K i|}2 ddlZddlZddlmZddlmZddlmZm Z m Z ddl m Z m Z mZmZmZmZmZmZddlmZddlmZddlmZmZdd lmZdd lmZdd lm Z m!Z!dd l"m#Z#m$Z$m%Z%dd l&m'Z'm(Z(m)Z)ddl*m+Z+ddl,m-Z-ddl.m/Z/m0Z0m1Z1ddl2m3Z3m4Z4ddl5m6Z6ddl7m8Z8ddl9m:Z:ddl;mm?Z?ddl@mAZAmBZBmCZCddlDmEZEddlFmGZGddlHmIZIddlJmKZKmLZLmMZMmNZNmOZOmPZPmQZQmRZRmSZSmTZTmUZUmVZVmWZWmXZXmYZYmZZZm[Z[m\Z\m]Z]m^Z^m_Z_m`Z`maZambZbddlHmcZcddldmeZemfZfddlgmhZhddlimjZjmkZkmlZldd lmmnZndd!lompZpmqZqmrZrmsZsmtZtmuZudd"lvmwZwdd#lxmyZydd$lzm{Z{dd%l|m}Z}dd&l~mZdd'lmZdd(lmZmZmZmZmZmZmZmZeNeOeLeMfZdd)lmZmZdd*lmZmZeu5Gd+d,eeeZdddeu5Gd-d.eeeZdddd/Zd0Zd1Zd2Zd3Zd4Zd5Zd6Zd7Zd8Zd9Zd:Zd;Zd<Zd=Zd>Zd?Zd@ZdAZdBZdCZdDZdEZdFZdGZdHZdIZdJZdKZdLZdMZdNZdOZdPZdQZdRZdSZdTZdUZdVZdWZdXZdYZdZZd[Zd\Zd]Zd^Zd_Zd`ZdaZdbZdcZddZdeZdfZdgZdhZdiZdjZdkZdlZdmZdnZdoZdpZdqZdrZdsZdtZduZdvZdwZdxZdyZdzZd{Zd|Zd}Zd~ZdZdZdZdZdZdZdZdZdZdZdZdZdZdZdZdZdZdZdZdZdZdZdZdZdZdZdZdZdZdZdZdZdZdZdZdZdZdZ dZ dZ dZ dZ dZdZdZdZdZdZdZdZdZdZdZdZdZdZdZdZdZdZdZ dZ!dZ"dZ#dZ$dZ%dZ&d„Z'dÄZ(dĄZ)eqdńZ*dƄZ+dDŽZ,dȄZ-dɄZ.dʄZ/d˄Z0erd̄Z1d̈́Z2d΄Z3dτZ4dЄZ5dфZ6d҄Z7dӄZ8dԄZ9dՄZ:dքZ;dׄZdڄZ?dۄZ@d܄ZAd݄ZBdބZCd߄ZDdZEdZFdZGdZHdZIdZJetddZKdZLdZMdZNdZOdZPdZQdZRdZSdZTdZUdZVdZWdZXdZYdZZy#1swYxYw#1swYxYw)N)Hashable)Add)Functiondiffexpand)EFloatIIntegerRationalnanoopi)Pow)S)Symbolsymbols)sympify)Abs)explog)MaxMinsqrt)cossintan) integrate) transpose)HermitianOperatorOperatorDagger)PolyPurePoly)RootOf)sstr) FiniteSet)signsimpsimplify)trigsimp) ShapeError MatrixErrorNonSquareMatrixErrorDeferredVector)_find_reasonable_pivot_naive) _simplify) GramSchmidtImmutableMatrixImmutableSparseMatrixMatrix SparseMatrix casoratiandiageyehessianmatrix_multiply_elementwiseones randMatrix rot_axis1 rot_axis2 rot_axis3 wronskianzerosMutableDenseMatrixImmutableDenseMatrix MatrixSymbol dotprodsimp rot_ccw_axis1 rot_ccw_axis2 rot_ccw_axis3)_dotprodsimp_state)TupleWild)KroneckerDelta)flattencaptureiterable)ignore_warnings)raisesXFAILslowskipskip_under_pyodidewarns_deprecated_sympyQ)Array)ArrayDerivative)MatPow) Quaternion)O)abcdxyzt)_MinimalMatrix_CastableMatrix)MatrixSubspacesMatrixReductionsc eZdZy)SubspaceOnlyMatrixN__name__ __module__ __qualname__h/mnt/ssd/data/python-lab/Trading/venv/lib/python3.12/site-packages/sympy/matrices/tests/test_matrices.pyrlrlG rrrlc eZdZy)ReductionsOnlyMatrixNrmrqrrrsrvrvLrtrrrvct||dS)Nct||k(SN)intijs rsz eye_Reductions..Qs3qAv;rrrvns rseye_ReductionsrPs 1&> ??rrct||dS)NcyNrrqr{s rsr~z"zeros_Reductions..Urrrrs rszeros_ReductionsrTs 1n 55rrcttD]\}}|jdd}|jdk(rt d|jDsJ|j dk(rt |j tusJ|jdk(rt |jtusJ|dzs-t |jtttfvrJt |jturJy)N)rrc3>K|]}t|tuywry)typerz).0r|s rs ztest_args..\s(IAaC(Is) enumerateclassesrBshapeallrowsrrzcolsflatlisttuplerKtodokdict)rclsms rs test_argsrXsG$ +3 IIaOww& S(I(I%IIIvv{tAFF|s222vv{tAFF|s2221u>dE5%99 99 ?d* ** +rrcttfD]H}|jdd}t5|j}ddd|j k(rHJt tfD]H}|jdd}t5|j}ddd|jk(rHJy#1swYxxYw#1swY-xYwNrr) r5r3rBrW_matrr6r4_smatr)rrmatsmats rstest_deprecated_mat_smatres& IIaO # % &&C affh  22! IIaO # % 77D qwwy   !     s B0 B<0B9 <C ctddttg}|tz tddttz ttz gk(sJyNr)r5rcrdre)vs rs test_divisionrrs;q!aVA Q3&A!QqSz* ** *rrc Ftgdtttgdtzdttzggztgddtzdtzdtzgdtzddtztzggk(sJtddddgt t fdy) Nrrrri)rrirczSryrqrrsrsr~ztest_sum..{s q1urr)r5rcrdrerRr+rs@@rstest_sumrws Aq!9qsC1o67A q5FI!QqS!A#1dAaCE8JKL LL Lq!aVA :}%rrctdddtg}tdddttg}t||k(sJy)Nrrr)r5rcrabsrs rstest_absr}s:q!b!WAq!aQ[!A q6Q;;rrctd}td}||z|j|cxk(rtddgddggk(sJJy)N)rrrrr)rrrrrr)r5addr_r`s rs test_additionrs] A  A q5EAEE!H 8AA'7 8 88 88 8rrc ttfD]}|ddtd}||ddddfk(sJ|dddftddgdk(sJ|dddftgdk(sJ|ddgddftgdgdgk(sJ|ddgdf|ddgdgfk(sJ|dddgf|dgddgfk(sJ|ddddgftddgdd gd d ggk(sJ|d dk(sJ|ddddftgdgdgk(sJ|ddddftddgdd gd d ggk(sJ|ddddf|ddgdfk(sJ|ddddf|dddgfk(sJ|ddtd}|gd ddftgdgdgdgdgdgk(sJ|ddgd ftgd gdgdgk(rJtjd}d|d<d|d<d |d<|jddgdgtdgdggk(sJ|jddggdtgdgdgk(sJ|jgdgdtgdgdgdgdgk(sJy)Nr rrr)rrrrrrrrrrrr)rrrrr)rr)rrrrr)rrrrrrrrrr)rrrrrr)rrrr)rrrrrrrr)rrrr)rrrr)r5r6rangerBextract)Mr_s rstest_fancy_index_matrixrs!l # aE!H AadG||Aw&Ay1111Aw&++++!Q|vy)&<====!Q|q!Q!~---QF|q!q!f~---QF|v1v1v1v&>????w!||1ayFIy#9::::AaCyFQFQFQF#;<<<<1ayAq!faiL(((CaCyAa!QiL((( aE!H !#$      0)  K F   ,% +4 1AAdGAdGAdG 199aVaS !VCC- &     199aVY '6  3,   199\< 0F <5  rrcHtdtdz}|ddk(sJ|ddk(sJ|ddk(sJ|d dk(sJ|d d k(sJ|d d k(sJ td|ddk(sJ|ddk(sJ|ddk(sJ|d dk(sJ|d d k(sJ|d d k(sJt|}|j|k(sJ|ddk(sJ|ddk(sJ|dd k(sJ|d dk(sJ|d d k(sJ|d d k(sJt t fdtdz}t|tsJ|dtk(sJ|ddtzk(sJ|ddtzk(sJ|d d k(sJtz}||k(sJdz}t|tsJ|ddk(sJ|ddk(sJ|ddk(sJ|d d k(sJ tdt|tsJ|ddk(sJ|ddk(sJ|ddk(sJ|d d k(sJy#t$rYowxYw#t$rYywxYw)N)rrrrrrrrrrrrrrrrrrz c = a @ brctSry)r;rsrsr~z%test_multiplication..s:1a@rrrcrr z c = 5 @ b) r5eval SyntaxErrorr;multiply_elementwiserRr+r isinstancerc)rahc2r_r`s @@rstest_multiplicationrs A  A !A T7a<< T7a<< T7a<< T7a<< T7b== T7a<<  [w!||w!||w!||w!||w"}}w!||#Aq)A &&&q) )) ) T7a<< T7a<< T7b== T7a<< T7a<< T7a<< :@A F3KA a  T7a<< T7ac>> T7ac>> T7a<< QB 7N7 AA a  T7a<< T7c>> T7c>> T7a<<  [!V$$$w!||w#~~w#~~w!||]    N    s$ H? H HH H! H!c ttdgdtgg}|dz|k(sJtttgddgg}|dztttgttggk(sJtdddtd dz ggdgdtd dz dddggttt dzzdtt zt dzzdz ttzt dzzdz ztt dzztt dzzdz tt dzzt d zzd z zttzt zt d zzd z zttdzzt d zzd z ztt d zzgdtt dzzdz tt d ztt dzgtt zt dzzdz ttzt dzzdz ztt dzztt d ztt dzzt d zzd z ttzt zt d zzd z zttdzzt d zzd z ztt d zztt zt d zzd z ttzt d zzd z ztt d zzgtt dzzdz tt dzzt d zzd z zttzt zt d zzd z zttdzzt d zzd z ztt d zztt dztt zt d zzd z ttzt d zzd z ztt d zztt d zzdz dtzt dzzt dzzdz zttzt zt dzzd z zdtztdzzt dzzdz ztt dzzggtt t dzzdz tt dzzt d zzdz z ttzt zt d zzdz z ttdzzt d zzdz z tt d zztt dzt t zt d zzdz ttzt d zzdz z tt d zzt t d zzd z dtzt dzzt dzzdz z ttzt zt dzzdz z dtztdzzt dzzdz z tt dzzgdtt dzzdz tt d ztt dzgtt zt dzzdz ttzt dzzdz ztt dzztt d ztt dzzt d zzd z ttzt zt d zzd z zttdzzt d zzd z ztt d zztt zt d zzd z ttzt d zzd z ztt d zzgt t dzzdz dt t zt dzzdz ttzt dzzdz z tt dzzt t dzzdz tt dzzt d zzdz z ttzt zt d zzdz z ttdzzt d zzdz z tt d zzgg}tddfd}z|cxk(r|k(sJJy)Nrrrrrrrrrrrrrrr 0r r@r`cBtfdtdDS)Nc3<K|]}|f|fzywryrq)rkABr|r}s rsrzAtest_multiplication_inf_zero....s%(I11Q3!A#(Isr)rr)r|r}rrs``rsr~z.test_multiplication_inf_zero..s3(Ia(I#Jrr) r5rr rrrcr`r_r^)rCC2rrs @@rstest_multiplication_inf_zerors. Q!R!"A 6Q;;R1a&!"A 6Vc3Z#s45 55 5 Aq1Q4%' A$q!Q  A  AqD!RT!Q$Yq[2a419Q;.1a48"QT'!)bAgaQRdlSUo:UXZ[\X\]^X^_`bc_cXcdfXf:fiklmoplpipqrtuquiuvxix:x{|}~AB~B|C;C D Bq!tGAIqAw!Q$( Aad1r!tAqDy{ "Qq!tW ,a1gr!Q$wq!t|BAaPQSTPTUW7WZ\]^`a]aZabcefbfZfgiZi7ilmnoqrnrls7suwxyuyz{}~z~u~@BvBEGHIEIJKMNJNENOQEQvQTUVWYZVZT[v[ \ AqDR1WQT\"_ $r!tAvad{2~ 51a41 R G!AqD' QSTUVXYUYSZ\^_`\`abdeae\efh\hkmnokopqstptktuwkw\wz{|}@A}A{B]BDFGHJKGKDKLMDMPQRTPTUVXYUYPYZ[]^Z^P^_aPaDadfghdhijdjklnokodoprdrDruvwyuyz{}~z~u~@BCCuCDFuFDFIJKLNOKOIPDP Q R SA SAXaZ"QT'!Q$,r/!BqDF1a4KN2R1WQT\"_DqAwNRSTUWXTXRYrtqtuvqvwxz{w{q{|~q~BDEFBFGHJKGKBKLNBNrNQRSTVWSWQXrX[]Z]^_ab^bZbcdZdghikgklmoplpgpqrtuquguvygyZy|~@|@AB|BCDFGCG|GHJ|JZJMNOQMQRSUVRVMVWXZ[W[M[\_M_Z_bcdeghdhbiZijMNPRSTVWSWPWXYPYQRSTVWSWQXbcdeghdhbij+-a419Q;Aad1+DqAw+NRSTUWXTXRY[]^_ab^b[bcdfgcg[ghj[jmopqmqrsmstuwxtxmxy{m{[{ABCEFBFFGHJKGKKLNN\NQRSTVWSWQX\XDFGHDHIJLMIMDMNPDPSUVWSWXY[\X\S\]_S_D_bcdeghdhbiDijEGC1HQJXYrtqtuvqvwxz{w{q{|~q~BDEFBFGHJKGKBKLNBNrNQRSTVWSWQXrXac`cdeghdh`hij`jmopqstptmtuvxyuymyz|m|`|ABCCDEEFGIJFJJKMM`MPRSTVWSWPWXY[\X\P\]_P_`_bcdeghdhbi`ij k lA 1J KB Q3!>r>>>rrc  ttdt}tddgddggdzdd|ddz |d dz |d dz |d dz gk(sJdzddgd k(sJtgd gdgdgdzddgdk(sJdzt dk(sJdzk(sJtdggdzdddzk(sJt ddzt dk(sJtddgddggt dztddgddggk(sJtddgddggt jzddgdk(sJtddgddggt jzdzk(sJtddgddggt jztddgt jdggk(sJtddgddggd ztddgd dggk(sJdd!lm tdtgddggztdtzgddggk(sJtttgdtggzttzttdz zzzgdtzggk(sJttztdz zztzdzztzzz dtdzzz gdtztdz zzgddtzggsJttddgdtdgddtggzttztdz zzdgdtzdgddtzggk(sJtddgddggjt djdk(sJtdggdztd"ggcxk(r3jt dcxk(rjdk(sJJtgd#gd$gd%gd&gd'gttfd(ttd)tgd*gd+gd,gd-ztgd,gd,gd,gk(sJttfd.ttfd/tddgddggd-ztd0d1gd2d3ggk(sJtgd+gd+gd+gd-ztgd+gd+gd+gk(sJtgd*gd+gd+gd-ztgd+gd+gd+gk(sJt!d4d56t#zt$sJt!d4d5d57ttfd8t!d4d5d59ztt'dt'dt'd t'dz dzgdt'ddt'dz ggd+gk(sJdzztgd+gd+gd+gk(sJttfd:tgd+gd;gd<gd=ztgd>gd?gd@gk(sJd=zdzk(sJtgd*gdAgd,gt!d4zj)dj+dzk(sJttfdBzdzzk(sJtgd,gd,gd,gt!d4d5d5Czk(sJt!d4d5d59zt-dzdzdzk(sJzj)dt dk(sJzj)dt/dk(sJtgdDgdEgdFgdGzt-dHdHdHk(sJt0zt-dt0zdt0zdt0zk(sJtgd*gd+gd+gttfdIttfdJtt jt jgt jt jggt jzk(sJtddgddggt jztt jt jgdt jzdt jzggk(sJy)KNctddzSNrrr5rqrrrsr~ztest_power..#s):rrrrrrrir3i)iii,*i7)rrr)rrr)rrr) i"iiiipiiirrdrirrr!rr9)rrrrg?ri)rrrrr)rrrrr)rrrrr)rrrrr)rrrrrc8jtdSNr)_matrix_pow_by_jordan_blocksrrsrsr~ztest_power..Ls > >qu ErrcTtddgddggjtdS)Nrr)r5rrrqrrrsr~ztest_power..Os*AA'7 8 U UVWX[V\ ]rrrrrrrrr$@cdzSN@rqrsrsr~ztest_power..R q#vrrc"tddzSrr rsrsr~ztest_power..Sq(1a.0rrihiO<iv0irT)integer)r negativeczSryrq)rrsrsr~ztest_power..]s q!trr)r  nonnegativec"tddzSrr rsrsr~ztest_power..dr rr)rrr)rrrg@)HY)i#)i<i iIrrrcDjdjS)N)subsdoit)Anrsrsr~ztest_power..lsrwwq"~224rr)r positiverrr)rrrrrrrgd%%@cdzSrrqrsrsr~ztest_power..{rrrctzSryr rsrsr~ztest_power..