Doctest improvements to symbolic GCD

[rwst]

The following all give errors:

sage: gcd(I-I*x, x^2-1)
sage: gcd(I+I*x, x^2-1)
sage: alg = SR(QQbar(sqrt(2)+I*sqrt(3)))
sage: gcd(alg+alg*x, x^2-1)
sage: gcd(alg-alg*x, x^2-1)
sage: sqrt2 = SR(QQbar(sqrt(2)))
sage: gcd(sqrt2+sqrt2*x, x^2-1)
sage: gcd(sqrt2-sqrt2*x, x^2-1)

This is fixed in Pynac master and should be doctested here.

Note that although Singular supports algebraic GCD Pynac uses Singular only in rational mode. Use a dedicated polynomial ring instead of symbolics if you want algebraic GCD.

Depends on #23950

Component: symbolics

Author: Ralf Stephan

Branch/Commit: 41ea681

Reviewer: Travis Scrimshaw

Issue created by migration from https://trac.sagemath.org/ticket/23845

[rwst]

Changed dependencies from pynac-0.7.12 to #23950

[rwst]

Changed upstream from Fixed upstream, in a later stable release. to none

[frederichan-IMJPRG]

comment:2

Can you reproduce this, I have with 8.1beta9:

sage: x=SR('x')
sage: P=(x+1)^2+1
sage: gcd(P,P.expand())
1

[rwst]

comment:3

Confirmed. We don't expand automatically because products allow quick solutions and need time to expand. I should add this to the ex.gcd docstring.

[rwst]

comment:4

Maybe this can be fixed. If so, this ticket will add doctests.

[rwst]

Changed dependencies from #23950 to #23950, #24262

[EmmanuelCharpentier]

comment:6

#24262 fixes the problem. No doctests yet, as far as I can tell...

[rwst]

Branch: u/rws/doctest_improvements_to_symbolic_gcd

[sagetrac-git]

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

0aa6a98

23845: Doctest GCD bug fix