K iDddlmZmZmZddlmZddlmZddlm Z ddl m Z ddl m Z mZddlmZmZmZmZmZddlmZdd lmZmZdd lmZdd lmZdd lmZdd l m!Z!m"Z"ddl#m$Z$m%Z%ddl&m'Z'ddl(m)Z)m*Z*m+Z+m,Z,m-Z-m.Z.m/Z/ddl0m1Z1ddl2m3Z3m4Z4m5Z5m6Z6m7Z7m8Z8m9Z9m:Z:m;Z;mZ>ddl?m@Z@ddlAmBZBddlCmDZEddlFmGZGmHZHmIZIdZJe5Gdde)e*e+ZKddddZLdZMe5Gdde)e*e,ZNddddZOd ZPe5Gd!d"e)e*e-ZQdddd#ZRd$ZSe5Gd%d&e)e*e.ZTdddd'ZUd(ZVe5Gd)d*e)e*e/ZWddde5Gd+d,e)e*e1ZXdddd-ZYd.ZZd/Z[d0Z\d1Z]d2Z^d3Z_d4Z`d5Zad6Zbd7Zcd8Zdd9Zed:Zfd;Zgd<Zhd=Zid>Zjd?Zkd@ZldAZmdBZndCZodDZpdEZqdFZrdGZsdHZtdIZudJZvdKZwdLZxdMZydNZzdOZ{dPZ|dQZ}dRZ~dSZdTZdUZdVZdWZdXZdYZdZZd[Zd\Zd]Zd^Zd_Zd`ZdaZdbZdcZddZdeZdfZdgZdhZdiZdjZdkZdlZdmZdnZdoZdpZdqZedrZdsZdtZduZdvZdwZdxZdyZdzZd{Zy#1swYxYw#1swYxYw#1swYzxYw#1swYdxYw#1swYNxYw#1swY>xYw)|)raisesXFAILwarns_deprecated_sympy)Q)Expr)Add)Function) NumberKind UndefinedKind)IIntegeroopiRational)S)Symbolsymbols)Abs)exp)sqrt)cossin) ShapeErrorNonSquareMatrixError) MatrixKind)_MinimalMatrix_CastableMatrix MatrixShapingMatrixPropertiesMatrixOperationsMatrixArithmetic MatrixSpecial)MatrixCalculus) Matrixdiageyematrix_multiply_elementwiseoneszeros SparseMatrixbandedMutableDenseMatrixMutableSparseMatrixImmutableDenseMatrixImmutableSparseMatrix)Poly)flatten)ImmutableDenseNDimArray)xyzc ddlm}m}m}m}m}m}m}ddlm }m }m } m } m } m} ddlm} m}m}m}|||||||||| | | | f }| |||f}|Dcgc]}|ddgddgg}}d }|D]Q}|D]&}t)5t+||d usJ ddd(t)5t+||d usJ dddSycc}w#1swY^xYw#1swYoxYw) Nr)MatrixRequiredrr"rr r! MatrixCommon)MatrixDeterminantMatrixReductionsMatrixSubspaces MatrixEigenr#MatrixDeprecated)r$ImmutableMatrixr*r/TF)sympy.matrices.commonr7rr"rr r!r8sympy.matrices.matricesr9r:r;r<r#r=sympyr$r>r*r/r isinstance)r7rr"rr r!r8r9r:r;r<r#r=r$r>r*r/ all_mixins all_matricesMMstmixins l/mnt/ssd/data/python-lab/Trading/venv/lib/python3.12/site-packages/sympy/matrices/tests/test_commonmatrix.py!test_matrix_deprecated_isinstancerO's%  J  L(4 4!!aVaV   4B 4 A1 4A') 4!!U+t333 4 4 4$ % 1a'50 00 1 1 1 5  4 4 1 1sB85B=C =C C c eZdZy)ShapingOnlyMatrixN__name__ __module__ __qualname__rCrNrQrQi rVrQNct||dS)Nct||k(SNintijs rNzeye_Shaping..nsAF rVrQns rN eye_Shapingrdms Q#; <.rrVrarbs rN zeros_Shapingriqs Q> 22rVc eZdZy)PropertiesOnlyMatrixNrRrCrVrNrkrkvrWrVrkct||dS)Nct||k(SrZr[r]s rNr`z eye_Properties..{3qAv;rVrkrbs rNeye_Propertiesrpz 1&> ??rVct||dS)NcyrgrCr]s rNr`z"zeros_Properties..rhrVrorbs rNzeros_Propertiesrt~ 1n 55rVc eZdZy)OperationsOnlyMatrixNrRrCrVrNrwrwrWrVrwct||dS)Nct||k(SrZr[r]s rNr`z eye_Operations..rnrVrwrbs rNeye_Operationsr{rqrVct||dS)NcyrgrCr]s rNr`z"zeros_Operations..rhrVrzrbs rNzeros_Operationsr~rurVc eZdZy)ArithmeticOnlyMatrixNrRrCrVrNrrrWrVrct||dS)Nct||k(SrZr[r]s rNr`z eye_Arithmetic..rnrVrrbs rNeye_ArithmeticrrqrVct||dS)NcyrgrCr]s rNr`z"zeros_Arithmetic..rhrVrrbs rNzeros_ArithmeticrrurVc eZdZy)SpecialOnlyMatrixNrRrCrVrNrrrWrVrc eZdZy)CalculusOnlyMatrixNrRrCrVrNrrrWrVrchtddgd}|jdk(sJ|jdk(sJ|ddk(sJ|ddk(sJt|gdk(sJt|dddfgdk(sJt|dddfddgk(sJt|ddddft|k(sJ|ddddf|k(sJt||k(sJtgdgdg|k(sJtgdgdf|k(sJtddg|k(sJtd |k(sJtddgdd gdd gg|k(rJy) Nr@rA)r?r@rArBr?r?rr?rBrrr?r@rA)rrrBr)rrowscolslistr3s rNtest__MinimalMatrixrsfq!