def test_coset_enumeration(self):
g1 = Permutation.read_cycle_form([[1,2,3,4]], 4)
g2 = Permutation.read_cycle_form([[1,2]], 4)
h1 = Permutation.read_cycle_form([[1,2,3]], 4)
h2 = Permutation.read_cycle_form([[1,2]], 4)
G = PermGroup([g1, g2])
H = PermGroup([h1, h2])
cosets = G._left_cosets(H)
total = 0
elements = []
for coset in cosets:
temp_eles = coset._list_elements()
elements += temp_eles
self.assertEqual(len(temp_eles),len(H))
total += len(temp_eles)
self.assertEqual(len(G), total)
self.assertEqual(sorted(G._list_elements()), sorted(elements))
cosets = G._right_cosets(H)
total = 0
elements = []
for coset in cosets:
temp_eles = coset._list_elements()
elements += temp_eles
self.assertEqual(len(temp_eles),len(H))
total += len(temp_eles)
self.assertEqual(len(G), total)
self.assertEqual(sorted(G._list_elements()), sorted(elements))
from group import PermGroup
from permutation import Permutation
_base_size = 6
cf = lambda x : Permutation.read_cycle_form(x, _base_size)
a= cf([[1,2,3,4]])
b= cf([[1,2]])
c= cf([[1,2,3]])
s4 = PermGroup([a,b])
s3 = PermGroup([b,c])
for coset in s4._right_cosets(s3):
print(coset._list_elements())
for coset in s4._left_cosets(s3):
print(coset._list_elements())
cf = Permutation.read_cycle_form
a = cf([[1, 2, 3,4,5]],5)
b = cf([[1,2,3]], 5)
G=PermGroup([a,b])
print(len(G))