o *ήc/Äã@sÚddlmZmZmZmZmZmZmZmZm Z m Z m Z m Z m Z mZmZmZmZmZmZmZmZddlmZmZddlmZmZmZmZddlmZm Z m!Z!m"Z"ddl#m$Z$ddl%m&Z&ddl'm(Z(m)Z)ddl*m+Z+dd l,m-Z-m.Z.m/Z/dd l0m1Z1m2Z2m3Z3dd l4m5Z5m6Z6m7Z7m8Z8dd l9m:Z:dd l;mZ>m?Z?m@Z@ddlAmBZBmCZCmDZDmEZEddlFmGZGddlHmIZImJZJmKZKmLZLddlMmNZNddlOmPZPddlQmRZRddlSmTZTddlUmVZVddlWmXZXmYZYmZZZm[Z[m\Z\ddl]m^Z^m_Z_ddl`maZambZbmcZcmdZdmeZemfZfe)dƒ\ZgZhZidd„Zjdd„Zkdd„ZleYeXd d!„ƒƒZmd"d#„Znd$d%„ZoeYd&d'„ƒZpeYd(d)„ƒZqeYd*d+„ƒZreYd,d-„ƒZseYd.d/„ƒZtd0d1„Zud2d3„Zvd4d5„Zwd6d7„Zxd8d9„Zyd:d;„Zzdd?„Z|d@dA„Z}dBdC„Z~dDdE„ZdFS)Gé)Úmellin_transformÚinverse_mellin_transformÚlaplace_transformÚinverse_laplace_transformÚfourier_transformÚinverse_fourier_transformÚsine_transformÚinverse_sine_transformÚcosine_transformÚinverse_cosine_transformÚhankel_transformÚinverse_hankel_transformÚLaplaceTransformÚFourierTransformÚ SineTransformÚCosineTransformÚInverseLaplaceTransformÚInverseFourierTransformÚInverseSineTransformÚInverseCosineTransformÚIntegralTransformError)ÚFunctionÚ expand_mul)Ú EulerGammaÚSubsÚ DerivativeÚdiff)ÚIÚRationalÚooÚpi)ÚEq)ÚS)ÚSymbolÚsymbols)Ú factorial)ÚAbsÚreÚ unpolarify)ÚexpÚ exp_polarÚlog)ÚcoshÚsinhÚcothÚasinh)Úsqrt)ÚatanÚatan2ÚcosÚsinÚtan)ÚbesseliÚbesseljÚbesselkÚbessely)Ú Heaviside)ÚerfÚerfcÚexpintÚEi)Úgamma)Úmeijerg)Ú gammasimp)Ú hyperexpand)Útrigsimp)ÚXFAILÚslowÚskipÚraisesÚwarns_deprecated_sympy)ÚMatrixÚeye)ÚxÚsÚaÚbÚcÚdz nu beta rhocCs„ddlm}tdƒ}t|tƒttƒ||tƒttƒksJ‚t|tƒtt ƒttƒ||tƒttƒttdƒtdtfdfks@J‚dS)Nr)ÚMellinTransformÚféT) Úsympy.integrals.transformsrQrrrKrLr)r?r)rQrR©rUúL/tmp/pip-target-vg8gfxp4/lib/python/sympy/integrals/tests/test_transforms.pyÚtest_undefined_function$s $( ÿrWcCsJtdƒ}t|tƒttƒjthksJ‚t|tƒtttƒjtthks#J‚dS)NrR)rrrKrLÚ free_symbolsrM)rRrUrUrVÚtest_free_symbols,s&rYcCs€ddlm}tdƒ}t|tƒttƒ d¡|ttd|tƒtdtfƒks'J‚t|tƒttƒ d¡||tƒt dt t ttƒtt tfƒksKJ‚t |tƒttƒ d¡||tƒt t tƒtdtfƒksiJ‚t dt t t|tƒttttfƒ d¡ƒdksƒJ‚t dt t t|tƒttƒ d¡ƒd ksšJ‚t|tƒttƒ d¡||tƒt dt t ttƒtt tfƒks¾J‚dS) Nr)ÚIntegralrRrZrSéþÿÿÿéz.Integral(f(s)/x**s, (s, _c - oo*I, _c + oo*I))z2Integral(f(s)*exp(s*x), (s, _c - oo*I, _c + oo*I)))Úsympy.integrals.integralsrZrrrKrLÚrewriterrr)rr rÚstrrrMrNrr)rZrRrUrUrVÚtest_as_integral2s( ÿ,ÿ ÿ*ÿ$ÿ, ÿr`cCsÜtdƒt}tddd}tttdƒtttttdƒ}|| t| ¡ttƒdtddtdt|tdtdt ttƒt dtdtƒt dtƒt tƒ t tƒ dt j fdfkskJ‚tttdƒtt}|| t| ¡ttƒdtdtt|tdtt t dtƒt ttƒt t dƒt tƒ t tƒ dfdfks¹J‚|| t| tdi¡ttƒ|dtd t tƒt t t j ƒdtt ƒdtddƒfdfksìJ‚dS)NzRisch takes forever.rNT©Úpositiver\éÿÿÿÿrS)rFrr$r0rKrNrMÚsubsrLr?r'r"ÚHalfr