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]

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

[sagetrac-git]

Changed commit from 669ea22 to af82717

[sagetrac-git]

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

592ce87

24171: Py3 fixes

[sagetrac-git]

Changed commit from af82717 to 592ce87

[tscrim]

comment:9

LGTM. Thanks.

[tscrim]

Reviewer: Travis Scrimshaw

[rwst]

comment:10

Thanks for the review.

[vbraun]

comment:11

Merge conflictw

[sagetrac-git]

Changed commit from 592ce87 to aa11a3e

[sagetrac-git]

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

aa11a3e

Merge branch 'develop' into t/24171/formal_set_membership_function

[sagetrac-git]

Changed commit from 5e623bb to 7d19916

[sagetrac-git]

Changed commit from 7d19916 to 5310e04

[sagetrac-git]

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

9b4e224	24176: check set argument of element_of()
5310e04	Function_elementof: Remove use of is_Set

[mkoeppe]

comment:39

This branch works now as advertised, but a careful review of this design is needed

[tscrim]

comment:40

We could add more support for other infinite sets later on (e.g., number fields), but this would be good for most (perhaps all?) use-cases. I think everything else is good except I don't understand why this line is added (see the diff):

oo = infinity

[mkoeppe]

comment:41

that's just a leftover, I'll get rid of it

[sagetrac-git]

Changed commit from 5310e04 to 43cabe8

[sagetrac-git]

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

43cabe8

Do not use QQ.completion(oo,oo) - not implemented (fixup)

[tscrim]

comment:43

Thank you. Green bot => positive review. Please add yourself whether you think you are an author and/or reviewer.

[sagetrac-git]

Changed commit from 43cabe8 to c793fcc

[sagetrac-git]

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

c793fcc

Function_elementof: Remove use of is_Set (fixup)

[mkoeppe]

Changed reviewer from Travis Scrimshaw to Travis Scrimshaw, Matthias Koeppe

[sagetrac-git]

Changed commit from c793fcc to a8c94ca

[sagetrac-git]

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

a8c94ca

Function_elementof: Add conversion to sympy

[mkoeppe]

Changed author from Ralf Stephan to Ralf Stephan, Matthias Koeppe

[mkoeppe]

comment:49

Thanks!

[vbraun]

Changed branch from u/mkoeppe/24171-1 to a8c94ca