Trac 10513: use FreeModules(base_ring.category()) instead of FreeModu…

…les(base_ring)
sagemath · Jan 19, 2015 · f0957f0 · f0957f0
1 parent b1287e7
commit f0957f0
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Showing 5 changed files with 33 additions and 21 deletions.
diff --git a/src/sage/categories/category.py b/src/sage/categories/category.py
@@ -35,7 +35,7 @@
 
     sage: V = VectorSpace(RationalField(), 3)
     sage: V.category()
-    Category of vector spaces over Rational Field
+    Category of vector spaces with basis over quotient fields
     sage: G = SymmetricGroup(9)
     sage: G.category()
     Join of Category of finite permutation groups and Category of finite weyl groups

diff --git a/src/sage/categories/homset.py b/src/sage/categories/homset.py
@@ -652,7 +652,7 @@ def __reduce__(self):
             (<function Hom at ...>,
              (Vector space of dimension 2 over Rational Field,
               Vector space of dimension 3 over Rational Field,
-              Category of vector spaces over Rational Field,
+              Category of vector spaces with basis over quotient fields,
               False))
 
         TESTS::
@@ -1168,11 +1168,19 @@ def reversed(self):
         EXAMPLES::
 
             sage: H = Hom(ZZ^2, ZZ^3); H
-            Set of Morphisms from Ambient free module of rank 2 over the principal ideal domain Integer Ring to Ambient free module of rank 3 over the principal ideal domain Integer Ring in Category of modules with basis over Integer Ring
+            Set of Morphisms from Ambient free module of rank 2 over
+            the principal ideal domain Integer Ring to Ambient free
+            module of rank 3 over the principal ideal domain Integer
+            Ring in Category of modules with basis over (euclidean
+            domains and infinite enumerated sets)
             sage: type(H)
             <class 'sage.modules.free_module_homspace.FreeModuleHomspace_with_category'>
             sage: H.reversed()
-            Set of Morphisms from Ambient free module of rank 3 over the principal ideal domain Integer Ring to Ambient free module of rank 2 over the principal ideal domain Integer Ring in Category of modules with basis over Integer Ring
+            Set of Morphisms from Ambient free module of rank 3 over
+            the principal ideal domain Integer Ring to Ambient free
+            module of rank 2 over the principal ideal domain Integer
+            Ring in Category of modules with basis over (euclidean
+            domains and infinite enumerated sets)
             sage: type(H.reversed())
             <class 'sage.modules.free_module_homspace.FreeModuleHomspace_with_category'>
         """

diff --git a/src/sage/misc/functional.py b/src/sage/misc/functional.py
@@ -124,7 +124,7 @@ def category(x):
 
         sage: V = VectorSpace(QQ,3)
         sage: category(V)
-        Category of vector spaces over Rational Field
+        Category of vector spaces with basis over quotient fields
     """
     try:
         return x.category()

diff --git a/src/sage/modules/free_module.py b/src/sage/modules/free_module.py
@@ -675,15 +675,19 @@ def __init__(self, base_ring, rank, degree, sparse=False, category=None):
             Ambient free module of rank 3 over the integral domain Multivariate Polynomial Ring in x0, x1, x2 over Rational Field
 
             sage: FreeModule(GF(7),3).category()
-            Join of Category of vector spaces over Finite Field of size 7 and Category of finite enumerated sets
+            Join of Category of vector spaces with basis over
+            (finite fields and subquotients of monoids and quotients
+            of semigroups) and Category of finite enumerated sets
             sage: V = QQ^4; V.category()
-            Category of vector spaces over Rational Field
+            Category of vector spaces with basis over quotient fields
             sage: V = GF(5)**20; V.category()
-            Join of Category of vector spaces over Finite Field of size 5 and Category of finite enumerated sets
+            Join of Category of vector spaces with basis over
+            (finite fields and subquotients of monoids and quotients
+            of semigroups) and Category of finite enumerated sets
             sage: FreeModule(ZZ,3).category()
-            Category of modules with basis over Integer Ring
+            Category of modules with basis over (euclidean domains and infinite enumerated sets)
             sage: (QQ^0).category()
-            Join of Category of vector spaces over Rational Field and Category of finite enumerated sets
+            Join of Category of vector spaces with basis over quotient fields and Category of finite enumerated sets
 
         TESTS::
 
@@ -720,11 +724,8 @@ def __init__(self, base_ring, rank, degree, sparse=False, category=None):
             raise ValueError("degree (=%s) must be nonnegative"%degree)
 
         if category is None:
-            from sage.categories.all import Fields, FreeModules, VectorSpaces
-            if base_ring in Fields():
-                category = VectorSpaces(base_ring)
-            else:
-                category = FreeModules(base_ring)
+            from sage.categories.all import FreeModules
+            category = FreeModules(base_ring.category())
             try:
                 if base_ring.is_finite() or rank == 0:
                     # Put the module in the category of finite enumerated
@@ -2988,7 +2989,10 @@ def _Hom_(self, Y, category):
             sage: type(H)
             <class 'sage.modules.free_module_homspace.FreeModuleHomspace_with_category'>
             sage: H
-            Set of Morphisms from Vector space of dimension 2 over Rational Field to Ambient free module of rank 3 over the principal ideal domain Integer Ring in Category of vector spaces over Rational Field
+            Set of Morphisms from Vector space of dimension 2 over
+            Rational Field to Ambient free module of rank 3 over the
+            principal ideal domain Integer Ring in Category of vector
+            spaces with basis over quotient fields
         """
         if Y.base_ring().is_field():
             import vector_space_homspace

diff --git a/src/sage/modules/free_module_homspace.py b/src/sage/modules/free_module_homspace.py
@@ -27,11 +27,11 @@
     sage: V2 = FreeModule(IntegerRing(),2)
     sage: H = Hom(V3,V2)
     sage: H
-    Set of Morphisms from Ambient free module of rank 3
-    over the principal ideal domain Integer Ring to
-    Ambient free module of rank 2
-    over the principal ideal domain Integer Ring
-    in Category of modules with basis over Integer Ring
+    Set of Morphisms from Ambient free module of rank 3 over the
+    principal ideal domain Integer Ring to Ambient free module
+    of rank 2 over the principal ideal domain Integer Ring in
+    Category of modules with basis over (euclidean domains and
+    infinite enumerated sets)
     sage: B = H.basis()
     sage: len(B)
     6