|s q!trr)rRr-r r5r9r rHalf sympy.abcrr_r`r_eval_pow_by_recursionr, ValueErrorrrr\rMrrr8rBr )Rrrrrs @@@@rs test_powerr&"s !:;AAA A rE1:!D'!)QsVAXquQw#qA AA A qD!92 22 2 9j12A qD!9E EE E a43q6>> a4199 QC5MS $ '1c6 11 1 q68 s1v %% % Aq6Aq6" #WQZ /6Ar7RH:M3N NN NR2r(#$A qvvIq>\ )) )AQ !A qvvI>Q   Aq6Aq6" #QVV +v1v{6K/L LL L Aq6Aq6" #S (FQFS!H3E,F FF F Aq6Aq6" #Q &&1ac(QF1C*D DD D Aq6Aq6" #Q &&1a41qs8A2FAqD 1R*S SS S  Aq1q5z!|ad1a4i!Q$q&01QT6:; q!ta!a%jl; !ad;= >> > Aq!9q!Qi!Q3 4a 76 Aq1Q3xz1 AqD! Aq!t C<   AA A ) )!A$ /13K3KA3N NN Nu A b5FUG9% %)G)G")N %   $ %% %% %  "3_oWfghA ;EF ;]^ 9i01A d7fiI>? ?? ? :~& :01AA A d7fz95 97MNO OO O 9i01A d7fiI>? ?? ? 9i01A d7fiI>? ?? ?sD!A adF ## #sD40A :|$sDd3A a46 1 ~a3nQ6J5J^\]_`Ma5ade5ef~a3QQ_`acdQeMeffhi ii i q1u:Iy AB BB B :01 9i01A c6V_oOP PP P c6QT>> *Y/0As A AB 771a=   1a4 '' ' :45 7a!A#h   ()AsD40A a4199sDd3A a441adAqD) )) ) qD;;q! A && & qD;;q! a (( ()*A c6T6662 22 2 a44Aq!tQT* ** * 9i01A :~& :|$ 166166"234A aff9>>A1vA aff9!&&!&&!1AaffHah3G HI II Irrc tdtzdtz gdtz dtzgg}td5|jj ttdtztdzdz tdtz tdzdz gtdtz tdzdz tdtztdzdz ggk(sJ dddy#1swYyxYw)NrTr)r5rcrFrrrs rs$test_issue_17247_expression_blowup_1r)s1ac QqS!A#J'(A T ?uuw~~61Q3x#a& !#s1Q3xi#a&&8!%; <1Q3xi#a& ! #s1Q3x#a&'8!&; <+>$?? ?????s B1C44C=ctdtzdtz gdtz dtzgg}td5|j\}}||z|j zsJ dddy#1swYyxYwNrT)r5rcrF jordan_forminvrPJs rs$test_issue_17247_expression_blowup_2r1sl1ac QqS!A#J'(A T }}1s1557{{s ,A//A8c :tdtzdtz gdtz dtzgg}td5|dztdtdzzdzddtdzzz gddtdzzz dtdzzdzggk(sJ dddy#1swYyxYw)NrTrl)r5rcrFr(s rs$test_issue_17247_expression_blowup_3r3s1ac QqS!A#J'(A T _#v +AsF 25S SUswUVWY\V\w\V\ ] +.LQPSV.S SUstuwztzUz~\V\ ]!^__ _____s ABBcttd}td5|dzttdk(sJ dddy#1swYyxYw)Na1[ [ -3/4, 45/32 - 37*I/16, 1/4 + I/2, -129/64 - 9*I/64, 1/4 - 5*I/16, 65/128 + 87*I/64], [-149/64 + 49*I/32, -177/128 - 1369*I/128, 125/64 + 87*I/64, -2063/256 + 541*I/128, 85/256 - 33*I/16, 805/128 + 2415*I/512], [ 1/2 - I, 9/4 + 55*I/16, -3/4, 45/32 - 37*I/16, 1/4 + I/2, -129/64 - 9*I/64], [ -5/8 - 39*I/16, 2473/256 + 137*I/64, -149/64 + 49*I/32, -177/128 - 1369*I/128, 125/64 + 87*I/64, -2063/256 + 541*I/128], [ 1 + I, -19/4 + 5*I/4, 1/2 - I, 9/4 + 55*I/16, -3/4, 45/32 - 37*I/16], [ 21/8 + I, -537/64 + 143*I/16, -5/8 - 39*I/16, 2473/256 + 137*I/64, -149/64 + 49*I/32, -177/128 - 1369*I/128]]Tra[ [ 7369525394972778926719607798014571861/604462909807314587353088 - 229284202061790301477392339912557559*I/151115727451828646838272, -19704281515163975949388435612632058035/1208925819614629174706176 + 14319858347987648723768698170712102887*I/302231454903657293676544, -3623281909451783042932142262164941211/604462909807314587353088 - 6039240602494288615094338643452320495*I/604462909807314587353088, 109260497799140408739847239685705357695/2417851639229258349412352 - 7427566006564572463236368211555511431*I/2417851639229258349412352, -16095803767674394244695716092817006641/2417851639229258349412352 + 10336681897356760057393429626719177583*I/1208925819614629174706176, -42207883340488041844332828574359769743/2417851639229258349412352 - 182332262671671273188016400290188468499*I/4835703278458516698824704], [50566491050825573392726324995779608259/1208925819614629174706176 - 90047007594468146222002432884052362145*I/2417851639229258349412352, 74273703462900000967697427843983822011/1208925819614629174706176 + 265947522682943571171988741842776095421*I/1208925819614629174706176, -116900341394390200556829767923360888429/2417851639229258349412352 - 53153263356679268823910621474478756845*I/2417851639229258349412352, 195407378023867871243426523048612490249/1208925819614629174706176 - 1242417915995360200584837585002906728929*I/9671406556917033397649408, -863597594389821970177319682495878193/302231454903657293676544 + 476936100741548328800725360758734300481*I/9671406556917033397649408, -3154451590535653853562472176601754835575/19342813113834066795298816 - 232909875490506237386836489998407329215*I/2417851639229258349412352], [ -1715444997702484578716037230949868543/302231454903657293676544 + 5009695651321306866158517287924120777*I/302231454903657293676544, -30551582497996879620371947949342101301/604462909807314587353088 - 7632518367986526187139161303331519629*I/151115727451828646838272, 312680739924495153190604170938220575/18889465931478580854784 - 108664334509328818765959789219208459*I/75557863725914323419136, -14693696966703036206178521686918865509/604462909807314587353088 + 72345386220900843930147151999899692401*I/1208925819614629174706176, -8218872496728882299722894680635296519/1208925819614629174706176 - 16776782833358893712645864791807664983*I/1208925819614629174706176, 143237839169380078671242929143670635137/2417851639229258349412352 + 2883817094806115974748882735218469447*I/2417851639229258349412352], [ 3087979417831061365023111800749855987/151115727451828646838272 + 34441942370802869368851419102423997089*I/604462909807314587353088, -148309181940158040917731426845476175667/604462909807314587353088 - 263987151804109387844966835369350904919*I/9671406556917033397649408, 50259518594816377378747711930008883165/1208925819614629174706176 - 95713974916869240305450001443767979653*I/2417851639229258349412352, 153466447023875527996457943521467271119/2417851639229258349412352 + 517285524891117105834922278517084871349*I/2417851639229258349412352, -29184653615412989036678939366291205575/604462909807314587353088 - 27551322282526322041080173287022121083*I/1208925819614629174706176, 196404220110085511863671393922447671649/1208925819614629174706176 - 1204712019400186021982272049902206202145*I/9671406556917033397649408], [ -2632581805949645784625606590600098779/151115727451828646838272 - 589957435912868015140272627522612771*I/37778931862957161709568, 26727850893953715274702844733506310247/302231454903657293676544 - 10825791956782128799168209600694020481*I/302231454903657293676544, -1036348763702366164044671908440791295/151115727451828646838272 + 3188624571414467767868303105288107375*I/151115727451828646838272, -36814959939970644875593411585393242449/604462909807314587353088 - 18457555789119782404850043842902832647*I/302231454903657293676544, 12454491297984637815063964572803058647/604462909807314587353088 - 340489532842249733975074349495329171*I/302231454903657293676544, -19547211751145597258386735573258916681/604462909807314587353088 + 87299583775782199663414539883938008933*I/1208925819614629174706176], [ -40281994229560039213253423262678393183/604462909807314587353088 - 2939986850065527327299273003299736641*I/604462909807314587353088, 331940684638052085845743020267462794181/2417851639229258349412352 - 284574901963624403933361315517248458969*I/1208925819614629174706176, 6453843623051745485064693628073010961/302231454903657293676544 + 36062454107479732681350914931391590957*I/604462909807314587353088, -147665869053634695632880753646441962067/604462909807314587353088 - 305987938660447291246597544085345123927*I/9671406556917033397649408, 107821369195275772166593879711259469423/2417851639229258349412352 - 11645185518211204108659001435013326687*I/302231454903657293676544, 64121228424717666402009446088588091619/1208925819614629174706176 + 265557133337095047883844369272389762133*I/1208925819614629174706176]])r5rrFr(s rs$test_issue_17247_expression_blowup_4r5so8 qKL MA T J "uq"H  I J J  J J J J J s AActddd}td5|jdttdzddt zz tdzzzdt ztdzzztd k(sJ dddy#1swYyxYw) Nrc&dd||zztzzSNrrr r{s rsr~z6test_issue_17247_expression_blowup_5..!rQqSk!m"3rrTrcr$rEXdomain)r5rFcharpolyr$rcr r(s rs$test_issue_17247_expression_blowup_5r@s|q!34A T _zz#(1a42!8QT/+ABqDAI+MqY]"^^^^___s AA==Bc tddtdDcgc] }t|z c}}td5|j ddk(sJ dddycc}w#1swYyxYw)NrrTbareissrr5rrcrFdetr|rs rs$test_issue_17247_expression_blowup_6rFsaq!5":.aac./A T %uuY1$$$%%/%%A AA&ctddd}td5|jddk(sJ dddy#1swYyxYw)Nrc&dd||zztzzSr8r r{s rsr~z6test_issue_17247_expression_blowup_7..r9rrT berkowitzr)r5rFrDr(s rs$test_issue_17247_expression_blowup_7rKsEq!34A T 'uu[!Q&&&'''s ;Ac tddtdDcgc] }t|z c}}td5|j ddk(sJ dddycc}w#1swYyxYw)NrrTlurrCrEs rs$test_issue_17247_expression_blowup_8rNs`q!5":.aac./A T  uuT{a  /  rGc tddtdDcgc] }t|z c}}td5|j tgdgdgdgdgdgdgdgdgdfk(sJ dddycc}w#1swYyxYw)NrrT)rrrrrr:rrrrrrrrrrrrrrrrr)r5rrcrFrrefrEs rs$test_issue_17247_expression_blowup_9rUsq!5":.aac./A T  6vvxF * * * * * * * *$,-/566 66 6 6/ 6 6sA: 9A??Bctddd}td5|jdddk(sJ dddy#1swYyxYw)Nrc&dd||zztzzSr8r r{s rsr~z7test_issue_17247_expression_blowup_10..r9rrTr)r5rFcofactorr(s rs%test_issue_17247_expression_blowup_10rYsGq!34A T %zz!Q1$$$%%%s <Actddd}td5|jtdddgdzk(sJ dddy#1swYyxYw)Nrc&dd||zztzzSr8r r{s rsr~z7test_issue_17247_expression_blowup_11..r9rrTrr;)r5rFcofactor_matrixr(s rs%test_issue_17247_expression_blowup_11r]sTq!34A T ;  "fQA3r6&::::;;;s %A  Actddd}td5|jdddtzdddik(sJ dddy#1swYyxYw)Nrc&dd||zztzzSr8r r{s rsr~z7test_issue_17247_expression_blowup_12..r9rrTrrr)r5rF eigenvalsr r(s rs%test_issue_17247_expression_blowup_12rasSq!34A T 5{{}AqsAq! 