B [*@s|ddlmZmZddlmZddlmZddlmZej Z ddZ ddd Z d d Z dd dZ dddZddZddZd S))print_functiondivision)range)_distribute_gens_by_base) PermutationcCsdd|Ddd|DkS)aN Compare two lists of permutations as sets. This is used for testing purposes. Since the array form of a permutation is currently a list, Permutation is not hashable and cannot be put into a set. Examples ======== >>> from sympy.combinatorics.permutations import Permutation >>> from sympy.combinatorics.testutil import _cmp_perm_lists >>> a = Permutation([0, 2, 3, 4, 1]) >>> b = Permutation([1, 2, 0, 4, 3]) >>> c = Permutation([3, 4, 0, 1, 2]) >>> ls1 = [a, b, c] >>> ls2 = [b, c, a] >>> _cmp_perm_lists(ls1, ls2) True cSsh|] }t|qS)tuple).0arr;lib/python3.7/site-packages/sympy/combinatorics/testutil.py sz"_cmp_perm_lists..cSsh|] }t|qSr)r)r r rrr r !sr)firstsecondrrr _cmp_perm_lists s rFcsddlm}ddlmt|drt|jdd}dd|jDfd d }g}|sxF|D]}||r^|t |q^Wn x|D]}||r||qW|St|d rt ||||St|d rt |||g|SdS) Nr)PermutationGroup)_af_commutes_with generatorsT)afcSsg|] }|jqSr)Z _array_form)r xrrr ?sz+_naive_list_centralizer..cstfddDS)Nc3s|]}|VqdS)Nr)r gen)rrrr @sz<_naive_list_centralizer....)all)r)rgens)rr @sz)_naive_list_centralizer..getitem array_form) sympy.combinatorics.perm_groupsr sympy.combinatorics.permutationsrhasattrlistgenerate_diminorappendrZ_af_new_naive_list_centralizer)selfotherrrelementsZcommutes_with_gensZcentralizer_listelementr)rrr r#$s&       r#cCsrddlm}t||}|}xBtt|D]2}|||}||krLdS|||}q(W|dkrndSdS)a Verify the correctness of a base and strong generating set. This is a naive implementation using the definition of a base and a strong generating set relative to it. There are other procedures for verifying a base and strong generating set, but this one will serve for more robust testing. Examples ======== >>> from sympy.combinatorics.named_groups import AlternatingGroup >>> from sympy.combinatorics.testutil import _verify_bsgs >>> A = AlternatingGroup(4) >>> A.schreier_sims() >>> _verify_bsgs(A, A.base, A.strong_gens) True See Also ======== sympy.combinatorics.perm_groups.PermutationGroup.schreier_sims r)rFT)rrrrlenorderZ stabilizer)groupbaserrZstrong_gens_distrZcurrent_stabilizeri candidaterrr _verify_bsgsQs    r/NcCs:|dkr||}t|jdd}t||dd}t||S)a3 Verify the centralizer of a group/set/element inside another group. This is used for testing ``.centralizer()`` from ``sympy.combinatorics.perm_groups`` Examples ======== >>> from sympy.combinatorics.named_groups import (SymmetricGroup, ... AlternatingGroup) >>> from sympy.combinatorics.perm_groups import PermutationGroup >>> from sympy.combinatorics.permutations import Permutation >>> from sympy.combinatorics.testutil import _verify_centralizer >>> S = SymmetricGroup(5) >>> A = AlternatingGroup(5) >>> centr = PermutationGroup([Permutation([0, 1, 2, 3, 4])]) >>> _verify_centralizer(S, A, centr) True See Also ======== _naive_list_centralizer, sympy.combinatorics.perm_groups.PermutationGroup.centralizer, _cmp_perm_lists NT)r)Z centralizerr r!r#r)r+argZcentrZ centr_listZcentr_list_naiverrr _verify_centralizerws  r1c Csddlm}|dkr||}t}t|dr6|j}n t|drF|}nt|drV|g}x,|D] }x|D]}|||AqjWq`W|t|}| |S)Nr)rr __getitem__r) rrZnormal_closuresetrrr!addr