ó
¡¼™\c           @   sf  d  d l  m Z m Z m Z m Z m Z m Z m Z m Z m	 Z	 m
 Z
 m Z m Z m Z m Z m Z m Z m Z m Z m Z m Z m Z m Z m Z d  d l m Z m Z m Z m Z m Z m Z m Z d  d l  m! Z! d  d l" m# Z# d  d l$ m% Z% m& Z' d  d l( m) Z) d  d l* m+ Z+ m, Z, m- Z- m. Z. m/ Z/ m0 Z0 m1 Z1 m2 Z2 m3 Z3 d „  Z4 d	 „  Z5 d
 „  Z6 d „  Z7 d „  Z8 d „  Z9 e# d „  ƒ Z: d „  Z; d „  Z< d „  Z= d „  Z> e# d „  ƒ Z? d „  Z@ d „  ZA e# d „  ƒ ZB e# d „  ƒ ZC d „  ZD d „  ZE d „  ZF d „  ZG d „  ZH d „  ZI d „  ZJ d „  ZK d  „  ZL d! „  ZM d" „  ZN d# „  ZO d$ S(%   iÿÿÿÿ(   t   meijergt   It   St	   integratet   Integralt   oot   gammat   cosht   sinct   hyperexpandt   expt   simplifyt   sqrtt   pit   erft   erfct   sint   cost	   exp_polart	   polygammat   hypert   logt   expand_func(   t   _rewrite_singlet	   _rewrite1t   meijerint_indefinitet
   _inflate_gt   _create_lookup_tablet   meijerint_definitet   meijerint_inversion(   t   default_sort_key(   t   slow(   t   verify_numericallyt   random_complex_number(   t   range(	   t   xt   yt   at   bt   ct   dt   st   tt   zc       
   C   sz  d „  }  d „  } |  t  d t  ƒ |  t  d d t  d ƒ |  t  d t t  d t d t  d ƒ | t  d t  ƒ | t  t ƒ d „  } | t t  ƒ t t  ƒ t  ƒ t t t  ƒ t t  ƒ t  ƒ t d ƒ d t t ƒ d t t d ƒ d d t d ƒ d t d ƒ d t d ƒ d f d f d t d ƒ d d f f d	 t	 d
 t
 t ƒ t  d ƒ f g t f k svt ‚ d  S(   Nc         S   s—   t  t t g t g | g t g |  ƒ t ƒ } | d  k	 s? t ‚ t | d d d t ƒ s` t ‚ | d d d j	 j
 t ƒ | | f f k s“ t ‚ d  S(   Ni    i   (   R   R    R%   R&   R(   R#   t   Nonet   AssertionErrort
   isinstancet   argumentt   as_coeff_mul(   t   exprR'   t   mt   e(    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_meijerint.pyR*      s    -!c         S   s=   t  t t g t g t g t g |  ƒ t ƒ d  k s9 t ‚ d  S(   N(	   R   R    R%   R&   R'   R(   R#   R,   R-   (   R1   (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_meijerint.pyt   tn   s    i   i   c         S   s‚   d d l  m } m } m } t |  | ƒ } | g  | d D] } | d | d ^ q9 Œ  j | | ƒ } t | |  | ƒ s~ t ‚ d  S(   Niÿÿÿÿ(   t   AddR
   R   i    i   (   t   sympyR5   R
   R   R   t   replaceR    R-   (   R1   R#   R5   R
   R   t   rt   resR3   (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_meijerint.pyt   u   s
    /i    i   i   i@   iüÿÿÿ(   i   (    (   R#   R$   R
   R   R   R   R   R    R   R   R   t   TrueR-   (   R*   R4   R:   (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_meijerint.pyt   test_rewrite_single   s    		(	Dc           C   sŸ   t  t d t t g t g t g t g t d t t d ƒ d t ƒ d t d d d t t g t g t g t g t d t d ƒ f g t f k s› t	 ‚ d  S(   Ni   i   i   i   i    (
   R   R#   R    R%   R&   R'   R(   R$   R;   R-   (    (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_meijerint.pyt   test_rewrite18   s    Fc          C   sš   d „  }  |  d t  ƒ |  d t  ƒ |  d d t  ƒ |  d t  d ƒ |  d t  t d ƒ ƒ |  t  d t  ƒ |  d t  t d ƒ d t  t d ƒ ƒ d  S(	   Nc         S   sº   t  t g t g t g t g | ƒ |  } i t ƒ  d t 6t ƒ  d t t 6t ƒ  t 6t ƒ  t 6} t | t ƒ } | d  k	 sƒ t
 ‚ t | j | ƒ | j t ƒ j | ƒ t ƒ s¶ t