/0A 66Q;; 66Q;; Q4199 T7a<< 7( (( ( !Q$=I %% % !Q$=QF "" " !Q$=DG ## # QT7a<< !  !! ! 9i0 1Q 66 6 9i0 1Q 66 6 9i0 1Q 66 6 0 1Q 66 6AAA78A=> >=rVctddgddggjttk(sJtddgddggjttk(sJtddgjttk(sJttggjttk(sJtdtdggggjtt k(sJt dggjttk(sJt dtdggggjtt k(sJy)Nr?r@rArBr)r$kindrr r3r r*rCrVrN test_kindrs Aq6Aq6" # ( (Jz,B BB B Aq6Aq6" # ( (Jz,B BB B !Q  Jz$: :: : A3%=  J!7 77 7 Avse}%& ' , , =0I II I !  # #z*'= == = !VaSE]+, - 2 2j6O OO OrVctddgd}|j}|jdk(sJtdD]}|||dzk(rJy)Nr@)r?rAr@rBr?rB)rQvecrrange)mm_vecr^s rNtest_vecrsT!Q -A EEGE ::?? 1X!Qx1q5   !rVc^td\}}}}t||g||gg}t||g||gg}t||g||gg}t ||g||gg}|j |j cxk(r3|j cxk(r|j cxk(r ||||dk(sJJy)Nza:d)rrrr?r?rr)rr,r.r-r/todok)abcdm1m2m3m4s rN test_todokrsJAq!Q aVaV, -B 1v1v. /B q!fq!f- .B AA/ 0B 88: 5rxxz 5RXXZ 5Aq!4 55 55 5rVc tjtjttztj gttt tdzgttj t tzdgg}tjtjttztj ttt tdzttj t tzdg }tdd|}|j|k(sJy)Nr@rArB) rOneHalfr3r4Zeror5rQtolist)lstflat_lstrs rN test_tolistrs EE1661Q3 '!Q1a41quufac1:M NCqvvqsAFFAq!QT1quufac1MH!Q)A 88:  rVctddtjdgdtjgtdgg}dtjidtjidtid}|j |k(sJy)NrAr@rr?rr?r@)rQrrrr3todod)rdicts rN test_tododrs_!Q!%%a[1a& ABA155zq!&&kq!f 5D 779  rVctddgdttfdttfdttfdttfdjdjdcxk(rt gd gd gk(sJJj dj dcxk(rt d dgd d gddggk(sJJjd jdcxk(rt gd gdgk(sJJj d j dcxk(rt d dgd dgddggk(sJJy)NrA r?r@rArBrr c&jdSNrrow_delesrNr`z"test_row_col_del..qyy|rVc&jdSNrrsrNr`z"test_row_col_del..qyy}rVc&jdSrcol_delrsrNr`z"test_row_col_del..rrVc&jdSrrrsrNr`z"test_row_col_del..rrVr@rrr?rBrrrrrrrr)rQr IndexErrorrr$rrs@rNtest_row_col_delrs&!Q ;.s a!erV)rrAr?r@)rArBr@rArBrr@r))rr?r@rAr?r@)rArBr@rArBr)rdreshaper$rQm0rs rN test_reshaper s QB ::a va,GH HH H 1a!3 4B :: 1 DE FF F ::a v&NO OO OrVctddgd}|jdtddgdk(sJ|jdtddgdk(sJy)NrArrr?r)r?rBr)rQrowr$colrs rN test_row_colrsO!Q ; " "6)#4 5 <! " "" "rVctdjtgdgtgdgdgdgdgk(sJy)NrArr?rr)rr?r)rrr?)rdcol_joinr$rCrVrN test_col_joinr#sB q> " "69+#6 7 9   rVctgdg}tddD]^}gd}|j|dtt dj ||j dj|k(r^Jy)NrBrBrBrrrBrAr)r$rinsertr1rd row_insertrr)r4r^ls rNtest_row_insertr+so  B 2q\N  A{1~00B7;;A>EEGHAMMMNrVc tgd}tddD]^}gd}|j|dtt dj ||j dj|k(r^Jtdj dtd d gd d gd d gd d gd d gd d ggtgd gd gd gd gdgdgk(sJy)NrrrrrrrBrArrr@)r?rrr@r@rrr)rr?rr@r@rrr)rrr?r@r@rrr)rrrr@r@r?rr)rrrr@r@rr?r)rrrr@r@rrr?) r$rrr1ri col_insertrrrd)c4r^rs rNtest_col_insertr3s  B 2q\P  A}Q'221b9==a@GGIJaOOOP q> $ $QAAAAQRTUPVYZ\]X^/_(` a ++++++ - . .. .rVc`tdddjgdddgtddgdk(sJjddggd tddgd k(sJjtdtdk(sJt t fd t t fd y) NrBrAc|dz|zSNrArCr]s rNr`ztest_extract..DQqS1WrV)rr?rArr?r@)rr?rArBr rrr@)rrr@rr c,jdgdgS)NrBrextractrsrNr`ztest_extract..Hqyy!qc2rVc,jdgdgS)NrrAr