7^(h(ddlmZddlmZddlmZmZmZmZm Z m Z m Z ddl m Z ddlmZddlmZmZddlmZmZmZddlmZdd lmZmZmZmZmZmZdd l m!Z!dd lm"Z"dd l#m$Z$m%Z%m&Z&m'Z'dd l(m)Z)ddl*m+Z,m-Z.m/Z/edZ0edZ1eddZ2edZ3edZ4dZ5dZ6dZ7dZ8dZ9dZ:dZ;dZd Z?d!Z@d"ZAd#ZBd$ZCd%ZDy&)')Sum) expand_func)FloatIRationalnanoopizoo)S)Symbol)Abs polar_lift)exp exp_polarlog)sqrt) dirichlet_etalerchphipolylog riemann_xi stieltjeszeta)O)ArgumentIndexError) bernoulli factorialgenocchiharmonic)raises)test_derivative_numericallyrandom_complex_numberverify_numericallyxabT)negativezsc tttusJttttusJtdtddk(sJtdttj tz k(sJtdt tj t z k(sJtdtusJtddtusJtddtusJtdttusJtddtdzdz k(sJtddtdk(sJtdtdzdz k(sJtdtdzd z k(sJtdtdzd z k(sJtddtdzd z td d z k(sJtd dtd tddz k(sJttj djtk(sJtttj dttj dz k(sJttdjtk(sJtttdttdz ddtzz z k(sJtddtusJtddtusJtddtusJttdk(sJtdtddk(sJtddk(sJtdtddk(sJtddk(sJtdtddk(sJtddtddk(sJtdd tddk(sJtddtddk(sJtddtddk(sJtdddk(sJtdddk(sJtddtddk(sJtddtddk(sJtddtddk(sJtddtddk(sJtdjd jtd!d d"sJy)#NriZiiNiE xiiiiiiiiD"z1.2020569031595942854gҶOɃ;)rrr$rr Halfr&r r funcrr evalf epsilon_eqro/var/www/skyplay_api_hub/venv/lib/python3.12/site-packages/sympy/functions/special/tests/test_zeta_functions.pytest_zeta_evalrEs  9   3<3   7hr1o %% % 1:! ## # 1:! ## # 7c>> 1:   2;#   1:   1:Qq  1:a  7b!eAg   7b!eBh   7b!eCi   1:QrHR$44 44 4 1:a8FF#;; ;; ; ?  4 '' ' tAFFA '4rrsimplifyr strrr@rBrCrDtest_dirichlet_eta_evalrOWs  qvv %% %  A .. .  s1v %% % AFF # , , ."Q$ 66 6 A !c!f* ,, ,  r1uRx '' '  r1uXa%55 55 5 }Q%%%+ ,0O OO O }Q"((2(. /3P PP PrCc@tdtdz k(sJtdtddk(sJtdtddk(sJtdjtdt dzdtzz k(sJtdtdzdz k(sJy)Nr,r.rr-r/r0)rr rrewriterrBrCrDtest_riemann_xi_evalrScs a=BqD  a=HQN ** * a=HQN ** * a=  &!DG)QrT*: :: : a=BE"H $$ $rCcPddlm}tttj t |sJtttj t|sJt tj tttdddtz zz z k(sJt tj tdt tk(sJtttttj t tsJtttttj ttsJtt tt tj ttsJt ttj ttdttk(sJtttj ttttdtzk(sJtdttj t t ttk(sJttttdj tztttk(sJy)Nr Piecewiser-r,)r%)$sympy.functions.elementary.piecewiserV isinstancerr$rRrrr#r%rrr)r(rUs rDtest_rewritingrYks> mA&..t4i @@ @ mA&..x8) DD D 7??= )]1-=q1q1u:~-N NN N 7??=A? .$q' 99 9 mA. a0@0H0H0NPQ RR R mA. a0@0H0H0RTU VV V d1gtAw}'Eq II I 1:  h '8Aq!+< << < 1a=  *hq!Q.?.A AA A Aq!  $ $T *d1aj 88 8 XaA  & &w / /71a= @@ @rCcddlm}tttj t|ttttk(sJtttj tt ttdztzk(sJt tttj tt ttdz ttt tttzz tz k(sJt tttj tt t ttdztzk(sJtttj tttdz ttz k(sJttttttsJttttsJtt ttsJtt ttsJttfdttfdttfdttfdy)Nr) Derivativer-cDttjdS)Nr,rr$fdiffr&csrDz"test_derivatives..x1a'8'>'>q'ArCcDttjdS)Nr0r]r_srDraz"test_derivatives..rbrCcBttjdS)Nr-rr(r^r&srDraz"test_derivatives..wq!}':':1'=rCcBttjdS)Nr/rerfsrDraz"test_derivatives..rgrC)sympy.core.functionr[rr$r%diffrr(r)rrandcplxtdr r)r[r&r`s @@rDtest_derivativesrm|s. 1:??1 DAJ!: :: : 1:??1 !DQN!2 22 2  1a aXaQ2Qx1a7H5HH!K LL L Aq!  ! !! $8Aq1ua+@(@ @@ @ 1a=  a GAE1$5a$7 77 7 A A d1aj!   gamQ   hq!Q ## # hq!Q ## # AB AB => =>rCc8t|}|||k(S||k(ryi}|jD]}t||<t|j |j |j ttj |j z dkS)NFg|=) r free_symbolsrkabssubsrLreplacerr)r?targetexpandedrqr%s rDmyexpandrus4 H 6!!4 D   *Q tyy  "!!)S166t<>>@A BDI JJrCc ttddk(sJttdttk(sJttdtt k(sJttt t t ztddztttt t ztddzk(sJttt t t zdz tttt t zdz k(sJttdttdtz  sJttdttdtz z sJttdttdtz dzz sJdtz dzttdtzjtdtzzk(sJttdtdsJy) Nrr-r+r0r/r,r5r:)rr)rrrrr rrrur(rrrMrBrCrDtest_polylog_expansionrwsr 1a=A   1a=DG ## # 1b>mA.. .. . 1i"Xa^ 34 5C"XVWYZ^H[D\9] ]] ] 1i"oa' (GAs1R4y{,C CC C GAqMCAJ; // / GAqM1a!e9 -- - GBNAq1uqjL 11 1 qS1H{72q>2 2 < < >!QU) KK K GBND )) )rCc(tdtjtdttdzdz ztdzdz ztdzdz zttdzzk(sJtdt tjtdtdz tdzdz zt tztt ddz zdz ztt ddz zdz zttdzzk(sJtt ddz t jtddt t dtdzzdz zt dtdzzdz z tdzd z zttdzzk(sJy) Nr-r<rKr,r/r0r )rr(rGrrr rBrCrDtest_polylog_seriesr{sf 1a=  Q  '1q!tAv:1Q+>Aa+G!AqD'+Q QQ Q 1d1g  % %a1 % -1q!tAvQ1G ad1f+a-2ad1f+a-2(*+AqD'22 22 2 1Q46A2  % %aA .1"tAwq!t|A~2E q'!Q$,q.3a463"$%adG3, ,, ,rCctdd}ttdd|zdzdzz |dtjfj j dd z d ksJy) NiT)integerr-r/r,rr0gʡE?gMbP?)r rrr InfinitydoitrL)r}s rDtest_issue_8404rshsD!A s1acAg\>Aq!**#56;;=??B    rCc tddtdzdz ttztdzz k(sJtdtj tdzdz tddzdz z k(sJtj dt ddz dz t ddz dz t ddz dz dt dz dz fD]G}ttd|jtd|djz d krGJtd }d D]t}td D]d}tt||t||d|d dtj dsJtt||t||d|ddddrdJvddl m }td|dtddftj k(sJy)Nr,r0r6r<r-r/F)evaluategV瞯rrr@r ranger#sympy.integrals.integralsrr$)r(r)_rs rDtest_polylog_valuesrs 1a=BE!Gad3q6k1 11 1 1aff QrCFAIaK!7 77 7ffa$q'!)Q$q'!) Q$q'!) Q4PQ7TU VZ71a=&&(71a%+H+N+N+PPQTYYYYZs A >r >A%gamWQE5R&'2qvvD DD%gamWQE5R&'1a1> >> >>3 1hq1a), -!&& 88 8rCc ttdttt ttsJttt tdt tt t z sJttt dttdt z z t dt z dzz zsJttt dtdsJttt ttjdtdz zt ttt tt z t ttdtt ztt z z zsJttt tddt z t tt t dzz zsJttt ttdddsJttt ttdddsJttt ttdddsJttt ttdddsJttdttdt zt ttdz zdt zt ttdzdz zz sJtttttdsJttt ttdsJtttttztddzttdsJy) Nr-r+r,r7r/r4r:r<)rurr)r%rr(rr r>rrrrrr rBrCrDtest_lerchphi_expansionrsk HQ1%tAqz 22 2 HQ1%wq!}Q 77 7 HQA&1q5 Aq1uqjL(@ AA A HQA& -- - HQ166*AJ47 3DG ; ':b>$q'+A B47 J!KL MM M HQ1%r!tgamAqD.@'@ AA A HQ8Aq>2D 99 9 HQ8Aq>2D 99 9 HQ8B?3T :: : HQ8B?3T :: : HRA&GDAaCL(1r74AE193E+EE GG G HQ1%t ,, , HaRA& -- - HS2hq!n!45q!S  Q  ## # R=A-- -- - S>Q.. .. . Q?a// // / Q q00 00 0rCcttdjdz dksJttddjdz dksJttddjdzdksJy) Nrg;x?g& .>g?g0}j?r-r,g(?)rprr@rBrCrDtest_stieltjes_evalfrsv y|!!#k1 2T 99 9 yC &&(;6 7$ >> > yA$$&4 5 << 1"Q$-G GG G aCFac? 9QqS> )Qy1~-= >C !9  Y '3 .. . tAqs| $Q(1a.(@ @@ @ tQB| $ ++ + tQB{ #tQB{ 22 2s A !9QqS !! !rCN)Esympy.concrete.summationsrrirsympy.core.numbersrrrrr r r sympy.core.singletonr sympy.core.symbolr $sympy.functions.elementary.complexesrr&sympy.functions.elementary.exponentialrrr(sympy.functions.elementary.miscellaneousr&sympy.functions.special.zeta_functionsrrrrrrsympy.series.orderrr%sympy.functions.combinatorial.numbersrrrrsympy.testing.pytestr sympy.core.randomr!rlr"rkr#r$r%r&r(r)rErHrOrSrYrmrurwr{rrrrrrrrBrCrDrs)+EEE"$BHH9rr 2ZZ'MM 3K 3K 3 3K 3K7Kt@ Q%A"?* J *, 9"D21"= )$ "rC