r)ÚMTÚbposÚexprrUrUrVÚtest_mellin_transform_failEs< (:ÿ ÿþÿ*ÿ ÿ ÿýÿ4ÿ ÿricCs¸ddlm}m}t}tddd}|ttttdƒttƒdttt t tƒ fdfks/J‚|tttdtƒttƒdttt tƒ t fdfksMJ‚|dtt dtdtƒttƒt t ƒt tƒt t tƒdt ft t ƒdkfksxJ‚|tdt dttdƒttƒt t ƒt dt tƒt dtƒt dt t ƒft t ƒdkfks¬J‚|dtt ttƒt tƒt t tƒt t ƒdt t ƒfdfksÎJ‚|tdtƒt ttƒdttt dƒt dt ƒtttt dƒt tƒt t tƒtdt t ƒft t ƒdkfksJ‚|dtt dtdtƒttdt dttdƒttƒ}|dsKJ|ddt t ƒ dft t ƒdkfkƒ‚|ttttttttƒdttttdtttƒtttƒttttƒks~J‚|tt|tt|ttƒt|ttdtttƒtttƒttttƒ|dt tƒ ƒ|ddt tƒƒfdfksÁJ‚tttdƒtt}|| t|¡ttƒt d|tdtt tƒt t dtƒt t tdƒdt tƒ dfdfksJ‚tttdƒtttttdƒ}|| t|¡ttƒdtdt|tdtdt tƒt dtdtƒt dttƒdt tƒ dtjfdfks]J‚|tt ƒttƒt tƒdt fdfksrJ‚|tdtƒttƒt t ƒt dfdfksŠJ‚|ttƒd tdtƒttƒd td dt fdfks¨J‚|ttƒd ttdƒttƒd td t dfdfksÇJ‚|ttdƒttƒtttttƒddfksáJ‚|tdtdƒttƒtttttƒddfksýJ‚|ttdtƒƒttƒtttttƒddfksJ‚|ttddtƒƒttƒtttttƒddfks7J‚|tttƒƒttƒt ttjƒ ttƒttddƒdfdfksZJ‚dS)Nr©ÚMaxÚMinrNTrarSrcr\ééééé©rcr©rrS)Ú(sympy.functions.elementary.miscellaneousrkrlrr$rKÚnur:rLrr'Úbetar?ÚrhoÚabsr4r r3rMrNr0rdr"rer)r+r5r;r)rkrlrfrgÚmtrhrUrUrVÚtest_mellin_transformcs’ ÿÿ",ÿ""ÿÿ(ÿÿÿ ÿÿ ýÿÿ4": ÿ:"ÿ ÿDÿ ÿ(*ÿÿþ ÿ*0<>488<*ÿrzcCsât}|ttƒtdttƒ}|dd…dksJ‚t|ddd t¡r%J‚|ttƒdtdttƒ}|dd…dks=J‚t|ddd t¡rJJ‚|ttƒtddttƒ}|dd…dksbJ‚t|ddd t¡roJ‚dS)NrS)rsTrT)Ú allow_hyperr\))rr\T)rr+rKrLrBÚhasr@)rfryrUrUrVÚtest_mellin_transform2¢sr}c Cs˜ ddlm}t}|ttdttƒƒttƒttdtƒttdtdƒt tƒ dt ddƒfdfks6J‚|t ttƒƒttttƒƒttƒdttdtt j ƒttdtt j ƒtt dtdƒttdtdƒt tƒ dt j t ddƒfdfks†J‚|tttƒƒttttƒƒttƒdtttdtƒtdtt j ƒtt dtt j ƒttdtdƒt tƒ dt ddƒfdfksÑJ‚|ttttƒƒdttƒtttƒtt j tƒttƒtdtƒtdttƒt tƒ t j fdfks J‚|ttttƒƒtt ttƒƒttƒttƒtt j tƒttƒtdttƒtdttƒdt j fdfksDJ‚|ttdttƒƒttttƒƒttƒtdtƒtttt j ƒttƒtt ddƒtƒtttt j ƒt j t tƒt j fdfks‹J‚|ttttƒƒttttƒƒttƒdttddtƒtttdtƒtdtttdƒtdtttdƒtdtttdƒt tƒt tƒ dt j fdfkséJ‚|ttttƒƒdtt ttƒƒdttƒdd…|t tƒt tƒ ƒt j fdfksJ‚|ttdttƒƒttƒtttdtƒ tttdƒtttdƒt|t tƒ dt tƒdƒt ddƒfdfksWJ‚|t ttƒƒttttƒƒttƒdt t ttdtƒtt j dtƒtdtdtƒtdtdtƒttƒtdttdƒtdttdƒ|t tƒd dt tƒddƒt ddƒfdfksÇJ‚|tttƒƒttttƒƒttƒdt tttdtƒtttdƒtttdƒtt j dtƒttƒtt j ttdƒtt j ttdƒ|t tƒ dt tƒdƒt ddƒfdfks1J‚|ttttƒƒttttƒƒttƒtttƒ ttƒtttƒtt j tƒtt d ƒtdttƒ|t tƒ dƒt j fdfksxJ‚|ttttƒƒttttƒƒttƒdt tttdtdtƒtddtƒttdtdtƒttdtdtƒtttdtdtdƒttdtdtdƒ|t tƒ t tƒdt tƒ t tƒdƒt j fdfksùJ‚|ttttƒƒdttƒdd…|t tƒ dt tƒƒt j fdfksJ‚|ttdttƒƒttƒtttdƒtttdƒd|t tƒ dt tƒdƒtfdfksPJ‚|ttdtdttƒƒƒttdtdttƒƒƒttƒdt tdtƒttdtƒdttdtdƒ|dt tƒ dƒtfdfksJ‚|ttttƒƒttttƒƒttƒttƒtttƒtt t j ƒdttƒtttdƒ|t tƒ dƒt j fdfksÞJ‚|ttttƒƒttttƒƒttƒddtdtdtdƒtt dtdtƒttdtdtƒtt dtdtdƒttdtdtdƒ|t tƒ dt tƒdt tƒdt tƒdƒt j fdfksWJ‚|tt dƒtttdƒttƒ}ttt|djdd ƒƒƒ}|dtt ddƒtttƒtt j tƒtdttƒtdttƒtt tdƒtttdƒks³J‚|dd…|t tƒ t tƒƒtfdfksÊJ‚dS) Nr©rkr\rSrprmTr[z3/2©Úfunc)rtrkrr7rMr0rKrLr?r'rr4r"rer3r rNr9r8rr6r)rArCÚexpand)rkrfryÚmt0rUrUrVÚtest_mellin_transform_bessel²s: <ÿ .(ÿÿþÿ (*ÿÿþÿ"ÿþ ÿ$&ÿ þ ÿ&*ÿþ ÿ"*.ÿÿý ÿ4 ÿ8&ÿ ÿ .ÿÿ.þ.ý ÿ N2ÿ&þ ÿ".ÿþ ÿ"4ÿÿ:þ4ý ÿ  ÿ ÿÿÿ ÿ ÿÿÿÿÿÿ ÿ"ÿÿÿþ ÿ"8ÿÿÿÿÿý ÿ$,@ ÿ2rƒc Cs,ddlm}ddlm}m}m}m}ddlm}ddl m }t ddd}t d dd }t |t ƒt tƒttƒtdtfdfks?J‚tttƒttt dtfƒ t¡ ¡|t ƒksWJ‚t ttt ƒt tƒttƒttd |d ttƒdƒtfdfksxJ‚|ttttƒ|td tt d |tfƒ t¡jdd ƒƒt|t ƒksJ‚t |t ƒt tƒd t ttƒttd tjƒd ttt d d ƒddfksÉJ‚td t ttƒttd d ƒd ttt d d ƒtt dƒ|t ƒksòJ‚t |tt ƒƒt tƒd d td  ttƒttƒttt tjƒddfksJ‚tdt ttƒttƒd ttt tjƒt|dƒ ¡|t|ƒƒksFJ‚t|t ƒt tƒtd td ƒ d tddfksaJ‚tttt ƒt tƒ|ttttƒd tƒdttƒtj kfksJ‚ttd t ƒt tƒttd ƒtddfks˜J‚ttd t ƒt tƒtttd ƒtd ddfks³J‚t!td td ƒ d tt|ƒ ¡t"|ƒ||ƒksÑJ‚t!ttd ƒttt ƒ t¡t"t ƒ|t ƒksëJ‚t!tttd ƒtd tt ƒ t¡ ¡td t ƒt"t ƒ |¡ t¡ ¡ksJ‚dS)Nrr~)ÚCiÚE1r>ÚSi)Úlerchphi©ÚsimplifyrMT©ÚnegativeÚu)ÚpolarrSrr\rrrsrm)#rtrkÚ'sympy.functions.special.error_functionsr„r…r>r†Ú&sympy.functions.special.zeta_functionsr‡Úsympy.simplify.simplifyr‰r#rrKrLr?rrr^r=rrMr'r(r0r r"rerr+r*rÚZerorr:) rkr„r…r>r†r‡r‰ÚanegrŒrUrUrVÚ test_expints†     *ÿÿ*ÿ ÿ ÿÿý"ÿÿÿ"ÿÿþ: ÿ0þ þ6& ÿ. ÿ$ ÿ ÿÿ  þr“c sfddlm}ddlm}m}ddlm}ddlm‰ddl m ‰t }|t t ƒt tdtfƒtt ƒks4J‚|t t ƒt tt dfƒtdtƒksIJ‚ˆ|t dt ddt tdtfƒƒtdd td tƒd tksnJ‚|d t dd t td ƒt tt d ƒdttd ƒdtks“J‚|d t dd t td ƒt tt d ƒdttd ƒdtks¸J‚|t t ƒt t d ƒt td tfƒtd tt ƒtksÖJ‚td dd}|d t dd t tt ƒdtfƒ t|¡ t¡  ¡t|ƒtd t| ƒƒksJ‚tddd\}}||t |tt |ƒt t tdtfƒt| t|ƒks1J‚|t||t |ƒ|t t t| tfƒt|tt| ƒksUJ‚‡‡fdd„}tddd} |d| t t tt dfƒt| ttd ƒks}J‚|d | t t tdtfƒt| td tƒks—J‚||t tƒt t ƒt t tƒt tdtfƒƒd ttd td tƒks¿J‚||t tƒt d tt ƒt d t ƒt tt dfƒƒtd td ttd ƒksìJ‚||t t ƒt tt ƒt tƒt tdƒƒd td tks J‚||tttt d tttƒt t ƒt t tƒt d t ƒt d t tƒtt t|ttƒ dƒ|d ttƒd ƒfƒƒttttttks[J‚ˆ|d ttƒt dt t ƒt d tdt ƒt t dt ƒt d tt ƒt tdttƒ dfƒƒd ttd ƒtks J‚ˆ|dtdt ttdt d t t ƒt d tdt ƒt d tt ƒt tdttƒ d dfƒƒttd td ttdƒd td tdtd ttdƒtdttdtks J‚ˆ|dtdt  tttdt t t ƒt t dt ƒt t t d ƒt tdttƒ dfƒƒtttd ttdƒd tksWJ‚|dt dt tdtfƒt tƒd td tƒkssJ‚||dt d t tt dfƒddt tƒdttd ƒks”J‚|tt ttt ƒt tdƒt td ƒks¬J‚|tt ttt dƒt tdƒt tdd ƒksÈJ‚|tt tdtt ƒt tt!ddƒdfƒt ttƒd ƒkséJ‚|tt ttt ƒt tdƒt d d tƒksJ‚dd„} | | |tt t"tt ƒt tdƒƒƒt d tƒtd tƒt td ƒttd ƒt tƒttd ƒt d d tƒttd ƒt t d ƒtt d ƒfvs[J‚| |t|tt ƒt t tdƒƒt d td ƒtd tƒt d d tƒttd ƒt tƒ tt d ƒt d d tƒttd ƒt t d ƒtt d ƒfvs³J‚|t t t#j$ƒ ttƒt t tt!ddƒdfƒt%ttƒƒksÔJ‚ˆ|t tdt ƒt tdt d ƒt tttƒ dt!dd ƒfƒƒt&tdttƒƒksJ‚ˆ|dtt t#j$dt ƒt t td dƒt