gh-36985: ModulesWithBasis.ParentMethods.cardinality() for 0 dimensio…

…nal modules

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Currently this is not handled properly as $\infty^0$ is not well-defined
but we know a 0 dimensional free module is $\\{0\\}$ with one element.

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URL: #36985
Reported by: Travis Scrimshaw
Reviewer(s): Darij Grinberg

build/pkgs/configure/checksums.ini

@@ -1,4 +1,4 @@
 tarball=configure-VERSION.tar.gz
-sha1=05115739db242cb5a48ae17f97d06b179fc70334
-md5=adc8208885e6be527b089b682079c464
-cksum=3321256447
+sha1=4fe91fa22748b17eca220ba95748d603003e5d04
+md5=05a48b56c39217c02ecfc2fff86b3e78
+cksum=743962125

build/pkgs/configure/package-version.txt

@@ -1 +1 @@
-e95536ccbad199de456e804968a775f2744e4bff
+a8b72d73e2c6146ef64e627d7a88732b57952292

src/sage/categories/modules_with_basis.py

@@ -996,10 +996,10 @@ def cardinality(self):
                 sage: S = SymmetricGroupAlgebra(QQ, 4)
                 sage: S.cardinality()
                 +Infinity
-                sage: S = SymmetricGroupAlgebra(GF(2), 4)       # not tested
-                sage: S.cardinality()                           # not tested
+                sage: S = SymmetricGroupAlgebra(GF(2), 4)
+                sage: S.cardinality()
                 16777216
-                sage: S.cardinality().factor()                  # not tested
+                sage: S.cardinality().factor()
                 2^24
 
                 sage: # needs sage.modules
@@ -1013,10 +1013,19 @@ def cardinality(self):
                 sage: s = SymmetricFunctions(GF(2)).s()                                 # needs sage.combinat sage.modules
                 sage: s.cardinality()                                                   # needs sage.combinat sage.modules
                 +Infinity
+
+                sage: M = CombinatorialFreeModule(QQ, [])
+                sage: M.dimension()
+                0
+                sage: M.cardinality()
+                1
             """
             from sage.rings.infinity import Infinity
             if self.dimension() == Infinity:
                 return Infinity
+            if self.dimension() == 0:
+                from sage.rings.integer_ring import ZZ
+                return ZZ.one()
             return self.base_ring().cardinality() ** self.dimension()
 
         def is_finite(self):