Merge branch 'simple-species' into lazy-species

src/sage/groups/perm_gps/permgroup.py

@@ -2734,6 +2734,25 @@ def conjugate(self, g):
  raise TypeError("{0} does not convert to a permutation group element".format(g))
  return PermutationGroup(gap_group=libgap.ConjugateGroup(self, g))
 
+ def are_conjugate(self, H1, H2):
+ r"""
+ Return whether ``H1`` and ``H2`` are conjugate subgroups in ``G``.
+
+ EXAMPLES::
+
+ sage: G = SymmetricGroup(3)
+ sage: H1 = PermutationGroup([(1,2)])
+ sage: H2 = PermutationGroup([(2,3)])
+ sage: G.are_conjugate(H1, H2)
+ True
+ sage: G = SymmetricGroup(4)
+ sage: H1 = PermutationGroup([[(1,3),(2,4)], [(1,2),(3,4)]])
+ sage: H2 = PermutationGroup([[(1,2)], [(1,2),(3,4)]])
+ sage: G.are_conjugate(H1, H2)
+ False
+ """
+ return libgap.IsConjugate(self, H1, H2).sage()
+
  def direct_product(self, other, maps=True):
  """
  Wraps GAP's ``DirectProduct``, ``Embedding``, and ``Projection``.

src/sage/rings/lazy_species.py

@@ -208,11 +208,11 @@ def generating_series(self):
  P._laurent_poly_ring._indices._indices.variable_names())
  if P._arity == 1:
  def coefficient(n):
- return sum(c / M._group.cardinality()
+ return sum(c / M.group_and_partition()[0].cardinality()
  for M, c in self[n].monomial_coefficients().items())
  else:
  def coefficient(n):
- return sum(c / M._group.cardinality()
+ return sum(c / M.group_and_partition()[0].cardinality()
  * P.base_ring().prod(v ** d for v, d in zip(L.gens(), M.grade()))
  for M, c in self[n].monomial_coefficients().items())
  return L(coefficient)
@@ -240,7 +240,7 @@ def cycle_index_series(self):
  if P._arity == 1:
  L = LazySymmetricFunctions(p)
  def coefficient(n):
- return sum(c * M._group.cycle_index()
+ return sum(c * M.group_and_partition()[0].cycle_index()
  for M, c in self[n].monomial_coefficients().items())
  else:
  raise NotImplementedError
@@ -353,7 +353,7 @@ def structures(self, *labels):
  if c < 0:
  raise NotImplementedError("only implemented for proper non-virtual species")
  types = [tuple(S(rep)._act_on_list_on_position(l))[::-1]
- for rep in libgap.RightTransversal(S, M._group)]
+ for rep in libgap.RightTransversal(S, M.group_and_partition()[0])]
  if c == 1:
  for s in types:
  yield s, M
@@ -537,14 +537,14 @@ def coefficient(n):
  return R.zero()
  args_flat = [[(M, c) for i in range(n+1) for M, c in g[i]]
  for g in args]
- weights = [[M._tc for i in range(n+1) for M, _ in g[i]]
+ weights = [[sum(M.grade()) for i in range(n+1) for M, _ in g[i]]
  for g in args]
  result = R.zero()
  for i in range(n // gv + 1):
  # compute homogeneous components
  lF = defaultdict(R)
  for M, c in self[i]:
- lF[M._mc] += R._from_dict({M: c})
+ lF[M.grade()] += R._from_dict({M: c})
  for mc, F in lF.items():
  for degrees in weighted_vector_compositions(mc, n, weights):
  multiplicities = [c for alpha, g_flat in zip(degrees, args_flat)