d t tdƒt d dt tƒt tttƒd  dt!d d ƒfƒƒtttƒƒt&tttƒƒksQJ‚ˆ|dtt tdt ƒt t#j$dt ƒt t#j$t tdƒt d dt tƒt tttƒ dt!d d ƒfƒƒt'ttƒƒt&tttƒƒksœJ‚ˆ|t tt ƒt t#j$t ƒttƒt d t ƒt d tt ƒt tttƒ t#j$fƒƒt&tttƒƒdksÔJ‚ˆ|t t ƒt t#j$t ƒttƒt d t tƒt d tt ƒt tdt#j$fƒƒt&t ttƒƒt&tttƒƒksJ‚ˆ|d t t d t d ƒt tdtdt ƒt t dtdt d ƒt tdtdt d ƒt tdtdt d ƒt tttƒttƒ dt#j$fƒƒt&tttƒƒt&tttƒƒksvJ‚ˆ|ddt  t'ttdttdtt ƒt d t d ƒt tdtdt ƒt tdtdt ƒtt tdtdt d ƒt tdtdt d ƒt t|ttƒ dttƒdttƒ dttƒdƒt#j$fƒƒt&tttƒƒt&t ttƒƒt&tttƒƒt'ttƒ tttƒksJ‚|tt'tt ƒt tdt#j$fƒttƒtd ks1J‚dS)!Nr©rrj)Úcot©Úpowsimprˆrcr\rSrm)rcN©NrSÚrT©Úrealza bracs ˆˆt|ddddƒ tt¡S)NF)ÚdeepT©Úforce)rÚreplacer*r)©rh©r—r‰rUrVÚ simp_powsgó z0test_inverse_mellin_transform..simp_powsru)rNrnrorqrrprr)r[rrscSsJddlm}ddlm}ddlm}||||ddddddd tt¡S)Nrr”r–)Ú logcombineTr)ržrœ) Úsympy.core.functionrÚsympy.simplify.powsimpr—rr¤rŸr*r))rhrr—r¤rUrUrVÚmysimp’s   þþz-test_inverse_mellin_transform..mysimpr[)(r¥rrtrkrlÚ(sympy.functions.elementary.trigonometricr•r¦r—rr‰rr?rLrKrr)r:r$rdr^r4r%rvrwrPrOr r'r0rMrNr+rr5r"rer;r7r3) rrkrlr•ÚIMTr™Ú_aÚ_br¢rur§rUr¡rVÚtest_inverse_mellin_transformEsT    $*$ÿ*ÿ*ÿ< " þDH 64, ÿ& ÿ þ( ÿ"ÿ ÿ ÿÿÿ$þ ý4ÿÿþ ýBÿÿDÿÿ ÿ þBÿÿ" þ8" ÿ08B4$.4ÿ ÿ þ 68ÿ ÿ þ.  ÿD ÿ0&ÿþ ý,(ÿþ ý"ÿþ ý&ÿ þ ý28ÿÿý üDÿÿ:þ:üÿ ÿ û: r¬cCsä-ddlm}ddlm}ddlm}m}t}tddd\}}}tdƒ\}} } t d ƒ} t d ƒ} ||||d |t d ƒd |t ƒ|t d d t d dt t ƒdt t dƒd ddfkscJ‚|||||t ƒ| t| t ƒt| t ƒddfksƒJ‚|dt ||ƒ|t ƒt t ƒt dt ƒt|t ƒtt |ƒt t ƒƒddfks®J‚|t |ƒ|||t ƒt t |ƒt|t ƒtt |ƒt t ƒƒt t ƒt dt ƒddfksàJ‚|||t d ƒ d |t ƒdt t ƒt t ƒt|t ƒtt |ƒt t ƒƒd t |ƒddfksJ‚||t dƒd ||d|t ƒt t |ƒt|t ƒtt |ƒt t ƒƒt t ƒt dt ƒddfksNJ‚|d|t |ƒ|d|t ƒt t |ƒt|t ƒtt |ƒt t ƒƒddfkszJ‚|||||t ƒt | dt| t ƒ||d|t ƒddfks¡J‚||d |||t ƒd|d |d|t ƒddfksÀJ‚|t|ƒ|t ƒdt dddfksÔJ‚|td |ƒ|t ƒdt d d dfksêJ‚|t||ƒ|t ƒdt ||dfksJ‚|t|||ƒ|t ƒt| |ƒ| t |dfksJ‚||t| |ƒ|t ƒ|t d| dfks8J‚||t| ||ƒ|t ƒt||ƒ|t d | dfksZJ‚|||t| |ƒ|t ƒ||t d | dfksxJ‚||t dƒdtd|ƒtt dƒdƒ|t ƒt dt dƒ dddfks£J‚||t d ƒd td|ƒ|t ƒd t t ƒdt dt d ƒd ddfksÍJ‚|||t| |ƒ|t ƒ|t | dt|dƒ| dfksòJ‚||t| |d ƒ|t ƒt t ƒ|tt d d|ƒtt d t |ƒƒd t |ƒddfks'J‚|td|d ƒ|t ƒt d ƒt t ƒtt d dƒtt d ƒt dƒdddfksUJ‚||td |d ƒ|t ƒ|ttd |d ƒ|t ƒkstJ‚||t| |d ƒ|t ƒdd |t tt d t |ƒƒdt t ƒ|t d ƒd ddfks©J‚|t| |ƒ|t ƒd t |ƒt dt ƒtdd t |ƒt t ƒƒddfksÓJ‚|t |ƒt| |ƒ|t ƒt t ƒd t |ƒt t ƒdt t dƒtdt |ƒt t ƒƒd ddfks J‚|t| |ƒt |ƒ|t ƒt t ƒt dt ƒtdt |ƒt t ƒƒddfks7J‚|t| |ƒ|t |ƒ|t ƒt t ƒt d|ƒtdt |ƒt t ƒƒddfksdJ‚|tdt ||ƒƒ|t ƒdt t t ƒt |ƒt|t ƒtt |ƒt dt ƒƒt t d ƒd ddfksžJ‚|tdt ||ƒƒt |ƒ|t ƒt|t ƒtt |ƒt dt ƒƒt t ƒt dt ƒddfksÒJ‚||dtd|ƒ|t