rsrNr`ztest_extract..IrrV)rQr r$rrrrs@rN test_extractrCs!Q 45A 99YA '6!Q8K+L LL L 99aVY '6!Q8K+L LL L 99U1XuQx (A -- - :23 :23rVctdddtdddjk(sJjtjcxk(rtgdgdgdgdgk(sJJttfd tjtk(sJtj d d }tj d d }tj d d }tj d d}tj||||j d k(rjd k(sJy)NrBrAc|dz|zSrrCr]s rNr`ztest_hstack..MrrVc|dz|zSrrCr]s rNr`ztest_hstack..NacAgrV) rr?r@rr?r@rr?r@) rArBrrArBrrArBr) rrrrrrrrr) rrr rrr rrr c(jSrZ)hstackrrsrNr`ztest_hstack..Uqxx2rVrr?r@r)rQrr$rrr)rr)M1M2M3M4rrs @@rN test_hstackrLs)!Q 45A 1a!5 6B    88Aq!  1 8 8Aq A 4V1111 M3F4 44 44 4  :./ ==?fh && & a B a B a B a B  RR0A 66Q;166Q;& &;rVctdddtdddjk(sJjtjcxk(r3tgdgdgdgdgdgdgdgdgdgdgdgdg k(sJJttfd tjtk(sJy) NrBrAc|dz|zSrrCr]s rNr`ztest_vstack..brrVc|dz|zSrrCr]s rNr`ztest_vstack..crrVrr)rrr)rrr c(jSrZ)vstackrsrNr`ztest_vstack..rrrV)rQr"r$rrrs@@rN test_vstackr#as!Q 45A 1a!5 6B    88Aq!  1 8 8Aq A .V + + + + + + + + + + + + M- F. . . . . . :./ ==?fh && &rVc tddddtddtz z g}|jtjtdtj thk(sJ|jt thk(sJyNr@r?)rkr3atomsrr NegativeOnerrs rN test_atomsr(wsbQAq!Q1W#56A 779!ammQ7 77 7 776?qc !! !rVcRttgdggjthk(sJyrg)rkr3 free_symbolsrCrVrNtest_free_symbolsr+}s% !qc + 8 8QC ?? ?rVctttfdf}|jtsJ|jtrJ|jt sJtdtfdf}|jtrJy)N)r@rAr@)rkr3r4hasr5rrs rNtest_hasr/siq!ff-.A 558O8uuQx< 55==q!ff-.AuuQx.s!rV)rrkis_anti_symmetricr4expandrrr)r3rs rNtest_is_anti_symmetricr6s] A 1q!f - ? ? AU JJ JQAq!taczA~qAEA:+q!A#PQrTUSUVWSWYZ#[\A   D (( (    .% 77 7    4 == =Q#:1HAHHJ#:;A    .$ 66 6Q$q'!"+8M#N1HAHHJ#NOA   E )) )$;#Ns :E E c tddgd}|jrJ|jsJ|jdsJtddgd}|jsJtddtddd}|jsJ|jsJtddgd}|tdddk(sJtddt dd}|jrJ|jsJtd }|jsJtd }|jsJt dddt dzdt zzdztt dzdzdd td dg }|jsJ|jdrJ|jjdsJy) Nr@rr?r?rFr1r?rrr?rAr?) r?rrrr@rrrrA))rrrrr))rrr)rrrr) rk is_diagonal is_symmetricr%r)r$r3r4r5rs rNtest_diagonal_symmetricalr=sQ<0A}}  >>   >>5> )) )Q<0A ==??Q41a=1A ==?? >>  Q#>?A Q1  Q5A;/A~~  ==??56A ==??34A ==??q!aA!aQUQJ1aAFGA >>  ~~u~-- - 88: " "E " 22 2rVcbtdtgt dgg}|jsJtdtztgt dgg}|jdusJtttgt dgg}|jJttdgt dgg}|jdusJy)Nr?r@F)rkr is_hermitianr3rs rNtest_is_hermitianrAsq!fr1g./A >>>qsAh!Q01A >>U "" "q!fr1g./A >> !! !q!fr1g./A >>U "" "rVctdjsJttdjrJtt djrJtgdgjrJy)NrAr)rp is_Identityrkr)r(rCrVrNtest_is_IdentityrDs_ !  ( (( (#E!H-999 9#DG,888 8#YK0<<< <>  Q<0A~~ rVc$tgdgdgdg}|jsJtddgd}|jsJtddgd}|jdusJ|jdusJtgdgdgdg}|jrJy) N)rArBr?)r@rBrrrA) rAr@rrBrBr?r?rr@) rAr@rrBrBr?r?rr@Fr)rkis_upper_hessenbergis_lower_hessenbergr.s rNtest_is_hessenbergrYsiI>?A  Q#>?A  Q#?@A E )) ) E )) )iI>?A$$$ $$rVctddgjsJtddgddggjsJttddjsJttdjrJttdgddggjdk(sJttdgddggjdk(sJt dd}t|dgddggjdk(sJy) NrrArBr?FrT)nonzero)rkis_zero_matrixr)r&r3rr@s rN test_is_zeror]s 1b ) 8 88 8 !Q!Q 0 1 @ @@ @ a , ; ;; ;#CF+::: : !Q!Q 0 1 @ @D HH H !Q!Q 0 1 @ @E II IsD!A !Q!Q 0 1 @ @E II IrVc ttddgdjhdk(sJtdd}ttdd|dddgj|dhk(sJy) Nr@)rr?r@rA>r?r@rAr3Trealrr?)setrkvaluesrrs rN test_valuesrcsx #Aq, &(   !! !sA #Aq1aA, &( 