Replace Maxima with Pynac/Singular in Expression.factor()

[rwst]

The default for symbolic factorization should be changed. Maxima as default should be replaced with a call to Pynac's factor() implementation, which itself uses Singular at the moment. Maxima should be made available via ex.factor(algorithm=...).

As an example of performance gain here one of the Fateman benchmarks:

sage: var('a b c k s y z')
(a, b, c, k, s, y, z)
sage: f = (1+x+y+z)^20+1
sage: g = (f*(f+1)).expand()
sage: %time _=g.factor()

This takes 11 seconds on 8.1.beta5 and 3.3 seconds with Pynac factor (identical time using polynomial ring).

Depends on #23950

CC: @tscrim

Component: symbolics

Author: Ralf Stephan

Branch: 19cff3a

Reviewer: Travis Scrimshaw

Issue created by migration from https://trac.sagemath.org/ticket/23835

[rwst]

Dependencies: #23861

[rwst]

Branch: u/rws/replace_maxima_with_pynac_singular_in_expression_factor__

[rwst]

Changed dependencies from #23861 to pynac-0.7.12

[rwst]

Commit: 5157371

[rwst]

Author: Ralf Stephan

[rwst]

New commits:

5157371

23835: Replace Maxima with Pynac/Singular in Expression.factor()

[rwst]

Changed dependencies from pynac-0.7.12 to #23950

[sagetrac-git]

Changed commit from 5157371 to e9484ce

[sagetrac-git]

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

6a00170	Merge branch 'develop' into t/23835/replace_maxima_with_pynac_singular_in_expression_factor__
e9484ce	23835: fix doctest

[tscrim]

comment:8

If you rebase this to 8.4.beta0, I will review it.

[tscrim]

Reviewer: Travis Scrimshaw

[tscrim]

comment:9

Ping?

[rwst]

comment:10

Sorry, due to other work I'm restricting my activities to maintaining Pynac and its upgrade tickets.

[tscrim]

comment:11

No problem. It ended up being a trivial rebase. So I am treating this ticket as a needs_review.

While I do not see as big of a speed difference (9.5s to 3.2s), it still is quite an improvement. So positive review.

---

New commits:

19cff3a

Merge branch 'u/rws/replace_maxima_with_pynac_singular_in_expression_factor__' of git://trac.sagemath.org/sage into u/tscrim/expression_factor-23835

[tscrim]

Changed branch from u/rws/replace_maxima_with_pynac_singular_in_expression_factor__ to u/tscrim/expression_factor-23835

[tscrim]

Changed commit from e9484ce to 19cff3a

[vbraun]

Changed branch from u/tscrim/expression_factor-23835 to 19cff3a

[egourgoulhon]

Changed commit from 19cff3a to none

[egourgoulhon]

comment:13

See #27304 for a follow up (bug in factorization of exponentials).