 ‚ d  S(   Ni
   (   R    R%   R&   R'   R(   t   randcplxR   R   R#   R,   R-   R    t   subst   diff(   t   fact   argt   gR?   t   integral(    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_meijerint.pyR*   >   s    (#i   i   i   s   3/2i   i   s   7/3(   R#   R   (   R*   (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_meijerint.pyt%   test_meijerint_indefinite_numerically=   s    	c          C   sp   t  t t d d ƒ \ }  } |  j r0 | t k s6 t ‚ t  t t t t ƒ \ }  } |  j rf | t k sl t ‚ d  S(   Ni    (   R   R#   t   is_zeroR;   R-   R   (   t   vR&   (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_meijerint.pyt   test_meijerint_definiteN   s    c             s  i t  ƒ  d t 6t  ƒ  d t t 6t  ƒ  t 6t  ƒ  t 6t  ƒ  d t 6‰  ‡  f d †  }  |  t g t g g t g t g g t d ƒ sŠ t ‚ |  t t g t g g t g t g g t d ƒ sÀ t ‚ |  t g t g g t t g t g g d t d d ƒ sþ t ‚ d  S(   Ni
   c            se   d d l  m } t |  | | ƒ } | t | | ƒ Œ  } t | j ˆ  ƒ | j ˆ  ƒ t d d d d ƒS(   Niÿÿÿÿ(   t   MulR&   gš™™™™™¹?R(   gš™™™™™¹¿(   R6   RI   R    R   R    R?   R#   (   R%   R&   RB   t   nRI   t   m1t   m2(   R?   (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_meijerint.pyR*   Y   s    i   i   (	   R>   R%   R   R&   R'   R(   R$   R#   R-   (   R*   (    (   R?   sC   lib/python2.7/site-packages/sympy/integrals/tests/test_meijerint.pyt   test_inflateU   s    -36c          C   s•  d d l  m }  |  d d t ƒ\ } } } t t | d ƒ t t | d ƒ } t | t d t f d t ƒ} t | j ƒ  ƒ t	 d ƒ t	 t
 ƒ t t	 d ƒ | | d ƒ d t | d d | | | d d ƒ d	 k sê t ‚ t t t | d ƒ t t | d ƒ t | t ƒ t d t f d t ƒ} t | ƒ t	 d ƒ t	 t
 ƒ t t	 d ƒ d | d | | d	 ƒ d t | d | d d | d | | d d
 ƒ d	 k sÃt ‚ t t t t | | | d ƒ t d t f d t ƒƒ t	 t
 ƒ d d t | | | ƒ k s*t ‚ t t t t | | | d ƒ t d t f d t ƒƒ t	 t
 ƒ d d t | | | ƒ k s‘t ‚ d  S(   Niÿÿÿÿ(   t   symbolss   a b ct   positivei   i    R    i   i   i   (   R6   RN   R;   R
   R#   R   R   R   t   expandR   R   R   R-   (   RN   R%   R&   R'   R8   R3   (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_meijerint.pyt   test_recursivee   s    (jN	‚8/8c       	   C   sÊ
  d d l  m }  m } m } |  d d t ƒ\ } } } t t g  g  d g g  | | ƒ t g  g  | d g | d g | d d ƒ | d t f ƒ j sž t	 ‚ |  d d	 t ƒ} t t
 | t g  g  g d g g  g t
 ƒ t
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 ƒ k st	 ‚ t t
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 d t f d t ƒt ƒ s¨t	 ‚ t t t
 ƒ t
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 ƒ k sÏt	 ‚ |  d d	 t ƒ\ } } t t t
 | t
 d | ƒ d ƒ | | d
 | d
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 d
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 | d | d ƒ t
 d t ƒ \ }	 }
 t |	 ƒ t t ƒ | d t | d | ƒ k sÚt	 ‚ |
 t k sìt	 ‚ t t | t
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 ƒ d t f k s¿t	 ‚ d „  } x] t d ƒ D]O } t t t
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 | ƒ t
 d t f ƒ k sˆt	 ‚ t t t
 d ƒ t t
 ƒ t
 d t f d t ƒt t ƒ t d t d
 ƒ d ƒ d j ƒ  k sît	 ‚ d d l  m  } |  d d t ƒ} t t t t
 ƒ t
 | t
 d t ƒƒ | | d
 t
