Trac 15801: little fix in polynomial_default_category, and update doc…

…tests involving categories of polynomial rings
sagemath · Apr 14, 2014 · 9cc7ef4 · 9cc7ef4
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diff --git a/src/sage/rings/polynomial/polynomial_ring_constructor.py b/src/sage/rings/polynomial/polynomial_ring_constructor.py
@@ -617,27 +617,33 @@ def polynomial_default_category(base_ring_category, multivariate):
 
     EXAMPLES::
 
-        sage: QQ['t'].category() is Category.join([EuclideanDomains(), CommutativeAlgebras(QQ.category())])
+        sage: from sage.rings.polynomial.polynomial_ring_constructor import polynomial_default_category
+        sage: polynomial_default_category(Rings(), False) is Algebras(Rings())
         True
-        sage: QQ['s','t'].category() is Category.join([UniqueFactorizationDomains(), CommutativeAlgebras(QQ.category())])
+        sage: polynomial_default_category(Rings().Commutative(),False) is Algebras(Rings().Commutative()).Commutative()
         True
-        sage: QQ['s']['t'].category() is Category.join([UniqueFactorizationDomains(), CommutativeAlgebras(QQ['s'].category())])
+        sage: polynomial_default_category(Fields(),False) is EuclideanDomains() & Algebras(Fields())
+        True
+        sage: polynomial_default_category(Fields(),True) is UniqueFactorizationDomains() & CommutativeAlgebras(Fields())
         True
 
+        sage: QQ['t'].category() is EuclideanDomains() & CommutativeAlgebras(QQ.category())
+        True
+        sage: QQ['s','t'].category() is UniqueFactorizationDomains() & CommutativeAlgebras(QQ.category())
+        True
+        sage: QQ['s']['t'].category() is UniqueFactorizationDomains() & CommutativeAlgebras(QQ['s'].category())
+        True
     """
     category = Algebras(base_ring_category)
-    if base_ring_category.is_subcategory(_Fields):
-        if multivariate:
-            return category & _UniqueFactorizationDomains
-        else:
-            return category & _EuclideanDomains
+    if base_ring_category.is_subcategory(_Fields) and not multivariate:
+        return category & _EuclideanDomains
     elif base_ring_category.is_subcategory(_UniqueFactorizationDomains):
         return category & _UniqueFactorizationDomains
     elif base_ring_category.is_subcategory(_IntegralDomains):
         return category & _IntegralDomains
     elif base_ring_category.is_subcategory(_CommutativeRings):
         return category & _CommutativeRings
-    return base_ring_category
+    return category
 
 def BooleanPolynomialRing_constructor(n=None, names=None, order="lex"):
     """

diff --git a/src/sage/rings/ring.pyx b/src/sage/rings/ring.pyx
@@ -133,13 +133,13 @@ cdef class Ring(ParentWithGens):
     Test agaings another bug fixed in :trac:`9944`::
 
         sage: QQ['x'].category()
-        Join of Category of euclidean domains and Category of commutative algebras over Rational Field
+        Join of Category of euclidean domains and Category of commutative algebras over quotient fields
         sage: QQ['x','y'].category()
-        Join of Category of unique factorization domains and Category of commutative algebras over Rational Field
+        Join of Category of unique factorization domains and Category of commutative algebras over quotient fields
         sage: PolynomialRing(MatrixSpace(QQ,2),'x').category()
-        Category of algebras over Full MatrixSpace of 2 by 2 dense matrices over Rational Field
+        Category of algebras over algebras over quotient fields
         sage: PolynomialRing(SteenrodAlgebra(2),'x').category()
-        Category of algebras over mod 2 Steenrod algebra, milnor basis
+        Category of algebras over graded hopf algebras with basis over Finite Field of size 2
 
      TESTS::