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    7^(hZ-  ã                   ó¬  — d dl mZmZ d dlmZmZ d dlmZ d dlm	Z	 d dl
mZ d dlmZ d dlmZ d dlmZmZmZmZmZmZ eZeZeZeZeZeZd d	lmZmZ  ed
«      \  Z Z!Z" edd¬«      \  Z#Z$Z%Z&Z'Z( edd¬«      Z) edd¬«      Z* edddd¬«      \  Z+Z, eddddd¬«      \  Z-Z. edd¬«      Z/d„ Z0d„ Z1 edd¬«      \  Z2Z!ee2dz
  z  dez   e2 e!z
  z  z   ee2e!z   «      z   ee2«      z   ee!«      z  Z3 eddd¬«      Z4dde4dz  z
  z  ee4dz
  z  z   eedz   dz  «      z   ee4dz  «      z  Z5de) dz  z   ee)dz  «      z  ee)dz  dz
  z  z   ee dz  «      z  Z6e#e(z  ez  ee$z  e#e(z  z  z  dee#z  e$e#z  z  z   e(dz   z  z  Z7 edd¬«      \  Z8Z9 e	e8ez  e8z  e9e9z  z  e8ez  e9z   e8e9z   z  z  «      ez   ee8dz  «      z   ee9dz  «      z   ee8e9z   dz  «      z  Z: edd¬«      \  Z;Z<ee<dz  z   eedz  e;dz  z    dz  e<dz  z  «      z   ed ee;z  e<dz  z  «      z  Z= edd¬«      Z> e e?ee>z
  «       e$z  «      dz  e$z  Z@ edd¬ «      ZA ed!d¬«      ZBd"„ ZCg d#¢ZDd d$lEmEZE d d%lFmGZG d d&lHZHg ZIeJd'k(  rÛ eKeD«      D ]ž  \  ZLZM eG«         eE«       ZN eOeM«        eE«       eNz
  ZNeIeNeMfgz  ZIeHj                   j£                  d(«       eHj                   j¥                  «        eL eSeD«      d)z  z  d k(  sŒueHj                   j£                  d*d)eLz   eSeD«      z  z  «       Œ   eT«        eIj«                  d+„ ¬,«       eID ]  \  ZVZM eTd-eVeMfz  «       Œ y&y&).é    )ÚooÚpi)ÚSymbolÚsymbols©Úexp)Úsqrt)Úbesseli)Úgamma)Ú	integrate)Úmellin_transformÚinverse_fourier_transformÚinverse_mellin_transformÚlaplace_transformÚinverse_laplace_transformÚfourier_transform)ÚxÚyznu beta rhoza b c d k pT)ÚpositiveÚk)Úreal)Únegativezmu1 mu2)r   ÚnonzeroÚfinitezsigma1 sigma2)r   r   r   r   Úlambdac                 óp   — dt        dt        z  |dz  z  «      z  t        | |z
  dz   dz  |dz  z  «      z  S )Né   é   )r	   r   r   )r   ÚmuÚsigmas      ú^/var/www/skyplay_api_hub/venv/lib/python3.12/site-packages/sympy/benchmarks/bench_meijerint.pyÚnormalr"   !   s?   € ØŒT�!”B‘$�u˜a‘x‘-Ó Ñ ¤ q¨2¡v°¡k \°!¡^°E¸1±HÑ%<Ó!=Ñ=Ð=ó    c                 ó&   — |t        | | z  «      z  S )Nr   )r   Úrates     r!   Úexponentialr&   %   s   € Ø”�T�E˜!‘G“ÑÐr#   z
alpha betar   )Úintegerr   r   zd1 d2znu sigmar   Úu)ÚpolarÚtc                 óh  — t        | t        t        t        «      z  t	        t
        t        t        «      z  t        dt        ft
        t         t        fd¬«       t        | t        t        t        «      z  t	        t
        t        t        «      z  t
