\tab{5}\spadcommand{ST := SREGSET(R,E,V,P)\free{R }\free{E }\free{V }\free{P }\bound{ST }} +\indentrel{3}\begin{verbatim} + (26) + SquareFreeRegularTriangularSet(Integer,IndexedExponents + OrderedVariableList [b1,x,y,z,t,v,u,w],OrderedVariable + List [b1,x,y,z,t,v,u,w],NewSparseMultivariatePolynomial + (Integer,OrderedVariableList [b1,x,y,z,t,v,u,w])) + Type: Domain +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{LazardSetSolvingPackageXmpPageEmpty26} +\begin{paste}{LazardSetSolvingPackageXmpPageEmpty26}{LazardSetSolvingPackageXmpPagePatch26} +\pastebutton{LazardSetSolvingPackageXmpPageEmpty26}{\showpaste} +\tab{5}\spadcommand{ST := SREGSET(R,E,V,P)\free{R }\free{E }\free{V }\free{P }\bound{ST }} +\end{paste}\end{patch} + +\begin{patch}{LazardSetSolvingPackageXmpPagePatch27} +\begin{paste}{LazardSetSolvingPackageXmpPageFull27}{LazardSetSolvingPackageXmpPageEmpty27} +\pastebutton{LazardSetSolvingPackageXmpPageFull27}{\hidepaste} +\tab{5}\spadcommand{pack := LAZM3PK(R,E,V,P,T,ST)\free{R }\free{E }\free{V }\free{P }\free{T }\free{ST }\bound{pack }} +\indentrel{3}\begin{verbatim} + (27) + LazardSetSolvingPackage(Integer,IndexedExponents Ordere + dVariableList [b1,x,y,z,t,v,u,w],OrderedVariableList [b + 1,x,y,z,t,v,u,w],NewSparseMultivariatePolynomial(Intege + r,OrderedVariableList [b1,x,y,z,t,v,u,w]),RegularTriang + ularSet(Integer,IndexedExponents OrderedVariableList [b + 1,x,y,z,t,v,u,w],OrderedVariableList [b1,x,y,z,t,v,u,w] + ,NewSparseMultivariatePolynomial(Integer,OrderedVariabl + eList [b1,x,y,z,t,v,u,w])),SquareFreeRegularTriangularS + et(Integer,IndexedExponents OrderedVariableList [b1,x,y + ,z,t,v,u,w],OrderedVariableList [b1,x,y,z,t,v,u,w],NewS + parseMultivariatePolynomial(Integer,OrderedVariableList + [b1,x,y,z,t,v,u,w]))) + Type: Domain +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{LazardSetSolvingPackageXmpPageEmpty27} +\begin{paste}{LazardSetSolvingPackageXmpPageEmpty27}{LazardSetSolvingPackageXmpPagePatch27} +\pastebutton{LazardSetSolvingPackageXmpPageEmpty27}{\showpaste} +\tab{5}\spadcommand{pack := LAZM3PK(R,E,V,P,T,ST)\free{R }\free{E }\free{V }\free{P }\free{T }\free{ST }\bound{pack }} +\end{paste}\end{patch} + +\begin{patch}{LazardSetSolvingPackageXmpPagePatch28} +\begin{paste}{LazardSetSolvingPackageXmpPageFull28}{LazardSetSolvingPackageXmpPageEmpty28} +\pastebutton{LazardSetSolvingPackageXmpPageFull28}{\hidepaste} +\tab{5}\spadcommand{zeroSetSplit(lp,false)$pack\free{lp }\free{pack }} +\indentrel{3}\begin{verbatim} + (28) + [{w + 1,t + 1,z,y,b1 + 2}, + {w + 1,v,t + 1,z,b1 + y + 2}, + {w + 1,u,v,t + 1,b1 + y + z + 2}, + {w + 1,v - u,t + 1,y + z,x,b1 + 2}, + {w + 1,u,t + 1,y,x,b1 + z + 2}, + + 5 4 3 2 + {144w + 216w + 96w + 6w - 11w - 1, + 4 3 2 + u - 24w - 36w - 14w + w + 1, + 4 3 2 + 3v - 48w - 60w - 10w + 8w + 2, + 4 3 2 + t - 24w - 36w - 14w - w + 1, + 4 3 2 + 486z - 2772w - 4662w - 2055w + 30w + 127, + 4 3 2 + 2916y - 22752w - 30312w - 8220w + 2064w + 1561, + 4 3 2 + 356x - 3696w - 4536w - 968w + 822w + 371, + 4 3 2 + 2916b1 - 30600w - 46692w - 20274w - 8076w + 593} + ] +Type: List SquareFreeRegularTriangularSet(Integer,IndexedExponents OrderedVariableList [b1,x,y,z,t,v,u,w],OrderedVariableList [b1,x,y,z,t,v,u,w],NewSparseMultivariatePolynomial(Integer,OrderedVariableList [b1,x,y,z,t,v,u,w])) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{LazardSetSolvingPackageXmpPageEmpty28} +\begin{paste}{LazardSetSolvingPackageXmpPageEmpty28}{LazardSetSolvingPackageXmpPagePatch28} +\pastebutton{LazardSetSolvingPackageXmpPageEmpty28}{\showpaste} +\tab{5}\spadcommand{zeroSetSplit(lp,false)$pack\free{lp }\free{pack }} +\end{paste}\end{patch} + +\begin{patch}{LazardSetSolvingPackageXmpPagePatch29} +\begin{paste}{LazardSetSolvingPackageXmpPageFull29}{LazardSetSolvingPackageXmpPageEmpty29} +\pastebutton{LazardSetSolvingPackageXmpPageFull29}{\hidepaste} +\tab{5}\spadcommand{f0 := (w - v) ** 2 + (u - t) ** 2 - 1\free{b1 }\free{x }\free{y }\free{z }\free{t }\free{u }\free{v }\free{w }\bound{f0 }} +\indentrel{3}\begin{verbatim} + 2 2 2 2 + (29) t - 2u t + v - 2w v + u + w - 1 +Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [b1,x,y,z,t,v,u,w]) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{LazardSetSolvingPackageXmpPageEmpty29} +\begin{paste}{LazardSetSolvingPackageXmpPageEmpty29}{LazardSetSolvingPackageXmpPagePatch29} +\pastebutton{LazardSetSolvingPackageXmpPageEmpty29}{\showpaste} +\tab{5}\spadcommand{f0 := (w - v) ** 2 + (u - t) ** 2 - 1\free{b1 }\free{x }\free{y }\free{z }\free{t }\free{u }\free{v }\free{w }\bound{f0 }} +\end{paste}\end{patch} + +\begin{patch}{LazardSetSolvingPackageXmpPagePatch30} +\begin{paste}{LazardSetSolvingPackageXmpPageFull30}{LazardSetSolvingPackageXmpPageEmpty30} +\pastebutton{LazardSetSolvingPackageXmpPageFull30}{\hidepaste} +\tab{5}\spadcommand{f1 := t ** 2 - v ** 3\free{b1 }\free{x }\free{y }\free{z }\free{t }\free{u }\free{v }\free{w }\bound{f1 }} +\indentrel{3}\begin{verbatim} + 2 3 + (30) t - v +Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [b1,x,y,z,t,v,u,w]) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{LazardSetSolvingPackageXmpPageEmpty30} +\begin{paste}{LazardSetSolvingPackageXmpPageEmpty30}{LazardSetSolvingPackageXmpPagePatch30} +\pastebutton{LazardSetSolvingPackageXmpPageEmpty30}{\showpaste} +\tab{5}\spadcommand{f1 := t ** 2 - v ** 3\free{b1 }\free{x }\free{y }\free{z }\free{t }\free{u }\free{v }\free{w }\bound{f1 }} +\end{paste}\end{patch} + +\begin{patch}{LazardSetSolvingPackageXmpPagePatch31} +\begin{paste}{LazardSetSolvingPackageXmpPageFull31}{LazardSetSolvingPackageXmpPageEmpty31} +\pastebutton{LazardSetSolvingPackageXmpPageFull31}{\hidepaste} +\tab{5}\spadcommand{f2 := 2 * t * (w - v) + 3 * v ** 2 * (u - t)\free{b1 }\free{x }\free{y }\free{z }\free{t }\free{u }\free{v }\free{w }\bound{f2 }} +\indentrel{3}\begin{verbatim} + 2 2 + (31) (- 3v - 2v + 2w)t + 3u v +Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [b1,x,y,z,t,v,u,w]) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{LazardSetSolvingPackageXmpPageEmpty31} +\begin{paste}{LazardSetSolvingPackageXmpPageEmpty31}{LazardSetSolvingPackageXmpPagePatch31} +\pastebutton{LazardSetSolvingPackageXmpPageEmpty31}{\showpaste} +\tab{5}\spadcommand{f2 := 2 * t * (w - v) + 3 * v ** 2 * (u - t)\free{b1 }\free{x }\free{y }\free{z }\free{t }\free{u }\free{v }\free{w }\bound{f2 }} +\end{paste}\end{patch} + +\begin{patch}{LazardSetSolvingPackageXmpPagePatch32} +\begin{paste}{LazardSetSolvingPackageXmpPageFull32}{LazardSetSolvingPackageXmpPageEmpty32} +\pastebutton{LazardSetSolvingPackageXmpPageFull32}{\hidepaste} +\tab{5}\spadcommand{f3 := (3 * z * v ** 2 - 1) * (2 * z * t - 1)\free{b1 }\free{x }\free{y }\free{z }\free{t }\free{u }\free{v }\free{w }\bound{f3 }} +\indentrel{3}\begin{verbatim} + 2 2 2 + (32) 6v t z + (- 2t - 3v )z + 1 +Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [b1,x,y,z,t,v,u,w]) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{LazardSetSolvingPackageXmpPageEmpty32} +\begin{paste}{LazardSetSolvingPackageXmpPageEmpty32}{LazardSetSolvingPackageXmpPagePatch32} +\pastebutton{LazardSetSolvingPackageXmpPageEmpty32}{\showpaste} +\tab{5}\spadcommand{f3 := (3 * z * v ** 2 - 1) * (2 * z * t - 1)\free{b1 }\free{x }\free{y }\free{z }\free{t }\free{u }\free{v }\free{w }\bound{f3 }} +\end{paste}\end{patch} + +\begin{patch}{LazardSetSolvingPackageXmpPagePatch33} +\begin{paste}{LazardSetSolvingPackageXmpPageFull33}{LazardSetSolvingPackageXmpPageEmpty33} +\pastebutton{LazardSetSolvingPackageXmpPageFull33}{\hidepaste} +\tab{5}\spadcommand{lf := [f0, f1, f2, f3]\free{f0 }\free{f1 }\free{f2 }\free{f3 }\bound{lf }} +\indentrel{3}\begin{verbatim} + (33) + 2 2 2 2 2 3 + [t - 2u t + v - 2w v + u + w - 1, t - v , + 2 2 + (- 3v - 2v + 2w)t + 3u v , + 2 2 2 + 6v t z + (- 2t - 3v )z + 1] +Type: List NewSparseMultivariatePolynomial(Integer,OrderedVariableList [b1,x,y,z,t,v,u,w]) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{LazardSetSolvingPackageXmpPageEmpty33} +\begin{paste}{LazardSetSolvingPackageXmpPageEmpty33}{LazardSetSolvingPackageXmpPagePatch33} +\pastebutton{LazardSetSolvingPackageXmpPageEmpty33}{\showpaste} +\tab{5}\spadcommand{lf := [f0, f1, f2, f3]\free{f0 }\free{f1 }\free{f2 }\free{f3 }\bound{lf }} +\end{paste}\end{patch} + +\begin{patch}{LazardSetSolvingPackageXmpPagePatch34} +\begin{paste}{LazardSetSolvingPackageXmpPageFull34}{LazardSetSolvingPackageXmpPageEmpty34} +\pastebutton{LazardSetSolvingPackageXmpPageFull34}{\hidepaste} +\tab{5}\spadcommand{zeroSetSplit(lf,true)$T\free{lf }\free{T }} +\indentrel{3}\begin{verbatim} + (34) + [ + { + 6 3 2 4 + 729u + (- 1458w + 729w - 4158w - 1685)u + + + 6 5 4 3 2 + 729w - 1458w - 2619w - 4892w - 297w + + + 5814w + 427 + * + 2 + u + + + 8 7 6 5 4 3 + 729w + 216w - 2900w - 2376w + 3870w + 4072w + + + 2 + - 1188w - 1656w + 529 + , + + 4 3 2 2 + 2187u + (- 4374w - 972w - 12474w - 2868)u + + + 6 5 4 3 2 + 2187w - 1944w - 10125w - 4800w + 2501w + + + 4968w - 1587 + * + v + + + 3 2 2 6 5 4 + (1944w - 108w )u + 972w + 3024w - 1080w + + + 3 2 + 496w + 1116w + , + 2 2 + (3v + 2v - 2w)t - 3u v , + 2 2 2 + ((4v - 4w)t - 6u v )z + (2t + 3v )z - 1} + ] +Type: List RegularTriangularSet(Integer,IndexedExponents OrderedVariableList [b1,x,y,z,t,v,u,w],OrderedVariableList [b1,x,y,z,t,v,u,w],NewSparseMultivariatePolynomial(Integer,OrderedVariableList [b1,x,y,z,t,v,u,w])) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{LazardSetSolvingPackageXmpPageEmpty34} +\begin{paste}{LazardSetSolvingPackageXmpPageEmpty34}{LazardSetSolvingPackageXmpPagePatch34} +\pastebutton{LazardSetSolvingPackageXmpPageEmpty34}{\showpaste} +\tab{5}\spadcommand{zeroSetSplit(lf,true)$T\free{lf }\free{T }} +\end{paste}\end{patch} + +\begin{patch}{LazardSetSolvingPackageXmpPagePatch35} +\begin{paste}{LazardSetSolvingPackageXmpPageFull35}{LazardSetSolvingPackageXmpPageEmpty35} +\pastebutton{LazardSetSolvingPackageXmpPageFull35}{\hidepaste} +\tab{5}\spadcommand{zeroSetSplit(lf,false)$T\free{lf }\free{T }} +\indentrel{3}\begin{verbatim} + (35) + [ + { + 6 3 2 4 + 729u + (- 1458w + 729w - 4158w - 1685)u + + + 6 5 4 3 2 + 729w - 1458w - 2619w - 4892w - 297w + + + 5814w + 427 + * + 2 + u + + + 8 7 6 5 4 3 + 729w + 216w - 2900w - 2376w + 3870w + 4072w + + + 2 + - 1188w - 1656w + 529 + , + + 4 3 2 2 + 2187u + (- 4374w - 972w - 12474w - 2868)u + + + 6 5 4 3 2 + 2187w - 1944w - 10125w - 4800w + 2501w + + + 4968w - 1587 + * + v + + + 3 2 2 6 5 4 + (1944w - 108w )u + 972w + 3024w - 1080w + + + 3 2 + 496w + 1116w + , + 2 2 + (3v + 2v - 2w)t - 3u v , + 2 2 2 + ((4v - 4w)t - 6u v )z + (2t + 3v )z - 1} + , + + 4 3 2 + {27w + 4w - 54w - 36w + 23, u, + 2 2 2 + (12w + 2)v - 9w - 2w + 9, 6t - 2v - 3w + 2w + 3, + 2t z - 1} + , + + { + 6 5 4 3 2 + 59049w + 91854w - 45198w + 145152w + 63549w + + + 60922w + 21420 + , + + 5 4 + 31484448266904w - 18316865522574w + + + 3 2 + 23676995746098w + 6657857188965w + + + 8904703998546w + 3890631403260 + * + 2 + u + + + 5 4 + 94262810316408w - 82887296576616w + + + 3 2 + 89801831438784w + 28141734167208w + + + 38070359425432w + 16003865949120 + , + + 2 2 + (243w + 36w + 85)v + + + 2 3 2 3 2 + (- 81u - 162w + 36w + 154w + 72)v - 72w + 4w + , + 2 2 + (3v + 2v - 2w)t - 3u v , + 2 2 2 + ((4v - 4w)t - 6u v )z + (2t + 3v )z - 1} + , + + 4 3 2 + {27w + 4w - 54w - 36w + 23, u, + 2 2 2 + (12w + 2)v - 9w - 2w + 9, 6t - 2v - 3w + 2w + 3, + 2 + 3v z - 1} + ] +Type: List RegularTriangularSet(Integer,IndexedExponents OrderedVariableList [b1,x,y,z,t,v,u,w],OrderedVariableList [b1,x,y,z,t,v,u,w],NewSparseMultivariatePolynomial(Integer,OrderedVariableList [b1,x,y,z,t,v,u,w])) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{LazardSetSolvingPackageXmpPageEmpty35} +\begin{paste}{LazardSetSolvingPackageXmpPageEmpty35}{LazardSetSolvingPackageXmpPagePatch35} +\pastebutton{LazardSetSolvingPackageXmpPageEmpty35}{\showpaste} +\tab{5}\spadcommand{zeroSetSplit(lf,false)$T\free{lf }\free{T }} +\end{paste}\end{patch} + +\begin{patch}{LazardSetSolvingPackageXmpPagePatch36} +\begin{paste}{LazardSetSolvingPackageXmpPageFull36}{LazardSetSolvingPackageXmpPageEmpty36} +\pastebutton{LazardSetSolvingPackageXmpPageFull36}{\hidepaste} +\tab{5}\spadcommand{zeroSetSplit(lf,false)$pack\free{lf }\free{pack }} +\indentrel{3}\begin{verbatim} + (36) + [ + { + 6 3 2 4 + 729u + (- 1458w + 729w - 4158w - 1685)u + + + 6 5 4 3 2 + 729w - 1458w - 2619w - 4892w - 297w + + + 5814w + 427 + * + 2 + u + + + 8 7 6 5 4 3 + 729w + 216w - 2900w - 2376w + 3870w + 4072w + + + 2 + - 1188w - 1656w + 529 + , + + 4 3 2 2 + 2187u + (- 4374w - 972w - 12474w - 2868)u + + + 6 5 4 3 2 + 2187w - 1944w - 10125w - 4800w + 2501w + + + 4968w - 1587 + * + v + + + 3 2 2 6 5 4 + (1944w - 108w )u + 972w + 3024w - 1080w + + + 3 2 + 496w + 1116w + , + 2 2 + (3v + 2v - 2w)t - 3u v , + 2 2 2 + ((4v - 4w)t - 6u v )z + (2t + 3v )z - 1} + , + + 2 2 + {81w + 18w + 28, 729u - 1890w - 533, + 2 + 81v + (- 162w + 27)v - 72w - 112, + 11881t + (972w + 2997)u v + (- 11448w - 11536)u, + + 2 + 641237934604288z + + + (78614584763904w + 26785578742272)u + + + 236143618655616w + 70221988585728 + * + v + + + (358520253138432w + 101922133759488)u + + + 142598803536000w + 54166419595008 + * + z + + + (32655103844499w - 44224572465882)u v + + + (43213900115457w - 32432039102070)u + } + , + + 4 3 2 + {27w + 4w - 54w - 36w + 23, u, + 3 2 + 218v - 162w + 3w + 160w + 153, + 2 3 2 + 109t - 27w - 54w + 63w + 80, + 3 2 + 1744z + (- 1458w + 27w + 1440w + 505)t} + , + + 4 3 2 + {27w + 4w - 54w - 36w + 23, u, + 3 2 + 218v - 162w + 3w + 160w + 153, + 2 3 2 + 109t - 27w - 54w + 63w + 80, + 3 2 + 1308z + 162w - 3w - 814w - 153} + , + + 4 3 2 + {729w + 972w - 1026w + 1684w + 765, + 2 2 + 81u + 72w + 16w - 72, + 3 2 + 702v - 162w - 225w + 40w - 99, + 3 2 + 11336t + (324w - 603w - 1718w - 1557)u, + + 2 + 595003968z + + + 3 2 + - 963325386w - 898607682w + 1516286466w + + + - 3239166186 + * + u + + + 3 2 + - 1579048992w - 1796454288w + 2428328160w + + + - 4368495024 + * + z + + + 3 2 + 9713133306w + 9678670317w - 16726834476w + + + 28144233593 + * + u + } + ] +Type: List SquareFreeRegularTriangularSet(Integer,IndexedExponents OrderedVariableList [b1,x,y,z,t,v,u,w],OrderedVariableList [b1,x,y,z,t,v,u,w],NewSparseMultivariatePolynomial(Integer,OrderedVariableList [b1,x,y,z,t,v,u,w])) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{LazardSetSolvingPackageXmpPageEmpty36} +\begin{paste}{LazardSetSolvingPackageXmpPageEmpty36}{LazardSetSolvingPackageXmpPagePatch36} +\pastebutton{LazardSetSolvingPackageXmpPageEmpty36}{\showpaste} +\tab{5}\spadcommand{zeroSetSplit(lf,false)$pack\free{lf }\free{pack }} +\end{paste}\end{patch} + @ \section{lexp.ht} \pagehead{LieExponentialsXmpPage}{lexp.ht}{LieExponentials} @@ -12397,7 +32732,233 @@ Calculations \endscroll \autobuttons \end{page} -% + +\begin{patch}{LieExponentialsXmpPagePatch1} +\begin{paste}{LieExponentialsXmpPageFull1}{LieExponentialsXmpPageEmpty1} +\pastebutton{LieExponentialsXmpPageFull1}{\hidepaste} +\tab{5}\spadcommand{ a: Symbol := 'a\bound{a }} +\indentrel{3}\begin{verbatim} + (1) a + Type: Symbol +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{LieExponentialsXmpPageEmpty1} +\begin{paste}{LieExponentialsXmpPageEmpty1}{LieExponentialsXmpPagePatch1} +\pastebutton{LieExponentialsXmpPageEmpty1}{\showpaste} +\tab{5}\spadcommand{ a: Symbol := 'a\bound{a }} +\end{paste}\end{patch} + +\begin{patch}{LieExponentialsXmpPagePatch2} +\begin{paste}{LieExponentialsXmpPageFull2}{LieExponentialsXmpPageEmpty2} +\pastebutton{LieExponentialsXmpPageFull2}{\hidepaste} +\tab{5}\spadcommand{ b: Symbol := 'b\bound{b }} +\indentrel{3}\begin{verbatim} + (2) b + Type: Symbol +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{LieExponentialsXmpPageEmpty2} +\begin{paste}{LieExponentialsXmpPageEmpty2}{LieExponentialsXmpPagePatch2} +\pastebutton{LieExponentialsXmpPageEmpty2}{\showpaste} +\tab{5}\spadcommand{ b: Symbol := 'b\bound{b }} +\end{paste}\end{patch} + +\begin{patch}{LieExponentialsXmpPagePatch3} +\begin{paste}{LieExponentialsXmpPageFull3}{LieExponentialsXmpPageEmpty3} +\pastebutton{LieExponentialsXmpPageFull3}{\hidepaste} +\tab{5}\spadcommand{ coef := Fraction(Integer)\bound{coef }} +\indentrel{3}\begin{verbatim} + (3) Fraction Integer + Type: Domain +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{LieExponentialsXmpPageEmpty3} +\begin{paste}{LieExponentialsXmpPageEmpty3}{LieExponentialsXmpPagePatch3} +\pastebutton{LieExponentialsXmpPageEmpty3}{\showpaste} +\tab{5}\spadcommand{ coef := Fraction(Integer)\bound{coef }} +\end{paste}\end{patch} + +\begin{patch}{LieExponentialsXmpPagePatch4} +\begin{paste}{LieExponentialsXmpPageFull4}{LieExponentialsXmpPageEmpty4} +\pastebutton{LieExponentialsXmpPageFull4}{\hidepaste} +\tab{5}\spadcommand{ group := LieExponentials(Symbol, coef, 3)\free{coef }\bound{group }} +\indentrel{3}\begin{verbatim} + (4) LieExponentials(Symbol,Fraction Integer,3) + Type: Domain +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{LieExponentialsXmpPageEmpty4} +\begin{paste}{LieExponentialsXmpPageEmpty4}{LieExponentialsXmpPagePatch4} +\pastebutton{LieExponentialsXmpPageEmpty4}{\showpaste} +\tab{5}\spadcommand{ group := LieExponentials(Symbol, coef, 3)\free{coef }\bound{group }} +\end{paste}\end{patch} + +\begin{patch}{LieExponentialsXmpPagePatch5} +\begin{paste}{LieExponentialsXmpPageFull5}{LieExponentialsXmpPageEmpty5} +\pastebutton{LieExponentialsXmpPageFull5}{\hidepaste} +\tab{5}\spadcommand{ lpoly := LiePolynomial(Symbol, coef)\free{coef }\bound{lpoly }} +\indentrel{3}\begin{verbatim} + (5) LiePolynomial(Symbol,Fraction Integer) + Type: Domain +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{LieExponentialsXmpPageEmpty5} +\begin{paste}{LieExponentialsXmpPageEmpty5}{LieExponentialsXmpPagePatch5} +\pastebutton{LieExponentialsXmpPageEmpty5}{\showpaste} +\tab{5}\spadcommand{ lpoly := LiePolynomial(Symbol, coef)\free{coef }\bound{lpoly }} +\end{paste}\end{patch} + +\begin{patch}{LieExponentialsXmpPagePatch6} +\begin{paste}{LieExponentialsXmpPageFull6}{LieExponentialsXmpPageEmpty6} +\pastebutton{LieExponentialsXmpPageFull6}{\hidepaste} +\tab{5}\spadcommand{ poly := XPBWPolynomial(Symbol, coef)\free{coef }\bound{poly }} +\indentrel{3}\begin{verbatim} + (6) XPBWPolynomial(Symbol,Fraction Integer) + Type: Domain +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{LieExponentialsXmpPageEmpty6} +\begin{paste}{LieExponentialsXmpPageEmpty6}{LieExponentialsXmpPagePatch6} +\pastebutton{LieExponentialsXmpPageEmpty6}{\showpaste} +\tab{5}\spadcommand{ poly := XPBWPolynomial(Symbol, coef)\free{coef }\bound{poly }} +\end{paste}\end{patch} + +\begin{patch}{LieExponentialsXmpPagePatch7} +\begin{paste}{LieExponentialsXmpPageFull7}{LieExponentialsXmpPageEmpty7} +\pastebutton{LieExponentialsXmpPageFull7}{\hidepaste} +\tab{5}\spadcommand{ ea := exp(a::lpoly)$group\free{a }\free{lpoly }\free{group }\bound{ea }} +\indentrel{3}\begin{verbatim} + [a] + (7) e + Type: LieExponentials(Symbol,Fraction Integer,3) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{LieExponentialsXmpPageEmpty7} +\begin{paste}{LieExponentialsXmpPageEmpty7}{LieExponentialsXmpPagePatch7} +\pastebutton{LieExponentialsXmpPageEmpty7}{\showpaste} +\tab{5}\spadcommand{ ea := exp(a::lpoly)$group\free{a }\free{lpoly }\free{group }\bound{ea }} +\end{paste}\end{patch} + +\begin{patch}{LieExponentialsXmpPagePatch8} +\begin{paste}{LieExponentialsXmpPageFull8}{LieExponentialsXmpPageEmpty8} +\pastebutton{LieExponentialsXmpPageFull8}{\hidepaste} +\tab{5}\spadcommand{ eb := exp(b::lpoly)$group\free{b }\free{lpoly }\free{group }\bound{eb }} +\indentrel{3}\begin{verbatim} + [b] + (8) e + Type: LieExponentials(Symbol,Fraction Integer,3) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{LieExponentialsXmpPageEmpty8} +\begin{paste}{LieExponentialsXmpPageEmpty8}{LieExponentialsXmpPagePatch8} +\pastebutton{LieExponentialsXmpPageEmpty8}{\showpaste} +\tab{5}\spadcommand{ eb := exp(b::lpoly)$group\free{b }\free{lpoly }\free{group }\bound{eb }} +\end{paste}\end{patch} + +\begin{patch}{LieExponentialsXmpPagePatch9} +\begin{paste}{LieExponentialsXmpPageFull9}{LieExponentialsXmpPageEmpty9} +\pastebutton{LieExponentialsXmpPageFull9}{\hidepaste} +\tab{5}\spadcommand{ g: group := ea*eb\free{ea }\free{eb }\bound{g }} +\indentrel{3}\begin{verbatim} + 1 2 1 2 + Ä [a b ] Ä [a b] + [b] 2 [a b] 2 [a] + (9) e e e e e + Type: LieExponentials(Symbol,Fraction Integer,3) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{LieExponentialsXmpPageEmpty9} +\begin{paste}{LieExponentialsXmpPageEmpty9}{LieExponentialsXmpPagePatch9} +\pastebutton{LieExponentialsXmpPageEmpty9}{\showpaste} +\tab{5}\spadcommand{ g: group := ea*eb\free{ea }\free{eb }\bound{g }} +\end{paste}\end{patch} + +\begin{patch}{LieExponentialsXmpPagePatch10} +\begin{paste}{LieExponentialsXmpPageFull10}{LieExponentialsXmpPageEmpty10} +\pastebutton{LieExponentialsXmpPageFull10}{\hidepaste} +\tab{5}\spadcommand{ g :: poly\free{g }\free{poly }} +\indentrel{3}\begin{verbatim} + (10) + 1 1 + 1 + [a] + [b] + Ä [a][a] + [a b] + [b][a] + Ä [b][b] + 2 2 + + + 1 1 2 1 2 + Ä [a][a][a] + Ä [a b] + [a b][a] + Ä [a b ] + 6 2 2 + + + 1 1 1 + Ä [b][a][a] + [b][a b] + Ä [b][b][a] + Ä [b][b][b] + 2 2 6 + Type: XPBWPolynomial(Symbol,Fraction Integer) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{LieExponentialsXmpPageEmpty10} +\begin{paste}{LieExponentialsXmpPageEmpty10}{LieExponentialsXmpPagePatch10} +\pastebutton{LieExponentialsXmpPageEmpty10}{\showpaste} +\tab{5}\spadcommand{ g :: poly\free{g }\free{poly }} +\end{paste}\end{patch} + +\begin{patch}{LieExponentialsXmpPagePatch11} +\begin{paste}{LieExponentialsXmpPageFull11}{LieExponentialsXmpPageEmpty11} +\pastebutton{LieExponentialsXmpPageFull11}{\hidepaste} +\tab{5}\spadcommand{ log(g)$group\free{g }\free{group }} +\indentrel{3}\begin{verbatim} + 1 1 2 1 2 + (11) [a] + [b] + Ä [a b] + ÄÄ [a b] + ÄÄ [a b ] + 2 12 12 + Type: LiePolynomial(Symbol,Fraction Integer) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{LieExponentialsXmpPageEmpty11} +\begin{paste}{LieExponentialsXmpPageEmpty11}{LieExponentialsXmpPagePatch11} +\pastebutton{LieExponentialsXmpPageEmpty11}{\showpaste} +\tab{5}\spadcommand{ log(g)$group\free{g }\free{group }} +\end{paste}\end{patch} + +\begin{patch}{LieExponentialsXmpPagePatch12} +\begin{paste}{LieExponentialsXmpPageFull12}{LieExponentialsXmpPageEmpty12} +\pastebutton{LieExponentialsXmpPageFull12}{\hidepaste} +\tab{5}\spadcommand{ g1: group := inv(g)\free{g }\free{group }\bound{g1 }} +\indentrel{3}\begin{verbatim} + - [b] - [a] + (12) e e + Type: LieExponentials(Symbol,Fraction Integer,3) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{LieExponentialsXmpPageEmpty12} +\begin{paste}{LieExponentialsXmpPageEmpty12}{LieExponentialsXmpPagePatch12} +\pastebutton{LieExponentialsXmpPageEmpty12}{\showpaste} +\tab{5}\spadcommand{ g1: group := inv(g)\free{g }\free{group }\bound{g1 }} +\end{paste}\end{patch} + +\begin{patch}{LieExponentialsXmpPagePatch13} +\begin{paste}{LieExponentialsXmpPageFull13}{LieExponentialsXmpPageEmpty13} +\pastebutton{LieExponentialsXmpPageFull13}{\hidepaste} +\tab{5}\spadcommand{ g*g1\free{g }\free{g1 }} +\indentrel{3}\begin{verbatim} + (13) 1 + Type: LieExponentials(Symbol,Fraction Integer,3) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{LieExponentialsXmpPageEmpty13} +\begin{paste}{LieExponentialsXmpPageEmpty13}{LieExponentialsXmpPagePatch13} +\pastebutton{LieExponentialsXmpPageEmpty13}{\showpaste} +\tab{5}\spadcommand{ g*g1\free{g }\free{g1 }} +\end{paste}\end{patch} @ \section{lextripk.ht} @@ -12663,6 +33224,2559 @@ the \axiomOpFrom{realSolve}{ZeroDimensionalSolvePackage} operation. \autobuttons \end{page} +\begin{patch}{LexTriangularPackageXmpPagePatch1} +\begin{paste}{LexTriangularPackageXmpPageFull1}{LexTriangularPackageXmpPageEmpty1} +\pastebutton{LexTriangularPackageXmpPageFull1}{\hidepaste} +\tab{5}\spadcommand{R := Integer\bound{R }} +\indentrel{3}\begin{verbatim} + (1) Integer + Type: Domain +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{LexTriangularPackageXmpPageEmpty1} +\begin{paste}{LexTriangularPackageXmpPageEmpty1}{LexTriangularPackageXmpPagePatch1} +\pastebutton{LexTriangularPackageXmpPageEmpty1}{\showpaste} +\tab{5}\spadcommand{R := Integer\bound{R }} +\end{paste}\end{patch} + +\begin{patch}{LexTriangularPackageXmpPagePatch2} +\begin{paste}{LexTriangularPackageXmpPageFull2}{LexTriangularPackageXmpPageEmpty2} +\pastebutton{LexTriangularPackageXmpPageFull2}{\hidepaste} +\tab{5}\spadcommand{ls : List Symbol := [a,b,c,d,e,f]\bound{ls }} +\indentrel{3}\begin{verbatim} + (2) [a,b,c,d,e,f] + Type: List Symbol +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{LexTriangularPackageXmpPageEmpty2} +\begin{paste}{LexTriangularPackageXmpPageEmpty2}{LexTriangularPackageXmpPagePatch2} +\pastebutton{LexTriangularPackageXmpPageEmpty2}{\showpaste} +\tab{5}\spadcommand{ls : List Symbol := [a,b,c,d,e,f]\bound{ls }} +\end{paste}\end{patch} + +\begin{patch}{LexTriangularPackageXmpPagePatch3} +\begin{paste}{LexTriangularPackageXmpPageFull3}{LexTriangularPackageXmpPageEmpty3} +\pastebutton{LexTriangularPackageXmpPageFull3}{\hidepaste} +\tab{5}\spadcommand{V := OVAR(ls)\free{ls }\bound{V }} +\indentrel{3}\begin{verbatim} + (3) OrderedVariableList [a,b,c,d,e,f] + Type: Domain +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{LexTriangularPackageXmpPageEmpty3} +\begin{paste}{LexTriangularPackageXmpPageEmpty3}{LexTriangularPackageXmpPagePatch3} +\pastebutton{LexTriangularPackageXmpPageEmpty3}{\showpaste} +\tab{5}\spadcommand{V := OVAR(ls)\free{ls }\bound{V }} +\end{paste}\end{patch} + +\begin{patch}{LexTriangularPackageXmpPagePatch4} +\begin{paste}{LexTriangularPackageXmpPageFull4}{LexTriangularPackageXmpPageEmpty4} +\pastebutton{LexTriangularPackageXmpPageFull4}{\hidepaste} +\tab{5}\spadcommand{P := NSMP(R, V)\free{R }\free{V }\bound{P }} +\indentrel{3}\begin{verbatim} + (4) + NewSparseMultivariatePolynomial(Integer,OrderedVariable + List [a,b,c,d,e,f]) + Type: Domain +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{LexTriangularPackageXmpPageEmpty4} +\begin{paste}{LexTriangularPackageXmpPageEmpty4}{LexTriangularPackageXmpPagePatch4} +\pastebutton{LexTriangularPackageXmpPageEmpty4}{\showpaste} +\tab{5}\spadcommand{P := NSMP(R, V)\free{R }\free{V }\bound{P }} +\end{paste}\end{patch} + +\begin{patch}{LexTriangularPackageXmpPagePatch5} +\begin{paste}{LexTriangularPackageXmpPageFull5}{LexTriangularPackageXmpPageEmpty5} +\pastebutton{LexTriangularPackageXmpPageFull5}{\hidepaste} +\tab{5}\spadcommand{p1: P := a*b*c*d*e*f - 1\free{P }\bound{p1 }} +\indentrel{3}\begin{verbatim} + (5) f e d c b a - 1 +Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [a,b,c,d,e,f]) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{LexTriangularPackageXmpPageEmpty5} +\begin{paste}{LexTriangularPackageXmpPageEmpty5}{LexTriangularPackageXmpPagePatch5} +\pastebutton{LexTriangularPackageXmpPageEmpty5}{\showpaste} +\tab{5}\spadcommand{p1: P := a*b*c*d*e*f - 1\free{P }\bound{p1 }} +\end{paste}\end{patch} + +\begin{patch}{LexTriangularPackageXmpPagePatch6} +\begin{paste}{LexTriangularPackageXmpPageFull6}{LexTriangularPackageXmpPageEmpty6} +\pastebutton{LexTriangularPackageXmpPageFull6}{\hidepaste} +\tab{5}\spadcommand{p2: P := a*b*c*d*e +a*b*c*d*f +a*b*c*e*f +a*b*d*e*f +a*c*d*e*f +b*c*d*e*f\free{P }\bound{p2 }} +\indentrel{3}\begin{verbatim} + (6) + ((((e + f)d + f e)c + f e d)b + f e d c)a + f e d c b +Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [a,b,c,d,e,f]) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{LexTriangularPackageXmpPageEmpty6} +\begin{paste}{LexTriangularPackageXmpPageEmpty6}{LexTriangularPackageXmpPagePatch6} +\pastebutton{LexTriangularPackageXmpPageEmpty6}{\showpaste} +\tab{5}\spadcommand{p2: P := a*b*c*d*e +a*b*c*d*f +a*b*c*e*f +a*b*d*e*f +a*c*d*e*f +b*c*d*e*f\free{P }\bound{p2 }} +\end{paste}\end{patch} + +\begin{patch}{LexTriangularPackageXmpPagePatch7} +\begin{paste}{LexTriangularPackageXmpPageFull7}{LexTriangularPackageXmpPageEmpty7} +\pastebutton{LexTriangularPackageXmpPageFull7}{\hidepaste} +\tab{5}\spadcommand{p3: P := a*b*c*d + a*b*c*f + a*b*e*f + a*d*e*f + b*c*d*e + c*d*e*f\free{P }\bound{p3 }} +\indentrel{3}\begin{verbatim} + (7) (((d + f)c + f e)b + f e d)a + e d c b + f e d c +Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [a,b,c,d,e,f]) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{LexTriangularPackageXmpPageEmpty7} +\begin{paste}{LexTriangularPackageXmpPageEmpty7}{LexTriangularPackageXmpPagePatch7} +\pastebutton{LexTriangularPackageXmpPageEmpty7}{\showpaste} +\tab{5}\spadcommand{p3: P := a*b*c*d + a*b*c*f + a*b*e*f + a*d*e*f + b*c*d*e + c*d*e*f\free{P }\bound{p3 }} +\end{paste}\end{patch} + +\begin{patch}{LexTriangularPackageXmpPagePatch8} +\begin{paste}{LexTriangularPackageXmpPageFull8}{LexTriangularPackageXmpPageEmpty8} +\pastebutton{LexTriangularPackageXmpPageFull8}{\hidepaste} +\tab{5}\spadcommand{p4: P := a*b*c + a*b*f + a*e*f + b*c*d + c*d*e + d*e*f\free{P }\bound{p4 }} +\indentrel{3}\begin{verbatim} + (8) ((c + f)b + f e)a + d c b + e d c + f e d +Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [a,b,c,d,e,f]) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{LexTriangularPackageXmpPageEmpty8} +\begin{paste}{LexTriangularPackageXmpPageEmpty8}{LexTriangularPackageXmpPagePatch8} +\pastebutton{LexTriangularPackageXmpPageEmpty8}{\showpaste} +\tab{5}\spadcommand{p4: P := a*b*c + a*b*f + a*e*f + b*c*d + c*d*e + d*e*f\free{P }\bound{p4 }} +\end{paste}\end{patch} + +\begin{patch}{LexTriangularPackageXmpPagePatch9} +\begin{paste}{LexTriangularPackageXmpPageFull9}{LexTriangularPackageXmpPageEmpty9} +\pastebutton{LexTriangularPackageXmpPageFull9}{\hidepaste} +\tab{5}\spadcommand{p5: P := a*b + a*f + b*c + c*d + d*e + e*f\free{P }\bound{p5 }} +\indentrel{3}\begin{verbatim} + (9) (b + f)a + c b + d c + e d + f e +Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [a,b,c,d,e,f]) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{LexTriangularPackageXmpPageEmpty9} +\begin{paste}{LexTriangularPackageXmpPageEmpty9}{LexTriangularPackageXmpPagePatch9} +\pastebutton{LexTriangularPackageXmpPageEmpty9}{\showpaste} +\tab{5}\spadcommand{p5: P := a*b + a*f + b*c + c*d + d*e + e*f\free{P }\bound{p5 }} +\end{paste}\end{patch} + +\begin{patch}{LexTriangularPackageXmpPagePatch10} +\begin{paste}{LexTriangularPackageXmpPageFull10}{LexTriangularPackageXmpPageEmpty10} +\pastebutton{LexTriangularPackageXmpPageFull10}{\hidepaste} +\tab{5}\spadcommand{p6: P := a + b + c + d + e + f\free{P }\bound{p6 }} +\indentrel{3}\begin{verbatim} + (10) a + b + c + d + e + f +Type: NewSparseMultivariatePolynomial(Integer,OrderedVariableList [a,b,c,d,e,f]) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{LexTriangularPackageXmpPageEmpty10} +\begin{paste}{LexTriangularPackageXmpPageEmpty10}{LexTriangularPackageXmpPagePatch10} +\pastebutton{LexTriangularPackageXmpPageEmpty10}{\showpaste} +\tab{5}\spadcommand{p6: P := a + b + c + d + e + f\free{P }\bound{p6 }} +\end{paste}\end{patch} + +\begin{patch}{LexTriangularPackageXmpPagePatch11} +\begin{paste}{LexTriangularPackageXmpPageFull11}{LexTriangularPackageXmpPageEmpty11} +\pastebutton{LexTriangularPackageXmpPageFull11}{\hidepaste} +\tab{5}\spadcommand{lp := [p1, p2, p3, p4, p5, p6]\free{p1 }\free{p2 }\free{p3 }\free{p4 }\free{p5 }\free{p6 }\bound{lp }} +\indentrel{3}\begin{verbatim} + (11) + [f e d c b a - 1, + ((((e + f)d + f e)c + f e d)b + f e d c)a + f e d c b, + (((d + f)c + f e)b + f e d)a + e d c b + f e d c, + ((c + f)b + f e)a + d c b + e d c + f e d, + (b + f)a + c b + d c + e d + f e, + a + b + c + d + e + f] +Type: List NewSparseMultivariatePolynomial(Integer,OrderedVariableList [a,b,c,d,e,f]) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{LexTriangularPackageXmpPageEmpty11} +\begin{paste}{LexTriangularPackageXmpPageEmpty11}{LexTriangularPackageXmpPagePatch11} +\pastebutton{LexTriangularPackageXmpPageEmpty11}{\showpaste} +\tab{5}\spadcommand{lp := [p1, p2, p3, p4, p5, p6]\free{p1 }\free{p2 }\free{p3 }\free{p4 }\free{p5 }\free{p6 }\bound{lp }} +\end{paste}\end{patch} + +\begin{patch}{LexTriangularPackageXmpPagePatch12} +\begin{paste}{LexTriangularPackageXmpPageFull12}{LexTriangularPackageXmpPageEmpty12} +\pastebutton{LexTriangularPackageXmpPageFull12}{\hidepaste} +\tab{5}\spadcommand{lextripack := LEXTRIPK(R,ls)\free{R }\free{ls }\bound{lextripack }} +\indentrel{3}\begin{verbatim} + (12) LexTriangularPackage(Integer,[a,b,c,d,e,f]) + Type: Domain +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{LexTriangularPackageXmpPageEmpty12} +\begin{paste}{LexTriangularPackageXmpPageEmpty12}{LexTriangularPackageXmpPagePatch12} +\pastebutton{LexTriangularPackageXmpPageEmpty12}{\showpaste} +\tab{5}\spadcommand{lextripack := LEXTRIPK(R,ls)\free{R }\free{ls }\bound{lextripack }} +\end{paste}\end{patch} + +\begin{patch}{LexTriangularPackageXmpPagePatch13} +\begin{paste}{LexTriangularPackageXmpPageFull13}{LexTriangularPackageXmpPageEmpty13} +\pastebutton{LexTriangularPackageXmpPageFull13}{\hidepaste} +\tab{5}\spadcommand{lg := groebner(lp)$lextripack\free{lp }\free{lextripack }\bound{lg }} +\indentrel{3}\begin{verbatim} + (13) + [a + b + c + d + e + f, + + 2 + 3968379498283200b + 15873517993132800f b + + + 2 + 3968379498283200d + 15873517993132800f d + + + 3 5 4 4 + 3968379498283200f e - 15873517993132800f e + + + 5 3 + 23810276989699200f e + + + 6 2 + (206355733910726400f + 230166010900425600)e + + + 43 37 + - 729705987316687f + 1863667496867205421f + + + 31 + 291674853771731104461f + + + 25 + 365285994691106921745f + + + 19 + 549961185828911895f + + + 13 + - 365048404038768439269f + + + 7 + - 292382820431504027669f - 2271898467631865497f + * + e + + + 44 38 + - 3988812642545399f + 10187423878429609997f + + + 32 + 1594377523424314053637f + + + 26 20 + 1994739308439916238065f + 1596840088052642815f + + + 14 + - 1993494118301162145413f + + + 8 2 + - 1596049742289689815053f - 11488171330159667449f + , + + (23810276989699200c - 23810276989699200f)b + + + 2 + 23810276989699200c + 71430830969097600f c + + + 2 + - 23810276989699200d - 95241107958796800f d + + + 3 5 4 4 + - 55557312975964800f e + 174608697924460800f e + + + 5 3 + - 174608697924460800f e + + + 6 2 + (- 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76144952817052723145495f + + + 11 + - 60933629892463517546975f + + + 5 + - 411415071682002547795f + * + e + + + 42 36 + - 209493533143822f + 535045979490560586f + + + 30 24 + 83737947964973553146f + 104889507084213371570f + + + 18 12 + 167117997269207870f - 104793725781390615514f + + + 6 + - 83842685189903180394f - 569978796672974242 + , + + 6 3 + (25438330117200f + 25438330117200)e + + + 7 2 + (76314990351600f + 76314990351600f)e + + + 44 38 + - 1594966552735f + 4073543370415745f + + + 32 26 + 637527159231148925f + 797521176113606525f + + + 20 14 + 530440941097175f - 797160527306433145f + + + 8 2 + - 638132320196044965f - 4510507167940725f + * + e + + + 45 39 + - 6036376800443f + 15416903421476909f + + + 33 27 + 2412807646192304449f + 3017679923028013705f + + + 21 15 + 1422320037411955f - 3016560402417843941f + + + 9 3 + - 2414249368183033161f - 16561862361763873f + , + + 12 2 + (1387545279120f - 1387545279120)e + + + 43 37 + 4321823003f - 11037922310209f + + + 31 25 + - 1727510711947989f - 2165150991154425f + + + 19 13 + - 5114342560755f + 2162682824948601f + + + 7 + 1732620732685741f + 13506088516033f + * + e + + + 44 38 + 24177661775f - 61749727185325f + + + 32 26 + - 9664106795754225f - 12090487758628245f + + + 20 14 + - 8787672733575f + 12083693383005045f + + + 8 2 + 9672870290826025f + 68544102808525f + , + + 48 42 36 30 18 + f - 2554f - 399710f - 499722f + 499722f + + + 12 6 + 399710f + 2554f - 1 + ] +Type: List NewSparseMultivariatePolynomial(Integer,OrderedVariableList [a,b,c,d,e,f]) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{LexTriangularPackageXmpPageEmpty13} +\begin{paste}{LexTriangularPackageXmpPageEmpty13}{LexTriangularPackageXmpPagePatch13} +\pastebutton{LexTriangularPackageXmpPageEmpty13}{\showpaste} +\tab{5}\spadcommand{lg := groebner(lp)$lextripack\free{lp }\free{lextripack }\bound{lg }} +\end{paste}\end{patch} + +\begin{patch}{LexTriangularPackageXmpPagePatch14} +\begin{paste}{LexTriangularPackageXmpPageFull14}{LexTriangularPackageXmpPageEmpty14} +\pastebutton{LexTriangularPackageXmpPageFull14}{\hidepaste} +\tab{5}\spadcommand{lexTriangular(lg,false)$lextripack\free{lg }\free{lextripack }} +\indentrel{3}\begin{verbatim} + (14) + [ + 6 + {f + 1, + 6 5 2 4 3 3 4 2 5 + e - 3f e + 3f e - 4f e + 3f e - 3f e - 1, + 2 5 3 4 4 3 5 2 + 3d + f e - 4f e + 4f e - 2f e - 2e + 2f, c + f, + 2 5 3 4 4 3 5 2 + 3b + 2f e - 5f e + 5f e - 10f e - 4e + 7f, + 2 5 3 4 4 3 5 2 + a - f e + 3f e - 3f e + 4f e + 3e - 3f} + , + + 6 2 2 + {f - 1, e - f, d - f, c + 4f c + f , + 2 + (c - f)b - f c - 5f , a + b + c + 3f} + , + 6 2 2 + {f - 1,e - f,d - f,c - f,b + 4f b + f ,a + b + 4f}, + + 6 2 2 + {f - 1, e - f, d + 4f d + f , + 2 + (d - f)c - f d - 5f , b - f, a + c + d + 3f} + , + + { + 36 30 24 18 12 + f - 2554f - 399709f - 502276f - 399709f + + + 6 + - 2554f + 1 + , + + 12 2 + (161718564f - 161718564)e + + + 31 25 19 + - 504205f + 1287737951f + 201539391380f + + + 13 7 + 253982817368f + 201940704665f + 1574134601f + * + e + + + 32 26 20 + - 2818405f + 7198203911f + 1126548149060f + + + 14 8 2 + 1416530563364f + 1127377589345f + 7988820725f + , + + 6 + (693772639560f - 693772639560)d + + + 2 5 3 4 + - 462515093040f e + 1850060372160f e + + + 4 3 + - 1850060372160f e + + + 11 5 2 + (- 24513299931120f - 23588269745040f )e + + + 30 24 + - 890810428f + 2275181044754f + + + 18 12 + 355937263869776f + 413736880104344f + + + 6 + 342849304487996f + 3704966481878 + * + e + + + 31 25 + - 4163798003f + 10634395752169f + + + 19 13 + 1664161760192806f + 2079424391370694f + + + 7 + 1668153650635921f + 10924274392693f + , + + 6 31 + (12614047992f - 12614047992)c - 7246825f + + + 25 19 + 18508536599f + 2896249516034f + + + 13 7 + 3581539649666f + 2796477571739f - 48094301893f + , + + 6 + (693772639560f - 693772639560)b + + + 2 5 3 4 + - 925030186080f e + 2312575465200f e + + + 4 3 + - 2312575465200f e + + + 11 5 2 + (- 40007555547960f - 35382404617560f )e + + + 30 24 + - 3781280823f + 9657492291789f + + + 18 12 + 1511158913397906f + 1837290892286154f + + + 6 + 1487216006594361f + 8077238712093 + * + e + + + 31 25 + - 9736390478f + 24866827916734f + + + 19 13 + 3891495681905296f + 4872556418871424f + + + 7 + 3904047887269606f + 27890075838538f + , + a + b + c + d + e + f} + , + + 6 2 2 2 + {f - 1, e + 4f e + f , (e - f)d - f e - 5f , + c - f, b - f, a + d + e + 3f} + ] + Type: List RegularChain(Integer,[a,b,c,d,e,f]) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{LexTriangularPackageXmpPageEmpty14} +\begin{paste}{LexTriangularPackageXmpPageEmpty14}{LexTriangularPackageXmpPagePatch14} +\pastebutton{LexTriangularPackageXmpPageEmpty14}{\showpaste} +\tab{5}\spadcommand{lexTriangular(lg,false)$lextripack\free{lg }\free{lextripack }} +\end{paste}\end{patch} + +\begin{patch}{LexTriangularPackageXmpPagePatch15} +\begin{paste}{LexTriangularPackageXmpPageFull15}{LexTriangularPackageXmpPageEmpty15} +\pastebutton{LexTriangularPackageXmpPageFull15}{\hidepaste} +\tab{5}\spadcommand{lts := lexTriangular(lg,true)$lextripack\free{lg }\free{lextripack }\bound{lts }} +\indentrel{3}\begin{verbatim} + (15) + [ + 6 + {f + 1, + 6 5 2 4 3 3 4 2 5 + e - 3f e + 3f e - 4f e + 3f e - 3f e - 1, + 2 5 3 4 4 3 5 2 + 3d + f e - 4f e + 4f e - 2f e - 2e + 2f, c + f, + 2 5 3 4 4 3 5 2 + 3b + 2f e - 5f e + 5f e - 10f e - 4e + 7f, + 2 5 3 4 4 3 5 2 + a - f e + 3f e - 3f e + 4f e + 3e - 3f} + , + 6 2 2 + {f - 1,e - f,d - f,c + 4f c + f ,b + c + 4f,a - f}, + 6 2 2 + {f - 1,e - f,d - f,c - f,b + 4f b + f ,a + b + 4f}, + 6 2 2 + {f - 1,e - f,d + 4f d + f ,c + d + 4f,b - f,a - f}, + + { + 36 30 24 18 12 + f - 2554f - 399709f - 502276f - 399709f + + + 6 + - 2554f + 1 + , + + 2 + 1387545279120e + + + 31 25 + 4321823003f - 11037922310209f + + + 19 13 + - 1727506390124986f - 2176188913464634f + + + 7 + - 1732620732685741f - 13506088516033f + * + e + + + 32 26 + 24177661775f - 61749727185325f + + + 20 14 + - 9664082618092450f - 12152237485813570f + + + 8 2 + - 9672870290826025f - 68544102808525f + , + + 1387545279120d + + + 30 24 + - 1128983050f + 2883434331830f + + + 18 12 + 451234998755840f + 562426491685760f + + + 6 + 447129055314890f - 165557857270 + * + e + + + 31 25 + - 1816935351f + 4640452214013f + + + 19 13 + 726247129626942f + 912871801716798f + + + 7 + 726583262666877f + 4909358645961f + , + + 31 25 + 1387545279120c + 778171189f - 1987468196267f + + + 19 13 + - 310993556954378f - 383262822316802f + + + 7 + - 300335488637543f + 5289595037041f + , + + 1387545279120b + + + 30 24 + 1128983050f - 2883434331830f + + + 18 12 + - 451234998755840f - 562426491685760f + + + 6 + - 447129055314890f + 165557857270 + * + e + + + 31 25 + - 3283058841f + 8384938292463f + + + 19 13 + 1312252817452422f + 1646579934064638f + + + 7 + 1306372958656407f + 4694680112151f + , + + 31 + 1387545279120a + 1387545279120e + 4321823003f + + + 25 19 + - 11037922310209f - 1727506390124986f + + + 13 7 + - 2176188913464634f - 1732620732685741f + + + - 13506088516033f + } + , + 6 2 2 + {f - 1,e + 4f e + f ,d + e + 4f,c - f,b - f,a - f}] + Type: List RegularChain(Integer,[a,b,c,d,e,f]) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{LexTriangularPackageXmpPageEmpty15} +\begin{paste}{LexTriangularPackageXmpPageEmpty15}{LexTriangularPackageXmpPagePatch15} +\pastebutton{LexTriangularPackageXmpPageEmpty15}{\showpaste} +\tab{5}\spadcommand{lts := lexTriangular(lg,true)$lextripack\free{lg }\free{lextripack }\bound{lts }} +\end{paste}\end{patch} + +\begin{patch}{LexTriangularPackageXmpPagePatch16} +\begin{paste}{LexTriangularPackageXmpPageFull16}{LexTriangularPackageXmpPageEmpty16} +\pastebutton{LexTriangularPackageXmpPageFull16}{\hidepaste} +\tab{5}\spadcommand{[[init(p) for p in (ts :: List(P))] for ts in lts]\free{lts }} +\indentrel{3}\begin{verbatim} + (16) + [[1,3,1,3,1,1], [1,1,1,1,1,1], [1,1,1,1,1,1], + [1,1,1,1,1,1], + + [1387545279120, 1387545279120, 1387545279120, + 1387545279120, 1387545279120, 1] + , + [1,1,1,1,1,1]] +Type: List List NewSparseMultivariatePolynomial(Integer,OrderedVariableList [a,b,c,d,e,f]) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{LexTriangularPackageXmpPageEmpty16} +\begin{paste}{LexTriangularPackageXmpPageEmpty16}{LexTriangularPackageXmpPagePatch16} +\pastebutton{LexTriangularPackageXmpPageEmpty16}{\showpaste} +\tab{5}\spadcommand{[[init(p) for p in (ts :: List(P))] for ts in lts]\free{lts }} +\end{paste}\end{patch} + +\begin{patch}{LexTriangularPackageXmpPagePatch17} +\begin{paste}{LexTriangularPackageXmpPageFull17}{LexTriangularPackageXmpPageEmpty17} +\pastebutton{LexTriangularPackageXmpPageFull17}{\hidepaste} +\tab{5}\spadcommand{squareFreeLexTriangular(lg,true)$lextripack\free{lg }\free{lextripack }} +\indentrel{3}\begin{verbatim} + (17) + [ + 6 + {f + 1, + 6 5 2 4 3 3 4 2 5 + e - 3f e + 3f e - 4f e + 3f e - 3f e - 1, + 2 5 3 4 4 3 5 2 + 3d + f e - 4f e + 4f e - 2f e - 2e + 2f, c + f, + 2 5 3 4 4 3 5 2 + 3b + 2f e - 5f e + 5f e - 10f e - 4e + 7f, + 2 5 3 4 4 3 5 2 + a - f e + 3f e - 3f e + 4f e + 3e - 3f} + , + 6 2 2 + {f - 1,e - f,d - f,c + 4f c + f ,b + c + 4f,a - f}, + 6 2 2 + {f - 1,e - f,d - f,c - f,b + 4f b + f ,a + b + 4f}, + 6 2 2 + {f - 1,e - f,d + 4f d + f ,c + d + 4f,b - f,a - f}, + + { + 36 30 24 18 12 + f - 2554f - 399709f - 502276f - 399709f + + + 6 + - 2554f + 1 + , + + 2 + 1387545279120e + + + 31 25 + 4321823003f - 11037922310209f + + + 19 13 + - 1727506390124986f - 2176188913464634f + + + 7 + - 1732620732685741f - 13506088516033f + * + e + + + 32 26 + 24177661775f - 61749727185325f + + + 20 14 + - 9664082618092450f - 12152237485813570f + + + 8 2 + - 9672870290826025f - 68544102808525f + , + + 1387545279120d + + + 30 24 + - 1128983050f + 2883434331830f + + + 18 12 + 451234998755840f + 562426491685760f + + + 6 + 447129055314890f - 165557857270 + * + e + + + 31 25 + - 1816935351f + 4640452214013f + + + 19 13 + 726247129626942f + 912871801716798f + + + 7 + 726583262666877f + 4909358645961f + , + + 31 25 + 1387545279120c + 778171189f - 1987468196267f + + + 19 13 + - 310993556954378f - 383262822316802f + + + 7 + - 300335488637543f + 5289595037041f + , + + 1387545279120b + + + 30 24 + 1128983050f - 2883434331830f + + + 18 12 + - 451234998755840f - 562426491685760f + + + 6 + - 447129055314890f + 165557857270 + * + e + + + 31 25 + - 3283058841f + 8384938292463f + + + 19 13 + 1312252817452422f + 1646579934064638f + + + 7 + 1306372958656407f + 4694680112151f + , + + 31 + 1387545279120a + 1387545279120e + 4321823003f + + + 25 19 + - 11037922310209f - 1727506390124986f + + + 13 7 + - 2176188913464634f - 1732620732685741f + + + - 13506088516033f + } + , + 6 2 2 + {f - 1,e + 4f e + f ,d + e + 4f,c - f,b - f,a - f}] +Type: List SquareFreeRegularTriangularSet(Integer,IndexedExponents OrderedVariableList [a,b,c,d,e,f],OrderedVariableList [a,b,c,d,e,f],NewSparseMultivariatePolynomial(Integer,OrderedVariableList [a,b,c,d,e,f])) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{LexTriangularPackageXmpPageEmpty17} +\begin{paste}{LexTriangularPackageXmpPageEmpty17}{LexTriangularPackageXmpPagePatch17} +\pastebutton{LexTriangularPackageXmpPageEmpty17}{\showpaste} +\tab{5}\spadcommand{squareFreeLexTriangular(lg,true)$lextripack\free{lg }\free{lextripack }} +\end{paste}\end{patch} + +\begin{patch}{LexTriangularPackageXmpPagePatch18} +\begin{paste}{LexTriangularPackageXmpPageFull18}{LexTriangularPackageXmpPageEmpty18} +\pastebutton{LexTriangularPackageXmpPageFull18}{\hidepaste} +\tab{5}\spadcommand{reduce(+,[degree(ts) for ts in lts])\free{lts }} +\indentrel{3}\begin{verbatim} + (18) 156 + Type: PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{LexTriangularPackageXmpPageEmpty18} +\begin{paste}{LexTriangularPackageXmpPageEmpty18}{LexTriangularPackageXmpPagePatch18} +\pastebutton{LexTriangularPackageXmpPageEmpty18}{\showpaste} +\tab{5}\spadcommand{reduce(+,[degree(ts) for ts in lts])\free{lts }} +\end{paste}\end{patch} + +\begin{patch}{LexTriangularPackageXmpPagePatch19} +\begin{paste}{LexTriangularPackageXmpPageFull19}{LexTriangularPackageXmpPageEmpty19} +\pastebutton{LexTriangularPackageXmpPageFull19}{\hidepaste} +\tab{5}\spadcommand{ls2 : List Symbol := concat(ls,new()$Symbol)\free{ls }\bound{ls2 }} +\indentrel{3}\begin{verbatim} + (19) [a,b,c,d,e,f,%A] + Type: List Symbol +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{LexTriangularPackageXmpPageEmpty19} +\begin{paste}{LexTriangularPackageXmpPageEmpty19}{LexTriangularPackageXmpPagePatch19} +\pastebutton{LexTriangularPackageXmpPageEmpty19}{\showpaste} +\tab{5}\spadcommand{ls2 : List Symbol := concat(ls,new()$Symbol)\free{ls }\bound{ls2 }} +\end{paste}\end{patch} + +\begin{patch}{LexTriangularPackageXmpPagePatch20} +\begin{paste}{LexTriangularPackageXmpPageFull20}{LexTriangularPackageXmpPageEmpty20} +\pastebutton{LexTriangularPackageXmpPageFull20}{\hidepaste} +\tab{5}\spadcommand{zdpack := ZDSOLVE(R,ls,ls2)\free{R }\free{ls }\free{ls2 }\bound{zdpack }} +\indentrel{3}\begin{verbatim} + (20) + ZeroDimensionalSolvePackage(Integer,[a,b,c,d,e,f],[a,b, + c,d,e,f,%A]) + Type: Domain +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{LexTriangularPackageXmpPageEmpty20} +\begin{paste}{LexTriangularPackageXmpPageEmpty20}{LexTriangularPackageXmpPagePatch20} +\pastebutton{LexTriangularPackageXmpPageEmpty20}{\showpaste} +\tab{5}\spadcommand{zdpack := ZDSOLVE(R,ls,ls2)\free{R }\free{ls }\free{ls2 }\bound{zdpack }} +\end{paste}\end{patch} + +\begin{patch}{LexTriangularPackageXmpPagePatch21} +\begin{paste}{LexTriangularPackageXmpPageFull21}{LexTriangularPackageXmpPageEmpty21} +\pastebutton{LexTriangularPackageXmpPageFull21}{\hidepaste} +\tab{5}\spadcommand{concat [univariateSolve(ts)$zdpack for ts in lts]\free{lts }\free{zdpack }} +\indentrel{3}\begin{verbatim} + (21) + [ + 4 2 + [complexRoots= ? - 13? + 49, + + coordinates = + 3 3 + [7a + %A - 6%A, 21b + %A + %A, + 3 3 + 21c - 2%A + 19%A, 7d - %A + 6%A, + 3 3 + 21e - %A - %A, 21f + 2%A - 19%A] + ] + , + + 4 2 + [complexRoots= ? + 11? + 49, + + coordinates = + 3 3 + [35a + 3%A + 19%A, 35b + %A + 18%A, + 3 3 + 35c - 2%A - %A, 35d - 3%A - 19%A, + 3 3 + 35e - %A - 18%A, 35f + 2%A + %A] + ] + , + + [ + complexRoots = + 8 7 6 5 4 3 + ? - 12? + 58? - 120? + 207? - 360? + + + 2 + 802? - 1332? + 1369 + , + + coordinates = + [ + 7 6 5 + 43054532a + 33782%A - 546673%A + 3127348%A + + + 4 3 2 + - 6927123%A + 4365212%A - 25086957%A + + + 39582814%A - 107313172 + , + + 7 6 5 + 43054532b - 33782%A + 546673%A - 3127348%A + + + 4 3 2 + 6927123%A - 4365212%A + 25086957%A + + + - 39582814%A + 107313172 + , + + 7 6 5 + 21527266c - 22306%A + 263139%A - 1166076%A + + + 4 3 2 + 1821805%A - 2892788%A + 10322663%A + + + - 9026596%A + 12950740 + , + + 7 6 5 + 43054532d + 22306%A - 263139%A + 1166076%A + + + 4 3 2 + - 1821805%A + 2892788%A - 10322663%A + + + 30553862%A - 12950740 + , + + 7 6 5 + 43054532e - 22306%A + 263139%A - 1166076%A + + + 4 3 2 + 1821805%A - 2892788%A + 10322663%A + + + - 30553862%A + 12950740 + , + + 7 6 5 + 21527266f + 22306%A - 263139%A + 1166076%A + + + 4 3 2 + - 1821805%A + 2892788%A - 10322663%A + + + 9026596%A - 12950740 + ] + ] + , + + [ + complexRoots = + 8 7 6 5 4 3 + ? + 12? + 58? + 120? + 207? + 360? + + + 2 + 802? + 1332? + 1369 + , + + coordinates = + [ + 7 6 5 + 43054532a + 33782%A + 546673%A + 3127348%A + + + 4 3 2 + 6927123%A + 4365212%A + 25086957%A + + + 39582814%A + 107313172 + , + + 7 6 5 + 43054532b - 33782%A - 546673%A - 3127348%A + + + 4 3 2 + - 6927123%A - 4365212%A - 25086957%A + + + - 39582814%A - 107313172 + , + + 7 6 5 + 21527266c - 22306%A - 263139%A - 1166076%A + + + 4 3 2 + - 1821805%A - 2892788%A - 10322663%A + + + - 9026596%A - 12950740 + , + + 7 6 5 + 43054532d + 22306%A + 263139%A + 1166076%A + + + 4 3 2 + 1821805%A + 2892788%A + 10322663%A + + + 30553862%A + 12950740 + , + + 7 6 5 + 43054532e - 22306%A - 263139%A - 1166076%A + + + 4 3 2 + - 1821805%A - 2892788%A - 10322663%A + + + - 30553862%A - 12950740 + , + + 7 6 5 + 21527266f + 22306%A + 263139%A + 1166076%A + + + 4 3 2 + 1821805%A + 2892788%A + 10322663%A + + + 9026596%A + 12950740 + ] + ] + , + + 4 2 + [complexRoots= ? - ? + 1, + + coordinates = + 3 3 + [a - %A, b + %A - %A, c + %A , d + %A, + 3 3 + e - %A + %A, f - %A ] + ] + , + + 8 6 4 2 + [complexRoots= ? + 4? + 12? + 16? + 4, + + coordinates = + 7 5 3 + [4a - 2%A - 7%A - 20%A - 22%A, + 7 5 3 + 4b + 2%A + 7%A + 20%A + 22%A, + 7 5 3 + 4c + %A + 3%A + 10%A + 10%A, + 7 5 3 + 4d + %A + 3%A + 10%A + 6%A, + 7 5 3 + 4e - %A - 3%A - 10%A - 6%A, + 7 5 3 + 4f - %A - 3%A - 10%A - 10%A] + ] + , + + 4 3 2 + [complexRoots= ? + 6? + 30? + 36? + 36, + + coordinates = + 3 2 + [30a - %A - 5%A - 30%A - 6, + 3 2 + 6b + %A + 5%A + 24%A + 6, + 3 2 + 30c - %A - 5%A - 6, + 3 2 + 30d - %A - 5%A - 30%A - 6, + 3 2 + 30e - %A - 5%A - 30%A - 6, + 3 2 + 30f - %A - 5%A - 30%A - 6] + ] + , + + 4 3 2 + [complexRoots= ? - 6? + 30? - 36? + 36, + + coordinates = + 3 2 + [30a - %A + 5%A - 30%A + 6, + 3 2 + 6b + %A - 5%A + 24%A - 6, + 3 2 + 30c - %A + 5%A + 6, + 3 2 + 30d - %A + 5%A - 30%A + 6, + 3 2 + 30e - %A + 5%A - 30%A + 6, + 3 2 + 30f - %A + 5%A - 30%A + 6] + ] + , + + 2 + [complexRoots= ? + 6? + 6, + + coordinates = + [a + 1,b - %A - 5,c + %A + 1,d + 1,e + 1,f + 1] + ] + , + + 2 + [complexRoots= ? - 6? + 6, + + coordinates = + [a - 1,b - %A + 5,c + %A - 1,d - 1,e - 1,f - 1] + ] + , + + 4 3 2 + [complexRoots= ? + 6? + 30? + 36? + 36, + + coordinates = + 3 2 + [6a + %A + 5%A + 24%A + 6, + 3 2 + 30b - %A - 5%A - 6, + 3 2 + 30c - %A - 5%A - 30%A - 6, + 3 2 + 30d - %A - 5%A - 30%A - 6, + 3 2 + 30e - %A - 5%A - 30%A - 6, + 3 2 + 30f - %A - 5%A - 30%A - 6] + ] + , + + 4 3 2 + [complexRoots= ? - 6? + 30? - 36? + 36, + + coordinates = + 3 2 + [6a + %A - 5%A + 24%A - 6, + 3 2 + 30b - %A + 5%A + 6, + 3 2 + 30c - %A + 5%A - 30%A + 6, + 3 2 + 30d - %A + 5%A - 30%A + 6, + 3 2 + 30e - %A + 5%A - 30%A + 6, + 3 2 + 30f - %A + 5%A - 30%A + 6] + ] + , + + 2 + [complexRoots= ? + 6? + 6, + + coordinates = + [a - %A - 5,b + %A + 1,c + 1,d + 1,e + 1,f + 1] + ] + , + + 2 + [complexRoots= ? - 6? + 6, + + coordinates = + [a - %A + 5,b + %A - 1,c - 1,d - 1,e - 1,f - 1] + ] + , + + 4 3 2 + [complexRoots= ? + 6? + 30? + 36? + 36, + + coordinates = + 3 2 + [30a - %A - 5%A - 30%A - 6, + 3 2 + 30b - %A - 5%A - 30%A - 6, + 3 2 + 6c + %A + 5%A + 24%A + 6, + 3 2 + 30d - %A - 5%A - 6, + 3 2 + 30e - %A - 5%A - 30%A - 6, + 3 2 + 30f - %A - 5%A - 30%A - 6] + ] + , + + 4 3 2 + [complexRoots= ? - 6? + 30? - 36? + 36, + + coordinates = + 3 2 + [30a - %A + 5%A - 30%A + 6, + 3 2 + 30b - %A + 5%A - 30%A + 6, + 3 2 + 6c + %A - 5%A + 24%A - 6, + 3 2 + 30d - %A + 5%A + 6, + 3 2 + 30e - %A + 5%A - 30%A + 6, + 3 2 + 30f - %A + 5%A - 30%A + 6] + ] + , + + 2 + [complexRoots= ? + 6? + 6, + + coordinates = + [a + 1,b + 1,c - %A - 5,d + %A + 1,e + 1,f + 1] + ] + , + + 2 + [complexRoots= ? - 6? + 6, + + coordinates = + [a - 1,b - 1,c - %A + 5,d + %A - 1,e - 1,f - 1] + ] + , + + [ + complexRoots = + 8 7 6 5 4 2 + ? + 6? + 16? + 24? + 18? - 8? + 4 + , + + coordinates = + [ + 7 6 5 4 3 + 2a + 2%A + 9%A + 18%A + 19%A + 4%A + + + 2 + - 10%A - 2%A + 4 + , + + 7 6 5 4 3 + 2b + 2%A + 9%A + 18%A + 19%A + 4%A + + + 2 + - 10%A - 4%A + 4 + , + 7 6 5 4 3 + 2c - %A - 4%A - 8%A - 9%A - 4%A - 2%A - 4, + 7 6 5 4 3 + 2d + %A + 4%A + 8%A + 9%A + 4%A + 2%A + 4, + + 7 6 5 4 3 + 2e - 2%A - 9%A - 18%A - 19%A - 4%A + + + 2 + 10%A + 4%A - 4 + , + + 7 6 5 4 3 + 2f - 2%A - 9%A - 18%A - 19%A - 4%A + + + 2 + 10%A + 2%A - 4 + ] + ] + , + + [ + complexRoots = + 8 7 6 5 4 3 + ? + 12? + 64? + 192? + 432? + 768? + + + 2 + 1024? + 768? + 256 + , + + coordinates = + [ + 7 6 5 4 + 1408a - 19%A - 200%A - 912%A - 2216%A + + + 3 2 + - 4544%A - 6784%A - 6976%A - 1792 + , + + 7 6 5 4 + 1408b - 37%A - 408%A - 1952%A - 5024%A + + + 3 2 + - 10368%A - 16768%A - 17920%A - 5120 + , + + 7 6 5 4 + 1408c + 37%A + 408%A + 1952%A + 5024%A + + + 3 2 + 10368%A + 16768%A + 17920%A + 5120 + , + + 7 6 5 4 + 1408d + 19%A + 200%A + 912%A + 2216%A + + + 3 2 + 4544%A + 6784%A + 6976%A + 1792 + , + 2e + %A, 2f - %A] + ] + , + + 8 6 4 2 + [complexRoots= ? + 4? + 12? + 16? + 4, + + coordinates = + 7 5 3 + [4a - %A - 3%A - 10%A - 6%A, + 7 5 3 + 4b - %A - 3%A - 10%A - 10%A, + 7 5 3 + 4c - 2%A - 7%A - 20%A - 22%A, + 7 5 3 + 4d + 2%A + 7%A + 20%A + 22%A, + 7 5 3 + 4e + %A + 3%A + 10%A + 10%A, + 7 5 3 + 4f + %A + 3%A + 10%A + 6%A] + ] + , + + 8 6 4 2 + [complexRoots= ? + 16? - 96? + 256? + 256, + + coordinates = + 7 5 3 + [512a - %A - 12%A + 176%A - 448%A, + 7 5 3 + 128b - %A - 16%A + 96%A - 256%A, + 7 5 3 + 128c + %A + 16%A - 96%A + 256%A, + 7 5 3 + 512d + %A + 12%A - 176%A + 448%A, 2e + %A, + 2f - %A] + ] + , + + [ + complexRoots = + 8 7 6 5 4 3 + ? - 12? + 64? - 192? + 432? - 768? + + + 2 + 1024? - 768? + 256 + , + + coordinates = + [ + 7 6 5 4 + 1408a - 19%A + 200%A - 912%A + 2216%A + + + 3 2 + - 4544%A + 6784%A - 6976%A + 1792 + , + + 7 6 5 4 + 1408b - 37%A + 408%A - 1952%A + 5024%A + + + 3 2 + - 10368%A + 16768%A - 17920%A + 5120 + , + + 7 6 5 4 + 1408c + 37%A - 408%A + 1952%A - 5024%A + + + 3 2 + 10368%A - 16768%A + 17920%A - 5120 + , + + 7 6 5 4 + 1408d + 19%A - 200%A + 912%A - 2216%A + + + 3 2 + 4544%A - 6784%A + 6976%A - 1792 + , + 2e + %A, 2f - %A] + ] + , + + [ + complexRoots = + 8 7 6 5 4 2 + ? - 6? + 16? - 24? + 18? - 8? + 4 + , + + coordinates = + [ + 7 6 5 4 3 + 2a + 2%A - 9%A + 18%A - 19%A + 4%A + + + 2 + 10%A - 2%A - 4 + , + + 7 6 5 4 3 + 2b + 2%A - 9%A + 18%A - 19%A + 4%A + + + 2 + 10%A - 4%A - 4 + , + 7 6 5 4 3 + 2c - %A + 4%A - 8%A + 9%A - 4%A - 2%A + 4, + 7 6 5 4 3 + 2d + %A - 4%A + 8%A - 9%A + 4%A + 2%A - 4, + + 7 6 5 4 3 + 2e - 2%A + 9%A - 18%A + 19%A - 4%A + + + 2 + - 10%A + 4%A + 4 + , + + 7 6 5 4 3 + 2f - 2%A + 9%A - 18%A + 19%A - 4%A + + + 2 + - 10%A + 2%A + 4 + ] + ] + , + + 4 2 + [complexRoots= ? + 12? + 144, + + coordinates = + 2 2 2 + [12a - %A - 12, 12b - %A - 12, 12c - %A - 12, + 2 2 + 12d - %A - 12, 6e + %A + 3%A + 12, + 2 + 6f + %A - 3%A + 12] + ] + , + + 4 3 2 + [complexRoots= ? + 6? + 30? + 36? + 36, + + coordinates = + 3 2 + [6a - %A - 5%A - 24%A - 6, + 3 2 + 30b + %A + 5%A + 30%A + 6, + 3 2 + 30c + %A + 5%A + 30%A + 6, + 3 2 + 30d + %A + 5%A + 30%A + 6, + 3 2 + 30e + %A + 5%A + 30%A + 6, + 3 2 + 30f + %A + 5%A + 6] + ] + , + + 4 3 2 + [complexRoots= ? - 6? + 30? - 36? + 36, + + coordinates = + 3 2 + [6a - %A + 5%A - 24%A + 6, + 3 2 + 30b + %A - 5%A + 30%A - 6, + 3 2 + 30c + %A - 5%A + 30%A - 6, + 3 2 + 30d + %A - 5%A + 30%A - 6, + 3 2 + 30e + %A - 5%A + 30%A - 6, + 3 2 + 30f + %A - 5%A - 6] + ] + , + + 4 2 + [complexRoots= ? + 12? + 144, + + coordinates = + 2 2 2 + [12a + %A + 12, 12b + %A + 12, 12c + %A + 12, + 2 2 + 12d + %A + 12, 6e - %A + 3%A - 12, + 2 + 6f - %A - 3%A - 12] + ] + , + + 2 + [complexRoots= ? - 12, + + coordinates = + [a - 1,b - 1,c - 1,d - 1,2e + %A + 4,2f - %A + 4] + ] + , + + 2 + [complexRoots= ? + 6? + 6, + + coordinates = + [a + %A + 5,b - 1,c - 1,d - 1,e - 1,f - %A - 1] + ] + , + + 2 + [complexRoots= ? - 6? + 6, + + coordinates = + [a + %A - 5,b + 1,c + 1,d + 1,e + 1,f - %A + 1] + ] + , + + 2 + [complexRoots= ? - 12, + + coordinates = + [a + 1,b + 1,c + 1,d + 1,2e + %A - 4,2f - %A - 4] + ] + , + + 4 3 2 + [complexRoots= ? + 6? + 30? + 36? + 36, + + coordinates = + 3 2 + [30a - %A - 5%A - 30%A - 6, + 3 2 + 30b - %A - 5%A - 30%A - 6, + 3 2 + 30c - %A - 5%A - 30%A - 6, + 3 2 + 6d + %A + 5%A + 24%A + 6, + 3 2 + 30e - %A - 5%A - 6, + 3 2 + 30f - %A - 5%A - 30%A - 6] + ] + , + + 