def RubikGroup(n):
"""Return a group of Rubik's cube generators.
>>> from sympy.combinatorics.named_groups import RubikGroup
>>> RubikGroup(2).is_group()
False
"""
from sympy.combinatorics.generators import rubik
assert n > 1
return PermutationGroup(rubik(n))
def RubikGroup(n):
"""Return a group of Rubik's cube generators.
>>> from sympy.combinatorics.named_groups import RubikGroup
>>> RubikGroup(2).is_group()
False
"""
from sympy.combinatorics.generators import rubik
assert n > 1
return PermutationGroup(rubik(n))
def RubikGroup(n):
"""Return a group of Rubik's cube generators.
>>> from sympy.combinatorics.named_groups import RubikGroup
>>> RubikGroup(2).is_group()
False
"""
from sympy.combinatorics.generators import rubik
if n <= 1:
raise ValueError("Invalid cube . n has to be greater than 1")
return PermutationGroup(rubik(n))
def RubikGroup(n):
"""Return a group of Rubik's cube generators.
>>> from sympy.combinatorics.named_groups import RubikGroup
>>> RubikGroup(2).is_group()
False
"""
from sympy.combinatorics.generators import rubik
if n <= 1:
raise ValueError("Invalid cube . n has to be greater than 1")
return PermutationGroup(rubik(n))
def test_generators():
assert list(cyclic(6)) == [
Permutation([0, 1, 2, 3, 4, 5]),
Permutation([1, 2, 3, 4, 5, 0]),
Permutation([2, 3, 4, 5, 0, 1]),
Permutation([3, 4, 5, 0, 1, 2]),
Permutation([4, 5, 0, 1, 2, 3]),
Permutation([5, 0, 1, 2, 3, 4])]
assert list(cyclic(10)) == [
Permutation([0, 1, 2, 3, 4, 5, 6, 7, 8, 9]),
Permutation([1, 2, 3, 4, 5, 6, 7, 8, 9, 0]),
Permutation([2, 3, 4, 5, 6, 7, 8, 9, 0, 1]),
Permutation([3, 4, 5, 6, 7, 8, 9, 0, 1, 2]),
Permutation([4, 5, 6, 7, 8, 9, 0, 1, 2, 3]),
Permutation([5, 6, 7, 8, 9, 0, 1, 2, 3, 4]),
Permutation([6, 7, 8, 9, 0, 1, 2, 3, 4, 5]),
Permutation([7, 8, 9, 0, 1, 2, 3, 4, 5, 6]),
Permutation([8, 9, 0, 1, 2, 3, 4, 5, 6, 7]),
Permutation([9, 0, 1, 2, 3, 4, 5, 6, 7, 8])]
assert list(alternating(4)) == [
Permutation([0, 1, 2, 3]),
Permutation([0, 2, 3, 1]),
Permutation([0, 3, 1, 2]),
Permutation([1, 0, 3, 2]),
Permutation([1, 2, 0, 3]),
Permutation([1, 3, 2, 0]),
Permutation([2, 0, 1, 3]),
Permutation([2, 1, 3, 0]),
Permutation([2, 3, 0, 1]),
Permutation([3, 0, 2, 1]),
Permutation([3, 1, 0, 2]),
Permutation([3, 2, 1, 0])]
assert list(symmetric(3)) == [
Permutation([0, 1, 2]),
Permutation([0, 2, 1]),
Permutation([1, 0, 2]),
Permutation([1, 2, 0]),
Permutation([2, 0, 1]),
Permutation([2, 1, 0])]
assert list(symmetric(4)) == [
Permutation([0, 1, 2, 3]),
Permutation([0, 1, 3, 2]),
Permutation([0, 2, 1, 3]),
Permutation([0, 2, 3, 1]),
Permutation([0, 3, 1, 2]),
Permutation([0, 3, 2, 1]),
Permutation([1, 0, 2, 3]),
Permutation([1, 0, 3, 2]),
Permutation([1, 2, 0, 3]),
Permutation([1, 2, 3, 0]),
Permutation([1, 3, 0, 2]),
Permutation([1, 3, 2, 0]),
Permutation([2, 0, 1, 3]),
Permutation([2, 0, 3, 1]),
Permutation([2, 1, 0, 3]),
Permutation([2, 1, 3, 0]),
Permutation([2, 3, 0, 1]),
Permutation([2, 3, 1, 0]),
Permutation([3, 0, 1, 2]),
Permutation([3, 0, 2, 1]),
Permutation([3, 1, 0, 2]),
Permutation([3, 1, 2, 0]),
Permutation([3, 2, 0, 1]),
Permutation([3, 2, 1, 0])]
assert list(dihedral(1)) == [
Permutation([0, 1]), Permutation([1, 0])]
assert list(dihedral(2)) == [
Permutation([0, 1, 2, 3]),
Permutation([1, 0, 3, 2]),
Permutation([2, 3, 0, 1]),