4444555s #AAc tddtz tdzdtz gdtz tdzdtdzgddtz tdzdtz gdddtz dgg}|j}|dddtgdgfk(sJ|ddttdtdz zz dzk(sJ|dddk(sJ|dddj ddtt tdtdz zzdz tdz z gdtztdzdtzz dzz tdzttdtdz zz dzztdzdtzz dzz zgt tdtdz zzdz tdz z gdggk(sJ|ddttdtdz zzdzk(sJ|dddk(sJ|dddj ddtt tdtdz zz dz tdz z gdtztdzdtzz dzz tdzttdtdz zzdzztdzdtzz dzz zgt tdtdz zz dz tdz z gdggk(sJy) Nrrr)rrrrFT)deepnumerrP)r5rc eigenvectsrr)revs rs%test_issue_17247_expression_blowup_13rgs Aq1ua!e$ QA1a!e$ Aq1ua!e$ A1q5!$ & 'A B a5QF=123 33 3 a58q47AE?*Q. .. . a58q== a58A;  5  5 "tAwA  "QU +, Aq!taczA~ !a%!d1gq1uo*=*A!BAqD1Q3JQRN!S ST "tAwA  "QU +,  A:   a58q47AE?*Q. .. . a58q== a58A;  5  5 "tAwA  "QU +, Aq!taczA~ !a%!d1gq1uo*=*A!BAqD1Q3JQRN!S ST "tAwA  "QU +,  A:  rrctdddtzdtz gdzdtz dtzgdzzdz}td5|jttdzdtz tdzdtz tdzdtz tdzdtz gddtzddtzddtzddtzggdgdgdgdgdgdgk(sJ dddy#1swYyxYw)NrrrTrrS)r5rcrF echelon_formr(s rs%test_issue_17247_expression_blowup_14rjsq!qsAaCjlac1Q3Z\1145A T  G~~6 UAE1q5!a%QAq1ua!e DacqAaCQ!A#1! D D D D D D D+F$GG GG G G Gs BC&&C/ctdddtzdtz gdzdtz dtzgdzzdz}td5|jttdzdtz tdzdtz tdzdtz tdzdtz ggtddtzddtzddtzddtzgggk(sJ dddy#1swYyxYw)NrrrTr)r5rcrFrowspacer(s rs%test_issue_17247_expression_blowup_15rms"q!qsAaCjlac1Q3Z\1145A T Pzz|QAq1ua!eQUAPQESTWXSXZ[^_Z_(`'a bdjmnpqrspsuvxyz{x{}~ABCDADFGIJKLILmMlNeO PP PPPPPs BCC(c*tdddtzdtz gdzdtz dtzgdzzdz}td5|jttdzgdtz gtdzgdtz gtdzgdtz gtdzgdtz ggtdtz gtdzgdtz gtdzgdtz gtdzgdtz gtdzgggk(sJ dddy#1swYyxYw)NrrrT)r5rcrF columnspacer(s rs%test_issue_17247_expression_blowup_16rp!sq!qsAaCjlac1Q3Z\1145A T y}}6AE7AE7AE7AE7APQE7TUXYTYSZ\]`a\a[bdehidicj*k#lntwx{|w|v}@ADE@EFHILMHMGNPQTUPUOVXY\]X]W^`ade`e_fhilmhmgnpqtupuovvwox#yy yyyyys B:D  DctddtdDcgc] }t|z c}}td5|j tdgdgdgdgdgdgdgdggtdgdgdgdgdgdgdgdggtd gd gdgdgdgdgdgdggtd gd gdgdgdgdgdgdggtd gdgdgdgdgdgdgdggtdgdgdgdgdgdgdgdgggk(sJ dddycc}w#1swYyxYw)NrrTrrrrrrrPrrQrr:r)r5rrcrF nullspacerEs rs%test_issue_17247_expression_blowup_17rt&s]q!5":.aac./A T 8{{} QCaS!aS!aS!5 6 QCaS!aS!aS!5 6 QCaS!aS!aS!5 6 QCaS!aS!aS!5 6 QCaS!aS!aS!5 6 QCaS!aS!aS!5 6 !88 8888/88sC3 B2C88Dctdddtzdtz gdzdtz dtzgdzzdz}td5|jrJ dddy#1swYyxYw)NrrrT)r5rcrF is_nilpotentr(s rs%test_issue_17247_expression_blowup_18rw1sjq!qsAaCjlac1Q3Z\1145A T $>>####$$$s A""A+cttd}td5|jrJ dddy#1swYyxYw)Nay[ [ -3/4, 0, 1/4 + I/2, 0], [ 0, -177/128 - 1369*I/128, 0, -2063/256 + 541*I/128], [ 1/2 - I, 0, 0, 0], [ 0, 0, 0, -177/128 - 1369*I/128]]T)r5rrFis_diagonalizabler(s rs%test_issue_17247_expression_blowup_19rz6sOqab cA T )&&(((()))s =Ac ttdzdtz ddgdtz tdzdtdzgddtz tdzdgdddtdzgg}td5|jtdddtdztdz z ggdgdgdgtgdddtzddgddtdzdgdddtdzggfk(sJ dddy#1swYyxYw) NrrT)rrrrrrrrrrrrrr)r5rcrF diagonalizer(s rs%test_issue_17247_expression_blowup_20r?s UQU#UQUQU# QUQU# QU# % &A T  &}}6 AAA ' ' ' ' +)$*  " ! " !QU " !AE " $ % #& & & & & & &s #A0CC&cttd}td5|jdttdk(sJ dddy#1swYyxYw)N[ [ -3/4, 45/32 - 37*I/16, 0, 0], [-149/64 + 49*I/32, -177/128 - 1369*I/128, 0, -2063/256 + 541*I/128], [ 0, 9/4 + 55*I/16, 2473/256 + 137*I/64, 0], [ 0, 0, 0, -177/128 - 1369*I/128]]TGEmethodv[ [-26194832/3470993 - 31733264*I/3470993, 156352/3470993 + 10325632*I/3470993, 0, -7741283181072/3306971225785 + 2999007604624*I/3306971225785], [4408224/3470993 - 9675328*I/3470993, -2422272/3470993 + 1523712*I/3470993, 0, -1824666489984/3306971225785 - 1401091949952*I/3306971225785], [-26406945676288/22270005630769 + 10245925485056*I/22270005630769, 7453523312640/22270005630769 + 1601616519168*I/22270005630769, 633088/6416033 - 140288*I/6416033, 872209227109521408/21217636514687010905 + 6066405081802389504*I/21217636514687010905], [0, 0, 0, -11328/952745 + 87616*I/952745]]r5rrFr-r(s rs%test_issue_17247_expression_blowup_21rQjqcd eA T <uuDu!VA/:-;&<< <<<<< *AActtd}td5|jdttdk(sJ dddy#1swYyxYw)NrTLUrrrr(s rs%test_issue_17247_expression_blowup_22r^rrcttd}td5|jdj ttdk(sJ dddy#1swYyxYw)NrTADJrr)r5rrFr-rr(s rs%test_issue_17247_expression_blowup_23rkssqcd eA T <uuEu"))+va9:7;0<< <<<<.svaE"I6rrctddgS)Nrrrrqrrrsr~ztest_creation..svaR0rrctddSrrrqrrrsr~ztest_creation..svf~a0rrrrrrrr)rrrr rrrrrrrrrr)rrrrr)rrrrrFevaluaterrrrcBttdtddgS)Nrrrr5r<rqrrrsr~ztest_creation..4vtAwQ &;<rrcBttdtddgS)Nrrrrrqrrrsr~ztest_creation..5rrr)rrr)rRr$ IndexErrorr5rWtolistTrEmptySetrcrrrr9r3 as_immutable as_mutabler<rE) rr_rr`c23c13radatrr|M2s rs test_creationrsH :67 :01 :01  vq 8vbz 5VAq"%5 55 55 5 2$<6!Q+ ++ + 2r( vaB/ // / !?T{m$++-A3+>>>?  !CT{m$&&--/aSED6?BBBCu A  !**$ AA A A 66QVV   66Q;; Q4Aq!Q<  q!aAq\"A A 66QVV   66Q;; Q4Aq!Q<   6M6 !9>> AuQ{ #C AuQ| $CSzA 66Q;; 66Q;; Q4. .. . #a&>SV ## # ?3q62 3s1v7N NN N 1 !1 11 1 /!$ %);)F)F)H HH H F1I   1ItAay{ #d1Qik4!9Q;%? @Cs A     88:   # & - - /3 66 6S!QA 7A,C #;& A AtWagtWag "   !JcE*113S7I7IIIIJ 47DG$ %a ): :: : :<= :<= AA A F B !Q!Q!Q01 11 1W??CCh8JJJsNT 'T2T T-<T? T:%T?TT T*-T7:T??Uc  tjdtddtdddztdddztdddztdddztdddztdddztgdgdgd gd gk(sJy) Nrrrrrrr)rrrrrr)rrrrrr)rrrrrr)r5 irregularr<rqrrrstest_irregular_blockr=s   AtAay$q)A+tAay{ Qq ! T!AYq[$q)A+tAay{ .W 1q5rrrrrr)rrrrrrrrrrr r rr)rrrrr)r9rBr5)m0m1m2s rs test_slicingrRs QB bqb"1"f:Q   ac1Q3h<58 ## # 1( )B ad8vaI. .. . ac1f:1f- -- - |^=MN OB ae9q!^4 44 4 bc1f:1A BC CC Crrctd}td|ddddf<|tdk(sJtd|ddddf<|tdk(sJtddd|dddf<|tdk(sJtd|ddddf<|tdk(sJgd|ddddf<|tdk(sJddg|dddf<|td k(sJy) Nrr)rrrrrrr}rrrrrr)rrrr)rrrr)rrrr)rrrrrrrrrrrrrrrrr))rrrr)rrrrrr)rBr9r5rs rstest_submatrix_assignmentr`s$ aAa&Aac1Q3hK &' '' 'AAbqb"1"fI A;;Q<(AadG &' '' 'AhAadG a==MAadG *+ ++ +1vAbqb!eH *+ ++ +rrc`tdddjgdddgtddgdk(sJjddggd tddgd k(sJjtdtdk(sJttfd ttfd y) Nrrc|dz|zSNrrqr{s rsr~ztest_extract..}s!A#'rr)rrrrrr)rrrrrrr)rrrrrrc,jdgdgS)Nrrrrsrsr~ztest_extract..qyy!qc2rrc,jdgdgSrrrsrsr~ztest_extract..rrr)r5rrrRrrs@rs test_extractr|sq!)*A 99YA '6!Q8K+L LL L 99aVY '6!Q8K+L LL L 99U1XuQx (A -- - :23 :23rrctd}|jddtdddk(sJtddd}|jddtdk(sJ|jdd td k(sJy) Nrrr) rrrrrrrrrrc ||zSryrqr{s rsr~ztest_reshape..rrr)rrrr)rrrrrr))rrrrrr)rrrrrr)r9reshaper5rrs rs test_reshapers QB ::a va,GH HH H 1( )B :: 1 DE FF F ::a v&NO OO Orrctd}|jdtddzk(sJ|jdtdk(sJy)Nrc d|zSNrrqrcs rsr~z test_applyfunc..s !A#rrrcyrrqrs rsr~z test_applyfunc..rrr)r9 applyfuncrB)rs rstest_applyfuncrsE QB << &#a&( 22 2 << $a 00 0rrc  ttttzzdgttztztztttttzzzzgg}|j}|tttztdzzdgttdzzttdzzzttzttdzzztdzzggk(sJt dd}tt t |zgjdtt|t t|zzgk(sJtgdgdgd gj td d tddggd gd gk(sJy) Nrrr_Treal)complexr)rrrrr)rrrr) r5rcrdrrrr rrr )rrr_s rs test_expandrsW !QU)QAE19a-A1q5 M1B!CD EB B  A#1*a1QT6AadF?AaC!AqD&L1a4,?@AC CC C sA 3qs8*  $ $T $ 2A3q6!"# $$ $ 9j)4 5 9 9 ;v Ax1~G@  rrc (tttdzttdzgttdzttdzzttdzttdzzgg}|j t jtt jtz}|ttdzttgtdzttztdzttzggk(sJ|j t jtt jtz}|ttdztgttdzztdztzggk(sJ|j t jtt jtz}|ttdzt gt tdzztdz tzggk(sJyr) r5rrcrrdrefinerYrrr rs rs test_refinerst #a&!)T!Q$Z(adCFAI%tAqDz#a&!)';<> ?B 166!9qvvay( )B !Q$A!Q$s1v+q!tCF{)CDE EE E 1::a=1::a=0 1B !Q$Qq!tVQT!V$456 66 6 1::a=1::a=0 1B !Q$qbAg1uQw%789 99 9rrcztdd}tddd}|tdddk(sJtdddd}tddd}|tdddk(sJ|j}|j||k(sJtjd}|tdd|k(sJd D])}d D]"}t|d|| }||j k(r"J+td d d}d}t |jdD]/}t |jd D]}|||fdk(s|d z }1|dk(sJy)Nr)seedrrT)r symmetric)rprng)rr)rF)rpercentrrrr)minrr)r=copyr)randomRandomrrr)rrrngsizer zero_countr|r}s rs test_randomr sb1aA1aa A 1aa( (( (1aC A11-A 115 55 5 AAJJL 6M6 -- C 137 77 7$ G44sKA8O8  21b)AJ 1771:  qwwqz" AAw!|a      rrctd}|jtdk(sJ|jdtdk(sJ|jdtdk(sJ|jdtdk(sJ|jdtdk(sJ|jdtdk(sJtgdgd gd g}|j}||ztd k(sJ|jd|k(sJ|jd|k(sJ|jd|k(sJ|jd|k(sJ|jd|k(sJtgd gd gdgdgdgdgdgdgdgdgdgdgdgdgdgdgdgdgdgdgd gd!gd"gd#gd$g}|jd%|zt|jd&k(sJtgd'gd(gd)gt fd*d+j DsJtgd'gd(gd)gt fd,d+j DsJy)-NrrrrrrQR)rrr)rrr)rrrr)rrrrrrrrrrrrrrrrrrrrrrrrr)rrrrrrrrrrrrrrrrrrrrrrrrr)rrrrrrrrrrrrrrrrrrrrrrrrr)rrrrrrrrrrrrrrrrrrrrrrrrr)rrrrrrrrrrrrrrrrrrrrrrrrr)rrrrrrrrrrrrrrrrrrrrrrrrr)rrrrrrrrrrrrrrrrrrrrrrrrr)rrrrrrrrrrrrrrrrrrrrrrrrr)rrrrrrrrrrrrrrrrrrrrrrrrr)rrrrrrrrrrrrrrrrrrrrrrrrr)rrrrrrrrrrrrrrrrrrrrrrrrr)rrrrrrrrrrrrrrrrrrrrrrrrr)rrrrrrrrrrrrrrrrrrrrrrrrr)rrrrrrrrrrrrrrrrrrrrrrrrr)rrrrrrrrrrrrrrrrrrrrrrrrr)rrrrrrrrrrrrrrrrrrrrrrrrr)rrrrrrrrrrrrrrrrrrrrrrrrr)rrrrrrrrrrrrrrrrrrrrrrrrr)rrrrrrrrrrrrrrrrrrrrrrrrr)rrrrrrrrrrrrrrrrrrrrrrrrr)rrrrrrrrrrrrrrrrrrrrrrrrr)rrrrrrrrrrrrrrrrrrrrrrrrr)rrrrrrrrrrrrrrrrrrrrrrrrr)rrrrrrrrrrrrrrrrrrrrrrrrr)rrrrrrrrrrrrrrrrrrrrrrrrrBLOCKr)r1)rG^);Ac3VK|] }tj|u"ywryrr-rsrrs rsrztest_inverse.."LtAEE!H~$L&)zGE ADJ LU CH LDL QRc3VK|] }tj|u"ywryrrs rsrztest_inverse..rr)r9r-r5rr3rsplitr4)rAinvAArrs @@rs test_inverser sm AA 557c!f   555 Q '' ' 555 #a& (( ( 555 Q '' ' 555 #a& (( ( 555 Q '' '  A 557D T6SV   555  %% % 555 $ && & 555  %% % 555 $ && & 555  %% % \ W W W W W W W W W W W W W W W W W W W W W W W W1Y ZB2 666 !B &#bhhqk*: :: : C \    A L.C.I.I.KL LL L C \    A L.C.I.I.KL LL Lrrctddtdztzdtdzzttzzg}ttg}|j|tdtztztdzgtdtztzggk(sJtddttdztdzzg}|j|tddgdtztdzztdzdztdzzggk(sJtdztz}ttg}t ||tdtzdtzgdtzdggk(sJtdztdzz}t ||tdtdzzdtztdzzgdtztdzzdtdzztzggk(sJt ttdzzz}tdzdtdzzz}tddtzgdtzdtzgg}|t |tttgk(sJ|t |tttgj k(sJt |ttf|gtddtdzzdtzgdtdzzdtzdtzgdtzdtzdggk(sJy)Nrrrrrr)r5rcrdjacobianr:rer)Lsymsfganss rstest_jacobian_hessianr( sq!ad1fa1fqsl+,A q6D ::d v!Aq!t}q!A#'l&CD DD Dq!aAad^$A ::d v1v!AqD!Q$q&A+/F&GH HH H 1QA q6D 1d v!QqSzAaC8&<= == = 1QT A 1d 1a41QT"QqSAXqAvax$89: ;; ; AadF A 1qAv A 1!