1v  rVcttd}|jdtddzk(sJ|jdtdk(sJ|jdt dk(sJy)NrAc d|zSNr@rCrs rNr`z test_applyfunc..s !A#rVr@cyrgrCrs rNr`z test_applyfunc..rhrVcyNr?rCrs rNr`z test_applyfunc..rhrV)rwr& applyfuncr)r()rs rNtest_applyfuncrkse c!f %B << &#a&( 22 2 << $a 00 0 << $Q // /rVcdtgddgg}tddgt dgg}|jt|k(sJy)Nrr?)r rwadjointr$)datanss rN test_adjointrp!sE q6Aq6 C A!Q0 1C ;;=F3K '' 'rVc  tddgd}tdddtjzddtjzzddtjzzddtjzzg}|j\}}||k(sJ||k(sJy)Nr@rFr?rArB)rwr ImaginaryUnit as_real_imag)rrrrs rNtest_as_real_imagrt's aL 1B a Q__ a!AOO"33 Aaoo q1Q__#44 6 7B ?? DAq 7N7 7N7rVctdtdggdg}|jtddgtdgddggk(sJ|jtdt dggdgk(sJ|j|j k(sJ|j |jjk(sJ|j tddgt dgddggk(sJy)Nrrr?r@rr?r@)rwr Tr$r conjugateHrJs rNtest_conjugater{2sq!Qi A 33&1a&a&a&"# ## # 33&1qb!*$&' '' ' 33!++-   33!##%%<< 33&Aq'2q'q'#$ $$ $rVcttttdgg}|ddtzk7sJ|jt dtzggk(sJy)NF)evaluaterr@)rwrr3doitr$r@s rN test_doitrDsOs1a%89:;A Q41Q3;; 668v!ug && &rVctddtddgtfdtdDsJtfdtdDsJtfdtdDsJy)Nr@r?rrc3lK|]+}j||jk(-ywrZevalf.0r^rs rN ztest_evalf..Ls*>qwwy|qtzz|+>s14c3pK|]-}jd||jdk(/ywr@Nrrs rNrztest_evalf..Ms.@!qwwqz!}! 1 -@36c3pK|]-}jd||jdk(/ywrrbrs rNrztest_evalf..Ns.8!qss1vayAaDFF1I%8r)rwrallrr@s@rN test_evalfrJsaQDGQ<0A >U1X> >> > @uQx@ @@ @ 8uQx8 88 8rVc ttttzzdgttztztztttttzzzzgg}|j}|t ttztdzzdgttdzzttdzzzttzttdzzztdzzggk(sJt dd}tddt t|zgjdt t|tt|zzgk(sJy)Nr@rArTr_r?)complex) rwr3r4r5r$rrr rr)rrrs rN test_expandrQs 1q5 1~!a%A q!aQi-?P/QR SB B  A#1*a1QT6AadF?AaC!AqD&L1a4,?@AC CC C sA 1s1Q3xj 1 8 8 8 F 3q6Ac!fH$% & '' 'rVc (tttdzttdzgttdzttdzzttdzttdzzgg}|j t jtt jtz}|ttdzttgtdzttztdzttzggk(sJ|j t jtt jtz}|ttdztgttdzztdztzggk(sJ|j t jtt jtz}|ttdzt gt tdzztdz tzggk(sJyrf) rwrr3rr4refinerr`r$positivenegativers rN test_refiner^su A 41:6q!t*SVQY&QT 3q619(<=? @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 9rVctdt\tddfd}tddfd}|j}||k(sJy)NF, Gclsr@c||zSrZrC)r^r_Gs rNr`ztest_replace..m!A#rVc||zSrZrCr^r_Fs rNr`ztest_replace..nrrVrr rwreplace)KrJNrrs @@rN test_replacerksK 6x (DAqQ#67AQ#67A !QA 6M6rVc Ttdt\}tdd|dd|dif|dd|dif|dd|dif|dd|difg}tddfd}|j|d}||k(sJy)Nrrr@rr?c||zSrZrCrs rNr`z"test_replace_map..wrrVTr)rrrJrrs @rNtest_replace_maprss 6x (DAqQQqTAaD!A$<$81Q4!A$!:NQRSTQUXYZ[X\PQRSPTXVQWYZ[\Y]`abc`dfghifj_kXl$n oAQ#67A !QA 6M6rVcHtddgddgg}||jdcxk(r|jdk(sJJ|jd|jdcxk(r$|jdcxk(rtdk(sJJ|jd|jd cxk(r$|jd cxk(rtd k(sJJ|j|jd cxk(r$|jd cxk(rtdk(sJJy)Nr?r@rArBrrr))rBrAr@r?rr))r@rBr?rAi)rAr?)rBr@)r$rot90r.s rN test_rot90r|sAA A  (aggaj (( (( ( 771: N Nf=M6N NN NN N 771: N Nf=M6N NN NN N 779 Nqwwr{ Nf=M6N NN NN NrVc td}td}tdtz dtz ztttzztz g|tt|tzz|tz dd|z t |t z|z z zt z gg}|jtttzttzz dtzgdtzdddt t |zzz t |zz zggk(sJdtzdz}t|gg}|jt|ggk(sJ|jtt|jtggk(sJtddgddgg}d|jz jtdd k(sJy) Nrcfr?r@)ratiorArB") rr rwr3r4rrr2r$rtracer)rcrrJeqrs rN test_simplifyrss A A1Q319q1Q3wRSmVQ4!AaD&=!A$&QqS3q2v;q=-@(AB(FHJ KA ::<6a!ea!e_QQRU#T$%E1q1SAY;A.F+GI#KL