These are the {0,1}- and {+oo,0}-valued functions on the ambient space that indicate set membership. The main focus of this ticket is on indicator_function.

indicator_functions form algebras in which multiplication is the pointwise multiplication; it corresponds to taking intersections. Every indicator function is an idempotent.

The indicator functions of the faces of a PolyhedralComplex form a basis. The indicator functions of their relative interiors form another basis - of orthogonal idempotents.
The algebra is isomorphic to the MoebiusAlgebra of the opposite of the face poset.

convex_indicator_functions merely form a cone of functions. We introduce them on this ticket only to clarify the terminology, and in preparation for a connection to cvxpy (https://www.cvxpy.org/api_reference/cvxpy.transforms.html#cvxpy.transforms.indicator) in #31981

Depends on #31748
Depends on #31881

CC: @tscrim @kliem @yuan-zhou

Component: geometry

Branch/Commit: u/mkoeppe/sets_subobjects_parentmethods_indicator_function__convexset_base_indicator_function__convexset_base_convex_indicator_function @ beaea83

Issue created by migration from https://trac.sagemath.org/ticket/32201