CVXPY is a system for disciplined convex programming in which finite dimensional optimization problems are expressed using expression trees.

We monkey-patch caching _sage_ methods into the CVXPY classes, along the same lines as it is done for SymPy in sage.interfaces.sympy.

• Each leaf is a scalar, vector or matrix, subject to a domain restriction such as nonneg or PSD. _sage_ methods return symbolic variables or expressions or vectors/matrices thereof. _sage_domain_ methods return the domain as a set. (For the PSD domain, see Cone of positive-semidefinite matrices #30172.) _sage_manifold_ method returns the pullback (Pullbacks (preimages) of manifold subsets under continuous maps #31688), defining a manifold subset / submanifold etc.

• A subclass of cvxpy.Problem would provide a method feasible_set an instance of class ConditionSet_cvxpy (see ConditionSet, ImageSet: Implement formal Set comprehension #24176) or ConvexSet_cvxpy, representing sets of points that satisfy a list of cvxpy.Constraints.

Depends on #31962
Depends on #31688
Depends on #30172
Depends on #31982

CC: @dimpase @yuan-zhou @egourgoulhon

Component: manifolds

Author: Matthias Koeppe, ...

Branch/Commit: u/mkoeppe/manifoldsubset_corresponding_to_a_cvxpy_leaf__variable_parameter_ @ 84a5868

Issue created by migration from https://trac.sagemath.org/ticket/31981