
    MZdp                        d dl mZmZmZmZ d dlmZmZ d dlm	Z	m
Z
mZmZ d dlmZ d dlmZmZmZ d dlmZ d dlmZmZ d dlmZ d d	lmZmZ d d
lmZmZm Z  d dl!m"Z"m#Z#m$Z$m%Z% d dl&m'Z' d dl(m)Z)m*Z*m+Z+ d dl,m-Z-m.Z. d dl/m0Z0m1Z1 d dl2m3Z3 d dl4m5Z5m6Z6m7Z7m8Z8m9Z9m:Z:m;Z;m<Z< d dl=m>Z>m?Z?m@Z@mAZA d dlBmCZCmDZD d dlEmFZFmGZG d dlHmIZI eCd        ZJeCd        ZKeCd        ZLy)    )laplace_transforminverse_laplace_transformLaplaceTransformInverseLaplaceTransform)Function
expand_mul)
EulerGammaSubs
Derivativediff)factor_terms)Ioopi)S)Symbolsymbolssimplify)Absre)explog	exp_polar)coshsinhcothasinh)sqrt)atancossin)
lowergammagamma)
DiracDelta	Heaviside)lerchphi)fresnelcfresnelserferfcEiCiexpintE1)besselibesseljbesselkbessely)slowwarns_deprecated_sympy)Matrixeye)sc                  Xy   t         } t        dd      \  }}}t        d      \  }}}t        d      }t        d      }dt        t	        |      |t
              z  dz
  j                         d	dt
        dz
  z  z   k(  sJ  | ||z  |dz  z   |t        d
      dz  z  z   |t
              |t
        dz  z  dt
        dz  z  z   dt        t              z  dt
        t        d      dz  z  z  z  z   ddfk(  sJ  | |||z   z  |t
              | t	        | t
        z        z  t        | t
        z        z  ddfk(  sJ  | dt        ||z         z  |t
              t        t              t        dt
        z        z  t	        |t
        z        z  t        t        |      t        t
              z        z  ddfk(  sJ  | t        |      ||z   z  |t
              t         t        |      z  t	        |t
        z        z  t        t        |      t        t
              z        z  t        t              t        dt
        z        z  z   ddfk(  sJ  | ||z   t        d       dz  z  |t
              dt        t              z  t        t
              z  t	        |t
        z        z  t        t        |      t        t
              z        z  dt        |      z  z   ddfk(  sJ  | |t        d      dz  z  ||z   d	z  z  |t
              t         t        |      z  t	        |t
        z        z  t        t        |      t        t
              z        z  t        t              t        dt
        z        z  z   ddfk(  sJ  | d|t        |      z  |dz  z   z  |t
              t        t        |      z  t	        |t
        z        z  t        t        |      t        t
              z        z  ddfk(  sJ  | ||z   |z  |t
              t
        | dz
  z  t	        | t
        z        z  t        |dz   |t
        z        z  ddfk(  sJ  | |d
z  ||z   z  |t
              d|d
z  z  t        d|t
        z        z  ddfk(  sJ  | t	        |      |t
              dt
        dz
  z  ddfk(  sJ  | t	        d|z        |t
              dt
        dz
  z  ddfk(  sJ  | t	        ||z        |t
              dt
        |z
  z  |dfk(  sJ  | t	        |||z
  z        |t
              t	        | |z        | t
        z   z  |dfk(  sJ  | |t	        | |z        z  |t
              |t
        z   dz  | dfk(  sJ  | |t	        | ||z
  z        z  |t
              t	        ||z        |t
        z   dz  z  | dfk(  sJ  | ||z  t	        | |z        z  |t
              ||t
        z   dz  z  | dfk(  sJ  | |t        d      dz  z  t	        d|z        z  t        t        d      dz        z  |t
              t
        dz   t        d       dz  z  ddfk(  sJ  | |t        d      dz  z  t	        d|z        z  |t
              dt        t              z  dt
        dz   t        d
      dz  z  z  z  ddfk(  sJ  | ||z  t	        | |z        z  |t
              |t
        z   | dz
  z  t        |dz         z  | dfk(  sJ  | |t	        | |dz  z        z  |t
              t        t              |z  t	        t
        dz  d|z  z        z  t        t
        dt        |      z  z        z  dt        |      z  z  ddfk(  sJ  | t	        d|dz  z        |t
              t        d      t        t              z  t	        t
        dz  dz        z  t        t        d      t
        z  dz        z  dz  ddfk(  sJ  | |t	        d|dz  z        z  |t
              |t        t	        d|dz  z        |t
              z  t         dfk(  sJ  | |t	        | |dz  z        z  |t
              dd|z  z  t
        t        t
        dt        |      z  z        z  dt        t              z  |t        d      dz  z  z  z  z
  ddfk(  sJ  | t	        | |z        |t
              dt        |      z  t        dt
        z        z  t        ddt        |      z  t        t
              z        z  ddfk(  sJ  | t        |      t	        | |z        z  |t
        d      t        t              t        |      t        t
              z  dt        d      z  z   z  t        t
        dz        z  t	        dt        |      z  t        t
              z        z  ddfk(  sJ  | t	        | |z        t        |      z  |t
              t        t              t        dt
        z        z  t	        dt        |      z  t        t
              z        z  ddfk(  sJ  | t	        | |z        |t        |      z  z  |t
              t        t              t        d|z        z  t	        dt        |      z  t        t
              z        z  ddfk(  sJ  | t	        dt        ||z        z        |t
              dt
        z  t        t              t        |      z  t	        |t
        z        z  t        t        |      t        dt
        z        z        z  t
        t        d      dz  z  z  z
  ddfk(  sJ  | t	        dt        ||z        z        t        |      z  |t
              t	        |t
