def test_coset_enumeration(self):
g1 = Permutation.read_cycle_form([[1,2,3,4]], 4)
g2 = Permutation.read_cycle_form([[1,2]], 4)
h1 = Permutation.read_cycle_form([[1,2,3]], 4)
h2 = Permutation.read_cycle_form([[1,2]], 4)
G = PermGroup([g1, g2])
H = PermGroup([h1, h2])
cosets = G._left_cosets(H)
total = 0
elements = []
for coset in cosets:
temp_eles = coset._list_elements()
elements += temp_eles
self.assertEqual(len(temp_eles),len(H))
total += len(temp_eles)
self.assertEqual(len(G), total)
self.assertEqual(sorted(G._list_elements()), sorted(elements))
cosets = G._right_cosets(H)
total = 0
elements = []
for coset in cosets:
temp_eles = coset._list_elements()
elements += temp_eles
self.assertEqual(len(temp_eles),len(H))
total += len(temp_eles)
self.assertEqual(len(G), total)
self.assertEqual(sorted(G._list_elements()), sorted(elements))
def test_len(self):
s1 = Permutation.read_cycle_form([[1,2,3,4]], 4)
s2 = Permutation.read_cycle_form([[1,2]], 4)
G = PermGroup([s1, s2])
self.assertEqual(len(G), len(G._list_elements()))
self.assertEqual(len(G), 24)
self.assertTrue(Permutation.read_cycle_form([[3,4]], 4) in G._list_elements())
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_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 = RefinementUnion([fam_part_stab, fam_subgroup])
prop = CosetPropertyUnion([prop_part_stab, prop_subgroup])
con = PartitionStackConstraint()
mods = ModifierUnion([fam, prop, con])
ls = LeonSearch(mods, size)
gens = ls.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.property_check(ele):
found.append(ele)
self.assertEqual(len(PermGroup(gens)), len(found))
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_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 = RefinementUnion([fam_part_stab])
prop = CosetPropertyUnion([prop_part_stab])
con = PartitionStackConstraint()
mods = ModifierUnion([fam, prop, con])
ls = LeonSearch(mods, size)
gens = ls.subgroup()
found = []
s6 = PermGroup([cf([[1,2]],6),cf([[1,2,3,4,5,6]],6)])
for ele in s6._list_elements():
if prop.property_check(ele):
found.append(ele)
self.assertEqual(sorted(PermGroup(gens)._list_elements()), sorted(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 = RefinementUnion([fam_subgroup])
prop = CosetPropertyUnion([prop_subgroup])
con = PartitionStackConstraint()
mods = ModifierUnion([fam, prop, con])
ls = LeonSearch(mods, 5)
gens = ls.subgroup()
found = []
s5 = PermGroup([cf([[1,2]],5),cf([[1,2,3,4,5]],5)])
for ele in s5._list_elements():
if prop.property_check(ele):
found.append(ele)
self.assertEqual(sorted(PermGroup(gens)._list_elements()), sorted(found))
from permutation import Permutation
from group import PermGroup as Group
from coset_property import permutation_commuter
cf =Permutation.read_cycle_form
a = cf([[1, 2]],4)
check = permutation_commuter(a)
b = cf([[1,2,3,4]], 4)
c = cf([[3, 4]], 4)
d = cf([[2, 3]], 4)
e = cf([[3, 4]], 4)
G = Group([a,b])
G1 = Group([c,d])
G2 = Group([e])
identity = cf([],4)
sub = Group([identity])
for g in G._list_elements():
d = sub * g * sub
p_flag = check(g)
d_flag = d.mid_minimal()
if g != identity and p_flag and d_flag:
sub = Group([t for t in sub.generators + [g] if t != identity])
print("{}\nprop: {}\nmin: {} sub: {}\nd: {}\n".format(g, p_flag, d_flag, sub.generators, d._list_elements()))
Dcosets = [(G2*g*G1, g) for g in G._list_elements()]
for d, g in sorted(Dcosets,key = lambda x: x[0]._list_elements()):
eles = d._list_elements()
#print("{} ({}) {}:\n{}\n".format(g,len(eles),d.mid_minimal(),eles))
a = cf([[1,2],[3,4]],4)
b = cf([[1,2,3]],4)
print(len(Group([a,b])))