Group constructors

sympy.combinatorics.group_constructs.DirectProduct(*groups)

Returns the direct product of several groups as a permutation group.

Explanation

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

sympy.combinatorics.perm_groups.PermutationGroup.__mul__