        z        t        t        |      t        dt
        z        z        z  t        t              t        dt
        z        z  z  ddfk(  sJ  | |dz  t	        d|z        z  |t
              dt        d      z  dt
        z  t        d
      dz  z  z  t        d
dt        d      z  t        t
              z        z  ddfk(  sJ  | t!        ||z        |t
              ||dz   t
        dz  z   z  |dfk(  sJ  | |t!        ||z        dz  z  |t
              d|dz  z  |z  d|dz  z  t
        z  t
        dz  z   z  d|z  dfk(  sJ  | |t!        ||z        dz  z  |t
        d      d|dz  z  |z  t
        d|dz  z  t
        dz  z   z  z  d|z  dfk(  sJ  | t#        d|z        |t
              t
        dt
        dz  z   z  ddfk(  sJ  | t#        ||z        |t
              t
        |dz   t
        dz  z   z  |dfk(  sJ  | t#        ||z        dz  |t
        d      d|dz  z  t
        dz  z
  t
        d|dz  z  t
        dz  z
  z  z  d|z  dfk(  sJ  | t!        |dz         |t
        d      t
        t!        d      z  t#        d      z   t
        dz  dz
  z  ddfk(  sJ  | dt%        ||z  |z         dz  z  |t
              \  }	}
}
|	dt
        dz  t
        t
         t'        d|z        z  d|z  t%        d|z        z  z   z  z   d|dz  z  z   z  t
        t
        dz  d|dz  z  z   z  z  z
  j)                         dk(  sJ  | t!        ||z        t#        ||z        z  |t
        d      |d|dz  z  t
        dz  z   z  d|z  dfk(  sJ  | t!        ||z        |z  |t
              t+        |t
        z   | t
        z   z        dz  |dfk(  sJ  | |t        d       dz  z  t!        ||z        z  |t
              t        t               t        | t
        z         t        |t
        z         z
  z  |dfk(  sJ  | t!        dt        ||z        z        |t
              t        t              t        |      z  t	        |t
        z        z  t
        t        d      dz  z  z  ddfk(  sJ  | t        |      t!        dt        ||z        z        z  |t
        d      t        |       t
        t        d
      dz  z  z  t        t              t
        dz  z  d|z  t
        z   z  t	        |t
        z        z  t-        t        |      t        dt
        z        z        z  dz  z   t
        t        d      dz  z  z  ddfk(  sJ  | t!        dt        ||z        z        t        |      z  |t
              t        t              t	        |t
        z        z  t-        t        |      t        dt
        z        z        z  t        t
              z  ddfk(  sJ  | t!        t        ||z              dz  t        |      z  |t
              t        t              t	        |t
        z        dz
  z  dt        t
              z  z  ddfk(  sJ  | |t        d      dz  z  t#        ||z        z  |t
              |t
        z   t        d       dz  z  | t
        z   t        d       dz  z  z   t        t        d      dz        z  dz  |dfk(  sJ  | t#        dt        ||z        z        |t
              t        t              t        |      z  t	        |t
        z        z  t-        t        |      t        dt
        z        z        z  t
        t        d      dz  z  z  dt
        z  z   ddfk(  sJ  | t        |      t#        dt        ||z        z        z  |t
              t        t              |t
        dz  z   z  t	        |t
        z        z  t
        t        d
      dz  z  z  ddfk(  sJ  | t#        dt        ||z        z        t        |      z  |t
              t        t              t	        |t
        z        z  t        t
              z  ddfk(  sJ  | t#        t        ||z              dz  t        |      z  |t
              t        t              t	        |t
        z        dz   z  dt        t
              z  z  ddfk(  sJ  | t+        |      |t
        d      t+        t
               t.        z
  t
        z  ddfk(  sJ  | t+        ||z         |t
        d      t+        |      t+        t
              z   t.        z   t
        z  ddfk(  sJ  | t+        d||z  z         |t
              t	        t
        |z         t        t
         |z        z  t
        z  ddfk(  sJ  | t+        ||z         |t
        d      t
        t+        |      z  t	        t
        |z        t        t
         |z        z  z
  t
        dz  z  ddfk(  sJ  | t+        |      t        |      z  |t
        d      t        t              t+        t
               t+        d      z
  t.        z
  z  t        t
              z  ddfk(  sJ  | |t        d
      dz  z  t+        |      z  |t
        d      t        t              dt+        t
              z  t+        d      z
  dt.        z  z
  d z   z  dt
        t        d      dz  z  z  z  ddfk(  sJ  | |dz  t+        |      z  |t
        dd!      d"t+        t
               t        j.                  z
  t        d      d"z  z   z  t
        dz  z  z
  j)                         t        j0                  k(  sJ  | t+        |      dz  |t
        d      t+        t
              t.        z   dz  t        dz  d"z  z   t
        z  ddfk(  sJ  | t	        | |z        t+        |      z  |t
        d      t+        |t
        z          t.        z
  |t
        z   z  | dfk(  sJ  | t%        ||z        |t
              ||dz  t
        dz  z   z  ddfk(  sJ  | t3        t%        ||z              |t
              |t5        t        t
        z  d|z  z        z  |dz  t
        dz  z   z  ddfk(  sJ  | t%        ||z        |z  |t
              t7        |t
        z        ddfk(  sJ  | t%        ||z        dz  |z  |t
              t+        d|dz  z  t
