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_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)
