ó ¡¼™\c@s…ddlmZddlmZddlmZejZd„Zed„Z d„Z d d„Z d d„Z d „Zd „Zd S( iÿÿÿÿ(t Permutation(t_distribute_gens_by_base(trangecCsd„|Dƒd„|DƒkS(sN 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|ƒ’qS((ttuple(t.0ta((s;lib/python2.7/site-packages/sympy/combinatorics/testutil.pys s cSsh|]}t|ƒ’qS((R(RR((s;lib/python2.7/site-packages/sympy/combinatorics/testutil.pys s ((tfirsttsecond((s;lib/python2.7/site-packages/sympy/combinatorics/testutil.pyt_cmp_perm_listss c s?ddlm}ddlm‰t|dƒrît|jdtƒƒ}g|jD]}|j ^qQ‰‡‡fd†}g}|s½xc|D]+}||ƒr‹|j t j |ƒƒq‹q‹Wn-x*|D]"}||ƒrÄ|j |ƒqÄqÄW|St|dƒrt |||ƒ|ƒSt|dƒr;t |||gƒ|ƒSdS( Niÿÿÿÿ(tPermutationGroup(t_af_commutes_witht generatorstafcst‡‡fd†ˆDƒƒS(Nc3s|]}ˆˆ|ƒVqdS(N((Rtgen(R tx(s;lib/python2.7/site-packages/sympy/combinatorics/testutil.pys >s(tall(R(R tgens(Rs;lib/python2.7/site-packages/sympy/combinatorics/testutil.pyt>ttgetitemt array_form(tsympy.combinatorics.perm_groupsR t sympy.combinatorics.permutationsR thasattrtlisttgenerate_diminotTrueR t _array_formtappendRt_af_newt_naive_list_centralizer( tselftotherR R telementsRtcommutes_with_genstcentralizer_listtelement((R Rs;lib/python2.7/site-packages/sympy/combinatorics/testutil.pyR"s&     cCs›ddlm}t||ƒ}|}xYtt|ƒƒD]E}|||ƒ}|jƒ|jƒkrjtS|j||ƒ}q8W|jƒdkr—tStS(s® 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 iÿÿÿÿ(R i( RR RRtlentordertFalset stabilizerR(tgrouptbaseRR tstrong_gens_distrtcurrent_stabilizertit candidate((s;lib/python2.7/site-packages/sympy/combinatorics/testutil.pyt _verify_bsgsOscCsX|dkr|j|ƒ}nt|jdtƒƒ}t||dtƒ}t||ƒS(s3 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 R N(tNonet centralizerRRRRR(R)targtcentrt centr_listtcentr_list_naive((s;lib/python2.7/site-packages/sympy/combinatorics/testutil.pyt_verify_centralizerus  c CsÝddlm}|dkr.|j|ƒ}ntƒ}t|dƒrR|j}n3t|dƒrj|}nt|dƒr…|g}nx6|jƒD](}x|D]}|j||AƒqŸWq’W|t |ƒƒ}|j |ƒS(Niÿÿÿÿ(R R t __getitem__R( RR R0tnormal_closuretsetRR RtaddRt is_subgroup( R)R2tclosureR t conjugatest subgr_genstelR t naive_closure((s;lib/python2.7/site-packages/sympy/combinatorics/testutil.pyt_verify_normal_closure™s      cGsfddlm}ddlm}m}ddlm}m}g} xPtt |ƒƒD]<} || \} } } }| j | | gg| |fƒqUW|| Œ\}}}||||dƒ}t |t ƒrêd}|g}|g}n t |ƒ}g}x9t|ƒD]+} |j ||| || |dƒƒq W||ƒ}|g|D]}||ƒ^qNƒ}t|jdtƒƒ}|j}tƒ}x\|jdtƒD]H}|||ƒ}x0|D](}t|||ƒƒ}|j|ƒqÂWq¦Wt|ƒ}|jƒd |}xC|D];}|d |d krN|d|dkrNdSn|}qWt|dƒS( s 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] iÿÿÿÿ(R (t gens_productst dummy_sgs(Rt_af_rmuliiR iiþÿÿÿ(i(RR tsympy.combinatorics.tensor_canRBRCRRRDRR%Rt isinstancetinttextendRtgenerateRRR9RR:tsort(tgtdummiestsymtvR RBRCRRDtv1R-tbase_itgens_itn_itsym_itsizetsbasetsgenstdgenst num_typestSRtDtdlisttsttsthtdtqRtprev((s;lib/python2.7/site-packages/sympy/combinatorics/testutil.pytcanonicalize_naiveÂsH$   ) %        cCsŸddlm}ddlm}m}t|jƒƒ}|jdd„dtƒg|D]}|d^qX}||ƒ}d}x$|D]\}} |t | ƒ7}q‡Wg|D] } g^q®} d} xt|D]l\}} x]| D]U} |||| krà| ||j | ƒ| || j | dƒ| d 7} qàqàWqÍWg} x| D]}| j |ƒqJWt | ƒ|ksyt ‚| ||dg7} |d }t | ƒtt|ƒƒks»t ‚t| ƒ} dgt | dƒd}x$| D]} |t | ƒcd7>> 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 iÿÿÿÿ(t _af_invert(tget_symmetric_group_sgst canonicalizetkeycSst|dƒS(Ni(R%(R((s;lib/python2.7/site-packages/sympy/combinatorics/testutil.pyR(Rtreverseiii(RRcRERdReRtitemsRJRR%RRHtAssertionErrortsortedRRRg(tgrRcRdReRhRtpvertt num_indicesRNtneighR-tverticestv2RKRTtvlentnR*RRLtcan((s;lib/python2.7/site-packages/sympy/combinatorics/testutil.pytgraph_certificatesL    $     N(tsympy.combinatoricsRtsympy.combinatorics.utilRtsympy.core.compatibilityRtrmulRR'RR/R0R6RARbRt(((s;lib/python2.7/site-packages/sympy/combinatorics/testutil.pyts   - & $ ) F