LL L a%!BrdV$A ::<6B4&> )) ) ::B: 6BKKbK,A+B*C#D DD D Q!Q !A qwwyM # # %!R 88 8rVc0tdtgtdggjtdtddgddggk(sJttdgttzdggjtdgtdggtddgddggk(sJttdgttzdggjtdftdfgtddgddggk(sJttdgttzdggjtdtditddgddggk(sJtttzggjttdz ttdz id ttdz tdz zggk(sJy) Nr?rBrr@rrrT) simultaneous)rwr3subsr$r4rCrVrN test_subsrs !Q!Q 0 1 6 6q! <AQRTUPVGW@X XX X !Q!a% 4 5 : :QGaW;M N B7RG$ % && & !Q!a% 4 5 : :QGaW;M N B7RG$ % && & !Q!a% 4 5 : :Ar1b> J B7RG$ % && & !A# ( - -q!a%AE.BQU - V QUQUO$% & '' 'rVcVtgdgdgdg}|jdk(sJy)Nr)rrr)rrr)rwrrzs rN test_tracers-i A 779??rVc&tdtgtdggjtditddgddggk(sJttdgttzdggjtdtditddgddggk(sJy)Nr?rBrr@rrr)rwr3xreplacer$r4rCrVrN test_xreplacers !Q!Q 0 1 : :Aq6 B Aq6Aq6" # $$ $ !Q!a% 4 5 > >2q"~ N B7RG$ % && &rVctddgdttfdttfdj ddgddgg}j ddgddgg|cxk(rt gd gd gd gk(sJJjddgddgg}j ddgddggd |cxk(rt gdgdgdgk(sJJjddgddggd}j ddgddggd d|cxk(rt gdgdgdgk(sJJj gdt gd gd gd gk(sJddlm }j |gdt gd gd gd gk(sJy)NrArB) r?r@rArBrrrrrrr  c,jddggS)Nrr)permuter@srNr`ztest_permute..sqyy1a&2rVc8jtdS)Nr3)rrr@srNr`ztest_permute..sqyy5rVrr@r?rG)rrr rrFr) orientation)r@rAr?rB)rrrr)rr rrbackward) direction)rr)rAr?r@rB)rrrr)r rrr)r?r@rrA) Permutation) rwrr ValueError permute_rowsrr$ permute_colssympy.combinatoricsr)rrrs @rN test_permutersQ#JKA :23 :56 AA'(A 99q!fq!f% &! >v,;,;,;7=0> >> >> > AA'(A 99q!fq!f%69 :a ."+++$-. .. .. . AA':>A 99q!fq!f%6Z9 PTU ."+++$-. .. .. . 99\ "f,;,;,;.='> >> > 0 99[. /6,;,;,;;=4> >> >rVc>tgdgdgdgdg}|jd}|tgdgdgdgdgk(sJ|jd}|tgdgdgdgdgk(sJ|j}|tgdgdgdgdgk(sJy)Nr?r?r?r?r@)rrr?r?)rrrr?rrrrr)rr?r?r?)rwupper_triangular)rRs rNtest_upper_triangularrs  A 1A $$$$$ &   2A $$$$$ &   A $$$$$ &  rVc>tgdgdgdgdg}|j}|tgdgdgdgdgk(sJ|jd}|tgdgdgdgdgk(sJ|jd}|tgdgdgdgdgk(sJy)Nr)r?rrr)r?r?rr)r?r?r?rr@rr)rwlower_triangularr)rLs rNtest_lower_triangularrs$$$$  A A $$$$$ &&' '' ' 1A $$$$$ &   2A $$$$$ &  rVctddgttgg}t|tddgt tt tggk(sJy)Nr?rr@)rr3r4absrrs rNtest_absrsGq"g1v./A q6)Aq6CFCF3C*DE EE ErVc Ftgdtttgdtzdttzggztgddtzdtzdtzgdtzddtztzggk(sJtddddgt t fdy) Nrr@i)r@rBrrBir?czSrZrCrrcsrNr`ztest_add..s q1urV)rr3r4r5rrrs@@rNtest_addrsi!QQqS#qsODEA q5()ac1Q3!_qsDRSTURUVWRWFX)YZ ZZ ZQAq6*A :}%rVc>tdtdttfdttfdz}|ddk(sJ|ddk(sJ|d d k(sJ|d d k(sJ|d d k(sJ|ddk(sJ t d|ddk(sJ|ddk(sJ|d d k(sJ|d d k(sJ|d d k(sJ|ddk(sJj |}|t|k(sJ|ddk(sJ|ddk(sJ|d d k(sJ|d d k(sJ|d dk(sJ|ddk(sJttfdtdz}t|tsJ|dtk(sJ|ddtzk(sJ|d dtzk(sJ|d dk(sJtz}||k(sJdz}t|tsJ|ddk(sJ|ddk(sJ|d dk(sJ|d dk(sJ t dt|tsJ|ddk(sJ|ddk(sJ|d dk(sJ|d dk(sJttdd}tdd }t|||g}|j |t|g|g|ggk(sJy#t $rYwxYw#t $rYqwxYw)N)rrr:)r)rArczSrZrCrrsrNr`z%test_multiplication..-s qsrVcizSrZrCr@srNr`z%test_multiplication...s adrVrrrr@rrr)r@rrrz c = a @ brBc&jSrZ)multiply_elementwisersrNr`z%test_multiplication..Lsq55a8rVr3rArrz c = 5 @ br?)rrr TypeErroreval SyntaxErrorrr'rrGr3r$r(r)rhc2r_hrrrs @@rNtest_multiplicationr!sf A  A  :{# 9l# !A T7a<< T7a<< T7a<< T7a<< T7b== T7a<<  [w!