splitting_field: polred -> polredbest

[AurelPage]

This PR partially addresses #22165. It removes one (in splitting_field) of the two uses of the Pari deprecated function polred. The other one is less trivial to remove and should probably be discussed in the issue.

📝 Checklist

• The title is concise, informative, and self-explanatory.
• 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. [the code is meant to be functionally equivalent]
• I have updated the documentation accordingly.

⌛ Dependencies

None

[videlec]

Wouldn't it be better to use directly pari nfsplitting?

[AurelPage]

@videlec Yes it would be. But I was planning to do that in a separate change. The reason is that nfsplitting does not have all the options that sage's splitting_field allows (namely abort_degree; in addition, Pari always uses the equivalent of the option simplify), so if we don't keep the sage code, the interface will not be backwards compatible. So we may as well fix the sage code first, unless you are happy to change the interface.

[github-actions]

Documentation preview for this PR (built with commit c1d0859; changes) is ready! 🎉

[videlec]

@videlec Yes it would be. But I was planning to do that in a separate change. The reason is that nfsplitting does not have all the options that sage's splitting_field allows (namely abort_degree; in addition, Pari always uses the equivalent of the option simplify), so if we don't keep the sage code, the interface will not be backwards compatible. So we may as well fix the sage code first, unless you are happy to change the interface.

Indeed, it seems more reasonable to make pari nfsplitting an available option to splitting_field. And also to do that in a further change.