ƒdt d ƒdt t d ƒd td d t d ƒt t ƒƒddfksJ‚|t||ƒ|t ƒ||d  t d |dfksJ‚||t||ƒd |t ƒd |d |d|d t d t d d |dfksJJ‚|td |ƒ|t ƒt dt d d dfksbJ‚|t||ƒ|t ƒt |d  t d |dfks}J‚|t||ƒd |t ƒd|d t d d|d t d t d d |dfks©J‚|t| d ƒ| t ƒt t dtdƒdtdƒt dt dd dtt ƒdkfksØJ‚|t||ƒt||ƒ|t ƒ|d|d t d d |dfksüJ‚|t||ƒ||t ƒt|t | t ƒd |dfksJ‚||t d ƒ d t||ƒ|t ƒt t ƒ t | t ƒt |t ƒ|dfksFJ‚|td t ||ƒƒ|t ƒt t ƒt |ƒt|t ƒt t d ƒd ddfkspJ‚|t |ƒtd t ||ƒƒ|t ƒt |ƒ t d t t ƒ|t d t|t ƒtt |ƒt dt ƒƒt t d ƒd ddfksµJ‚|td t ||ƒƒt |ƒ|t ƒt t ƒt|t ƒtt |ƒt dt ƒƒt t ƒddfksçJ‚|tt ||ƒƒd t |ƒ|t ƒt t ƒt|t ƒdd t t ƒddfksJ‚||t d ƒdt||ƒ|t ƒ|t t dƒ d| t t dƒ dtt dƒdƒd |dfksJJ‚|td t ||ƒƒ|t ƒt t ƒt |ƒt|t ƒtt |ƒt dt ƒƒt t d ƒd dt ddfks„J‚|t |ƒtd t ||ƒƒ|t ƒt t ƒ|t d t|t ƒt t d ƒd ddfks´J‚|td t ||ƒƒt |ƒ|t ƒt t ƒt|t ƒt t ƒddfksÚJ‚|tt ||ƒƒd t |ƒ|t ƒt t ƒt|t ƒdd t t ƒddfksJ‚|t|ƒ|t ƒtt t jƒ t ddfksJ‚|t||ƒ|t ƒt|t t jƒ t ddfks8J‚|td||ƒ|t ƒtt |ƒ tt |ƒt ddfksZJ‚|t||ƒ|t ƒt|ƒtt |ƒtt |ƒt t ddfksJ‚|t|ƒt |ƒ|t ƒt t ƒtt ƒ d td ƒt jt t ƒddfks§J‚||t d ƒd t|ƒ|t ƒdt t ƒtt ƒ d td ƒt jt dƒddt t dƒd ddfksáJ‚||d t|ƒ|t dddtt ƒ t jt dƒdt d ¡t jk s J‚|t|ƒd |t ƒtt ƒtd t d dt ddfk s+J‚|t| |ƒt|ƒ|t ƒt|t ƒ t j|t | dfk sOJ‚|t||ƒ|t ƒ||d t d ddfk siJ‚|tt||ƒƒ|t ƒ|tt t d |ƒ|d t d ddfk sJ‚|t||ƒ||t ƒt|t ƒddfk s§J‚|t||ƒd ||t ƒtd|d t d dƒdddfk sËJ‚|t||ƒd |d |t ƒ|td |t ƒt td|d t d dƒdddfk sýJ‚|td t ||ƒƒ|t ƒt t ƒt |ƒt| t ƒt t d ƒd ddfk s(J‚|td t ||ƒƒ||t ƒt tt |ƒt dt ƒƒddfk sLJ‚|t||ƒ|t ƒt |d t d ddfk sfJ‚|t||ƒd |t ƒd |d t d t d|d t d ddfk sŽJ‚|t |ƒtd t ||ƒƒ|t ƒt t ƒd|t t| t ƒd t t d ƒd ddfk sÁJ‚|td t ||ƒƒt |ƒ|t ƒt t ƒt dt ƒt| t ƒddfk sêJ‚|t||ƒt||ƒ|t ƒd ||t t d ||d t d ||d ddfk sJ‚|t||ƒt||ƒ|t ƒ||d  |d t d t d ||d t d ||d ddfk sUJ‚|t||ƒt||ƒ|t ƒt |d |d t d t d ||d t d ||d ddfk sJ‚||t| |ƒt||ƒ|t ƒ|||d |t d | dfk sµJ‚||t| |ƒt||ƒ|t ƒ|t ||d |t d | dfk sßJ‚|t| d ƒ| t ƒt td ƒtd ƒt d dddfk sÿJ‚|t||ƒ|t ƒtt d d|d ƒtt d |ƒt ddfk s%J‚|tt ||ƒƒ|t ƒt |ƒt t |t ƒddfk sCJ‚|t||ƒtt ||ƒƒ|t ƒt |ƒt t ƒ| t |dfk shJ‚|tt ||ƒd ƒ|t ƒdtt |ƒ t t ƒƒt ddfk s‹J‚|tt ||ƒƒ|t ƒt |ƒ t |t ƒt t |t ƒddfk s°J‚|t||ƒtt ||ƒƒ|t ƒdt |ƒt t ƒt ddfk sÔJ‚|tt ||ƒd ƒ|t ƒtt |ƒ t t ƒƒt ddfk sõJ‚|t d||ƒ|t ƒdt |d t d ƒddfk sJ‚|t d||ƒ|t ƒ|t |d t d ƒt t |d t d ƒddfk s;J‚|t d ||ƒ|t ƒ|d t |d t d ƒt t |d t d ƒd ddfk shJ‚||t d||ƒ|t ƒt |d t d t d ƒd ddfk s‹J‚||t d||ƒ|t ƒ||d t d t d ƒd ddfk s®J‚||d t d ||ƒ|t ƒd |d |d t d t d ƒd ddfk s×J‚|t dd t ||ƒƒ|t ƒt| t ƒt ddfk sõJ‚||t d ƒd t d d t ||ƒƒ|t ƒ|t d ƒd t| t ƒt dddfks%J‚|t d|t |d ||ƒƒ|t ƒt|t |t |d t d ƒƒt |d t d ƒddfksZJ‚|t!d||ƒ|t ƒdt |d  t d ƒ|dfksxJ‚|t!d||ƒ|t ƒ|t |d  t d ƒt t |d  t d ƒ|dfks£J‚|t!d ||ƒ|t ƒ|d t |d  t d ƒt t |d  t d ƒd |dfksÒJ‚||t!d||ƒ|t ƒt |d  t d t d ƒd |dfksöJ‚||t!d||ƒ|t ƒ||d  t d t d ƒd |dfksJ‚||d t!d ||ƒ|t ƒd |d |d  t d t d ƒd |dfksDJ‚||t d ƒd t!d d t ||ƒƒ|t ƒ|t d ƒd t|t ƒt dddfkssJ‚|t"d||ƒ|t ƒdt#t |ƒt t |d t d ƒddfks˜J‚|td||ƒ|t ƒtt t |d  t d ƒƒt |d  t d ƒ|dfksÃJ‚|t||ƒd|t ƒd |dt d!