        t         t        ft        dt        fd¬«       y )Nr   T)Úmeijerg)	r   r&   r   r%   r"   r   Úmu1Úsigma1r   )Úexprs    r!   ÚEr0   ;   st   € Üˆd”;œq¤$Ó'Ñ'¬¬q´#´vÓ(>Ñ>Ü˜œB�Z¤!¤b S¬" °tõ=äˆd”;œq¤$Ó'Ñ'¬¬q´#´vÓ(>Ñ>Üœ"˜œb�\¤A q¬" :°tö=r#   )˜z MT(x**nu*Heaviside(x - 1), x, s)z MT(x**nu*Heaviside(1 - x), x, s)z*MT((1-x)**(beta - 1)*Heaviside(1-x), x, s)z*MT((x-1)**(beta - 1)*Heaviside(x-1), x, s)zMT((1+x)**(-rho), x, s)zMT(abs(1-x)**(-rho), x, s)zKMT((1-x)**(beta-1)*Heaviside(1-x) + a*(x-1)**(beta-1)*Heaviside(x-1), x, s)zMT((x**a-b**a)/(x-b), x, s)z!MT((x**a-bpos**a)/(x-bpos), x, s)zMT(exp(-x), x, s)zMT(exp(-1/x), x, s)z"MT(log(x)**4*Heaviside(1-x), x, s)z"MT(log(x)**3*Heaviside(x-1), x, s)zMT(log(x + 1), x, s)zMT(log(1/x + 1), x, s)zMT(log(abs(1 - x)), x, s)zMT(log(abs(1 - 1/x)), x, s)zMT(log(x)/(x+1), x, s)zMT(log(x)**2/(x+1), x, s)zMT(log(x)/(x+1)**2, x, s)zMT(erf(sqrt(x)), x, s)zMT(besselj(a, 2*sqrt(x)), x, s)z*MT(sin(sqrt(x))*besselj(a, sqrt(x)), x, s)z*MT(cos(sqrt(x))*besselj(a, sqrt(x)), x, s)z MT(besselj(a, sqrt(x))**2, x, s)z2MT(besselj(a, sqrt(x))*besselj(-a, sqrt(x)), x, s)z5MT(besselj(a - 1, sqrt(x))*besselj(a, sqrt(x)), x, s)z1MT(besselj(a, sqrt(x))*besselj(b, sqrt(x)), x, s)z:MT(besselj(a, sqrt(x))**2 + besselj(-a, sqrt(x))**2, x, s)zMT(bessely(a, 2*sqrt(x)), x, s)z*MT(sin(sqrt(x))*bessely(a, sqrt(x)), x, s)z*MT(cos(sqrt(x))*bessely(a, sqrt(x)), x, s)z1MT(besselj(a, sqrt(x))*bessely(a, sqrt(x)), x, s)z1MT(besselj(a, sqrt(x))*bessely(b, sqrt(x)), x, s)z MT(bessely(a, sqrt(x))**2, x, s)zMT(besselk(a, 2*sqrt(x)), x, s)zEMT(besselj(a, 2*sqrt(2*sqrt(x)))*besselk(a, 2*sqrt(2*sqrt(x))), x, s)z1MT(besseli(a, sqrt(x))*besselk(a, sqrt(x)), x, s)z1MT(besseli(b, sqrt(x))*besselk(a, sqrt(x)), x, s)z#MT(exp(-x/2)*besselk(a, x/2), x, s)z>LT((t-apos)**bpos*exp(-cpos*(t-apos))*Heaviside(t-apos), t, s)zLT(t**apos, t, s)zLT(Heaviside(t), t, s)zLT(Heaviside(t - apos), t, s)zLT(1 - exp(-apos*t), t, s)zBLT((exp(2*t)-1)*exp(-bpos - t)*Heaviside(t)/2, t, s, noconds=True)zLT(exp(t), t, s)zLT(exp(2*t), t, s)zLT(exp(apos*t), t, s)zLT(log(t/apos), t, s)zLT(erf(t), t, s)zLT(sin(apos*t), t, s)zLT(cos(apos*t), t, s)z"LT(exp(-apos*t)*sin(bpos*t), t, s)z"LT(exp(-apos*t)*cos(bpos*t), t, s)z%LT(besselj(0, t), t, s, noconds=True)z%LT(besselj(1, t), t, s, noconds=True)z&FT(Heaviside(1 - abs(2*apos*x)), x, k)z2FT(Heaviside(1-abs(apos*x))*(1-abs(apos*x)), x, k)z#FT(exp(-apos*x)*Heaviside(x), x, k)z0IFT(1/(apos + 2*pi*I*x), x, posk, noconds=False)z1IFT(1/(apos + 2*pi*I*x), x, -posk, noconds=False)z!IFT(1/(apos + 2*pi*I*x), x, negk)z%FT(x*exp(-apos*x)*Heaviside(x), x, k)z/FT(exp(-apos*x)*sin(bpos*x)*Heaviside(x), x, k)zFT(exp(-apos*x**2), x, k)z-IFT(sqrt(pi/apos)*exp(-(pi*k)**2/apos), k, x)zFT(exp(-apos*abs(x)), x, k)z=integrate(normal(x, mu1, sigma1), (x, -oo, oo), meijerg=True)z?integrate(x*normal(x, mu1, sigma1), (x, -oo, oo), meijerg=True)zBintegrate(x**2*normal(x, mu1, sigma1), (x, -oo, oo), meijerg=True)zBintegrate(x**3*normal(x, mu1, sigma1), (x, -oo, oo), meijerg=True)zkintegrate(normal(x, mu1, sigma1)*normal(y, mu2, sigma2),          (x, -oo, oo), (y, -oo, oo), meijerg=True)zmintegrate(x*normal(x, mu1, sigma1)*normal(y, mu2, sigma2),          (x, -oo, oo), (y, -oo, oo), meijerg=True)zmintegrate(y*normal(x, mu1, sigma1)*normal(y, mu2, sigma2),          (x, -oo, oo), (y, -oo, oo), meijerg=True)zointegrate(x*y*normal(x, mu1, sigma1)*normal(y, mu2, sigma2),          (x, -oo, oo), (y, -oo, oo), meijerg=True)zsintegrate((x+y+1)*normal(x, mu1, sigma1)*normal(y, mu2, sigma2),          (x, -oo, oo), (y, -oo, oo), meijerg=True)z|integrate((x+y-1)*normal(x, mu1, sigma1)*normal(y, mu2, sigma2),                   (x, -oo, oo), (y, -oo, oo), meijerg=True)zvintegrate(x**2*normal(x, mu1, sigma1)*normal(y, mu2, sigma2),                (x, -oo, oo), (y, -oo, oo), meijerg=True)zpintegrate(y**2*normal(x, mu1, sigma1)*normal(y, mu2, sigma2),          (x, -oo, oo), (y, -oo, oo), meijerg=True)z9integrate(exponential(x, rate), (x, 0, oo), meijerg=True)z;integrate(x*exponential(x, rate), (x, 0, oo), meijerg=True)z>integrate(x**2*exponential(x, rate), (x, 0, oo), meijerg=True)zE(1)zE(x*y)z	E(x*y**2)zE((x+y+1)**2)zE(x+y+1)zE((x+y-1)**2)z-integrate(betadist, (x, 0, oo), meijerg=True)z/integrate(x*betadist, (x, 0, oo), meijerg=True)z2integrate(x**2*betadist, (x, 0, oo), meijerg=True)z(integrate(chi, (x, 0, oo), meijerg=True)z*integrate(x*chi, (x, 0, oo), meijerg=True)z-integrate(x**2*chi, (x, 0, oo), meijerg=True)z/integrate(chisquared, (x, 0, oo), meijerg=True)z1integrate(x*chisquared, (x, 0, oo), meijerg=True)z4integrate(x**2*chisquared, (x, 0, oo), meijerg=True)zDintegrate(((x-k)/sqrt(2*k))**3*chisquared, (x, 0, oo), meijerg=True)z*integrate(dagum, (x, 0, oo), meijerg=True)z,integrate(x*dagum, (x, 0, oo), meijerg=True)z/integrate(x**2*dagum, (x, 0, oo), meijerg=True)z&integrate(f, (x, 0, oo), meijerg=True)z(integrate(x*f, (x, 0, oo), meijerg=True)z+integrate(x**2*f, (x, 0, oo), meijerg=True)z)integrate(rice, (x, 0, oo), meijerg=True)z.integrate(laplace, (x, -oo, oo), meijerg=True)z0integrate(x*laplace, (x, -oo, oo), meijerg=True)z3integrate(x**2*laplace, (x, -oo, oo), meijerg=True)z=integrate(log(x) * x**(k-1) * exp(-x) / gamma(k), (x, 0, oo))zEintegrate(sin(z*x)*(x**2-1)**(-(y+S(1)/2)), (x, 1, oo), meijerg=True)úIintegrate(besselj(0,x)*besselj(1,x)*exp(-x**2), (x, 0, oo), meijerg=True)zKintegrate(besselj(0,x)*besselj(1,x)*besselk(0,x), (x, 0, oo), meijerg=True)r1   z>integrate(besselj(a,x)*besselj(b,x)/x, (x,0,oo), meijerg=True)zŠhyperexpand(meijerg((-s - a/2 + 1, -s + a/2 + 1), (-a/2 - S(1)/2, -s + a/2 + S(3)/2), (a/2, -a/2), (-a/2 - S(1)/2, -s + a/2 + S(3)/2), 1))aÔ  gammasimp(S('2**(2*s)*(-pi*gamma(-a + 1)*gamma(a + 1)*gamma(-a - s + 1)*gamma(-a + s - 1/2)*gamma(a - s + 3/2)*gamma(a + s + 1)/(a*(a + s)) - gamma(-a - 1/2)*gamma(-a + 1)*gamma(a + 1)*gamma(a + 3/2)*gamma(-s + 3/2)*gamma(s - 1/2)*gamma(-a + s + 1)*gamma(a - s + 1)/(a*(-a + s)))*gamma(-2*s + 1)*gamma(s + 1)/(pi*s*gamma(-a - 1/2)*gamma(a + 3/2)*gamma(-s + 1)*gamma(-s + 3/2)*gamma(s - 1/2)*gamma(-a - s + 1)*gamma(-a + s - 1/2)*gamma(a - s + 1)*gamma(a - s + 3/2))'))zmellin_transform(E1(x), x, s)z3inverse_mellin_transform(gamma(s)/s, s, x, (0, oo))z$mellin_transform(expint(a, x), x, s)zmellin_transform(Si(x), x, s)z^inverse_mellin_transform(-2**s*sqrt(pi)*gamma((s + 1)/2)/(2*s*gamma(-s/2 + 1)), s, x, (-1, 0))z#mellin_transform(Ci(sqrt(x)), x, s)zWinverse_mellin_transform(-4**s*sqrt(pi)*gamma(s)/(2*s*gamma(-s + S(1)/2)),s, u, (0, 1))zlaplace_transform(Ci(x), x, s)z%laplace_transform(expint(a, x), x, s)z%laplace_transform(expint(1, x), x, s)z%laplace_transform(expint(2, x), x, s)z3inverse_laplace_transform(-log(1 + s**2)/2/s, s, u)z-inverse_laplace_transform(log(s + 1)/s, s, x)z6inverse_laplace_transform((s - log(s + 1))/s**2, s, x)zlaplace_transform(Chi(x), x, s)zlaplace_transform(Shi(x), x, s)z>integrate(exp(-z*x)/x, (x, 1, oo), meijerg=True, conds="none")zAintegrate(exp(-z*x)/x**2, (x, 1, oo), meijerg=True, conds="none")z@integrate(exp(-z*x)/x**3, (x, 1, oo), meijerg=True,conds="none")z1integrate(-cos(x)/x, (x, tpos, oo), meijerg=True)z1integrate(-sin(x)/x, (x, tpos, oo), meijerg=True)z,integrate(sin(x)/x, (x, 0, z), meijerg=True)z-integrate(sinh(x)/x, (x, 0, z), meijerg=True)z%integrate(exp(-x)/x, x, meijerg=True)z(integrate(exp(-x)/x**2, x, meijerg=True)z$integrate(cos(u)/u, u, meijerg=True)z%integrate(cosh(u)/u, u, meijerg=True)z(integrate(expint(1, x), x, meijerg=True)z(integrate(expint(2, x), x, meijerg=True)z!integrate(Si(x), x, meijerg=True)z!integrate(Ci(u), u, meijerg=True)z"integrate(Shi(x), x, meijerg=True)z"integrate(Chi(u), u, meijerg=True)z2integrate(Si(x)*exp(-x), (x, 0, oo), meijerg=True)z8integrate(expint(1, x)*sin(x), (x, 0, oo), meijerg=True))Útime)Úclear_cacheNÚ__main__ú.é
   z%sc                 ó   — | d    S )Nr   © )r   s    r!   ú<lambda>r9     s   €   !¡˜u€ r#   )Úkeyz%.2fs %s)WÚsympy.core.numbersr   r   Úsympy.core.symbolr   r   Ú&sympy.functions.elementary.exponentialr   Ú(sympy.functions.elementary.miscellaneousr	   Úsympy.functions.special.besselr
   Ú'sympy.functions.special.gamma_functionsr   Úsympy.integrals.integralsr   Úsympy.integrals.transformsr   r   r   r   r   r   ÚLTÚFTÚMTÚIFTÚILTÚIMTÚ	sympy.abcr   r   ÚnuÚbetaÚrhoÚaposÚbposÚcposÚdposÚposkÚpr   Únegkr-   Úmu2r.   Úsigma2r%   r"   r&   ÚalphaÚbetadistÚkintÚchiÚ
chisquaredÚdagumÚd1Úd2ÚfÚnuposÚsigmaposÚricer   ÚabsÚlaplacer(   Útposr0   Úbenchr2   Úsympy.core.cacher3   ÚsysÚtimingsÚ__name__Ú	enumerateÚnÚstringÚ_tÚexecÚstdoutÚwriteÚflushÚlenÚprintÚsortÚtir8   r#   r!   ú<module>rv      s  ðç 'ß /Ý 6Ý 9Ý 2Ý 9Ý /÷E÷ Eð €Ø€Ø€Ø€Ø€Ø€ç Ù˜Ó&�€€Dˆ#á")¨-À$Ô"GÑ €€dˆD�$˜˜aÙ
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