def test_partition_backtrack_subgroup_two_prop_subgroup_stab(self):
cf = Permutation.read_cycle_form
a = cf([[3,2,6]], 7)
b = cf([[3,2],[6,7]], 7)
G = PermGroup([a,b])
fam_subgroup = SubgroupFamily(G)
prop_subgroup = SubgroupProperty(G)
stab = Partition([[1,3,5,7],[2,4,6]])
fam_part_stab = PartitionStabaliserFamily(stab)
prop_part_stab = PartitionStabaliserProperty(stab)
size = 7
fam = Refinement([fam_part_stab, fam_subgroup])
prop = CosetProperty([prop_part_stab, prop_subgroup])
pbw = PBW(prop, fam, size)
gens = pbw.find_partition_backtrack_subgroup()
found = []
s7 = PermGroup([cf([[1,2]],7),cf([[1,2,3,4,5,6,7]],7)])
for ele in s7._list_elements():
if prop.check(ele):
found.append(ele)
self.assertEqual(len(PermGroup(gens)), len(found))
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_multi_coset_property(self):
cf = Permutation.read_cycle_form
a = cf([[1,2,3]],4)
b = cf([[1,2],[3,4]],4)
gens = [a,b]
G= PermGroup(gens)
prop1 = SubgroupProperty(G)
prop2 = PartitionStabaliserProperty(Partition([[2,3],[1,4]]))
co_prop = CosetProperty([prop1,prop2])
pos = cf([[2,3],[1,4]])
self.assertTrue(co_prop.check(pos))
def test_subgroup_property(self):
cf = Permutation.read_cycle_form
a = cf([[1,2,3]],4)
b = cf([[1,2],[3,4]],4)
gens = [a,b]
G= PermGroup(gens)
prop = CosetProperty([SubgroupProperty(G)])
pos = cf([[2,3,4]],4)
neg = cf([[3,4]],4)
self.assertTrue(prop.check(pos))
self.assertFalse(prop.check(neg))
def test_partition_backtrack_subgroup_one_prop_stab(self):
cf = Permutation.read_cycle_form
stab = Partition([[1,3,5],[2,4,6]])
fam_part_stab = PartitionStabaliserFamily(stab)
prop_part_stab = PartitionStabaliserProperty(stab)
size = 6
fam = Refinement([fam_part_stab])
prop = CosetProperty([prop_part_stab])
pbw = PBW(prop, fam, size)
gens = pbw.find_partition_backtrack_subgroup()
found = []
s6 = PermGroup([cf([[1,2]],6),cf([[1,2,3,4,5,6]],6)])
for ele in s6._list_elements():
if prop.check(ele):
found.append(ele)
self.assertEqual(len(PermGroup(gens)), len(found))
def test_partition_backtrack_subgroup_one_prop_subgroup(self):
cf = Permutation.read_cycle_form
a = cf([[1,2,3]], 5)
b = cf([[1,2],[3,4]], 5)
G = PermGroup([a,b])
fam_subgroup = SubgroupFamily(G)
prop_subgroup = SubgroupProperty(G)
fam = Refinement([fam_subgroup])
prop = CosetProperty([prop_subgroup])
pbw = PBW(prop, fam, 5)
gens = pbw.find_partition_backtrack_subgroup()
found = []
s5 = PermGroup([cf([[1,2]],5),cf([[1,2,3,4,5]],5)])
for ele in s5._list_elements():
if prop.check(ele):
found.append(ele)
self.assertEqual(len(PermGroup(gens)), len(found))
def test_permutation_commuter_property(self):
prop = CosetProperty([PermutationCommuterProperty(Permutation([2,1,3,4]))])
pos = Permutation.read_cycle_form([[3,4]],4)
neg = Permutation.read_cycle_form([[2,3]],4)
self.assertTrue(prop.check(pos))
self.assertFalse(prop.check(neg))
def test_partition_stabaliser_property(self):
prop = CosetProperty([PartitionStabaliserProperty(Partition([[1,2],[3,4],[5]]))])
pos = Permutation.read_cycle_form([[1,2]],5)
neg = Permutation.read_cycle_form([[1,2],[4,5]],5)
self.assertTrue(prop.check(pos))
self.assertFalse(prop.check(neg))
def test_coset_property_init(self):
prop = CosetProperty([IdentityProperty()])
self.assertTrue(prop.check(Permutation.read_cycle_form([[1,2,3,4]], 5)))
