K i6ddlmZmZmZmZmZmZmZmZm Z m Z m Z m Z m Z mZmZddlmZmZmZmZmZmZddlmZmZmZmZmZmZmZddlmZddl m!Z!ddl"m#Z#m$Z$m%Z%m&Z&m'Z'm(Z(ddl)m*Z*m+Z+m,Z,m-Z-m.Z.m/Z/m0Z0m1Z1m2Z2m3Z3m4Z4m5Z5ddlm6Z6dd l7m8Z8ed \Z9Z:Z;d ZdZ?dZ@dZAdZBdZCdZDdZEdZFdZGdZHdZIdZJdZKe6dZLdZMdZNdZOdZPd ZQd!ZRd"ZSd#ZTd$ZUd%ZVd&ZWd'ZXd(ZYd)ZZd*Z[d+Z\d,Z]y-).)SpioosymbolsFunctionRationalIntegerTupleSymbolEqNeLeLtGtGe) EulerGamma GoldenRatioCatalanLambdaMulPow) Piecewisesqrtceilingexpsincossinc)raises)implemented_function)eyeMatrix MatrixSymbolIdentityHadamardProduct SparseMatrix) jnynbesseljbesselybesselibesselkhankel1hankel2airyaiairybi airyaiprime airybiprime)XFAIL julia_codezx,y,zchttddk(sJttddk(sJy)NC67z-1)r5r e/mnt/ssd/data/python-lab/Trading/venv/lib/python3.12/site-packages/sympy/printing/tests/test_julia.py test_Integerr=s0 gbk "d ** * gbk "d ** *r;cXttdddk(sJttdddk(sJttdddk(sJttd ddk(sJtttddzd k(sJttddtzd k(sJy) Nz3 // 7 2iz-3 // 7z x + 3 // 7z (3 // 7) * x)r5rxr:r;r< test_RationalrFs hq!n % 11 1 hr1o &# -- - hq"o &) 33 3 hr2& '8 33 3 a(1a.( )\ 99 9 hq!nQ& '> 99 9r;cttttdk(sJtt ttdk(sJtt ttdk(sJtt ttdk(sJttttdk(sJttttdk(sJy)Nzx == yzx != yzx <= yzx < yzx > yzx >= y) r5r rEyr rrrrr:r;r<test_RelationalrI!s bAh 8 ++ + bAh 8 ++ + bAh 8 ++ + bAh 7 ** * bAh 7 ** * bAh 8 ++ +r;ctttttzdk(sJtt tdk(sJtt tdk(sJy)Nzsin(x) .^ cos(x)zabs(x)zceil(x))r5rrErabsrr:r;r< test_FunctionrL*sQ c!fA& '+= == = c!f  )) ) gaj !Y .. .r;c ttdzdk(sJtttdzzdk(sJtttddzdk(sJt dt tdtz}td|tdztttzz zz tdztzz d k(sJtt d ttt ttd d d d dk(sJy)Nr?zx .^ 3z x .^ (y .^ 3)z x .^ (2 // 3)gg @z.(3.5 * 2 * x) .^ (-x + y .^ x) ./ (x .^ 2 + y)F)evaluater9z-2 * x ./ (y .* y))r5rErHrr rrr)rOs r<test_PowrS0s ad x '' ' a!Q$i O 33 3 a!Q' (O ;; ;S&AaC.1A a1cQAX..1q9 :8 99 9 c"aS1e%@ ADX YY Yr;ctttzdk(sJtttzdk(sJtttz dk(sJtt dk(sJy)Nx .* yzx + yzx - yz-x)r5rErHr:r;r<test_basic_opsrV<sZ ac?h && & a!e  '' ' a!e  '' ' qb>T !! !r;ctdtz dk(sJttdzttdzcxk(rdk(sJJtdttz dk(sJtttj zttdzcxk(rdk(sJJtttdk(sJtttjzttdzcxk(rdk(sJJtdt z d k(sJtt dztt dzcxk(rd k(sJJtt dzd k(sJy) NrPz1 ./ xr9gz 1 ./ sqrt(x)gzsqrt(x)g?z1 / piz 1 / sqrt(pi))r5rErrHalfrr:r;r<test_1_over_x_and_sqrtrYCs0 ac?h && & ae  1d7 3 ?x ?? ?? ? aQi N 22 2 a!