Reworked Simplify to work better on Polynomials (with ripple effects)

[kwesiRutledge]

Summary

• Redid the AsSimplifiedExpression method for Polynomial to clean it up + remove extra polynomials OR return a Monomial, or Variable, or Constant, if it makes sense.
• Refactored a lot of the Plus, Multiply, and more to not make assumptions (especially for Polynomial objects) on output types.
• Introduced some more templates.
  • Need to add more templates.
• Added ToScalarExpressions() method for the all VectorExpressions.

[codecov]

Codecov Report

❌ Patch coverage is 87.16578% with 72 lines in your changes missing coverage. Please review.
✅ Project coverage is 87.09%. Comparing base (5fc58d9) to head (8ccf772).
⚠️ Report is 1 commits behind head on main.

Files with missing lines	Patch %	Lines
symbolic/monomial.go	65.38%	13 Missing and 5 partials ⚠️
symbolic/vector_expression.go	67.44%	14 Missing ⚠️
symbolic/matrix_expression.go	58.62%	9 Missing and 3 partials ⚠️
symbolic/variable.go	79.06%	9 Missing ⚠️
symbolic/polynomial_vector.go	83.72%	7 Missing ⚠️
symbolic/constant_matrix.go	90.90%	5 Missing ⚠️
symbolic/variable_vector.go	83.33%	5 Missing ⚠️
symbolic/monomial_vector.go	97.43%	1 Missing ⚠️
symbolic/polynomial.go	99.05%	1 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main      #27      +/-   ##
==========================================
- Coverage   87.46%   87.09%   -0.38%     
==========================================
  Files          42       42              
  Lines        6432     6516      +84     
==========================================
+ Hits         5626     5675      +49     
- Misses        719      743      +24     
- Partials       87       98      +11     

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[Copilot]

Pull Request Overview

This PR reworks the AsSimplifiedExpression method for Polynomial types and refactors arithmetic operations to avoid making assumptions about output types, particularly for Polynomial objects. The changes introduce template functions for vector operations and add a ToScalarExpressions() method to all VectorExpression types.

Key changes:

• Enhanced polynomial simplification that can return Constants, Variables, or Monomials when appropriate
• Refactored arithmetic operations to use templates and avoid type assumptions
• Added ToScalarExpressions() method to vector expression types

Reviewed Changes

Copilot reviewed 27 out of 27 changed files in this pull request and generated 3 comments.

Show a summary per file

File	Description
symbolic/polynomial.go	Enhanced AsSimplifiedExpression() and Simplify() methods, refactored arithmetic operations
symbolic/vector_expression.go	Added ToScalarExpressions() method and vector operation templates
symbolic/variable_vector.go	Refactored Plus() and Multiply() to use templates
symbolic/polynomial_vector.go	Updated arithmetic operations to use ConcretizeExpression()
symbolic/monomial.go	Added IsVariable(), ToVariable() methods and enhanced Plus()
testing/symbolic/*.go	Updated tests to expect simplified return types (Monomials, Variables, Constants)
examples/	Added new example scripts demonstrating substitution and derivatives

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