        dz  z  dz         dz  ddfk(  sJ  | t%        ||z        dz  |dz  z  |t
              |t7        d|z  t
        z        z  t
        t+        d|dz  z  t
        dz  z  dz         z  dz  z
  ddfk(  sJ  | t%        dt        ||z        z        |t
              t        t              t        |      z  t	        | t
        z        z  t
        t        d      dz  z  z  ddfk(  sJ  | t%        dt        ||z        z        |z  |t
              t        t-        t        |      t        dt
        z        z        z  ddfk(  sJ  | t'        ||z        |t
              t
        |dz  t
        dz  z   z  ddfk(  sJ  | t'        ||z        dz  |t
              d|dz  z  t
        dz  z   t
        d|dz  z  t
        dz  z   z  z  ddfk(  sJ  | t        |      t'        dt        ||z        z        z  |t
        d      t        t              | t
        dz  z   z  t	        | t
        z        z  t
        t        d
      dz  z  z  ddfk(  sJ  | t'        dt        ||z        z        t        |      z  |t
              t        t              t        dt
        z        z  t	        | t
        z        z  ddfk(  sJ  | t%        ||z        t%        ||z        z  |t
              d|z  |z  t
        z  t
        dz  ||z
  dz  z   t
        dz  ||z   dz  z   z  z  ddfk(  sJ  | t'        ||z        t%        ||z        z  |t
              ||dz   |dz  z   t
        dz  z   z  t
        dz  ||z
  dz  z   t
        dz  ||z   dz  z   z  z  ddfk(  sJ  | t'        ||z        t'        ||z        z  |t
              t
        |dz  |dz  z   t
        dz  z   z  t
        dz  ||z
  dz  z   t
        dz  ||z   dz  z   z  z  ddfk(  sJ  | | |z  t'        ||z        z  t%        ||z        z   |t
        d      d|dz  z  |dz  d|dz  z  t
        dz  z  z   t
        dz  z   z  ddfk(  sJ  | |t	        | |z        z  t%        ||z        z  |t
              ||z  |dz  |t
        z   dz  z   z  | dfk(  sJ  | |t	        | |z        z  t'        ||z        z  |t
              ||t
        z   z  |dz  |t
        z   dz  z   z  | dfk(  sJ  | t'        |dz         |t
        d      \  }	}}|dk(  sJ |	t
        t'        d      z  t%        d      z
  t
        dz  dz   z  z
  dk(  sJ  | t-        ||z        |t
              t	        t
        dz  d|dz  z  z        t        t
        d|z  z        z  t
        z  ddfk(  sJ  | t-        t        ||z              |t
              t        |      t
        t        |t
        z         z  z  ddfk(  sJ  | t	        ||z        t-        t        ||z              z  |t
        d      t        |       t        t
              |t
        z
  z  z  |dfk(  sJ  | t-        t        ||z        dz        |t
        d      dt
        z  t	        t        |       t        t
              z        t
        z  z
  ddfk(  sJ  | t        t        ||z              |t
        d      t        |       t
        t        |t
        z         z  z  dt
        z  z   | dfk(  sJ  | t	        ||z        t        t        ||z              z  |t
              dt        |      t        t
              z  t
        z   z  ddfk(  sJ  | t        t        ||z        dz        |t
              t	        t        |       t        t
              z        t
        z  ddfk(  sJ  | t9        d||z        |t
              dt        |dz  t
        dz  z         z  ddfk(  sJ  | t9        d||z        |t
        d      ||dz  t
        dz  z   t
        t        |dz  t
        dz  z         z  z   z  ddfk(  sJ  | t9        d||z        |t
        d      |dz  t        |dz  t
        dz  z         t
        t        |dz  t
        dz  z         z   dz  z  z  ddfk(  sJ  | |t9        d||z        z  |t
              t
        |dz  t
        dz  z   t        d      dz  z  z  ddfk(  sJ  | |t9        d||z        z  |t
              ||dz  t
        dz  z   t        d      dz  z  z  ddfk(  sJ  | |dz  t9        d||z        z  |t
              d|dz  z  |dz  t
        dz  z   t        d
      dz  z  z  ddfk(  sJ  | t9        ddt        ||z        z        |t
              t	        | t
        z        t
        z  ddfk(  sJ  | |t        d      dz  z  t9        ddt        ||z        z        z  |t
              |t        d      dz  z  t	        | t
        z        z  t
        dz  z  ddfk(  sJ  | t9        d|t        |dz  ||z  z         z        |t
        d      t	        |t
        t        |dz  t
        dz  z         z
  z        t        |dz  t
        dz  z         z  ddfk(  sJ  | t;        d||z        |t
              dt        |dz   t
        dz  z         z  |dfk(  sJ  | t;        d||z        |t
        d      ||dz   t
        dz  z   t
        t        |dz   t
        dz  z         z  z   z  |dfk(  sJ  | t;        d||z        |t
        d      |dz  t        |dz   t
        dz  z         t
        t        |dz   t
        dz  z         z   dz  z  z  |dfk(  sJ  | |t;        d||z        z  |t
              t
        |dz   t
        dz  z   t        d      dz  z  z  |dfk(  sJ  | |t;        d||z        z  |t
              ||dz   t
        dz  z   t        d      dz  z  z  |dfk(  sJ  | |dz  t;        d||z        z  |t
              d|dz  z  |dz   t
        dz  z   t        d
      dz  z  z  |dfk(  sJ  | |t        d      dz  z  t;        ddt        ||z        z        z  |t
              |t        d      dz  z  t	        |t
        z        z  t
        dz  z  ddfk(  sJ  | t=        d||z        |t
              dt?        t
        |z        z  t        t        |dz  t
        dz  z         z  z  ddfk(  sJ  | t        d||z        |t