4 3 2 + [complexRoots= ? - 6? + 30? - 36? + 36, + + coordinates = + 3 2 + [30a - %A + 5%A - 30%A + 6, + 3 2 + 30b - %A + 5%A - 30%A + 6, + 3 2 + 30c - %A + 5%A - 30%A + 6, + 3 2 + 6d + %A - 5%A + 24%A - 6, + 3 2 + 30e - %A + 5%A + 6, + 3 2 + 30f - %A + 5%A - 30%A + 6] + ] + , + + 2 + [complexRoots= ? + 6? + 6, + + coordinates = + [a + 1,b + 1,c + 1,d - %A - 5,e + %A + 1,f + 1] + ] + , + + 2 + [complexRoots= ? - 6? + 6, + + coordinates = + [a - 1,b - 1,c - 1,d - %A + 5,e + %A - 1,f - 1] + ] + ] +Type: List Record(complexRoots: SparseUnivariatePolynomial Integer,coordinates: List Polynomial Integer) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{LexTriangularPackageXmpPageEmpty21} +\begin{paste}{LexTriangularPackageXmpPageEmpty21}{LexTriangularPackageXmpPagePatch21} +\pastebutton{LexTriangularPackageXmpPageEmpty21}{\showpaste} +\tab{5}\spadcommand{concat [univariateSolve(ts)$zdpack for ts in lts]\free{lts }\free{zdpack }} +\end{paste}\end{patch} + +\begin{patch}{LexTriangularPackageXmpPagePatch22} +\begin{paste}{LexTriangularPackageXmpPageFull22}{LexTriangularPackageXmpPageEmpty22} +\pastebutton{LexTriangularPackageXmpPageFull22}{\hidepaste} +\tab{5}\spadcommand{concat [realSolve(ts)$zdpack for ts in lts]\free{lts }\free{zdpack }} +\indentrel{3}\begin{verbatim} + (22) + [[%R1,%R1,%R1,%R5,- %R5 - 4%R1,%R1], + [%R1,%R1,%R1,%R6,- %R6 - 4%R1,%R1], + [%R2,%R2,%R2,%R3,- %R3 - 4%R2,%R2], + [%R2,%R2,%R2,%R4,- %R4 - 4%R2,%R2], + [%R7,%R7,%R7,%R7,%R11,- %R11 - 4%R7], + [%R7,%R7,%R7,%R7,%R12,- %R12 - 4%R7], + [%R8,%R8,%R8,%R8,%R9,- %R9 - 4%R8], + [%R8,%R8,%R8,%R8,%R10,- %R10 - 4%R8], + [%R13,%R13,%R17,- %R17 - 4%R13,%R13,%R13], + [%R13,%R13,%R18,- %R18 - 4%R13,%R13,%R13], + [%R14,%R14,%R15,- %R15 - 4%R14,%R14,%R14], + [%R14,%R14,%R16,- %R16 - 4%R14,%R14,%R14], + + [%R19, %R29, + + 7865521 31 6696179241 25 + ÄÄÄÄÄÄÄÄÄÄ %R19 - ÄÄÄÄÄÄÄÄÄÄ %R19 + 6006689520 2002229840 + + + 25769893181 19 1975912990729 13 + - ÄÄÄÄÄÄÄÄÄÄÄ %R19 - ÄÄÄÄÄÄÄÄÄÄÄÄÄ %R19 + 49235160 3003344760 + + + 1048460696489 7 21252634831 + - ÄÄÄÄÄÄÄÄÄÄÄÄÄ %R19 - ÄÄÄÄÄÄÄÄÄÄÄ %R19 + 2002229840 6006689520 + , + + 778171189 31 1987468196267 25 + - ÄÄÄÄÄÄÄÄÄÄÄÄÄ %R19 + ÄÄÄÄÄÄÄÄÄÄÄÄÄ %R19 + 1387545279120 1387545279120 + + + 155496778477189 19 191631411158401 13 + ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ %R19 + ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ %R19 + 693772639560 693772639560 + + + 300335488637543 7 755656433863 + ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ %R19 - ÄÄÄÄÄÄÄÄÄÄÄÄ %R19 + 1387545279120 198220754160 + , + + 1094352947 31 2794979430821 25 + ÄÄÄÄÄÄÄÄÄÄÄÄ %R19 - ÄÄÄÄÄÄÄÄÄÄÄÄÄ %R19 + 462515093040 462515093040 + + + 218708802908737 19 91476663003591 13 + - ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ %R19 - ÄÄÄÄÄÄÄÄÄÄÄÄÄÄ %R19 + 231257546520 77085848840 + + + 145152550961823 7 1564893370717 + - ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ %R19 - ÄÄÄÄÄÄÄÄÄÄÄÄÄ %R19 + 154171697680 462515093040 + , + + 4321823003 31 + - %R29 - ÄÄÄÄÄÄÄÄÄÄÄÄÄ %R19 + 1387545279120 + + + 180949546069 25 863753195062493 19 + ÄÄÄÄÄÄÄÄÄÄÄÄ %R19 + ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ %R19 + 22746643920 693772639560 + + + 1088094456732317 13 1732620732685741 7 + ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ %R19 + ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ %R19 + 693772639560 1387545279120 + + + 13506088516033 + ÄÄÄÄÄÄÄÄÄÄÄÄÄÄ %R19 + 1387545279120 + ] + , + + [%R19, %R30, + + 7865521 31 6696179241 25 + ÄÄÄÄÄÄÄÄÄÄ %R19 - ÄÄÄÄÄÄÄÄÄÄ %R19 + 6006689520 2002229840 + + + 25769893181 19 1975912990729 13 + - ÄÄÄÄÄÄÄÄÄÄÄ %R19 - ÄÄÄÄÄÄÄÄÄÄÄÄÄ %R19 + 49235160 3003344760 + + + 1048460696489 7 21252634831 + - ÄÄÄÄÄÄÄÄÄÄÄÄÄ %R19 - ÄÄÄÄÄÄÄÄÄÄÄ %R19 + 2002229840 6006689520 + , + + 778171189 31 1987468196267 25 + - ÄÄÄÄÄÄÄÄÄÄÄÄÄ %R19 + ÄÄÄÄÄÄÄÄÄÄÄÄÄ %R19 + 1387545279120 1387545279120 + + + 155496778477189 19 191631411158401 13 + ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ %R19 + ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ %R19 + 693772639560 693772639560 + + + 300335488637543 7 755656433863 + ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ %R19 - ÄÄÄÄÄÄÄÄÄÄÄÄ %R19 + 1387545279120 198220754160 + , + + 1094352947 31 2794979430821 25 + ÄÄÄÄÄÄÄÄÄÄÄÄ %R19 - ÄÄÄÄÄÄÄÄÄÄÄÄÄ %R19 + 462515093040 462515093040 + + + 218708802908737 19 91476663003591 13 + - ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ %R19 - ÄÄÄÄÄÄÄÄÄÄÄÄÄÄ %R19 + 231257546520 77085848840 + + + 145152550961823 7 1564893370717 + - ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ %R19 - ÄÄÄÄÄÄÄÄÄÄÄÄÄ %R19 + 154171697680 462515093040 + , + + 4321823003 31 + - %R30 - ÄÄÄÄÄÄÄÄÄÄÄÄÄ %R19 + 1387545279120 + + + 180949546069 25 863753195062493 19 + ÄÄÄÄÄÄÄÄÄÄÄÄ %R19 + ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ %R19 + 22746643920 693772639560 + + + 1088094456732317 13 1732620732685741 7 + ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ %R19 + ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ %R19 + 693772639560 1387545279120 + + + 13506088516033 + ÄÄÄÄÄÄÄÄÄÄÄÄÄÄ %R19 + 1387545279120 + ] + , + + [%R20, %R27, + + 7865521 31 6696179241 25 + ÄÄÄÄÄÄÄÄÄÄ %R20 - ÄÄÄÄÄÄÄÄÄÄ %R20 + 6006689520 2002229840 + + + 25769893181 19 1975912990729 13 + - ÄÄÄÄÄÄÄÄÄÄÄ %R20 - ÄÄÄÄÄÄÄÄÄÄÄÄÄ %R20 + 49235160 3003344760 + + + 1048460696489 7 21252634831 + - ÄÄÄÄÄÄÄÄÄÄÄÄÄ %R20 - ÄÄÄÄÄÄÄÄÄÄÄ %R20 + 2002229840 6006689520 + , + + 778171189 31 1987468196267 25 + - ÄÄÄÄÄÄÄÄÄÄÄÄÄ %R20 + ÄÄÄÄÄÄÄÄÄÄÄÄÄ %R20 + 1387545279120 1387545279120 + + + 155496778477189 19 191631411158401 13 + ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ %R20 + ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ %R20 + 693772639560 693772639560 + + + 300335488637543 7 755656433863 + ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ %R20 - ÄÄÄÄÄÄÄÄÄÄÄÄ %R20 + 1387545279120 198220754160 + , + + 1094352947 31 2794979430821 25 + ÄÄÄÄÄÄÄÄÄÄÄÄ %R20 - ÄÄÄÄÄÄÄÄÄÄÄÄÄ %R20 + 462515093040 462515093040 + + + 218708802908737 19 91476663003591 13 + - ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ %R20 - ÄÄÄÄÄÄÄÄÄÄÄÄÄÄ %R20 + 231257546520 77085848840 + + + 145152550961823 7 1564893370717 + - ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ %R20 - ÄÄÄÄÄÄÄÄÄÄÄÄÄ %R20 + 154171697680 462515093040 + , + + 4321823003 31 + - %R27 - ÄÄÄÄÄÄÄÄÄÄÄÄÄ %R20 + 1387545279120 + + + 180949546069 25 863753195062493 19 + ÄÄÄÄÄÄÄÄÄÄÄÄ %R20 + ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ %R20 + 22746643920 693772639560 + + + 1088094456732317 13 1732620732685741 7 + ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ %R20 + ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ %R20 + 693772639560 1387545279120 + + + 13506088516033 + ÄÄÄÄÄÄÄÄÄÄÄÄÄÄ %R20 + 1387545279120 + ] + , + + [%R20, %R28, + + 7865521 31 6696179241 25 + ÄÄÄÄÄÄÄÄÄÄ %R20 - ÄÄÄÄÄÄÄÄÄÄ %R20 + 6006689520 2002229840 + + + 25769893181 19 1975912990729 13 + - ÄÄÄÄÄÄÄÄÄÄÄ %R20 - ÄÄÄÄÄÄÄÄÄÄÄÄÄ %R20 + 49235160 3003344760 + + + 1048460696489 7 21252634831 + - ÄÄÄÄÄÄÄÄÄÄÄÄÄ %R20 - ÄÄÄÄÄÄÄÄÄÄÄ %R20 + 2002229840 6006689520 + , + + 778171189 31 1987468196267 25 + - ÄÄÄÄÄÄÄÄÄÄÄÄÄ %R20 + ÄÄÄÄÄÄÄÄÄÄÄÄÄ %R20 + 1387545279120 1387545279120 + + + 155496778477189 19 191631411158401 13 + ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ %R20 + ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ %R20 + 693772639560 693772639560 + + + 300335488637543 7 755656433863 + ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ %R20 - ÄÄÄÄÄÄÄÄÄÄÄÄ %R20 + 1387545279120 198220754160 + , + + 1094352947 31 2794979430821 25 + ÄÄÄÄÄÄÄÄÄÄÄÄ %R20 - ÄÄÄÄÄÄÄÄÄÄÄÄÄ %R20 + 462515093040 462515093040 + + + 218708802908737 19 91476663003591 13 + - ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ %R20 - ÄÄÄÄÄÄÄÄÄÄÄÄÄÄ %R20 + 231257546520 77085848840 + + + 145152550961823 7 1564893370717 + - ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ %R20 - ÄÄÄÄÄÄÄÄÄÄÄÄÄ %R20 + 154171697680 462515093040 + , + + 4321823003 31 + - %R28 - ÄÄÄÄÄÄÄÄÄÄÄÄÄ %R20 + 1387545279120 + + + 180949546069 25 863753195062493 19 + ÄÄÄÄÄÄÄÄÄÄÄÄ %R20 + ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ %R20 + 22746643920 693772639560 + + + 1088094456732317 13 1732620732685741 7 + ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ %R20 + ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ %R20 + 693772639560 1387545279120 + + + 13506088516033 + ÄÄÄÄÄÄÄÄÄÄÄÄÄÄ %R20 + 1387545279120 + ] + , + + [%R21, %R25, + + 7865521 31 6696179241 25 + ÄÄÄÄÄÄÄÄÄÄ %R21 - ÄÄÄÄÄÄÄÄÄÄ %R21 + 6006689520 2002229840 + + + 25769893181 19 1975912990729 13 + - ÄÄÄÄÄÄÄÄÄÄÄ %R21 - ÄÄÄÄÄÄÄÄÄÄÄÄÄ %R21 + 49235160 3003344760 + + + 1048460696489 7 21252634831 + - ÄÄÄÄÄÄÄÄÄÄÄÄÄ %R21 - ÄÄÄÄÄÄÄÄÄÄÄ %R21 + 2002229840 6006689520 + , + + 778171189 31 1987468196267 25 + - ÄÄÄÄÄÄÄÄÄÄÄÄÄ %R21 + ÄÄÄÄÄÄÄÄÄÄÄÄÄ %R21 + 1387545279120 1387545279120 + + + 155496778477189 19 191631411158401 13 + ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ %R21 + ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ %R21 + 693772639560 693772639560 + + + 300335488637543 7 755656433863 + ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ %R21 - ÄÄÄÄÄÄÄÄÄÄÄÄ %R21 + 1387545279120 198220754160 + , + + 1094352947 31 2794979430821 25 + ÄÄÄÄÄÄÄÄÄÄÄÄ %R21 - ÄÄÄÄÄÄÄÄÄÄÄÄÄ %R21 + 462515093040 462515093040 + + + 218708802908737 19 91476663003591 13 + - ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ %R21 - ÄÄÄÄÄÄÄÄÄÄÄÄÄÄ %R21 + 231257546520 77085848840 + + + 145152550961823 7 1564893370717 + - ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ %R21 - ÄÄÄÄÄÄÄÄÄÄÄÄÄ %R21 + 154171697680 462515093040 + , + + 4321823003 31 + - %R25 - ÄÄÄÄÄÄÄÄÄÄÄÄÄ %R21 + 1387545279120 + + + 180949546069 25 863753195062493 19 + ÄÄÄÄÄÄÄÄÄÄÄÄ %R21 + ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ %R21 + 22746643920 693772639560 + + + 1088094456732317 13 1732620732685741 7 + ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ %R21 + ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ %R21 + 693772639560 1387545279120 + + + 13506088516033 + ÄÄÄÄÄÄÄÄÄÄÄÄÄÄ %R21 + 1387545279120 + ] + , + + [%R21, %R26, + + 7865521 31 6696179241 25 + ÄÄÄÄÄÄÄÄÄÄ %R21 - ÄÄÄÄÄÄÄÄÄÄ %R21 + 6006689520 2002229840 + + + 25769893181 19 1975912990729 13 + - ÄÄÄÄÄÄÄÄÄÄÄ %R21 - ÄÄÄÄÄÄÄÄÄÄÄÄÄ %R21 + 49235160 3003344760 + + + 1048460696489 7 21252634831 + - ÄÄÄÄÄÄÄÄÄÄÄÄÄ %R21 - ÄÄÄÄÄÄÄÄÄÄÄ %R21 + 2002229840 6006689520 + , + + 778171189 31 1987468196267 25 + - ÄÄÄÄÄÄÄÄÄÄÄÄÄ %R21 + ÄÄÄÄÄÄÄÄÄÄÄÄÄ %R21 + 1387545279120 1387545279120 + + + 155496778477189 19 191631411158401 13 + ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ %R21 + ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ %R21 + 693772639560 693772639560 + + + 300335488637543 7 755656433863 + ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ %R21 - ÄÄÄÄÄÄÄÄÄÄÄÄ %R21 + 1387545279120 198220754160 + , + + 1094352947 31 2794979430821 25 + ÄÄÄÄÄÄÄÄÄÄÄÄ %R21 - ÄÄÄÄÄÄÄÄÄÄÄÄÄ %R21 + 462515093040 462515093040 + + + 218708802908737 19 91476663003591 13 + - ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ %R21 - ÄÄÄÄÄÄÄÄÄÄÄÄÄÄ %R21 + 231257546520 77085848840 + + + 145152550961823 7 1564893370717 + - ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ %R21 - ÄÄÄÄÄÄÄÄÄÄÄÄÄ %R21 + 154171697680 462515093040 + , + + 4321823003 31 + - %R26 - ÄÄÄÄÄÄÄÄÄÄÄÄÄ %R21 + 1387545279120 + + + 180949546069 25 863753195062493 19 + ÄÄÄÄÄÄÄÄÄÄÄÄ %R21 + ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ %R21 + 22746643920 693772639560 + + + 1088094456732317 13 1732620732685741 7 + ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ %R21 + ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ %R21 + 693772639560 1387545279120 + + + 13506088516033 + ÄÄÄÄÄÄÄÄÄÄÄÄÄÄ %R21 + 1387545279120 + ] + , + + [%R22, %R23, + + 7865521 31 6696179241 25 + ÄÄÄÄÄÄÄÄÄÄ %R22 - ÄÄÄÄÄÄÄÄÄÄ %R22 + 6006689520 2002229840 + + + 25769893181 19 1975912990729 13 + - ÄÄÄÄÄÄÄÄÄÄÄ %R22 - ÄÄÄÄÄÄÄÄÄÄÄÄÄ %R22 + 49235160 3003344760 + + + 1048460696489 7 21252634831 + - ÄÄÄÄÄÄÄÄÄÄÄÄÄ %R22 - ÄÄÄÄÄÄÄÄÄÄÄ %R22 + 2002229840 6006689520 + , + + 778171189 31 1987468196267 25 + - ÄÄÄÄÄÄÄÄÄÄÄÄÄ %R22 + ÄÄÄÄÄÄÄÄÄÄÄÄÄ %R22 + 1387545279120 1387545279120 + + + 155496778477189 19 191631411158401 13 + ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ %R22 + ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ %R22 + 693772639560 693772639560 + + + 300335488637543 7 755656433863 + ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ %R22 - ÄÄÄÄÄÄÄÄÄÄÄÄ %R22 + 1387545279120 198220754160 + , + + 1094352947 31 2794979430821 25 + ÄÄÄÄÄÄÄÄÄÄÄÄ %R22 - ÄÄÄÄÄÄÄÄÄÄÄÄÄ %R22 + 462515093040 462515093040 + + + 218708802908737 19 91476663003591 13 + - ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ %R22 - ÄÄÄÄÄÄÄÄÄÄÄÄÄÄ %R22 + 231257546520 77085848840 + + + 145152550961823 7 1564893370717 + - ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ %R22 - ÄÄÄÄÄÄÄÄÄÄÄÄÄ %R22 + 154171697680 462515093040 + , + + 4321823003 31 + - %R23 - ÄÄÄÄÄÄÄÄÄÄÄÄÄ %R22 + 1387545279120 + + + 180949546069 25 863753195062493 19 + ÄÄÄÄÄÄÄÄÄÄÄÄ %R22 + ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ %R22 + 22746643920 693772639560 + + + 1088094456732317 13 1732620732685741 7 + ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ %R22 + ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ %R22 + 693772639560 1387545279120 + + + 13506088516033 + ÄÄÄÄÄÄÄÄÄÄÄÄÄÄ %R22 + 1387545279120 + ] + , + + [%R22, %R24, + + 7865521 31 6696179241 25 + ÄÄÄÄÄÄÄÄÄÄ %R22 - ÄÄÄÄÄÄÄÄÄÄ %R22 + 6006689520 2002229840 + + + 25769893181 19 1975912990729 13 + - ÄÄÄÄÄÄÄÄÄÄÄ %R22 - ÄÄÄÄÄÄÄÄÄÄÄÄÄ %R22 + 49235160 3003344760 + + + 1048460696489 7 21252634831 + - ÄÄÄÄÄÄÄÄÄÄÄÄÄ %R22 - ÄÄÄÄÄÄÄÄÄÄÄ %R22 + 2002229840 6006689520 + , + + 778171189 31 1987468196267 25 + - ÄÄÄÄÄÄÄÄÄÄÄÄÄ %R22 + ÄÄÄÄÄÄÄÄÄÄÄÄÄ %R22 + 1387545279120 1387545279120 + + + 155496778477189 19 191631411158401 13 + ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ %R22 + ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ %R22 + 693772639560 693772639560 + + + 300335488637543 7 755656433863 + ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ %R22 - ÄÄÄÄÄÄÄÄÄÄÄÄ %R22 + 1387545279120 198220754160 + , + + 1094352947 31 2794979430821 25 + ÄÄÄÄÄÄÄÄÄÄÄÄ %R22 - ÄÄÄÄÄÄÄÄÄÄÄÄÄ %R22 + 462515093040 462515093040 + + + 218708802908737 19 91476663003591 13 + - ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ %R22 - ÄÄÄÄÄÄÄÄÄÄÄÄÄÄ %R22 + 231257546520 77085848840 + + + 145152550961823 7 1564893370717 + - ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ %R22 - ÄÄÄÄÄÄÄÄÄÄÄÄÄ %R22 + 154171697680 462515093040 + , + + 4321823003 31 + - %R24 - ÄÄÄÄÄÄÄÄÄÄÄÄÄ %R22 + 1387545279120 + + + 180949546069 25 863753195062493 19 + ÄÄÄÄÄÄÄÄÄÄÄÄ %R22 + ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ %R22 + 22746643920 693772639560 + + + 1088094456732317 13 1732620732685741 7 + ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ %R22 + ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ %R22 + 693772639560 1387545279120 + + + 13506088516033 + ÄÄÄÄÄÄÄÄÄÄÄÄÄÄ %R22 + 1387545279120 + ] + , + [%R31,%R35,- %R35 - 4%R31,%R31,%R31,%R31], + [%R31,%R36,- %R36 - 4%R31,%R31,%R31,%R31], + [%R32,%R33,- %R33 - 4%R32,%R32,%R32,%R32], + [%R32,%R34,- %R34 - 4%R32,%R32,%R32,%R32]] + Type: List List RealClosure Fraction Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{LexTriangularPackageXmpPageEmpty22} +\begin{paste}{LexTriangularPackageXmpPageEmpty22}{LexTriangularPackageXmpPagePatch22} +\pastebutton{LexTriangularPackageXmpPageEmpty22}{\showpaste} +\tab{5}\spadcommand{concat [realSolve(ts)$zdpack for ts in lts]\free{lts }\free{zdpack }} +\end{paste}\end{patch} + @ \section{lib.ht} \pagehead{LibraryXmpPage}{lib.ht}{Library} @@ -12729,7 +35843,135 @@ For more information on related topics, see \endscroll \autobuttons \end{page} -% + +\begin{patch}{LibraryXmpPagePatch1} +\begin{paste}{LibraryXmpPageFull1}{LibraryXmpPageEmpty1} +\pastebutton{LibraryXmpPageFull1}{\hidepaste} +\tab{5}\spadcommand{stuff := library "/tmp/Neat.stuff"\bound{stuff }} +\indentrel{3}\begin{verbatim} + (1) "/tmp/Neat.stuff" + Type: Library +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{LibraryXmpPageEmpty1} +\begin{paste}{LibraryXmpPageEmpty1}{LibraryXmpPagePatch1} +\pastebutton{LibraryXmpPageEmpty1}{\showpaste} +\tab{5}\spadcommand{stuff := library "/tmp/Neat.stuff"\bound{stuff }} +\end{paste}\end{patch} + +\begin{patch}{LibraryXmpPagePatch2} +\begin{paste}{LibraryXmpPageFull2}{LibraryXmpPageEmpty2} +\pastebutton{LibraryXmpPageFull2}{\hidepaste} +\tab{5}\spadcommand{stuff.int := 32**2\free{stuff }\bound{stuffa }} +\indentrel{3}\begin{verbatim} + (2) 1024 + Type: PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{LibraryXmpPageEmpty2} +\begin{paste}{LibraryXmpPageEmpty2}{LibraryXmpPagePatch2} +\pastebutton{LibraryXmpPageEmpty2}{\showpaste} +\tab{5}\spadcommand{stuff.int := 32**2\free{stuff }\bound{stuffa }} +\end{paste}\end{patch} + +\begin{patch}{LibraryXmpPagePatch3} +\begin{paste}{LibraryXmpPageFull3}{LibraryXmpPageEmpty3} +\pastebutton{LibraryXmpPageFull3}{\hidepaste} +\tab{5}\spadcommand{stuff."poly" := x**2 + 1\free{stuffa }\bound{stuffb }} +\indentrel{3}\begin{verbatim} + 2 + (3) x + 1 + Type: Polynomial Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{LibraryXmpPageEmpty3} +\begin{paste}{LibraryXmpPageEmpty3}{LibraryXmpPagePatch3} +\pastebutton{LibraryXmpPageEmpty3}{\showpaste} +\tab{5}\spadcommand{stuff."poly" := x**2 + 1\free{stuffa }\bound{stuffb }} +\end{paste}\end{patch} + +\begin{patch}{LibraryXmpPagePatch4} +\begin{paste}{LibraryXmpPageFull4}{LibraryXmpPageEmpty4} +\pastebutton{LibraryXmpPageFull4}{\hidepaste} +\tab{5}\spadcommand{stuff.str := "Hello"\free{stuffb }\bound{stuffc }} +\indentrel{3}\begin{verbatim} + (4) "Hello" + Type: String +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{LibraryXmpPageEmpty4} +\begin{paste}{LibraryXmpPageEmpty4}{LibraryXmpPagePatch4} +\pastebutton{LibraryXmpPageEmpty4}{\showpaste} +\tab{5}\spadcommand{stuff.str := "Hello"\free{stuffb }\bound{stuffc }} +\end{paste}\end{patch} + +\begin{patch}{LibraryXmpPagePatch5} +\begin{paste}{LibraryXmpPageFull5}{LibraryXmpPageEmpty5} +\pastebutton{LibraryXmpPageFull5}{\hidepaste} +\tab{5}\spadcommand{keys stuff\free{stuffa stuffb stuffc }\bound{stuffabc }} +\indentrel{3}\begin{verbatim} + (5) ["str","poly","int"] + Type: List String +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{LibraryXmpPageEmpty5} +\begin{paste}{LibraryXmpPageEmpty5}{LibraryXmpPagePatch5} +\pastebutton{LibraryXmpPageEmpty5}{\showpaste} +\tab{5}\spadcommand{keys stuff\free{stuffa stuffb stuffc }\bound{stuffabc }} +\end{paste}\end{patch} + +\begin{patch}{LibraryXmpPagePatch6} +\begin{paste}{LibraryXmpPageFull6}{LibraryXmpPageEmpty6} +\pastebutton{LibraryXmpPageFull6}{\hidepaste} +\tab{5}\spadcommand{stuff.poly\free{stuffb }} +\indentrel{3}\begin{verbatim} + 2 + (6) x + 1 + Type: Polynomial Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{LibraryXmpPageEmpty6} +\begin{paste}{LibraryXmpPageEmpty6}{LibraryXmpPagePatch6} +\pastebutton{LibraryXmpPageEmpty6}{\showpaste} +\tab{5}\spadcommand{stuff.poly\free{stuffb }} +\end{paste}\end{patch} + +\begin{patch}{LibraryXmpPagePatch7} +\begin{paste}{LibraryXmpPageFull7}{LibraryXmpPageEmpty7} +\pastebutton{LibraryXmpPageFull7}{\hidepaste} +\tab{5}\spadcommand{stuff("poly")\free{stuffb }} +\indentrel{3}\begin{verbatim} + 2 + (7) x + 1 + Type: Polynomial Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{LibraryXmpPageEmpty7} +\begin{paste}{LibraryXmpPageEmpty7}{LibraryXmpPagePatch7} +\pastebutton{LibraryXmpPageEmpty7}{\showpaste} +\tab{5}\spadcommand{stuff("poly")\free{stuffb }} +\end{paste}\end{patch} + +\begin{patch}{LibraryXmpPagePatch8} +\begin{paste}{LibraryXmpPageFull8}{LibraryXmpPageEmpty8} +\pastebutton{LibraryXmpPageFull8}{\hidepaste} +\tab{5}\spadcommand{)system rm -rf /tmp/Neat.stuff\free{stuff }\bound{rmstuff }} +\indentrel{3}\begin{verbatim} +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{LibraryXmpPageEmpty8} +\begin{paste}{LibraryXmpPageEmpty8}{LibraryXmpPagePatch8} +\pastebutton{LibraryXmpPageEmpty8}{\showpaste} +\tab{5}\spadcommand{)system rm -rf /tmp/Neat.stuff\free{stuff }\bound{rmstuff }} +\end{paste}\end{patch} @ \section{link.ht} @@ -13751,6 +36993,86 @@ list. \autobuttons \end{page} +\begin{patch}{ugxListCreatePagePatch1} +\begin{paste}{ugxListCreatePageFull1}{ugxListCreatePageEmpty1} +\pastebutton{ugxListCreatePageFull1}{\hidepaste} +\tab{5}\spadcommand{[2, 4, 5, 6]} +\indentrel{3}\begin{verbatim} + (1) [2,4,5,6] + Type: List PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxListCreatePageEmpty1} +\begin{paste}{ugxListCreatePageEmpty1}{ugxListCreatePagePatch1} +\pastebutton{ugxListCreatePageEmpty1}{\showpaste} +\tab{5}\spadcommand{[2, 4, 5, 6]} +\end{paste}\end{patch} + +\begin{patch}{ugxListCreatePagePatch2} +\begin{paste}{ugxListCreatePageFull2}{ugxListCreatePageEmpty2} +\pastebutton{ugxListCreatePageFull2}{\hidepaste} +\tab{5}\spadcommand{[1]} +\indentrel{3}\begin{verbatim} + (2) [1] + Type: List PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxListCreatePageEmpty2} +\begin{paste}{ugxListCreatePageEmpty2}{ugxListCreatePagePatch2} +\pastebutton{ugxListCreatePageEmpty2}{\showpaste} +\tab{5}\spadcommand{[1]} +\end{paste}\end{patch} + +\begin{patch}{ugxListCreatePagePatch3} +\begin{paste}{ugxListCreatePageFull3}{ugxListCreatePageEmpty3} +\pastebutton{ugxListCreatePageFull3}{\hidepaste} +\tab{5}\spadcommand{list(1)} +\indentrel{3}\begin{verbatim} + (3) [1] + Type: List PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxListCreatePageEmpty3} +\begin{paste}{ugxListCreatePageEmpty3}{ugxListCreatePagePatch3} +\pastebutton{ugxListCreatePageEmpty3}{\showpaste} +\tab{5}\spadcommand{list(1)} +\end{paste}\end{patch} + +\begin{patch}{ugxListCreatePagePatch4} +\begin{paste}{ugxListCreatePageFull4}{ugxListCreatePageEmpty4} +\pastebutton{ugxListCreatePageFull4}{\hidepaste} +\tab{5}\spadcommand{append([1,2,3],[5,6,7])} +\indentrel{3}\begin{verbatim} + (4) [1,2,3,5,6,7] + Type: List PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxListCreatePageEmpty4} +\begin{paste}{ugxListCreatePageEmpty4}{ugxListCreatePagePatch4} +\pastebutton{ugxListCreatePageEmpty4}{\showpaste} +\tab{5}\spadcommand{append([1,2,3],[5,6,7])} +\end{paste}\end{patch} + +\begin{patch}{ugxListCreatePagePatch5} +\begin{paste}{ugxListCreatePageFull5}{ugxListCreatePageEmpty5} +\pastebutton{ugxListCreatePageFull5}{\hidepaste} +\tab{5}\spadcommand{cons(10,[9,8,7])} +\indentrel{3}\begin{verbatim} + (5) [10,9,8,7] + Type: List PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxListCreatePageEmpty5} +\begin{paste}{ugxListCreatePageEmpty5}{ugxListCreatePagePatch5} +\pastebutton{ugxListCreatePageEmpty5}{\showpaste} +\tab{5}\spadcommand{cons(10,[9,8,7])} +\end{paste}\end{patch} + @ \pagehead{ugxListAccessPage}{list.ht}{Accessing List Elements} <>= @@ -13838,6 +37160,182 @@ extracts the element from the list. \autobuttons \end{page} +\begin{patch}{ugxListAccessPagePatch1} +\begin{paste}{ugxListAccessPageFull1}{ugxListAccessPageEmpty1} +\pastebutton{ugxListAccessPageFull1}{\hidepaste} +\tab{5}\spadcommand{empty? [x+1]} +\indentrel{3}\begin{verbatim} + (1) false + Type: Boolean +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxListAccessPageEmpty1} +\begin{paste}{ugxListAccessPageEmpty1}{ugxListAccessPagePatch1} +\pastebutton{ugxListAccessPageEmpty1}{\showpaste} +\tab{5}\spadcommand{empty? [x+1]} +\end{paste}\end{patch} + +\begin{patch}{ugxListAccessPagePatch2} +\begin{paste}{ugxListAccessPageFull2}{ugxListAccessPageEmpty2} +\pastebutton{ugxListAccessPageFull2}{\hidepaste} +\tab{5}\spadcommand{([] = nil)@Boolean} +\indentrel{3}\begin{verbatim} + (2) true + Type: Boolean +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxListAccessPageEmpty2} +\begin{paste}{ugxListAccessPageEmpty2}{ugxListAccessPagePatch2} +\pastebutton{ugxListAccessPageEmpty2}{\showpaste} +\tab{5}\spadcommand{([] = nil)@Boolean} +\end{paste}\end{patch} + +\begin{patch}{ugxListAccessPagePatch3} +\begin{paste}{ugxListAccessPageFull3}{ugxListAccessPageEmpty3} +\pastebutton{ugxListAccessPageFull3}{\hidepaste} +\tab{5}\spadcommand{k := [4,3,7,3,8,5,9,2]\bound{k }} +\indentrel{3}\begin{verbatim} + (3) [4,3,7,3,8,5,9,2] + Type: List PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxListAccessPageEmpty3} +\begin{paste}{ugxListAccessPageEmpty3}{ugxListAccessPagePatch3} +\pastebutton{ugxListAccessPageEmpty3}{\showpaste} +\tab{5}\spadcommand{k := [4,3,7,3,8,5,9,2]\bound{k }} +\end{paste}\end{patch} + +\begin{patch}{ugxListAccessPagePatch4} +\begin{paste}{ugxListAccessPageFull4}{ugxListAccessPageEmpty4} +\pastebutton{ugxListAccessPageFull4}{\hidepaste} +\tab{5}\spadcommand{first k\free{k }} +\indentrel{3}\begin{verbatim} + (4) 4 + Type: PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxListAccessPageEmpty4} +\begin{paste}{ugxListAccessPageEmpty4}{ugxListAccessPagePatch4} +\pastebutton{ugxListAccessPageEmpty4}{\showpaste} +\tab{5}\spadcommand{first k\free{k }} +\end{paste}\end{patch} + +\begin{patch}{ugxListAccessPagePatch5} +\begin{paste}{ugxListAccessPageFull5}{ugxListAccessPageEmpty5} +\pastebutton{ugxListAccessPageFull5}{\hidepaste} +\tab{5}\spadcommand{k.first\free{k }} +\indentrel{3}\begin{verbatim} + (5) 4 + Type: PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxListAccessPageEmpty5} +\begin{paste}{ugxListAccessPageEmpty5}{ugxListAccessPagePatch5} +\pastebutton{ugxListAccessPageEmpty5}{\showpaste} +\tab{5}\spadcommand{k.first\free{k }} +\end{paste}\end{patch} + +\begin{patch}{ugxListAccessPagePatch6} +\begin{paste}{ugxListAccessPageFull6}{ugxListAccessPageEmpty6} +\pastebutton{ugxListAccessPageFull6}{\hidepaste} +\tab{5}\spadcommand{k.1\free{k }} +\indentrel{3}\begin{verbatim} + (6) 4 + Type: PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxListAccessPageEmpty6} +\begin{paste}{ugxListAccessPageEmpty6}{ugxListAccessPagePatch6} +\pastebutton{ugxListAccessPageEmpty6}{\showpaste} +\tab{5}\spadcommand{k.1\free{k }} +\end{paste}\end{patch} + +\begin{patch}{ugxListAccessPagePatch7} +\begin{paste}{ugxListAccessPageFull7}{ugxListAccessPageEmpty7} +\pastebutton{ugxListAccessPageFull7}{\hidepaste} +\tab{5}\spadcommand{k(1)\free{k }} +\indentrel{3}\begin{verbatim} + (7) 4 + Type: PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxListAccessPageEmpty7} +\begin{paste}{ugxListAccessPageEmpty7}{ugxListAccessPagePatch7} +\pastebutton{ugxListAccessPageEmpty7}{\showpaste} +\tab{5}\spadcommand{k(1)\free{k }} +\end{paste}\end{patch} + +\begin{patch}{ugxListAccessPagePatch8} +\begin{paste}{ugxListAccessPageFull8}{ugxListAccessPageEmpty8} +\pastebutton{ugxListAccessPageFull8}{\hidepaste} +\tab{5}\spadcommand{n := \#k\free{k }} +\indentrel{3}\begin{verbatim} + (8) 8 + Type: PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxListAccessPageEmpty8} +\begin{paste}{ugxListAccessPageEmpty8}{ugxListAccessPagePatch8} +\pastebutton{ugxListAccessPageEmpty8}{\showpaste} +\tab{5}\spadcommand{n := \#k\free{k }} +\end{paste}\end{patch} + +\begin{patch}{ugxListAccessPagePatch9} +\begin{paste}{ugxListAccessPageFull9}{ugxListAccessPageEmpty9} +\pastebutton{ugxListAccessPageFull9}{\hidepaste} +\tab{5}\spadcommand{last k\free{k }} +\indentrel{3}\begin{verbatim} + (9) 2 + Type: PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxListAccessPageEmpty9} +\begin{paste}{ugxListAccessPageEmpty9}{ugxListAccessPagePatch9} +\pastebutton{ugxListAccessPageEmpty9}{\showpaste} +\tab{5}\spadcommand{last k\free{k }} +\end{paste}\end{patch} + +\begin{patch}{ugxListAccessPagePatch10} +\begin{paste}{ugxListAccessPageFull10}{ugxListAccessPageEmpty10} +\pastebutton{ugxListAccessPageFull10}{\hidepaste} +\tab{5}\spadcommand{k.last\free{k }} +\indentrel{3}\begin{verbatim} + (10) 2 + Type: PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxListAccessPageEmpty10} +\begin{paste}{ugxListAccessPageEmpty10}{ugxListAccessPagePatch10} +\pastebutton{ugxListAccessPageEmpty10}{\showpaste} +\tab{5}\spadcommand{k.last\free{k }} +\end{paste}\end{patch} + +\begin{patch}{ugxListAccessPagePatch11} +\begin{paste}{ugxListAccessPageFull11}{ugxListAccessPageEmpty11} +\pastebutton{ugxListAccessPageFull11}{\hidepaste} +\tab{5}\spadcommand{k.(\#k)\free{k }} +\indentrel{3}\begin{verbatim} + (11) 2 + Type: PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxListAccessPageEmpty11} +\begin{paste}{ugxListAccessPageEmpty11}{ugxListAccessPagePatch11} +\pastebutton{ugxListAccessPageEmpty11}{\showpaste} +\tab{5}\spadcommand{k.(\#k)\free{k }} +\end{paste}\end{patch} + @ \pagehead{ugxListChangePage}{list.ht}{Changing List Elements} <>= @@ -13904,6 +37402,134 @@ It changed too! \autobuttons \end{page} +\begin{patch}{ugxListChangePagePatch1} +\begin{paste}{ugxListChangePageFull1}{ugxListChangePageEmpty1} +\pastebutton{ugxListChangePageFull1}{\hidepaste} +\tab{5}\spadcommand{k := [4,3,7,3,8,5,9,2]\bound{k }} +\indentrel{3}\begin{verbatim} + (1) [4,3,7,3,8,5,9,2] + Type: List PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxListChangePageEmpty1} +\begin{paste}{ugxListChangePageEmpty1}{ugxListChangePagePatch1} +\pastebutton{ugxListChangePageEmpty1}{\showpaste} +\tab{5}\spadcommand{k := [4,3,7,3,8,5,9,2]\bound{k }} +\end{paste}\end{patch} + +\begin{patch}{ugxListChangePagePatch2} +\begin{paste}{ugxListChangePageFull2}{ugxListChangePageEmpty2} +\pastebutton{ugxListChangePageFull2}{\hidepaste} +\tab{5}\spadcommand{k.1 := 999\free{k }\bound{k1 }} +\indentrel{3}\begin{verbatim} + (2) 999 + Type: PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxListChangePageEmpty2} +\begin{paste}{ugxListChangePageEmpty2}{ugxListChangePagePatch2} +\pastebutton{ugxListChangePageEmpty2}{\showpaste} +\tab{5}\spadcommand{k.1 := 999\free{k }\bound{k1 }} +\end{paste}\end{patch} + +\begin{patch}{ugxListChangePagePatch3} +\begin{paste}{ugxListChangePageFull3}{ugxListChangePageEmpty3} +\pastebutton{ugxListChangePageFull3}{\hidepaste} +\tab{5}\spadcommand{k\free{k1 }} +\indentrel{3}\begin{verbatim} + (3) [999,3,7,3,8,5,9,2] + Type: List PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxListChangePageEmpty3} +\begin{paste}{ugxListChangePageEmpty3}{ugxListChangePagePatch3} +\pastebutton{ugxListChangePageEmpty3}{\showpaste} +\tab{5}\spadcommand{k\free{k1 }} +\end{paste}\end{patch} + +\begin{patch}{ugxListChangePagePatch4} +\begin{paste}{ugxListChangePageFull4}{ugxListChangePageEmpty4} +\pastebutton{ugxListChangePageFull4}{\hidepaste} +\tab{5}\spadcommand{k := [1,2]\bound{k2 }} +\indentrel{3}\begin{verbatim} + (4) [1,2] + Type: List PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxListChangePageEmpty4} +\begin{paste}{ugxListChangePageEmpty4}{ugxListChangePagePatch4} +\pastebutton{ugxListChangePageEmpty4}{\showpaste} +\tab{5}\spadcommand{k := [1,2]\bound{k2 }} +\end{paste}\end{patch} + +\begin{patch}{ugxListChangePagePatch5} +\begin{paste}{ugxListChangePageFull5}{ugxListChangePageEmpty5} +\pastebutton{ugxListChangePageFull5}{\hidepaste} +\tab{5}\spadcommand{m := cons(0,k)\free{k2 }\bound{m }} +\indentrel{3}\begin{verbatim} + (5) [0,1,2] + Type: List Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxListChangePageEmpty5} +\begin{paste}{ugxListChangePageEmpty5}{ugxListChangePagePatch5} +\pastebutton{ugxListChangePageEmpty5}{\showpaste} +\tab{5}\spadcommand{m := cons(0,k)\free{k2 }\bound{m }} +\end{paste}\end{patch} + +\begin{patch}{ugxListChangePagePatch6} +\begin{paste}{ugxListChangePageFull6}{ugxListChangePageEmpty6} +\pastebutton{ugxListChangePageFull6}{\hidepaste} +\tab{5}\spadcommand{m.2 := 99\free{m }\bound{m2 }} +\indentrel{3}\begin{verbatim} + (6) 99 + Type: PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxListChangePageEmpty6} +\begin{paste}{ugxListChangePageEmpty6}{ugxListChangePagePatch6} +\pastebutton{ugxListChangePageEmpty6}{\showpaste} +\tab{5}\spadcommand{m.2 := 99\free{m }\bound{m2 }} +\end{paste}\end{patch} + +\begin{patch}{ugxListChangePagePatch7} +\begin{paste}{ugxListChangePageFull7}{ugxListChangePageEmpty7} +\pastebutton{ugxListChangePageFull7}{\hidepaste} +\tab{5}\spadcommand{m\free{m2 }} +\indentrel{3}\begin{verbatim} + (7) [0,99,2] + Type: List Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxListChangePageEmpty7} +\begin{paste}{ugxListChangePageEmpty7}{ugxListChangePagePatch7} +\pastebutton{ugxListChangePageEmpty7}{\showpaste} +\tab{5}\spadcommand{m\free{m2 }} +\end{paste}\end{patch} + +\begin{patch}{ugxListChangePagePatch8} +\begin{paste}{ugxListChangePageFull8}{ugxListChangePageEmpty8} +\pastebutton{ugxListChangePageFull8}{\hidepaste} +\tab{5}\spadcommand{k\free{m2 k2 }} +\indentrel{3}\begin{verbatim} + (8) [99,2] + Type: List PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxListChangePageEmpty8} +\begin{paste}{ugxListChangePageEmpty8}{ugxListChangePagePatch8} +\pastebutton{ugxListChangePageEmpty8}{\showpaste} +\tab{5}\spadcommand{k\free{m2 k2 }} +\end{paste}\end{patch} + @ \pagehead{ugxListOtherPage}{list.ht}{Other Functions} <>= @@ -13955,6 +37581,102 @@ list \spad{k}.\footnote{\spad{reverse(rest(reverse(k)))} works.} \autobuttons \end{page} +\begin{patch}{ugxListOtherPagePatch1} +\begin{paste}{ugxListOtherPageFull1}{ugxListOtherPageEmpty1} +\pastebutton{ugxListOtherPageFull1}{\hidepaste} +\tab{5}\spadcommand{k := [1,2,3]\bound{k }} +\indentrel{3}\begin{verbatim} + (1) [1,2,3] + Type: List PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxListOtherPageEmpty1} +\begin{paste}{ugxListOtherPageEmpty1}{ugxListOtherPagePatch1} +\pastebutton{ugxListOtherPageEmpty1}{\showpaste} +\tab{5}\spadcommand{k := [1,2,3]\bound{k }} +\end{paste}\end{patch} + +\begin{patch}{ugxListOtherPagePatch2} +\begin{paste}{ugxListOtherPageFull2}{ugxListOtherPageEmpty2} +\pastebutton{ugxListOtherPageFull2}{\hidepaste} +\tab{5}\spadcommand{rest k\free{k }} +\indentrel{3}\begin{verbatim} + (2) [2,3] + Type: List PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxListOtherPageEmpty2} +\begin{paste}{ugxListOtherPageEmpty2}{ugxListOtherPagePatch2} +\pastebutton{ugxListOtherPageEmpty2}{\showpaste} +\tab{5}\spadcommand{rest k\free{k }} +\end{paste}\end{patch} + +\begin{patch}{ugxListOtherPagePatch3} +\begin{paste}{ugxListOtherPageFull3}{ugxListOtherPageEmpty3} +\pastebutton{ugxListOtherPageFull3}{\hidepaste} +\tab{5}\spadcommand{removeDuplicates [4,3,4,3,5,3,4]} +\indentrel{3}\begin{verbatim} + (3) [4,3,5] + Type: List PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxListOtherPageEmpty3} +\begin{paste}{ugxListOtherPageEmpty3}{ugxListOtherPagePatch3} +\pastebutton{ugxListOtherPageEmpty3}{\showpaste} +\tab{5}\spadcommand{removeDuplicates [4,3,4,3,5,3,4]} +\end{paste}\end{patch} + +\begin{patch}{ugxListOtherPagePatch4} +\begin{paste}{ugxListOtherPageFull4}{ugxListOtherPageEmpty4} +\pastebutton{ugxListOtherPageFull4}{\hidepaste} +\tab{5}\spadcommand{reverse [1,2,3,4,5,6]} +\indentrel{3}\begin{verbatim} + (4) [6,5,4,3,2,1] + Type: List PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxListOtherPageEmpty4} +\begin{paste}{ugxListOtherPageEmpty4}{ugxListOtherPagePatch4} +\pastebutton{ugxListOtherPageEmpty4}{\showpaste} +\tab{5}\spadcommand{reverse [1,2,3,4,5,6]} +\end{paste}\end{patch} + +\begin{patch}{ugxListOtherPagePatch5} +\begin{paste}{ugxListOtherPageFull5}{ugxListOtherPageEmpty5} +\pastebutton{ugxListOtherPageFull5}{\hidepaste} +\tab{5}\spadcommand{member?(1/2,[3/4,5/6,1/2])} +\indentrel{3}\begin{verbatim} + (5) true + Type: Boolean +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxListOtherPageEmpty5} +\begin{paste}{ugxListOtherPageEmpty5}{ugxListOtherPagePatch5} +\pastebutton{ugxListOtherPageEmpty5}{\showpaste} +\tab{5}\spadcommand{member?(1/2,[3/4,5/6,1/2])} +\end{paste}\end{patch} + +\begin{patch}{ugxListOtherPagePatch6} +\begin{paste}{ugxListOtherPageFull6}{ugxListOtherPageEmpty6} +\pastebutton{ugxListOtherPageFull6}{\hidepaste} +\tab{5}\spadcommand{member?(1/12,[3/4,5/6,1/2])} +\indentrel{3}\begin{verbatim} + (6) false + Type: Boolean +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxListOtherPageEmpty6} +\begin{paste}{ugxListOtherPageEmpty6}{ugxListOtherPagePatch6} +\pastebutton{ugxListOtherPageEmpty6}{\showpaste} +\tab{5}\spadcommand{member?(1/12,[3/4,5/6,1/2])} +\end{paste}\end{patch} + @ \pagehead{ugxListDotPage}{list.ht}{Dot, Dot} <>= @@ -13995,6 +37717,54 @@ See \downlink{`Stream'}{StreamXmpPage}\ignore{Stream} for more information. \autobuttons \end{page} +\begin{patch}{ugxListDotPagePatch1} +\begin{paste}{ugxListDotPageFull1}{ugxListDotPageEmpty1} +\pastebutton{ugxListDotPageFull1}{\hidepaste} +\tab{5}\spadcommand{[1..3,10,20..23]} +\indentrel{3}\begin{verbatim} + (1) [1..3,10..10,20..23] + Type: List Segment PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxListDotPageEmpty1} +\begin{paste}{ugxListDotPageEmpty1}{ugxListDotPagePatch1} +\pastebutton{ugxListDotPageEmpty1}{\showpaste} +\tab{5}\spadcommand{[1..3,10,20..23]} +\end{paste}\end{patch} + +\begin{patch}{ugxListDotPagePatch2} +\begin{paste}{ugxListDotPageFull2}{ugxListDotPageEmpty2} +\pastebutton{ugxListDotPageFull2}{\hidepaste} +\tab{5}\spadcommand{expand [1..3,10,20..23]} +\indentrel{3}\begin{verbatim} + (2) [1,2,3,10,20,21,22,23] + Type: List Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxListDotPageEmpty2} +\begin{paste}{ugxListDotPageEmpty2}{ugxListDotPagePatch2} +\pastebutton{ugxListDotPageEmpty2}{\showpaste} +\tab{5}\spadcommand{expand [1..3,10,20..23]} +\end{paste}\end{patch} + +\begin{patch}{ugxListDotPagePatch3} +\begin{paste}{ugxListDotPageFull3}{ugxListDotPageEmpty3} +\pastebutton{ugxListDotPageFull3}{\hidepaste} +\tab{5}\spadcommand{expand [1..]} +\indentrel{3}\begin{verbatim} + (3) [1,2,3,4,5,6,7,8,9,10,...] + Type: Stream Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxListDotPageEmpty3} +\begin{paste}{ugxListDotPageEmpty3}{ugxListDotPagePatch3} +\pastebutton{ugxListDotPageEmpty3}{\showpaste} +\tab{5}\spadcommand{expand [1..]