Fix doctests related to singular: make them compatible with newer releases of Singular.

[jhpalmieri]

Singular doctests: make compatible with new versions of Singular

New versions of Singular, at least on OS X via homebrew, lead to doctest failures: see #40873. This addresses most of those failures.

• In the sandpiles code, it can now handle trailing zeros which may or may not be included in resolutions; this fix is very similar to what was done in fix is_free method for new version Singular #41138.
• In algebraic_scheme.py, the doctest now will not depend on which particular scalar multiples of a polynomial are used to define an ideal, etc.
• In singular/function.pyx, the previous test now no longer produces an error with some versions of Singular, so it is no longer testing what it was intended to. We delete this doctest.
• Various other doctests have been modified to be compatible with both old and new versions.

This will fix all but one of the failures in #40873; the failure in sage/schemes/curves/affine_curve.py remains.

📝 Checklist

• The title is concise and informative.
• The description explains in detail what this PR is about.
• I have linked a relevant issue or discussion.
• I have created tests covering the changes.
• I have updated the documentation and checked the documentation preview.

⌛ Dependencies

[dimpase]

works for me on Intel macOS

[dimpase]

let's see how it goes on the CI

[github-actions]

Documentation preview for this PR (built with commit fd08f92; changes) is ready! 🎉
This preview will update shortly after each push to this PR.

[antonio-rojas]

Which version of singular did this target? I'm getting many other failures with 4.4.1.p5, including some segfaults

python3 -m sage.doctest --long /usr/lib/python3.14/site-packages/sage/schemes/curves/affine_curve.py  # 2 doctests failed
python3 -m sage.doctest --long /usr/lib/python3.14/site-packages/sage/rings/polynomial/multi_polynomial_libsingular.pyx  # 4 doctests failed
python3 -m sage.doctest --long /usr/lib/python3.14/site-packages/sage/rings/polynomial/polynomial_element.pyx  # SignalError in doctesting framework
python3 -m sage.doctest --long /usr/lib/python3.14/site-packages/sage/rings/polynomial/multi_polynomial_ideal.py  # SignalError in doctesting framework
python3 -m sage.doctest --long /usr/lib/python3.14/site-packages/sage/rings/tate_algebra_ideal.pyx  # 1 doctest failed
python3 -m sage.doctest --long /usr/lib/python3.14/site-packages/sage/libs/singular/ring.pyx  # 3 doctests failed
python3 -m sage.doctest --long /usr/lib/python3.14/site-packages/sage/rings/polynomial/polynomial_singular_interface.py  # 1 doctest failed
python3 -m sage.doctest --long /usr/lib/python3.14/site-packages/sage/schemes/elliptic_curves/addition_formulas_ring.py  # SignalError in doctesting framework

[dimpase]

segfaults appear to indicate that your version of Singular has problems

[antonio-rojas]

Yes, that's why I asked which version was this tested with. It turns out 4.4.1.p5 causes segfaults, which are fixed upstream in Singular/Singular@56681f1

The other failures seem less severe, will follow up in another PR.

[cxzhong]

Yes, that's why I asked which version was this tested with. It turns out 4.4.1.p5 causes segfaults, which are fixed upstream in Singular/Singular@56681f1

The other failures seem less severe, will follow up in another PR.

may let them to release a new version

[antonio-rojas]

Yes, that's why I asked which version was this tested with. It turns out 4.4.1.p5 causes segfaults, which are fixed upstream in Singular/Singular@56681f1

The other failures seem less severe, will follow up in another PR.

Looks like another upstream bug, reported at Singular/Singular#1334

[antonio-rojas]

Opened #41798 to fix the remaining issues on the sage side