7^(hjVddlmZmZmZmZmZmZmZmZm Z m Z m Z m Z m Z mZmZmZmZddlmZmZddlmZmZddlmZddlmZmZmZmZddlm Z ddl!m"Z"m#Z#ddl$m%Z%dd l&m'Z'm(Z(dd l)m*Z*m+Z+m,Z,dd l-m.Z.dd l/m0Z0m1Z1m2Z2m3Z3dd l4m5Z5m6Z6m7Z7m8Z8ddl9m:Z:ddl;mm?Z?ddl@mAZAddlBmCZCddlDmEZEddlFmGZGddlHmIZImJZJmKZKmLZLddlMmNZNmOZOmPZPmQZQmRZRmSZSe#d\ZTZUZVdZWdZXdZYeJeIdZZdZ[dZ\eJdZ]eJdZ^eJd Z_d!Z`d"Zad#Zbd$Zcd%Zdd&Zed'Zfy()))mellin_transforminverse_mellin_transformfourier_transforminverse_fourier_transformsine_transforminverse_sine_transformcosine_transforminverse_cosine_transformhankel_transforminverse_hankel_transformFourierTransform SineTransformCosineTransformInverseFourierTransformInverseSineTransformInverseCosineTransformIntegralTransformError)laplace_transforminverse_laplace_transform)Function expand_mul) EulerGamma)IRationaloopi)S)Symbolsymbols) factorial)re unpolarify)exp exp_polarlog)sqrt)atancossintan)besselibesseljbesselkbessely) Heaviside)erfexpint)gamma)meijerg) gammasimp) hyperexpand)trigsimp)XFAILslowskipraises)xsabcdz nu beta rhocddlm}td}t|ttt ||ttt k(sJt|tt t ztt ||ttt tt dzt z zdtfdfk(sJy)Nr)MellinTransformfT) sympy.integrals.transformsrBrrr;r<r#r2r)rBrCs c/var/www/skyplay_api_hub/venv/lib/python3.12/site-packages/sympy/integrals/tests/test_transforms.pytest_undefined_functionrG$s: A AaD!Q '?1Q4A+F FF F AaD3r7NAq 1 1q! $uQU|A~ 52wE FF Fctd}t|tttjthk(sJt|tt zttjtt hk(sJy)NrC)rrr;r< free_symbolsr=)rCs rFtest_free_symbolsrK,sW A AaD!Q ' 4 4 ;; ; AaDFAq ) 6 61a& @@ @rHc ddlm}td}t|ttt j d|tt dz z|tztdtfk(sJt|ttt j d||ttdtztzt ztzztt tfk(sJt|ttt dj d||ttt tzztdtfk(sJtd tztzt|t t ttt fj dzd k(sJtd tztzt#|t t tj dzd k(sJt%|t t tj d||t td tztzt ztzzt t tfk(sJy) Nr)IntegralrCrMrDTnocondsz.Integral(f(s)/x**s, (s, _c - oo*I, _c + oo*I))z2Integral(f(s)*exp(s*x), (s, _c - oo*I, _c + oo*I)))sympy.integrals.integralsrMrrr;r<rewriterrr#rrrstrrr=r>rr)rMrCs rFtest_as_integralrU2s2 A AaD!Q ' / / ;QUAaD1a*- .. . QqT1a ( 0 0 <1c"Q$r'!)A+&&RC 5 66 6 QqT1a 6 > >z J1c1"Q$i!Q, -- - qtAv.qtQAq6BJJ:VV W ; << < qtAv/!a;CCJOO P< == = $QqT1a 0 8 8 D1c!A#b&(1*o%B3|4 55 5rHcxtdt}tdd}ttt dzzt zt zttt dzzz }||jt | ttdt