              t+        t
        t        |dz   t
        dz  z         z   |z        t        |dz   t
        dz  z         z  | dfk(  sJ  | t%        ||z        dz  |t
        d      d#|dz  z  t
        d$|dz  z  d%|dz  z  t
        dz  z  z   t
        dz  z   z  z  ddfk(  sJ  | tA        |dz
        t'        |dz
        z  |t
              t
        t	        t
               z  t
        dz  dz   z  ddfk(  sJ  | | ||      z  ||      |t         ||      ||      z  t         dfk(  sJ  | |tA        |dz         z   ||dz         z  |t
              |t         ||dz         |t
              z  t         dfk(  sJ  | |tA        |dz
        z   ||dz
        z  |t
              |t         ||      |t
              z  t	        t
               z  t         dfk(  sJ  | | |||z        z  |t
              ||z  t         ||      ||t
        z        z  t         dfk(  sJ  | t	         ||       |z        |t
              dt
         ||      z   z  tC         ||             dfk(  sJ  | t	        | |z         ||      z  |t
              t         ||      ||t
        z         t         dfk(  sJ  | t	        | |z        t        t        ||z        dz        z  |t
              t	        t        |       t        |t
        z         z        |t
        z   z  | dfk(  sJ  | t!        ||z         ||      z  |t
              t         ||      || t
        z         dz  t         ||      ||t
        z         dz  z
  t         dfk(  sJ  | t!        ||z        |z  |t
        d      d|z  t
        z  |dz  d|dz  z  t
        dz  z  z
  t
        dz  z   z  |dfk(  sJ  | t#        ||z         ||      z  |t
              t         ||      || t
        z         dz  t         ||      ||t
        z         dz  z   t         dfk(  sJ  | t#        ||z        |z  |t
        d      dd|t
        z   dz  z  z  dd|t
        z
  dz  z  z  z   |dfk(  sJ  | t%        ||z         ||      z  |t
        d      tD        t         ||      |tD         |z  t
        z          t         ||      |tD        |z  t
        z         z   z  dz  t         dfk(  sJ  | t%         ||            |t
              t        t%         ||            |t
              t         dfk(  sJ  | t%        ||z        |z  |t
        d      d|z  t
        z  |dz  d|dz  z  t
        dz  z  z   t
        dz  z   z  ddfk(  sJ  | t'        ||z         ||      z  |t
              t         ||      |tD         |z  t
        z         dz  t         ||      |tD        |z  t
        z         dz  z   t         dfk(  sJ  | t'        ||z        |z  |t
        d      |dz   t
        dz  z   |dz  d|dz  z  t
        dz  z  z   t
        dz  z   z  ddfk(  sJ  | t%        ||z  |z         dz   ||      z  |t
              \  }	}}
|t         k(  sJ |	 t         ||      |t
              dz  t         ||      |dtD        z  |z  t
        z         t	        dtD        z  |z        z  dz  z
  t         ||      |dtD        z  |z  t
        z         t	        dtD        z  |z        z  dz  z
  z   dk(  sJ  | t%        ||z        dz  t#        ||z        z  |t
              \  }	}}
||k(  sJ |	 d|z  dd|dz  z  |dz  z   d|z  t
        z  z   t
        dz  z   z  z  z
  d|z  dd|dz  z  |dz  z   d|z  t
        z  z
  t
        dz  z   z  z  z
  d|z  d|dz  |dz  z   d|z  t
        z  z   t
        dz  z   z  z  z   d|z  d|dz  |dz  z   d|z  t
        z  z
  t
        dz  z   z  z  z   j)                         dk(  sJ  | |dz  t	        |dz         z  |t
              t        t              t
        dz  z  t	        t
        dz  dz        z  t        t
        dz        z  dz  t
        dz  z
  t        t              t	        t
        dz  dz        z  t        t
        dz        z  dz  z   ddfk(  sJ  | ||dz  z  ||z  z   |z    ||      z  |t
              |tG        t         ||      |t
              t
        df      z  |tG        t         ||      |t
              t
              z  z
  |t         ||      |t
              z  z   t         dfk(  sJ  | tI         ||      |df      |t
        d&      t
        t         ||      |t
              z   |d      z
  k(  sJ  | tI         ||      |df      |t
        d&      t
        dz  t         ||      |t
              z  t
        dz   |d      z  z
  t
        tK        tG         ||      |      |d      z  z
  tK        tG         ||      |df      |d      z
  k(  sJ  | tI         ||||      |d      |t
              t
        dz  t         ||||      |t
              z  t
         ||d|      z  z
  tK        tG         ||||      |      |d      z
  t         dfk(  sJ  | dtI         ||      |df      z  |t
        d&      dt
        z  t         ||      |t
              z  d |d      z  z
  k(  sJ  | | |||z        z   |||z        z   |t
        d&      |t         ||      |t
        |z        z  |z  t         ||      |t
        |z        |z  z   k(  sJ tM         ||      ||d'      tO         ||      ||d      k(  sJ  |  ||       ||      z  |t
        d&      t         ||       ||      z  |t
              k(  sJ  | | |||z        z  |t
        d&      |t         ||      |t
        |z        z  |z  k(  sJ  | dt	        |      z  tA        |      z  |t
              dt
        dz
  z  ddfk(  sJ  | dt%        |      z  tA        |      z  |t
        d      dt
        dz  dz   z  ddfk(  sJ  | ||z
  |z  t	        | ||z
  z        z  tA        ||z
        z  |t
              |t
        z   | dz
  z  t	        | t
        z        z  t        |dz         z  | dfk(  sJ  | t	        d|z        dz
  t	        | |z
        z  tA        |      z  dz  |t