||w!||w!||w!||w"}}w!|| q!A +Aq1 11 1 T7a<< T7a<< T7b== T7a<< T7a<< T7a<< :89 F3KA a- .. . T7a<< T7ac>> T7ac>> T7a<< QB 7N7 AA a- .. . T7a<< T7c>> T7c>> T7a<<  [!1222w!||w#~~w#~~w!|| tAqzA 1a.BB|A ! !! $   0)  i    N    s$ J% J J  J  JJc"tddgddgg}|jdtk(sJ|jdtk(sJ t d t dy#t $rYt $rY"wxYw#t $rYyt $rYywxYw)Nr?r@rArBz2 @ aza @ 2)r$ __matmul__NotImplemented __rmatmul__rrrr@s rN test_matmulrtsAA A <<?n ,, , == ~ -- -  W   W            s0 A A8 A5*A54A58 BB BcGddt}tddgddgg}|}||zt|d|zgd|zd|zggk(sJ||zt|d|zgd|zd|zggk(sJy)zd Test that if explicitly specified as non-matrix, mul reverts to scalar multiplication. ceZdZdZdZdZy)test_non_matmul..fooFrN)rSrTrU is_Matrix is_MatrixLikerrCrVrNfoors  rVrr?r@rArBN)rr$)rrrs rNtest_non_matmulrs d AA A A Q3&1ac(QqS!A#J/0 00 0 Q3&1ac(QqS!A#J/0 00 0rVcttdtddgddgg}|dzdddk(sJtgdgdgd g}|dzddd k(sJ|d ztdk(sJ|d z|k(sJtdggd zddd zk(sJtd dgddggt dztddgddggk(sJt d dgddgg}|j dd|j ddk(sJy)NctddzS)Nrr@r$rCrVrNr`ztest_power..s):rVr@rArBr)iii,*i7)r@r?rA)rBr@rB)rrr?) i"iiiipiiirr?drrrrcayley)methodmultiply)rrrr&r r$powr.s rN test_powerrs- !:;q!fq!f-.A qD!92 22 2iJ?@A qD!9E EE E a43q6>> a4199 1# '3 . 5C ?? ? !Q!Q 0 171: =AUXY[]W^aceg`hViAj jj j1qe}A 55H5 %r*)E EE ErVcLtddddg}| tddddgk(sJy)Nr?r@rrrrbs rNtest_negrs2QAq6*A 2%aRH5 55 5rVcPtddddg}||z tddddgk(sJy)Nr?r@rrrbs rNtest_subr s4QAq6*A q5(A1v6 66 6rVc tddddg}|dz tddtjtddz gk(sJyrQ)rrrrbs rNtest_divr sAQAq6*A Q3&q!affad1f-=> >> >rVcBttjddgdk(sJttjdgdk(sJttjdtk(sJttjdttk(sJy)Nr@r9r)rrr&typer$rCrVrNtest_eyers !%%a+ , << < !%%a( )\ 99 9 !%%a( )-> >> > !%%aV%4 5 ?? ?rVcttjddgdk(sJttjdgdk(sJtjddtgdgdgk(sJt tjdtk(sJt tjdttk(sJy)Nr@rrAr?r?r?r)rrr(r$r rCrVrN test_onesrs !&&q!, - == = !&&q) *l :: :  ! !!Q '69i2H+I II I !&&q) *.? ?? ? !&&qf&5 6& @@ @rVcttjddgdk(sJttjdgdk(sJtjddtgdgdgk(sJt tjdtk(sJt tjdttk(sJy)Nr@rrArr)rrr)r$r rCrVrN test_zerosrs !''1- ., >> > !''* +| ;; ;  " "1a (FIy3I,J JJ J !''* +/@ @@ @ !''v'6 76 AA ArVc tjtddgddggtdtgtdggtdtdgtdt gttt ggtgdgddddtddgddtdddgdddddtgddddtdggk(sJtgdgddddtdddgddtddddgdddddtdgddddtdt gddddttt ggk(sJtgdgddddtdddgddtdt ddgddttt ddgddddddtgdddddtdggk(sJtttt gtddgdd ggtd d ggd ttdddddgtdddddgt dddddggd gdgdgdgk(sJt tfddtdggk(sJddtddgddggk(sJddtddgddggk(sJdddtddgddgddggk(sJddgtddgddggk(sJtddgtdgdggk(sJdddgd gddgddgd ggdcxk(rtddgddgd dggk(sJJtdtk(sJtdttk(sJtjgdtjdddk(sJtjgddjdk(sJtjgdgjdk(sJtjgdgdjdk(sJtjgdggjdk(sJtjtddddtgdgdgk(sJtjtddddtddgddgddgddggk(sJy)Nr?r@rA)r?r@rrrr)r@rArrrrr)r?r@rrrrr)r@rArrrrrrBrrr)rrrrrr)rrr?r@rr)rrrArBrr)rrrrrrcddS)NrrrrCrrrr%srNr`z test_diag_make..stAq!QQ7rVr)r)rrF)unpackrrrr)rrr?r)rrrr@) rr%r$r3r4r5rrr rr(rs@@@@rNtest_diag_makersT  ! !DAA AAA AAq Aq!9q!Qi01A 1a=F Aq!Q Aq!Q Aq!Q Aq!Q $   1a=F Aq!Q1 Aq!Q1 Aq!Q1 Aq!Q1 Aq!Q1$   1a=F Aq!Q1 Aq!Q1 Aq!Q1 Aq!Q1 Aq!Q1$   