Doctest improvements to symbolic GCD

[Ralf Stephan]

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.

[Han Frederic]

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

[Ralf Stephan]

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.

[Ralf Stephan]

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

[Emmanuel Charpentier]

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

[git]

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

​0aa6a98

23845: Doctest GCD bug fix

[Travis Scrimshaw]

Trivial typo: kind -> kinds. You can set a positive review once done.

[git]

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

​41ea681

23845: cosmetics

[Ralf Stephan]

Thanks.