        dd!      t	        |       t
        dz  dz
  z  k(  sJ  | tQ        |      |t
              dt         dfk(  sJ  | tQ        ||z        |t
              d|z  t         dfk(  sJ  | tQ        |dz        |t
              dt         dfk(  sJ  | tQ        |dz         |t
              dt         dfk(  sJ  | tQ        |      tQ        |dz
        z   |t
              dt	        d(t
        z        z   t         dfk(  sJ  | tQ        |      |t	        | |z        z  z
  |t
        d      t
        |t
        z   z  | dfk(  sJ  | t	        |       tQ        |      tQ        |dz
        z   z  |t
        d      t	        d(t
        z  dz
        dz   t         dfk(  sJ  |  ||      tQ        |dz
        z  |t
               |d      t	        d(t
        z        z  t         dfk(  sJ  |  ||      tQ        ||z  |z
        z  |t
               |||z        t	        | t
        z  |z        z  |z  t         dfk(  sJ  |  ||      tQ        ||z  |z         z  |t
              dt         dfk(  sJ  | tQ        |dz        |t
        d&      t        tQ        |dz        |t
              k(  sJ  | tQ        |dz  dz
        |t
              t	        t
               dz  t         dfk(  sJ  | tQ        |d|z
  z        |t
              dt	        t
               z
  t         dfk(  sJ  | tQ        |      dz   tQ        |dz
        dz   z  |t
              t        tQ        |      tQ        |dz
        z  |t
              dz   t	        t
               z   dt
        z  z   ddfk(  sJ  | tQ        d|z  dt	        |      z  z
        |t
              t	        t
         t	        |      z        dz  t         dfk(  sJ  | tQ        d|z  dt	        |      z  z         |t
              t	        t
         t	        |      z        dz  t         dfk(  sJ  | tA        |      |t
              dt
        z  ddfk(  sJ  | tA        ||z
        |t
              t	        | t
        z        t
        z  ddfk(  sJ  | tA        |dz
        |t
              t	        t
               t
        z  ddfk(  sJ  | tA        d|z  dz
        |t
              t	        dt
        z        t
        z  ddfk(  sJ  | tA        d|z  dz         |t
              dt
        z  ddfk(  sJ  | tA        d|z  dz         |t
        d      dt
        z  t	        dt
        z        t
        z  z
  ddfk(  sJ  |  ||      tA        ||z
        z  |t
              t         ||      tA        ||z
        z  |t
              t         dfk(  sJ t        tS        |      |t
        d      t%        t
        dz  dt        z  z         tS        t
        t        z        z  t        d      t%        t
        dz  dt        z  z  t        dz  z         z  dz  z   t'        t
        dz  dt        z  z        tU        t
        t        z        z  z
  t
        z  ddfk(  sJ t        tU        |      |t
        d      t%        t
        dz  dt        z  z        tU        t
        t        z        z  t'        t
        dz  dt        z  z        tS        t
        t        z        z  z
  t        d      t'        t
        dz  dt        z  z  t        dz  z         z  dz  z   t
        z  ddfk(  sJ tW        t	        |      |t	        |       z  g|t	        |       z  t	        |      gg      }tW        dt
        dz
  z  t
        dz   dz  gt
        dz   dz  dt
        dz
  z  gg      }tY               5  tW        dt
        dz
  z  ddft
        dz   dz  d	dfgt
        dz   dz  d	dfdt
        dz
  z  ddfgg      }d d d        tY               5   | ||t
              k(  sJ 	 d d d         | ||t
        d)*      |ddfk(  sJ  | ||t
        d&      |k(  sJ  | ||t
        d)d+      |k(  sJ y # 1 sw Y   txY w# 1 sw Y   YxY w),Nza, b, cTpositivezt, w, xfg                     r   g      ?x      i   r   *      	   
   ii   @.   )nocondsr         @      rR   )planeiF)legacy_matrix)rY   rR   )-r   r   r   r   r   r8   doitr   r   r   r,   r+   r#   r$   r   r2   r   r   r"   r!   r   r   r*   r	   Zeror   r   r    r1   r0   r3   r   r&   r   r   r   r   r
   r   r   r%   r)   r(   r6   r5   )LTabctwxr<   r=   L_rX   condMtMsMs_condss                   D/usr/lib/python3/dist-packages/sympy/integrals/tests/test_laplace.pytest_laplace_transformrj      s=   	By40HAq!i GAq!AA s1vq!,,q0668BAENJJJqs1a4xAaDF#Q*q!tVa1f_r$r({Aa!A$q&kM::AtDE F Ea1gq!!C1Ib!Ah!64 @@@@qac{Aq!"Xd1Q3iAaC(d1gd1go)>>4HI J ItAw!}a#Sa[QqS!$tAwtAw"77$r(4!9:LL   !!uQwA&R[a QqS)$tAwtAw*??!DG)K   q1Q46{AaC2;&1-Sa[QqS!$tAwtAw"77$r(4!9:LL   q!DG)a#h&'A.QZAaC d1gd1go!664@A B A!axA!a[aRT":a!eQqS#991dCD E DadAaCj!QC1HZAaC-@$@!T#JJJJc!fa1q5	1d3333c!A#h1!QU)Q!5555c!A#h1!QU)Q!5555c!QqS'lAq!c1"Q$i!a&8!T%BBBBaQBFmQ"A}qb$&????aQB!Hoq!$QqS1q51*)<qb$(GGGGac#qbd)mQ"q!a%!|aR&>>>>q1Q46{3r!t9$U1R57^3Q:!e"vax "d+, - ,q1Q46{3r!t9$a+tBxZAEQqT!V,,-r489 : 9ad3r!t9na#11eAaCj(@1"d'KKKKqaR1W~q!$"XaZAqD!A#J'Q$q'	](;;QtAwYG   s2ad7|Q"!WT"Xc!Q$q&k)$tAwqy{*;;A=q$GH I HqQq!tV}a#AadFQ22RC>? @ ?qaR1W~q!$!Wqa47m,,aRjQqT!V.DEE   sA2a4y!QtAwYtAaCy Ad1gId1g,=!>>4HI J Id1gc1"Q$iA5R$q'$q'/AadF*+DRM9BtAwJtAw	 !"D:* * * * sA2a4ya !Q'"Xd1Q3iBtAwJtAw$6 77DAB C BsA2a4y!DG)$a+"Xd1Q3iBtAwJtAw$6 77DAB C B 	3r$qs)|a#	
1tBxQ#ac(*4QQqS	0A+BB	
QqT!V 
		 	 c"T!A#Y,Q'A.AaCd1gQqS	)**DHT!A#Y,>?D3J J J Jq!tC1I~q!$tAwY!qtAv&wq!DG)DG2C'DD   d1Q3iA1q!teadl#3Q"====qacA~q!$q!tVAXr!Q$wqy1a4'(!A#t45 6 5qacA~q!d3q!tVAXq"QT'AqD.)*AaC67 8 7 d1Q3iA1b1a4i=!T"::::d1Q3iA1q!teadl#3Q"====tAaCy!|QD11fq!tma1a4!Q$/0!A#t<= > =tAaCy!Q.Qi$q'!AqD1H-q$78 9 8C!AJM!1a(GAq!	
AqD1qbQqSkAaCAaCL011adF 	1qAv&	(	()1q9 9 9
