K i*ddlmZmZmZmZmZmZmZmZm Z m Z m Z m Z m Z mZmZddlmZddlmZddlmZmZmZmZmZmZmZmZmZmZmZm Z m!Z!m"Z"m#Z#m$Z$m%Z%m&Z&m'Z'm(Z(m)Z)m*Z*m+Z+m,Z,m-Z-m.Z.m/Z/m0Z0m1Z1m2Z2m3Z3m4Z4m5Z5m6Z6m7Z7m8Z8m9Z9m:Z:m;Z;mZ>m?Z?m@Z@mAZAmBZBmCZCmDZDddlEmFZGed\ZHZIZJZKedZLdZMd ZNd ZOd ZPd ZQd ZRdZSdZTdZUdZVdZWdZXdZYdZZdZ[dZ\y))SpioosymbolsFunctionRationalIntegerTuple DerivativeEqNeLeLtGtGe)Integral)Sum)0expsincosfresnelcfresnels conjugateMaxMingamma polygammaloggammaerferfierfcerf2expinterfinverfcinvEiSiCiliShiChi uppergammabeta subfactorialerf2inv factorial factorial2catalanRisingFactorialFallingFactorialharmonicatan2secacschermitelaguerreassoc_laguerrejacobi gegenbauer chebyshevt chebyshevulegendreassoc_legendreLiLambertW)mathematica_codezx,y,z,wfchttddk(sJttddk(sJy)NC67-1)mcoder k/mnt/ssd/data/python-lab/Trading/venv/lib/python3.12/site-packages/sympy/printing/tests/test_mathematica.py test_IntegerrOs0   %% %   %% %rMcXttdddk(sJttdddk(sJttdddk(sJttd ddk(sJtttddzd k(sJttddtzd k(sJy) Nz3/7 2iz-3/7zx + 3/7z(3/7)*x)rKrxrLrMrN test_RationalrXs !Q E )) ) "a !S (( ( !R !V ++ + "b! "e ++ + Xa^# $ 11 1 !Q! "i // /rMcttttdk(sJtt ttdk(sJtt ttdk(sJtt ttdk(sJttttdk(sJttttdk(sJy)Nzx == yzx != yzx <= yzx < yzx > yzx >= y) rKr rWyr rrrrrLrMrNtest_Relationalr[#s Aq?h && & Aq?h && & Aq?h && & Aq?g %% % Aq?g %% % Aq?h && &rMc tttttdk(sJtt tt tzdk(sJtttttzdk(sJttttdk(sJtttdk(sJttttttttzdk(sJtttdk(sJtttdk(sJtttd k(sJtt!ttd k(sJtt#ttd k(sJtt%td k(sJtt'td k(sJtt)tdk(sJtt+tdk(sJtt-ttdk(sJtt/ttdk(sJtt1tdk(sJtt3tdk(sJtt5ttdk(sJtt7tdk(sJtt9tdk(sJtt;tdk(sJtt=tdk(sJtt?tdk(sJttAtdk(sJttCttdk(sJttEtdk(sJttGtdk(sJttItdk(sJttKttdk(sJttMttd k(sJttOtd!k(sJttQtd"k(sJttQttd#k(sJttStd$k(sJttUtd%k(sJttUtd&d'k(sJttUttd(k(sJy))Nz f[x, y, z]z Sin[x]^Cos[x]zArcCsc[x]*Sec[x]z ArcTan[x, y]z Conjugate[x]zMax[x, y, z]*Min[y, z]z FresnelC[x]z FresnelS[x]zGamma[x]z Gamma[x, y]zPolyGamma[x, y]z LogGamma[x]zErf[x]zErfc[x]zErfi[x]z Erf[x, y]zExpIntegralE[x, y]zInverseErfc[x]z InverseErf[x]zInverseErf[x, y]zExpIntegralEi[x]zCosIntegral[x]zLogIntegral[x]zSinIntegral[x]zSinhIntegral[x]zCoshIntegral[x]z Beta[x, y]z Factorial[x]z Factorial2[x]zSubfactorial[x]zFactorialPower[x, y]zPochhammer[x, y]zCatalanNumber[x]zHarmonicNumber[x]zHarmonicNumber[x, y]zLogIntegral[x] - LogIntegral[2]z ProductLog[x]rIzProductLog[-1, x]zProductLog[y, x])+rKrErWrZzrrr7r8r6rrrrrrr,rrrr!r r"r#r%r$r/r&r(r)r'r*r+r-r0r1r.r4r3r2r5rBrCrLrMrN test_Functionr^,s 1a  ,, , Q3q6! "o 55 5 Q$q'! "&8 88 8 q!  // / 1 . 00 0 Q1c!Qi' (,D DD D !  .. . !  .. . q?j (( ( Aq! "m 33 3 1a !%6 66 6 !  .. . Q=H $$ $ a>Y && & a>Y && & a  ++ + 1 "6 66 6   0 00 0   .. . A #5 55 5 A<- -- - A<+ ++ + A<+ ++ + A<+ ++ + Q=- -- - Q=- -- - a  ,, , 1 . 00 0 A ? 22 2 a !%6 66 6 !!Q' (,B BB B A& '+= == =   2 22 2 ! !4 44 4 !Q $: :: : A<< << < !  00 0 !R !%8 88 8 !Q $6 66 6rMcttttdk(sJtt ttdk(sJtt ttt dk(sJttttt tdk(sJttttt dk(sJttttdk(sJttttdk(sJttttdk(sJttttt d k(sJy) NzHermiteH[x, y]zLaguerreL[x, y]zLaguerreL[x, y, z]zJacobiP[x, y, z, w]zGegenbauerC[x, y, z]zChebyshevT[x, y]zChebyshevU[x, y]zLegendreP[x, y]zLegendreP[x, y, z])rKr9rWrZr:r;r]r<wr=r>r?r@rArLrMrNtest_special_polynomialsraVs A #3 33 3 !Q $5 55 5 1a( )-A AA A 1a# $(= == = Aq!$ %)? ?? ? Aq! "&8 88 8 Aq! "&8 88 8 !Q $5 55 5 1a( )-A AA ArMcpttdzdk(sJtttdzzdk(sJtdttdztttzz zz tdztzz dk(sJttdzd k(sJttt ddzd k(sJy) NrQzx^3zx^(y^3)g @z(3.5*f[x])^(-x + y^x)/(x^2 + y)gzx^(-1.0)zx^(2/3))rKrWrZrErrLrMrNtest_Powrebs A;%   QT y (( ( AaDHAqD))1a4!84 5) ** * D>Z '' ' HQN" #y 00 0rMctdd\}}}}tttztzdk(sJtttz|zdk(sJtttz|z|zdk(sJtttz|z|z|zdk(sJtt|z|z||zz|ztzdk(sJy) NzA B C DF) commutativezx*y*zzx*y*Azx*y*A**Bz x*y*A**B**Czx*y*A**B**(C + D)**A)rrKrWrZr])ABCDs rNtest_Mulrlks6JAq!Q 1Q<7 "" " 1Q<7 "" " 1Qq>Z '' ' 1Qq } ,, , 1QAq" #'= == =rMcttjdk(sJttjdk(sJttjdk(sJttj dk(sJttj dk(sJttdk(sJttjdk(sJttjdk(sJttjd k(sJttjd k(sJttd k(sJttjd k(sJttjd k(sJtdtjzdk(sJttjdk(sJttj dk(sJy)N01rJz1/2IInfinityz -InfinityComplexInfinity IndeterminateEPi GoldenRatiozE(1/3 + (1/3)*(19 - 3*33^(1/2))^(1/3) + (1/3)*(3*33^(1/2) + 19)^(1/3))rdzG2*(1/3 + (1/3)*(19 - 3*33^(1/2))^(1/3) + (1/3)*(3*33^(1/2) + 19)^(1/3)) EulerGammaCatalan)rKrZeroOne NegativeOneHalf ImaginaryUnitrNegativeInfinityrrNaNExp1rrvTribonacciConstantrwrxrLrMrNtest_constantsrts =C   <3    4 '' ' =E !! !  !S (( ( 9 "" " ## $ 33 3 "" #'8 88 8 1q"gr: ;3 44 4  $4 44 4 !:   ;%    " #{ 22 2rMcddlm}m}m}m}|gdgdgdgdg}||}||}||}t |t |cxk(rdk(sJJt |t |cxk(rdk(sJJt |ddgd k(sJt |ddgd k(sJt |dd gd k(sJt |dd gd k(sJt |d dgd k(sJt |d dgdk(sJy)Nr)MutableDenseMatrixMutableSparseMatrixImmutableDenseMatrixImmutableSparseMatrix)rcrIrr)rrcrIr)rrrcrI)rrrrcz;{{1, -1, 0, 0}, {0, 1, -1, 0}, {0, 0, 1, -1}, {0, 0, 0, 1}}zsSparseArray[{{1, 1} -> 1, {1, 2} -> -1, {2, 2} -> 1, {2, 3} -> -1, {3, 3} -> 1, {3, 4} -> -1, {4, 4} -> 1}, {4, 4}]z{}zSparseArray[{}, {0, 0}]rQzSparseArray[{}, {0, 3}]z {{}, {}, {}}zSparseArray[{}, {3, 0}])sympy.matricesrrrrrK)rrrrrhrirjrks rN test_matricesrs\44      A AAQAa A 8uQx      8uQx      #Aq"- .