dzzdt dtzzzz|t dtzzdz zztt tzztdt z dtzz ztdtz z tt  tt  dz tjzfdfk(sJttt dzzt zt z}||jt | ttdt dtzzzt z|t dtzzzztt dtzz ztt tzztt dzz tt  tt  dz fdfk(sJ||jt | t ditt|dtzdzz ttztt tjz zdttzz dtddfdfk(sJy)NzRisch takes forever.r>TpositiverQrD)r9rrr&r;r>r=subsr<r2r!rHalfrr)MTbposexprs rFtest_mellin_transform_failr_EsO  B 3 &D QTNQ  "4AqD> 1D diiD5!1a ( Aq1qs7| #D1qs7Q;$7 7a!e D A!  "1q5\ *eVbeVAX& ' / // / QTNQ  "D diiD5!1a ( AaCLN4!ac'? *5!a72, AEl ##(!a= 1eVbeVAX  & && & diiTE1a()1a 0 1q/ %( "5!aff#5 5qbz B "a !4 ) )) )rHc ddlm}m}t}t dd}|t t ztt dz zt tdt tzz t tt  fdfk(sJ|t t ztdt z zt tdt tzz tt  tfdfk(sJ|dt z tdz ztdt z zt tttttztttzz dtfttdkDfk(sJ|t dz tdz ztt dz zt ttttdtz tz ztdtz z t dttz fttdkDfk(sJ|dt zt zt ttttttz zttz dttfdfk(sJ|tdt z t zt tdtt tzdz ztdtz zt#t ttdz z zzttztttz zt z dttfttdkfk(sJ|dt z tdz ztdt z zt$t dz tdz zztt dz zzt t}|ds2J|ddtt dzfttdkDfk(|t t$zt&t$zz t t&z z t tdt t&t$tzdz zztt t$zztt tztt t$tzzzz k(sJ|t t$z|t$zz t |z z t tt |t$tzdz zztt t$zztt tztt t$tzzzz |dtt$ |ddtt$z fdfk(sJt)t t&dzzt&zt$z}||j+t&|t tt$ d|zt$dtzzzzttztt$ dtzz ztt$ tz dzz dtt$ dz fdfk(sJt)t t&dzzt&zt$zt)t t&dzzz }||j+t&|t tdt$dtzzz|t$dtzzdz zzttztdt$z dtzz ztdt$z tz z dtt$ dz t,j.zfdfk(sJ|t1t t tttdtfdfk(sJ|t1dt z t ttt t dfdfk(sJ|t3t d ztdt z zt td td zz dtfdfk(sJ|t3t d ztt dz zt td td zz t dfdfk(sJ|t3t dzt tt ttt tzzz ddfk(sJ|t3dt z dzt tt ttt tzzz ddfk(sJ|t3tdt z t tt tt5t tzzz ddfk(sJ|t3tddt z z t tt tt5t tzzz ddfk(sJ|t7t)t t tttt,j.z t)t tzz t9dddfdfk(sJy)NrMaxMinr>TrWrDrYrQrYrrrD)(sympy.functions.elementary.miscellaneousrbrcrrr;nur/r<rr!betar2rhoabsr)rr(r=r>r&rZrr[r#r%r*r0r)rbrcr\r]mtr^s rFtest_mellin_transformrqcsC B 3 &D aeIa!e$$a + R!VsRVGnd+ ,, , aeIa!e$$a + BFr"vgr]D) ** * q1uq!)AE"22Aq 9 tU1X eD1Ho -2w41 E FF F q1uq!)AE"22Aq 9 tU1t8a<( (q1u 5S!bh, DA / // / q1uoq! $ q%a. s +aC\4@ AA A c!a%jC4 !Q ' #bfQh-a#g& BCE N !!H %%*3q5\ 224 5 BsG bgk,# ## # QUdQh  !a% 0 0Q$(##Ia!e$44 567 1D dii4 !Q ' Q1WdQ1Wq[) )%( 2*/A! *< ==B1q519=M N Aq166! "D * ** * c1"gq! qAr7D 9 99 9 c"Q$iA 5!9sAh"= == = c!fai !a%((!Q /Bq!tGaWd3K KK K c!fai !a%((!Q /AadFbS!Hd3K KK K c!a%j!Q B#bd) $4gt#D DD D c!A#'lAq !b!C1I+&6%E EE E c#a!e*oq! $Qs2a4y[)97D(I II I c#a!A#g,A &2qRT{+;VT*J JJ J c$q'lAq ! AFF  T"XaZ (8B?A*>E FF FrHc,t}|tttdzz tt}|dddk(sJt |ddj t rJ|ttdztdzz tt}|dddk(sJt |ddj t rJ|tttdzdzz tt}|dddk(sJt |ddj t rJy)NrD)rjTrT) allow_hyperrQ))rrQT)rr%r;r<r5hasr3)r\rps rFtest_mellin_transform2rus B CFAENAq !B ab6^ ## #2a5d377@@ @ CFAIq1u q! $B ab6^ ## #2a5d377@@ @ CFAEA: q! $B ab6^ ## #2a5d377@@ @@rHc %ddlm}t}|ttdt t zt tttdz tzttdz tz dzz tt dz tddfdfk(sJ|tt t ttt t zt tdtztdtztjzzttdz tztjzztt dz tz dzttdtzz dzzz tt dz tjz tddfdfk(sJ|tt t ttt t zt tdtzttdz tzztdtztjzztt dz tz tjzttdtzz dzzz tt dz tddfdfk(sJ|ttt t dzt ttttzttjtz zt ttdtz ztdtztz zz tt tjfdfk(sJ|ttt t tt t t zt tttttjtz zt ttdtz tz ztdtztz zz dtjfdfk(sJ|ttdz t t ttt t zt ttdtz tttztjz zt tttddtz ztttz tjzzz tjttz tjfdfk(sJ|ttt t tt t t zt tdtztddtzz zttt zdz tzztdtz t tz dz ztdtz tt z dz zztdtz tt zdz zzz tttt z dz tjfdfk(sJ|ttt t dztt t t dzzt tdd|tttt tjfdfk(sJ|t#tdt t zt ttttdz tz z tttdz z ztttdz zztz |tt dz ttdz tddfdfk(sJ|tt t t#tt t zt tdtz tttdz tz zzttjdtzz ztdtz dz tzztdtzdz tzzt ttdtz tdz z ztdtz tdz zzz |ttdz dz ttdz dz tddfdfk(sJ|tt t t#tt t zt tdtz tttdz tz zztttdz z ztttdz zzttjdtzz zt tttjtz tdz z zttjtz tdz zzz |tt dz ttdz tddfdfk(sJ|ttt t t#tt t zt ttttz ttztttzzttjtz zttd ztdtztz zz |tt dtjfdfk(sJ|ttt t t#t t t zt tdtz tttdz t dz z tzzztddtzz zttdz t dz z tzzttdz t dz ztzztttdz t dz z tz dzzttdz t dz ztz dzzz |tt tt zdz tt tt z dz tjfdfk(sJ|t#tt t dzt tdd|tt dtttjfdfk(sJ|t%tdt t zt ttttdz z tttdz zzdz |tt dz ttdz t&fdfk(sJ|ttdt dt t zzt%tdt dt t zzzt tdt ztdtzzttdz tzzdttdz tz dzzz |dtt dz t&fdfk(sJ|t)tt t t%tt t zt ttttttzztt tjzzdt tztttz dzzz |tt dtjfdfk(sJ|t)t t t t%tt t zt tddtzdz ztdtzdzztt dz t dz ztzzttdz t dz ztzztt dz t dz ztz dzttdz t dz ztz dzzz |tt dz tt dz z ttdz tt dz z tjfdfk(sJ|t+t dz t%tt dz zt t}t-t/t-|dj1d }|dttddzztttzzttjtz ztdtztztdtztzz tt tz dzztttz dzzz k(sJ|dd|tt ttt&fdfk(sJy) NrrbrQrDrgrdTrNz3/2func)rkrbrr,r=r&r;r<r2r!rr)rr[r(rr>r.r-rr+r#r4r6expand)rbr\rpmt0s rFtest_mellin_transform_besselr|s3< B ga47#Q * qsQwacAgk* *beVAXx1~,FM NN N c$q'l71d1g..1 5 AeBqD166M" "51q166)9#: : qbdQhlE!ac'A+.. 