 d1Q3iQqS	!1a$7Ar!Q$wA~<N<=aC<G G G Gd1Q3ik1a S!a%1"q&)9%:1%<a$FFFFqAaD57|D1I%q!,2hYaR!VtAE{23Q=> ? >tAd1Q3iK !Q'"Xd1gc!A#h&q1Q46{2At<= > =tAwtAd1Q3iK((!Q>Awhq1Q46{"T"Xad]AaC!G%<S1X%E$q'$qs)#$&%%&&' '()AaDF456>> ? > tAd1Q3iK a(!Q/"Xc!A#hs474!9#455d1g=q$GH I HtD1I!$q')1a0"Xs1Q3x!|$aQi0!T:; < ;q1Q46{4!9$a+1u2q!aRTaeVAX$66aeAgFqH   tAd1Q3iK !Q'"Xd1gc!A#h&s474!9+<'==a!A$q&kIqST   tAwtAd1Q3iK((!Q/"Xq1Q3wAaC(QqT!V4a>? @ ?tAd1Q3iK a(!Q/"Xc!A#htAw&401 2 1tD1I!$q')1a0"Xs1Q3x!|$aQi0!T:; < ;c!faT*
a&:	q !T/+ + + +AaCy!Q.!fs1vo
*A-q$78 9 8c!AaC%j!QS1XIb!Ah$6q$8!T#BBBBs1Q3xA-AhQqS"aRT(**AqD0!T:; < ;s1vd1g~q!d3"XAwQ'*45d1g=q$GH I Hq1Q46{3q6!1a$7"Xs3q6zC
O3bmCbHIAaDFm'' ( ' q!tCF{Aq$>Aw%"a/0A567?xzQVVL L Ls1vqy!Q.1v
"Q&Qq0!3Q=> ? >sA2a4yQA51q5zkJ&Q/!T:; < ;c!A#h1!QTAqD[/1d!;;;;s3qs8}a#tBqD!A#JA1-q$78 9 8c!A#hqj!QD1Iq$#7777c!A#hk!mQ"s1QT6!Q$;?';A'=q$&GGGGs1Q3x{1a4A&tAaCE{]Qs1QT6!Q$;?33A55q$?@ A @s1T!A#Y;A&"Xd1gc1"Q$i'AaDF3Q=> ? >c!D1I+q !Q'Bs474!93D/E,Eq$+OOOOc!A#h1!QTAqD[/1d!;;;;s1Q3x{Aq!1fq!tma1a4!Q$/0!T:; < ;tAws1T!A#Y;''A="XrAaCx aRT*1qtAv;64@A B As1T!A#Y;Q'A."Xd1Q3iQBqD	)1d34 5 4s1Q3xAaC !Q'qSU1Wq!tq1uqj(1a41q51*+<=>4HI J Is1Q3xAaC !Q'A1q!t#$q!tq1uqj'81a41q51*;L&MN   s1Q3xAaC !Q'1q!tad"#ada!eaZ&7!Q$!a%!:K%LM   r!tC!H}s1Q3x'A=q!tVQTAadF1a4K'!Q$./D9: ; :aQBqD	k#ac("Aq)a.//012AQ
1B/DFGR.O O O OaQBqD	k#ac("Aq)aQiAQ
9J.K/0b$.8 8 8 8AE
Aq48NAudA::#a&3q6!AqD1H--222c!A#h1#adAadFm"4T!QqS']"B1"Da!NNNNc$qs)na#Q4A;(?D'IIIIs1Q3xD1I&1t<1gXtAwA'D12 3 2s4!9Q;A5qS3QxQ'(**At45 6 5tD1I1t41gXqa!e}%!+aR67 8 7s1Q3xT!A#Y'A.QQ!#$a./ 0 /d4!9Q;A&3QxQ/?+@+BAt*LLLLga1oq!$41q!t+<)<a(FFFFwq!A#1t41q!taQTAqD[ 1112At<= > =wq!A#1t4T41q!t$a$q!tad{*;&;a%??@!TJK L KqAaC !Q'1q!tqtAv&&401 2 1qAaC !Q'1q!tqtAv&&401 2 1q!tGAqsO#Q*q!tVQTAqD[AaDF++Q56 7 6ga4!9%q!,aRT1a0FFFFq1Q46{71aQqS	k22Aq91a[aRT"1a4'D12 3 2wq!DAacN*+QDAAQTAqD[))*+DA1,==q$GH I Hga1oq!$4A1+=)=q$(GGGGwq!A#1t4A1qq!teadl!3334a>? @ ?wq!A#1t4T4A1%q4A1+='=&AABAtLM N Ma1Q3A&1q!teadlad1f-E+Eq$*OOOOa1Q3A&1q!teadlad1f-E+Eq$*OOOOq!tGAqsO#Q*q!tVadUQT\QqT!V,,a67 8 7q1Q46{71aQqS	k22Aq91a[QqS!!Q$&401 2 1wq!A#1%ac
]BtAqD1a4K0011d;< = <wq!A#1%!dAqD51a4<((!+,T1a4%!Q$,-??!TJK L Ks1Q3x{Aq401WaAqD2ad71a4</!Q$678!TBC D C i!nS1X%q!,3r7AqD1H1Eq$0OOOOa!fa"21Q4A"> >TJJJJq1Q3!A#&1-!a%!Q//"d;< = <q1Q3!A#&1-!a++CG3bS$?@ A @q1Q3xAqS!!A$1Q3//"d;< = <c1Q4%'lAq!aQqTlR!XIt%DDDDsA2a4y1~q!$adAq1u-sD9: ; :sA2a4yd1Q3ik**Aq1$q'$q1u+%&A.D9: ; :tAaCy1~q!$adArAv.q0adAq1u-a/024d<< = < tAaCy{Aq40qSUAqD1QT6!Q$;&A-.489 : 9tAaCy1~q!$adArAv.q0adAq1u-a/024d<< = < tAaCy{Aq401q51*1a!eaZ< 00!T:; < ;s1Q3x!}aT2!!A$A2a4!844 1q!A#'23 44568:sDBB C B s1Q4y!Qc!A$iA.T:; < ;s1Q3xz1a$/qSUAqD1QT6!Q$;&A-.489 : 9s1Q3x!}a#adAr!tax02adAqsQw/12463>> ? > s1Q3xz1a$/!teadlQTAadF1a4K/!Q$67DAB C BS1QZ]1Q4'A.KAuaRC<<	
QqT1a(*QqT1bd1fqj1#ac!e*<Q>?QqT1ac!eai0RT!V<Q>?	@ EF	F F F
 S1Xq[ac*Aq1KAuaA::	
QqS!Qq!tVad]QqSU*QT1233	!Q!Q$A!A%1,-.	/	!Q1q!tac!e#ad*+,	- 	
!Q1q!tac!e#ad*+,	- /7hjA	> > >
 q!tCAJ1%"Xad]3q!tAv;&tAaCy02QqS8"Xc!Q$q&k!$qs)+A-./0$88 9 8 !Q$1q !A$&1-z*1Q4A6A??z*1Q4A6::;qtQ**+-/C77 8 7
 tAaD1a&!1a6qtQ**QqT12 3 2tAaD1a&!1a6qD!!A$1--1QqT	9d:adA&1--.AaD1a&)1a011 2 1
 tAaAJ1%q!,T"1Q1:q!44q1a|C*Qq!QZ+Q2357C?? @ ? r$qtaV$$aD9qD!!A$1--1Q478 9 8q1Q3x!A#1d3qtQ!,,Q.QqT1ac*1,-- . - %	!a! 7!aA FG G GqtAaDy!Q-QqT!A$Y1-. / . q1Q3xAt,qtQ!,,Q./ 0 /aAhy|#Q*q!a%y!T.BBBBqQx	!$aT:1q\1d#$ % $ Az#qb!a%j/))AE*::AqA!erAvsA2a4y(q1u5r4@A B A 	C!HQJQBqD	!)A,.q0!Q	QBA		 jmQ"q2#tn444j1oq!$1rc4(8888j21%"rc4888j21%!bS$777z!}Z"--q!4SU^bS$'( ) (z!}QsA2a4y[(!Q>AYD!" # " 	3r7JqM*QrT"223QDI	SURZ1	rc4(	)*	)ad:ad##Q*quSQZ/?"d.KKKKad:ac!e$$a+!A#sA2a46{0B10D13T0; ; ; ;ad:ac!e$$a+B3~=== z!Q$At4Z1-q!45 6 5jA"Aq)c1"gai"d-CCCCjAE#Q*q3r7{RC.FFFF
1!Jq1u$5$9:AqAjmJq1u,==q!DaRQ3 !4)) * ) j1Qs1vX&1-#qbQi.2BRC1NNNNjAaAh'A.3r#a&y>!3CbS$2OOOOilAq!ac1d^333iA1%#qbd)A+q$)????i!na#QB	1d';;;;i!A1%#bd)A+q$)????i!A1%!A#q$777yAa !Q6qS3r!t9Q;4() * )qtIa!e$$a+ad9QU#33Q:RCFG H G hqk1a$?1a42;2.1gc!Q$"+1,--a/0!Q$"+x"~-./0123T;; < ; hqk1a$?!Q$"+x"~-!Q$"+x"~-.1gc!Q$"+1,--a/012345t== > =
 
#a&!CG)$qaRy#a&&9:	;B	!QU)a!er]+q5B-QAY/1 
2B 
 	! A!a%y!T"a!er]B$=>A}b$'!QU)Q)=>@AA 
 	! ("a|x'''( b!Qe,Q=== b!Q%+++b!QeT:b@@@A A( (s!   oACrp3Cr rCrr Cr)c                  %   ddl m}  t        }t        dd      \  }}}}t        dd      \  }}t        d      \  }}	t	        d	      }
d
 } |dt
        |       | |      k(  sJ  |dt
        z  t
        |      t        |      k(  sJ  |||t
        z   z  t
        |      |t        | |z        z  t        |      z  k(  sJ  |t
        |t
        z   z  t
        |      | t        | |z        z  t        |      z   | |      z   k(  sJ  |t
        |t
        z   dz  z  t
        |d      || |z  dz   z  t        | |z        z  t        |      z  dz  k(  sJ  |dt
        |t
        z   dz  z  z  t
        |d      |dz   |dz  z  d|z  |z  z
  dt        ||z        z  z   dz
  t        | |z        z  t        |      z  d|dz  z  z  k(  sJ  |dt
        |t
        z   |z  z  z  t
        |      t        |      t        |||z        z  ||z  t        |      z  z  k(  sJ  |t
        |z
  | z  t
        |      ||dz
  z  t        ||z        z  t        |      z  t        |      z  k(  sJ  ||t
        z   dz  t
        |      |t        | |z        z  t        |      z  k(  sJ  ||t
        z   dz  t
        |      |dz  t        | |z        z  t        |      z  dz  k(  sJ  |||dz  t
        dz  z   z  t
        |      t        ||z        t        |      z  k(  sJ  |t
        t
        dz  |dz  z   z  t
        |      t        ||z        t        |      z  k(  sJ  |||dz  |t
        z   dz  z   z  t
        |      t        | |z        t        ||z        z  t        |      z  k(  sJ  ||t