Z is_subgroup) r+r0ZclosurerZ conjugatesZ subgr_gensZelrZ naive_closurerrr _verify_normal_closures       r5csddlm}ddlm}m}ddlmm}g}xW||\}}}||||d}t |t rd}|g}|g}nt |}g}x.t|D]"} | ||| || |dqW||}|fdd|D}t|jd d }|j}t}xH|jd d D]8}|||}x&|D]}t|||}||q@Wq,Wt|}|d |}xB|D]:}|d d |d d kr|d|dkrdS|}qWt|dS)a Canonicalize tensor formed by tensors of the different types g permutation representing the tensor dummies list of dummy indices msym symmetry of the metric v is a list of (base_i, gens_i, n_i, sym_i) for tensors of type `i` base_i, gens_i BSGS for tensors of this type n_i number ot tensors of type `i` sym_i symmetry under exchange of two component tensors of type `i` None no symmetry 0 commuting 1 anticommuting Return 0 if the tensor is zero, else return the array form of the permutation representing the canonical form of the tensor. Examples ======== >>> from sympy.combinatorics.testutil import canonicalize_naive >>> from sympy.combinatorics.tensor_can import get_symmetric_group_sgs >>> from sympy.combinatorics import Permutation, PermutationGroup >>> g = Permutation([1, 3, 2, 0, 4, 5]) >>> base2, gens2 = get_symmetric_group_sgs(2) >>> canonicalize_naive(g, [2, 3], 0, (base2, gens2, 2, 0)) [0, 2, 1, 3, 4, 5] r)r) gens_products dummy_sgs)r_af_rmulr(csg|] }|qSrr)r r)rrr rsz&canonicalize_naive..T)r)rN)rrsympy.combinatorics.tensor_canr6r7rrr8rr)r" isinstanceintextendr Zgeneraterr3rr4sort)gdummiesZsymvrr6r7r8Zv1r-Zbase_iZgens_iZn_iZsym_isizeZsbaseZsgensZdgensZ num_typesSDZdliststshdqr prevr)rr canonicalize_naivesH  "    rMcCsddlm}ddlm}m}t|}|jdddddd |D}||}d}x|D]\}}|t|7}qZWd d |D} d} x^|D]V\}}xL|D]D} |||| kr| || | | ||  | d | d 7} qWqWg} x| D]}| |qWt| |kst | ||d g7} |d } t | tt | ksDt t| } dgt| dd }x"| D]}|t|d 7<qhWg}xBt t|D]2} || }|r|| \}}| |||dfqW|tt |}|| |df|}|S) a Return a certificate for the graph gr adjacency list The graph is assumed to be unoriented and without external lines. Associate to each vertex of the graph a symmetric tensor with number of indices equal to the degree of the vertex; indices are contracted when they correspond to the same line of the graph. The canonical form of the tensor gives a certificate for the graph. This is not an efficient algorithm to get the certificate of a graph. Examples ======== >>> from sympy.combinatorics.testutil import graph_certificate >>> gr1 = {0:[1, 2, 3, 5], 1:[0, 2, 4], 2:[0, 1, 3, 4], 3:[0, 2, 4], 4:[1, 2, 3, 5], 5:[0, 4]} >>> gr2 = {0:[1, 5], 1:[0, 2, 3, 4], 2:[1, 3, 5], 3:[1, 2, 4, 5], 4:[1, 3, 5], 5:[0, 2, 3, 4]} >>> c1 = graph_certificate(gr1) >>> c2 = graph_certificate(gr2) >>> c1 [0, 2, 4, 6, 1, 8, 10, 12, 3, 14, 16, 18, 5, 9, 15, 7, 11, 17, 13, 19, 20, 21] >>> c1 == c2 True r) _af_invert)get_symmetric_group_sgs canonicalizecSs t|dS)Nr()r))rrrr r*sz#graph_certificate..T)keyreversecSsg|] }|dqS)rr)r rrrr r+sz%graph_certificate..cSsg|]}gqSrr)r r-rrr r6sr(r9)rrNr<rOrPr itemsr@r)r"r?AssertionErrorsortedrrrR)ZgrrNrOrPrSZpvertZ num_indicesrCZneighZverticesr-Zv2rArDZvlennr,rrBZcanrrr graph_certificate sL       rW)F)N)N)Z __future__rrZsympy.core.compatibilityrZsympy.combinatorics.utilrZsympy.combinatoricsrZrmulrr#r/r1r5rMrWrrrr s    -& $ )F