A formulation representing an equality constraint as two inequality constraints can create some issues for a nlp solver (particularly for nonconvex constraints).
[ ] Conic & Quadratic functions: 1) Canonically order each function 2) check if function has hash in a dictionary storing negations, if not store an index to the function the hash of it's negation, otherwise delete the function.
[ ] Linear: Follow the approach for conic/quadratics. Will look into a linear algebra approach to this later.
[ ] Nonlinear: This introduces a bit of complexity as a canonical form of nonlinear functions currently doesn't exist. However, we only need this standardization to work when the lhs function is negated. One options would be distributing the negation through subtraction, addition operators to the coefficients of participating terms.
A formulation representing an equality constraint as two inequality constraints can create some issues for a nlp solver (particularly for nonconvex constraints).