        z  |dz  |t
        z   dz  z   z  t
        |      || t        | |z        z  t        ||z        z  |z  t        | |z        t        ||z        z  z   z  t        |      z  k(  sJ  |t        | t
        z        t
        z  t
        |      t        | |z         k(  sJ  |t        | t
        z        |t
        z   z  t
        |      t        |||z
  z        t        | |z         z  k(  sJ  ||t
        z   |dz  |t
        z   dz  z   z  t
        |      t        | |z        t        ||z        z  t        |      z  k(  sJ  |t        | t
        z        t
        |z  z  t
        |      | |z   |dz
  z  t        | |z         z  t        |      z  k(  sJ  |t        | t
        z        t        t
        dz  dz         z  t
        |      t        | |z         t        d||z
        z  k(  sJ  |dt
        t        t
        dz         z  z  t
        |      t        |      t        t        |            z  k(  sJ  |dt
        dz  t
        dz  dz   z  z  t
        |      |t        |      z  t        |      t        |      z  z
  k(  sJ  |t
        dz  t
        dz  dz   z  t
        |      t        |       t        |      z   | |      z   k(  sJ  |ddt
        dz  dz   z  z
  t
        |      t        |       t        |      z   | |      z   k(  sJ  |dt
        dz  z  t
        |      |t        |      z  k(  sJ  |dt
        dz  z  t
        |      |dz  t        |      z  dz  k(  sJ  |dt
        |z  z  t
        |      ||dz
  z  t        |      z  t        |      z  k(  sJ  |t
        dz   t
        dz   t
        dz  dt
        z  z   dz   z  z  t
        |d      dt        d|z        z  dt        d|z        z  z
  t        |      z  dz   t        d|z        z  t        |      z  dz  k(  sJ  | ||t
        dz  |dz  z
  z  t
        |            t        ||z        t        |      z  k(  sJ  | |t
        t
        dz  |dz  z
  z  t
        |            t!        ||z        t        |      z  k(  sJ  |t        | t
        z        t
        |z  z  t
        |      ||z
  |dz
  z  t        ||z
        z  t        |      z  k(  sJ  |t        | t
        z        t        dt
        dz  z         z  t
        |      t        ||z
        t        d||z
        z  k(  sJ t#         |||z  t
        t        t
        dz  |dz  z
        z   | z  z  t        t
        dz  |dz  z
        z  t
        |      j%                  t                    t        |      t'        |||z        z  k(  sJ  |||z  t
        t        t
        dz  |dz  z         z   | z  z  t        t
        dz  |dz  z         z  t
        |d      j%                  t              t        |      t        |||z        z  k(  sJ  |dt
        t        t
        dz         z  z  t
        |      t        |      t        t        |            z  k(  sJ  |dt
        dz  t
        dz  dz   z  z  t
        |d      |t        |      z
  t        |      z  k(  sJ  |t
        t)        d      z  t+        ddgddgg      z
  j-                         t
        |      t+        t        |      t        |      z  dgdt        d|z        t        |      z  gg      k(  sJ  ||t
        dz  |dz  z
  z  t
        |d      |t        ||z        z  t        |      z  |z  k(  sJ  ||t
        dz  |dz  z
  z  t
        |      |t        ||z        t        |      z  d|z  z  t        | |z        t        |      z  d|z  z  z
  z  k(  sJ  ||t
        z  t
        dz  |dz  z
  z  t
        |d      |t!        ||z        z  t        |      z  k(  sJ  ||t
        t
        |z   z  z  t
        |      |t        |      |z  t        | |z        t        |      z  |z  z
  z  k(  sJ  ||t
        z  t
        |z   dz  z  t
        |      || |z  t        | |z        z  t        |      z  t        | |z        t        |      z  z   z  k(  sJ  ||t
        |z   t
        |z   z  z  t
        |d      |t        ||z        t        ||z        z
  z  t        | ||z   z        z  t        |      z  ||z
  z  k(  sJ  ||t
        z  t
        |z   t
        |z   z  z  t
        |d      ||t        ||z        z  |t        ||z        z  z
  z  t        | ||z   z        z  t        |      z  ||z
  z  k(  sJ  ||t
        z  |dz  t
        |z   dz  z  |dz  z   z  t
        |d      || |z  t        ||z  |z        z  |t        ||z  |z        z  z   z  t        | |z        z  t        |      z  ||dz  z  z  k(  sJ  |t
        dz   |
t
              z  t
        |      t/        t1         |
t
              t
        |d       |df      k(  sJ  ||t
        dz  z  |z   |dz  t
        dz  z   dz  z  t
        |d      |dz  |z  |z  t        ||z        z  d|dz  z  |z  t        ||z        z  z   ||z  |z  t        ||z        z  z
  |t        ||z        z  z   t        |      z  d|dz  z  z  k(  sJ  |t        t
              t
        |      t1        t        t
              t
        |d       k(  sJ  |dt
        |      d | |      z  k(  sJ  |dt        dt
        z        z  dt        dt
        z        z  z
  t
        |      dt1        t        dt
        z        t
        |d       z  d | |dz
        z  z
  k(  sJ t        t        d      dz        } ||t        dt
        z        z  t
        |      | | |dz
        z  k(  sJ  |t        dt
        z        t
        |      t1        t        dt
        z        t
        |d       k(  sJ t3        dd      } |t        |t
        z        t
        |      t1        t        |t
        z        t
        |d       k(  sJ  |t
        dz  |dz  t
        dz  z   z  t
        |      | t        ||z        z  t        |      z   | |      z   k(  sJ  |t
