py3: fix doctests in symmetric group algebra

src/sage/combinat/symmetric_group_algebra.py

@@ -1,18 +1,18 @@
 r"""
 Symmetric Group Algebra
 """
-#*****************************************************************************
+# ****************************************************************************
 #       Copyright (C) 2007 Mike Hansen <[email protected]>,
 #
 #  Distributed under the terms of the GNU General Public License (GPL)
-#                  http://www.gnu.org/licenses/
-#*****************************************************************************
+#                  https://www.gnu.org/licenses/
+# ****************************************************************************
 from __future__ import print_function, absolute_import
 import itertools
 import six
 from six.moves import range
 
-from sage.misc.cachefunc import cached_method, cached_function
+from sage.misc.cachefunc import cached_method
 from sage.misc.lazy_attribute import lazy_attribute
 from sage.misc.superseded import deprecated_function_alias
 from sage.combinat.combinatorial_algebra import CombinatorialAlgebra
@@ -23,7 +23,6 @@
 from sage.combinat.tableau import Tableau, StandardTableaux_size, StandardTableaux_shape, StandardTableaux
 from sage.algebras.group_algebra import GroupAlgebra_class
 from sage.categories.weyl_groups import WeylGroups
-from sage.categories.algebras import Algebras
 from sage.rings.all import QQ, PolynomialRing
 from sage.arith.all import factorial
 from sage.matrix.all import matrix
@@ -32,6 +31,8 @@
 
 # TODO: Remove this function and replace it with the class
 # TODO: Create parents for other bases (such as the seminormal basis)
+
+
 def SymmetricGroupAlgebra(R, W, category=None):
     r"""
     Return the symmetric group algebra of order ``W`` over the ring ``R``.
@@ -223,6 +224,7 @@ def SymmetricGroupAlgebra(R, W, category=None):
         category = W.category()
     return SymmetricGroupAlgebra_n(R, W, category.Algebras(R))
 
+
 class SymmetricGroupAlgebra_n(GroupAlgebra_class):
 
     def __init__(self, R, W, category):
@@ -1444,6 +1446,7 @@ def semi_rsw_element(self, k):
         n = self.n
         if n < k:
             return self.zero()
+
         def complement(xs):
             res = list(range(1, n + 1))
             for x in xs:
@@ -1452,7 +1455,7 @@ def complement(xs):
         P = Permutations(n)
         I = self._indices
         return self.sum_of_monomials([I(P(complement(q) + list(q)))
-                                      for q in itertools.permutations(range(1, n+1), n-k)])
+                                      for q in itertools.permutations(range(1, n+1), int(n - k))])
 
     def binary_unshuffle_sum(self, k):
         r"""
@@ -1536,14 +1539,15 @@ def binary_unshuffle_sum(self, k):
         n = self.n
         if n < k:
             return self.zero()
+
         def complement(xs):
             res = list(range(1, n + 1))
             for x in xs:
                 res.remove(x)
             return res
         P = Permutations(n)
         return self.sum_of_monomials([self._indices(P(list(q) + complement(q)))
-                                      for q in itertools.combinations(range(1, n+1), k)])
+                                      for q in itertools.combinations(range(1, n+1), int(k))])
 
     def jucys_murphy(self, k):
         r"""
@@ -1603,8 +1607,6 @@ def jucys_murphy(self, k):
             res += self.monomial(self._indices(p))
         return res
 
-
-
     def seminormal_basis(self, mult='l2r'):
         r"""
         Return a list of the seminormal basis elements of ``self``.
@@ -1762,7 +1764,6 @@ def seminormal_basis(self, mult='l2r'):
                     basis.append(self.epsilon_ik(t1, t2, mult=mult))
         return basis
 
-
     def dft(self, form="seminormal", mult='l2r'):
         """
         Return the discrete Fourier transform for ``self``.
@@ -2139,6 +2140,7 @@ def kappa(alpha):
         n = sum(alpha)
     return factorial(n) / StandardTableaux(alpha).cardinality()
 
+
 def a(tableau, star=0, base_ring=QQ):
     r"""
     The row projection operator corresponding to the Young tableau
@@ -2205,6 +2207,7 @@ def a(tableau, star=0, base_ring=QQ):
     rd = dict((P(h), one) for h in rs)
     return sgalg._from_dict(rd)
 
+
 def b(tableau, star=0, base_ring=QQ):
     r"""
     The column projection operator corresponding to the Young tableau
@@ -2467,6 +2470,7 @@ def e_ik(itab, ktab, star=0):
     e_ik_cache[(it,kt)] = res
     return res
 
+
 def seminormal_test(n):
     """
     Run a variety of tests to verify that the construction of the
@@ -2595,6 +2599,7 @@ def HeckeAlgebraSymmetricGroupT(R, n, q=None):
 
     return HeckeAlgebraSymmetricGroup_t(R, n, q)
 
+
 class HeckeAlgebraSymmetricGroup_generic(CombinatorialAlgebra):
     def __init__(self, R, n, q=None):
         """
@@ -2640,7 +2645,6 @@ def q(self):
         """
         return self._q
 
-
     def _coerce_start(self, x):
         """
         EXAMPLES::
@@ -2659,6 +2663,7 @@ def _coerce_start(self, x):
                                                list(range(len(x)+1, self.n+1))))
         raise TypeError
 
+
 class HeckeAlgebraSymmetricGroup_t(HeckeAlgebraSymmetricGroup_generic):
 
     def __init__(self, R, n, q=None):
@@ -2710,7 +2715,6 @@ def t_action_on_basis(self, perm, i):
             z_elt = {perm_i:q, perm:q-1}
             return self._from_dict(z_elt)
 
-
     def t_action(self, a, i):
         r"""
         Return the product `T_i \cdot a`.
@@ -2727,7 +2731,6 @@ def t_action(self, a, i):
         t_i = lambda x: self.t_action_on_basis(x, i)
         return self._apply_module_endomorphism(a, t_i)
 
-
     def _multiply_basis(self, perm1, perm2):
         """
         EXAMPLES::