Permutation([3, 2, 1, 0])]
assert list(dihedral(3)) == [
Permutation([0, 1, 2]),
Permutation([2, 1, 0]),
Permutation([1, 2, 0]),
Permutation([0, 2, 1]),
Permutation([2, 0, 1]),
Permutation([1, 0, 2])]
assert list(dihedral(5)) == [
Permutation([0, 1, 2, 3, 4]),
Permutation([4, 3, 2, 1, 0]),
Permutation([1, 2, 3, 4, 0]),
Permutation([0, 4, 3, 2, 1]),
Permutation([2, 3, 4, 0, 1]),
Permutation([1, 0, 4, 3, 2]),
Permutation([3, 4, 0, 1, 2]),
Permutation([2, 1, 0, 4, 3]),
Permutation([4, 0, 1, 2, 3]),
Permutation([3, 2, 1, 0, 4])]
raises(ValueError, lambda: rubik(1))
def test_generators():
assert list(cyclic(6)) == [
Permutation([0, 1, 2, 3, 4, 5]),
Permutation([1, 2, 3, 4, 5, 0]),
Permutation([2, 3, 4, 5, 0, 1]),
Permutation([3, 4, 5, 0, 1, 2]),
Permutation([4, 5, 0, 1, 2, 3]),
Permutation([5, 0, 1, 2, 3, 4]),
]
assert list(cyclic(10)) == [
Permutation([0, 1, 2, 3, 4, 5, 6, 7, 8, 9]),
Permutation([1, 2, 3, 4, 5, 6, 7, 8, 9, 0]),
Permutation([2, 3, 4, 5, 6, 7, 8, 9, 0, 1]),
Permutation([3, 4, 5, 6, 7, 8, 9, 0, 1, 2]),
Permutation([4, 5, 6, 7, 8, 9, 0, 1, 2, 3]),
Permutation([5, 6, 7, 8, 9, 0, 1, 2, 3, 4]),
Permutation([6, 7, 8, 9, 0, 1, 2, 3, 4, 5]),
Permutation([7, 8, 9, 0, 1, 2, 3, 4, 5, 6]),
Permutation([8, 9, 0, 1, 2, 3, 4, 5, 6, 7]),
Permutation([9, 0, 1, 2, 3, 4, 5, 6, 7, 8]),
]
assert list(alternating(4)) == [
Permutation([0, 1, 2, 3]),
Permutation([0, 2, 3, 1]),
Permutation([0, 3, 1, 2]),
Permutation([1, 0, 3, 2]),
Permutation([1, 2, 0, 3]),
Permutation([1, 3, 2, 0]),
Permutation([2, 0, 1, 3]),
Permutation([2, 1, 3, 0]),
Permutation([2, 3, 0, 1]),
Permutation([3, 0, 2, 1]),
Permutation([3, 1, 0, 2]),
Permutation([3, 2, 1, 0]),
]
assert list(symmetric(3)) == [
Permutation([0, 1, 2]),
Permutation([0, 2, 1]),
Permutation([1, 0, 2]),
Permutation([1, 2, 0]),
Permutation([2, 0, 1]),
Permutation([2, 1, 0]),
]
assert list(symmetric(4)) == [
Permutation([0, 1, 2, 3]),
Permutation([0, 1, 3, 2]),
Permutation([0, 2, 1, 3]),
Permutation([0, 2, 3, 1]),
Permutation([0, 3, 1, 2]),
Permutation([0, 3, 2, 1]),
Permutation([1, 0, 2, 3]),
Permutation([1, 0, 3, 2]),
Permutation([1, 2, 0, 3]),
Permutation([1, 2, 3, 0]),
Permutation([1, 3, 0, 2]),
Permutation([1, 3, 2, 0]),
Permutation([2, 0, 1, 3]),
Permutation([2, 0, 3, 1]),
Permutation([2, 1, 0, 3]),
Permutation([2, 1, 3, 0]),
Permutation([2, 3, 0, 1]),
Permutation([2, 3, 1, 0]),
Permutation([3, 0, 1, 2]),
Permutation([3, 0, 2, 1]),
Permutation([3, 1, 0, 2]),
Permutation([3, 1, 2, 0]),
Permutation([3, 2, 0, 1]),
Permutation([3, 2, 1, 0]),
]
assert list(dihedral(1)) == [Permutation([0, 1]), Permutation([1, 0])]
assert list(dihedral(2)) == [
Permutation([0, 1, 2, 3]),
Permutation([1, 0, 3, 2]),
Permutation([2, 3, 0, 1]),
Permutation([3, 2, 1, 0]),
]
assert list(dihedral(3)) == [
Permutation([0, 1, 2]),
Permutation([2, 1, 0]),
Permutation([1, 2, 0]),
Permutation([0, 2, 1]),
Permutation([2, 0, 1]),
Permutation([1, 0, 2]),
]
assert list(dihedral(5)) == [
Permutation([0, 1, 2, 3, 4]),
Permutation([4, 3, 2, 1, 0]),
Permutation([1, 2, 3, 4, 0]),
Permutation([0, 4, 3, 2, 1]),
Permutation([2, 3, 4, 0, 1]),
Permutation([1, 0, 4, 3, 2]),
Permutation([3, 4, 0, 1, 2]),
Permutation([2, 1, 0, 4, 3]),
Permutation([4, 0, 1, 2, 3]),
Permutation([3, 2, 1, 0, 4]),
]
raises(ValueError, lambda: rubik(1))
