def test_rotate():
A = [0, 1, 2, 3, 4]
assert rotate_left(A, 2) == [2, 3, 4, 0, 1]
assert rotate_right(A, 1) == [4, 0, 1, 2, 3]
A = []
B = rotate_right(A, 1)
assert B == []
B.append(1)
assert A == []
B = rotate_left(A, 1)
assert B == []
B.append(1)
assert A == []
def test_rotate():
A = [0, 1, 2, 3, 4]
assert rotate_left(A, 2) == [2, 3, 4, 0, 1]
assert rotate_right(A, 1) == [4, 0, 1, 2, 3]
A = []
B = rotate_right(A, 1)
assert B == []
B.append(1)
assert A == []
B = rotate_left(A, 1)
assert B == []
B.append(1)
assert A == []
def cyclic(n):
"""
Generates the cyclic group of order n, Cn.
Examples
========
>>> from diofant.combinatorics.permutations import Permutation
>>> Permutation.print_cyclic = True
>>> from diofant.combinatorics.generators import cyclic
>>> list(cyclic(5))
[Permutation(4), Permutation(0, 1, 2, 3, 4), Permutation(0, 2, 4, 1, 3),
Permutation(0, 3, 1, 4, 2), Permutation(0, 4, 3, 2, 1)]
See Also
========
dihedral
"""
gen = list(range(n))
for i in range(n):
yield Permutation(gen)
gen = rotate_left(gen, 1)
def dihedral(n):
"""
Generates the dihedral group of order 2n, Dn.
The result is given as a subgroup of Sn, except for the special cases n=1
(the group S2) and n=2 (the Klein 4-group) where that's not possible
and embeddings in S2 and S4 respectively are given.
Examples
========
>>> from diofant.combinatorics.permutations import Permutation
>>> Permutation.print_cyclic = True
>>> from diofant.combinatorics.generators import dihedral
>>> list(dihedral(3))
[Permutation(2), Permutation(0, 2), Permutation(0, 1, 2),
Permutation(1, 2), Permutation(0, 2, 1), Permutation(2)(0, 1)]
See Also
========
cyclic
"""
if n == 1:
yield Permutation([0, 1])
yield Permutation([1, 0])
elif n == 2:
yield Permutation([0, 1, 2, 3])
yield Permutation([1, 0, 3, 2])
yield Permutation([2, 3, 0, 1])
yield Permutation([3, 2, 1, 0])
else:
gen = list(range(n))
for i in range(n):
yield Permutation(gen)
yield Permutation(gen[::-1])
gen = rotate_left(gen, 1)
