from sympy.combinatorics.named_groups import AlternatingGroup, \
PermutationGroup, Permutation
# indexed from zero
H = PermutationGroup([Permutation(0), Permutation(0, 1, 2), Permutation(0, 2, 1)])
A4 = AlternatingGroup(4)
left_coset = []
right_coset = []
# for i in all permutations in A4
for i in A4.generate_schreier_sims():
# Compute the cosets
left = PermutationGroup([i*H[0], i*H[1], i*H[2]])
right = PermutationGroup([H[0]*i, H[1]*i, H[2]*i])
# check if we already have an equivalent coset
if left not in left_coset:
left_coset.append(left)
if right not in right_coset:
right_coset.append(right)
# print results
print('left cosets')
for i in left_coset:
print(i)
print('right cosets')
for i in right_coset:
print(i)
from sympy.combinatorics.named_groups import AlternatingGroup, \
PermutationGroup, Permutation
# indexed from zero
H = PermutationGroup(
[Permutation(0),
Permutation(0, 1, 2),
Permutation(0, 2, 1)])
A4 = AlternatingGroup(4)
left_coset = []
right_coset = []
# for i in all permutations in A4
for i in A4.generate_schreier_sims():
# Compute the cosets
left = PermutationGroup([i * H[0], i * H[1], i * H[2]])
right = PermutationGroup([H[0] * i, H[1] * i, H[2] * i])
# check if we already have an equivalent coset
if left not in left_coset:
left_coset.append(left)
if right not in right_coset:
right_coset.append(right)
# print results
print('left cosets')
for i in left_coset:
print(i)
print('right cosets')