&&j !Z4%8 JN JJ JJ J d1g ) ++ + ai Jq#v$6 C) CC CC C ad x '' ' b"f BH!5 A AA AA A b$h > 11 1r;ctdtzdk(sJtttzdk(sJtdtz dk(sJtttz dk(sJttdz dk(sJtttz dk(sJtttzdk(sJtdtztzd k(sJtdtztztzd k(sJtttz d k(sJtdtztz d k(sJtttztz d k(sJtttz tzdk(sJtdtz tz dk(sJtdtztztz tz dk(sJtdtztz dk(sJtt ddz dk(sJtt ddz tzdk(sJtttz tz dk(sJtttztz dk(sJtttzttzz dk(sJtttzt z dk(sJttdz tz dk(sJtt ddz tztztz dk(sJy)Nr?z3 * xzpi * xz3 ./ xzpi ./ xzx / 3zx / pirUz 3 * x .* yz3 * pi * x .* yzx ./ yz 3 * x ./ yz x .* y ./ zz x .* z ./ yrPz 1 ./ (x .* y)rNz2 * pi * x ./ (y .* z)z 3 * pi ./ xz3 // 5z (3 // 5) * xz x ./ (y .* z)z (x + y) ./ zz(x + y) ./ (x + z)z(x + y) / eulergammaz x / (3 * pi)z(3 // 5) * x .* y / pi)r5rErrHzrrr:r;r<test_mix_number_mult_symbolsr]Qs ac?g %% % bd x '' ' ac?h && & bd y (( ( ac?g %% % ad x '' ' ac?h && & ac!e  ,, , ad1fQh #4 44 4 ac?h && & ac!e  ,, , ac!e  -- - ac!e  -- - ac!e  // / ad1fQhqj !%= == = ad1f  .. . ad1f  )) ) ad1fQh > 11 1 ac!e  // / qsAg . 00 0 qsQqSk "&: :: : qsJ& '+A AA A ac"f  // / ad1fQhqjm $(@ @@ @r;cZttdzdk(sJttdzdk(sJtttdzzdk(sJtttzdk(sJttttzzdk(sJtttztzdk(sJy) Nr?zpi ^ 3rNzx .^ 2z x .^ (pi ^ 3)zx .^ yz x .^ (y .^ z)z (x .^ y) .^ z)r5rrErHr\r:r;r<test_mix_number_pow_symbolsr_ls b!e  (( ( ad x '' ' a"a%j !_ 44 4 ad x '' ' a!Q$i O 33 3 q!tai O 33 3r;ctd}t|dk(sJtd|zdk(sJttddz |zdk(sJtdd|zzd k(sJy) NIimr[5imr?rNz (3 // 2) * imz3 + 4im)rr5)ras r< test_imagreusm #A a=D  ac?e ## # qtAvqj !_ 44 4 a!e  )) )r;cdttdk(sJttdk(sJtt dk(sJttjdk(sJttj dk(sJttj dk(sJttddk(sJy)NrInfz-InfNaNerP)r5rrrNegativeInfinityrhExp1rr:r;r<test_constantsrl}s b>T !! ! b>U "" " rc?f $$ $ a(( )V 33 3 aee  %% % aff  $$ $ c!f  $$ $r;ctdtzdk(sJtdtzdk(sJtdtzdk(sJy)NrNz 2 * goldenz 2 * catalanz2 * eulergamma)r5rrrr:r;r<test_constants_otherrnsH a m $ 44 4 ai M 11 1 a l #'7 77 7r;ctttzdk(sJtttzdk(sJttdk(sJtttztzdk(sJtttztzdk(sJtttztzdk(sJtttztzdk(sJy)Nzx && yzx || yz!xz x && y && zz x || y || zz z || x && yz z && (x || y))r5rErHr\r:r;r< test_booleanrps a!e  (( ( a!e  (( ( qb>T !! ! a!eai M 11 1 a!eai M 11 1 q1uk "m 33 3 q1uk "o 55 5r;ctttdk(sJtttdzdk(sJttttdzzdk(sJy)Nz sinc(x / pi)r?zsinc((x + 3) / pi)z sinc(x + 3))r5rrErr:r;r< test_sincrrsU d1g . 