cleaning and enhancement to PolyDict

[videlec]

📚 Description

Fixes #34000 (and more complete version of the proposition at #35020).

A discussion about the general problem of inexact zeros has been opened at #35319

📝 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.

[roed314]

@videlec I'm currently in Chamonix with bad internet; I'll try to take a look at this over the weekend.

[codecov-commenter]

Codecov Report

Patch coverage: 97.13% and project coverage change: +0.03 🎉

Comparison is base (e28bd1a) 88.58% compared to head (db9aed3) 88.61%.

Additional details and impacted files

@@             Coverage Diff             @@
##           develop   #35174      +/-   ##
===========================================
+ Coverage    88.58%   88.61%   +0.03%     
===========================================
  Files         2141     2148       +7     
  Lines       397475   398873    +1398     
===========================================
+ Hits        352106   353472    +1366     
- Misses       45369    45401      +32     

Impacted Files	Coverage Δ
src/sage/schemes/elliptic_curves/ell_generic.py	93.25% <66.66%> (+0.01%)	⬆️
src/sage/interfaces/tachyon.py	87.93% <90.00%> (+0.43%)	⬆️
src/sage/schemes/elliptic_curves/gal_reps.py	82.23% <90.00%> (+0.04%)	⬆️
src/sage/quadratic_forms/quadratic_form.py	90.30% <90.90%> (+0.20%)	⬆️
.../sage/rings/polynomial/multi_polynomial_element.py	90.71% <94.00%> (-0.39%)	⬇️
src/sage/modular/quasimodform/element.py	99.20% <100.00%> (+0.06%)	⬆️
src/sage/rings/polynomial/multi_polynomial_ring.py	86.25% <100.00%> (+0.35%)	⬆️
src/sage/rings/qqbar.py	95.30% <100.00%> (+<0.01%)	⬆️
src/sage/schemes/affine/affine_morphism.py	90.33% <100.00%> (ø)
src/sage/schemes/elliptic_curves/BSD.py	43.75% <100.00%> (+0.21%)	⬆️
... and 42 more

... and 149 files with indirect coverage changes

Help us with your feedback. Take ten seconds to tell us how you rate us. Have a feature suggestion? Share it here.

☔ View full report in Codecov by Sentry.
📢 Do you have feedback about the report comment? Let us know in this issue.

[videlec]

The situation with trailing zeros evaluating to False is extremely annoying. For example equality of polynomials is not equality of coefficients

sage: from sage.rings.polynomial.polydict import PolyDict
sage: R.<t> = PowerSeriesRing(QQ)
sage: PolyDict({(1, 0): O(t)}) == PolyDict({})
False
sage: PolyDict({(1, 0): O(t)}) == PolyDict({(1, 0): O(t^2)})
True

Similarly, bool(p) is probably wrong. Of course the same question holds for matrices, etc.

[tscrim]

I will take a look at this tonight.

Indeed, the removal of zeros in general (not just trailing) definitely is useful at keeping this consistent and fast an should be done as much as possible.

[github-actions]

Documentation preview for this PR is ready! 🎉
Built with commit: 1a7eeac

[videlec]

Actually changing bool(x) to mean x is not an exact zero would solve all issues here! But Julian does not seems convinced about it yet at #35319.

[tscrim]

Thank you. LGTM. We can always do more changes later should we find other improvements.