Add user-defined constraint system (Perp, Para)

[vkotaru]

Summary

Implement a general constraint system where users can declare geometric relationships between vectors, and have them applied during simplification. Based on the original Scala implementation in symbolic_lhdynamics.ast.ConstraintRules.

Desired API

from geomech import Perp, Para, UserConstraints

q = S2('q')
omega = q.get_tangent_vector()
xi = q.get_variation_vector()

# Declare constraints
UserConstraints.append([
    Perp(omega, q),   # Dot(ω, q) → 0
    Perp(xi, q),      # Dot(ξ, q) → 0
    # Para(a, b),     # Cross(a, b) → 0
])

# Constraints applied during simplification
result = simplify(expr)  # or UserConstraints.apply(expr)

Constraint types

• Perp(a, b) — substitutes Dot(a, b) → 0 (and Dot(b, a) → 0 by commutativity)
• Para(a, b) — substitutes Cross(a, b) → 0

Reference

Original Scala implementation: /home/prasanth/Workspace/git/vkotaru/symbolic_lhdynamics in symbolic_lhdynamics/ast/ConstraintRules.scala

Key design from old package:

• UserConstraints is a global mutable list of active constraints
• ConstraintRules.apply(expr, rule) uses expr.subs(Dot(u,v), Number(0)) for Perp
• Constraints are applied as a post-processing step

Notes

• This is more general than hardcoding S2/SO3 orthogonality rules in vector_rules.py
• Should support reset() to clear constraints between different systems
• Consider whether to integrate into simplify() pipeline or keep as a separate apply step
• The commented-out code in the Scala version shows plans for vector/matrix substitution rules (applyConstraintsV, applyConstraintsM) — consider this for future extension

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