Factorization of multivariate polynomials over the integers

[bgrenet]

Currently, Sage does not know how to factor multivariate polynomials over the integers:

sage: R.<x,y> = ZZ[]
sage: p = 12 * (x*y - 1) * (x + 2*y + 3)
sage: p.factor()
Traceback (most recent call last):
...
NotImplementedError: Factorization of multivariate polynomials over non-fields is not implemented.

I propose to implement it using the factorization over QQ. Of course it may not be the best possible solution, but at least it is some (temporary?) workaround. This now gives:

sage: R.<x,y> = ZZ[]
sage: p = 12 * (x*y - 1) * (x + 2*y + 3)
sage: p.factor()
2^2 * 3 * (x + 2*y + 3) * (x*y - 1)

Component: factorization

Keywords: multivariate integer polynomial

Author: Bruno Grenet

Branch: c41d743

Reviewer: Jeroen Demeyer

Issue created by migration from https://trac.sagemath.org/ticket/17840

[bgrenet]

Branch: u/bruno/factorization_of_multivariate_polynomials_over_the_integers

[bgrenet]

Commit: 60bffcb

[bgrenet]

New commits:

60bffcb

Add factorization of multivariate polynomials over the integers

[jdemeyer]

comment:3

Add a doctest with a negative sign to show that signs are preserved.

[sagetrac-git]

Changed commit from 60bffcb to 28f89b6

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

28f89b6

Sign are now preserved + improvements

[bgrenet]

comment:5

Replying to @jdemeyer:

Add a doctest with a negative sign to show that signs are preserved.

They were not! Thanks for spotting this :-).