|dd"|dt d d#|dt dd|d t dt dddfksJ‚|t$|dƒt|dƒ|t ƒt tt ƒt d dddfks(J‚||| |ƒ|| ƒ|t| |ƒ|| ƒks?J‚||t$|dƒ| |dƒ|t ƒ|t| |dƒt$|dƒ|t ƒksfJ‚||t$|dƒ| |dƒ|t ƒ|t| |ƒ|t ƒtt ƒksŠJ‚||| ||ƒ|t ƒ||t| |ƒ||t ƒks§J‚|t| | ƒ |ƒ|t ƒdt | | ƒ| | ƒ dfksÅJ‚|t| |ƒ| |ƒ|t ƒt| |ƒ||t ƒksáJ‚|t| |ƒtt ||ƒd ƒ|t ƒtt |ƒ t |t ƒƒ|t | dfksJ‚|t||ƒ| |ƒ|t ƒt| |ƒ|| t ƒd t| |ƒ||t ƒd ks8J‚|t||ƒ||t ƒdd |t d dd | t d |dfks_J‚|t||ƒ| |ƒ|t ƒt| |ƒ|| t ƒd t| |ƒ||t ƒd ks‰J‚|t||ƒ||t ƒdd |t d dd | t d |dfks°J‚|t||ƒ| |ƒ|t ƒt%t| |ƒ|t% |t ƒ t| |ƒ|t%|t ƒd ksßJ‚|t||ƒ||t ƒd |t |dd |d t d t dddfks J‚|t||ƒ| |ƒ|t ƒt| |ƒ|t% |t ƒd t| |ƒ|t%|t ƒd ks7J‚|t||ƒ||t ƒ|d  t d |dd |d t d t dddfksdJ‚|t&| |ƒ|dfƒ|t ƒt t| |ƒ|t ƒ| dƒks‚J‚|t&| |ƒ|d fƒ|t ƒt d t| |ƒ|t ƒt d | dƒt t't(| |ƒ|ƒ|dƒt't(| |ƒ|d fƒ|dƒksÀJ‚|dt&| |ƒ|dfƒ|t ƒdt t| |ƒ|t ƒd| dƒksäJ‚||| ||ƒ| ||ƒ|t ƒ|t| |ƒ|t |ƒ|t| |ƒ|t |ƒ|ksJ‚t)| | ƒ| |dd$t*| | ƒ| |dƒks)J‚|| |ƒ| |ƒ|t ƒt| |ƒ| |ƒ|t ƒksDJ‚||||t| ||ƒt$||ƒ|t ƒt || dt| t ƒt|dƒ| dfkszJ‚|td |ƒdt| |ƒt$|ƒd |t ddt| ƒt d dks£J‚|||ƒ|t ƒd%ks°J‚||||ƒ|t ƒd|ddfksÄJ‚|||d&ƒ|t ƒd'ksÓJ‚|||d&ƒ|t ƒd(ksâJ‚|||ƒ||d&ƒ|t ƒdtd)t ƒddfksþJ‚|||ƒ|t| |ƒ|t ƒt |t ddfksJ‚|t| ƒ||ƒ||d&ƒ|t ƒtd)t d&ƒdt+ dfks?J‚|||d ƒ|t ƒt||d ƒ|t ƒksVJ‚|||d dƒ|t ƒtt ƒd t+ dfkspJ‚|||d|ƒ|t ƒt||d  |ƒ|t ƒksŒJ‚|||ƒd||dƒd|t ƒt||ƒ||dƒ|t ƒdtt ƒdt ddfks½J‚||d |d t|ƒƒ|t ƒtt t|ƒƒd ddfksÞJ‚||d|d t|ƒƒ|t ƒtt t|ƒƒd ddfksÿJ‚|t$|ƒ|t ƒdt ddfksJ‚|t$||ƒ|t ƒt| t ƒt ddfks*J‚|t$|dƒ|t ƒtt ƒt ddfksAJ‚|t$d |dƒ|t ƒtdt ƒt ddfks[J‚|t$d|dƒ|t ƒdtdt ƒt ddfkswJ‚|t$d |dƒ|t ƒdt ddfksJ‚|t$d|dƒ|t ƒdtdt ƒt ddfks©J‚t||ƒ|t ƒtt d d t ƒ |t t ƒtt d d t ƒd tt d d t ƒ|t t ƒtt d d t ƒd t ddfksòJ‚t||ƒ|t ƒd tt d d t ƒ|t t ƒd tt d d t ƒ|t t ƒt d ƒtt d d t t dƒd t ddfks:J‚t,t|ƒ|t| ƒg|t| ƒt|ƒggƒ} t,dt dt ddgt dddt dggƒ}t-ƒ.t,dt dddft ddddfgt ddddfdt dddfggƒ}Wdƒn 1s¡wYt-ƒ|| |t ƒ|ksµJ‚Wdƒn 1sÀwY|| |t d*d+|ddfksÕJ‚|| |t dd|ksâJ‚|| |t d*dd,|ksðJ‚dS)-Nr)Ú lowergamma©Ú DiracDelta)ÚfresnelcÚfresnelsza, b, cTrazt, w, xrRÚgr\rorpééérSr[rcgø?éxéûÿÿÿrmiøÿÿÿé éýÿÿÿéüÿÿÿrqé é.©Únocondsi€i@iÍi)Úplane)rSrTé*)rÀrT)rrTiÖÿÿÿF)Ú legacy_matrix)rÁr¾).