Free module does not correctly check domains

[tscrim]

Consider

sage: R.<x,y> = QQ[]
sage: I = R.ideal([x^2 - y^2 - 1])
sage: Q = R.quo(I)
sage: Q.is_integral_domain()
True

However

sage: Q2 = FreeModule(Q, 2)
sage: Q2.__class__.__mro__
(<class 'sage.modules.free_module.FreeModule_ambient_with_category'>,
 <class 'sage.modules.free_module.FreeModule_ambient'>,
 <class 'sage.modules.free_module.FreeModule_generic'>,
 <class 'sage.modules.free_module.Module_free_ambient'>,
 <class 'sage.modules.module.Module'>,
 ...

does not know it is a module over a domain. Contrast this with

sage: R2 = FreeModule(R, 2)
sage: R2.__class__.__mro__
(<class 'sage.modules.free_module.FreeModule_ambient_domain_with_category'>,
 <class 'sage.modules.free_module.FreeModule_ambient_domain'>,
 <class 'sage.modules.free_module.FreeModule_generic_domain'>,
 <class 'sage.modules.free_module.FreeModule_ambient'>,
 <class 'sage.modules.free_module.FreeModule_generic'>,
 <class 'sage.modules.free_module.Module_free_ambient'>,
 <class 'sage.modules.module.Module'>,
 ...

The issue is because the try-except block encapsulates too many things:

sage: Q.is_field()
...
NotImplementedError:

causes it to bail out too early. We need to test more things.

CC: @kwankyu @videlec @simonbrandhorst @yyyyx4

Component: linear algebra

Author: Travis Scrimshaw

Branch/Commit: bb5e329

Reviewer: Kwankyu Lee

Issue created by migration from https://trac.sagemath.org/ticket/34380

[tscrim]

comment:1

cc-ing some people who might be interested.

---

New commits:

bb5e329

Refine the try-except block in FreeModuleFactoy to run subsequent tests as they might work even if one of the earlier ones fail.

[tscrim]

Commit: bb5e329

[tscrim]

Branch: public/linear_algebra/refined_free_module_check-34380

[kwankyu]

Reviewer: Kwankyu Lee

[kwankyu]

comment:2

Looks good to me. Set positive review when all badges are green.

[tscrim]

comment:4

Thank you.

[vbraun]

Changed branch from public/linear_algebra/refined_free_module_check-34380 to bb5e329