Error when taking resultant of polynomials over complicated base ring

[pjbruin]

The following apparently tries to convert p and q into a wrong common ring (even though they already both have parent S):

A.<a,b,c> = Frac(PolynomialRing(QQ,'a,b,c'))
B.<d,e,f> = PolynomialRing(A,'d,e,f')
R.<x>= PolynomialRing(B,'x')
S.<y> = PolynomialRing(R,'y')
p = ((1/b^2*d^2+1/a)*x*y^2+a*b/c*y+e+x^2)
q = -4*c^2*y^3+1
print(p.resultant(q))
Traceback (most recent call last):
...
TypeError: not a constant polynomial

This ticket solves the bug by simply passing the variable with respect to which we want to take the resultant to PARI, instead of trying to change the variable names. The documentation is also updated.

See also #2693, #16749.

CC: @miguelmarco

Component: algebra

Keywords: polynomial resultant

Author: Peter Bruin

Branch/Commit: 02345b7

Reviewer: Marc Mezzarobba

Issue created by migration from https://trac.sagemath.org/ticket/17817

[pjbruin]

Branch: u/pbruin/17817-resultant_variables

[pjbruin]

Commit: 02345b7

[pjbruin]

Author: Peter Bruin

[mezzarobba]

comment:2

So some resultants that used to be computed using Singular will now go through sylvester_matrix—is that correct? Do you know if it makes a significant difference in terms of speed?

[miguelmarco]

comment:3

We would need to run benchmarks to make sure, but it is certainly possible that the sylvester matrix method would be faster than singular, at least in some cases.

[pjbruin]

comment:4

Replying to @mezzarobba:

So some resultants that used to be computed using Singular will now go through sylvester_matrix—is that correct?

Possibly, but this is only relevant when the polynomials are univariate polynomials over a multivariate polynomial ring. The Sylvester matrix is only used if the coefficients cannot be converted to PARI; what probably happens in most cases is that the resultant is computed through PARI rather than Singular. For genuine multivariate polynomials, Singular is still used via MPolynomial_libsingular.resultant().

Do you know if it makes a significant difference in terms of speed?

I don't know. How about adding an algorithm keyword (which could be pari, singular or sylvester for now) so that the user can easily choose an implementation and we can compare the speed of the implementations?

[mezzarobba]

Reviewer: Marc Mezzarobba

[mezzarobba]

comment:5

Replying to @pjbruin:

I don't know. How about adding an algorithm keyword (which could be pari, singular or sylvester for now) so that the user can easily choose an implementation and we can compare the speed of the implementations?

Ok, but then let's not block this ticket in the meantime if there is no significant regression to be expected.

[vbraun]

Changed branch from u/pbruin/17817-resultant_variables to 02345b7