Make category(GF(3)[x]) enumerated

src/sage/rings/polynomial/polynomial_ring.py

@@ -275,7 +275,7 @@ def __init__(self, base_ring, name=None, sparse=False, implementation=None,
             and Category of commutative algebras over
               (finite enumerated fields and subquotients of monoids
                and quotients of semigroups)
-            and Category of infinite sets
+            and Category of infinite enumerated sets
 
         TESTS:
 
@@ -1051,7 +1051,7 @@ def __iter__(self):
             sage: [*R]
             [0]
             sage: R.<x> = QQ[]
-            sage: list(islice(iter(R), 10))
+            sage: list(islice(iter(R), 10))  # when this is implemented add Enumerated() to category(R)
             Traceback (most recent call last):
             ...
             NotImplementedError: iteration over infinite base ring not yet implemented

src/sage/rings/polynomial/polynomial_ring_constructor.py

@@ -892,6 +892,7 @@ def _multi_variate(base_ring, names, sparse=None, order='degrevlex', implementat
 from sage import categories
 from sage.categories.algebras import Algebras
 # Some fixed categories, in order to avoid the function call overhead
+_EnumeratedSets = categories.sets_cat.Sets().Enumerated()
 _FiniteSets = categories.sets_cat.Sets().Finite()
 _InfiniteSets = categories.sets_cat.Sets().Infinite()
 _EuclideanDomains = categories.euclidean_domains.EuclideanDomains()
@@ -938,12 +939,27 @@ def polynomial_default_category(base_ring_category, n_variables):
         True
         sage: QQ['s']['t'].category() is UniqueFactorizationDomains() & CommutativeAlgebras(QQ['s'].category()).WithBasis().Infinite()
         True
+
+    TESTS::
+
+        sage: category(GF(7)['x'])
+        Join of Category of euclidean domains
+         and Category of algebras with basis over
+          (finite enumerated fields and subquotients of monoids
+           and quotients of semigroups)
+        and Category of commutative algebras over
+          (finite enumerated fields and subquotients of monoids
+           and quotients of semigroups)
+        and Category of infinite enumerated sets
     """
     category = Algebras(base_ring_category).WithBasis()
 
     if n_variables:
         # here we assume the base ring to be nonzero
         category = category.Infinite()
+        if base_ring_category.is_subcategory(_FiniteSets) and n_variables == 1:
+            # base_ring_category.is_subcategory(_EnumeratedSets) suffices but this is not yet implemented
+            category = category.Enumerated()
     else:
         if base_ring_category.is_subcategory(_Fields):
             category = category & _Fields