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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)
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