*Q3!* C '!VQF^, ,, , '!VQF^--. .. . 1q!fqc "f1a41 1a4AaC1 aCAaC1.'    rrc tttttgtttdzttdzzk(sJtt tt dtzgtt dtzk(sJtt ttgtt ttt tzz k(sJtdttdzgtdk(sJdt tzttztzdttzt tztdzzzdt tzttztzz t tttztdzzz t tttztdzzz}tt ttttdzgtj |k(sJtt ttttdzgtdj |k(sJtdz ttdzztdzttdzzz dtzttdzzz dtzttdzzz }ttttttdzgtj |k(sJttttttdzgtdj |k(sJtgtdk(sJy)Nrrrr:rrJr)rArrcrrr)w1w2s rstest_wronskianr,&s c!fc!f%q )SVQYQ-B BB B c!fc!A#h' +s1Q3x 77 7 c!fa[! $A3q6(9 99 9 aAqD\1 % ** * CF3q6 ! aAhs1voad2 2Qs1vXc!f_Q5F F As1v ad  VCF]1a4/ 0B c!fc!fad+Q / 6 6 8B >> > c!fc!fad+Q{ C J J L    Q$s1vqy1a4A > )AaCA M 9AaCA M IB c!fc!fad+Q / 6 6 8B >> > c!fc!fad+Q{ C J J L    R q  rrctdtgtdggjtdtddgddggk(sJttdgttzdggjtdgtdggtddgddggk(sJttdgttzdggjtdftdfgtddgddggk(sJttdgttzdggjtdtditddgddggk(sJtttzgjttdz ttdz id ttdz tdz zgk(sJtD]7}tdd gd dgg|j djddk(r7Jy) NrrrrrrrT) simultaneousr)r5rcrrdrr9rs rs test_subsr07s Aq6Aq6" # ( (A .&1a&1a&9I2J JJ J Aq6AE1:& ' , ,q"g2w-? @Q"a!" ## # Aq6AE1:& ' , ,q"g2w-? @Q"a!" ## # Aq6AE1:& ' , ,aQ^ <Q"a!" ## # 1Q3%=  q!a%AE2  FQQ ! "" "A1v1v&'3771:??1a+@@@@Arrctdtgtdggjtditddgddggk(sJttdgttzdggjtdtditddgddggk(sJtD]8}tddgddgg|j djddik(r8Jy) Nrrrrrrrr)r5rcxreplacerdrr9r/s rs test_xreplacer3Es Aq6Aq6" # , ,aV 4AA  !! ! Aq6AE1:& ' 0 0!RB @Q"a!" ## #G1v1v&'3771:+>+>1v+FFFFGrrc td}td}tdtz dtz ztttzztz g|tt|tzz|tz dd|z t |t z|z z zt z gg}|j|tttzttzz dtzgdtzdddt t |zzz t |zz zggk(sJdtzdz}t|gg}|j|t|ggk(sJ|jt|t|jtggk(sJy)Nrr%rr)ratio) rrr5rcrdrrr)r)rr%reqs rs test_simplifyr7Ms\s A AQqS1Q3YQqSA HQ4!AaD&=!A$&QqS3q2v;q=-@(AB(FHJ KAJJL 1q51q5/!a%I$%E1q1SAY;A.F+GIKL LL L a%!BvAJJL v  JJRJ 2./01 11 1rrc tgdgdg}|jtddgddgddgddgddgddgddgd d gd d gd d gg k(sJ|jj|k(sJ|j|jk(sJy) N) rrrrrrrrrrrrrrrrrrrr)r5rrr(s rstest_transposer9^s..0 1A 33&QFFFFFFFFFF % & & & & 3355A:: 33!++-  rrctdtdggdg}|jtddgtdgddggk(sJ|jtdt dggdgk(sJ|j|j k(sJ|j |jjk(sJ|j tddgt dgddggk(sJy)Nrr)rrrrr)r5r rr conjugateHr(s rstest_conjugater=osAq  A 33&1a&a&a&"# ## # 33&1qb!*$&' '' ' 33!++-   33!##%%<< 33&Aq'2q'q'#$ $$ $rrc "ttdtdtttgddttgdddtggdg}|jtgdt dddgt t ddgt t tdggk(sJy)Nc,tdjSr)r9Drqrrrsr~z!test_conj_dirac..s3q688rrrrr}rr)rRAttributeErrorr5r r@r(s rstest_conj_diracrBs >+,Aq! Aq! Aq!  A 33&*2A*2r2*2rAr*,- -- -rrcVtgdgdgdg}|jdk(sJy)Nrrrrrr)rrrrr5tracer(s rs test_tracerHs-  A 779??rrc\ttddgdtdgg}|jdk(sJy)Nrr)r5rcrdrr(s rs test_shaperJs4Aq Aq  A 77f  rrcttddgdtdgg}|jdd|ttddgdtdzdggk(sJ|j dd|ttdzddgdtztdzdggk(sJ|j dttdzddggk(sJ|j d}d|d<|dtdzk(sJ|ddd f}d|d<|dtdzk(sJ|j d}|ttdzdtzgk(sJd|d<|dtdzk(sJ|dddf}d|d<|dtdzk(sJy) Nrrc||zdzSNrrq)rr}s rsr~z!test_col_row_op..sQUQYrrrrc|t|zzSry)rd)rar}s rsr~z!test_col_row_op..sQAXrr*rr)r5rcrdrow_opcol_oprowcol)rr1c1s rstest_col_row_oprWsAq Aq  AHHQ&' 1 AE1 '( (( (HHQ%& QAq)QAq)+, ,, , 558vAq!}o. .. . qB BqE T7a!e   1crc6B BqE T7a!e   qB QA' '' ' BqE T7a!e   1a4B BqE T7a!e  rrctgdgdg}|jdd|ddk(sJ|ddk(sJ|dd k(sJy) Nrrrrrrrrrrr)r5row_multr(s rs test_row_multr[sS AJJqO S6R<< S6Q;; S6R<.AaCrrrDrrrrrrc|d|zzSrrqrcs rsr~z!test_zip_row_op..rerr)rrr)rrrr)rr9 zip_row_op)rrs rstest_zip_row_oprisr{ & GGAJ Q/0C""$%% %% GGAJqL$ Q/0!C##%&& && &rrctgd}tgd}tgd}|dvsJ|dvsJ|dk7sJ||k(sJ||k7sJy)Nr)rrrrq)rrr)rr_r`s rstest_issue_3950rksYyAyAyARS 6M6 6M6 6M6rrcdGdd}Gdd}|}|}tgd}||dk(sJd||<|ddk(sJtgdgd g}|||fd k(sJ|d |fd k(sJ||dfd k(sJd |||f<|d d k(sJd |d |f<|d d k(sJd||df<|d dk(sJy)NceZdZdZy)test_issue_3981..Index1cyrMrqselfs rs __index__z)test_issue_3981..Index1.__index__rrNrnrorprrrqrrrsIndex1rn rrruceZdZdZy)test_issue_3981..Index2cyrrqrps rsrrz)test_issue_3981..Index2.__index__rsrrNrtrqrrrsIndex2rxrvrrrzrrrrrYrrrrrr)rurzindex1index2rs rstest_issue_3981r}sXF XFyA V9>>AfI Q4199 9%&A VV^  !! ! QY<1   VQY<1  Affn T7a<<AaiL T7a<<AfaiL T7a<.s,>wqwwy|qtzz|+>25rc3rK|].}jd||jdk(0ywrNrrs rsrztest_evalf..s0@!wqwwqz!}! 1 -@47c3rK|].}jd||jdk(0ywrrrs rsrztest_evalf.. s08!sqss1vayAaDFF1I%8r)r5rrrr_s@rs test_evalfrs]Q|A >U1X> >> > @uQx@ @@ @ 8uQx8 88 8rrcJtttgttgg}|jdusJtgdgdg}|jdusJtgdddtdgg}|jdusJtdtd gg}|jdusJtgd g}|jdusJtdgtgd gg}|jdusJtdgd gd gg}|jdusJy) NTrrFrrrrrrr)r5rc is_symbolicrs rstest_is_symbolicr s#AA A 1==?d "" " l+,A 1==?e ## # q!Ql+,A 1==?d "" "Aq {A 1==?d "" " {A 1==?e ## #aS1#A 1==?d "" "aS1#A 1==?e ## #rrctgdg}|jdusJtdgdgdgg}|jdusJtdd}|jdusJy)NrTrrrFr)r5is_upperrBrs rs test_is_upperrse {A ::  aS1#A ::   a A ::  rrctgdg}|jdusJtdgdgdgg}|jdusJy)NrFrrrT)r5is_lowerrs rs test_is_lowerr&sH {A ::  aS1#A ::  rrctddgd}|jsJtddgddgg}|jrJtg}|jsJy)Nr)rrrrrrrrrrrrrrrrrrr5rvrs rstest_is_nilpotentr-sgq!EFA 1>>  AA Aq~~ r A 1>>  rrc|d\}}t||}|jddt||z}||k(sJ|j|jcxk(rdk(sJJ|j|jcxk(rdk(sJJ|j |j cxk(rdk(sJJtdtddk(sJtdtddk(sJtddt dddgdzk(sJtddt dddgdzk(sJ|jd|t||k(sJy)N)rrrrrrrr)rBfillr<rrrr5)rrr_r`s rstest_zeros_ones_fillr6s7 DAq a A AFFAK DAJA 6M6 66QVV q   66QVV q   77agg ' '' '' ' 8uQ{ "" " 7d1aj  A;&As1u- -- - 1:1qc!e, ,, , AFF1I a  rrctd}|tk(sJtdd}|jdk(sJ|jdk(sJtdd}|jdk(sJ|jdk(sJy)Nrr)rBr5rrrs rstest_empty_zerosrKso aA == a A 66Q;; 66Q;; a A 66Q;; 66Q;;rrc ttdzttzgtttztt tzgg}|j ttdtztgttt tggk(sJttt tdzgt tdtz t t z tdtz zggjttttt tgtdtggk(sJtt tdz tz dtzttzzttzgdtz tttttdzggjtdtgdtdtdggk(sJ|jtttddtdzzttdzzdz gtdzttzdz tdzt tzdz ggk(sJy)Nrrr)rrrr) r5rcrdrrrrlimitrrrr rs rstest_issue_3749rVsAqs aAh#a&123A 166!91a3q63q6*:;< << <  QB1 Q1sA2wAaC(* ++05B<bS" Ar{+, -- -  a&1*a1qsAqD* 1c!fc#a!e*o&( )).q! B3q6?+, -- - 1;;q>V !Q1 a1fQh' Ac!fQ1SV A &%() )) )rrctd}|jdddD]+}|j|d|jdk(r+Jy) Nrrr)rrc |dk(Srrqrs rsr~z%test_inv_iszerofunc..js arr)r iszerofuncrr)r9col_swapr-)rrs rstest_inv_iszerofuncrfsV AAJJq! uuF/?u@ EEE     rrc&td\}}t|t|z|t|zg}t||g}|j |}||j |j k(sJ||j j |k(sJ||j j |j k(sJ|j t |jdz|z}|jt}|tddgd|dzggk(sJy)Nrho,phirrr) rr5rrr"rr9rrr*)rhophiXYr0r&s rstest_jacobian_metricsrnsy!HCCH c#c(l+,ASzA 1 A  133   q! !! ! qss# ## # C OAA HA ACF ,- -- -rrc<td\}}t|t|z|t|z|dzg}t||g}tt|| t|zgt||t|zgd|zdgg}|j ||k(sJy)Nrrr)rr5rrr")rrrrr0s rstest_jacobian2r{sy!HCCH c#c(lCF34ASzA SC4C=! SCCL! cEq! A ::a=A  rrcttttztztttztztttztzg}ttttg}t ddD]z}t ddD]i}|d|ddf}|d|ddf}|j |}|j|k(sJ|j|k(sJt |D]}|dd|f|k(rJk|yNrr) r5rrcrdrerr"rr)rrr|r}X_sliceY_slicer0rs rstest_issue_4564rsAEAIAEAIAEAI?@A1ayA 1a[*q! *AAhGAhG  )A66Q; ;66Q; ;1X *Aw'))) *  **rrcttttztztttztzgtttztztttztzggt t fddddftttgttggt t fdt t fdy)NcVjttttgSryr"r5rcrdrersrsr~z(test_nonvectorJacobian..sajjAq ):;rrrc&jSry)r"rrsrsr~z(test_nonvectorJacobian..sajjmrrcdjtttgttggSryrrsrsr~z(test_nonvectorJacobian..s"ajj1a&1a&0B)CDrr)r5rrcrdrerR TypeErrorrs@@rstest_nonvectorJacobianrsQUQYQUQY0QUQYQUQY02 3A 9;< !Q$AAA A 9+, 9DErrctddgddgg}|j}|jdk(sJtdD]}|||dzk(rJyNrrrr)r5vecrr)rm_vecr|s rstest_vecrs]AA A EEGE ::?? 1X!Qx1q5   !rrctddgddgg}|j}|jdk(sJtdD]}|||dzk(rJ|jd}|ddk(sJtdttt zzgt tztdzzdgg}|jd}|dt tztdzzk(sJtdttt zzgt tzdgg}|jdd}|dt tzk(sJt tdt td t td t td y) NrrrF)diagonalr)rcheck_symmetryc:tddggjSrr5vechrqrrrsr~ztest_vech..v1vh/446rrc@tddgddggjSrrrqrrrsr~ztest_vech..!v1v1v&67<<>rrc:tddggjSrrrqrrrsr~ztest_vech..rrrc@tddgddggjSrrrqrrrsr~ztest_vech..rrr) r5rrrrcrdrRr+r$)rm_vechr|s rs test_vechrsOAA A VVXF ;;!   1X"ayAE!!!" VVUV #F !9>>Aq1uI1q!tQ01A VVUV #F !9!ad "" "Aq1uI1a)*A VVU5V 9F !9!   :67 :>? :67 :>?rrctgdtgdk(sJdddggttfdtdtgdk(sJy)NrrrrctSry)r8rsrsr~ztest_diag..s tAwrrF)strict)r8r5rRr$rs@rs test_diagrsK  ?fY/ // / As A :' % F9$5 55 5rrc@tddgddgg}tdtgtdgg}tdtdgtdtgtttgg}|j|gk(sJ|j|gk(sJ|j|gk(sJyNrrr)r5rcrdreget_diag_blocksr_r`ras rstest_get_diag_blocks1rsAA AAA AAq Aq!9q!Qi01A 1   1# %% % 1   1# %% % 1   1# %% %rrctddgddgg}tdtgtdgg}tdtdgtdtgtttgg}t |||j |||gk(sJt |||j |||gk(sJt |||j |||gk(sJt |||j |||gk(sJyr)r5rcrdrer8rrs rstest_get_diag_blocks2rsAA AAA AAq Aq!9q!Qi01A 1a= ( ( *q!Qi 77 7 1a= ( ( *q!Qi 77 7 1a= ( ( *q!Qi 77 7 1a= ( ( *q!Qi 77 7rrc tddgddgg}tdtgtdgg}tdtdgtdtgtttgg}t |||}|j dt |j |j |j k(sJt |||}|j dt |j |j |j k(sJt |||}|j dt |j |j |j k(sJt ||||||}|j dt |j |j |j |j |j |j k(sJ|j ddt |j d|j d|j d|j d|j d|j dk(sJy) NrrrT)try_block_diagr)rrr)r5rcrdrer8r-)r_r`rars rstest_inv_blockrsAA AAA AAq Aq!9q!Qi01A Q1 A 555 %eaeeguquuw)H HH H Q1 A 555 %eaeeguquuw)H HH H Q1 A 555 %eaeeguquuw)H HH H Q1aAA 555 % %!%%'51557EAEEGUQUUW*> >> > 55U5 3t UUQUU%0%!%%u2E UUQUU%0%!%%u2E8G GG Grrc\ttdttdtt dtdk(sJtt dtdk(sJttdt t dt dk(sJt t dt dk(sJttdtt dt dtddk(sJttdttdttd y ) zg Check that matrix dimensions can be specified using any reasonable type (see issue 4614). ctddS)NrrrBrqrrrsr~z$test_creation_args..s uQ|rrctddddSNrrrrrrqrrrsr~z$test_creation_args..seAq!Q/rrrctdSN@rrqrrrsr~z$test_creation_args..s uRyrrctdSrr9rqrrrsr~z$test_creation_args..s s2wrrrctdSNrrrqrrrsr~z$test_creation_args..s fQirrctddSrrrqrrrsr~z$test_creation_args..s fQlrrctddggSrrrqrrrsr~z$test_creation_args..svq1#h/rrN)rRr$rrBrzr r9r<rqrrrstest_creation_argsrs  :+, 9/0 Q=E!H $$ $  a (( ( :() s1v;#a&  wqz?c!f $$ $ :' A #tAqz 11 1 9'( 9*+ :/0rrc jtddgd}|jrJ|jsJ|jdsJtddgd}|jsJtddd}|jsJ|jsJtddgd}|tdddk(sJtddt dd}|jrJ|jsJtd }|jsJtd }|jsJtdddt dzdt zzdzt t dzdzdd t d dg }|jsJ|jdrJ|jjdsJy) NrrrrrFr)rrrrrr) rrrrrrrrr))rrrr)rrr)rrrr)r5 is_diagonal is_symmetricr8rBrcrdrrs rstest_diagonal_symmetricalrsq!