def test_read_partitions(self):
a = Partition([[1], [2], [3], [4], [5]])
b = Partition([[2], [3], [4], [5], [1]])
c = Partition([[2], [1], [4], [3], [5]])
perm1 = Permutation([2, 3, 4, 5, 1])
perm1alt = Permutation.read_partitions(a, b)
perm2 = Permutation([2, 1, 4, 3, 5])
perm2alt = Permutation.read_partitions(a, c)
perm3 = Permutation([5, 2, 1, 4, 3])
perm3alt = Permutation.read_partitions(b, c)
self.assertEqual(perm1, perm1alt)
self.assertEqual(perm2, perm2alt)
self.assertEqual(perm3, perm3alt)
def subgroup(self):
#Needs to be done in this order.
self.initialise_partition_stacks()
self.initialise_r_base()
self.initialise_search_tree()
gens = []
while self._cur_height > -1:
#alt_1 rule out.
backtrack_index = self.tree_modifiers.exclude_backtrack_index(self.left, self.right, self._cur_position, self._cur_height)
if backtrack_index is not None:
self.backtrack(backtrack_index)
#alt_2 discrete check.
elif self.right.discrete():
perm = Permutation.read_partitions(self.left[self._cur_height], self.right[self._cur_height])
if not perm.trivial() and self.tree_modifiers.property_check(perm):
gens.append(perm)
backtrack_index = self.tree_modifiers.leaf_pass_backtrack_index(self.left,self.right,self._cur_position)
else:
backtrack_index = self.tree_modifiers.leaf_fail_backtrack_index(self.left,self.right,self._cur_position)
self.backtrack(backtrack_index)
#alt_3 function to extend.
elif self._r_base[self._cur_height] is not None:
func = self._r_base[self._cur_height]
func(self.right)
self._cur_height += 1
#alt_4 special level.
else:
self._extend_right()
return gens
def find_partition_backtrack_coset(self):
#Assume the refinement families are LR-symmetric.
r_base = self._r_base()
count = 0
while self._cur_height > -1:
count += 1
#a = self._cur_position
#b = self.right[self._cur_height]
#c = self.left[self._cur_height]
#if self.size == 13:
#print("\n{}:{}\n{} -> {}".format(self._cur_height,a,c,b))
#Alternatice 1: premature rule out.
if self.alt1():
#print("alt_1")
self.backtrack(self._cur_height - 1)
#Alternative 2: discrete check.
elif self.right.discrete():
#print("alt_2")
perm = Permutation.read_partitions(self.left[self._cur_height], self.right[self._cur_height])
if self.group_property.check(perm):
return perm
#self.backtrack()
self.backtrack(self._cur_position.min_changed_index())
#Alternative 3: not a special level
elif r_base[self._cur_height] is not None:
#print("alt_3")
r_base[self._cur_height](None, self.right)
self._cur_height += 1
#Alternative 4: is a special level
else:
#print("alt_4")
self.extend_right()
print(count)
return generators
def find_partition_backtrack_subgroup(self):
#Assume the refinement families are symmetric.
generators = []
self.functions = self.preprocess()
self.extension_indices = [0] * len(self.functions)
while self.function_index > 0:
#Alternative 3-4
self.extend_right()
#Alternatice 1: premature rule out.
if self.alt1():
self.backtrack()
#Alternative 2: discrete check.
elif self.right.discrete():
perm = Permutation.read_partitions(left[func_index], right[func_index])
if not perm.trivial() and self.prop_check(perm):
generators.append(perm)
self.backtrack()
return generators
def find_partition_backtrack_subgroup(self):
#Assume the refinement families are symmetric.
generators = []
r_base = self._r_base()
count = 0
leaf_count = 0
if self.printing:
print("-----------------------------------")
print("Traversing tree:")
while self._cur_height > -1:
count += 1
if self.printing:
a = self._cur_position
b = self.right[self._cur_height]
c = self.left[self._cur_height]
print("\n{}: {}\n{} -> {}".format(self._cur_height,a,c,b))
#Alternatice 1: premature rule out.
if self.alt1():
if self.printing:
print("Alternative 1: partition violation")
#print("alt_1")
self.backtrack(self._cur_height - 1)
#Alternative 2: discrete check.
elif self.right.discrete():
leaf_count += 1
#print("alt_2")
perm = Permutation.read_partitions(self.left[self._cur_height], self.right[self._cur_height])
if self.double_coset_check and self.printing:
G=PermGroup(generators)
Dco = G*perm*G
perm_key = ordering.ordering_to_perm_key(self.left.fix())
if Dco.mid_minimal(key = perm_key):
print("Actually minimal in own double coset: {}".format(Dco._list_elements(Perm_key)))
added = False
if not perm.trivial() and self.group_property.check(perm):
generators.append(perm)
added = True
#self.backtrack()
if self.printing:
print("Alternative 2 found permutation: {} ({})".format(perm, added))
if self.multi_backtrack and added:
self.backtrack(self._cur_position.min_changed_index())
else:
self.backtrack()
#Alternative 3: not a special level
elif r_base[self._cur_height] is not None:
#print("alt_3")
r_base[self._cur_height](None, self.right)
if self.printing:
print("Alternative 3 applying function: {}".format(r_base[self._cur_height]._info))
self._cur_height += 1
#Alternative 4: is a special level
else:
if self.printing:
print("Alternative 4 special level")
#print("alt_4")
self.extend_right()
if self.printing:
print("\nFinished tree traversal.")
print("Visited {} vertices ({} of which were terminal).".format(count, leaf_count))
return generators
