sage.quadratic_forms: Modularization fixes for imports

[mkoeppe]

📚 Description

We make sage.quadratic_forms ready for modularized distributions by:

• moving imports from some packages, such as sage.rings.padics.factory, into methods
• using lazy_import to provide the methods of QuadraticForm implemented in separate modules
• adding # optional annotations to doctests

Also some improvements to the code style of doctests and the Sphinx markup of some docstrings have been made.

This has been and can be tested by merging into:

• 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
  sagemath-polyhedra ships vector spaces etc. and now also portions of sage.quadratic_forms – see https://github.com/sagemath/sage/pull/35095/files#diff-f4c7c1beea87ae44c426de0a55459daef63b75b701b72bc136d88f4e7c9285cfR104

Resolves #35243

Part of:

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

📝 Checklist

• I have made sure that the title is self-explanatory and the description concisely explains the PR.
• I have linked an issue or discussion.
• I have created tests covering the changes.
• I have updated the documentation accordingly.

⌛ Dependencies

• Depends on using "change_ring" in quadratic_forms #35248
• Depends on Improve CM testing for elliptic curves over number fields #35166

[codecov-commenter]

Codecov Report

Patch coverage: 91.08% and project coverage change: -0.30 ⚠️

Comparison is base (c00e6c2) 88.62% compared to head (ff2df56) 88.32%.

Additional details and impacted files

@@             Coverage Diff             @@
##           develop   #35305      +/-   ##
===========================================
- Coverage    88.62%   88.32%   -0.30%     
===========================================
  Files         2148     2145       -3     
  Lines       398855   398750     -105     
===========================================
- Hits        353480   352193    -1287     
- Misses       45375    46557    +1182     

Impacted Files	Coverage Δ
src/sage/arith/all.py	100.00% <ø> (ø)
src/sage/modules/fg_pid/fgp_module.py	94.16% <ø> (ø)
src/sage/quadratic_forms/constructions.py	37.03% <ø> (-51.86%)	⬇️
src/sage/quadratic_forms/extras.py	86.44% <ø> (-8.48%)	⬇️
src/sage/quadratic_forms/qfsolve.py	68.88% <ø> (-31.12%)	⬇️
src/sage/quadratic_forms/quadratic_form__genus.py	80.00% <ø> (-7.50%)	⬇️
..._forms/quadratic_form__local_density_congruence.py	84.12% <ø> (ø)
..._forms/quadratic_form__local_density_interfaces.py	80.00% <ø> (ø)
...quadratic_form__local_representation_conditions.py	40.19% <ø> (-44.05%)	⬇️
src/sage/quadratic_forms/ternary_qf.py	66.60% <ø> (-0.59%)	⬇️
... and 29 more

... and 41 files with indirect coverage changes

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[mkoeppe]

#35166 makes is_fundamental_discriminant a method of Integer, should rebase on top of this

[kwankyu]

Otherwise, LGTM.

[kwankyu]

I looked through the rendered documentation. There are many math formulas with asterisks * representing multiplication. It seems they are not new. So you don't have to remove them. But it would be nice if you do it while we are here.

[mkoeppe]

Yes, these don't look very pretty. But I thought the intention is that "*" shows up in the text version (I don't know if that would be important.)

In sage.misc.sagedoc.math_substitutes (see also #35493), one can see the mapping (r'\\cdot', ' *').
LaTeX also has the discretionary multiplication symbol \*. Wondering if we should create a mapping (r'\\*', '*') -- such multiplication signs would then be displayed as * in the text help, implicit multiplication (no symbol) in the Sphinx HTML, and as implicit multiplication (no symbol unless at the end of a print line) in Sphinx PDF.

[mkoeppe]

I have changed * to \cdot

[kwankyu]

In sage.misc.sagedoc.math_substitutes (see also #35493), one can see the mapping (r'\\cdot', ' *'). LaTeX also has the discretionary multiplication symbol \*. Wondering if we should create a mapping (r'\\*', '*') -- such multiplication signs would then be displayed as * in the text help, implicit multiplication (no symbol) in the Sphinx HTML, and as implicit multiplication (no symbol unless at the end of a print line) in Sphinx PDF.

For me, \cdot means inner product, and is distinct from multiplication sign. But I didn't investigate if \cdot is used for inner product or multiplication (or perhaps for both) in sage docstrings.

For multiplication, I like the mapping (r'\\*', '*') that you suggested.

[kwankyu]

I have changed * to \cdot

I am not sure since I don't read \cdot as multiplication, except cases like $2 \cdot 3$. (I never doubted that I belong to the majority, but now I do :-)

[kwankyu]

But I didn't investigate if \cdot is used for inner product or multiplication (or perhaps for both) in sage docstrings.

I did. \cdot is used in many cases for multiplication in sage.

[kwankyu]

I have changed * to \cdot

Okay now.

[mkoeppe]

git grep 'cdot[^s]' shows lots of uses that look like multiplication (of all kinds of objects) to me.
But I'll try the \* tomorrow.

[kwankyu]

I am okay with either way.

[github-actions]

Documentation preview for this PR is ready! 🎉
Built with commit: a937a04

[mkoeppe]

OK, then I'll leave experimentation with \* for another ticket, probably #35493.

[kwankyu]

Thanks for fixes. LGTM.

[mkoeppe]

Thanks very much for reviewing!