00 0 d1q5k "&: :: : d2Q<( )] :: :r;c &ttdddgdk(sJtdttdz t tgddt gdt dttgg}d}t||k(sJt|dddfdk(sJt|dddfdk(sJttddgd k(sJttdd gd k(sJtttttz t ggd k(sJy) NrP z[10]rNrzB[1 sin(x / 2) abs(x); 0 1 pi; 0 e ceil(x)]z [1, 0, 0]z[1 sin(x / 2) abs(x)]z zeros(0, 0)r?z zeros(0, 3)z [x x - y -y]) r5r"rrErKrrrrHAexpecteds r< test_Matricesrxs fQB4( )V 33 3C!Hc!f%Ar CFGAJ') *A(H a=H $$ $ a!f  ,, , a!f !8 88 8 fQ2& '= 88 8 fQ2& '= 88 8 fq!a%!n-. /> AA Ar;ctdtdtz dtztz dz gg}t |dk(sJt |j dk(sJy)NrPrNr?r[z"[1 sin(2 ./ x) (3 // 5) * pi ./ x]z$[1, sin(2 ./ x), (3 // 5) * pi ./ x])r"rrErr5Trvs r<test_vector_entries_hadamardr|sTC!Had1fQh'()A a=@ @@ @ acc?D DD Dr;ctdtdtz dtztz dz gddttzgg}d}t ||k(sJy)NrPrNr?r[z.[1 sin(2/x) 3*pi/(5*x); 1 2 x*y])r"rrErrHr5rus r<"test_Matrices_entries_not_hadamardr~sQ C!Had1fQh'!Q!56A)H a=H $$ $r;ctdd}td||}td||}t||zdk(sJt||zdk(sJtd|z|zd k(sJt|dz|zd k(sJt||d t|zzzd k(sJt|tdzzd k(sJt|d zdk(sJt|t j zdk(sJy)NnT)integerrvBzA * BzB * ArNz 2 * A * Bz 2 * B * Ar?zA * (3 * eye(n) + B)z A ^ (x .^ 2)zA ^ 3z A ^ (1 // 2))r r#r5r$rErrX)rrvrs r<test_MatrixSymbolrssD!AS!QAS!QA ac?g %% % ac?g %% % ac!e  ++ + ac!e  ++ + aQx{]*+ ,0F FF F a!Q$i N 22 2 ad w && & ai N 22 2r;c<tdtdzdk(sJy)Nr?z 6 * eye(3))r5r$r:r;r<test_special_matricesrs a m $ 44 4r;c ptdddddddggdd d gd gd k(sJtd dk(sJtdgdk(sJtddk(sJttgddk(sJtdttzdtdzffdk(sJtdt dt ddggfdk(sJy)NrPrNr?rdr[rr@rBrt z5Any[1, 2, 3, Any[4, 5, Any[6, 7]], 8, Any[9, 10], 11])rPrN)r?rdz(1, 2, (3, 4))zAny[1])rPz(1,)rPrNr?z (1, 2, 3)z(1, x .* y, (3, x .^ 2))rz.(1, [1 0 0; 0 1 0; 0 0 1], zeros(0, 0), Any[]))r5r rErHr!r"r:r;r<test_containersrs q!QA1vAr7B? @? @@ @ n %)9 99 9 qc?h && & d v %% % eY' (K 77 7 q!A#1a4y) *.H HH H q#a&&Ar"2B7 8z&test_julia_piecewise..s z$/r;)rrEr5rr ValueError)rwrs @r<test_julia_piecewisers> aQZ!Q$ .D d ; ;; ; dc *( ** * dc% 8    adAE]QT1q5MAqD!a%=1a4, OD1H d x '' ' dc *fx.? ?? ? dc% 8     aQZ!Q$AQQ @D :/0r;ctttdkftdzdf}td|zdk(sJt|tz dk(sJt|ttzz dk(sJt|dz dk(sJy) NrPrNTz2 * ((x < 1) ? (x) : (x .^ 2))z((x < 1) ? (x) : (x .^ 2)) ./ xz&((x < 1) ? (x) : (x .^ 2)) ./ (x .* y)r?z((x < 1) ? (x) : (x .^ 2)) / 3)rrEr5rH)pws r< test_julia_piecewise_times_constrs Aq1u:1d| ,B ad ? ?? ? bd @ @@ @ b!A#h #K KK K bd ? ?? ?r;ctgdg}t|ddk(sJtddgddgg}t|d d k(sJy) Nrarz a = [1 2 3]rPrNr?rdrvzA = [1 2; 3 4])r"r5r{s r<test_julia_matrix_assign_torsP {A a3 '= 88 8AA A a3 '+< << .sz!q9r;ctSrr4rvrsr<rz2test_julia_matrix_assign_to_more..z!q9r;r"r#r5rrrrvrs @@r< test_julia_matrix_assign_to_morersV {AS!QAS!QA a1 % 66 6 :9: :9:r;ctdggtddd}tdddt|dk(sJttfdy) Nr?rrPrrNrzB = [3]ctSrr4rsr<rz'test_julia_matrix_1x1..'rr;rrs @@r<test_julia_matrix_1x1r sNu AS!QAS!QA a1 % 22 2 :9:r;cFttdttzgg}t|ddz|dz|dzdk(sJt ddd}t|dk(sJt|ddzt |dz|dzd k(sJtt |d k(sJy) NrNrr)rrP)rrNzx .