1ayAAA AAxA 1a v Aq!Q Aq!Q Aq!Q'    :78 7fqcUm ## # ?fq!fq!f%56 66 6 ?fq!fq!f%56 66 6  "fq!fq!fq!f-E&F FF F !Q=F A A$   1v 6  + $   QFAu - 1#1vs#E 2 6< A A A>7    Q=- -- - QF# $ .. . ;;y !V[[Aq%9 99 9 ;;y / 5 5 ?? ? ;; { # ) )V 33 3 ;; {5 1 7 76 AA A ;; } % + +v 55 5 ;;tAqz1a (F4-   ;;tAqz1a (F A A A A 4-  rVc tddtdj}|jdk(sJt|dk(sJtjddk(sJtjddk(sJtjd d k(sJt jt k(sJt ddd di}t |jt |k(sJt t |k7sJt tfd t tfd t tfdtd d}ttd|jz |jDcic]}|t|j|c}|k(sJycc}w)NrArr)rrBrr?)r?rr)rArr@)r@rc&jdSrdiagonalrsrNr`ztest_diagonal..,sqzz!}rVc&jdS)NrrrsrNr`ztest_diagonal..-sqzz"~rVc.jtSrZ)rrrsrNr`ztest_diagonal...sqzz"~rV) r$rrtupler r*rrr(r+rrr)rsrJr^rs @rN test_diagonalr" sq!U1XA A  1   8y  A 6 )) ) B F ** * A 4 '' '  a (( (QFA;'A  a (( ( 7d1g   :,- :-. :-. Q A qx(* d1::a=))* +./ 00 0*s"F?ctjddtjddcxk(rktjddcxk(rPtjdddcxk(r4tjdddcxk(rtgdgd gd gk(sJJtjddd tgd gd gdgk(sJttdttdttdttdtjddtjddk(sJy)NrAr@ eigenvalue)sizer%upper)band)r&eigenvalr%)r@r?r)rr@r?r lower)r@rrrvrc,tjdSrfr jordan_blockrCrVrNr`z#test_jordan_block..Ds0==a@rVc.tjddS)Ng @r@r,rCrVrNr`z#test_jordan_block..Fs0==c1ErVc.tjdS)Nr@r$r,rCrVrNr`z#test_jordan_block..Hs0===KrVc0tjddS)Nr@rB)r%r)r,rCrVrNr`z#test_jordan_block..Ks  * *q + "rV)r&r))rr-r$rrrCrVrNtest_jordan_blockr14sV  ) )!Q /3D3Q3QRS`a3Q3b  --1-C  --a-A !--q.2        ) )!QW ) =IB     :@A :EF :KL :"#  ) )qQ ) ?&&A&: ;; ;rVc tddgddgg}|jtdgdggtdgdgggk(sJ|jtdgdggdtdtdzdz gtddz gggk(sJ|jtdgdggtdgdggtdgdggttd dgtd dgggk(sJ|jtd gd ggtdgdggtdgdgggk(sJ|jtd gd gggk(sJtgd gd gdg}tdgdggtdgdggtdgdggg|jtdgdggttddgtddgggk(sJtgdtgdtgdgt t fdtgdtgdtgdgt t fdy)Nr?r@rArBT) normalizerrirr)rr?r)rArr)rrr@rrrr)r?rBrc.tjddiSN rankcheckTr$ orthogonalizevecssrNr`z$test_orthogonalize..dv33TJTJrVrrc.tjddiSr7r9r;srNr`z$test_orthogonalize..gr=rV)r$r:rrrr)rrcr<s @rNtest_orthogonalizer?Ss`AA A ??6A3*- .6A3*3E2F FF F ??6A3*-? > !DG)A+a , -. // / ??6A3*-vtaSk/B C !qc VhsA&6%7(1a.9I$JKL MM M ??6A3*-vtaSk/B C "s    ??6A3*- ." 44 4 :y12A RD1#; "s !4frdRD\6J KD 1??D ! "s fx2&7(2r:J9K%LMN OO O 9 vi0&2C DD :JK 9 vi0&2C DD :JKrVc \tjd\}}|tgdgdgdgk(sJ|tgdgdgdgk(sJtjd\}}|tgdgdgd gd gd gd gd gk(sJ|tgdgdgdgd gd gd gd gk(sJy)Nr?)rr?r)r?rr?)rr?r?)r?r?rrA)rr?rrrrr)r?rr?rrrr)rr?rr?rrr)rrr?rr?rr)rrrr?r?r?r)rrrrr?r@r?)rrrrrr?rA)rAr?rrrrr)r?r@r?rrrr)rr?r?r?rrr)r$ wilkinson)wminuswpluss rNtest_wilkinsonrDis$$Q'MFE V * ) )+, ,, , F%%%'( (( ( $$Q'MFE V 8 7 7 7 7 7     F111111134 44 4rVctd\}}tdd||g}|j|tddddgk(sJy)Nx yr@r?r)rrdiffr$r3r4rs rN test_diffrIsD 5>DAq1a!Q(A 66!9q!aV, ,, ,rVctd\}}tdd||g}|j|tdd|dzdz ||zgk(sJy)NrFr@r?)rr integrater$rHs rNtest_integraterLsP 5>DAq1a!Q(A ;;q>VAq1a461Q3-8 88 8rVc td\}}tdd|t|z|t|z|dzg}tdd||g}t t|| t|zgt||t|zgd|zdgg}|j ||k(sJtddgdtddgdt tfdt tfd y) Nzrho,phirAr?r@rrFrBc<jtddgSrQ)jacobianr$rsrNr`z test_jacobian2..sajjA8rVc&jSrZ)rOrsrNr`z test_jacobian2..sbkk!nrV)rrrrr$rOrr)rhophiXYJrrs @@rNtest_jacobian2rVsy!HC1a#c#h,CH c1f!EFA1a#s,A SC4C=! SCCL! cEq! A ::a=A  1a.A Aq, /B 989 9,-rVc td\}}tddd|z |g}|j|dtddt dd|gk(sJy)NrFr@r?r)rrlimitr$rrHs rN test_limitrYsQ 5>DAq1a!A#q*A 771a=F1a(1a.!)