\"A}}  >>   >>5> )) )q!\"A ==?? Q1 A ==?? >>  q!01A Q1  q!U1a[!A~~  ==??'(A ==??%&A ==??q!aA!aQUQJ1aAFGA >>  ~~u~-- - 88: " "E " 22 2rrctddtzgdtz dggjsJtddgdjrJjrJt t fdt dddj\}}|tdk(sJ|k(sJtddgdjsJjsJj\}}|jz|z|k(sJtddgdjsJjsJj\}}|jz|z|k(sJ|tdk(sJ|k(sJtddgdjsJj\}}|jz|z|k(sJtddgd jsJj\}}|jz|z|k(sJ|D]}|jddk(rJtddgd jsJjsJj\}}|jz|z|k(sJ|td dgdd ggk(sJtddgd jd rJt tfdjsJj\}}|jz|z|k(sJtddgdjrJt tfdtddgdjrJt tfdtd\}}}}tdd||||gjsJjsJy)Nrrrrrrrrrc$jSryr~rsrsr~z&test_diagonalization..% rrr)rrrrrrrr) rrrrrrrrPrrr)rrrrTc&jdS)NTrrsrsr~z&test_diagonalization..Qs d 3rrrc$jSryrrsrsr~z&test_diagonalization..Y  rr) rrrrrrrrrc$jSryrrsrsr~z&test_diagonalization..]rrra b c d)r5r ryrrRr-r8r~r9r-as_numer_denomrr,r)r/r@r|r_r`rarbrs @rstest_diagonalizationrsAaC1Q3(#$A    q!+,A""$$ $~~  !89 Q1 A ]]_FQ A;; 6M6q!\"A >>      ]]_FQ 557Q;?a  q!\"A >>      ]]_FQ 557Q;?a   A;; 6M6q!\"A    ]]_FQ 557Q;?a  q!12A    ]]_FQ 557Q;?a   *!!$)))* q!\"A ==??    ]]_FQ 557Q;?a   AA'( (( ( q!]#A""4(( ( ;34    ]]_FQ 557Q;?a   q!\"A""$$ $ ;/0q!56A""$$ $ ;/0#JAq!Qq!aAq\"A >>      rrctddgddggjdusJdd<jdusJtddgddggjdd<ttfdy)NrrTrFc&jSryrrsrsr~z"test_issue_15887..ps  rr)rCryr~rRr,rs@rstest_issue_15887rfsQFQF+,A 1   D (( (AdG 1   E )) )QFQF+,AAMMOAdG ;/0rrctddgdttfdtddgdtddgd}j\}}||k(sJ|j dk(sJtddgdtddgd }j\}}||k(sJtddgd tddgd }j\}}||k(sJtddgd tddgd }j\}}||k(sJtddgdtddgd}j\}}||k(sJtddgdtddgd}j\}}||k(sJtddgdj rJtddgd}j\}}||k(sJtt ddt ddgt ddt ddggj\}}|jD]$}t|t s|jdk(r$Jy)Nrrrc$jSry)r,rsrsr~z"test_jordan_form..vrrr) rrrrirrir) rrrrrrrrrr rrrrPrrrrr) rrrrrrrrr) rrrrrQrrr:) rrrrrrrrr) rrQrrrrrrr) rrrrrrrrrr)rrrrrrrrrrrrrrrr)rrrrrrrrrrrrrrrr)rrr:rrrrrrrr:rrrr)rrrrrrrrrrrrrrrr)rrrrrrrrrrrrrrrr)rrrrrrrrrrrrrrrrz1.0n) precisionz2.0z3.14159265358979323846264338327z4.0) r5rRr-r,r~ryr valuesr_prec)Jmustr/r0termrs @rstest_jordan_formr sssq!+,A !89 q!:;A 1a5 6E ==?DAq A:: AMMOA& && & q!23A 1a4 5E ==?DAq A:: q!45A 1a7 8E ==?DAq A:: q!34A 1a4 5E ==?DAq A::q!LMA 1a E ==?DAq A::q!LMA 1a' (E ==?DAq A::q!JKA""$$ $ 1aI JE ==?DAq A:: u,eES.IJ8CH%PUadJefh iA ==?DAq % dE "::$ $$%rrc dtgdgdgdgdg}ddtzz }ddtzz}t|dddgd|ddgdd|dgddd|gg}t|dddgd|ddgdd|dgddd|gg}|j\}}||k(s||k(sJt||z|j z|k(sJy) N)rrrr)rPrrr)rrrr)rrrPrrrrr)r5r r,r)r-)rpqJmust1Jmust2r/r0s rs#test_jordan_form_complex_issue_9274rs    " #A AaCA AaCA aAq\Aq\Aq\Aq\#$FaAq\Aq\Aq\Aq\#$F ==?DAq ;!v+% % AaCK A %% %rrctgdgdgdgdg}|j\}}|tgdgdgdgdgk(sJ|tgd gdgdgdgk(sJy) Nrr)rrrrr}rrrrrrrr)r5r,r.s rstest_issue_10220rs  A ==?DAq  $$$&' '' ' $$$$ &' '' 'rrc tgdgdgdgdg}|j\}}|jtt t dz ttdz gdtzddtz dgdt d dz tdz z dt d dz tdz zggd gk(sJ|tt dddgdt ddgddtdgdddtggk(sJy) Nr|rrrrrrrrrrrrrrrrr)r5r,rr r)rr/r0s rstest_jordan_form_issue_15858rs  A ]]_FQ 88:R1"Q$Q!A#6 aQQA6!A$q1Q3Q1a!A# 66 !89 99 9  Q1 QB1 Aq! Aq!   rrcNtd\}}}t| |z |dz||zz z||z||zz g||z||zz | |dz||zz zgg}|jt}|t tdz||z||zzd|z|zz||zz tzz||z|z||zz ztdk(sJt |t usJtddgddgg}|j|jtcxk(r t tdztz dz k(sJJtddgtdgg}|jt}|jtk7sJ|jj|jttdzdtzz k(sJy) Nz UA K_i K_wrzZZ(K_i,K_w,UA)r=rrrr) rr5r?rcr#rr$genas_exprr)UAK_iK_wrr?rs rstest_Matrix_berkowitz_charpolyr"s<(LBS#S!VS3Y//s3wc 7JKGS3Y/#Qc 8J1JKM NAzz!}H  QTSVc"f_quSy039=a? ? C C#I !*: < << < >X %% %AA A ::<1::a= BHQTAX\,B BB BB BAA A 1 A 55A:: 99;  AEE1 %A! 33 3rrc td}tjd|}|jtt |ggk(sJtjd|}|jtt |t |t |dz gdt |t |gddt |ggk(sJy)Nlamdarrrr)rr5 jordan_block_eval_matrix_exp_jblockrlrs rstest_exp_jordan_blockr) swAAq!A $ $ &&3q6(*< << <Aq!A $ $ & VSVSVAX & AA  3q6N   rrc tddgddgg}ttddtdzdz dtdzdz zgdtdgg}|j|k(sJt||k(sJtddgddgg}|jttdgdtggk(sJt|ttdgdtggk(sJtddgddgg}|jtttdzt t dzgtt dzttdzggk(sJy) NrrrrrPrrr)r5rrrr)rm_exps rstest_expr,s<AB !A SVRBZ\Ac!fHQJ67!SWF GE 557e   q6U??AA A 557fq!fq!f-. .. . q6VaVaV,- -- -B!Q !A 557fqQx!CF3aAh#a&5IJK KK Krrc td}tjd|jtt |ggk(sJtjd|jtt |d|z dd|dzzz dd|dzzz gdt |d|z dd|dzzz gddt |d|z gdddt |ggk(sJtgdgd gd gt t fd y) Nr$rrrrrrrrrc$jSry)rrsrsr~ztest_log..=s rr)rr5r%_eval_matrix_log_jblockrrRr,r's @rstest_logr0'swAAq!A $ $ &&3q6(*< << <Aq!A $ $ &Q1b!AqD&k1a1f:6CFAaCQq!tV-As1vqs#Aq#a&!          A  ;(rrctttfdf}|jtsJ|jtrJ|jt sJ|j td}|jtrJy)Nrr)r5rcrdhasrerrrs rstest_hasr3@seA A 558O8uuQx< 55== q! AuuQx>rrc ftd}tdd|t|dzt|dzz|zt|dzt|dzzg}t |t \}}}}t |dk(sJ|dddk(sJ|ddd|zk(sJ|dddk(sJ|dddk(sJy)Nrcrrrr=r)rr5rrr0r1lenr5s rs+test_find_reasonable_pivot_naive_simplifiesrBes s A AqVQYs1vqy(*VQYs1vqy(*+F %Vi@?L)2J z?a   a= q  a= qs "" " a= q  a= q  rrcPttdttdttdttdttdttdttdtt dttd ttd ttd ttd tt d ttdttdttdttdttdttdttdttdttdtt dttdttdtt dttdtt dttdtt dtt dtt d ttd!ttd"ttd#ttd$ttd%ttd&ttd'ttd(t d)ttfd*t gd+gt gd,gd-gd.gttfd/t gd,gd-gd.gttfd0y)1Nc"tddgdggSrrrqrrrsr~ztest_errors..xsv1vsm4rrc$tddggdS)Nrr)g333333?rrrqrrrsr~ztest_errors..yv1vh/7rrc$tddggdS)Nrr)rg@rrqrrrsr~ztest_errors..zrFrrctdddS)NrrT)rar)r=rqrrrsr~ztest_errors..{sz!qDArrc<tddgjddS)Nrrrr)r5rrqrrrsr~ztest_errors..|svq!f~55a;rrc^tddgddggjddgtddgSNrrrrr)r5 copyin_matrixrqrrrsr~ztest_errors..~s1AA'(661vvq!f~NrrcXtddgddggjddgtSrK)r5 copyin_listsetrqrrrsr~ztest_errors..s3fq!fq!f%56BBA Durrc@tgdgdgjS)Nr)rrrr5r-rqrrrsr~ztest_errors..sI0F)G)K)K)Mrrc\tddddgjtddgddggSr)r5row_joinrqrrrsr~ztest_errors..s0q!aV$--fq!fq!f5E.FGrrcXtddgjtddgddggSr)r5col_joinrqrrrsr~ztest_errors..s+FAq6N33FQFQF;K4LMrrcXtdgjdtddgddggSr)r5 row_insertrqrrrsr~ztest_errors..8vqc{55a! B1vA: rrcXtdgjdtddgddggSr)r5 col_insertrqrrrsr~ztest_errors..rXrrc8tddgjSrrFrqrrrsr~ztest_errors..sA)=)=)?rrc8tdgjdSrM)r5rrqrrrsr~ztest_errors..sfaSk33A6rrcDtddgddggjddSNrrrrr)r5minorrqrrrsr~ztest_errors..s%v1v1v&67==aCrrcDtddgddggjddSr^)r5minor_submatrixrqrrrsr~ztest_errors..s%v1v1v&67GG1Mrrc:tgdjdSNrrr5crossrqrrrsr~ztest_errors..sfY/55a8rrc:tgdjdSrcr5dotrqrrrsr~ztest_errors..sfY/33A6rrcPtgdjtddgS)Nrrrrgrqrrrsr~ztest_errors..svi044VQF^Drrc:tddgjgSrrgrqrrrsr~ztest_errors..svq!f~11"5rrc:tddgjdS)Nrrr_rgrqrrrsr~ztest_errors..sfaVn005rrc>tddgjgdS)Nrrrrgrqrrrsr~ztest_errors..svq!f~11)<rrc8tgdjS)Nr)r5rrqrrrsr~ztest_errors..s ):)>)>)@rrc@tddgddggjSr)r5 normalizedrqrrrsr~ztest_errors..!v1v1v&67BBDrrc<tddgjdS)Nrrz not a methodrrQrqrrrsr~ztest_errors..svq!f~111Hrrc8tddgjSrr5 inverse_GErqrrrsr~ztest_errors..A)B)B)Drrc@tddgddggjSrrsrqrrrsr~ztest_errors..rprrc8tddgjSrr5 inverse_ADJrqrrrsr~ztest_errors..sA)C)C)Errc@tddgddggjSrrxrqrrrsr~ztest_errors..s!v1v1v&67CCErrc8tddgjSr)r5 inverse_LUrqrrrsr~ztest_errors..rurrc8tddgjSrrrqrrrsr~ztest_errors..sA)D)D)Frrc8tddgjSrr5rDrqrrrsr~ztest_errors..sA););)=rrcDtddgddggjdS)NrrrrzNot a real methodrrrqrrrsr~ztest_errors..s'AA'(,,4G,HrrcPtgdgdgdgdgjdS)Nrrrrz Not functionrrrqrrrsr~ztest_errors..s) l)+,,/C>C,JrrcPtgdgdgdgdgjdS)NrrrrFrrrqrrrsr~ztest_errors..s) l)+,,/C5C,ArrcVttddgddggtddgddggSrr:r5rqrrrsr~ztest_errors..s1AA/0&1a&1a&9I2JKrrc8ttddgddgggSrrrqrrrsr~ztest_errors..swv1v1v.>'?Drrc2ttddzdS)Nrcrr_)r:rrqrrrsr~ztest_errors..swvc{A~s;rrctddS)Nr)rrrrqrrrsr~ztest_errors..s1vd|rrctddS)Nr)rrrrqrrrsr~ztest_errors..rrrrc&jdS)Nzmethod=LU_decomposition())rDr(srsr~ztest_errors..squu%@Arr)rrrrrrrrc(jdS)Ng@)rWrVsrsr~ztest_errors..sq||C3rrc(jdS)Ng)rZrsrsr~ztest_errors..sq||D!4rr)rRr$rr+rr-r5rs@@rs test_errorsrwsI :45 :78 :78 :AB :;< :NP 9 !MN :GI MO : : !?@ 967 :CD :MN 989 967 :DE :56 956 :<= !@A :DE :HI !DE :DE !EF :EF !DE !FG !=> :HJ : KL : BC :KM :DE :;< :+, :+,NOA :AB ~A 9i01A :34 9i01A :45rrcttdk(sJttddggttdgdggcxk(rdk(sJJttdddttdddcxk(rdk(sJJttgdgdgdk(sJtdgtdggk(sJtrJttgk(sJy) Nrrrcyrrqr{s rsr~ztest_len..rrrcyrrqr{s rsr~ztest_len..rrrrrr)rAr5rqrrrstest_lenrs vx=A   v1vh CaSz(:$; @q @@ @@ @ vaN+ , F1a () /-. // // / vy),- .! 33 3 1#;&1#- '' 'x< 8vbz !! !rrc ,tddtftddfddtdzff}|jtttdtztdzdz fttzdtzdtzfdtzdtztdzdz ffk(sJ|jtttdtzttzftdzdz dtzdtzfdtzdtzttdzzffk(sJy)Nrrrrrr)r5rcrdrrs rstest_integratersAq Aq!9r1adm45A ;;q>AaCAa 1Q3!QqS/BqD!A#q!tAv3FGH II I ;;q>AaC1 1Q!QqS1BqD!A#qAv3FGH II Irrctddtttz ftddfddtdzdzff}|j tdtdtddfdfk(sJy) Nrrrrrr)rrr)rrr)r5rrcrdrrs rs test_limitrsaAs1vax 1a)b!QTAX->?@A 771a=FI1ay*#EF FF Frrc 4tddtftddfddtdzdzff}t|j tt |sJ|j ttdddddtzffk(sJ|j ttd k(sJt |ttdddddtzffk(sJt |ttd k(sJ|j }t|j tt |sJ|j ttdddddtzffk(sJ|j ttd k(sJt |ttdddddtzffk(sJt |ttd k(sJ|j td t|td k(sJt |td t|td k(sJy) Nrrrrrrrr)rrDrFr) rCrcrdrrrrrDr[)rA_imms rs test_diffrsQ1I1ay2q!Q$(2CDEA affQia )) ) 66!9*Iy1a1++NO OO O 66!9*+LM MM M 1:+Y Aq!A#;,OP PP P 1:+,MN NN N NN E ejjmT%[ 11 1 ::a=0)YAqQRs 1TU UU U ::a=01RS SS S q>19i!QPQRSPS2UV VV V q>12ST TT T 66!e6 $1u(M MM M 1u %A)N NN Nrrc tttgttgg}|j |t ddgddggddgddgggddgddggddgddggggk(sJt ||t ddgddggddgddgggddgddggddgddggggk(sJ|j}|j |t ddgddggddgddgggddgddggddgddggggk(sJt ||t ddgddggddgddgggddgddggddgddggggk(sJ|j ttddgddggk(sJtttg}|j |t jddddk(sJ|j |t ddgddggddgddgggddgddggddgddggggk(sJ|j ttgg}|jdk(sJ|t dgdggdgdgggk(sJtd}|ttt}|j tttggt |j t|j t|j tgk(sJ|j tttgdft |j td|j tt|j ttg|j tt|j td|j ttg|j tt|j tt|j tdggk(sJttttz}|j ttggt t!tttzttttzgk(sJ|j tttfft t!tttzttttzgk(sJ|j tttfft tt ttzt!tttzgk(sJ|j ttffttggt t!tttztt ttzgttttzt!tttzggk(sJ|j tj tj t|j tttffddk(sJ|j tj tj t|j tttffddk(sJ|j tttggtttfft tttfDcgc]?