Formal set membership function

[rwst]

To express solution sets from solvers an expression-is-element-of-set relation is needed. For ease of implementation this can be made a formal function element_of.

It depends on sets being made coercible into SR. The present ticket plays safe and only does this for finite sets and a few standard infinite sets: NN, ZZ, QQ, AA; and RealSets.

element_of converts to SymPy's Contains. This is useful in combination with #31931, which adds SymPy conversions to some of the above sets.

Depends on #31877

CC: @videlec

Component: symbolics

Author: Ralf Stephan, Matthias Koeppe

Branch/Commit: a8c94ca

Reviewer: Travis Scrimshaw, Matthias Koeppe

Issue created by migration from https://trac.sagemath.org/ticket/24171

[rwst]

Description changed:

--- 
+++ 
@@ -1 +1 @@
-To express solution sets from solvers an expression-is-element-of-set relation is needed. For ease of implementation this can be made a formal function, likely named "contains". It would depend on sets being made coercible into SR.
+To express solution sets from solvers an expression-is-element-of-set relation is needed. For ease of implementation this can be made a formal function, likely named "contains" or "element_of". It would depend on sets being made coercible into SR.

[rwst]

Branch: u/rws/formal_set_membership_function

[rwst]

Author: Ralf Stephan

[rwst]

New commits:

669ea22

24171: Formal set membership function

[rwst]

Commit: 669ea22

[tscrim]

comment:4

I can reproduce this error

**********************************************************************
File "src/sage/misc/dev_tools.py", line 438, in sage.misc.dev_tools.import_statements
Failed example:
    load_submodules(sage.sets)
Expected:
    load sage.sets.real_set... succeeded
    load sage.sets.set_from_iterator... succeeded
Got:
    load sage.sets.set_from_iterator... succeeded

I think why this now fails is because real_set is now loaded on startup.

[rwst]

comment:5

I think it would be good if RealSet answered positive to is_Set, I'm just not sure how to accomplish it correctly. If done it wouldn't need to be loaded at start.

[sagetrac-git]

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

34c9773	24171: make RealSet inherit from Set_generic
af82717	24171: remove RealSet import; SR set coercion doctests