def AbelianGroup(*cyclic_orders):
"""
Returns the direct product of cyclic groups with the given orders.
According to the structure theorem for finite abelian groups ([1]),
every finite abelian group can be written as the direct product of finitely
many cyclic groups.
[1] http://groupprops.subwiki.org/wiki/Structure_theorem_for_finitely
_generated_abelian_groups
Examples
========
>>> from sympy.combinatorics.named_groups import AbelianGroup
>>> AbelianGroup(3,4)
PermutationGroup([Permutation([1, 2, 0, 3, 4, 5, 6]),\
Permutation([0, 1, 2, 4, 5, 6, 3])])
See Also
========
DirectProduct
"""
groups = []
degree = 0
order = 1
for size in cyclic_orders:
degree += size
order *= size
groups.append(CyclicGroup(size))
G = DirectProduct(*groups)
G._is_abelian = True
G._degree = degree
G._order = order
return G
def AbelianGroup(*cyclic_orders):
"""
Returns the direct product of cyclic groups with the given orders.
According to the structure theorem for finite abelian groups ([1]),
every finite abelian group can be written as the direct product of finitely
many cyclic groups.
[1] http://groupprops.subwiki.org/wiki/Structure_theorem_for_finitely
_generated_abelian_groups
Examples
========
>>> from sympy.combinatorics.named_groups import AbelianGroup
>>> AbelianGroup(3,4)
PermutationGroup([Permutation([1, 2, 0, 3, 4, 5, 6]),\
Permutation([0, 1, 2, 4, 5, 6, 3])])
See Also
========
DirectProduct
"""
groups = []
degree = 0
order = 1
for size in cyclic_orders:
degree += size
order *= size
groups.append(CyclicGroup(size))
G = DirectProduct(*groups)
G._is_abelian = True
G._degree = degree
G._order = order
return G
def test_direct_product_n():
C = CyclicGroup(4)
D = DihedralGroup(4)
G = DirectProduct(C, C, C)
assert G.order() == 64
assert G.degree == 12
assert len(G.orbits()) == 3
assert G.is_abelian == True
H = DirectProduct(D, C)
assert H.order() == 32
assert H.is_abelian == False