Trac #20317: bug in Permutations_msetk cardinality

{{{
sage: P = Permutations([1,1,1,2,2,2,3,3,3], 3)
sage: P.cardinality()
1680
sage: _ = P.list()
sage: P.cardinality()
27
}}}

See the original report on [https://groups.google.com/forum/#!topic
/sage-support/rowWX-_gzFo this sage-support thread]

URL: https://trac.sagemath.org/20317
Reported by: vdelecroix
Ticket author(s): Frédéric Chapoton
Reviewer(s): Travis Scrimshaw

src/sage/combinat/permutation.py

@@ -244,7 +244,7 @@
 from sage.categories.finite_permutation_groups import FinitePermutationGroups
 from sage.structure.list_clone import ClonableArray
 from sage.structure.global_options import GlobalOptions
-from sage.interfaces.all import gap
+from sage.libs.gap.libgap import libgap
 from sage.rings.all import ZZ, Integer, PolynomialRing
 from sage.arith.all import factorial, multinomial
 from sage.matrix.matrix_space import MatrixSpace
@@ -666,11 +666,11 @@ def _latex_(self):
             redword = self.reduced_word()
             if not redword:
                 return self.parent().options.latex_empty_str
-            return " ".join("%s_{%s}"%(let, i) for i in redword)
+            return " ".join("%s_{%s}" % (let, i) for i in redword)
         if display == "twoline":
-            return "\\begin{pmatrix} %s \\\\ %s \\end{pmatrix}"%(
-                    " & ".join("%s"%i for i in range(1, len(self._list)+1)),
-                    " & ".join("%s"%i for i in self._list))
+            return "\\begin{pmatrix} %s \\\\ %s \\end{pmatrix}" % (
+                    " & ".join("%s" % i for i in range(1, len(self._list)+1)),
+                    " & ".join("%s" % i for i in self._list))
         if display == "list":
             return repr(self._list)
         if display == "cycle":
@@ -1883,7 +1883,7 @@ def _icondition(self, i):
             :meth:`ishift`, :meth:`iswitch`
         """
         if i not in range(2, len(self)):
-            raise ValueError("i (= %s) must be between 2 and n-1"%i)
+            raise ValueError("i (= %s) must be between 2 and n-1" % i)
         pos_i   = self.index(i)
         pos_ip1 = self.index(i+1)
         pos_im1 = self.index(i-1)
@@ -5310,7 +5310,7 @@ def __classcall_private__(cls, n=None, k=None, **kwargs):
                     if k is None:
                         return Permutations_mset(n)
                     else:
-                        return Permutations_msetk(n,k)
+                        return Permutations_msetk(n, k)
         elif 'descents' in kwargs:
             #Descent positions specified
             if isinstance(kwargs['descents'], tuple):
@@ -5518,6 +5518,7 @@ def random_element(self):
         """
         return sample(range(1, self.n+1), self._k)
 
+
 class Permutations_mset(Permutations):
     r"""
     Permutations of a multiset `M`.
@@ -5669,6 +5670,8 @@ def __iter__(self):
 
     def cardinality(self):
         """
+        Return the cardinality of the set.
+
         EXAMPLES::
 
             sage: Permutations([1,2,2]).cardinality()
@@ -5791,6 +5794,8 @@ def __iter__(self):
 
     def cardinality(self):
         """
+        Return the cardinality of the set.
+
         EXAMPLES::
 
             sage: Permutations([1,2,3]).cardinality()
@@ -5855,7 +5860,8 @@ def __contains__(self, x):
             sage: [2,1] in p
             True
         """
-        if len(x) != self._k: return False
+        if len(x) != self._k:
+            return False
         s = list(self.mset)
         for i in x:
             if i in s:
@@ -5871,7 +5877,18 @@ def _repr_(self):
             sage: Permutations([1,2,2],2)
             Permutations of the multi-set [1, 2, 2] of length 2
         """
-        return "Permutations of the multi-set %s of length %s"%(list(self.mset), self._k)
+        return "Permutations of the multi-set %s of length %s" % (list(self.mset), self._k)
+
+    def cardinality(self):
+        """
+        Return the cardinality of the set.
+
+        EXAMPLES::
+
+            sage: Permutations([1,2,2],2).cardinality()
+            3
+        """
+        return ZZ.sum(1 for z in self)
 
     def __iter__(self):
         """
@@ -5883,10 +5900,11 @@ def __iter__(self):
         mset = self.mset
         lmset = list(mset)
         mset_list = [lmset.index(x) for x in lmset]
-        indices = eval(gap.eval('Arrangements(%s,%s)'%(mset_list, self._k)))
+        indices = libgap.Arrangements(mset_list, self._k).sage()
         for ktuple in indices:
             yield self.element_class(self, [lmset[x] for x in ktuple])
 
+
 class Permutations_setk(Permutations_set):
     """
     Length-`k` partial permutations of an arbitrary given finite set.