Trac #34372: Make is_integral_domain() have the same signature

This is not fully consistent within Sage:
{{{
travis@tscrim:~/sage-build$ grep -R "def is_integral_domain" src/sage/*
src/sage/algebras/steenrod/steenrod_algebra.py:    def
is_integral_domain(self, proof=True):
src/sage/algebras/quatalg/quaternion_algebra.py:    def
is_integral_domain(self, proof=True) -> bool:
src/sage/categories/integral_domains.py:        def
is_integral_domain(self):
src/sage/categories/group_algebras.py:        def
is_integral_domain(self, proof=True):
src/sage/combinat/sf/sfa.py:        def is_integral_domain(self,
proof=True):
src/sage/manifolds/chart_func.py:    def is_integral_domain(self,
proof=True):
src/sage/rings/quotient_ring.py:    def is_integral_domain(self,
proof=True):
src/sage/rings/ring.pyx:    def is_integral_domain(self, proof = True):
src/sage/rings/ring.pyx:    def is_integral_domain(self, proof = True):
src/sage/rings/finite_rings/integer_mod_ring.py:    def
is_integral_domain(self, proof=None):
src/sage/rings/multi_power_series_ring.py:    def
is_integral_domain(self, proof=False):
src/sage/rings/polynomial/laurent_polynomial_ring.py:    def
is_integral_domain(self, proof=True):
src/sage/rings/polynomial/multi_polynomial_ring_base.c: *     def
is_integral_domain(self, proof=True):
src/sage/rings/polynomial/multi_polynomial_ring_base.c: *     def
is_integral_domain(self, proof=True):             # <<<<<<<<<<<<<<
src/sage/rings/polynomial/multi_polynomial_ring_base.c: *     def
is_integral_domain(self, proof=True):             # <<<<<<<<<<<<<<
src/sage/rings/polynomial/polynomial_quotient_ring.py:    def
is_integral_domain(self, proof = True):
src/sage/rings/polynomial/infinite_polynomial_ring.py:    def
is_integral_domain(self, *args, **kwds):
src/sage/rings/polynomial/polynomial_ring.py:    def
is_integral_domain(self, proof = True):
src/sage/rings/polynomial/multi_polynomial_ring_base.pyx:    def
is_integral_domain(self, proof=True):
src/sage/rings/polynomial/multi_polynomial_ring.py:    def
is_integral_domain(self, proof=True):
src/sage/rings/tate_algebra.py:    def is_integral_domain(self):
src/sage/rings/ring.c: *     def is_integral_domain(self, proof = True):
src/sage/rings/ring.c: *     def is_integral_domain(self, proof = True):
# <<<<<<<<<<<<<<
src/sage/rings/ring.c: *     def is_integral_domain(self, proof = True):
# <<<<<<<<<<<<<<
src/sage/rings/ring.c: *     def is_integral_domain(self, proof = True):
src/sage/rings/ring.c: *     def is_integral_domain(self, proof = True):
# <<<<<<<<<<<<<<
src/sage/rings/ring.c: *     def is_integral_domain(self, proof = True):
# <<<<<<<<<<<<<<
}}}
This causes failures for the tests that also pass a proof argument. For
example:
{{{
sage: A.<x,y> = TateAlgebra(Zp(3))
sage: R.<a,b> = PolynomialRing(A)
sage: R.is_integral_domain()
------------------------------------------------------------------------
---
TypeError                                 Traceback (most recent call
last)
Input In [3], in <cell line: 1>()
----> 1 R.is_integral_domain()

File
~/sage/src/sage/rings/polynomial/multi_polynomial_ring_base.pyx:108, in
sage.rings.polynomial.multi_polynomial_ring_base.MPolynomialRing_base.is
_integral_domain()
    106         False
    107     """
--> 108     return self.base_ring().is_integral_domain(proof)
    109
    110 def is_noetherian(self):

TypeError: TateAlgebra_generic.is_integral_domain() takes 1 positional
argument but 2 were given
}}}

URL: https://trac.sagemath.org/34372
Reported by: tscrim
Ticket author(s): Travis Scrimshaw
Reviewer(s): Frédéric Chapoton

src/sage/categories/integral_domains.py

@@ -96,17 +96,23 @@ def _contains_helper(cls):
         return Category_contains_method_by_parent_class(cls())
 
     class ParentMethods:
-        def is_integral_domain(self):
-            """
-            Return True, since this in an object of the category of integral domains.
+        def is_integral_domain(self, proof=True):
+            r"""
+            Return ``True``, since this in an object of the category
+            of integral domains.
 
             EXAMPLES::
 
                 sage: QQ.is_integral_domain()
                 True
-                sage: Parent(QQ,category=IntegralDomains()).is_integral_domain()
+                sage: Parent(QQ, category=IntegralDomains()).is_integral_domain()
                 True
 
+                sage: L.<z> = LazyLaurentSeriesRing(QQ)
+                sage: L.is_integral_domain()
+                True
+                sage: L.is_integral_domain(proof=True)
+                True
             """
             return True
 
@@ -138,3 +144,4 @@ def _test_fraction_field(self, **options):
 
     class ElementMethods:
         pass
+

src/sage/rings/tate_algebra.py

@@ -1275,8 +1275,8 @@ def random_element(self, degree=2, terms=5, integral=False, prec=None):
             gens = [ self.element_class(self, g) for g in self._integer_ring._gens ]
         return self.element_class(self, polring.random_element(degree, terms)(*gens), prec)
 
-    def is_integral_domain(self):
-        """
+    def is_integral_domain(self, proof=True):
+        r"""
         Return ``True`` since any Tate algebra is an integral domain.
 
         EXAMPLES::
@@ -1285,5 +1285,14 @@ def is_integral_domain(self):
             sage: A.is_integral_domain()
             True
 
+        TESTS:
+
+        Check that :trac:`34372` is fixed::
+
+            sage: A.<x,y> = TateAlgebra(Zp(3))
+            sage: R.<a,b> = PolynomialRing(A)
+            sage: R.is_integral_domain(proof=True)
+            True
         """
         return True
+