 ƒ k sS	t	 ‚ |  d d	 t ƒ} t d t
 | t | t
 ƒ t
 d d ƒ t t ƒ | t | d
 ƒ t d | d t d
 ƒ d | d d
 f f d d t d
 ƒ d f t d
 ƒ d f f | t d ƒ d ƒ d t f k s)
t	 ‚ |  d d	 t ƒ\ } } t t t
 | t | t
 d ƒ t
 t t f ƒ ƒ | | d t d
 ƒ d d | d
 t | d t d
 ƒ d ƒ d k sÆ
t	 ‚ d  S(   Niÿÿÿÿ(   RN   RP   RB   s   s t mut   reali    i   i   R)   RO   i   R    s   a bi   i   s   sigma muc         S   s0   d d t  d j t  |  ƒ j t  d ƒ d |  S(   Ni   i   iÿÿÿÿ(   R#   R@   R?   (   RJ   (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_meijerint.pyR9   ±   s    i   s   a b s(   t   Andt   reiþÿÿÿi   (   t
   lowergammaRJ   t   integert   alphas   a s(    (!   R6   RN   RP   RB   R;   R   R    R   t   is_PiecewiseR-   R#   R   R.   t   FalseR   R   R
   R   R   R   R   R   R   t   absR   R   R   R"   RS   RT   R   R   RU   (   RN   RP   RB   R)   R*   t   muR%   R&   t   sigmat   iR'   t   _R9   RJ   RS   RT   RU   RW   (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_meijerint.pyt   test_meijerintw   s€    -88,' 2284 4;#495&=3"2B	46+i?[b3906'(œ3c          C   s€  d d l  m }  m } t t |  t t ƒ |  t t ƒ t t d t f d t	 d d ƒƒ d t
 t t d t d ƒ t t t t t k s” t ‚ t t |  t t ƒ |  t t ƒ t t d t f d t	 d d ƒƒ d d t k sì t ‚ t t t
 t t ƒ t d d t t d ƒ d t d t f d t	 d d ƒd t d t t t ƒ t t d ƒ d t ƒ ƒ |  t t ƒ k s†t ‚ t t |  d t ƒ t d t	 ƒt |  d t ƒ k sÁt ‚ t t | d t ƒ t d t	 ƒt | d t ƒ k süt ‚ t |  d t ƒ t d t	 ƒ|  d t ƒ k s0t ‚ t |  d t ƒ d t t d t	 ƒ|  d t ƒ d |  d t ƒ d d k s…t ‚ t |  d t ƒ d t d t d t	 ƒd	 t |  d t ƒ d d t |  d t ƒ d d |  d t ƒ |  d t ƒ |  d t ƒ d t k st ‚ t |  d t ƒ |  d t ƒ t d t	 ƒ|  d t ƒ d d k set ‚ t t d |  d t ƒ |  d t ƒ t d t	 ƒt d |  d t ƒ d d k s½t ‚ t |  d t ƒ |  d t ƒ t t d t	 ƒt |  d t ƒ d t |  d t ƒ d |  d t ƒ |  d t ƒ k s8t ‚ t |  d t d ƒ t t d t	 ƒ|  d t d ƒ d k s|t ‚ d  S(
   Niÿÿÿÿ(   t   besseljt   besselii    R    t   condst   nonei   i   iþÿÿÿ(   R6   R`   Ra   R   R   R%   R+   R&   R   R;   R   R   R-   R#   R$   R   R   R   (   R`   Ra   (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_meijerint.pyt   test_besselá   s2    2=2&;;4#2'p(!0(,)&	#c             s”  d d l  m ‰  m }  m } m } m } m } ‡  f d †  } | d t d d ƒ | t ƒ | t ƒ k sq t	 ‚ | t t d d ƒ | t ƒ | t ƒ k s¥ t	 ‚ | t
 t ƒ t ƒ | t d ƒ k sÒ t	 ‚ | d | d t d ƒ ƒ |  d t ƒ | t ƒ k st	 ‚ t | t ƒ | d t d ƒ t t ƒ d  k sEt	 ‚ | t
 t d ƒ ƒ d  k sgt	 ‚ t t
 t d ƒ t t ƒ d  k st	 ‚ d  S(   Niÿÿÿÿ(   t   piecewise_foldR`   R   R   R   t	   Heavisidec            s   ˆ  t  |  t t ƒ ƒ S(   N(   R   R)   R*   (   t   f(   Re   (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_meijerint.pyt   inv  s    i   i   i    (   R6   Re   R`   R   R   R   Rf   R)   R*   R-   R
   R   R,   (   R`   R   R   R   Rf   Rh   (    (   Re   sC   lib/python2.7/site-packages/sympy/integrals/tests/test_meijerint.pyt   test_inversion  s    .44-=6"c          C   sM  d d l  m }  m } |  d d t ƒ} t t | ƒ t d t | ƒ t t ƒ ƒ } t | t t	 ƒ } | j
 sx t ‚ |  d d t ƒ} | j | | ƒ } t | t t	 ƒ } | j
 s½ t ‚ | j d d | j | | ƒ k sæ t ‚ | j d d	 sý t ‚ | | t t	 d  ƒ } | j d d | k sI| j d d | j k sIt ‚ d  S(
