The Axiom polynomial factorization polynomial:factorization facilities are available for all polynomial types and a wide variety of coefficient domains. factorization Here are some examples.
Polynomials with integer polynomial:factorization:integer coefficients coefficients can be be factored.
Also, Axiom can factor polynomials with polynomial:factorization:rational number coefficients rational number coefficients.
Polynomials with coefficients in a finite field polynomial:factorization:finite field coefficients can be also be factored. finite field:factoring polynomial with coefficients in
These include the integers mod , where is prime, and extensions of these fields.
Convert this to have coefficients in the finite field with elements. See ugProblemFinite for more information about finite fields.
Polynomials with coefficients in simple algebraic extensions polynomial:factorization:algebraic extension field coefficients of the rational numbers can be factored. algebraic number number:algebraic
Here, and are symbolic roots of polynomials.
Note that the second argument to factor can be a list of algebraic extensions to factor over.
This factors over the integers.
Factor the same polynomial over the field obtained by adjoining to the rational numbers.
Factor over the same field.
Factor again over the field obtained by adjoining both and to the rational numbers.
Since fractions of polynomials form a field, every element (other than zero) rational function:factoring divides any other, so there is no useful notion of irreducible factors. Thus the factor operation is not very useful for fractions of polynomials.
There is, instead, a specific operation factorFraction that separately factors the numerator and denominator and returns a fraction of the factored results.
You can also use map. This expression applies the factor operation to the numerator and denominator.