0 Aq1668Aq>2+,0 2 22 2 c$q'l71d1g..1 5 AeAaC!Gn U2a4!&&=1 1 qbdQh q1Q3w{!33 5 Aq(1a.7"#' ) )) ) gaa!1$a + q1ueAFFQJ' ' HU1q5\ !%A "2 2 4eVQVV d $ $$ $ gaa!'1"d1g"661 = q% # # HU1q519% %eAEAI&6 6 8 K    ga!eT!W%gaa&991a @ q1ueAEAFFN+ + HU8Aq>A-. .uQUQVV^/D D F VVbe^QVV $d , ,, , gaa!'!T!W"55q! < AeA!Gn UAE19q=1 1 !a%1q5!)# $U1q5AE19+<%= = AEQUAI% & ' (!ur!u} a  ($ 0 00 0 gaa!1$wr47';Q'>>1 Eab I bebeV aff %t, -- - ga47#Q * b!A#'l  E!ac'N *5QqS> 9" < "Q%2a57 #Xa^ 4d < << < c$q'l71d1g..1 5 Q$s2qsQw< qvv!|!4 4 !a%Q  %q1uai!m 4 5 HU1q51Q3;' 'a!eack(: : <2a519a"Q%!)Q /!Q @$ H HH H c$q'l71d1g..1 5 Q$s2qsQw< q1Q3w /a!A#g >uQVVaPQc\?R R HU166A:!+, ,U166A:!3C-D D F "Q%2a57 #Xa^ 4d < << < gaa!'!T!W"55q! < bd)E!H U1q5\ )% *; ; %Lq1uqy) ) + "Q%^QVV $d , ,, , gaa!'!T!W"55q! < Q$s2qsQqSy1}%& &uQ1W~ 5 1qsQ  %acAaCi!m 4 5 uQqS1Q3Y]Q&' 'acAaCi!ma.?(@ @ B2a5&2a5.!#r!ufr!una%7 8!&& A4 I II I gaa!1$a +AB /BqE61be$aff-t 4 55 5 ga47#Q *  QqS AaC. !!" #%("Q%2a57%;R$@$ H HH H ga4$q' ?*+G 1T!DG)_ - ! %)*aRqs); acAg*%!a! ,,*.03A1vax0@"/Et)M MM M gaa!'!T!W"55q! < q% A aR!&&[! "#$T"X:eAEAI.>#> @ beVQ $ ( (( ( gaa!'!T!W"55q! < QqS1WeBqD1Ho %eQBqD1Q3JN&; ; acAaCi!m #QBqD1Q3JNQ$67 acAaCi!ma ! "$'Aq2a57(: 1a"Q%'%FF$$%) + ++ + C1Iga1o %q! ,B HYr!u|||'>?@ AC !BA&&s2a4y0qvvz1BB QrT!Vs1R46{ "E1"q&1*$55eAEAI6FFH HH H ab6sBqE62a5)2.5 55 5rHc ddlm}ddlm}m}m}ddlm}tdd}tdd }t|ttttttz dtfdfk(sJttttz ttdtfjt j#|tk(sJtt!t$tttttt$tzd z z |d t't$z dtfdfk(sJ|t)ttt|tzd z z ttd |z tfjt j#d t!|tk(sJt|tttd tz t+t,zttd z t.j0zzd tztt d z d zzz d dfk(sJtd tz t+t,zttd zd z zd tztt d z d zzz ttd |tk(sJt|t+tttd d tzd z z t+t,zttzttt t.j0zzz ddfk(sJtdtz t+t,zttzd tztt t.j0zzz t|dj#|t+|k(sJy)Nrrw)CiE1Sisimplifyr=Tnegativeu)polarrDrxrQrirjrd)rkrb'sympy.functions.special.error_functionsr~rrsympy.simplify.simplifyrrrr;r<r2rrrSr1rzr=r!r"r&rrr[)rbr~rrranegrs rF test_expintrs<BB0 # %Ds$A BqE1a (U1XaZ!R$,G GG G #E!HQJ1"g wvvvx2a5 99 9 F1aL!Q / q1q519 A1Iq 126= >> > J,U1Xtax!|-Dat8R."")'