^ 2 + x .* y + 2AArPr?z%sin(AA[1,2]) + AA[1,1] .^ 2 + AA[1,3]zAA[1,1] + AA[1,2] + AA[1,3])r"rErHr5r#rsumr{s r<test_julia_matrix_elementsr*sAqs }A agqj1T7*QtW4 59N NN NT1a A a=D  agqj3qv;.37 8 2 33 3 c!f !> >> >r;ctddk(sJttjdk(sJtddk(sJttjdk(sJy)NTtrueFfalse)r5rrrr:r;r<test_julia_booleanr4sV d v %% % aff  '' ' e  '' ' agg ' )) )r;ctt5ttjdddt d}t|t jt ddk(sJy#1swYDxYw)NfF)strictz:# Not supported in Julia: # Derivative Derivative(f(x), x))rNotImplementedErrorr5rComplexInfinityrrEdiff)rs r<test_julia_not_supportedr;sc # $&1$$%&  A adiil5 1    &&s A--A6ctd}td}t|tdkf|tdkfd}t|ddk(sJy) Nendless elsewhererrP)rPTF)rzCif (x < 0) endless elseif (x <= 1) elsewhere else 1 end)rrrEr5)t1t2rs r<%test_trick_indent_with_end_else_wordsrGsP 9B ;B BA;Q!V i 8B b '   r;cXtddd}tddd}tddd}tddd}t||}t|dk(sJt||zdk(sJt||z|zd k(sJt||zd k(sJt|tztzd k(sJy) Nrvr?rvrPhzA .* Bz (A .* B) * vzh * (A .* B) * vz (A .* B) * Az(x .* y) * (A .* B))r#r%r5rErH)rvrrrrs r< test_haramardrVsS!QAS!QAS!QAS!QA1A a=H $$ $ ac?n ,, , ac!e  2 22 2 ac?n ,, , ac!e  5 55 5r;ctddi}d|d<d|d<d|d<d |d <ttz|d <t|d k(sJy) Nr[rrt)rNrN)rPrN)rPr?)rr?)r?rzHsparse([4, 2, 3, 1, 2], [1, 3, 3, 4, 4], [x .* y, 20, 10, 30, 22], 5, 6))r&rErHr5)Ms r< test_sparserdsZQ2AAdGAdGAdGAdGcAdG a=R  r;ctd}ttttfD]*}t ||t |jdzk(r*JttttfD])}t |t |jdzk(r)Jt t|t dk(sJt t|t dk(sJt t|t dk(sJt t|t dk(sJy)Nrz(n, x)z(x)zhankelh1(n, x)zhankelh2(n, x)z?sqrt(2) * sqrt(pi) * sqrt(1 ./ x) .* besselj(n + 1 // 2, x) / 2z?sqrt(2) * sqrt(pi) * sqrt(1 ./ x) .* bessely(n + 1 // 2, x) / 2)r r)r*r+r,r5rE__name__r/r1r0r2r-r.r'r()rrs r< test_specfunrpss Aw 1<!Aq'"ajj8&;;;;<k6; 76!A$1::#55556 gam $(8 88 8 gam $(8 88 8 bAh #d dd d bAh #d dd dr;ctddd}tddd}tddd}t|ddk(sJtd|dzdk(sJ|dj|||z }t|d k(sJy) NrvrPr?rrrzA[1,1]z 3 * A[1,1]z (A - B)[1,1])r#r5subs)rvrrFs r<test_MatrixElement_printingr|sS!QAS!QAS!QA ag ( *+ * a!D'k "l 23 2 $ QAA a=N *+ *r;N)^ sympy.corerrrrrrr r r r r rrrrrrrrrrsympy.functionsrrrrrrrsympy.testing.pytestrsympy.utilities.lambdifyr sympy.matricesr!r"r#r$r%r&sympy.functions.special.besselr'r(r)r*r+r,r-r.r/r0r1r2r3sympy.printing.juliar5rErHr\r=rFrIrLrSrVrYr]r_rerlrnrprrrxr|r~rrrrrrrrrrrrrrrrrr:r;r<rs.?????IIIII'9;;NNNN'+ ' 1a+ :,/ Y" 2A64*%8 6; B&E%% 35 o1@@=;;?*   6  e ,r;