propagate the variable domain to the assumptions database

[rwst]

While this works as expected:

sage: n = var('n')
sage: assume(n, 'integer')
sage: solve([n^2 == 3],n)
[]

this does not:

sage: forget()
sage: n = var('n', domain='integer')
sage: solve([n^2 == 3],n)
[n == -sqrt(3), n == sqrt(3)]

So, either solve should also look at the variable domain, or better, let's propagate domain settings to the assumption list.
Also:

sage: _ = var('n', domain='integer')
sage: n.is_integer()
False

Creating a non-complex var will invoke Maxima with this. I think this is acceptable for now. Alternatively, examine if assumptions can be done lazily, i.e., before any call to Maxima.

Depends on #18877

Component: symbolics

Author: Ralf Stephan

Branch/Commit: c142a5f

Reviewer: Vincent Delecroix

Issue created by migration from https://trac.sagemath.org/ticket/18695

[rwst]

Branch: u/rws/setting_domain_integer_on_var_has_no_effect_with_solve

[rwst]

Author: Ralf Stephan

[rwst]

New commits:

e7fe81a

18695: propagate the variable domain to the assumptions database

[rwst]

Commit: e7fe81a

[sagetrac-git]

Changed commit from e7fe81a to 95f63a6

[sagetrac-git]

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

95f63a6

18695: fix first attempt; enable exception for wrong domain

[sagetrac-git]

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

e103b56

18695: fix indentation

[sagetrac-git]

Changed commit from 95f63a6 to e103b56

[rwst]

comment:7

Together with #18877 this should be able to doctest:

sage: _ = var('n', domain='integer')
sage: n.is_integer()
True

[rwst]

Dependencies: #18877

[rwst]

comment:9

Replying to @rwst:

Together with #18877 this should be able to doctest:

sage: _ = var('n', domain='integer')
sage: n.is_integer()
True

No, this would actually need #18921 and is included there.

[videlec]

Reviewer: Vincent Delecroix

[videlec]

comment:11

Hello,

It looks good. Though I found confusing that the functions sage_domain_to_ginac and sage_domain_to_maxima have the same name. The first one return something (and does nothing) while the second one is communicating with maxima.

[sagetrac-git]

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

d3bf439	Merge branch 'develop' into t/18695/setting_domain_integer_on_var_has_no_effect_with_solve
c142a5f	18695: clearer names for helpers

[sagetrac-git]

Changed commit from e103b56 to c142a5f

[vbraun]

Changed branch from u/rws/setting_domain_integer_on_var_has_no_effect_with_solve to c142a5f