&/&&d&2CE F tQ   BqE1a ( Q$tBxacAFFl+ + !E1"Q$(O %t - -- - $QTE$r(N5!a%3C$C&'c%1q/&9%;<=q' K a5   BtAwKA . acAg,tBx a (!E1"qvv+,>*> ?N OO O # Ad2huQx1UA2;%7!78 1f fh"T!W+ .. .rHc* ddlm}ddlm}m}ddlm}ddlm ddl m t}|ttttdtft!t k(sJ|tt ttt dft!dtz k(sJ |tdtdzzdz z ttdtftdzd zt#d tz zd tzz k(sJ|d tdzd z z ttd t t#t d zzdz t#td z dtzz z k(sJ|d tdzd z z ttd t t#t d zzdz t#td z dtzz z k(sJ|ttttd z zttd tftd zt!t ztz k(sJt%d d}|d tdzd zz tt!t dtfj't|j)t*jt+|t#d t!| z zk(sJt%dd\}}||t |z zt-t|z ztz ttdtft!| t|zzk(sJ|t-||z t|z z|tzz tt| tft|zt!t|z zk(sJ fd}t%dd} |d| tzz ttt dft| zt#td z zk(sJ|d | tzz ttdtft| zt#d tz zk(sJ||tt.ttzttt.zz ttdtfd tz t.d z zt#d tz zk(sJ||tt.td t.z tz ztd tz z ttt dftd z t.d z zt#td z zk(sJ||tttt0tz ztt0z ttdd td zz t0zk(sJ|t2t4zt2td z zzt+t6t4zzttzttt4zztd tz ztd tz t4z zt6z tt|t9t4 d|d t9t4z d f}  t;| dj=t>t jt2t4z tt4zzt2 tzz k(sJ |d tAt6z t4 dz zttztd t4z dz tz ztt4 dz tz ztd t4z tz z ttdt9t4 dz fd tAtd zzt4zk(sJ |dtBdtzzztDtBdtzzd z zzttztd tBz dtzz ztd tBz tz z ttdt9tB d zdz ftDtBd z ztDdztAd ttDdzz zd ztBzzttAd ttDdzz zd ztBd z zzzztDdztzz k(sJ |dt4dtzzz t4ztDt4dtzzzzttztt4 dtzz ztt4 tz d zz ttdt9t4 dz ftDt4ztAd ttDdzz zd zt4zzk(sJ|dtdzz ttdtftGtd zt#d tz zk(sJ||dtd zz ttt dfdtGtdzt#td z zk(sJ|t6tt+t6tzzz ttdtGtd zk(sJ|t6tt+t6tzdz zz ttdtGtdzd zk(sJ|t6tt+dt6ztzzz tttIdddftGtAtd zk(sJ|t6tt+t6tzzz ttdtGd d tz zk(sJd} | | |t6ttKt6tzzz ttdtGd tz t#d tz ztGtd z t#td z zztGtt#td z ztGd d tz z t#td z zztGt d zt#t d zzzfvsJ| |t6|t6tzztz ttdtGd tz d z t#d tz ztGd d tz z t#td z zztGt t#t d zztGd d tz z t#td z zztGt d zt#t d zzzfvsJ|tttLjNz tAt6tzz tttIdddftQtAtk(sJ |ttBdz tzttBdz tz d zz ttt9tB dz tIdd ftStBdtAtzk(sJ |dtBzttLjNdtzz ztttBd zdz zztd tz tBdz z td dtzz tBzzz ttt9tBd z dz tId d ft+tAttStBtAtzk(sJ |dtBzttBdz tzzttLjNdtzz zttLjNtz tBdz z td dtzz tBzzz ttt9tB dz tId d ftUtAttStBtAtzk(sJ |ttBtzttLjNtz ztAt6td tz ztd tBztz zz ttt9tB tLjNftStBtAtdzk(sJ |ttttLjNtz ztAt6td tz tBz ztd tBztz zz ttdtLjNftStB tAttStBtAtzk(sJ |d tztd tzd zzttBdz tDdz ztzzttB dz tDdz ztz d zttBdz tDdz z tz d zzttBdz tDdz ztz d zzz ttt9tBt9tDz dz tLjNftStBtAttStDtAtzk(sJ |ddtzz tUt6tBzdz t6tDzdz z t6tzzztd tzd zzttBdz tDdz z tzzttBdz tDdz ztzzt6ttBdz tDdz z tz d zzttBdz tDdz ztz d zzz tt|t9tB dz t9tDdz z t9tB dz t9tDdz ztLjNftStBtAttStD tAttStDtAttUt6tDzzz zt+t6tDzz k(sJ|t6tUt6tzz ttdtLjNftAttd zz k(sJy)!Nrrzra)cotpowsimprrYrQrDrd)rYNNrDrTrealza brWcjt|ddjttS)NFdeepTforce)rreplacer$r#)r^rrs rF simp_powsz0test_inverse_mellin_transform..simp_powsWs+ 4e .mysimps:.26 Jt404 H 3/ 0rHrN)+rrzrkrbrc(sympy.functions.elementary.trigonometricrrrrrrr2r<r;rr#r/rrZrSr)r rmrnr@r?rr!rrr$r&r=r>r%rr*rr[r0r,r()rzrbrcrIMTr_a_brrlr^rrrs @@rFtest_inverse_mellin_transformr5s*C<.0 "C uQxA2w '3r7 22 2 uaRy!Q"a )SAY 66 6 C1QT6A:1q"g6 7 A9QU##QqS) ** * q!Q$(|Q: . 9aR!V Q1q5!11Q3!77 88 8 q!Q$(|Q9 - 9aR!V Q1q5!11Q3!77 88 8 uQx%A,&1q"g 61q5#qb'/!:K KK K $A q!Q$(|QQB$ Q 773< q6)AQBK( ( )) ) UT *FB rQBrE{9QrT?*1,aQG <RC2I NN N yB2&Q/ARy AQU3PQSUPUv;EV VV Vc D !B r26{AqB3+ .!R% !a%8H2H HH H q"q&z1a$ ,2iA6F0F FF F StU1X-eAHo=q!aWM N ETAX yQ/ / 00 0 StU1t8a<%88q1uEAT{, - ETAX yQ/ / 00 0 Sq%a.0s;Q9M N q1uI    q!tAAJs2a4y((##(Q<005a!e ==B1q519=MNNPQARUFAA1Iq0AB DD :d/ 0 8 8C H Q Q S TEAqDLA26 " ## # C$r( QBqD)%(25!a%Q3GGr!tax)).q1uqy)9:1q2a5&(m- . T!a%[1   CA!G QQqS1%55eAh>uQUQqS[?QQq1uqy)*+,a!r!ufqj!^1DF G AE AqD$q1QT6z*Q.22QQ1a4Z8H18L E86 TAX    CQ1W aA!G 4U1X=eQB1HoMQ +,-.A1vax=B C 1d1qAv:"Q && '' ' r!Q$w1q"g &#a&!)Ia!e4D*D DD D #a1fabS!H-T : A )AE"" ## # r1SAY;Aw /3q1u: == = r1SAa[=!1a 1SA] BB B r1S2a[=!1a(2q/1)= >#d1gPQkBR RR R r1SAY;Av .#a!A#g, >> >0 &R3r!t9-q!W=> ? AE 9QU##c!a%j1q51A&AA AyQ#a!A#g,yQ/?"??#qb G C aR!V C D   #bRTl1naF3 4 AaC!G Yq1u%%A!G Yq1u5E(EE Q 1"q&!!CAaCL1q51A$AAC I E aR!V E 9    a!&&j!!48A:.1xA6J K DG    CacAguQqS1Wq['991a2a5&(HUVXYNA[\ ] 1aQi  !! ! C1U166AaC<00qAE19}1EEq1uqs{+E!ac'A+,>>@r!uqy\!^Xa^<> ? DG WQQ(( )) ) C1U1Q37^+E!&&1Q3,,??qvvzAaC/0q1Q3w{1CCEbeVAXx1~68 9 DG WQQ(( )) ) Ca!e U166A:%66b%A,.uQUQY/??AbeVQVV,. / 47Q   Caqvvz!22b%A "225Q3CCEQK) * DGWQQ00 11 1 C1U2a4!8_,U1Q319q=-AAr!taczA~1251qsQ9J3KK!ac A  1234r!ur!u}-a/8: ; 47GAtAw//  00 0 CQqS #bd1fr!tAvo1&<"==eBqD1HoM!A#!)a-()).qsQqSy1})=>acAaCi!ma/00qsQqSy1}q7H1IIKq"Q%BqE!G+beVAX1a-?