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

[mkoeppe]

Description changed:

--- 
+++ 
@@ -1,3 +1,5 @@
 https://docs.sympy.org/latest/modules/sets.html
 
 
+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.
+

[mkoeppe]

Description changed:

--- 
+++ 
@@ -3,3 +3,10 @@
 
 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.
 
+We could also consider to make an adapter (wrapper) class
+that provides the sympy API. The `_sympy_` method of a Sage set could return this wrapper.
+
+
+Sets would provide a foundation for an improved symbolic assumptions facility, and for representing solution sets to symbolic equations etc.
+
+

[mkoeppe]

Description changed:

--- 
+++ 
@@ -6,6 +6,10 @@
 We could also consider to make an adapter (wrapper) class
 that provides the sympy API. The `_sympy_` method of a Sage set could return this wrapper.
 
+See also:
+- https://github.com/symengine/symengine/blob/master/symengine/sets.h
+
+
 
 Sets would provide a foundation for an improved symbolic assumptions facility, and for representing solution sets to symbolic equations etc.
 

[mkoeppe]

Description changed:

--- 
+++ 
@@ -13,4 +13,10 @@
 
 Sets would provide a foundation for an improved symbolic assumptions facility, and for representing solution sets to symbolic equations etc.
 
+Tickets:
 
+- #20877 Meta-ticket - `RealSet`, piecewise functions, ...
+- #31916 `{Polyhedron, ConvexRationalPolyhedralCone}.{interior, relative_interior}`
+- #31919 ABC for convex sets
+
+

[mkoeppe]

Description changed:

--- 
+++ 
@@ -1,14 +1,15 @@
-https://docs.sympy.org/latest/modules/sets.html
-
+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.
 
-We could also consider to make an adapter (wrapper) class
+Existing conversions:
+- from various sympy set types to Sage `SR` relation expressions: `sage.interfaces.sympy.sympy_set_to_list`
+- `RealSet._sympy_condition_`
+
+We could consider to make an adapter (wrapper) class
 that provides the sympy API. The `_sympy_` method of a Sage set could return this wrapper.
-
-See also:
-- https://github.com/symengine/symengine/blob/master/symengine/sets.h
-
 
 
 Sets would provide a foundation for an improved symbolic assumptions facility, and for representing solution sets to symbolic equations etc.

[mkoeppe]

Description changed:

--- 
+++ 
@@ -6,7 +6,7 @@
 
 Existing conversions:
 - from various sympy set types to Sage `SR` relation expressions: `sage.interfaces.sympy.sympy_set_to_list`
-- `RealSet._sympy_condition_`
+- `RealSet._sympy_condition_` - used internally in `sage.functions.piecewise`
 
 We could consider to make an adapter (wrapper) class
 that provides the sympy API. The `_sympy_` method of a Sage set could return this wrapper.

[mkoeppe]

Description changed:

--- 
+++ 
@@ -19,5 +19,5 @@
 - #20877 Meta-ticket - `RealSet`, piecewise functions, ...
 - #31916 `{Polyhedron, ConvexRationalPolyhedralCone}.{interior, relative_interior}`
 - #31919 ABC for convex sets
+- #31931 `_sympy_` methods for some parent classes
 
-

[mkoeppe]

Description changed:

--- 
+++ 
@@ -20,4 +20,4 @@
 - #31916 `{Polyhedron, ConvexRationalPolyhedralCone}.{interior, relative_interior}`
 - #31919 ABC for convex sets
 - #31931 `_sympy_` methods for some parent classes
-
+- #31935 solve: Add option `solution_set`

[mkoeppe]

Description changed:

--- 
+++ 
@@ -20,4 +20,6 @@
 - #31916 `{Polyhedron, ConvexRationalPolyhedralCone}.{interior, relative_interior}`
 - #31919 ABC for convex sets
 - #31931 `_sympy_` methods for some parent classes
+- #31938 Wrapper class for Sage sets as SymPy sets
 - #31935 solve: Add option `solution_set`
+

[mkoeppe]

Description changed:

--- 
+++ 
@@ -21,5 +21,7 @@
 - #31919 ABC for convex sets
 - #31931 `_sympy_` methods for some parent classes
 - #31938 Wrapper class for Sage sets as SymPy sets
+- #24171 Formal set membership function
+- #24176 Implement formal Set comprehension
 - #31935 solve: Add option `solution_set`
 

[mkoeppe]

Description changed:

--- 
+++ 
@@ -23,5 +23,6 @@
 - #31938 Wrapper class for Sage sets as SymPy sets
 - #24171 Formal set membership function
 - #24176 Implement formal Set comprehension
+- #24142 Improve interface to SymPy solvers
 - #31935 solve: Add option `solution_set`
 

[mkoeppe]

Description changed:

--- 
+++ 
@@ -26,3 +26,6 @@
 - #24142 Improve interface to SymPy solvers
 - #31935 solve: Add option `solution_set`
 
+See also:
+- #31942 `_sympy_` methods for matrices and vectors
+

[mkoeppe]

Description changed:

--- 
+++ 
@@ -28,4 +28,4 @@
 
 See also:
 - #31942 `_sympy_` methods for matrices and vectors
-
+- #31949 Add `_sympy_...` methods that construct `Domain`s

[mkoeppe]

Description changed:

--- 
+++ 
@@ -29,3 +29,5 @@
 See also:
 - #31942 `_sympy_` methods for matrices and vectors
 - #31949 Add `_sympy_...` methods that construct `Domain`s
+- #31958 Meta-ticket: Use the SymPy assumptions facility
+

[mkoeppe]

Description changed:

--- 
+++ 
@@ -22,6 +22,7 @@
 - #31931 `_sympy_` methods for some parent classes
 - #31938 Wrapper class for Sage sets as SymPy sets
 - #24171 Formal set membership function
+- #32015 `_sympy_` methods for `Set_object_binary` subclasses
 - #24176 Implement formal Set comprehension
 - #24142 Improve interface to SymPy solvers
 - #31935 solve: Add option `solution_set`