}tttfDcgc]"}|j |j |$c}Ac}}k(sJtj t#ttgg} t%| tsJ| t#ddggk(sJtdzj t#ttgg} t%| tsJ| t#dtdzzdggk(sJycc}wcc}}w) Nrrr)rrrr%rrrf)rCrcrdrerfrrZrr_rDr`rBrrrrrr5r) rrrdBr%fxyzexprr}r|ress rstest_diff_by_matrixrs QFQF+,A 66!9!Q!Q 0Aq6Aq62BC1vPQSTvFVZ[]^Y_bcefagXhEijk kk k 1:1a&1a&!1QFQF3C DAQRTUPVGW[\^_Z`cdfgbhYiFjkl ll l NN E ::e !Q!Q(8Aq6Aq6:J'KPQSTvXY[\W]N^bcefagjkmnio`pMq&r s ss s u 1a&1a&)9QFQF;K(LQRTUPVYZ\]X^O_cdfgbhklnojpaqNr's!t tt t 66!9*QFQF+;< << <aV$A 66!9 Aq!Q/ // / 66!9!Q!Q 0Aq6Aq62BC1vPQSTvFVZ[]^Y_bcefagXhEijk kk k !Q B 88y  !qc aS1#J/0 00 0 A Q1:D 99q!Qi[ !UDIIaL$))A, RS +U%V VV V 99q!Qi^ $ 1a$))Aq/499Q?; 1a$))Aq/499Q?; 1a$))Aq/499Q?;/)   q6#a&=D 99q!fX %QAAs1v (F"G GG G 99Q!Q "eSVCF]CF3q6M,J&K KK K 99Q!Q "ec!fWSV^SVCF],K&L LL L 99q!fY!Q )USVCF]SVGCPQFN4SVYZ[V\]`ab]cVcehijeklopqlrerUs3t-u uu u 99Q<  Q  $ $Q '499q!Qi\1+Eg+N NN N 99Q<  Q  $ $Q '499q!Qi\1+Eg+N NN N 99q!Qi[Aq!9, /5noqrtumv9whiZ[]^`aYb:cTU499Q<;L;LQ;O:c9w3x xx x &&!Q! "C c/ 00 0 &1a&" "" " a4++fq!fX& 'C c/ 00 0 &1QT61+' '' ';d9ws;^: '^5:^: 5^: c tddtftddfddtdzdzffttfdt dttdd d d dtzffk(sJy) NrrrrrcjSry)nonexistantattributersrsr~ztest_getattr..s 1#9#9rrrrrr)r5rcrdrRrAgetattrrs@rs test_getattrrslAq Aq!9r1adQh&789A >9: 71f a FIy1a1++N$O OO Orrctgdgdgdg}|jsJ|j}|jsJd|d<|jdusJtgdgdgdg}|jrJt dd }|jsJy) N)rrr)rrrrr)rrFrrr)r5is_upper_hessenbergris_lower_hessenbergrBrs rstest_hessenbergrs 9i01A   A  AeH E )) ) 9i01A$$$ $ a A  rrc @ttdttdttdttdttdtdtzdfdfj d tt dtzdgdd ggk(sJtd }|j d }|td dgdd t dztzggk(sJ||jz|k(sJtd}|j }||jz|k(sJ|jsJ|tgdgdgdgk(sJtddtzd d tzzfd tzd dtzfd d tzz dtz dff}|j jtdtd dfd tz ddffk(sJttdttdttdttdttdtdtzdfdfj d tt dtzdgdd ggk(sJtd }|j d }|td dgdd t dztzggk(sJ||jz|k(sJtd}|j }||jz|k(sJ|jsJ|tgdgdgdgk(sJtddtzd d tzzfd tzd dtzfd d tzz dtz dff}|j tdtd dfd tz ddffk(sJy)Nc4tdjSNrr5choleskyrqrrrsr~ztest_cholesky...s)@)@)Brrc4tdjSNr)rrrrqrrrsr~ztest_cholesky../v&67@@BrrcJtdtzdfdfjSNrrr)r5r rrqrrrsr~ztest_cholesky..0s!vAqz6&:;DDFrrc4tdjSN)rr)rrrrqrrrsr~ztest_cholesky..1rrrc8tdjdSNrF hermitianrrqrrrsr~ztest_cholesky..2sv&67@@5@QrrrrrFrrrrr))rrQ)rrr)rQrrr)rrr)rrrrrrrrrc4tdjSrr6rrqrrrsr~ztest_cholesky..Asf)=)F)F)Hrrc4tdjSrrrqrrrsr~ztest_cholesky..B|,<=FFHrrcJtdtzdfdfjSr)r6r rrqrrrsr~ztest_cholesky..Cs!|a!eQZ,@AJJLrrc4tdjSrrrqrrrsr~ztest_cholesky..Drrrc8tdjdSrrrqrrrsr~ztest_cholesky..Es|,<=FFQVFWrr) rRr-r$r5r rrrrrr6)rr#s rs test_choleskyr-sk !BC :BC :FG :BC :QR AE1:v& ' 0 05 0 AV a!ea1a&M"F# ## # A U #A AAd1gIaK 012 22 2 QSS5A::78A A qss7a<< :::  9j9: :: :BqD!ac'"QqS!R!V$4q1Q3wQ6KLMA ::<   FI1ay1q5!Q-+P$Q QQ Q !HI :HI :LM :HI :WX !a%V, - 6 6 6 G6 a!ea1a&S"L# ## #%&A U #A AAd1gIaK 012 22 2 QSS5A::=>A A qss7a<< :::  9j9: :: :q"Q$AaC(1Q326*:Q1Wb1fb> 66":?? 66+ ! ## # r7<<?c"gll2. 3! 33 33 3 66":?? Aq Aqvvs+,-A FF5M8B?Qs1vqy[02q581a4?@ AB A  Q8B?345A 66!9Xc1-U A => >> > 66":   66+ $s)A+ -- - AA AAQ !AQB!Q !AAB !A Aq! A 7 &E Qx}}U#qvv--- "A "vve}qvve}4ULL'(q! " " Q1 AE!G>>%0J./0C!8O8  $ 1qs7B A!Q A|A1ayA hq#.23A Aq!QA 7 &EQB A,>,>C  19)$))%0AFF: :: A: 88A66%=166%=8Q U+,C#C1H-7778 8 Q2r1::q/A/AB B a~~e4Z!&&-/ 12axx  & q!23A 66!9??rrc tddtd}d|d<tdd|d<|jd k(sJ|d <|jt dt t tddt z k(sJtttgt tgg}|jtfd tdd tjtddtd z tttddzfDsJtgjdk(sJy)NrcTrrrrrrrrrc3K|]<}tdjj|j>yw)?N)r epsilon_eqrr)rvalMcrcs rsrz(test_condition_number..s9QuRy##BGGAsO$9$9$;<QsAArrrrr)rr9r condition_numberrrrr5rrrrr!r)rrrrcs @@rstest_condition_numberrs-sA AAAdGq"oAdG   3 && &AdG   3r3q6?S!R#a&5Q#Q QQ QQQ CF7CF"345A   B Q !Q!R"Q$Bx1~|jddjS)NrT)rchop)ris_zerors rsr~z!test_normalized..s2D199rrr)r5ror rs rstest_normalizedrs 1a&> $ $ &AA/0 11 1 )  ' ' )VI-> >> > }A <<9      rrcHtddk(sJtddk(sJy)Nc4tdjSrr9 print_nonzerorqrrrsr~z$test_print_nonzero..s3q6//1rrz[X ] [ X ] [ X] c6tdjdS)Nr.rrqrrrsr~z$test_print_nonzero..s3q6//4rrz[. ] [ . ] [ .] )rOrqrrrstest_print_nonzerors8 1 2   4 5   rrctjdtdk(sJtjdtdk(sJtddtdddgdzk(sJtddgddgg}tddgddgg}tD]v}|jd}||k(sJ|td|k(sJt ||k(sJ|jd}||k(sJ|td|k(sJt ||k(rvJy)Nrrrrrrr/)r5r9rBr<rr)r|rerrs rstest_zeros_eyer s ::a=CF "" " <<?eAh && & 1:1qc"f- -- -AA AAA A GGAJAv vCsO###Aw#~~ IIaLAv vE!%%%%Aw#~~rrctjsJtddgddggjsJtddjsJtdjrJttdgddggjdk(sJt tdgddggjdk(sJt tdgddggjdk(sJttdgddggjdk(sJttdgddggjdk(sJtdd}t|dgddggjdk(sJy) NrrrrFr_T)nonzero) r5is_zero_matrixrBr9rcr6r3r4rrs rs test_is_zeror sL 8 " "" " Aq6Aq6" # 2 22 2 A; % %% %1v$$$ $ Aq6Aq6" # 2 2d :: : !Q!Q( ) 8 8D @@ @ QFQF+ , ; ;t CC C 1a&1a&!1 2 A AT II I Aq6Aq6" # 2 2e ;; ;sD!A Aq6Aq6" # 2 2e ;; ;rrcJtdz }t|}t| }t|}t| }t|}t| }||zt dzt dk(sJ||zt dzt dk(sJ||zt dzt dk(sJ|j ddt |zzk(sJ|j ddt |zzk(sJ|j ddt |zzk(sJtdt dk(sJtdt dk(sJtdt dk(sJtjgdtdz }tjgdtdz }tjgdtdz } tt dz |jk(sJtt dz |jk(sJtt dz | jk(sJttdz |jk(sJttdz |jk(sJttdz | jk(sJy)NrrrrrDrr) rr@r?r>r9rGrr]from_axis_angleto_rotation_matrixrGrHrI) thetar3_plusr3_minusr2_plusr2_minusr1_plusr1_minusq1q2q3s rstest_rotation_matricesr # sf qDEG% HG% HG% H G CF "c!f ,, , G CF "c!f ,, , G CF "c!f ,, , ==?a!CJ,. .. . ==?a!CJ,. .. . ==?a!CJ,. .. . Q<3q6 !! ! Q<3q6 !! ! Q<3q6 !! !  # #IrAv 6B  # #IrAv 6B  # #IrAv 6B rTAX ""7"7"9 99 9 rTAX ""7"7"9 99 9 rTAX ""7"7"9 99 9 2 "b&;&;&= == = 2 "b&;&;&= == = 2 "b&;&;&= == =rrcttdddk(sJttdtdk(sJttdttddk(sJt tddk(sJy)Nvectorrz vector[4]rbctddS)Nrbrr.rqrrrsr~z%test_DeferredVector..K s~c226rrtestzDeferredVector('test'))strr/rrRrreprrqrrrstest_DeferredVectorrH sx ~h'* +{ :: : >#& '>#+> >> > :67 ~c" #s ** * v& '+C CC Crrc0ttdrJy)Nr)rPr/rqrrrs test_DeferredVector_not_iterablerO ss+,, ,,rrc&ttdy)Nc*ttdS)Nr)r5r/rqrrrsr~z,test_DeferredVector_Matrix..S sf^C%89rr)rRrrqrrrstest_DeferredVector_MatrixrR s  99:rrc t}tddddg}tddddg}t||gtddddgtdd|ddz |ddz ggk(sJt|j|jgtddddgtdd|ddz |ddz ggk(sJttddgtddggdtdt dzdz t ddz gtt d dz dt dzdz ggk(sJt tdg}t|tdgggk(sJy)NrrrrrTr)r r5r2rrr')r%rrr#s rstest_GramSchmidtrU s}A 1q!f B 1q!f B Bx 1q!f vaQqT!VQrU1W,=>? @@ @ bdd| $ 1q!f vaQqT!VQrU1W,=>? @@ @ 1v1v7 >$r( 2 tBx{+,b " aRjm,-C/ // / &!+A q>fqcUm_ ,, ,rrcTtgdddk(sJtgddddk(sJy)NrrrF)zero)r7rqrrrstest_casoratianrf s. lA &! ++ + lAE 2a 77 7rrcttddzjdk(sJtddtddztddk(sJtddtddztk(sJy)Nrr)rr)r5rBrrqrrrstest_zero_dimension_multiplyrk si HU1a[ ' '6 11 1 A;uQ{ "eAqk 11 1 A;uQ{ "fh .. .rrcvtddtddddftddggk(sJdddftddggk(sJdddftddggjk(sJdddftddggjk(sJttfdttfdy)NrrrrrcdddfSrrqrsrsr~z'test_slice_issue_2884..w sqAwrrcdS)Nrrqrsrsr~z'test_slice_issue_2884..x s qwrr)r5rrrRrrs@rstest_slice_issue_2884r!q sq!U1XA QT7fq!fX& && & RU8v1vh' '' ' QT7fq!fX&(( (( ( QU8v1vh')) )) ) :' :'rrctdddddfjdk(sJtdddddftddgk(sJy)Nrrrrr)rBrr5rqrrrstest_slice_issue_3401r#{ sK A;q"u  # #v -- - A;q!t q!R 0 00 0rrctdd}d|d<|dddftgdk(sJ|ddk(sJ|dddgk(sJd|d<|ddk(sJ|dddftddggk(sJtdd gg|dddf<|dddftgd gk(sJdd gg|dddf<|dddftgd gk(sJd |d<|ddddftgdk(sJgd|d<|dddftgdk(sJtgd|d<|dddftgdk(sJtgd|d<|dddftgdk(sJy)NrrrrrrPrrr)rrr+)rrPr%r)r&rrr])rBr5r6)rs rs test_copyinr' s a A AaD QT7fY' '' ' Q4199 Q7qc>>AdG T7b== QU8vAwi( (( (1vhAaeH QT7fi[) )) )RzAaeH QT7fk]+ ++ +AdG QU8vj) )) )AdG QT7fY' '' 'YAdG QT7fY' '' '9%AdG QT7fY' '' 'rrc&tddgddggjtddgddggdfk(sJttdtgdtddgdtdggt jdj k7sJjdtdk7sJjt dtdk7sJttfd ttfd ttfd y) Nrrr)rc@tddgddggjSrrQrqrrrsr~z'test_invertible_check.. s!v1v1v&67;;=rr)rrrrrrc(jdS)Nrrr-rsrsr~z'test_invertible_check.. squuEu2rrc(jdS)Nrrr+rsrsr~z'test_invertible_check.. quuDu1rrc(jdS)Nrrr+rsrsr~z'test_invertible_check.. r-rr) r5rTrRr$rcrArr9r(rs@rstest_invertible_checkr/ s Aq6Aq6" # ( ( *v1v1v6F/G.N NN N :=> a! a  A qvvx{ qvv %% % 668A;#a&  6686 $Q '3q6 11 1 :23 :12 :12rrctd\}}||z}|j|tgdtgd|zk(sJy)Nzx, y)rrr)rrr5)rcrdrs rstest_issue_3959r1 s@ 6?DAq !A 66!VI& '6)+ >> >rrcBttddgddggdk(sJy)NrrrrzMatrix([[1, 2], [3, 4]]))rr5rqrrrstest_issue_5964r3 s( v1v1v&' (,F FF Frrcptd\}}tt|d|zg|dz|dzggdk(sJy)Nx yrrz'Matrix([ [ x, 2*y], [y**2, x + 3]]))rr&r5)rcrds rstest_issue_7604r6 sG 5>DAq AaC1a4Q-01 23 44 4rrc tdjsJtdjjsJtdjrJt djrJt gdgjrJt ddddddjsJt ddtdjrJt dddddjrJt ddddddddjrJy) NrrDr)rrrrr)rr)rrrrr^)r9 is_IdentityrrBr<r5r6rrqrrrstest_is_Identityr9 s q6    q6   , ,, ,Qx### #Aw""" "yk"... . !AQa8 9 E EE EAaq*666 6Aa!34@@@ @Aa!1A!NO[[[ [[rrctddjtdddk(sJtddjgddk(sJtgdjtgddk(sJtdddtzgjttddtzgdtzk(sJtdddtzgjttddtzgd dtzk(sJtdddtzgjttddtzgd d tzk(sJtdddtzgjttddtzgd d d tz k(sJtdddtzgjtddtzdgd d ddtzzk(sJtdddtzgjtddtzdgd d ddtzz k(sJttdtzgjttdtzgdd dk(sJttdtzgjttdtzgddk(sJt t dy)Nrrr]rrrrQFrTrphysicsrconjugate_conventionrrrrightrleft)r=cVtddgjtddgddS)NrrrrTrr<rgrqrrrsr~ztest_dot.. s)vq!f~11&!Q.Dgm1nrr)r<rhr5r rRr$rqrrrstest_dotrA s 1:>>$q!