$ 66 6 $Q2. /3L LL L #Aq"- .$ 66 6 $Q2. /3L LL L #Aq"- .. @@ @ $Q2. /3L LL LrMcddlm}m}m}m}|gdgdgdggdgdgdgg}t |d k(sJ||}t |d k(sJ||}t |d k(sJ||}t |d k(sJy) Nr)MutableDenseNDimArrayImmutableDenseNDimArrayMutableSparseNDimArrayImmutableSparseNDimArray)rcrdrQr)rrrRr)rTrr ) )rS)zg{{{1, 2, 3, 4}, {5, 6, 7, 8}, {9, 10, 11, 12}}, {{13, 14, 15, 16}, {17, 18, 19, 20}, {21, 22, 23, 24}}}aSparseArray[{{1, 1, 1} -> 1, {1, 1, 2} -> 2, {1, 1, 3} -> 3, {1, 1, 4} -> 4, {1, 2, 1} -> 5, {1, 2, 2} -> 6, {1, 2, 3} -> 7, {1, 2, 4} -> 8, {1, 3, 1} -> 9, {1, 3, 2} -> 10, {1, 3, 3} -> 11, {1, 3, 4} -> 12, {2, 1, 1} -> 13, {2, 1, 2} -> 14, {2, 1, 3} -> 15, {2, 1, 4} -> 16, {2, 2, 1} -> 17, {2, 2, 2} -> 18, {2, 2, 3} -> 19, {2, 2, 4} -> 20, {2, 3, 1} -> 21, {2, 3, 2} -> 22, {2, 3, 3} -> 23, {2, 3, 4} -> 24}, {2, 3, 4}])sympy.tensor.arrayrrrrrK)rrrrexamples rN test_NDArrayrs::$         G >> >> >&g.G >> >> >%W-G >    'w/G >    rMc ttttttdk(sJttt tdz t dzz tt t ft t t fdk(sJy)NzHold[Integrate[Sin[Sin[x]], x]]rdzTHold[Integrate[Exp[-x^2 - y^2], {x, -Infinity, Infinity}, {y, -Infinity, Infinity}]])rKrrrWrrZrrLrMrN test_Integralrss #c!f+q) *.O OO O #q!teadl+rc2,rc2,( ) % %% %rMc tttttdk(sJttttdk(sJtttttdzztddk(sJtttttdzztttdk(sJtttttdzzttdtdk(sJy) NzHold[D[Sin[x], x]]z Hold[D[x, x]]rrdzHold[D[y^4*Sin[x], {x, 2}]]zHold[D[y^4*Sin[x], x, y, x]]rQz!Hold[D[y^4*Sin[x], x, {y, 3}, x]])rKr rrWrZrLrMrNtest_Derivativers CFA& '+? ?? ? Aq! "o 55 5 CF1a4KA. /3P PP P CF1a4KAq1 26T TT T CF1a4KAq!4 59\ \\ \rMc  tttttddfdk(sJttt tdz t dzz tt t ft t t fdk(sJy)NrrzHold[Sum[Sin[x], {x, 0, 10}]]rdzNHold[Sum[Exp[-x^2 - y^2], {x, -Infinity, Infinity}, {y, -Infinity, Infinity}]])rKrrrWrrZrrLrMrNtest_Sumrsu SVaBZ( )-L LL L S!Q$A&"b\"b\# $ % %% %rMcFddlm}|jddk(sJy)Nr MCodePrinterz Hello Worldz(* Hello World *))sympy.printing.mathematicar _get_commentrs rN test_commentrs'7 > & &} 5  rMctdt}ddi}t|t|dk(sJt|t|dk(sJdddfgi}t|t|dk(sJy) N some_function)cls SomeFunction)user_functionszSomeFunction[z]cy)NTrL)rWs rNz test_userfuncs..srMSomeOtherFunctionzSomeOtherFunction[z])rrrKr])rmy_user_functionss rNtest_userfuncsr sO:M(.9 a( *    a( *    N,?@AB a( *   rMN)] sympy.corerrrrrrr r r r r rrrrsympy.integralsrsympy.concretersympy.functionsrrrrrrrrrrrrr r!r"r#r$r%r&r'r(r)r*r+r,r-r.r/r0r1r2r3r4r5r6r7r8r9r:r;r<r=r>r?r@rArBrCrrDrKrWrZr]r`rErOrXr[r^rarerlrrrrrrrrrrLrMrNrs<<<<<$;;;;;;;;;;;;;A Y  1a SM& 0''7T B1>)23MB2j%]% rM