Initialize a Set from a ConvexSet_base instance

[mkoeppe]

A Polyhedron is not a Parent, so Set refuses to construct the set of its elements.

We change this by creating a new abstract base class for non-necessarily-parent sets with methods union, intersection, etc.

ConvexSet_base (from #31919) and RealSet now both inherit from Set_base. To complete the implementation of the Set_base protocol, we add an implementation of RealSet.symmetric_difference.

So we can now do the following things:

sage: Set(polytopes.cube())                                                                                                                                                                          
Set of elements of A 3-dimensional polyhedron in ZZ^3 defined as the convex hull of 8 vertices
sage: polytopes.cube().union(polytopes.tetrahedron())                                                                                                                                                
Set-theoretic union of Set of elements of A 3-dimensional polyhedron in ZZ^3 defined as the convex hull of 8 vertices and Set of elements of A 3-dimensional polyhedron in ZZ^3 defined as the convex hull of 4 vertices

Depends on #30473

CC: @kliem @tscrim

Component: geometry

Author: Matthias Koeppe

Branch/Commit: fff2a79

Reviewer: Travis Scrimshaw

Issue created by migration from https://trac.sagemath.org/ticket/32013

[mkoeppe]

Branch: u/mkoeppe/initialize_a_set_from_a_convexset_base_instance

[mkoeppe]

Last 10 new commits:

f02ca28	src/sage/geometry/polyhedron/face.py: Remove unused import
1744ffa	Merge #31959
bd8e702	Merge #31990
f351eb8	src/sage/sets/set.py: Split out mix-in classes Set_base, Set_boolean_operators, Set_add_sub_operators from Set_object; pycodestyle fixes
f1db666	Polyhedron_base.*contains: Return False for non-iterables - do not raise an exception
6237fbc	ConvexSet_base.is_finite, cardinality: New
18270ce	Set_object._an_element_: Handle non-iterable objects by delegating to __object.an_element
b8f5978	Set: Create a wrapper instance also for Elements that subclass Set_base
b67092c	Set_base.union, intersection, difference, symmetric_difference: Convert to Set if necessary
e144389	ConvexSet_base.intersection: Remove abstract method; now inherits Set_base.intersection

[mkoeppe]

Commit: e144389

[mkoeppe]

Author: Matthias Koeppe

[mkoeppe]

Dependencies: #31990

[mkoeppe]

Description changed:

--- 
+++ 
@@ -1 +1,15 @@
+A `Polyhedron` is not a `Parent`, so `Set` refuses to construct the set of its elements.
 
+We change this by creating a new abstract base class for non-necessarily-parent sets with methods `union`, `intersection`, etc.
+
+`ConvexSet_base` (from #31919) now inherits from `Set_base`. 
+
+So we can now do the following things:
+
+```
+sage: Set(polytopes.cube())                                                                                                                                                                          
+Set of elements of A 3-dimensional polyhedron in ZZ^3 defined as the convex hull of 8 vertices
+sage: polytopes.cube().union(polytopes.tetrahedron())                                                                                                                                                
+Set-theoretic union of Set of elements of A 3-dimensional polyhedron in ZZ^3 defined as the convex hull of 8 vertices and Set of elements of A 3-dimensional polyhedron in ZZ^3 defined as the convex hull of 4 vertices
+```
+

[sagetrac-git]

Changed commit from e144389 to bc26d4f

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

bc26d4f

{LatticePolytopeClass, ConvexRationalPolyhedralCone._some_elements_: New

[mkoeppe]

Changed dependencies from #31990 to #31990, #32025

[mkoeppe]

Changed dependencies from #31990, #32025 to #31990, #31877, #32025

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. Last 10 new commits:

5b8ceca	InternalRealInterval, RealSet: Add `_latex_` methods
69ca854	RealSet._repr_: Use unicode cup sign instead of +
dbdfc06	InternalRealInterval, RealSet: Remove extra whitespace in latex, add documentation
7f56338	PiecewiseFunction: Adjust doctests for changed RealSet repr
8abdc8b	src/sage/functions/piecewise.py: Add coding header
5b0f85d	Merge #31880
e768463	Merge #31877
cb93c99	RealSet: Inherit from Set_base, Set_boolean_operators, Set_add_sub_operators
3a6f9bd	RealSet.symmetric_difference: New
afad76f	sage.sets.set.Set_object: Add `_sympy_` methods to subclasses

[sagetrac-git]

Changed commit from bc26d4f to afad76f

[sagetrac-git]

Changed commit from afad76f to 34d920b

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

34d920b

Set_base._test_as_set_object: Skip _test_pickling

[mkoeppe]

Changed dependencies from #31990, #31877, #32025 to #31990, #31877