<= == =rVctgdgdgdggdttfdttfdy)NrrrrczSrZrCrJvsrNr`z"test_issue_13774.. acrVczSrZrCr\srNr`z"test_issue_13774..r^rV)r$rrr\s@@rNtest_issue_13774r`s- 9i01AA 9k" 9k"rVc:tdtdttdttfdttfdttfdtd\}}}t j t d|gt | gk(sJt j t d||gt d | gd| ggk(sJt j t d|||gt d d | gdd | gd d| ggk(sJy) Nr3r4c,tjdSri)r$ companionrCrVrNr`z test_companion..sv//2rVcDtjtdgSrir$rcr0rsrNr`z test_companion..sv//aS! =rVcFtjtddgSr%rersrNr`z test_companion..sv//aVQ@rVcLtjtzgSrZre)r3r4srNr`z test_companion..s!v//QqS1a&0ABrVzc0:3r?r)rrrrr$rcr0)c0c1rr3r4s @@rNtest_companionrjss As A :23 :=> :@A :BCJBB   D!R!, -" >> >   D!Ra0 1RC1rc(#$ %% %   D!RR!4 5As aRC[1a"+67 88 8rVc Ptd\}}}t|||g}|jt|||ggd}|tdgdgdggk(sJt|||||g|||||g|||||gg}|jt|gdg}|tgdgdgdgk(sJy)Nzx, y zrr?r@rA)r?r?r?r?r?)rr$rzip)r3r4r5rrs rNtest_issue_10589rmshGAq! Aq B aAY * +B !qcA3( (( ( !Q1a1aAq/Aq!Q?C DB aS1# B /?KL LL LrVcGddt}tddgd}|ddgd}||z}t||sJ|tddgddggk(sJy) Nc*eZdZejdzZy)test_rmul_pr19860..Foog{Gz?N)rSrTrUr, _op_priorityrCrVrNFoorps)66= rVrrr@rFrrrr)r.r$rG)rrrrrs rNtest_rmul_pr19860rssh>"> q!\"A Aq,A !A a   B"b*+ ++ +rVctddgddggtddgddggttfdttfdy)Nr?r@rArBczSrZrCrrsrNr`z"test_issue_18956.. a!erVczSrZrCrvsrNr`z"test_issue_18956..rwrV)Arrayr$rrrvs@@rNtest_issue_18956rzsD 1v1vA1qe}A 9m$ 9m$rVcGddt}tddddg}||k7sJGdd|}||k(sJy)NceZdZdZdZy)test__eq__..Myc3KddywrQrCselfs rN__iter__ztest__eq__..My.__iter__sGG s ct||SrZ)r)rr^s rN __getitem__z"test__eq__..My.__getitem__s:a= rVN)rSrTrUrrrCrVrNMyr}s   !rVrr@r?ceZdZdZy)test__eq__..My_sympyct|SrZrrs rN_sympy_z$test__eq__..My_sympy._sympy_s $< rVN)rSrTrUrrCrVrNMy_sympyrs rVr)objectr$)rrrs rN test__eq__rsL!V! q!aVA 99 2   ??rV)sympy.testing.pytestrrrsympy.assumptionsrsympy.core.exprrsympy.core.addrsympy.core.functionr sympy.core.kindr r sympy.core.numbersr r rrrsympy.core.singletonrsympy.core.symbolrr$sympy.functions.elementary.complexesr&sympy.functions.elementary.exponentialr(sympy.functions.elementary.miscellaneousr(sympy.functions.elementary.trigonometricrrsympy.matrices.exceptionsrrsympy.matrices.kindrrDrrrrr r!r"rEr#sympy.matricesr$r%r&r'r(r)r*r+r,r-r.r/sympy.polys.polytoolsr0sympy.utilities.iterablesr1#sympy.tensor.array.dense_ndim_arrayr2ry sympy.abcr3r4r5rOrQrdrirkrprtrwr{r~rrrrrrrrrrrrrrrrrrrrrrrr#r(r+r/r6r=rArDrIrLrOrSrUrYr]rcrkrprtr{rrrrrrrrrrrrrrrrrrrrrr r rrrrr"r1r?rDrIrLrVrYr`rjrmrsrzrrCrVrNrshGF (5;;"-469=F*7773'-P:1B  NO]  =3  ~@P  @6  ~@P  @6  ~@P  @6  NO]    ^_n  ?&P!5  M& ,  P/ "N . 4'*'," @ *3@#=$"  %J0( $$' 9 ' :O9$ '&">HBBF &Pf 2 1 F6 7 ? @ABL^0(;>L,4D--9 ."> # 8M ,% {#            sH I;,JJ2J"J/2J<;JJJ"J,/J9<K