Úsympyr­Ú'sympy.functions.special.delta_functionsr¯rŽr°r±rr$rr"rLr0r r)r>r<r?rr8r-r,r&r+r;rr‰r‘r4r.r1r3r7r6r9r/r:rrrrrrrrIrH)r­r¯r°r±ÚLTrMrNrOÚtÚwrKrRr²ÚMtÚMsÚMs_condsrUrUrVÚtest_laplace_transformÒsV  &<ÿ@8ÿ@ÿÿ>ÿ ÿ"@ÿ ÿ0 ÿ2 ÿ>(,,<4D<2 ÿ"( ÿJD ÿ< ÿ>D ÿ6 ÿ6ÿÿÿ ÿ0 ÿ 0 ÿ8ÿÿ ÿ4 ÿÿ ÿ> ÿ6D ÿ06D ÿ@ ÿH>$( ÿ0 ÿ"6 ÿÿÿ ÿ"8 ÿ"( ÿ"F ÿJÿ ÿ"4 ÿ"  ÿ"( ÿ08DJ0 ÿFÿ ÿ* ÿÿ ÿ$ ÿ" ÿ4, ÿ0H< ÿ2 ÿH40 ÿ": ÿ"& ÿ< ÿDÿ ÿBÿ ÿ> ÿB ÿ@L<" ÿF* ÿ" ÿB:4 ÿ< ÿ$ ÿ$ ÿ, ÿ<,* ÿ$< ÿ<8 ÿ@ ÿHH. ÿ,( ÿ, ÿ8 ÿ>ÿÿÿ ÿF."" ÿ" ÿ:<8(( ÿ0 ÿ. ÿ0 ÿ. ÿÿÿ ÿ4 ÿÿ ÿ: ÿ* ÿ.ÿÿ þ2  ÿ< ÿ ÿ ÿ602 ÿ4 ÿ( ÿ:$ ÿ.4 ÿ"ÿÿÿÿ ÿBB$2.48,88ÿÿÿÿ ÿF"ÿÿÿ ÿ0ÿÿ"ÿÿÿ  rÊcs ddlm‰ddlm}ddlm}t}tddd\}}}tdƒ}‡fd d „}|d t|ƒ||ƒks3J‚|d tt|ƒt |ƒksAJ‚|||tt|ƒ|t | |ƒt |ƒksZJ‚|t|tt|ƒ| t | |ƒt |ƒ||ƒksxJ‚||td t|ƒ|t | |ƒt |ƒks‘J‚||td t|ƒ|dt | |ƒt |ƒdks®J‚|||dtdt|ƒt ||ƒt |ƒksÈJ‚|ttd|dt|ƒt ||ƒt |ƒksâJ‚|||d|tdt|ƒt | |ƒt ||ƒt |ƒksJ‚||t|d|tdt|ƒ|t ||ƒ|t ||ƒt | |ƒt |ƒdks8J‚|t | tƒtt|ƒt | |ƒksOJ‚|t | tƒ|tt|ƒt |||ƒt | |ƒkspJ‚||t|d|tdt|ƒt | |ƒt ||ƒt |ƒks–J‚|t | tƒt|t|ƒ| ||d t | |ƒt |ƒks¼J‚|t | tƒttdd ƒt|ƒt | |ƒtd||ƒksàJ‚|d tttd ƒt|ƒt |ƒtt|ƒƒksûJ‚|d tdtdd t|ƒ|t |ƒt |ƒksJ‚|tdtdd t|ƒt |ƒ t |ƒ||ƒks6J‚|d d tdd t|ƒt |ƒ t |ƒ||ƒksTJ‚|d tdt|ƒ|t |ƒksgJ‚|d tdt|ƒ|dt |ƒdks~J‚|||td|dt|ƒƒt||ƒt |ƒks›J‚||ttd|dt|ƒƒt||ƒt |ƒks¸J‚|t | tƒt|t|ƒ|||d t ||ƒt |ƒksÜJ‚|t | tƒtd tdƒt|ƒt ||ƒtd||ƒksÿJ‚||||tttd|dƒ| ttd|dƒt|ƒ t ¡ƒt |ƒt|||ƒks3J‚|||tttd|dƒ| ttd|dƒt|ƒ t ¡t |ƒt|||ƒkseJ‚|d tttd ƒt|ƒt |ƒtt|ƒƒks€J‚|d tdtdd t|ƒ|t |ƒt |ƒksJ‚|ttdƒtd dgddggƒ ¡t|ƒtt |ƒt |ƒdgdt d|ƒt |ƒggƒksÎJ‚dS)Nr©Ú factor_termsr®rˆúa b cTrarÅcsˆt|ƒƒ t¡S©N)rr^r4r rËrUrVÚsimp_hypsz0test_inverse_laplace_transform..simp_hyprSr[r·rmrnr\ro)Úsympy.core.exprtoolsrÌrÃr¯rr‰rr$rLr:r)r4r3r?r0r7r;r-r,r^r6rJrIÚinv)r¯r‰ÚILTrMrNrOrÅrÏrUrËrVÚtest_inverse_laplace_transform s€    2<2:44H"4ÿ ÿ.B"  ÿ& ÿ$ ÿ6:<<&.::" ÿ$ ÿ<ÿÿ þ:ÿ þ6:*.ÿrÓcCsddlm}t}tdƒ}|dt|ƒd||ƒksJ‚|dtdtƒdtdtƒt|ƒd||dƒd||dƒks@J‚ttdƒdƒ}||td tƒt|ƒ|||dƒks^J‚|tdtƒt|ƒ||dƒkspJ‚td d d }|t|tƒt|ƒ|||ƒksˆJ‚dS) Nrr®rÅr\rproiùÿÿÿrµr¹r™Trš) rÃr¯rr$rLr)r3r4r#)r¯rÒrÅrMr™rUrUrVÚ$test_inverse_laplace_transform_deltaFs &ÿ,$ (rÔcCs:ddlm}ddlm}t}tdƒ}tddd}|t|tƒt|dd |||ƒdfks.J‚td ƒ}|t|tƒt|dd |||ƒt ||ƒdƒfksMJ‚td dd td ddd fD] }|t|tƒt|dd }t |t ƒrq|dn|}|j |kszJ‚qZ|d tt|tƒtt|dd t |ƒt ||ƒdfks›J‚dS)Nr)Úimr®rÅr™TršFr½Úz)Ú extended_real)Ú imaginaryÚzerorS)Ú$sympy.functions.elementary.complexesrÕrÃr¯rr$r#r)rLr!