fix the base ring, tweak the category

Author: fchapoton

src/sage/rings/padics/witt_vector_ring.py

@@ -25,6 +25,7 @@
 from typing import Iterator
 
 from sage.categories.commutative_rings import CommutativeRings
+from sage.categories.integral_domains import IntegralDomains
 from sage.categories.fields import Fields
 from sage.misc.latex import latex
 from sage.rings.integer import Integer
@@ -278,8 +279,11 @@ def __init__(self, coefficient_ring, prec, prime) -> None:
         self._prec = prec
         self._prime = prime
 
-        Parent.__init__(self, base=coefficient_ring,
-                        category=CommutativeRings())
+        if self._coefficient_ring in IntegralDomains():
+            cat = IntegralDomains()
+        else:
+            cat = CommutativeRings()
+        Parent.__init__(self, base=ZZ, category=cat)
 
     def __iter__(self) -> Iterator:
         """
@@ -385,7 +389,7 @@ def _generate_sum_and_product_polynomials(self, coefficient_ring, prec, p):
         #
         # Remark: Since when is SIXTEEN bits sufficient for anyone???
         #
-        if p**(prec-1) >= 2**16:
+        if p**(prec - 1) >= 2**16:
             implementation = 'generic'
         else:
             implementation = 'singular'
@@ -811,7 +815,7 @@ def __init__(self, coefficient_ring, prec, prime) -> None:
             sage: type(W)
             <class 'sage.rings.padics.witt_vector_ring.WittVectorRing_phantom_with_category'>
 
-            sage: TestSuite(W).run()
+            sage: TestSuite(W).run(skip="_test_fraction_field")
         """
         if not (coefficient_ring.characteristic() == prime
                 and (coefficient_ring in Fields().Finite()