@!&&I K L AtAw''1"d1g*>AtAw'BqD 1+2)3336r!t9=  == = r#bd)|QAqvv; /47AE? BB BrHc v ddlm m m ddlm}ddlm t}t} fd}d}tdd }td }td d }td d }tdd } t|tt|t|tt|k(sJt|||tt|||tk(sJ||tdt!d|ztzz t||||z |z k(sJ||tdt!|tzz dt!|tzz zt||||z dz|z k(sJ||t#| tzttzt|t$d|dt&zt$z|zzz k(sJ|d|dt&zt$ztzzz t| dt#| | zdfk(sJ|d|dt&zt$ztzzz t| ddk(sJ|d|dt&zt$ztzzz ttddddk(sJ||tt#| tzzttzt|t$d|dt&zt$z|zzdzz k(sJ|t#| tzt)|tzzttzt|||dz|dt$zt&z|zzdzzz k(sJ|t#| tdzzt|t+t&t#t&dz |dzz|z zt+|z k(sJ|t+t&|z t#t&|zdz |z z|tt#| tdzzk(sJ|t#| t!tzt|d|z|dzdt&dzz|dzzzz k(sJy)Nr)rzexpand_complex expand_trig)factorrc 8|SN)r;rzrrrs rFsimpz$test_fourier_transform..simps N6!9$=>??rHc:tt|zt|zz Sr)r)r)r;s rFsincz$test_fourier_transform..sincs2a4y"Q$rHkTrrCr=rWr>poskrDrQ) extensionFrO)rTrrd)rrzrrsympy.polys.polytoolsrrrrrrrr;r rr/ror#rrr)r&)rFTIFTrrrrCr=r>rrzrrrs @@@@rFtest_fourier_transformrsII,0 B #C@ $A A d#Ad#A 6D )D QqT1a (,? DGHA2w OO O  QBqD 1a  GAItBxA1'=> ?? ? ! Q 48QTAqD[)*Aq 258!AY ?? ?  Aq!Q 748+c!Q$i!J,.F,GGI JJ J  #qbAg,1 !%a31uac{+;!;Qq(1a.?P=P!Q RR R ! Q #q!teQqSk""Aa!Q&7$78!Q @CDS!AqD\> RR RrHc  ddlm}m}td}td}td}t d}t ||||t ||||k(sJt||||t||||k(sJt dt|z ||dt|z k(sJtdt|z ||dt|z k(sJt d|dz|dzzz ||tdttzt| |zzd|zz k(sJt || z||d| tjzz||dz zzt| dzdz zt|dz z k(sJtd| tddz zz||dz zzt| dz tjzzt|dz z |||| zk(sJt t| |z||td|ztt|dz|dzzzz k(sJttd|ztt|dz|dzzzz ||t| |zk(sJt t| t|zt|t|zz|||t|dz d|zz zd|t!d dzzz k(sJt d||zz ||tdd |||zztzt#||zzdz t||z|||zzz zttz k(sJttdt%tjdfd ftjddftjff|dz|dzzd z zdtzz ||d||zz k(sJt dt|dz|dzzz ||tdt%tjfd fd tjff|dz|dzzd z zdttzz k(sJttdt%tjfd fd tjff|dz|dzzd z zdttzz ||d|t|dz|dzz dzzz k(sJy)Nr)r~rrrr=rCrDrQrgrNrrd)rr)rr~rrrr rr rr&rr#rr[r2r(rr)r3)r~rrrr=rCs rFtest_cosine_transformr s@ A A A A AaD!Q '?1Q4A+F FF F # !a -adAq9 :: : Ad1gIq! ,$q' 99 9 #Ad1gIq! 4$q' AA A A 1q!t  #AwtBx/QBqD 91Q3? @@ @ A   1"qvv+&q1q5z1%!a 2CCE!A#JN OO O #AQ . . ) %!a%j%r!taff}-%..3AaCj%9:;Q @CDr7 KK K  QBqD 1a  GAItBxA1'=> ?? ? # Q 48QTAqD[)*Aq 258!AY ?? ? C47 OC$ 3 1 -   QTE1Q3K((!Ax1~,=*=> ?? ? Aq1uIq! ,Q BqsGb#ac("1$s1Q3x1Q3'77199=b1B BB B #DGGaffa["4E A