Ticket #9944: 9944-poly-cat.patch

sage/categories/principal_ideal_domains.py

@@ -9 +9 @@
 #******************************************************************************
 
 from sage.categories.category import Category
-from sage.categories.basic import GcdDomains
 from sage.misc.cachefunc import cached_method
 
 class PrincipalIdealDomains(Category):
@@ -27 +26 @@
       sage: PrincipalIdealDomains()
       Category of principal ideal domains
       sage: PrincipalIdealDomains().super_categories()
-      [Category of gcd domains]
+      [Category of unique factorization domains]
 
     See also: http://en.wikipedia.org/wiki/Principal_ideal_domain
 
@@ -42 +41 @@
         EXAMPLES::
 
             sage: PrincipalIdealDomains().super_categories()
-            [Category of gcd domains]
+            [Category of unique factorization domains]
         """
-        return [GcdDomains()]
+        from sage.categories.basic import UniqueFactorizationDomains
+        return [UniqueFactorizationDomains()]
 
     class ParentMethods:
         pass

sage/rings/polynomial/polynomial_ring.py

@@ -94 +94 @@
 
 from sage.structure.element import Element
 import sage.algebras.algebra
+import sage.categories.basic as categories
 import sage.rings.commutative_ring as commutative_ring
 import sage.rings.commutative_algebra as commutative_algebra
 import sage.rings.ring as ring
@@ -183 +184 @@
             0
             sage: (x - 2/3)*(x^2 - 8*x + 16)
             x^3 - 26/3*x^2 + 64/3*x - 32/3
+            
+            sage: category(ZZ['x'])
+            Category of unique factorization domains
+            sage: category(GF(7)['x'])
+            Category of euclidean domains
         """
-        sage.algebras.algebra.Algebra.__init__(self, base_ring, names=name, normalize=True)
+        R_cat = base_ring.category()
+        if R_cat.is_subcategory(categories.Fields()):
+            category = categories.EuclideanDomains()
+        elif R_cat.is_subcategory(categories.UniqueFactorizationDomains()):
+            category = categories.UniqueFactorizationDomains()
+        elif R_cat.is_subcategory(categories.IntegralDomains()):
+            category = categories.IntegralDomains()
+        else:
+            category = categories.CommutativeRings()
+        sage.algebras.algebra.Algebra.__init__(self, base_ring, names=name, normalize=True, category=category)
         self.__is_sparse = sparse
         if element_class:
             self._polynomial_class = element_class