Meta-ticket: Connect Sage sets to sympy sets

[mkoeppe]

API reference:

• https://docs.sympy.org/latest/modules/sets.html
• see also: https://github.com/symengine/symengine/blob/master/symengine/sets.h

sympy uses properties for many things, so we probably cannot achieve direct API compatibility, put perhaps we can use the same vocabulary when it makes sense.

Existing conversions:

• from various sympy set types to Sage SR relation expressions: sage.interfaces.sympy.sympy_set_to_list
• RealSet._sympy_condition_ - used internally in sage.functions.piecewise

In #31938 we provide an adapter (wrapper) class
that provides the sympy API. The _sympy_ method of a Sage set can return this wrapper.

Sets would provide a foundation for an improved symbolic assumptions facility, and for representing solution sets to symbolic equations etc.

Tickets:

• Meta-ticket: Piecewise functions, polyhedral complexes, piecewise functions of several variables, periodic piecewise functions #20877 Meta-ticket - RealSet, piecewise functions, ...
• {Polyhedron, ConvexRationalPolyhedralCone}.{interior, relative_interior} #31916 {Polyhedron, ConvexRationalPolyhedralCone}.{interior, relative_interior}
• ABC for convex sets #31919 ABC for convex sets
• _sympy_ methods for some parent classes #31931 _sympy_ methods for some parent classes
• Wrapper class for Sage sets as SymPy sets #31938 Wrapper class for Sage sets as SymPy sets
• Formal set membership function #24171 Formal set membership function
• _sympy_ methods for Set_object_binary subclasses #32015 _sympy_ methods for Set_object_binary subclasses
• Initialize a Set from a ConvexSet_base instance #32013 Initialize a Set from a ConvexSet_base instance
• ConditionSet #32089 ConditionSet
• Set_base.contains, ConvexSet.contains: Handle symbolic argument #31947 Set_base.contains, ConvexSet.contains: Handle symbolic argument
• ConditionSet, ImageSet: Implement formal Set comprehension #24176 Implement formal Set comprehension
• Improve interface to SymPy solvers #24142 Improve interface to SymPy solvers
• solve: Add option "solution_set" #31935 solve: Add option solution_set

See also:

• _sympy_ methods for matrices and vectors #31942 _sympy_ methods for matrices and vectors
• Add _sympy_... methods that construct Domains #31949 Add _sympy_... methods that construct Domains
• Meta-ticket: Use the SymPy assumptions facility #31958 Meta-ticket: Use the SymPy assumptions facility

CC: @kliem @tscrim @EmmanuelCharpentier @isuruf

Component: geometry

Issue created by migration from https://trac.sagemath.org/ticket/31926