* % ** * 1:>>) $ )) ) )   !2 3r 99 9 1a1+  " "61a1+#6 726 AA A 1a1+  " "61a1+#6% " HBQRF RR R 1a1+  " "61a1+#6$ " G2PQ6 QQ Q 1a1+  " "61a1+#6$]f " gkmpqkq qq q 1a1+  " "61ac1+#6$]d " eijmnopmpip pp p 1a1+  " "61ac1+#6$]c " dhilmnoloho oo o 1ac(   1Q3x 0EX^  _ce ee e 1ac(   1Q3x 0v  NRS SS S :norrc tdd\}}}}}}td|||f| d|| f| | d|f| || dff}td| | | f|d|| f|| d|f||| dff}|jj|sJt djjt dsJ|jjj| sJy)NzB_x B_y B_z E_x E_y E_zTrrr)rr5dualequalsr9rB)B_xB_yB_zE_xE_yE_zFFds rs test_dualrM s#*!$. Cc3S cC !cC4 tC cTa  A  sdSD3$ S3$ sdq3 sSDQ  B 668??2   q6;;=  a )) ) 668==? ! !1" %% %rrc ,tddgjdusJtdddtdzdtzzdzttdzdz dttzt t tzdg }|jdusJ|jdJ|jdJ|d  |d <|jJ|d  |d <|j }|jddusJd|d <|jdusJy) NrrFrrTrc|Sryrqrs rsr~z%test_anti_symmetric.. s!rrrr)r5is_anti_symmetricrcrdrrs rstest_anti_symmetricrQ s/ 1a&> + + - 66 6q!aA!aa!eaZKAaC!aRT1MNA   D (( (    . 66 6    4 << <whAdG   (( (whAdG  A    .$ 66 6AdG   E )) )rrctd}|jd\}}||jz|j|zcxk(rt|jk(sJJ|jdd\}}||jz|j|zcxk(rt|jk(sJJ||z|j z|k(sJy)N)rrT) normalize)rSsort)r5r~rr9rr-)rr/rYs rs#test_normalize_sort_diogonalizationrU s A ==4= (DAq QSS5ACCE (S[ (( (( ( ==4d= 3DAq QSS5ACCE (S[ (( (( ( Q3quuw;!  rrc&ttdy)Nc6tgdtddggS)Nrrrrrqrrrsr~z!test_issue_5321.. svy&Ar2B&CDrr)rRr$rqrrrstest_issue_5321rX s  :DErrc tjtddtdztgdgdgk(sJtjtddtdztddgddgddgddggk(sJt}|j|td|dtdztgdgdgk(sJy)Nr)rrrr)rrrrrr)r5hstackr9vstackr6r/s rstest_issue_5320r\ s ==Q3q6 *f6/   ==Q3q6 *f A A A A 6/   C ::c#a&k3qQx= 1V=6  rrctdgg}t|}tj||tddggk(sJtj||tdgdggk(sJyrM)r5rrZr[)rAIms rstest_issue_11944r_ sbu A !*C ==a FQF8$4 44 4 ==a FQC!:$6 66 6rrcgd}gd}tgd}|j}fd}tD]|}|}||j||||j|j|||jj|j|||jj||t t dy)Nrr)rrrc4||k(sJt|k(sJyry)r)rr'rs rsrztest_cross..test) saxxAw#~~rrcXtddddgjtddddgSrrdrqrrrsr~ztest_cross..3 s/q!aV""6!QA#78rr)r5rrrerRr+)r_r`rTrSrrrrs @rs test_crossrc# sAA  C %%C  F F QWWQZ QWWQSS\3 QSSYYqss^S! QSSYYq\3   :9:rrc@ttttg}ttt t g}|j|z|j|k(sJ|jjsJ|jj|k(sJyry) r5rcrdrer_r`rahatrerPvee)v1v2s rs test_hat_veeri6 st Aq B Aq B 668b=BHHRL (( ( 668 % % '' ' 668<<>R  rrc&tddD]V}|jd|jdh}t|dk(r#|j|jdk(rVJtddD]#}t |jdt s#Jy)Nrrr)rr9rApoprr)rrs rs test_hashrl= srs|5 WWQZ $1v{quuw#''!*4445r{4cggaj(3334rrc>tdttfdy)Nrc8tjdSrM)hashr9r/srsr~z!test_issue_3979..K s4 #3rr)rrRrAr/s@rstest_issue_3979rpF s !*C >34rrcdtgddgg}tddgt dgg}tD]}|||jk(rJyNrr)r r5radjoint)rr'rs rs test_adjointrtN sW q6Aq6 C 1a&A2q'" #C)c#h&&(((()rrcPddl}|jjjj d}|jjj |}dt |zgd|gg}tddgt |z|gg}tD]}|||jk(rJy)Nrr_) sympy.physics.quantumr;quantumoperatorr!r"r r5rrs)sympyr_a_dagrr'rs rstest_adjoint_with_operatorr{U s  &&//4A MM ! ! ( ( +E q1u:5z "C 1a&A2:q/* +C)c#h&&(((()rrcttttdzt tdzzggtdggk(sJy)Nrr)r)r3rrcrrqrrrstest_simplify_immutabler}` sE Oc!fai#a&!)&;%<$=> ?#aSE* ++ +rrctdt\tddfd}tddfd}|j}||k(sJy)NzF, Gr/rc||zSryrq)r|r}Gs rsr~ztest_replace..f !AaC&rrc||zSryrq)r|r}rKs rsr~ztest_replace..g rrr)rrr5replace)KrNrKrs @@rs test_replacerd sK 6x (DAqq!()Aq!()A !QA 6M6rrctddgtddtz z gg}|jtjtdtj thk(sJ|jt thk(sJyr)r5rcatomsrr NegativeOnerrs rs test_atomsrl sbAA!G %&A 779qtAMM15 55 5 776?qc !! !rrc  tttgttgg}t |j dt |jk(sJtddgddgddggtgd gd gtttgg}|D]f}|j d}||z}||z}t ||z|k(sJt ||z|k(sJ|j|k(sJ|j|k(rfJ|D]o}t |j d }||z}||z}t ||z|k(sJt ||z|k(sJ|j|k(sJ|j|k(roJd d l m |j d }|j}tdtdtdtdi}t fdt|j||j|DsJy)NRDrrhirrr)rrr)rr&EDr)compi_ib,iijc3nK|],\}}|j|j.ywryr)rr|r}rs rsrztest_pinv.. s0 Aq QSSUACCE r)r5r_r`rarbr)pinvr-r<sympy.core.numbersrrzipr) A1AsrA_pinvAApApArwrepsrs @rs test_pinvrr s !Q!Q !B BGG4G( )Xbffh-? ?? ? 2s)dAYQ0 1 )\* + !Q. Bt$&jqja A%%%f %///uu||uu||!&&&-.&jqja A%%%f %///uu||uu||( tA A vq%E1e 4D  t affTl3    rrc tgdgdgdgdgdgdgg}|D]G}|jd}||z}||z}|j|k(sJd }||j|rGJy) N)=r7rrr)>rUrrr)E8r&r6r)rr[)rr)rrrrZr)rrrrrrrrc|jt}|Dcic]}||j}}||z j|j}t d|DScc}w)Nc38K|]}t|dkyw)g|=Nrrrs rsrzXtest_pinv_rank_deficient_when_diagonalization_fails..allclose.. s;!s1v~;s)rr%rr2r)M1rrootofsrNrootofs_approx diff_approxs rsallclosezEtest_pinv_rank_deficient_when_diagonalization_fails..allclose s`hhv&G4;. s0u1v1v.!Q!Q0@ABCrrrrrrN) numpyr ImportErrorrUr5rcrdrerRNotImplementedErrorrs@rstest_from_ndarrayr s{P % " #vi'8 88 8 % $ % )< << < %I./ 0 9%& '' ' %Aq " #vq!Qi'8 88 8 CE 5!Q=%A-0 1VaVaV=E>c^ddlm} ddlm}m}|ddgddgg}|ddk(sJt|gd k(sJtt5|ddgddgg}ddd|ddk(sJt|gd k(sJy#t $rt dYwxYw#1swY@xYw) Nr _matrixify)rmatrixzPNumPy must be available to test indexing matrixified NumPy ndarrays and matricesrrrrr) sympy.matrices.commonrrrrrrUrrQPendingDeprecationWarning)rrrrs rstest_17522_numpyr s0a' 51a&1a&)*+A Q4199 7l "" " 2 31 v1v1v./ 01 Q4199 7l "" " a _`a11sB B# B B #B,cddlm} ddlm}|ddgddgg}|dd k(sJt |gd k(sJy#t$rt dYGwxYw) Nrr)rzEmpmath must be available to test indexing matrixified mpmath matricesrrrr@)rg@rr)rrmpmathrrrUr)rrrs rstest_17522_mpmathr sk0V! 6Aq6Aq6*+,A Q43;; 7* ** * V TUV?AAcddlm} ddlm}|ddgddgg}|ddk(sJt |gd k(sJy#t$rt dYGwxYw) Nrr) csr_matrixzJSciPy must be available to test indexing matrixified SciPy sparse matricesrrrrr)rr scipy.sparserrrUr)rrrs rstest_17522_scipyr sj0[+ :1v1v./0A Q4199 7l "" " [ YZ[rc8tdtgt dgg}|jsJdtz|d<|jdusJt|d<|jJ|dtz|d<|jdusJt d}t d}t|ggjd usJt||gt ||ggjd usJt||g||ggjdusJt||gt||ggjdusJy) NrrrFrrr`raT)r5r is_hermitianrcr r!r"rrs rstest_hermitianr s,A!Q !A >>>cAdG >>U "" "AdG >> !! !gaiAdG >>U "" "#A A A3%= % % -- - Aq6F1Iq>* + 8 8D @@ @ Aq6Aq6" # 0 0E 99 9 Aq6IaL!,- . ; ;u DD Drrcttttdgg}|ddtzk7sJ|jtdtzggk(sJy)NFrrr)r5rrcrrs rs test_doitr sQQq5)*+,A Q41Q3;; 1668v!ug && &rrctgdgdgdg}|jd|tgdgdgk(sJtgdgdgdg}|jd|tgdgdgk(sJtgdgdgdg}|jd|tgdgdgk(sJtgdgdgdgttfd tgdgdgdgttfd tgdgdgdg}|j d|tdd gd d gd dggk(sJtgdgdgdg}|j d|tdd gd d gd dggk(sJtgdgdgdgttfdtgdgdgdgttfdy)Nrrrrr)rrr)rrrrc&jdSrrow_delr/srsr~z+test_issue_9457_9467_9876..& qyy}rrc(jdSNrrrXsrsr~z+test_issue_9457_9467_9876..( yqyy~rrrrrrc&jdSrcol_delrsrsr~z+test_issue_9457_9467_9876..2 rrrc(jdSrrrXsrsr~z+test_issue_9457_9467_9876..4 rrr)r5rrRrr)rrr^r/rYs @@rstest_issue_9457_9467_9876r s 9i01AIIaL  9-. .. . 9i01AIIbM  9-. .. . 9k23A AIIbM  9-. .. . 9i01A :,- 9i01A :-.  9i01AIIaL AAA/0 00 0 9i01AIIbM AAA/0 00 0 9i01A :,- 9i01A :-.rrcDtdd\}}td\}}td}tdd|||tg}||z|z||z|zk7sJ||z|z||z|zk(sJ||z||zk7sJ||z||zk(sJ||z|zt||zdgd||zggk(sJy)Nr5F) commutativeza brr)rr9r5re)rcrdr_r`rrs rstest_issue_9422r6 s 5e ,DAq 5>DAq AA 1q!Ql #B Q3q5AaCE>> Q3q5AaCE>> R42a4<< R42a4<< Q3q5FQqS!Hq!A#h/0 00 0rrc2tg}ddgtgdf}ddg|djf}ddgtddgdd ggf}|||fD]K\}}|D]A}t||}d |vr||n|d |}||k(rt|t|k7rAJMy) NrZrS)rrrrWrUrrrrjoinrP)r5rrid) rr_r`raopsropr%news rstest_issue_10770rB sr A z"F9$55A z"AaDFF*A |$fq!fq!f-=&>>Aa)1Q 1B2A B,!A$Ab!HC!832a5 0 00 11rrcdtgdgdgdg}|jgdgdtddgdd gd d ggk(sJ|jgdgd tdgdgd ggk(sJ|jgd gdtgdgk(sJ|jgd gdtgdgdgk(sJ|jgdgdtddgk(sJ|jgdgdtddgk(sJ|jgd gdtdgd ggk(sJy)NrrYrr)TTFrrrrrr)TFF)TFT)FFFrr)FTF)r5rrs rstest_issue_10658rN s8 9i01A 99Y 3 4AAA'( )) ) 99Y 4 5!qcA39P PP P 99)9 5 9L LL L 99() 4 9%& '' ' 99Y 5 6&Ar:J JJ J 99*I 6&Ar:J JJ J 99(*> ?aSz  rrc tddtdzzdgdtdzdz dzdtdzdz gg}|jdk(sJtddtdztzzdgdddtdztzzgg}t |j d tddddtdztzzz gd d ggz t ddk(sJtd \ }}}}}}}}} } } } t|||| z|| zd g|||| z|| zd g|||| z|| zdg|||| z|| zdg| | d| z| z| | zz d| z| z| | zz d gg}|jdk(sJy) NrQrrrrrrrr/a_x a_y b_x b_y c_x c_y d_x d_y e_x e_y t_0 t_1)r5rrr r)rTrBr) raxaybxbycxcydxdyexeyt0t1s rs!test_opportunistic_simplificationr[ s aQi$r$q'z!|a'7DGA&FGHA 668q== 1T!W9Q;#Qr!DG)A+~$678A AFFHQK&1b!aQik/.B*CaV)L"MM NRWXY[\R] ]] ]+22c*d'Br"R2bBr"RBr"uRU1%r"RU2b5&;R2b5Bq. sQrrrr)rrg4iҤIӿr)rrglٲerrrrN)r5rTr)rm_rref m_correctm_diffs rstest_iszero_substitutionr sr $%9:NOPA VV5V 6q 9F9:[\}~I i F ;;=5  #;!  rrc ddlm}dttt ddzzttt ddzt dzz }dt dzttt ddzdzzd ttt ddzzzd ttt ddzdzzz }|dd}|d t d }|||}t |t|z |t|z g}t ||z ||z g}t t||z t||z g}d } |jd | d k(sJ|jd | d k(sJ|jd | d k(sJy)Nr)Pointrr-rrrrrrc<t|jdkS)Ng#B ;)rrrs rsr~z"test_issue_11238.. s#cacce*u$rrT)r)r) sympy.geometry.pointrrrr rr5r)r) rxxyyp1p2p0rrm3Zs rstest_issue_11238r s* 3r(2r"" # #SHR,<)<%=Q%G HB T!W*SHR,,-q0 02c"Xb"=M:M6N3N NQSVYZ\]efhjl]mZmVnpqVqQq rB q!B q47( B r"B hrl"B"$56 7B b"r'" #B "r'"HR"W$56 7B %A 77DQ7 /1 44 4 77DQ7 /1 44 4 77DQ7 /1 44 4rrctddgd}|tjz}||z}tD]M}||j \}}t |t |k(sJt |t |k(rMJy)Nrr)r5r ImaginaryUnitr as_real_imagr)rrrklsr_r`s rstest_as_real_imagr# sx !I B AOO B bB#"g""$!Aw$r("""Aw$r("""#rrctddgd}|j\}}|dtdddgk(sJ|dtddgdk(sJy)Nrrrrr)rrrr)r5 jordan_cells)rr/Jcellss rstest_deprecatedr' s[ q!23A IAv !9q!aS) )) ) !9q!