62 lines
2.0 KiB
Python
62 lines
2.0 KiB
Python
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from sympy.combinatorics.perm_groups import PermutationGroup
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from sympy.combinatorics.permutations import Permutation
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from sympy.utilities.iterables import uniq
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_af_new = Permutation._af_new
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def DirectProduct(*groups):
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"""
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Returns the direct product of several groups as a permutation group.
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Explanation
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===========
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This is implemented much like the __mul__ procedure for taking the direct
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product of two permutation groups, but the idea of shifting the
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generators is realized in the case of an arbitrary number of groups.
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A call to DirectProduct(G1, G2, ..., Gn) is generally expected to be faster
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than a call to G1*G2*...*Gn (and thus the need for this algorithm).
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Examples
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========
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>>> from sympy.combinatorics.group_constructs import DirectProduct
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>>> from sympy.combinatorics.named_groups import CyclicGroup
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>>> C = CyclicGroup(4)
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>>> G = DirectProduct(C, C, C)
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>>> G.order()
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64
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See Also
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========
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sympy.combinatorics.perm_groups.PermutationGroup.__mul__
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"""
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degrees = []
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gens_count = []
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total_degree = 0
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total_gens = 0
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for group in groups:
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current_deg = group.degree
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current_num_gens = len(group.generators)
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degrees.append(current_deg)
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total_degree += current_deg
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gens_count.append(current_num_gens)
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total_gens += current_num_gens
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array_gens = []
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for i in range(total_gens):
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array_gens.append(list(range(total_degree)))
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current_gen = 0
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current_deg = 0
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for i in range(len(gens_count)):
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for j in range(current_gen, current_gen + gens_count[i]):
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gen = ((groups[i].generators)[j - current_gen]).array_form
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array_gens[j][current_deg:current_deg + degrees[i]] = \
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[x + current_deg for x in gen]
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current_gen += gens_count[i]
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current_deg += degrees[i]
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perm_gens = list(uniq([_af_new(list(a)) for a in array_gens]))
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return PermutationGroup(perm_gens, dups=False)
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