        dz   |
t
              d|dz  t
        dz  z   z  z   z  t
        |      | t        ||z        z  t        |      z   | |      z   t/        t1         |
t
              t
        |d       |df      z   k(  sJ  |t        |t
        z        t
        |d      t1        t        |t
        z        t
        |d       dfk(  sJ t3        dd       t3        ddd!      fD ]J  }	 |t        |	t
        z        t
        |d      }
t5        |
t6              r|
d   n|
}
|
j8                  | k7  rJJ   |d|t
        dz  z  |t
        z  z   |z   z  t
        |      dt        | |z  d|z  z        z  t        |t        d|z  |z  |dz  z
        z  d|z  z        z  t        |      z  t        d|z  |z  |dz  z
        z  k(  sJ y )"Nr   )r%   za b c dTr:   zn, r)realzt zr<   c                 P    t        t        |             j                  t              S )N)r   r   rewriter"   )exprs    ri   simp_hypz0test_inverse_laplace_transform.<locals>.simp_hyp  s    Jt,-55c::    r?   rB   r   rI   r>   rF   rH   rT   rA   rD   rP   rO   rC   rM   irE   rK   rFrW   z)extended_real)	imaginaryzero)'sympy.functions.special.delta_functionsr%   r   r   r   r8   r&   r   r#   r$   r"   r!   r   r1   r*   r   r   r   rn   r0   r7   r6   invr   r   r   
isinstancetuplefunc)r%   ILTr]   r^   r_   dnrr   r`   rs   r<   rp   s               ri   test_inverse_laplace_transformr     s   B
#CT2JAq!Q6%DAq5>DAqA; q!Q<:a=(((qsAq>Yq\)))q!a%y!Q1S!AY;y|#;;;;q!a%y!QA2c1"Q$i<	!#<z!}#LLLL1q51*aT2r!taxLaRT"9Q</12 3 21a!eaZ< !Q6dU1a4Z!A#a%!C!H*,q01Il#$%adF,, - , q!QUQJ,A&!Z1Q3''AeAh79 9 9!r{Aq!QQZAaC%81%EeAh%NNNNA}a#qaRT{9Q<'????A}a#q!tC1I~il'B2'EEEEq!Q$A+1%QqS)A,)>>>>q!Q$A+1%QqS)A,)>>>>q!Q$!a%!#$a+sA2a4yQqS/A)A,/NNNN!QTQUQJ&'A.r#qbd)|C!H$Q&aRT3qs8);;<Yq\IJ K JsA2a4y{Aq!YrAv%6666sA2a4y!a% !Q'3q!a%y>)QBF:K+KKKKQAQ
*+Q21Ic!A#hy|+, - ,QBqD	!Q$1%R!Vq1uiQ//a89 : 9QBqD	$q!tax.(!Q/qb1fgaQ//0 1 0q!DQK- !Q'9Q<DG+DDDD1a4A?#Q*ilNSVIaL001 2 1q!tQTAX1%#a&1)=
1)MMMMq1adQh<A&3q6')A,*>A*NNNNqAvq!)A,...qAvq!1Yq\ 1" 4444qAvq!AE
9Q< 7a @@@@Q!a%!Q$1*r/23QDIAaCj1S1X:%s1v-13r!t9<Yq\I"LM N MC1a4!Q$;A./4!9Yq\3IIIIC1a4!Q$;A./4!9Yq\3IIII QBqD	!Q$1%Ua!eYq1u--eAh67 8 7QBqD	$q1a4x.(!Q/a!eWQA../ 0 / 	QT1tAqD1a4K00QB77QTAqD[8II"73<	)!WQ!_$	%&	% 	AqD!d1a4!Q$;''A2..tAqD1a4K/@@q4	!!(!WQ!_$	%&	% q!DQK- !Q'9Q<DG+DDDD1a4A?#QD9QZ1%& ' &SVfq!fq!f%566;;=q!DSVIaL(!,q#ac(9Q<2G.HIJK L K 1a419q!d3d1Q3iK	!$Q&' ( '1a419q!$s1Q3x	!$ac*S!AYy|-CQqS-IIJK L K!QT!Q$YA5d1Q3iK	!$% & %1ac7Q"y|A~QBqD	)A, 6q 889: ; :!QqS1Ha#r!tC1I~il*S!AYy|-CCDE F EAaC!A#;A5s1Q3x#ac("#CAE
O3IaL@!a%HI J I!acAaC[!1a$7qQqSzAc!A#hJ&'QBAJ7	!Da!eLM N M!QT1Q3(]1a4'(!Q>r!tC!AJ3qs1u:-.sA2a4y81EqAvNO P O 2ad
Aq!.qtQ4@1b'JK L K1a4!adQTkA--q!dCT!VAXc!A#h1a4#ac(!22QqSU3qs8^Cs1Q3xZ"1&'(Av// 0 / s1vq! 7A1d KKKKq!Q<1Z]?***#ac(
Qs2a4y[(!Q/%c!A#h1d;;jQ   !   	CF1HAqRT{Aq!Qz!a%'8%8888s1Q3xA"9#ac(Aq$"OOOOsAs1Q3xA"9#ac(Aq$"OOOOq!tQTAqD[!1a(	
3qs8IaL :a=02 2 2q!tQqTAq!tad{O+,a3	
3qs8IaL :a=0*1Q4At<q!fE	FG G G AaC!Q.$S1Xq!T:DAB C B S.SDu57 $AaC!Q.q%(AaDavv###	$ 1QT6!A#:a< !Q'c1"Q$!*oc!D1QA$6"6!"<==aLac!eadl+,, - ,rq   c                  <   t        d      } t        d      }t        dd      }t        t        |       | t              t	        dt        dz  z          dz  t        z  ddfk(  sJ t        t        ||       | t        d	      t        t        t        t        t        z        z  d|      dt        |      t        j                  kD  fk(  sJ t        t        d|       | t        d	      t	        t        dz         t        z  ddfk(  sJ t        t        d|       | t        d	      t        t	        t        dz         z
  t        dz  z  ddfk(  sJ t        t	        dt        dz  z          dz  t        z  t        |      j                         t        |      t        |      z  k(  sJ t        t	        t        dz         t        z  t        | d	      j!                  t
              t        |       t#        |       z  k(  sJ t        t        t	        t        dz         z
  t        dz  z  t        | d	      j!                  t
              j                         t        d|       t        |       z  j!                  t$              j!                  t
              j                         k(  sJ y )
Nrb   r]   uT)polarr?   r>   r   r   )r   r   r-   r8   r   r.   r'   r   r   r   r   r   r[   r   expandr&   rn   r/   r,   )rb   r]   r   s      ri   test_expintr     s7   sAsAs$A RUAq)s1q!t8}nQ.>q.@!T-JJJJfQlAq4@a	!B$'A.2a5166>BC D CfQlAq4@QZ\1d#$ % $fQlAq4@#a!e*nad"At,- . -%s1q!t8}nQ&6q&8!Q?FFHaLA    	"#a!e*Q,1+/	118!RU		 	"QU^QT!1a	"76?668	1il	"++B/77?FFH	IJ	Irq   N)Msympy.integrals.laplacer   r   r   r   sympy.core.functionr   r   
sympy.corer	   r
   r   r   sympy.core.exprtoolsr   sympy.core.numbersr   r   r   sympy.core.singletonr   sympy.core.symbolr   r   sympy.simplify.simplifyr   $sympy.functions.elementary.complexesr   r   &sympy.functions.elementary.exponentialr   r   r   %sympy.functions.elementary.hyperbolicr   r   r   r   (sympy.functions.elementary.miscellaneousr   (sympy.functions.elementary.trigonometricr    r!   r"   'sympy.functions.special.gamma_functionsr#   r$   rw   r%   r&   &sympy.functions.special.zeta_functionsr'   'sympy.functions.special.error_functionsr(   r)   r*   r+   r,   r-   r.   r/   sympy.functions.special.besselr0   r1   r2   r3   sympy.testing.pytestr4   r5   sympy.matricesr6   r7   	sympy.abcr8   rj   r   r    rq   ri   <module>r      s   / / 5 9 9 - ( ( " - , 8 F F I I 9 C C E I ;7 7 7 M M = &  nA nAb }- }-@ J Jrq   