} +\end{paste}\end{patch} + @ \section{lodo.ht} \pagehead{LinearOrdinaryDifferentialOperatorXmpPage}{lodo.ht} @@ -14116,6 +37886,397 @@ Evaluate this for several values of \spad{n}. \autobuttons \end{page} +\begin{patch}{ugxLinearOrdinaryDifferentialOperatorSeriesPagePatch1} +\begin{paste}{ugxLinearOrdinaryDifferentialOperatorSeriesPageFull1}{ugxLinearOrdinaryDifferentialOperatorSeriesPageEmpty1} +\pastebutton{ugxLinearOrdinaryDifferentialOperatorSeriesPageFull1}{\hidepaste} +\tab{5}\spadcommand{Dx: LODO(EXPR INT, f +-> D(f, x))\bound{Dxd }} +\indentrel{3}\begin{verbatim} + Type: Void +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxLinearOrdinaryDifferentialOperatorSeriesPageEmpty1} +\begin{paste}{ugxLinearOrdinaryDifferentialOperatorSeriesPageEmpty1}{ugxLinearOrdinaryDifferentialOperatorSeriesPagePatch1} +\pastebutton{ugxLinearOrdinaryDifferentialOperatorSeriesPageEmpty1}{\showpaste} +\tab{5}\spadcommand{Dx: LODO(EXPR INT, f +-> D(f, x))\bound{Dxd }} +\end{paste}\end{patch} + +\begin{patch}{ugxLinearOrdinaryDifferentialOperatorSeriesPagePatch2} +\begin{paste}{ugxLinearOrdinaryDifferentialOperatorSeriesPageFull2}{ugxLinearOrdinaryDifferentialOperatorSeriesPageEmpty2} +\pastebutton{ugxLinearOrdinaryDifferentialOperatorSeriesPageFull2}{\hidepaste} +\tab{5}\spadcommand{Dx := D()\free{Dxd }\bound{Dx }} +\indentrel{3}\begin{verbatim} + (2) D +Type: LinearOrdinaryDifferentialOperator(Expression Integer,theMap NIL) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxLinearOrdinaryDifferentialOperatorSeriesPageEmpty2} +\begin{paste}{ugxLinearOrdinaryDifferentialOperatorSeriesPageEmpty2}{ugxLinearOrdinaryDifferentialOperatorSeriesPagePatch2} +\pastebutton{ugxLinearOrdinaryDifferentialOperatorSeriesPageEmpty2}{\showpaste} +\tab{5}\spadcommand{Dx := D()\free{Dxd }\bound{Dx }} +\end{paste}\end{patch} + +\begin{patch}{ugxLinearOrdinaryDifferentialOperatorSeriesPagePatch3} +\begin{paste}{ugxLinearOrdinaryDifferentialOperatorSeriesPageFull3}{ugxLinearOrdinaryDifferentialOperatorSeriesPageEmpty3} +\pastebutton{ugxLinearOrdinaryDifferentialOperatorSeriesPageFull3}{\hidepaste} +\tab{5}\spadcommand{Dop:= Dx**3 + G/x**2*Dx + H/x**3 - 1\free{Dx }\bound{Dop }} +\indentrel{3}\begin{verbatim} + 3 + 3 G - x + H + (3) D + ÄÄ D + ÄÄÄÄÄÄÄÄ + 2 3 + x x +Type: LinearOrdinaryDifferentialOperator(Expression Integer,theMap NIL) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxLinearOrdinaryDifferentialOperatorSeriesPageEmpty3} +\begin{paste}{ugxLinearOrdinaryDifferentialOperatorSeriesPageEmpty3}{ugxLinearOrdinaryDifferentialOperatorSeriesPagePatch3} +\pastebutton{ugxLinearOrdinaryDifferentialOperatorSeriesPageEmpty3}{\showpaste} +\tab{5}\spadcommand{Dop:= Dx**3 + G/x**2*Dx + H/x**3 - 1\free{Dx }\bound{Dop }} +\end{paste}\end{patch} + +\begin{patch}{ugxLinearOrdinaryDifferentialOperatorSeriesPagePatch4} +\begin{paste}{ugxLinearOrdinaryDifferentialOperatorSeriesPageFull4}{ugxLinearOrdinaryDifferentialOperatorSeriesPageEmpty4} +\pastebutton{ugxLinearOrdinaryDifferentialOperatorSeriesPageFull4}{\hidepaste} +\tab{5}\spadcommand{n == 3\bound{n3 }} +\indentrel{3}\begin{verbatim} + Type: Void +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxLinearOrdinaryDifferentialOperatorSeriesPageEmpty4} +\begin{paste}{ugxLinearOrdinaryDifferentialOperatorSeriesPageEmpty4}{ugxLinearOrdinaryDifferentialOperatorSeriesPagePatch4} +\pastebutton{ugxLinearOrdinaryDifferentialOperatorSeriesPageEmpty4}{\showpaste} +\tab{5}\spadcommand{n == 3\bound{n3 }} +\end{paste}\end{patch} + +\begin{patch}{ugxLinearOrdinaryDifferentialOperatorSeriesPagePatch5} +\begin{paste}{ugxLinearOrdinaryDifferentialOperatorSeriesPageFull5}{ugxLinearOrdinaryDifferentialOperatorSeriesPageEmpty5} +\pastebutton{ugxLinearOrdinaryDifferentialOperatorSeriesPageFull5}{\hidepaste} +\tab{5}\spadcommand{phi == reduce(+,[subscript(s,[i])*exp(x)/x**i for i in 0..n])\bound{phi }} +\indentrel{3}\begin{verbatim} + Type: Void +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxLinearOrdinaryDifferentialOperatorSeriesPageEmpty5} +\begin{paste}{ugxLinearOrdinaryDifferentialOperatorSeriesPageEmpty5}{ugxLinearOrdinaryDifferentialOperatorSeriesPagePatch5} +\pastebutton{ugxLinearOrdinaryDifferentialOperatorSeriesPageEmpty5}{\showpaste} +\tab{5}\spadcommand{phi == reduce(+,[subscript(s,[i])*exp(x)/x**i for i in 0..n])\bound{phi }} +\end{paste}\end{patch} + +\begin{patch}{ugxLinearOrdinaryDifferentialOperatorSeriesPagePatch6} +\begin{paste}{ugxLinearOrdinaryDifferentialOperatorSeriesPageFull6}{ugxLinearOrdinaryDifferentialOperatorSeriesPageEmpty6} +\pastebutton{ugxLinearOrdinaryDifferentialOperatorSeriesPageFull6}{\hidepaste} +\tab{5}\spadcommand{phi1 == Dop(phi) / exp x\bound{phi1 }\free{Dop phi }} +\indentrel{3}\begin{verbatim} + Type: Void +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxLinearOrdinaryDifferentialOperatorSeriesPageEmpty6} +\begin{paste}{ugxLinearOrdinaryDifferentialOperatorSeriesPageEmpty6}{ugxLinearOrdinaryDifferentialOperatorSeriesPagePatch6} +\pastebutton{ugxLinearOrdinaryDifferentialOperatorSeriesPageEmpty6}{\showpaste} +\tab{5}\spadcommand{phi1 == Dop(phi) / exp x\bound{phi1 }\free{Dop phi }} +\end{paste}\end{patch} + +\begin{patch}{ugxLinearOrdinaryDifferentialOperatorSeriesPagePatch7} +\begin{paste}{ugxLinearOrdinaryDifferentialOperatorSeriesPageFull7}{ugxLinearOrdinaryDifferentialOperatorSeriesPageEmpty7} +\pastebutton{ugxLinearOrdinaryDifferentialOperatorSeriesPageFull7}{\hidepaste} +\tab{5}\spadcommand{phi2 == phi1 *x**(n+3)\bound{phi2 }\free{phi1 }} +\indentrel{3}\begin{verbatim} + Type: Void +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxLinearOrdinaryDifferentialOperatorSeriesPageEmpty7} +\begin{paste}{ugxLinearOrdinaryDifferentialOperatorSeriesPageEmpty7}{ugxLinearOrdinaryDifferentialOperatorSeriesPagePatch7} +\pastebutton{ugxLinearOrdinaryDifferentialOperatorSeriesPageEmpty7}{\showpaste} +\tab{5}\spadcommand{phi2 == phi1 *x**(n+3)\bound{phi2 }\free{phi1 }} +\end{paste}\end{patch} + +\begin{patch}{ugxLinearOrdinaryDifferentialOperatorSeriesPagePatch8} +\begin{paste}{ugxLinearOrdinaryDifferentialOperatorSeriesPageFull8}{ugxLinearOrdinaryDifferentialOperatorSeriesPageEmpty8} +\pastebutton{ugxLinearOrdinaryDifferentialOperatorSeriesPageFull8}{\hidepaste} +\tab{5}\spadcommand{phi3 == retract(phi2)@(POLY INT)\bound{phi3 }\free{phi2 }} +\indentrel{3}\begin{verbatim} + Type: Void +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxLinearOrdinaryDifferentialOperatorSeriesPageEmpty8} +\begin{paste}{ugxLinearOrdinaryDifferentialOperatorSeriesPageEmpty8}{ugxLinearOrdinaryDifferentialOperatorSeriesPagePatch8} +\pastebutton{ugxLinearOrdinaryDifferentialOperatorSeriesPageEmpty8}{\showpaste} +\tab{5}\spadcommand{phi3 == retract(phi2)@(POLY INT)\bound{phi3 }\free{phi2 }} +\end{paste}\end{patch} + +\begin{patch}{ugxLinearOrdinaryDifferentialOperatorSeriesPagePatch9} +\begin{paste}{ugxLinearOrdinaryDifferentialOperatorSeriesPageFull9}{ugxLinearOrdinaryDifferentialOperatorSeriesPageEmpty9} +\pastebutton{ugxLinearOrdinaryDifferentialOperatorSeriesPageFull9}{\hidepaste} +\tab{5}\spadcommand{pans == phi3 ::UP(x,POLY INT)\free{phi3 }\bound{pans }} +\indentrel{3}\begin{verbatim} + Type: Void +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxLinearOrdinaryDifferentialOperatorSeriesPageEmpty9} +\begin{paste}{ugxLinearOrdinaryDifferentialOperatorSeriesPageEmpty9}{ugxLinearOrdinaryDifferentialOperatorSeriesPagePatch9} +\pastebutton{ugxLinearOrdinaryDifferentialOperatorSeriesPageEmpty9}{\showpaste} +\tab{5}\spadcommand{pans == phi3 ::UP(x,POLY INT)\free{phi3 }\bound{pans }} +\end{paste}\end{patch} + +\begin{patch}{ugxLinearOrdinaryDifferentialOperatorSeriesPagePatch10} +\begin{paste}{ugxLinearOrdinaryDifferentialOperatorSeriesPageFull10}{ugxLinearOrdinaryDifferentialOperatorSeriesPageEmpty10} +\pastebutton{ugxLinearOrdinaryDifferentialOperatorSeriesPageFull10}{\hidepaste} +\tab{5}\spadcommand{pans1 == [coefficient(pans, (n+3-i) :: NNI) for i in 2..n+1]\bound{pans1 }\free{pans }} +\indentrel{3}\begin{verbatim} + Type: Void +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxLinearOrdinaryDifferentialOperatorSeriesPageEmpty10} +\begin{paste}{ugxLinearOrdinaryDifferentialOperatorSeriesPageEmpty10}{ugxLinearOrdinaryDifferentialOperatorSeriesPagePatch10} +\pastebutton{ugxLinearOrdinaryDifferentialOperatorSeriesPageEmpty10}{\showpaste} +\tab{5}\spadcommand{pans1 == [coefficient(pans, (n+3-i) :: NNI) for i in 2..n+1]\bound{pans1 }\free{pans }} +\end{paste}\end{patch} + +\begin{patch}{ugxLinearOrdinaryDifferentialOperatorSeriesPagePatch11} +\begin{paste}{ugxLinearOrdinaryDifferentialOperatorSeriesPageFull11}{ugxLinearOrdinaryDifferentialOperatorSeriesPageEmpty11} +\pastebutton{ugxLinearOrdinaryDifferentialOperatorSeriesPageFull11}{\hidepaste} +\tab{5}\spadcommand{leq == solve(pans1,[subscript(s,[i]) for i in 1..n])\bound{leq }\free{pans1 }} +\indentrel{3}\begin{verbatim} + Type: Void +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxLinearOrdinaryDifferentialOperatorSeriesPageEmpty11} +\begin{paste}{ugxLinearOrdinaryDifferentialOperatorSeriesPageEmpty11}{ugxLinearOrdinaryDifferentialOperatorSeriesPagePatch11} +\pastebutton{ugxLinearOrdinaryDifferentialOperatorSeriesPageEmpty11}{\showpaste} +\tab{5}\spadcommand{leq == solve(pans1,[subscript(s,[i]) for i in 1..n])\bound{leq }\free{pans1 }} +\end{paste}\end{patch} + +\begin{patch}{ugxLinearOrdinaryDifferentialOperatorSeriesPagePatch12} +\begin{paste}{ugxLinearOrdinaryDifferentialOperatorSeriesPageFull12}{ugxLinearOrdinaryDifferentialOperatorSeriesPageEmpty12} +\pastebutton{ugxLinearOrdinaryDifferentialOperatorSeriesPageFull12}{\hidepaste} +\tab{5}\spadcommand{leq\free{n3 leq }} +\indentrel{3}\begin{verbatim} + (12) + [ + 2 + s G 3s H + s G + 6s G + 0 0 0 0 + [s = ÄÄÄ, s = ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ, + 1 3 2 18 + 3 2 + (9s G + 54s )H + s G + 18s G + 72s G + 0 0 0 0 0 + s = ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ] + 3 162 + ] + Type: List List Equation Fraction Polynomial Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxLinearOrdinaryDifferentialOperatorSeriesPageEmpty12} +\begin{paste}{ugxLinearOrdinaryDifferentialOperatorSeriesPageEmpty12}{ugxLinearOrdinaryDifferentialOperatorSeriesPagePatch12} +\pastebutton{ugxLinearOrdinaryDifferentialOperatorSeriesPageEmpty12}{\showpaste} +\tab{5}\spadcommand{leq\free{n3 leq }} +\end{paste}\end{patch} + +\begin{patch}{ugxLinearOrdinaryDifferentialOperatorSeriesPagePatch13} +\begin{paste}{ugxLinearOrdinaryDifferentialOperatorSeriesPageFull13}{ugxLinearOrdinaryDifferentialOperatorSeriesPageEmpty13} +\pastebutton{ugxLinearOrdinaryDifferentialOperatorSeriesPageFull13}{\hidepaste} +\tab{5}\spadcommand{n==4\bound{n4 }} +\indentrel{3}\begin{verbatim} + Type: Void +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxLinearOrdinaryDifferentialOperatorSeriesPageEmpty13} +\begin{paste}{ugxLinearOrdinaryDifferentialOperatorSeriesPageEmpty13}{ugxLinearOrdinaryDifferentialOperatorSeriesPagePatch13} +\pastebutton{ugxLinearOrdinaryDifferentialOperatorSeriesPageEmpty13}{\showpaste} +\tab{5}\spadcommand{n==4\bound{n4 }} +\end{paste}\end{patch} + +\begin{patch}{ugxLinearOrdinaryDifferentialOperatorSeriesPagePatch14} +\begin{paste}{ugxLinearOrdinaryDifferentialOperatorSeriesPageFull14}{ugxLinearOrdinaryDifferentialOperatorSeriesPageEmpty14} +\pastebutton{ugxLinearOrdinaryDifferentialOperatorSeriesPageFull14}{\hidepaste} +\tab{5}\spadcommand{leq\free{n4 leq }} +\indentrel{3}\begin{verbatim} + (14) + [ + 2 + s G 3s H + s G + 6s G + 0 0 0 0 + [s = ÄÄÄ, s = ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ, + 1 3 2 18 + 3 2 + (9s G + 54s )H + s G + 18s G + 72s G + 0 0 0 0 0 + s = ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ, + 3 162 + + s = + 4 + 2 2 4 + 27s H + (18s G + 378s G + 1296s )H + s G + 0 0 0 0 0 + + + 3 2 + 36s G + 396s G + 1296s G + 0 0 0 + / + 1944 + ] + ] + Type: List List Equation Fraction Polynomial Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxLinearOrdinaryDifferentialOperatorSeriesPageEmpty14} +\begin{paste}{ugxLinearOrdinaryDifferentialOperatorSeriesPageEmpty14}{ugxLinearOrdinaryDifferentialOperatorSeriesPagePatch14} +\pastebutton{ugxLinearOrdinaryDifferentialOperatorSeriesPageEmpty14}{\showpaste} +\tab{5}\spadcommand{leq\free{n4 leq }} +\end{paste}\end{patch} + +\begin{patch}{ugxLinearOrdinaryDifferentialOperatorSeriesPagePatch15} +\begin{paste}{ugxLinearOrdinaryDifferentialOperatorSeriesPageFull15}{ugxLinearOrdinaryDifferentialOperatorSeriesPageEmpty15} +\pastebutton{ugxLinearOrdinaryDifferentialOperatorSeriesPageFull15}{\hidepaste} +\tab{5}\spadcommand{n==7\bound{n7 }} +\indentrel{3}\begin{verbatim} + Type: Void +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxLinearOrdinaryDifferentialOperatorSeriesPageEmpty15} +\begin{paste}{ugxLinearOrdinaryDifferentialOperatorSeriesPageEmpty15}{ugxLinearOrdinaryDifferentialOperatorSeriesPagePatch15} +\pastebutton{ugxLinearOrdinaryDifferentialOperatorSeriesPageEmpty15}{\showpaste} +\tab{5}\spadcommand{n==7\bound{n7 }} +\end{paste}\end{patch} + +\begin{patch}{ugxLinearOrdinaryDifferentialOperatorSeriesPagePatch16} +\begin{paste}{ugxLinearOrdinaryDifferentialOperatorSeriesPageFull16}{ugxLinearOrdinaryDifferentialOperatorSeriesPageEmpty16} +\pastebutton{ugxLinearOrdinaryDifferentialOperatorSeriesPageFull16}{\hidepaste} +\tab{5}\spadcommand{leq\free{n7 leq }} +\indentrel{3}\begin{verbatim} + (16) + [ + 2 + s G 3s H + s G + 6s G + 0 0 0 0 + [s = ÄÄÄ, s = ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ, + 1 3 2 18 + 3 2 + (9s G + 54s )H + s G + 18s G + 72s G + 0 0 0 0 0 + s = ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ, + 3 162 + + s = + 4 + 2 2 4 + 27s H + (18s G + 378s G + 1296s )H + s G + 0 0 0 0 0 + + + 3 2 + 36s G + 396s G + 1296s G + 0 0 0 + / + 1944 + , + + s = + 5 + 2 + (135s G + 2268s )H + 0 0 + + + 3 2 + (30s G + 1350s G + 16416s G + 38880s )H + 0 0 0 0 + + + 5 4 3 2 + s G + 60s G + 1188s G + 9504s G + 25920s G + 0 0 0 0 0 + / + 29160 + , + + s = + 6 + 3 2 2 + 405s H + (405s G + 18468s G + 174960s )H + 0 0 0 0 + + + 4 3 2 + 45s G + 3510s G + 88776s G + 777600s G + 0 0 0 0 + + + 1166400s + 0 + * + H + + + 6 5 4 3 + s G + 90s G + 2628s G + 27864s G + 0 0 0 0 + + + 2 + 90720s G + 0 + / + 524880 + , + + s = + 7 + 3 + (2835s G + 91854s )H + 0 0 + + + 3 2 + 945s G + 81648s G + 2082996s G + 0 0 0 + + + 14171760s + 0 + * + 2 + H + + + 5 4 3 + 63s G + 7560s G + 317520s G + 0 0 0 + + + 2 + 5554008s G + 34058880s G + 0 0 + * + H + + + 7 6 5 4 + s G + 126s G + 4788s G + 25272s G + 0 0 0 0 + + + 3 2 + - 1744416s G - 26827200s G - 97977600s G + 0 0 0 + / + 11022480 + ] + ] + Type: List List Equation Fraction Polynomial Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxLinearOrdinaryDifferentialOperatorSeriesPageEmpty16} +\begin{paste}{ugxLinearOrdinaryDifferentialOperatorSeriesPageEmpty16}{ugxLinearOrdinaryDifferentialOperatorSeriesPagePatch16} +\pastebutton{ugxLinearOrdinaryDifferentialOperatorSeriesPageEmpty16}{\showpaste} +\tab{5}\spadcommand{leq\free{n7 leq }} +\end{paste}\end{patch} + @ \section{lodo1.ht} \pagehead{LinearOrdinaryDifferentialOperatorOneXmpPage}{lodo1.ht} @@ -14305,6 +38466,362 @@ is not necessarily divisible from both sides. \autobuttons \end{page} +\begin{patch}{ugxLinearOrdinaryDifferentialOperatorOneRatPagePatch1} +\begin{paste}{ugxLinearOrdinaryDifferentialOperatorOneRatPageFull1}{ugxLinearOrdinaryDifferentialOperatorOneRatPageEmpty1} +\pastebutton{ugxLinearOrdinaryDifferentialOperatorOneRatPageFull1}{\hidepaste} +\tab{5}\spadcommand{RFZ := Fraction UnivariatePolynomial('x, Integer)\bound{RFZ0 }} +\indentrel{3}\begin{verbatim} + (1) Fraction UnivariatePolynomial(x,Integer) + Type: Domain +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxLinearOrdinaryDifferentialOperatorOneRatPageEmpty1} +\begin{paste}{ugxLinearOrdinaryDifferentialOperatorOneRatPageEmpty1}{ugxLinearOrdinaryDifferentialOperatorOneRatPagePatch1} +\pastebutton{ugxLinearOrdinaryDifferentialOperatorOneRatPageEmpty1}{\showpaste} +\tab{5}\spadcommand{RFZ := Fraction UnivariatePolynomial('x, Integer)\bound{RFZ0 }} +\end{paste}\end{patch} + +\begin{patch}{ugxLinearOrdinaryDifferentialOperatorOneRatPagePatch2} +\begin{paste}{ugxLinearOrdinaryDifferentialOperatorOneRatPageFull2}{ugxLinearOrdinaryDifferentialOperatorOneRatPageEmpty2} +\pastebutton{ugxLinearOrdinaryDifferentialOperatorOneRatPageFull2}{\hidepaste} +\tab{5}\spadcommand{x : RFZ := 'x\free{RFZ0 }\bound{RFZ }} +\indentrel{3}\begin{verbatim} + (2) x + Type: Fraction UnivariatePolynomial(x,Integer) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxLinearOrdinaryDifferentialOperatorOneRatPageEmpty2} +\begin{paste}{ugxLinearOrdinaryDifferentialOperatorOneRatPageEmpty2}{ugxLinearOrdinaryDifferentialOperatorOneRatPagePatch2} +\pastebutton{ugxLinearOrdinaryDifferentialOperatorOneRatPageEmpty2}{\showpaste} +\tab{5}\spadcommand{x : RFZ := 'x\free{RFZ0 }\bound{RFZ }} +\end{paste}\end{patch} + +\begin{patch}{ugxLinearOrdinaryDifferentialOperatorOneRatPagePatch3} +\begin{paste}{ugxLinearOrdinaryDifferentialOperatorOneRatPageFull3}{ugxLinearOrdinaryDifferentialOperatorOneRatPageEmpty3} +\pastebutton{ugxLinearOrdinaryDifferentialOperatorOneRatPageFull3}{\hidepaste} +\tab{5}\spadcommand{Dx : LODO1 RFZ := D()\bound{Dx }\free{RFZ }} +\indentrel{3}\begin{verbatim} + (3) D +Type: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxLinearOrdinaryDifferentialOperatorOneRatPageEmpty3} +\begin{paste}{ugxLinearOrdinaryDifferentialOperatorOneRatPageEmpty3}{ugxLinearOrdinaryDifferentialOperatorOneRatPagePatch3} +\pastebutton{ugxLinearOrdinaryDifferentialOperatorOneRatPageEmpty3}{\showpaste} +\tab{5}\spadcommand{Dx : LODO1 RFZ := D()\bound{Dx }\free{RFZ }} +\end{paste}\end{patch} + +\begin{patch}{ugxLinearOrdinaryDifferentialOperatorOneRatPagePatch4} +\begin{paste}{ugxLinearOrdinaryDifferentialOperatorOneRatPageFull4}{ugxLinearOrdinaryDifferentialOperatorOneRatPageEmpty4} +\pastebutton{ugxLinearOrdinaryDifferentialOperatorOneRatPageFull4}{\hidepaste} +\tab{5}\spadcommand{b : LODO1 RFZ := 3*x**2*Dx**2 + 2*Dx + 1/x\free{Dx }\bound{b }} +\indentrel{3}\begin{verbatim} + 2 2 1 + (4) 3x D + 2D + Ä + x +Type: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxLinearOrdinaryDifferentialOperatorOneRatPageEmpty4} +\begin{paste}{ugxLinearOrdinaryDifferentialOperatorOneRatPageEmpty4}{ugxLinearOrdinaryDifferentialOperatorOneRatPagePatch4} +\pastebutton{ugxLinearOrdinaryDifferentialOperatorOneRatPageEmpty4}{\showpaste} +\tab{5}\spadcommand{b : LODO1 RFZ := 3*x**2*Dx**2 + 2*Dx + 1/x\free{Dx }\bound{b }} +\end{paste}\end{patch} + +\begin{patch}{ugxLinearOrdinaryDifferentialOperatorOneRatPagePatch5} +\begin{paste}{ugxLinearOrdinaryDifferentialOperatorOneRatPageFull5}{ugxLinearOrdinaryDifferentialOperatorOneRatPageEmpty5} +\pastebutton{ugxLinearOrdinaryDifferentialOperatorOneRatPageFull5}{\hidepaste} +\tab{5}\spadcommand{a : LODO1 RFZ := b*(5*x*Dx + 7)\free{b Dx }\bound{a }} +\indentrel{3}\begin{verbatim} + 3 3 2 2 7 + (5) 15x D + (51x + 10x)D + 29D + Ä + x +Type: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxLinearOrdinaryDifferentialOperatorOneRatPageEmpty5} +\begin{paste}{ugxLinearOrdinaryDifferentialOperatorOneRatPageEmpty5}{ugxLinearOrdinaryDifferentialOperatorOneRatPagePatch5} +\pastebutton{ugxLinearOrdinaryDifferentialOperatorOneRatPageEmpty5}{\showpaste} +\tab{5}\spadcommand{a : LODO1 RFZ := b*(5*x*Dx + 7)\free{b Dx }\bound{a }} +\end{paste}\end{patch} + +\begin{patch}{ugxLinearOrdinaryDifferentialOperatorOneRatPagePatch6} +\begin{paste}{ugxLinearOrdinaryDifferentialOperatorOneRatPageFull6}{ugxLinearOrdinaryDifferentialOperatorOneRatPageEmpty6} +\pastebutton{ugxLinearOrdinaryDifferentialOperatorOneRatPageFull6}{\hidepaste} +\tab{5}\spadcommand{p := x**2 + 1/x**2\bound{p }\free{RFZ }} +\indentrel{3}\begin{verbatim} + 4 + x + 1 + (6) ÄÄÄÄÄÄ + 2 + x + Type: Fraction UnivariatePolynomial(x,Integer) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxLinearOrdinaryDifferentialOperatorOneRatPageEmpty6} +\begin{paste}{ugxLinearOrdinaryDifferentialOperatorOneRatPageEmpty6}{ugxLinearOrdinaryDifferentialOperatorOneRatPagePatch6} +\pastebutton{ugxLinearOrdinaryDifferentialOperatorOneRatPageEmpty6}{\showpaste} +\tab{5}\spadcommand{p := x**2 + 1/x**2\bound{p }\free{RFZ }} +\end{paste}\end{patch} + +\begin{patch}{ugxLinearOrdinaryDifferentialOperatorOneRatPagePatch7} +\begin{paste}{ugxLinearOrdinaryDifferentialOperatorOneRatPageFull7}{ugxLinearOrdinaryDifferentialOperatorOneRatPageEmpty7} +\pastebutton{ugxLinearOrdinaryDifferentialOperatorOneRatPageFull7}{\hidepaste} +\tab{5}\spadcommand{(a*b - b*a) p\free{a b p }} +\indentrel{3}\begin{verbatim} + 4 + - 75x + 540x - 75 + (7) ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ + 4 + x + Type: Fraction UnivariatePolynomial(x,Integer) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxLinearOrdinaryDifferentialOperatorOneRatPageEmpty7} +\begin{paste}{ugxLinearOrdinaryDifferentialOperatorOneRatPageEmpty7}{ugxLinearOrdinaryDifferentialOperatorOneRatPagePatch7} +\pastebutton{ugxLinearOrdinaryDifferentialOperatorOneRatPageEmpty7}{\showpaste} +\tab{5}\spadcommand{(a*b - b*a) p\free{a b p }} +\end{paste}\end{patch} + +\begin{patch}{ugxLinearOrdinaryDifferentialOperatorOneRatPagePatch8} +\begin{paste}{ugxLinearOrdinaryDifferentialOperatorOneRatPageFull8}{ugxLinearOrdinaryDifferentialOperatorOneRatPageEmpty8} +\pastebutton{ugxLinearOrdinaryDifferentialOperatorOneRatPageFull8}{\hidepaste} +\tab{5}\spadcommand{ld := leftDivide(a,b)\bound{ld }\free{a b }} +\indentrel{3}\begin{verbatim} + (8) [quotient= 5x D + 7,remainder= 0] +Type: Record(quotient: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer),remainder: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxLinearOrdinaryDifferentialOperatorOneRatPageEmpty8} +\begin{paste}{ugxLinearOrdinaryDifferentialOperatorOneRatPageEmpty8}{ugxLinearOrdinaryDifferentialOperatorOneRatPagePatch8} +\pastebutton{ugxLinearOrdinaryDifferentialOperatorOneRatPageEmpty8}{\showpaste} +\tab{5}\spadcommand{ld := leftDivide(a,b)\bound{ld }\free{a b }} +\end{paste}\end{patch} + +\begin{patch}{ugxLinearOrdinaryDifferentialOperatorOneRatPagePatch9} +\begin{paste}{ugxLinearOrdinaryDifferentialOperatorOneRatPageFull9}{ugxLinearOrdinaryDifferentialOperatorOneRatPageEmpty9} +\pastebutton{ugxLinearOrdinaryDifferentialOperatorOneRatPageFull9}{\hidepaste} +\tab{5}\spadcommand{a = b * ld.quotient + ld.remainder\free{a b ld }} +\indentrel{3}\begin{verbatim} + (9) + 3 3 2 2 7 + 15x D + (51x + 10x)D + 29D + Ä = + x + 3 3 2 2 7 + 15x D + (51x + 10x)D + 29D + Ä + x +Type: Equation LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxLinearOrdinaryDifferentialOperatorOneRatPageEmpty9} +\begin{paste}{ugxLinearOrdinaryDifferentialOperatorOneRatPageEmpty9}{ugxLinearOrdinaryDifferentialOperatorOneRatPagePatch9} +\pastebutton{ugxLinearOrdinaryDifferentialOperatorOneRatPageEmpty9}{\showpaste} +\tab{5}\spadcommand{a = b * ld.quotient + ld.remainder\free{a b ld }} +\end{paste}\end{patch} + +\begin{patch}{ugxLinearOrdinaryDifferentialOperatorOneRatPagePatch10} +\begin{paste}{ugxLinearOrdinaryDifferentialOperatorOneRatPageFull10}{ugxLinearOrdinaryDifferentialOperatorOneRatPageEmpty10} +\pastebutton{ugxLinearOrdinaryDifferentialOperatorOneRatPageFull10}{\hidepaste} +\tab{5}\spadcommand{rd := rightDivide(a,b)\bound{rd }\free{a b }} +\indentrel{3}\begin{verbatim} + 5 + (10) [quotient= 5x D + 7,remainder= 10D + Ä] + x +Type: Record(quotient: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer),remainder: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer)) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxLinearOrdinaryDifferentialOperatorOneRatPageEmpty10} +\begin{paste}{ugxLinearOrdinaryDifferentialOperatorOneRatPageEmpty10}{ugxLinearOrdinaryDifferentialOperatorOneRatPagePatch10} +\pastebutton{ugxLinearOrdinaryDifferentialOperatorOneRatPageEmpty10}{\showpaste} +\tab{5}\spadcommand{rd := rightDivide(a,b)\bound{rd }\free{a b }} +\end{paste}\end{patch} + +\begin{patch}{ugxLinearOrdinaryDifferentialOperatorOneRatPagePatch11} +\begin{paste}{ugxLinearOrdinaryDifferentialOperatorOneRatPageFull11}{ugxLinearOrdinaryDifferentialOperatorOneRatPageEmpty11} +\pastebutton{ugxLinearOrdinaryDifferentialOperatorOneRatPageFull11}{\hidepaste} +\tab{5}\spadcommand{a = rd.quotient * b + rd.remainder\free{a b rd }} +\indentrel{3}\begin{verbatim} + (11) + 3 3 2 2 7 + 15x D + (51x + 10x)D + 29D + Ä = + x + 3 3 2 2 7 + 15x D + (51x + 10x)D + 29D + Ä + x +Type: Equation LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxLinearOrdinaryDifferentialOperatorOneRatPageEmpty11} +\begin{paste}{ugxLinearOrdinaryDifferentialOperatorOneRatPageEmpty11}{ugxLinearOrdinaryDifferentialOperatorOneRatPagePatch11} +\pastebutton{ugxLinearOrdinaryDifferentialOperatorOneRatPageEmpty11}{\showpaste} +\tab{5}\spadcommand{a = rd.quotient * b + rd.remainder\free{a b rd }} +\end{paste}\end{patch} + +\begin{patch}{ugxLinearOrdinaryDifferentialOperatorOneRatPagePatch12} +\begin{paste}{ugxLinearOrdinaryDifferentialOperatorOneRatPageFull12}{ugxLinearOrdinaryDifferentialOperatorOneRatPageEmpty12} +\pastebutton{ugxLinearOrdinaryDifferentialOperatorOneRatPageFull12}{\hidepaste} +\tab{5}\spadcommand{rightQuotient(a,b)\free{a b }} +\indentrel{3}\begin{verbatim} + (12) 5x D + 7 +Type: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxLinearOrdinaryDifferentialOperatorOneRatPageEmpty12} +\begin{paste}{ugxLinearOrdinaryDifferentialOperatorOneRatPageEmpty12}{ugxLinearOrdinaryDifferentialOperatorOneRatPagePatch12} +\pastebutton{ugxLinearOrdinaryDifferentialOperatorOneRatPageEmpty12}{\showpaste} +\tab{5}\spadcommand{rightQuotient(a,b)\free{a b }} +\end{paste}\end{patch} + +\begin{patch}{ugxLinearOrdinaryDifferentialOperatorOneRatPagePatch13} +\begin{paste}{ugxLinearOrdinaryDifferentialOperatorOneRatPageFull13}{ugxLinearOrdinaryDifferentialOperatorOneRatPageEmpty13} +\pastebutton{ugxLinearOrdinaryDifferentialOperatorOneRatPageFull13}{\hidepaste} +\tab{5}\spadcommand{rightRemainder(a,b)\free{a b }} +\indentrel{3}\begin{verbatim} + 5 + (13) 10D + Ä + x +Type: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxLinearOrdinaryDifferentialOperatorOneRatPageEmpty13} +\begin{paste}{ugxLinearOrdinaryDifferentialOperatorOneRatPageEmpty13}{ugxLinearOrdinaryDifferentialOperatorOneRatPagePatch13} +\pastebutton{ugxLinearOrdinaryDifferentialOperatorOneRatPageEmpty13}{\showpaste} +\tab{5}\spadcommand{rightRemainder(a,b)\free{a b }} +\end{paste}\end{patch} + +\begin{patch}{ugxLinearOrdinaryDifferentialOperatorOneRatPagePatch14} +\begin{paste}{ugxLinearOrdinaryDifferentialOperatorOneRatPageFull14}{ugxLinearOrdinaryDifferentialOperatorOneRatPageEmpty14} +\pastebutton{ugxLinearOrdinaryDifferentialOperatorOneRatPageFull14}{\hidepaste} +\tab{5}\spadcommand{leftExactQuotient(a,b)\free{a b }} +\indentrel{3}\begin{verbatim} + (14) 5x D + 7 +Type: Union(LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer),...) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxLinearOrdinaryDifferentialOperatorOneRatPageEmpty14} +\begin{paste}{ugxLinearOrdinaryDifferentialOperatorOneRatPageEmpty14}{ugxLinearOrdinaryDifferentialOperatorOneRatPagePatch14} +\pastebutton{ugxLinearOrdinaryDifferentialOperatorOneRatPageEmpty14}{\showpaste} +\tab{5}\spadcommand{leftExactQuotient(a,b)\free{a b }} +\end{paste}\end{patch} + +\begin{patch}{ugxLinearOrdinaryDifferentialOperatorOneRatPagePatch15} +\begin{paste}{ugxLinearOrdinaryDifferentialOperatorOneRatPageFull15}{ugxLinearOrdinaryDifferentialOperatorOneRatPageEmpty15} +\pastebutton{ugxLinearOrdinaryDifferentialOperatorOneRatPageFull15}{\hidepaste} +\tab{5}\spadcommand{e := leftGcd(a,b)\bound{e }\free{a b }} +\indentrel{3}\begin{verbatim} + 2 2 1 + (15) 3x D + 2D + Ä + x +Type: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxLinearOrdinaryDifferentialOperatorOneRatPageEmpty15} +\begin{paste}{ugxLinearOrdinaryDifferentialOperatorOneRatPageEmpty15}{ugxLinearOrdinaryDifferentialOperatorOneRatPagePatch15} +\pastebutton{ugxLinearOrdinaryDifferentialOperatorOneRatPageEmpty15}{\showpaste} +\tab{5}\spadcommand{e := leftGcd(a,b)\bound{e }\free{a b }} +\end{paste}\end{patch} + +\begin{patch}{ugxLinearOrdinaryDifferentialOperatorOneRatPagePatch16} +\begin{paste}{ugxLinearOrdinaryDifferentialOperatorOneRatPageFull16}{ugxLinearOrdinaryDifferentialOperatorOneRatPageEmpty16} +\pastebutton{ugxLinearOrdinaryDifferentialOperatorOneRatPageFull16}{\hidepaste} +\tab{5}\spadcommand{leftRemainder(a, e)\free{a e }} +\indentrel{3}\begin{verbatim} + (16) 0 +Type: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxLinearOrdinaryDifferentialOperatorOneRatPageEmpty16} +\begin{paste}{ugxLinearOrdinaryDifferentialOperatorOneRatPageEmpty16}{ugxLinearOrdinaryDifferentialOperatorOneRatPagePatch16} +\pastebutton{ugxLinearOrdinaryDifferentialOperatorOneRatPageEmpty16}{\showpaste} +\tab{5}\spadcommand{leftRemainder(a, e)\free{a e }} +\end{paste}\end{patch} + +\begin{patch}{ugxLinearOrdinaryDifferentialOperatorOneRatPagePatch17} +\begin{paste}{ugxLinearOrdinaryDifferentialOperatorOneRatPageFull17}{ugxLinearOrdinaryDifferentialOperatorOneRatPageEmpty17} +\pastebutton{ugxLinearOrdinaryDifferentialOperatorOneRatPageFull17}{\hidepaste} +\tab{5}\spadcommand{rightRemainder(a, e)\free{a e }} +\indentrel{3}\begin{verbatim} + 5 + (17) 10D + Ä + x +Type: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxLinearOrdinaryDifferentialOperatorOneRatPageEmpty17} +\begin{paste}{ugxLinearOrdinaryDifferentialOperatorOneRatPageEmpty17}{ugxLinearOrdinaryDifferentialOperatorOneRatPagePatch17} +\pastebutton{ugxLinearOrdinaryDifferentialOperatorOneRatPageEmpty17}{\showpaste} +\tab{5}\spadcommand{rightRemainder(a, e)\free{a e }} +\end{paste}\end{patch} + +\begin{patch}{ugxLinearOrdinaryDifferentialOperatorOneRatPagePatch18} +\begin{paste}{ugxLinearOrdinaryDifferentialOperatorOneRatPageFull18}{ugxLinearOrdinaryDifferentialOperatorOneRatPageEmpty18} +\pastebutton{ugxLinearOrdinaryDifferentialOperatorOneRatPageFull18}{\hidepaste} +\tab{5}\spadcommand{f := rightLcm(a,b)\bound{f }\free{a b }} +\indentrel{3}\begin{verbatim} + 3 3 2 2 7 + (18) 15x D + (51x + 10x)D + 29D + Ä + x +Type: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxLinearOrdinaryDifferentialOperatorOneRatPageEmpty18} +\begin{paste}{ugxLinearOrdinaryDifferentialOperatorOneRatPageEmpty18}{ugxLinearOrdinaryDifferentialOperatorOneRatPagePatch18} +\pastebutton{ugxLinearOrdinaryDifferentialOperatorOneRatPageEmpty18}{\showpaste} +\tab{5}\spadcommand{f := rightLcm(a,b)\bound{f }\free{a b }} +\end{paste}\end{patch} + +\begin{patch}{ugxLinearOrdinaryDifferentialOperatorOneRatPagePatch19} +\begin{paste}{ugxLinearOrdinaryDifferentialOperatorOneRatPageFull19}{ugxLinearOrdinaryDifferentialOperatorOneRatPageEmpty19} +\pastebutton{ugxLinearOrdinaryDifferentialOperatorOneRatPageFull19}{\hidepaste} +\tab{5}\spadcommand{rightRemainder(f, b)\free{f b }} +\indentrel{3}\begin{verbatim} + 5 + (19) 10D + Ä + x +Type: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxLinearOrdinaryDifferentialOperatorOneRatPageEmpty19} +\begin{paste}{ugxLinearOrdinaryDifferentialOperatorOneRatPageEmpty19}{ugxLinearOrdinaryDifferentialOperatorOneRatPagePatch19} +\pastebutton{ugxLinearOrdinaryDifferentialOperatorOneRatPageEmpty19}{\showpaste} +\tab{5}\spadcommand{rightRemainder(f, b)\free{f b }} +\end{paste}\end{patch} + +\begin{patch}{ugxLinearOrdinaryDifferentialOperatorOneRatPagePatch20} +\begin{paste}{ugxLinearOrdinaryDifferentialOperatorOneRatPageFull20}{ugxLinearOrdinaryDifferentialOperatorOneRatPageEmpty20} +\pastebutton{ugxLinearOrdinaryDifferentialOperatorOneRatPageFull20}{\hidepaste} +\tab{5}\spadcommand{leftRemainder(f, b)\free{f b }} +\indentrel{3}\begin{verbatim} + (20) 0 +Type: LinearOrdinaryDifferentialOperator1 Fraction UnivariatePolynomial(x,Integer) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxLinearOrdinaryDifferentialOperatorOneRatPageEmpty20} +\begin{paste}{ugxLinearOrdinaryDifferentialOperatorOneRatPageEmpty20}{ugxLinearOrdinaryDifferentialOperatorOneRatPagePatch20} +\pastebutton{ugxLinearOrdinaryDifferentialOperatorOneRatPageEmpty20}{\showpaste} +\tab{5}\spadcommand{leftRemainder(f, b)\free{f b }} +\end{paste}\end{patch} + @ \section{lodo2.ht} \pagehead{LinearODEOperatorTwoXmpPage}{lodo2.ht} @@ -14410,6 +38927,195 @@ Finally, note that operator expressions may be applied directly. \autobuttons \end{page} +\begin{patch}{ugxLinearODEOperatorTwoConstPagePatch1} +\begin{paste}{ugxLinearODEOperatorTwoConstPageFull1}{ugxLinearODEOperatorTwoConstPageEmpty1} +\pastebutton{ugxLinearODEOperatorTwoConstPageFull1}{\hidepaste} +\tab{5}\spadcommand{Q := Fraction Integer\bound{Q }} +\indentrel{3}\begin{verbatim} + (1) Fraction Integer + Type: Domain +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxLinearODEOperatorTwoConstPageEmpty1} +\begin{paste}{ugxLinearODEOperatorTwoConstPageEmpty1}{ugxLinearODEOperatorTwoConstPagePatch1} +\pastebutton{ugxLinearODEOperatorTwoConstPageEmpty1}{\showpaste} +\tab{5}\spadcommand{Q := Fraction Integer\bound{Q }} +\end{paste}\end{patch} + +\begin{patch}{ugxLinearODEOperatorTwoConstPagePatch2} +\begin{paste}{ugxLinearODEOperatorTwoConstPageFull2}{ugxLinearODEOperatorTwoConstPageEmpty2} +\pastebutton{ugxLinearODEOperatorTwoConstPageFull2}{\hidepaste} +\tab{5}\spadcommand{PQ := UnivariatePolynomial('x, Q)\free{Q }\bound{PQ0 }} +\indentrel{3}\begin{verbatim} + (2) UnivariatePolynomial(x,Fraction Integer) + Type: Domain +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxLinearODEOperatorTwoConstPageEmpty2} +\begin{paste}{ugxLinearODEOperatorTwoConstPageEmpty2}{ugxLinearODEOperatorTwoConstPagePatch2} +\pastebutton{ugxLinearODEOperatorTwoConstPageEmpty2}{\showpaste} +\tab{5}\spadcommand{PQ := UnivariatePolynomial('x, Q)\free{Q }\bound{PQ0 }} +\end{paste}\end{patch} + +\begin{patch}{ugxLinearODEOperatorTwoConstPagePatch3} +\begin{paste}{ugxLinearODEOperatorTwoConstPageFull3}{ugxLinearODEOperatorTwoConstPageEmpty3} +\pastebutton{ugxLinearODEOperatorTwoConstPageFull3}{\hidepaste} +\tab{5}\spadcommand{x: PQ := 'x\free{PQ0 }\bound{x }} +\indentrel{3}\begin{verbatim} + (3) x + Type: UnivariatePolynomial(x,Fraction Integer) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxLinearODEOperatorTwoConstPageEmpty3} +\begin{paste}{ugxLinearODEOperatorTwoConstPageEmpty3}{ugxLinearODEOperatorTwoConstPagePatch3} +\pastebutton{ugxLinearODEOperatorTwoConstPageEmpty3}{\showpaste} +\tab{5}\spadcommand{x: PQ := 'x\free{PQ0 }\bound{x }} +\end{paste}\end{patch} + +\begin{patch}{ugxLinearODEOperatorTwoConstPagePatch4} +\begin{paste}{ugxLinearODEOperatorTwoConstPageFull4}{ugxLinearODEOperatorTwoConstPageEmpty4} +\pastebutton{ugxLinearODEOperatorTwoConstPageFull4}{\hidepaste} +\tab{5}\spadcommand{Dx: LODO2(Q, PQ) := D()\free{Q PQ0 }\bound{Dx }} +\indentrel{3}\begin{verbatim} + (4) D +Type: LinearOrdinaryDifferentialOperator2(Fraction Integer,UnivariatePolynomial(x,Fraction Integer)) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxLinearODEOperatorTwoConstPageEmpty4} +\begin{paste}{ugxLinearODEOperatorTwoConstPageEmpty4}{ugxLinearODEOperatorTwoConstPagePatch4} +\pastebutton{ugxLinearODEOperatorTwoConstPageEmpty4}{\showpaste} +\tab{5}\spadcommand{Dx: LODO2(Q, PQ) := D()\free{Q PQ0 }\bound{Dx }} +\end{paste}\end{patch} + +\begin{patch}{ugxLinearODEOperatorTwoConstPagePatch5} +\begin{paste}{ugxLinearODEOperatorTwoConstPageFull5}{ugxLinearODEOperatorTwoConstPageEmpty5} +\pastebutton{ugxLinearODEOperatorTwoConstPageFull5}{\hidepaste} +\tab{5}\spadcommand{a := Dx + 1\bound{a }\free{Dx }} +\indentrel{3}\begin{verbatim} + (5) D + 1 +Type: LinearOrdinaryDifferentialOperator2(Fraction Integer,UnivariatePolynomial(x,Fraction Integer)) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxLinearODEOperatorTwoConstPageEmpty5} +\begin{paste}{ugxLinearODEOperatorTwoConstPageEmpty5}{ugxLinearODEOperatorTwoConstPagePatch5} +\pastebutton{ugxLinearODEOperatorTwoConstPageEmpty5}{\showpaste} +\tab{5}\spadcommand{a := Dx + 1\bound{a }\free{Dx }} +\end{paste}\end{patch} + +\begin{patch}{ugxLinearODEOperatorTwoConstPagePatch6} +\begin{paste}{ugxLinearODEOperatorTwoConstPageFull6}{ugxLinearODEOperatorTwoConstPageEmpty6} +\pastebutton{ugxLinearODEOperatorTwoConstPageFull6}{\hidepaste} +\tab{5}\spadcommand{b := a + 1/2*Dx**2 - 1/2\bound{b }\free{Dx }} +\indentrel{3}\begin{verbatim} + 1 2 1 + (6) Ä D + D + Ä + 2 2 +Type: LinearOrdinaryDifferentialOperator2(Fraction Integer,UnivariatePolynomial(x,Fraction Integer)) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxLinearODEOperatorTwoConstPageEmpty6} +\begin{paste}{ugxLinearODEOperatorTwoConstPageEmpty6}{ugxLinearODEOperatorTwoConstPagePatch6} +\pastebutton{ugxLinearODEOperatorTwoConstPageEmpty6}{\showpaste} +\tab{5}\spadcommand{b := a + 1/2*Dx**2 - 1/2\bound{b }\free{Dx }} +\end{paste}\end{patch} + +\begin{patch}{ugxLinearODEOperatorTwoConstPagePatch7} +\begin{paste}{ugxLinearODEOperatorTwoConstPageFull7}{ugxLinearODEOperatorTwoConstPageEmpty7} +\pastebutton{ugxLinearODEOperatorTwoConstPageFull7}{\hidepaste} +\tab{5}\spadcommand{p := 4*x**2 + 2/3\free{x }\bound{p }} +\indentrel{3}\begin{verbatim} + 2 2 + (7) 4x + Ä + 3 + Type: UnivariatePolynomial(x,Fraction Integer) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxLinearODEOperatorTwoConstPageEmpty7} +\begin{paste}{ugxLinearODEOperatorTwoConstPageEmpty7}{ugxLinearODEOperatorTwoConstPagePatch7} +\pastebutton{ugxLinearODEOperatorTwoConstPageEmpty7}{\showpaste} +\tab{5}\spadcommand{p := 4*x**2 + 2/3\free{x }\bound{p }} +\end{paste}\end{patch} + +\begin{patch}{ugxLinearODEOperatorTwoConstPagePatch8} +\begin{paste}{ugxLinearODEOperatorTwoConstPageFull8}{ugxLinearODEOperatorTwoConstPageEmpty8} +\pastebutton{ugxLinearODEOperatorTwoConstPageFull8}{\hidepaste} +\tab{5}\spadcommand{a p\free{a p }} +\indentrel{3}\begin{verbatim} + 2 2 + (8) 4x + 8x + Ä + 3 + Type: UnivariatePolynomial(x,Fraction Integer) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxLinearODEOperatorTwoConstPageEmpty8} +\begin{paste}{ugxLinearODEOperatorTwoConstPageEmpty8}{ugxLinearODEOperatorTwoConstPagePatch8} +\pastebutton{ugxLinearODEOperatorTwoConstPageEmpty8}{\showpaste} +\tab{5}\spadcommand{a p\free{a p }} +\end{paste}\end{patch} + +\begin{patch}{ugxLinearODEOperatorTwoConstPagePatch9} +\begin{paste}{ugxLinearODEOperatorTwoConstPageFull9}{ugxLinearODEOperatorTwoConstPageEmpty9} +\pastebutton{ugxLinearODEOperatorTwoConstPageFull9}{\hidepaste} +\tab{5}\spadcommand{(a * b) p = a b p\free{a b p }} +\indentrel{3}\begin{verbatim} + 2 37 2 37 + (9) 2x + 12x + ÄÄ= 2x + 12x + ÄÄ + 3 3 +Type: Equation UnivariatePolynomial(x,Fraction Integer) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxLinearODEOperatorTwoConstPageEmpty9} +\begin{paste}{ugxLinearODEOperatorTwoConstPageEmpty9}{ugxLinearODEOperatorTwoConstPagePatch9} +\pastebutton{ugxLinearODEOperatorTwoConstPageEmpty9}{\showpaste} +\tab{5}\spadcommand{(a * b) p = a b p\free{a b p }} +\end{paste}\end{patch} + +\begin{patch}{ugxLinearODEOperatorTwoConstPagePatch10} +\begin{paste}{ugxLinearODEOperatorTwoConstPageFull10}{ugxLinearODEOperatorTwoConstPageEmpty10} +\pastebutton{ugxLinearODEOperatorTwoConstPageFull10}{\hidepaste} +\tab{5}\spadcommand{c := (1/9)*b*(a + b)**2\free{a b }\bound{c }} +\indentrel{3}\begin{verbatim} + (10) + 1 6 5 5 13 4 19 3 79 2 7 1 + ÄÄ D + ÄÄ D + ÄÄ D + ÄÄ D + ÄÄ D + ÄÄ D + Ä + 72 36 24 18 72 12 8 +Type: LinearOrdinaryDifferentialOperator2(Fraction Integer,UnivariatePolynomial(x,Fraction Integer)) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxLinearODEOperatorTwoConstPageEmpty10} +\begin{paste}{ugxLinearODEOperatorTwoConstPageEmpty10}{ugxLinearODEOperatorTwoConstPagePatch10} +\pastebutton{ugxLinearODEOperatorTwoConstPageEmpty10}{\showpaste} +\tab{5}\spadcommand{c := (1/9)*b*(a + b)**2\free{a b }\bound{c }} +\end{paste}\end{patch} + +\begin{patch}{ugxLinearODEOperatorTwoConstPagePatch11} +\begin{paste}{ugxLinearODEOperatorTwoConstPageFull11}{ugxLinearODEOperatorTwoConstPageEmpty11} +\pastebutton{ugxLinearODEOperatorTwoConstPageFull11}{\hidepaste} +\tab{5}\spadcommand{(a**2 - 3/4*b + c) (p + 1)\free{a b c p }} +\indentrel{3}\begin{verbatim} + 2 44 541 + (11) 3x + ÄÄ x + ÄÄÄ + 3 36 + Type: UnivariatePolynomial(x,Fraction Integer) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxLinearODEOperatorTwoConstPageEmpty11} +\begin{paste}{ugxLinearODEOperatorTwoConstPageEmpty11}{ugxLinearODEOperatorTwoConstPagePatch11} +\pastebutton{ugxLinearODEOperatorTwoConstPageEmpty11}{\showpaste} +\tab{5}\spadcommand{(a**2 - 3/4*b + c) (p + 1)\free{a b c p }} +\end{paste}\end{patch} + @ \pagehead{ugxLinearODEOperatorTwoMatrixPage}{lodo2.ht} {Differential Operators with Matrix Coefficients Operating on Vectors} @@ -14499,6 +39205,316 @@ These operators can be applied to vector values. \autobuttons \end{page} +\begin{patch}{ugxLinearODEOperatorTwoMatrixPagePatch1} +\begin{paste}{ugxLinearODEOperatorTwoMatrixPageFull1}{ugxLinearODEOperatorTwoMatrixPageEmpty1} +\pastebutton{ugxLinearODEOperatorTwoMatrixPageFull1}{\hidepaste} +\tab{5}\spadcommand{PZ := UnivariatePolynomial(x,Integer)\bound{PZ0 }} +\indentrel{3}\begin{verbatim} + (1) UnivariatePolynomial(x,Integer) + Type: Domain +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxLinearODEOperatorTwoMatrixPageEmpty1} +\begin{paste}{ugxLinearODEOperatorTwoMatrixPageEmpty1}{ugxLinearODEOperatorTwoMatrixPagePatch1} +\pastebutton{ugxLinearODEOperatorTwoMatrixPageEmpty1}{\showpaste} +\tab{5}\spadcommand{PZ := UnivariatePolynomial(x,Integer)\bound{PZ0 }} +\end{paste}\end{patch} + +\begin{patch}{ugxLinearODEOperatorTwoMatrixPagePatch2} +\begin{paste}{ugxLinearODEOperatorTwoMatrixPageFull2}{ugxLinearODEOperatorTwoMatrixPageEmpty2} +\pastebutton{ugxLinearODEOperatorTwoMatrixPageFull2}{\hidepaste} +\tab{5}\spadcommand{x:PZ := 'x\free{PZ0 }\bound{PZ }} +\indentrel{3}\begin{verbatim} + (2) x + Type: UnivariatePolynomial(x,Integer) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxLinearODEOperatorTwoMatrixPageEmpty2} +\begin{paste}{ugxLinearODEOperatorTwoMatrixPageEmpty2}{ugxLinearODEOperatorTwoMatrixPagePatch2} +\pastebutton{ugxLinearODEOperatorTwoMatrixPageEmpty2}{\showpaste} +\tab{5}\spadcommand{x:PZ := 'x\free{PZ0 }\bound{PZ }} +\end{paste}\end{patch} + +\begin{patch}{ugxLinearODEOperatorTwoMatrixPagePatch3} +\begin{paste}{ugxLinearODEOperatorTwoMatrixPageFull3}{ugxLinearODEOperatorTwoMatrixPageEmpty3} +\pastebutton{ugxLinearODEOperatorTwoMatrixPageFull3}{\hidepaste} +\tab{5}\spadcommand{Mat := SquareMatrix(3,PZ)\free{PZ }\bound{Mat }} +\indentrel{3}\begin{verbatim} + (3) SquareMatrix(3,UnivariatePolynomial(x,Integer)) + Type: Domain +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxLinearODEOperatorTwoMatrixPageEmpty3} +\begin{paste}{ugxLinearODEOperatorTwoMatrixPageEmpty3}{ugxLinearODEOperatorTwoMatrixPagePatch3} +\pastebutton{ugxLinearODEOperatorTwoMatrixPageEmpty3}{\showpaste} +\tab{5}\spadcommand{Mat := SquareMatrix(3,PZ)\free{PZ }\bound{Mat }} +\end{paste}\end{patch} + +\begin{patch}{ugxLinearODEOperatorTwoMatrixPagePatch4} +\begin{paste}{ugxLinearODEOperatorTwoMatrixPageFull4}{ugxLinearODEOperatorTwoMatrixPageEmpty4} +\pastebutton{ugxLinearODEOperatorTwoMatrixPageFull4}{\hidepaste} +\tab{5}\spadcommand{Vect := DPMM(3, PZ, Mat, PZ);\free{PZ Mat }\bound{Vect }} +\indentrel{3}\begin{verbatim} + Type: Domain +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxLinearODEOperatorTwoMatrixPageEmpty4} +\begin{paste}{ugxLinearODEOperatorTwoMatrixPageEmpty4}{ugxLinearODEOperatorTwoMatrixPagePatch4} +\pastebutton{ugxLinearODEOperatorTwoMatrixPageEmpty4}{\showpaste} +\tab{5}\spadcommand{Vect := DPMM(3, PZ, Mat, PZ);\free{PZ Mat }\bound{Vect }} +\end{paste}\end{patch} + +\begin{patch}{ugxLinearODEOperatorTwoMatrixPagePatch5} +\begin{paste}{ugxLinearODEOperatorTwoMatrixPageFull5}{ugxLinearODEOperatorTwoMatrixPageEmpty5} +\pastebutton{ugxLinearODEOperatorTwoMatrixPageFull5}{\hidepaste} +\tab{5}\spadcommand{Modo := LODO2(Mat, Vect);\free{Mat Vect }\bound{Modo }} +\indentrel{3}\begin{verbatim} + Type: Domain +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxLinearODEOperatorTwoMatrixPageEmpty5} +\begin{paste}{ugxLinearODEOperatorTwoMatrixPageEmpty5}{ugxLinearODEOperatorTwoMatrixPagePatch5} +\pastebutton{ugxLinearODEOperatorTwoMatrixPageEmpty5}{\showpaste} +\tab{5}\spadcommand{Modo := LODO2(Mat, Vect);\free{Mat Vect }\bound{Modo }} +\end{paste}\end{patch} + +\begin{patch}{ugxLinearODEOperatorTwoMatrixPagePatch6} +\begin{paste}{ugxLinearODEOperatorTwoMatrixPageFull6}{ugxLinearODEOperatorTwoMatrixPageEmpty6} +\pastebutton{ugxLinearODEOperatorTwoMatrixPageFull6}{\hidepaste} +\tab{5}\spadcommand{m:Mat := matrix [[x**2,1,0],[1,x**4,0],[0,0,4*x**2]]\free{Mat }\bound{m }} +\indentrel{3}\begin{verbatim} + Ú 2 ¿ + ³x 1 0 ³ + ³ ³ + (6) ³ 4 ³ + ³1 x 0 ³ + ³ ³ + ³ 2³ + À0 0 4x Ù + Type: SquareMatrix(3,UnivariatePolynomial(x,Integer)) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxLinearODEOperatorTwoMatrixPageEmpty6} +\begin{paste}{ugxLinearODEOperatorTwoMatrixPageEmpty6}{ugxLinearODEOperatorTwoMatrixPagePatch6} +\pastebutton{ugxLinearODEOperatorTwoMatrixPageEmpty6}{\showpaste} +\tab{5}\spadcommand{m:Mat := matrix [[x**2,1,0],[1,x**4,0],[0,0,4*x**2]]\free{Mat }\bound{m }} +\end{paste}\end{patch} + +\begin{patch}{ugxLinearODEOperatorTwoMatrixPagePatch7} +\begin{paste}{ugxLinearODEOperatorTwoMatrixPageFull7}{ugxLinearODEOperatorTwoMatrixPageEmpty7} +\pastebutton{ugxLinearODEOperatorTwoMatrixPageFull7}{\hidepaste} +\tab{5}\spadcommand{p:Vect := directProduct [3*x**2+1,2*x,7*x**3+2*x]\free{Vect }\bound{p }} +\indentrel{3}\begin{verbatim} + 2 3 + (7) [3x + 1,2x,7x + 2x] +Type: DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),SquareMatrix(3,UnivariatePolynomial(x,Integer)),UnivariatePolynomial(x,Integer)) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxLinearODEOperatorTwoMatrixPageEmpty7} +\begin{paste}{ugxLinearODEOperatorTwoMatrixPageEmpty7}{ugxLinearODEOperatorTwoMatrixPagePatch7} +\pastebutton{ugxLinearODEOperatorTwoMatrixPageEmpty7}{\showpaste} +\tab{5}\spadcommand{p:Vect := directProduct [3*x**2+1,2*x,7*x**3+2*x]\free{Vect }\bound{p }} +\end{paste}\end{patch} + +\begin{patch}{ugxLinearODEOperatorTwoMatrixPagePatch8} +\begin{paste}{ugxLinearODEOperatorTwoMatrixPageFull8}{ugxLinearODEOperatorTwoMatrixPageEmpty8} +\pastebutton{ugxLinearODEOperatorTwoMatrixPageFull8}{\hidepaste} +\tab{5}\spadcommand{q: Vect := m * p\free{m p Vect }\bound{q }} +\indentrel{3}\begin{verbatim} + 4 2 5 2 5 3 + (8) [3x + x + 2x,2x + 3x + 1,28x + 8x ] +Type: DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),SquareMatrix(3,UnivariatePolynomial(x,Integer)),UnivariatePolynomial(x,Integer)) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxLinearODEOperatorTwoMatrixPageEmpty8} +\begin{paste}{ugxLinearODEOperatorTwoMatrixPageEmpty8}{ugxLinearODEOperatorTwoMatrixPagePatch8} +\pastebutton{ugxLinearODEOperatorTwoMatrixPageEmpty8}{\showpaste} +\tab{5}\spadcommand{q: Vect := m * p\free{m p Vect }\bound{q }} +\end{paste}\end{patch} + +\begin{patch}{ugxLinearODEOperatorTwoMatrixPagePatch9} +\begin{paste}{ugxLinearODEOperatorTwoMatrixPageFull9}{ugxLinearODEOperatorTwoMatrixPageEmpty9} +\pastebutton{ugxLinearODEOperatorTwoMatrixPageFull9}{\hidepaste} +\tab{5}\spadcommand{Dx : Modo := D()\bound{Dx }\free{Modo }} +\indentrel{3}\begin{verbatim} + (9) D +Type: LinearOrdinaryDifferentialOperator2(SquareMatrix(3,UnivariatePolynomial(x,Integer)),DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),SquareMatrix(3,UnivariatePolynomial(x,Integer)),UnivariatePolynomial(x,Integer))) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxLinearODEOperatorTwoMatrixPageEmpty9} +\begin{paste}{ugxLinearODEOperatorTwoMatrixPageEmpty9}{ugxLinearODEOperatorTwoMatrixPagePatch9} +\pastebutton{ugxLinearODEOperatorTwoMatrixPageEmpty9}{\showpaste} +\tab{5}\spadcommand{Dx : Modo := D()\bound{Dx }\free{Modo }} +\end{paste}\end{patch} + +\begin{patch}{ugxLinearODEOperatorTwoMatrixPagePatch10} +\begin{paste}{ugxLinearODEOperatorTwoMatrixPageFull10}{ugxLinearODEOperatorTwoMatrixPageEmpty10} +\pastebutton{ugxLinearODEOperatorTwoMatrixPageFull10}{\hidepaste} +\tab{5}\spadcommand{a : Modo := Dx + m\bound{a }\free{m Dx }} +\indentrel{3}\begin{verbatim} + Ú 2 ¿ + ³x 1 0 ³ + ³ ³ + (10) D + ³ 4 ³ + ³1 x 0 ³ + ³ ³ + ³ 2³ + À0 0 4x Ù +Type: LinearOrdinaryDifferentialOperator2(SquareMatrix(3,UnivariatePolynomial(x,Integer)),DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),SquareMatrix(3,UnivariatePolynomial(x,Integer)),UnivariatePolynomial(x,Integer))) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxLinearODEOperatorTwoMatrixPageEmpty10} +\begin{paste}{ugxLinearODEOperatorTwoMatrixPageEmpty10}{ugxLinearODEOperatorTwoMatrixPagePatch10} +\pastebutton{ugxLinearODEOperatorTwoMatrixPageEmpty10}{\showpaste} +\tab{5}\spadcommand{a : Modo := Dx + m\bound{a }\free{m Dx }} +\end{paste}\end{patch} + +\begin{patch}{ugxLinearODEOperatorTwoMatrixPagePatch11} +\begin{paste}{ugxLinearODEOperatorTwoMatrixPageFull11}{ugxLinearODEOperatorTwoMatrixPageEmpty11} +\pastebutton{ugxLinearODEOperatorTwoMatrixPageFull11}{\hidepaste} +\tab{5}\spadcommand{b : Modo := m*Dx + 1\bound{b }\free{m Dx }} +\indentrel{3}\begin{verbatim} + Ú 2 ¿ + ³x 1 0 ³ Ú1 0 0¿ + ³ ³ ³ ³ + (11) ³ 4 ³D + ³0 1 0³ + ³1 x 0 ³ ³ ³ + ³ ³ À0 0 1Ù + ³ 2³ + À0 0 4x Ù +Type: LinearOrdinaryDifferentialOperator2(SquareMatrix(3,UnivariatePolynomial(x,Integer)),DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),SquareMatrix(3,UnivariatePolynomial(x,Integer)),UnivariatePolynomial(x,Integer))) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxLinearODEOperatorTwoMatrixPageEmpty11} +\begin{paste}{ugxLinearODEOperatorTwoMatrixPageEmpty11}{ugxLinearODEOperatorTwoMatrixPagePatch11} +\pastebutton{ugxLinearODEOperatorTwoMatrixPageEmpty11}{\showpaste} +\tab{5}\spadcommand{b : Modo := m*Dx + 1\bound{b }\free{m Dx }} +\end{paste}\end{patch} + +\begin{patch}{ugxLinearODEOperatorTwoMatrixPagePatch12} +\begin{paste}{ugxLinearODEOperatorTwoMatrixPageFull12}{ugxLinearODEOperatorTwoMatrixPageEmpty12} +\pastebutton{ugxLinearODEOperatorTwoMatrixPageFull12}{\hidepaste} +\tab{5}\spadcommand{c := a*b\bound{c }\free{a b }} +\indentrel{3}\begin{verbatim} + (12) + Ú 2 ¿ + ³x 1 0 ³ + ³ ³ 2 + ³ 4 ³D + ³1 x 0 ³ + ³ ³ + ³ 2³ + À0 0 4x Ù + + + Ú 4 4 2 ¿ + ³x + 2x + 2 x + x 0 ³ + ³ ³ + ³ 4 2 8 3 ³D + ³ x + x x + 4x + 2 0 ³ + ³ ³ + ³ 4 ³ + À 0 0 16x + 8x + 1Ù + + + Ú 2 ¿ + ³x 1 0 ³ + ³ ³ + ³ 4 ³ + ³1 x 0 ³ + ³ ³ + ³ 2³ + À0 0 4x Ù +Type: LinearOrdinaryDifferentialOperator2(SquareMatrix(3,UnivariatePolynomial(x,Integer)),DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),SquareMatrix(3,UnivariatePolynomial(x,Integer)),UnivariatePolynomial(x,Integer))) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxLinearODEOperatorTwoMatrixPageEmpty12} +\begin{paste}{ugxLinearODEOperatorTwoMatrixPageEmpty12}{ugxLinearODEOperatorTwoMatrixPagePatch12} +\pastebutton{ugxLinearODEOperatorTwoMatrixPageEmpty12}{\showpaste} +\tab{5}\spadcommand{c := a*b\bound{c }\free{a b }} +\end{paste}\end{patch} + +\begin{patch}{ugxLinearODEOperatorTwoMatrixPagePatch13} +\begin{paste}{ugxLinearODEOperatorTwoMatrixPageFull13}{ugxLinearODEOperatorTwoMatrixPageEmpty13} +\pastebutton{ugxLinearODEOperatorTwoMatrixPageFull13}{\hidepaste} +\tab{5}\spadcommand{a p\free{p a }} +\indentrel{3}\begin{verbatim} + (13) + 4 2 5 2 5 3 2 + [3x + x + 8x,2x + 3x + 3,28x + 8x + 21x + 2] +Type: DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),SquareMatrix(3,UnivariatePolynomial(x,Integer)),UnivariatePolynomial(x,Integer)) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxLinearODEOperatorTwoMatrixPageEmpty13} +\begin{paste}{ugxLinearODEOperatorTwoMatrixPageEmpty13}{ugxLinearODEOperatorTwoMatrixPagePatch13} +\pastebutton{ugxLinearODEOperatorTwoMatrixPageEmpty13}{\showpaste} +\tab{5}\spadcommand{a p\free{p a }} +\end{paste}\end{patch} + +\begin{patch}{ugxLinearODEOperatorTwoMatrixPagePatch14} +\begin{paste}{ugxLinearODEOperatorTwoMatrixPageFull14}{ugxLinearODEOperatorTwoMatrixPageEmpty14} +\pastebutton{ugxLinearODEOperatorTwoMatrixPageFull14}{\hidepaste} +\tab{5}\spadcommand{b p\free{p b }} +\indentrel{3}\begin{verbatim} + 3 2 4 4 3 2 + (14) [6x + 3x + 3,2x + 8x,84x + 7x + 8x + 2x] +Type: DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),SquareMatrix(3,UnivariatePolynomial(x,Integer)),UnivariatePolynomial(x,Integer)) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxLinearODEOperatorTwoMatrixPageEmpty14} +\begin{paste}{ugxLinearODEOperatorTwoMatrixPageEmpty14}{ugxLinearODEOperatorTwoMatrixPagePatch14} +\pastebutton{ugxLinearODEOperatorTwoMatrixPageEmpty14}{\showpaste} +\tab{5}\spadcommand{b p\free{p b }} +\end{paste}\end{patch} + +\begin{patch}{ugxLinearODEOperatorTwoMatrixPagePatch15} +\begin{paste}{ugxLinearODEOperatorTwoMatrixPageFull15}{ugxLinearODEOperatorTwoMatrixPageEmpty15} +\pastebutton{ugxLinearODEOperatorTwoMatrixPageFull15}{\hidepaste} +\tab{5}\spadcommand{(a + b + c) (p + q)\free{a b c p q }} +\indentrel{3}\begin{verbatim} + (15) + [ + 8 7 6 5 4 3 2 + 10x + 12x + 16x + 30x + 85x + 94x + 40x + + + 40x + 17 + , + + 12 9 8 7 6 5 4 + 10x + 10x + 12x + 92x + 6x + 32x + 72x + + + 3 2 + 28x + 49x + 32x + 19 + , + + 8 7 6 5 4 3 + 2240x + 224x + 1280x + 3508x + 492x + 751x + + + 2 + 98x + 18x + 4 + ] +Type: DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),SquareMatrix(3,UnivariatePolynomial(x,Integer)),UnivariatePolynomial(x,Integer)) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxLinearODEOperatorTwoMatrixPageEmpty15} +\begin{paste}{ugxLinearODEOperatorTwoMatrixPageEmpty15}{ugxLinearODEOperatorTwoMatrixPagePatch15} +\pastebutton{ugxLinearODEOperatorTwoMatrixPageEmpty15}{\showpaste} +\tab{5}\spadcommand{(a + b + c) (p + q)\free{a b c p q }} +\end{paste}\end{patch} + @ \section{lpoly.ht} \pagehead{LiePolynomialXmpPage}{lpoly.ht}{LiePolynomial} @@ -14638,7 +39654,461 @@ Evaluation \endscroll \autobuttons \end{page} -% + +\begin{patch}{LiePolynomialXmpPagePatch1} +\begin{paste}{LiePolynomialXmpPageFull1}{LiePolynomialXmpPageEmpty1} +\pastebutton{LiePolynomialXmpPageFull1}{\hidepaste} +\tab{5}\spadcommand{RN := Fraction Integer\bound{RN }} +\indentrel{3}\begin{verbatim} + (1) Fraction Integer + Type: Domain +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{LiePolynomialXmpPageEmpty1} +\begin{paste}{LiePolynomialXmpPageEmpty1}{LiePolynomialXmpPagePatch1} +\pastebutton{LiePolynomialXmpPageEmpty1}{\showpaste} +\tab{5}\spadcommand{RN := Fraction Integer\bound{RN }} +\end{paste}\end{patch} + +\begin{patch}{LiePolynomialXmpPagePatch2} +\begin{paste}{LiePolynomialXmpPageFull2}{LiePolynomialXmpPageEmpty2} +\pastebutton{LiePolynomialXmpPageFull2}{\hidepaste} +\tab{5}\spadcommand{Lpoly := LiePolynomial(Symbol,RN)\bound{Lpoly }\free{RN }} +\indentrel{3}\begin{verbatim} + (2) LiePolynomial(Symbol,Fraction Integer) + Type: Domain +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{LiePolynomialXmpPageEmpty2} +\begin{paste}{LiePolynomialXmpPageEmpty2}{LiePolynomialXmpPagePatch2} +\pastebutton{LiePolynomialXmpPageEmpty2}{\showpaste} +\tab{5}\spadcommand{Lpoly := LiePolynomial(Symbol,RN)\bound{Lpoly }\free{RN }} +\end{paste}\end{patch} + +\begin{patch}{LiePolynomialXmpPagePatch3} +\begin{paste}{LiePolynomialXmpPageFull3}{LiePolynomialXmpPageEmpty3} +\pastebutton{LiePolynomialXmpPageFull3}{\hidepaste} +\tab{5}\spadcommand{Dpoly := XDPOLY(Symbol,RN)\bound{Dpoly }\free{RN }} +\indentrel{3}\begin{verbatim} + (3) XDistributedPolynomial(Symbol,Fraction Integer) + Type: Domain +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{LiePolynomialXmpPageEmpty3} +\begin{paste}{LiePolynomialXmpPageEmpty3}{LiePolynomialXmpPagePatch3} +\pastebutton{LiePolynomialXmpPageEmpty3}{\showpaste} +\tab{5}\spadcommand{Dpoly := XDPOLY(Symbol,RN)\bound{Dpoly }\free{RN }} +\end{paste}\end{patch} + +\begin{patch}{LiePolynomialXmpPagePatch4} +\begin{paste}{LiePolynomialXmpPageFull4}{LiePolynomialXmpPageEmpty4} +\pastebutton{LiePolynomialXmpPageFull4}{\hidepaste} +\tab{5}\spadcommand{Lword := LyndonWord Symbol\bound{Lword }} +\indentrel{3}\begin{verbatim} + (4) LyndonWord Symbol + Type: Domain +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{LiePolynomialXmpPageEmpty4} +\begin{paste}{LiePolynomialXmpPageEmpty4}{LiePolynomialXmpPagePatch4} +\pastebutton{LiePolynomialXmpPageEmpty4}{\showpaste} +\tab{5}\spadcommand{Lword := LyndonWord Symbol\bound{Lword }} +\end{paste}\end{patch} + +\begin{patch}{LiePolynomialXmpPagePatch5} +\begin{paste}{LiePolynomialXmpPageFull5}{LiePolynomialXmpPageEmpty5} +\pastebutton{LiePolynomialXmpPageFull5}{\hidepaste} +\tab{5}\spadcommand{a:Symbol := 'a\bound{a }} +\indentrel{3}\begin{verbatim} + (5) a + Type: Symbol +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{LiePolynomialXmpPageEmpty5} +\begin{paste}{LiePolynomialXmpPageEmpty5}{LiePolynomialXmpPagePatch5} +\pastebutton{LiePolynomialXmpPageEmpty5}{\showpaste} +\tab{5}\spadcommand{a:Symbol := 'a\bound{a }} +\end{paste}\end{patch} + +\begin{patch}{LiePolynomialXmpPagePatch6} +\begin{paste}{LiePolynomialXmpPageFull6}{LiePolynomialXmpPageEmpty6} +\pastebutton{LiePolynomialXmpPageFull6}{\hidepaste} +\tab{5}\spadcommand{b:Symbol := 'b\bound{b }} +\indentrel{3}\begin{verbatim} + (6) b + Type: Symbol +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{LiePolynomialXmpPageEmpty6} +\begin{paste}{LiePolynomialXmpPageEmpty6}{LiePolynomialXmpPagePatch6} +\pastebutton{LiePolynomialXmpPageEmpty6}{\showpaste} +\tab{5}\spadcommand{b:Symbol := 'b\bound{b }} +\end{paste}\end{patch} + +\begin{patch}{LiePolynomialXmpPagePatch7} +\begin{paste}{LiePolynomialXmpPageFull7}{LiePolynomialXmpPageEmpty7} +\pastebutton{LiePolynomialXmpPageFull7}{\hidepaste} +\tab{5}\spadcommand{c:Symbol := 'c\bound{c }} +\indentrel{3}\begin{verbatim} + (7) c + Type: Symbol +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{LiePolynomialXmpPageEmpty7} +\begin{paste}{LiePolynomialXmpPageEmpty7}{LiePolynomialXmpPagePatch7} +\pastebutton{LiePolynomialXmpPageEmpty7}{\showpaste} +\tab{5}\spadcommand{c:Symbol := 'c\bound{c }} +\end{paste}\end{patch} + +\begin{patch}{LiePolynomialXmpPagePatch8} +\begin{paste}{LiePolynomialXmpPage