def test_group_size(self):
cf = Permutation.read_cycle_form
a = cf([[1, 2, 3,4,5]],5)
b = cf([[1,2,3]], 5)
e = cf([],5)
base, _, _, graphs = schreier_sims_algorithm_fixed_base([a,b],[1,2,3,4,5], e)
self.assertEqual(group_size(graphs),60)
def test_memebership_index(self):
cf = Permutation.read_cycle_form
a = cf([[1, 2, 3,4,5]],5)
b = cf([[1,2,3]], 5)
c = cf([[1,2]], 5)
e = cf([],5)
ordering = [3,5,2,1,4]
base, _, _, graphs = schreier_sims_algorithm_fixed_base([a,b], ordering, e)
S5_base, _, _, S5_graphs = schreier_sims_algorithm_fixed_base([a,c], ordering, e)
real_group = []
S5_group = []
ele_key = ordering_to_key(ordering)
perm_key = ordering_to_perm_key(ordering)
for index in range(group_size(S5_graphs)):
S5_group.append(element_at_index(S5_base, S5_graphs, index, e, key=ele_key))
self.assertEquals(len(S5_group), 120)
self.assertEquals(S5_group, sorted(S5_group, key = perm_key))
for index in range(group_size(graphs)):
real_group.append(element_at_index(base, graphs, index, e, key=ele_key))
self.assertEquals(len(real_group), 60)
self.assertEquals(real_group, sorted(real_group, key = perm_key))
for ele in S5_group:
cand_index = membership_index(ele, graphs, base, e, key = ele_key)
if cand_index > -1:
#print("{}: {} {}?".format(cand_index, ele, real_group[cand_index]))
self.assertTrue(ele in real_group)
self.assertEquals(real_group[cand_index], ele)
else:
self.assertFalse(ele in real_group)
def test_element_at_index(self):
cf = Permutation.read_cycle_form
a = cf([[1, 2, 3,4,5]],5)
b = cf([[1,2,3]], 5)
e = cf([],5)
ordering = [3,5,2,1,4]
base, _, _, graphs = schreier_sims_algorithm_fixed_base([a,b], ordering, e)
full_group = []
ele_key = ordering_to_key(ordering)
perm_key = ordering_to_perm_key(ordering)
for index in range(group_size(graphs)):
full_group.append(element_at_index(base, graphs, index, e, key=ele_key))
ordered_group = sorted(full_group, key = perm_key)
#for x,y in zip(full_group, ordered_group):
#print("{!s:<20} {!s:<20}".format(x,y))
self.assertEqual(full_group, ordered_group)
def order(self):
return schreier_sims_tools.group_size(self.schreier_graphs)