Trac #34380: Free module does not correctly check domains

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.

URL: https://trac.sagemath.org/34380
Reported by: tscrim
Ticket author(s): Travis Scrimshaw
Reviewer(s): Kwankyu Lee

src/sage/modules/free_module.py

@@ -191,6 +191,7 @@
 import sage.rings.infinity
 import sage.rings.integer
 from sage.categories.principal_ideal_domains import PrincipalIdealDomains
+from sage.categories.integral_domains import IntegralDomains
 from sage.categories.infinite_enumerated_sets import InfiniteEnumeratedSets
 from sage.misc.randstate import current_randstate
 from sage.structure.factory import UniqueFactory
@@ -236,6 +237,17 @@ def create_object(self, version, key):
 
  sage: TestSuite(ZZ^6).run()
  sage: TestSuite(RDF^3).run()
+
+ Check that :trac:`34380` is fixed::
+
+ sage: R.<x,y> = QQ[]
+ sage: Q = R.quo(R.ideal([x^2 - y^2 - 1]))
+ sage: Q.is_integral_domain()
+ True
+ sage: Q2 = FreeModule(Q, 2)
+ sage: from sage.modules.free_module import FreeModule_ambient_domain
+ sage: isinstance(Q2, FreeModule_ambient_domain)
+ True
  """
  base_ring, rank, sparse, inner_product_matrix = key
 
@@ -254,29 +266,29 @@ def create_object(self, version, key):
  "done from the right side.")
  #raise TypeError, "The base_ring must be a commutative ring."
 
- try:
- if not sparse and isinstance(base_ring, sage.rings.abc.RealDoubleField):
- return RealDoubleVectorSpace_class(rank)
+ if not sparse and isinstance(base_ring, sage.rings.abc.RealDoubleField):
+ return RealDoubleVectorSpace_class(rank)
 
-  elif not sparse and isinstance(base_ring, sage.rings.abc.ComplexDoubleField):
-  return ComplexDoubleVectorSpace_class(rank)
+ if not sparse and isinstance(base_ring, sage.rings.abc.ComplexDoubleField):
+ return ComplexDoubleVectorSpace_class(rank)
 
- elif base_ring.is_field():
+ try:
+ if base_ring.is_field():
  return FreeModule_ambient_field(base_ring, rank, sparse=sparse)
+ except NotImplementedError:
+ pass
 
-  elif base_ring in PrincipalIdealDomains():
-  return FreeModule_ambient_pid(base_ring, rank, sparse=sparse)
+ if base_ring in PrincipalIdealDomains():
+ return FreeModule_ambient_pid(base_ring, rank, sparse=sparse)
 
-  elif isinstance(base_ring, sage.rings.abc.Order) \
-  and base_ring.is_maximal() and base_ring.class_number() == 1:
-  return FreeModule_ambient_pid(base_ring, rank, sparse=sparse)
+ if (isinstance(base_ring, sage.rings.abc.Order)
+ and base_ring.is_maximal() and base_ring.class_number() == 1):
+ return FreeModule_ambient_pid(base_ring, rank, sparse=sparse)
 
- elif isinstance(base_ring, ring.IntegralDomain) or base_ring.is_integral_domain():
- return FreeModule_ambient_domain(base_ring, rank, sparse=sparse)
- else:
- return FreeModule_ambient(base_ring, rank, sparse=sparse)
- except NotImplementedError:
- return FreeModule_ambient(base_ring, rank, sparse=sparse)
+ if isinstance(base_ring, ring.IntegralDomain) or base_ring in IntegralDomains():
+ return FreeModule_ambient_domain(base_ring, rank, sparse=sparse)
+
+ return FreeModule_ambient(base_ring, rank, sparse=sparse)
 
 FreeModuleFactory_with_standard_basis = FreeModuleFactory("FreeModule")