sage.groups, sage.rings.number_field: Modularization fixes, # needs

[mkoeppe]

• Cherry-picked from Modularization of sagelib: Distributions sagemath-{brial,combinat,eclib,flint,gap,giac,glpk,graphs,groups,homfly,lcalc,libbraiding,libecm,linbox,modules,mpmath,ntl,pari,plot,polyhedra,schemes,singular,standard-no-symbolics,symbolics} #35095

Standard modularization work:

• a new dynamically detected feature sage.libs.braiding
• using file-level and block-level # needs to simplify decorations
• adding some # needs, in particular for sage.libs.gap
• splitting GAP-dependent classes out from sage.groups.galois_group
• using more lazy_imports
• some doctest cosmetics

Part of:

• Meta-ticket: Modularize sagelib into separate distributions (pip-installable packages) sagemath-... for Sage 10.x #29705

📝 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.
• I have updated the documentation accordingly.

⌛ Dependencies

[dcoudert]

Don't you need to list the new file galois_group_perm.py in the right .rst file so that it appear in https://doc.sagemath.org/html/en/reference/groups/index.html ?

otherwise, LGTM.

[mkoeppe]

Also galois_group does not appear in any index.rst. I'm not sure if this was intentional

[dcoudert]

LGTM.

The addition to the appropriate place in some index.rst file can be done later.

[mkoeppe]

Thank you!

[mkoeppe]

rebased

[github-actions]

Documentation preview for this PR (built with commit 1d77a49; changes) is ready! 🎉