o FZh+@s`ddlmZddlmZejZddZdddZdd Zdd d Zdd dZ ddZ ddZ d S) Permutation)_distribute_gens_by_basecCsdd|Ddd|DkS)ao Compare two lists of permutations as sets. Explanation =========== 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 cSh|]}t|qStuple.0arrK/var/www/auris/lib/python3.10/site-packages/sympy/combinatorics/testutil.py z"_cmp_perm_lists..cSrrrr rrr r !rr)firstsecondrrr _cmp_perm_listss  rFcsddlm} ddlmt|drPt|jdd}dd|jDfd d }g}|s@|D]}||r=|t |q/|S|D] }||rM||qB|St|d r]t ||||St|d rkt |||g|SdS) NrPermutationGroup)_af_commutes_with generatorsTafcSsg|]}|jqSr)Z _array_formr xrrr Bsz+_naive_list_centralizer..cstfddDS)Nc3s|]}|VqdSNrr gen)rrrr Csz<_naive_list_centralizer....)allrrgensr r Csz)_naive_list_centralizer..getitem array_form) sympy.combinatorics.perm_groupsr sympy.combinatorics.permutationsrhasattrlistgenerate_diminorappendrZ_af_new_naive_list_centralizer)selfotherrrelementsZcommutes_with_gensZcentralizer_listelementrr!r r,$s0      r,cCspddlm}t||}|}tt|D]}|||}||kr&dS|||}q|dkr6dSdS)a Verify the correctness of a base and strong generating set. Explanation =========== This is a naive implementation using the definition of a base and a strong generating set relative to it. There are other procedures for verifying a base and strong generating set, but this one will serve for more robust testing. Examples ======== >>> from sympy.combinatorics.named_groups import AlternatingGroup >>> from sympy.combinatorics.testutil import _verify_bsgs >>> A = AlternatingGroup(4) >>> A.schreier_sims() >>> _verify_bsgs(A, A.base, A.strong_gens) True See Also ======== sympy.combinatorics.perm_groups.PermutationGroup.schreier_sims rrFT)r&rrrangelenorderZ stabilizer)groupbaser"rZstrong_gens_distrZcurrent_stabilizeri candidaterrr _verify_bsgsTs    r9NcCs:|dur ||}t|jdd}t||dd}t||S)a3 Verify the centralizer of a group/set/element inside another group. This is used for testing ``.centralizer()`` from ``sympy.combinatorics.perm_groups`` Examples ======== >>> from sympy.combinatorics.named_groups import (SymmetricGroup, ... AlternatingGroup) >>> from sympy.combinatorics.perm_groups import PermutationGroup >>> from sympy.combinatorics.permutations import Permutation >>> from sympy.combinatorics.testutil import _verify_centralizer >>> S = SymmetricGroup(5) >>> A = AlternatingGroup(5) >>> centr = PermutationGroup([Permutation([0, 1, 2, 3, 4])]) >>> _verify_centralizer(S, A, centr) True See Also ======== _naive_list_centralizer, sympy.combinatorics.perm_groups.PermutationGroup.centralizer, _cmp_perm_lists NTr)Z centralizerr)r*r,r)r5argZcentrZ centr_listZcentr_list_naiverrr _verify_centralizer}s   r;csddlm} |dur||}t}t|dr|j}nt|dr$|}nt|dr,|g}|D]|fdd|Dq0|t|}| |S)Nrrr __getitem__r%c3s|]}|AVqdSrrrelrr rsz)_verify_normal_closure..) r&rZnormal_closuresetr(rr*updater)Z is_subgroup)r5r:closurerZ conjugatesZ subgr_gensZ naive_closurerr=r _verify_normal_closures        rBcGsddlm}ddlm}m}ddlm}g}tt|D]} || \} } } } | | | gg| | fq||\}}}||||d}t |t rPd}|g}|g}nt|}g}t|D]} | ||| || |dqZ||}|dd|D}t |jd d }|j}t}|jd d D]}|||}|D]}t|||}||qqt |}|d |}|D]}|d d |d d kr|d|dkrdS|}qt |dS)au Canonicalize tensor formed by tensors of the different types. Explanation =========== sym_i symmetry under exchange of two component tensors of type `i` None no symmetry 0 commuting 1 anticommuting Parameters ========== g : Permutation representing the tensor. dummies : List of dummy indices. msym : Symmetry of the metric. v : 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 of tensors of type `i` Returns ======= Returns 0 if the tensor is zero, else returns 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 >>> 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] rr) gens_products dummy_sgs)_af_rmulr1cSsg|]}t|qSrrrrrr rrz&canonicalize_naive..TrrN)r&rsympy.combinatorics.tensor_canrCrDr'rEr2r3r+ isinstanceintextendr)generater%r?raddsort)gdummiessymvrrCrDrEv1r7Zbase_iZgens_iZn_iZsym_isizeZsbaseZsgensZdgensZ num_typesSDZdliststshdqr prevrrr canonicalize_naivesJ '       r_cCsddlm}ddlm}m}t|}|jdddddd |D}||}d}|D] \}}|t|7}q,d d |D} d} |D])\}}|D]"} |||| krj| || | | ||  | d | d 7} qHqBg} | D]}| |qpt| |ksJ| ||d g7} |d } t | tt | ksJt | } dgt| dd }| D] }|t|d 7<qg}t t|D]} || }|r|| \}}| |||dfq|tt |}|| |dg|R}|S) a Return a certificate for the graph Parameters ========== gr : adjacency list Explanation =========== 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)Nr1)r3r rrr r#=s z#graph_certificate..T)keyreversecSsg|]}|dqSrGrrrrr r>rz%graph_certificate..cSsg|]}gqSrr)r r7rrr rIsr1rF)r'r`rJrarbr)itemsrPr3r+rMsortedr2rrd)grr`rarbreZpvertZ num_indicesrTZneighZverticesr7v2rQrVZvlennr6r"rRZcanrrr graph_certificatesR #      rj)Fr) Zsympy.combinatoricsrZsympy.combinatorics.utilrZrmulrr,r9r;rBr_rjrrrr s  0 ) $( N