Ú isinstanceÚtupler€r:)rÕr¯rÒrÅr™rÖrRrUrUrVÚ)test_inverse_laplace_transform_delta_condTs&   ,ÿ  ÿ"ÿrÝc s¢ddlm‰m‰m‰ddlm}ddlm‰t}t }‡‡‡‡fdd„}dd„}t d d d }t d ƒ}t d d d}t dd d}t dd d} t|t ƒt |ƒt |t ƒt |ƒksUJ‚t ||ƒ|t ƒt||ƒ|t ƒksgJ‚||tdtd|t ƒƒt |ƒƒ|||ƒ|ksƒJ‚||tdt|t ƒƒdt|t ƒt |ƒƒ|||ƒd|ks§J‚||t| t ƒtt ƒt |ƒtdd|dtt|ksÈJ‚|d|dttt t | ddt| | ƒd fksåJ‚|d|dttt t | dddksüJ‚|d|dttt t t d d ddddksJ‚||t t| t ƒtt ƒt |ƒtdd|dtt|dks=J‚|t| t ƒt|t ƒtt ƒt |ƒ||d|dtt|dksgJ‚|t| t dƒt |ƒttƒttd |d|ƒt|ƒksŒJ‚|tt|ƒtt|d |ƒ|t ƒt| t dƒks­J‚|t| tt ƒƒt |ƒd||ddtd|dksÏJ‚dS)Nr)rÚexpand_complexÚ expand_trig)Úfactorrˆcsˆˆˆˆ|ƒƒƒƒSrÎrU©rK©rrÞrßr‰rUrVÚsimpoóz$test_fourier_transform..simpcSstt|ƒt|SrÎ)r4r rárUrUrVÚsincrräz$test_fourier_transform..sincÚkTršrRrMrarNÚposkrSr\)Ú extensionFr½)rTrŠrm)r¥rrÞrßÚsympy.polys.polytoolsràrr‰rrr$rrKrrr:rxr)rr r4r0) ràÚFTÚIFTrãrårærRrMrNrçrUrârVÚtest_fourier_transformhs^      $ ÿÿ8H$ÿÿÿÿÿ$ÿ ÿ( ÿ(" ÿJBHrìcCsþtdƒ}tdƒ}tdƒ}tdƒ}t||ƒ||ƒt||ƒ||ƒks"J‚t||ƒ||ƒt||ƒ||ƒks4J‚tdt|ƒ||ƒdt|ƒksFJ‚tdt|ƒ||ƒdt|ƒksXJ‚tdt|ƒd||ƒdt|ƒkslJ‚t|| ||ƒd| tj||dt | ddƒt |ddƒks–J‚td| tdƒd||dt | ddƒt |dtjƒ||ƒ|| ksÄJ‚tt | |ƒ||ƒtdƒ|tt ƒ|d|dksãJ‚ttdƒ|tt ƒ|d|d||ƒt | |ƒksJ‚tt |ƒ|||ƒtdƒtt ƒt |dƒdt  dks%J‚t|t | |dƒ||ƒtdƒ|t |d d|ƒd|tddƒksQJ‚ttdƒ|t |d d|ƒd|tddƒ||ƒ|t | |dƒks}J‚dS) NrÅrÆrMrRrSrpr\rm)r$rrrr rr0r"rer?r)r r+rr)rÅrÆrMrRrUrUrVÚtest_sine_transform¢s|$ ÿÿ$$( ÿ ÿÿ ÿ ÿÿ ÿÿÿÿÿÿ"ÿ&ÿ  ÿÿ( ÿÿ2 ÿ6ÿÿrícCs&ddlm}m}tdƒ}tdƒ}tdƒ}tdƒ}t||ƒ||ƒt||ƒ||ƒks*J‚t||ƒ||ƒt||ƒ||ƒkssÿz!test_issue_8882..) rMrLr0r)rr r4r1r?rGrrUrUrôrVÚtest_issue_8882s J ÿÿr÷c Cs ddlm}tddd\}}}tddd}|td|td|t|t|ƒƒ}|tt|ttdd |||dƒdƒt t d |||dƒƒ|ƒt |t tdd |||dƒdƒt t d |||dƒƒd|ƒt|ttdd |||dƒdƒt t d |||dƒƒ|ƒt|t tdd |||dƒdƒt t d |||dƒƒd|ƒtt |t tdd |||dƒdƒt t d |||dƒƒd|ƒt|t tdd |||dƒdƒt t d |||dƒƒd|ƒt| |ttdd |||dƒdƒt t d |||dƒƒd|ƒt d |||dƒksNJ‚dS) NrrˆrÍTrarÅrSr\rºrm) rr‰r$rrLrr)r3r2r0r&r4)r‰rMrNrOrÅÚftrUrUrVÚtest_issue_8514 sn  (8ÿÿ*ÿÿÿÿÿÿÿÿÿÿÿþÿÿÿü4ÿÿú(ÿÿùørùcCs8tddd\}}tt|ƒ||ƒtt|ƒ||ƒksJ‚dS)Nzx yTrš)r$rr)r)rKÚyrUrUrVÚtest_issue_125910s(rûcCsftddd}tdtt|ttƒt tt|tƒtd|ttttdƒƒddfks1J‚dS)NrNTrŠrSr\r) r#rrrKrLr)r=r*r )rNrUrUrVÚtest_issue_146925s 8 ÿrüN)€rTrrrrrrrr r r r r rrrrrrrrrr¥rrÚ sympy.corerrrrÚsympy.core.numbersrrrr Úsympy.core.relationalr!Úsympy.core.singletonr"Úsympy.core.symbolr#r$Ú(sympy.functions.combinatorial.factorialsr%rÚr&r'r(Ú&sympy.functions.elementary.exponentialr)r*r+Ú%sympy.functions.elementary.hyperbolicr,r-r.r/rtr0r¨r1r2r3r4r5Úsympy.functions.special.besselr6r7r8r9rÃr:rŽr;r<r=r>Ú'sympy.functions.special.gamma_functionsr?Úsympy.functions.special.hyperr@Úsympy.simplify.gammasimprAÚsympy.simplify.hyperexpandrBÚsympy.simplify.trigsimprCÚsympy.testing.pytestrDrErFrGrHÚsympy.matricesrIrJÚ sympy.abcrKrLrMrNrOrPrurvrwrWrYr`rirzr}rƒr“r¬rÊrÓrÔrÝrìrírîrðrñr÷rùrûrürUrUrUrVÚsr\             ? ` 1  8 <:#*