def leon_rbase6():
from permutation import Permutation
from refinement import SubgroupFamily, PartitionStabaliserFamily, Refinement
from partition import Partition
from group import PermGroup
from leon_search import PartitionBacktrackWorkhorse as PBW
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)
fam_subgroup = SubgroupFamily(PermGroup([a, b]))
stab = Partition([[1, 3, 5, 7, 9, 11], [2, 4, 6, 8, 10, 12, 13]])
fam_part_stab = PartitionStabaliserFamily(stab)
size = 13
print("Refinements: partition stabaliser refinement and subgroup refinement")
print(
"Desired property: partition stabaliser of [[1,3,5,7,9,11],[2,4,6,8,10,12,13]] and subgroup of <[[2,3],[4,6],[5,8],[9,11]], [[1,2,4,7,9,3,5,6,8,10,11,12,13]]>"
)
print("Heuristics: multi-backtrack")
print("Search space: Sym(13)")
fam = Refinement([fam_subgroup, fam_part_stab])
pbw = PBW(None, fam, size)
pbw.printing = True
r_base = pbw._r_base()
lookup = pbw._special_lookup
special_levels = sorted(list(lookup.keys()))
def leon_trivial2():
from permutation import Permutation
from refinement import SubgroupFamily, PartitionStabaliserFamily, Refinement
from partition import Partition
from group import PermGroup
from leon_search import PartitionBacktrackWorkhorse as PBW
from coset_property import CosetProperty, SubgroupProperty, PartitionStabaliserProperty
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, 2], [3, 4]])
fam_part_stab = PartitionStabaliserFamily(stab)
prop_part_stab = PartitionStabaliserProperty(stab)
size = 4
fam = Refinement([])
prop = CosetProperty([prop_part_stab])
pbw = PBW(prop, fam, size)
pbw.printing = True
pbw.multi_backtrack = True
print("Refinements: None")
print("Desired property: partition stabaliser of [[1,2],[3,4]]")
print("Heuristics: multi-backtrack")
print("Search space: Sym(4)")
gens = pbw.find_partition_backtrack_subgroup()
print("Generators found:")
for gen in gens:
print(gen)
def test_r_base(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)
fam_subgroup = SubgroupFamily(PermGroup([a,b]))
stab = Partition([[1,3,5,7,9,11],[2,4,6,8,10,12,13]])
fam_part_stab = PartitionStabaliserFamily(stab)
size = 13
fam = Refinement([fam_subgroup, fam_part_stab])
pbw = PBW(None, fam, size)
r_base = pbw._r_base()
lookup = pbw._special_lookup
special_levels = sorted(list(lookup.keys()))
special_cells = [lookup[level][0] for level in special_levels]
special_vals = [lookup[level][1] for level in special_levels]
self.assertTrue(pbw.left.discrete())
self.assertEqual(special_levels, [1,2,4])
self.assertEqual(special_cells, [1,1,1])
self.assertEqual(special_vals, [1,3,5])
f = pbw.left.fix()
b = fam_subgroup._group.base
self.assertEqual(f[:len(b)], b)
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_tree_traversal(self):
fam = Refinement([IdentityFamily()])
prop = CosetProperty([IdentityProperty()])
pbw = PBW(prop, fam, 4)
pbw.printing = True
gens = pbw.find_partition_backtrack_subgroup()
self.assertEqual(PermGroup(gens).order(), 24)
print(gens)
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 leon_trivial55():
from permutation import Permutation
from refinement import SubgroupFamily, PartitionStabaliserFamily, Refinement
from partition import Partition
from group import PermGroup
from leon_search import PartitionBacktrackWorkhorse as PBW
from coset_property import CosetProperty, SubgroupProperty, PartitionStabaliserProperty
cf = Permutation.read_cycle_form
a = cf([[1, 2, 3]], 4)
b = cf([[2, 3, 4]], 4)
G = PermGroup([a, b])
fam_subgroup = SubgroupFamily(G)
prop_subgroup = SubgroupProperty(G)
stab = Partition([[1, 2], [3, 4]])
fam_part_stab = PartitionStabaliserFamily(stab)
prop_part_stab = PartitionStabaliserProperty(stab)
size = 4
fam = Refinement([fam_subgroup, fam_part_stab])
prop = CosetProperty([prop_subgroup, prop_part_stab]) # [prop_part_stab])
pbw = PBW(prop, fam, size)
pbw.printing = True
pbw.multi_backtrack = True
pbw.double_coset_check = False
print("Refinements: partition stabaliser refinement and subgroup refinement")
print("Desired property: partition stabaliser of [[1,2],[3,4]] and subgroup of alt(3)")
print("Heuristics: multi-backtrack")
print("Search space: Sym(4)")
gens = pbw.find_partition_backtrack_subgroup()
print("Generators found:")
for gen in gens:
print(gen)