\2 22 2rrcddlm}tgd}tgd}||dtgdk(sJ||dtgdk(sJy) Nr)Mod)rrr)rrrr)rrrr)rrr)sympy.core.modr)r5)r)rrs rstest_issue_14489r+ sK"zA}A q!9y) )) ) q!9y) )) )rrc ddlm}t ddgddgg}|t j jd k(sJy#t$rtdYOwxYw) Nrrrrrrr)dtypefloat64)rrrrUr5floatr-name)rrs rstest_issue_14943r1 s`P 1!u~A % & & + +y 88 8 P NOPsAAAcdtddd}td}|ddkD}t|dk(sJy)Nrrr_rrz m[0, 0] > 0)rErr)rr_s rstest_case_6913r3 s8S!QAs A $ A q6] "" "rrcdtddd}td}|j|||ik(sJy)Nrrr_)rErLmatch)rr_s rstest_issue_11948r6 s3S!QA S A 771:!Q  rrcbtdtgtdt gg}tj|tdgtggtdgt gggk(sJtdtdgttdt gg}tj|tdgtgdggttdz gtddz gt gggk(sJtdtgdt gg}|j \}}||j ztj dk(sJy)Nrrr)r5r orthogonalizerQRdecompositionr<r9)vecsrrYr%s rstest_gramschmidt_conjugate_dotr; s' Aq6NFAr7O ,D    & !qc VaSA2$K01 22 2 Aq!9 vq!aRj1 2D    & !qcA3 &1Q3%!A$q&QB4)@"AB CC C 1a&1qb'" #C    DAq qss7fjjm ## #rrcttddd}ttddd}|j|}t||d}t||d}||dk(sJ|dk(sJy)Nr_rrr`rr)r5rErhr)r_r`rarbrs rstest_issue_8207r= sr|CA&'A|CA&'A aA Q$A Q$A $<< 6M6rrc ddlm}tddgddggjt t t zt tt t t dt zt t z gdt dt zggk(sJtddgddggtzdz jtt t ttddz td dz gtd dz tddz ggk(sJttdttfd tgd gd gd gd gjtt t jk(sJttfd tddgddggtjtt t dzk(sJtgdgdgdgtj|t dt dzk(sJtgdgdgdgdgjtt t jk(sJtgdgdgdgdgjtt t zt ttt zjk(sJy)Nr)nthrootrrrrrcZtdjtttSr)rB analytic_funcrrcrqrrrsr~ztest_func.. sa 6 6s1vq ArrcXtzjtttSry)rcrArrsrsr~ztest_func.. s1 3 3CFA >rr)rrrr)rrrr)rrrrcJjtttSry)rArrcrsrsr~ztest_func.. sQ ;rrrr")rrr)rrr)rrrr)rrrr)rrrr)rrrr)rrrr)rrrr)rrrrr)sympy.simplify.simplifyr?r5rArrcrfrrrrRr$rr)r)r?rs @rs test_funcrF sD/A1vA ??3qs8Q '6CFC!Hs1v? }MNA ??3q61 % 00 0 :;<R"b"#A AOODGQ/2 3q 88 8 [+67A AOOGAqM15q8 9Q >> > lL,GHA ??3q61 % 00 0 lL,GHA ??3qs8Q '6(AaC99;2G+H HH Hrrz$Cannot create threads under pyodide.cd}td5tjj5}|j |}|j sJ ddddddy#1swYxYw#1swYyxYw)NcRtjdk(sJtdgg}||z}yr+)rJstater5rs rsr%ztest_issue_19809..f s/!''4/// QC5M ErrT)rF concurrentfuturesThreadPoolExecutorsubmitresult)r%executorfutures rstest_issue_19809rQ sp T #    2 2 4 #__Q'F==? "? ### # ###s"A0$A$A0$A- )A00A9ctttg}t|tddftddfttj gtj ggk(sJyrr)r5rcrdrrr!r(s rstest_issue_23276rS sT1vA QAq Aq!9 -  92  rrcBtgdgdgdgdg}|j}|dtgdk(sJ|dtgdk(sJ|d tgd k(sJt|d k(sJtj|g|j|k(sJy) NrrrrrrrQrrrrrrrrrrrrrrr)rrrrr)rrQrrr)rrrrrr)rlror5rArZrbasiss rstest_columnspace_oner[! s00002 3A MMOE 8vm, ,, , 8vn- -- - 8vn- -- - u:?? == #U # / / 1U :: :rrctgdgdgdgdg}|j}|dtgdgk(sJ|dtgdgk(sJ|dtgd gk(sJt|d k(sJy) NrUrVrWrXrr)rrrrrr)rrrrrr)rlrlr5rArYs rs test_rowspacer]0 s00002 3A JJLE 8v/0 00 0 8v/01 11 1 8v/0 00 0 u:??rrctgdgdgdgdg}|j}|dtgdk(sJ|dtgdk(sJtd ||dzDsJtd ||dzDsJy) NrUrVrWrXr)rrrrrr)rrrrrc34K|]}|jywryrrs rsrz%test_nullspace_one..H -Qqyy-c34K|]}|jywryr`rs rsrz%test_nullspace_one..I rarb)rlrsr5rrYs rstest_nullspace_onerd> s00002 3A KKME 8v./ // / 8v01 11 1 -!E!H*- -- - -!E!H*- -- -rrcxtdttfdttfdttfdttfdttfdttfdttfdttfd ttfd ttfd ttfd ttfd ttfdjdddt gdgdgdgk(sJjdddt gdgdgdgk(sJjdddt gdgdgdgk(sJjdddt gdgdgdgk(sJjdddt gdgdgdgk(sJjdddt gdgdgdgk(sJjdddt gdgdgdgk(sJjddddt gdgdgdgk(sJjddddt gdgdgdgk(sJjdddd t gdgdgdgk(sJt d!ddgd"z}|jdddt d!ddgd"zk(sJ|jdddt d!ddgd"zk(sJ|jddddt d!ddgd"zk(sJy)#Nrc&jdSNabcelementary_row_oprsrsr~ztest_row_op..P q2259rrc$jSryrirksrsr~ztest_row_op..Q q224rrc,jdddS)Nn->knrrSrrirksrsr~ztest_row_op..R q227Q2Grrc,jdddS)NrprQrrqrirksrsr~ztest_row_op..S q227a2Hrrc,jdddS)Nn<->mrrrow1row2rirksrsr~ztest_row_op..T q2272Krrc,jdddS)Nrvrrrwrirksrsr~ztest_row_op..U rzrrc,jdddS)NrvrQrrwrirksrsr~ztest_row_op..V q227!2Lrrc,jdddS)NrvrrQrwrirksrsr~ztest_row_op..W q2272Lrrc.jddddSNn->n+kmrrrxryrrirksrsr~ztest_row_op..X q22911PQ2Rrrc.jddddS)Nrrrrrirksrsr~ztest_row_op..Y rrrc.jddddS)NrrQrrrrirksrsr~ztest_row_op..Z q2292AQR2Srrc.jddddS)NrrrQrrrirksrsr~ztest_row_op..[ q22912QR2Srrc.jddddSrrirksrsr~ztest_row_op..\ rrrrprrrrrrrDrErq)rxrrvrw)rSryr)rrr)rSrry)rxrryrr)rrRr$rjr5rvr_rs @rs test_row_oprM qA :9: :45 :GH :HI :KL :KL :LM :LM :RS :RS :ST :ST :RS  w1 -Iy8Y1Z ZZ Z  w1 -Iy8Y1Z ZZ Z  wA  3vy)U^>_7` `` `  wQ!  4 9V_?`8a aa a  w1 -Iy8Y1Z ZZ Z  wQQ  769iYbBc;d dd d  wAA  6&)YXaAb:c cc c  y!Q 2fiT]=^6_ __ _  ya11  =T]_hHiAj jj j  yqAA  >&)U^`iIjBk kk k QA3q5)A 1  w1 -1qc!e1D DD D 1  w1 -1qc!e1D DD D 1  y!Q 2fQA3q56I II Irrcxtdttfdttfdttfdttfdttfdttfdttfdttfd ttfd ttfd ttfd ttfd ttfdjdddt gdgdgdgk(sJjdddt gdgdgdgk(sJjdddt gdgdgdgk(sJjdddt gdgdgdgk(sJjdddt gdgdgdgk(sJjdddt gdgdgdgk(sJjdddt gdgdgdgk(sJjddddt gdgdgdgk(sJjddddt gdgdgdgk(sJjdddd t gdgdgdgk(sJt d!ddgd"z}|jdddt d!ddgd"zk(sJ|jdddt d!ddgd"zk(sJ|jddddt d!ddgd"zk(sJy)#Nrc&jdSrgelementary_col_oprksrsr~ztest_col_op..t rlrrc$jSryrrksrsr~ztest_col_op..u rnrrc,jdddS)NrprrTrrrksrsr~ztest_col_op..v rrrrc,jdddS)NrprQrrrrksrsr~ztest_col_op..w rtrrc,jdddS)Nrvrrcol1col2rrksrsr~ztest_col_op..x rzrrc,jdddS)Nrvrrrrrksrsr~ztest_col_op..y rzrrc,jdddS)NrvrQrrrrksrsr~ztest_col_op..z r}rrc,jdddS)NrvrrQrrrksrsr~ztest_col_op..{ rrrc.jddddSNrrrrrrrrksrsr~ztest_col_op..| rrrc.jddddS)Nrrrrrrksrsr~ztest_col_op..} rrrc.jddddS)NrrQrrrrrksrsr~ztest_col_op..~ rrrc.jddddS)NrrrQrrrrksrsr~ztest_col_op.. rrrc.jddddSrrrksrsr~ztest_col_op.. rrrrprrrrrrrDrEr)rrrvr)rTrr)rrr)rTrr)rrrrr)rrRr$rr5rvrs @rs test_col_oprq rrrctd}td}|jsJ|jsJtddg}|jsJtddgd}|jsJtddgd}|jrJt d}tdd|ddg}|jsJtdd||dg}|jrJtddgd}|jrJy) Nrrr)rrrrrr)rrrrrrrcr rrrrrrrrr)rr is_echelonrvr)zroidentr_rcs rstest_is_echelonr s 1 C 1 E >>>    Q2&A <<<Q#56A <<<Q#56A|| s AQAq!9-A <<<QAq!9-A|| Q#>?A|| |rrctd}td}|j|k(sJ|j|k(sJtddg}|j|k(sJtdddg}|j|k(sJfd}tddgd}t dgdgdggg}t |j Dcgc] }||ddf }}|jjsJ||||tddgd}g}t |j Dcgc] }||ddf }}|jjsJ||||tddgd }t td d gdgdggt td d gdgdggg}t |j Dcgc] }||ddf }}|jjsJ||||tddgd }t dgd gdggg}t |j Dcgc] }||ddf }}|jjsJ||||tddgd}t dgdgdggt dgd gdggg}t |j Dcgc] }||ddf }}|jjsJ||||td dgd}t d gdgdggg}t |j Dcgc] }||ddf }}|jjsJ||||ycc}wcc}wcc}wcc}wcc}wcc}w)Nrrrrc|D]}td|zDrJ|D]:}td|Drtd|jzDs:Jy)Nc34K|]}|jywryr`rrfs rsrzCtest_echelon_form..verify_row_null_space.. s6Qqyy6rbc34K|]}|jywryr`rs rsrzCtest_echelon_form..verify_row_null_space.. s,Qqyy,rbc34K|]}|jywryr`rs rsrzCtest_echelon_form..verify_row_null_space.. sJQqyyJrb)rr)rrnullsr a_echelons rsverify_row_null_spacez0test_echelon_form..verify_row_null_space sh 7A6)A+66 66 7 KA,!,,J)AKKM2IJJJJ Krrrr) rrrrrrrrr) rrrrrrrrrrrr) rrrrrrrrr) rrrrrrrrr)rrrrrr) rrrirvr5rrrr )r_rrrr|rrs @rstest_echelon_formr s AqA 1>> q  >> q  Q2&A 1>> q  QA3'A 1>> q  K Q#>?A TTT E#166] +AadG +D + I    !T5) Q#>?A E"166] +AadG +D + I    !T5)Q#>?A r1o VVr1o VV  E#166] +AadG +D + I    !T5) Q#>?A VVV E#166] +AadG +D + I    !T5)Q#>?A SSSTTT  E#166] +AadG +D + I    !T5)Q#56A TSS E#166] +AadG +D + I    !T5)y , , , , , ,s$M&*M+M04M57M:*M?c tddg}|jd|k(sJtdddg}tdddg}|jd|jdcxk(r|k(sJJtddgd}|jdtdgdgdggk(sJtddgd}|jdtgdgk(sJtddgd}|jdtgd gd gd gk(sJtddgd }tddgd }tddgd}tddgd}|jd|jdcxk(r4|jdcxk(r|jdcxk(r|k(sJJtd}t d}|jd|k(sJ|jd|k(sJtgdgdgdgdg}|j\}}|tgdgdgdgdgk(sJ|dk(sJtt ddt ddddggdgdgdg}|jdtdddt ddgdddt d dgdddt d!dggd"gk(sJt d#}tdd|ddt||dg}t|jdddt|| dzz|t ddz |zz dddt||zdzz gD]\} } t| | z jrJy)$NrF)pivotsrrrrr)rrrrr) rrrrrrrrr) rrrrrrrrrr) rrrrrrrrr)rrrrrrQr)rrrrrrrr)rrrrrrrQ)rrrrrrr)rrQrrrrr)rrrrrrr)rrrrrrr)rrrrrrr)rrrrrrrrirQrrc) rvrTr5rrr rrrr)r) rr_r`rarbrer pivot_offsetsrcr|r}s rs test_rrefr sQ2&A 666 1 $$ $QA3'AQA3'A 666 6166#7 <1 << << <Q9-A 166 6A3aS/#: :: :Q9-A 166 69+#6 66 6Q#>?A 166 6%/%/%/+1$2 22 2 Q#>?AQ#>?AQ#>?AQ#>?A 166  AFF%  & AFF%  & AFF%  &%& && && & qAA 666 1 $$ $ 166 1 $$ $ ' ' ' ' ) *A  C &---- /0 00 0 I %% %x2!QA!L0002 3A 166 6*+Q8C3E)F*+QHR4E)F*+Q8C3E)F); +=$> >> > s AQAq!T!Wa#;.p rzrrc,jdddS)Nrprrrqrirsrsr~z"test_issue_17827..q rrrrc.jddddS)Nrrrrrrirsrsr~z"test_issue_17827..r rrr)r5rjrRr$)r@rrKrs @rstest_issue_17827r_ s  A G!!4A IAAA#5:BIr:< =A1aBED52:,>)?@ !1aArD52:,?@ !1aTEBJ@@BC OffhOGV $w. /5!''? BB B _ $$ $rrctgdgdgdgdg}|tjdtzz }|jdk(sJ|dzjdk(sJ|dzjdk(sJy)Nr|rrrrrr)r5r9r r)rrs rstest_issue_15872r sn o~|LMA FJJqMA A 668q== qD;;=A   qD;;=A  rr([rconcurrent.futuresrJcollections.abcrsympy.core.addrsympy.core.functionrrrrrr r r r r rrsympy.core.powerrsympy.core.singletonrsympy.core.symbolrrsympy.core.sympifyr$sympy.functions.elementary.complexesr&sympy.functions.elementary.exponentialrr(sympy.functions.elementary.miscellaneousrrr(sympy.functions.elementary.trigonometricrrrsympy.integrals.integralsr$sympy.matrices.expressions.transposersympy.physics.quantum.operatorr r!r"sympy.polys.polytoolsr#r$sympy.polys.rootoftoolsr%sympy.printing.strr&sympy.sets.setsr'rEr(r)sympy.simplify.trigsimpr*sympy.matrices.exceptionsr+r,r-sympy.matrices.matrixbaser/sympy.matrices.determinantr0sympy.matrices.utilitiesr1sympy.matricesr2r3r4r5r6r7r8r9r:r;r<r=r>r?r@rArBrCrDrErFrGrHrIrJ sympy.corerKrL(sympy.functions.special.tensor_functionsrMsympy.utilities.iterablesrNrOrPsympy.utilities.exceptionsrQsympy.testing.pytestrRrSrTrUrVrWsympy.assumptionsrYsympy.tensor.arrayrZ$sympy.tensor.array.array_derivativesr[sympy.matrices.expressionsr\sympy.algebrasr]ryr^r"r_r`rarbrcrdrerfrrrgrhsympy.matrices.matricesrirjrlrvrrrrrrrrrrrr&r)r1r3r5r@rFrKrNrUrYr]rargrjrmrprtrwrzrrrrrrrrrrrrrrrrrrrrrrr r r(r,r0r3r7r9r=rBrHrJrWr[r`rirkr}rrrrrrrrrrrrrrrrrrrrrrrr rrrr"r)r,r0r3r;r?rBrrrrrrrrrrrrrrrrrrrr rrrrrrr!r#r'r/r1r3r6r9rArMrQrUrXr\r_rcrirlrprtr{r}rrrrrrrrrrrrrrrrrrrrr#r'r+r1r3r6r;r=rFrQrSr[r]rdrrrrrrrrrrrrqrrrsrs$66LLL "/&4=EEDD/:NN2*#%8,4C.LLLLLLL 8"C@@6::$@-%,,, <2G HBE  ^_o    ~@P  @6 + !+ &  9)XDN>^JB? _*J X_ % '  6% ; 5 8 GP y 8$ )&$ < < < < < K& d&K0O2d F D+84P1 $ :<7Mt 8!" AG2" "$$ - : &>9$"* )   .  *F!@.6&8G$1&3@E!P 1H%V&&'"$4.  L)2  !$;6z"IG O*4(nP !%IPZz.&"FH  $ <">JD-;-"8 / (1 (.3(? G4 \ p&(*&F"7 :& 455))+" * Z"$"$J71R$# + #E ' /8 1 1  20 5&#3*9#  $I<:; #< # ;  .!JH!JH6\*~>'B U*%(ij    sQ?#R ?R  R