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 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 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 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)
