def test_partition_backtrack_subgroup_leon_paper(self):
cf = Permutation.read_cycle_form
a = cf([[2,3],[4,6],[5,8],[9,11]], 13)
b = cf([[1,2,4,7,9,3,5,6,8,10,11,12,13]], 13)
G = PermGroup([a,b])
fam_subgroup = SubgroupFamily(G)
prop_subgroup = SubgroupProperty(G)
stab = Partition([[1,3,5,7,9,11],[2,4,6,8,10,12,13]])
fam_part_stab = PartitionStabaliserFamily(stab)
prop_part_stab = PartitionStabaliserProperty(stab)
size = 13
fam = Refinement([fam_subgroup, fam_part_stab])
prop = CosetProperty([prop_subgroup, prop_part_stab])
pbw = PBW(prop, fam, size)
gens = pbw.find_partition_backtrack_subgroup()
cand_G = PermGroup(gens)
leon_gens = []
leon_gens.append(cf([[2,12],[4,10],[5,7],[6,8]],13))
leon_gens.append(cf([[2,8],[3,5],[4,6],[10,12]],13))
leon_gens.append(cf([[1,9],[2,4],[6,8],[10,12]],13))
leon_G = PermGroup(leon_gens)
third_source = []
for ele in G._list_elements():
if prop.check(ele):
third_source.append(ele)
self.assertEqual(cand_G.order(), leon_G.order())
for perm in leon_gens:
self.assertTrue(perm in G)
self.assertTrue(perm in cand_G)
def test_order(self):
cf = lambda x : Permutation.read_cycle_form(x,6)
g1 = cf([[1,4,5,2,3]])
g2 = cf([[1,2],[3,4]])
g3 = cf([[1,2],[6,5]])
G = PermGroup([g1,g2,g3])
self.assertEqual(G.order(), 360)
