Improve Maxima backend usability and result handling

[Amin-El-Sayed]

Summary

• surface concrete Maxima assumption questions instead of parser failures
• preserve exact constants and broaden special-function round-tripping
• add exact simplification, numerical evaluation, status, and help utilities
• document the backend and prepare SymbolicIntegrationMaxima v0.2.0

Motivation

Parametric improper integrals could previously end in a raw parser error when Maxima asked for an assumption. Exact special-function values could also be converted to floating-point values too early, and unsupported Maxima functions stopped otherwise usable results from returning to Symbolics.

This update makes the backend suitable for interactive use while keeping assumptions explicit: the package does not silently choose mathematical domains or signs for the user.

Behavior

The backend now:

• captures Maxima's assumption requests and reports which assumption is missing
• distinguishes assumption, timeout, process, parse, and unsupported-result failures
• preserves exact %pi and %e
• handles incomplete gamma values and common special functions more naturally
• preserves unknown Maxima functions as symbolic calls when possible
• provides maxima_simplify, maxima_numeric, maxima_help, and maxima_status
• documents installation, assumptions, improper integrals, simplification, and diagnostics

Validation

• Julia 1.10: 90/90 basic tests passed
• Julia 1.12: 90/90 basic tests passed
• difficult corpus, 103 cases: 62 ok, 35 maybe, 0 fail, 4 unevaluated, 2 assumption-needed, 0 exceptions
• Documenter build and doctests passed
• git diff --check passed

Release and registry

The subpackage version is bumped to 0.2.0. After this PR is merged, the General registry source entry should first be updated to:

repo = "https://github.com/JuliaSymbolics/SymbolicIntegration.jl.git"
subdir = "lib/SymbolicIntegrationMaxima"

Then 0.2.0 can be registered from the merged commit. Existing entries in Versions.toml, especially the 0.1.1 tree hash, must remain unchanged.

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Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 54.51%. Comparing base (8647f0d) to head (fd973fe).
⚠️ Report is 11 commits behind head on main.
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Additional details and impacted files

@@            Coverage Diff             @@
##             main     #124      +/-   ##
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+ Coverage   50.98%   54.51%   +3.52%     
==========================================
  Files          23       23              
  Lines        4309     4309              
==========================================
+ Hits         2197     2349     +152     
+ Misses       2112     1960     -152     

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[Amin-El-Sayed]

Hi @ChrisRackauckas, all 24 checks are green and the PR is conflict-free. It includes the Maxima 5.46 assumption regression fix, expanded integration tests, and the dedicated backend documentation. Is there anything else you would like changed before merge?

[ChrisRackauckas]

Nope that looks great.

[Amin-El-Sayed]

Thanks for merging this. SymbolicIntegrationMaxima is now version 0.2.0 under lib/SymbolicIntegrationMaxima, and the subpackage TagBot step from #125 is also on main. General still points to the former standalone repository and only contains v0.1.1. Could a JuliaSymbolics maintainer please trigger the official subpackage registration with @JuliaRegistrator register subdir=lib/SymbolicIntegrationMaxima? The existing v0.1.1 tree hash must remain unchanged.

[JuliaRegistrator]

Error while trying to register: Register Failed
@Amin-El-Sayed, it looks like you are not a publicly listed member/owner in the parent organization (JuliaSymbolics).
If you are a member/owner, you will need to change your membership to public. See GitHub Help

[ChrisRackauckas]

oh yes misssed that sorry!