H#$%qDAIaK-1%123B$%89:A ?BCQU) LL L Ad1a4!Q$;//A 6$q'' &&B&166),ad1a4ikC;;;<=d2hJ;H HH H #DGGaffYOfqvviEXZ[]^Z^_`bc_cZcdeZe,f$fhijnoqjrhr$suvxy z~BCDHIJLMIMNOQRNRIRUVIVDWBWX XX XrHc btd}td}td}td}td}td|z ||dd|z k(sJtd|z ||dd|z k(sJtd||zz ||dd| dzz||dz zzt | dz dzzt |dz z k(sJtd| dzz||dz zzt | dz dzzt |dz z ||d|| zk(sJtd||zz |||dd| zz||dz zzt | dz |dz zdzzt |dz |dz zz k(sJtd| dzz||dz zzt | dz |dz zdzzt |dz |dz zz ||||| zk(sJt||zt | |zz|||d|dzz|z|| d z zz|dz|dzz dz| t d dz z zzt |td dzzttz k(sJtd|dzz|z|| d z zz|dz|dzz dz| td dz zzt |td dzzttz |||||zt | |zzk(sJy) Nrrrlmr=rDrrQrg) rrr r r2r#rrr&r)rrrlrr=s rFtest_hankel_transformrJss As A Bs A A AaCAq )QqS 00 0 #AaCAq 1QqS 88 8  !Q$1a QKAE 25!A?B51:M NN N # QBF AAJuaRTAX.uQqSz91a DGHA2w OO O AadFAq" - !qb' !a!e*UA2a4"Q$;?33E!A#1*4EE GG G #AQK A1%aRTBqD[1_%%&&+AaC"Q$J&7%89:Ar CFG1"g NN N ArE#qbd)OQ2 6 BF A a2#'l"AqDAIMbS156<889<:6:$; ;;@hqRSnAT;U VVZ[]V^ _ __ _ $ BF A a2#'l"AqDAIMbS8Aq>5I#JJ5 Xa^L !"X &'(!R 145rE#qbd)O DD DrHcLtddtz z ttdk7sJyr)rr;r<rrHrFtest_issue_7181rfs! Aq1uIq! , 44 4rHc ttt dzz ddtdzz zt dz zztdtdzz ztt tzt zzt tttdtdzz dz zzttzttfdy)NrDrdrQcDtttdtffidddS)NrYT) as_meijergneedeval)rr<r;rFsrFz!test_issue_8882..vs) Aq2r( 24 0 2rH) r=r<r&r#rrr)r'r2r:rrs@rFtest_issue_8882rjs aR!V a!AqD&jQBqD))$qAv,6sA2a47|C Ad4!Q$<>" "# $$)!H -A !$23rHctdd\}}tt|||tt|||k(sJy)Nzx yTr)rrr#r )r;ys rFtest_issue_12591r{s; 5t $DAq SVQ *.>s1vq!.L LL LrHN)grErrrrrrr r r r r rrrrrrsympy.integrals.laplacerrrrr sympy.corersympy.core.numbersrrrrsympy.core.singletonrsympy.core.symbolrr(sympy.functions.combinatorial.factorialsr $sympy.functions.elementary.complexesr!r"&sympy.functions.elementary.exponentialr#r$r%rkr&rr'r(r)r*sympy.functions.special.besselr+r,r-r.'sympy.functions.special.delta_functionsr/rr0r1'sympy.functions.special.gamma_functionsr2sympy.functions.special.hyperr3sympy.simplify.gammasimpr4sympy.simplify.hyperexpandr5sympy.simplify.trigsimpr6sympy.testing.pytestr7r8r9r: sympy.abcr;r<r=r>r?r@rlrmrnrGrKrUr_rqrur|rrrrrrrrrrrHrFrs2JJJJJ24!22"->?FF9HHMM=?91.2,::&& & D#FA 5&))8<F~ A [6[6@..BJCJCZ2At RF'XTD853"MrH