Square-free decomposition and any_root for polynomials

[pjbruin]

This patch improves the method Polynomial.squarefree_decomposition() and adds a new method Polynomial.any_root(). This has been split off from #8335, and is a dependency of that ticket.

Apply:

• attachment: trac_14957-squarefree_decomposition_any_root.patch
• attachment: trac_14957-doctests_14888.patch

Depends on #14888

CC: @roed314 @jpflori @sagetrac-mraum @fredstro @sagetrac-JCooley @loefflerd @sagetrac-dfesti

Component: algebra

Keywords: polynomial sd51

Author: David Roe, Jean-Pierre Flori, Peter Bruin

Reviewer: Jean-Pierre Flori, Peter Bruin

Merged: sage-5.13.beta0

Issue created by migration from https://trac.sagemath.org/ticket/14957

[pjbruin]

Attachment: squarefree_decomposition_any_root.patch.gz

enhance Polynomial.squarefree_decomposition(), add Polynomial.any_root()

[pjbruin]

Changed keywords from polynomial to polynomial sd51

[pjbruin]

comment:2

CC-ing the authors of #8335 and Sage Days 51 participants on this split-off ticket.

[pjbruin]

Attachment: trac_14957-squarefree_decomposition_any_root.patch.gz

enhance Polynomial.squarefree_decomposition(), add Polynomial.any_root()

[pjbruin]

comment:3

New patch with various improvements. Most importantly: improved documentation, removed unused parameter extend of any_root, which caused a doctest failure.

Patchbot: apply trac_14957-squarefree_decomposition_any_root.patch

[pjbruin]

Description changed:

--- 
+++ 
@@ -1,2 +1,5 @@
 This patch improves the method `Polynomial.squarefree_decomposition()` and adds a new method `Polynomial.any_root()`.  This has been split off from #8335, and is a dependency of that ticket.
 
+Apply: [attachment: trac_14957-squarefree_decomposition_any_root.patch](https://github.com/sagemath/sage-prod/files/10658189/trac_14957-squarefree_decomposition_any_root.patch.gz)
+
+

[jpflori]

Reviewer: Jean-Pierre Flori, Peter Bruin

[jpflori]

comment:4

I already reviewed David's code and did not really touch this part apart for a few fixes.

I also agree with Peter's changes.

Everything seems to work fine, but note that if I test this on top of #14888, then two doctests fail.
I think we should make this one depend on #14888, does anyone disagree?
If we go this way, this should get positive review.

[jpflori]

Changed author from David Roe, Jean-Pierre Flori to David Roe, Jean-Pierre Flori, Peter Bruin