/

# Source code for sympy.combinatorics.group_constructs

from __future__ import print_function, division

from sympy.combinatorics.perm_groups import PermutationGroup
from sympy.combinatorics.permutations import Permutation
from sympy.utilities.iterables import uniq
from sympy.core.compatibility import xrange

_af_new = Permutation._af_new

[docs]def DirectProduct(*groups):
"""
Returns the direct product of several groups as a permutation group.

This is implemented much like the __mul__ procedure for taking the direct
product of two permutation groups, but the idea of shifting the
generators is realized in the case of an arbitrary number of groups.
A call to DirectProduct(G1, G2, ..., Gn) is generally expected to be faster
than a call to G1*G2*...*Gn (and thus the need for this algorithm).

Examples
========

>>> from sympy.combinatorics.group_constructs import DirectProduct
>>> from sympy.combinatorics.named_groups import CyclicGroup
>>> C = CyclicGroup(4)
>>> G = DirectProduct(C,C,C)
>>> G.order()
64

See Also
========
__mul__

"""
degrees = []
gens_count = []
total_degree = 0
total_gens = 0
for group in groups:
current_deg = group.degree
current_num_gens = len(group.generators)
degrees.append(current_deg)
total_degree += current_deg
gens_count.append(current_num_gens)
total_gens += current_num_gens
array_gens = []
for i in range(total_gens):
array_gens.append(list(range(total_degree)))
current_gen = 0
current_deg = 0
for i in xrange(len(gens_count)):
for j in xrange(current_gen, current_gen + gens_count[i]):
gen = ((groups[i].generators)[j - current_gen]).array_form
array_gens[j][current_deg:current_deg + degrees[i]] = \
[ x + current_deg for x in gen]
current_gen += gens_count[i]
current_deg += degrees[i]
perm_gens = list(uniq([_af_new(list(a)) for a in array_gens]))
return PermutationGroup(perm_gens, dups=False)