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| from sympy.combinatorics.perm_groups import PermutationGroup | |
| from sympy.combinatorics.permutations import Permutation | |
| from sympy.utilities.iterables import uniq | |
| _af_new = Permutation._af_new | |
| def 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__ | |
| """ | |
| 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 range(len(gens_count)): | |
| for j in range(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) | |