   Niÿÿÿÿ(   t   Symbolt   InverseLaplaceTransformR%   RO   iþÿÿÿR&   RR   i    i   (   R6   Rj   Rk   R;   R   R   R
   R)   R   R*   RX   R-   R?   t   argsR,   t   as_integral(   Rj   Rk   R%   t   FRg   R&   t   f2t   ILT(    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_meijerint.pyt!   test_inversion_conditional_output!  s    .)c          C   s  d d l  m }  m } |  d d t ƒ} |  d d t ƒ} d d t } |  d ƒ } t t | t ƒ t t	 ƒ j
 sz t ‚ t t | t ƒ t t	 ƒ d  k s¢ t ‚ t t | t ƒ t t	 ƒ d  k sÊ t ‚ t t | t ƒ t t	 ƒ } | j
 sõ t ‚ t | j d	 d	 | ƒ st ‚ d  S(
   Niÿÿÿÿ(   Rj   t
   DiracDeltaR8   RR   R'   i   i   R+   i    (   R6   Rj   Rr   R;   RY   R   R   R
   R)   R*   RX   R-   R,   R.   Rl   (   Rj   Rr   R8   R'   R%   R+   Rg   (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_meijerint.pyt%   test_inversion_exp_real_nonreal_shift5  s    &((c          C   s  d d l  m }  m } d d l m } d d l m } i  } t | ƒ xÐt | j	 ƒ  ƒ D]¼\ } } x­t | d t
 ƒD]™\ } } }	 }
 i  } x_ t | j ƒ | g D]G } t | d ƒ rÛ | j rÛ | d d ƒ | | <q§ |  d	 d
 ƒ | | <q§ Wt | t ƒ s| | ƒ } n  g  | D] \ } } t | ƒ ^ q} t d „  | Dƒ ƒ sQt ‚ | g  | D] \ } } | | ^ q[Œ  } | j d | ƒ | j d | ƒ } } t t | ƒ t | ƒ ƒ } | d k  rët | | ƒ j ƒ  d k st ‚ qx t | | ƒ | j ƒ  d k sx t ‚ qx WqY Wd  S(   Niÿÿÿÿ(   t   uniformt	   randrange(   R5   (   R+   t   keyt
   propertiesi   i
   g      ø?g       @c         s   s(   |  ] } | j  p | j t ƒ Vq d  S(   N(   RX   t   hasR    (   t   .0R#   (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_meijerint.pys	   <genexpr>X  s    R?   g»½×Ùß|Û=(   t   randomRt   Ru   R6   R5   t   sympy.integrals.meijerintR+   R   t   sortedt   itemsR   t   listt   free_symbolst   hasattrRw   R.   R	   t   allR-   RJ   t   minRZ   (   Rt   Ru   R5   t   z_dummyt   tableR^   t   lt   formulat   termst   condt   hintR?   R%   RC   t   expandedRg   R#   R&   R8   (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_meijerint.pyt   test_lookup_tableC  s,    
%%)%%c          C   sR  d d l  m }  m } |  t t t d ƒ t d t ƒj t ƒ d t ƒd t t d ƒ t t	 d ƒ d ƒ d t t	 d ƒ d ƒ k s t
 ‚ t t t d ƒ t d t ƒd t t t d ƒ t t	 d ƒ d ƒ d t t	 d ƒ d ƒ d t t	 d ƒ d ƒ | t	 d ƒ d t d ƒ d t t ƒ t t	 d ƒ d ƒ k sNt
 ‚ d  S(	   Niÿÿÿÿ(   t	   powdenestRU   i   R    t   polari   i   i   (   R6   RŒ   RU   R   R   R#   R;   R@   R   R   R-   R   R   (   RŒ   RU   (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_meijerint.pyt   test_branch_bugd  s    +OAc          C   s†   d d l  m }  t t t d ƒ t d t ƒt d t ƒ k sF t ‚ t |  d t d ƒ t d t ƒ|  d d t ƒ k s‚ t ‚ d  S(   Niÿÿÿÿ(   R`   i   R    i    (   R6   R`   R   R   R#   R;   R   R-   (   R`   (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_meijerint.pyt   test_linear_subsn  s    6c    &   
      s¬  d d l  m ‰ m ‰ d d l m }  m } m } m ‰  m } m	 } m
 } |  d d t d t d t ƒ\ ‰ } |  d d t d t d t d	 t ƒ\ ‰ } | d
 d t d	 t d t ƒ‰ d „  ‰ d „  ‰ t ˆ ˆ ˆ ˆ ƒ ˆ t t f d t ƒd k sÿ t ‚ t ˆ ˆ ˆ ˆ ˆ ƒ ˆ t t f d t ƒˆ k s:t ‚ t ˆ d ˆ ˆ ˆ ˆ ƒ ˆ t t f d t ƒˆ d ˆ d k s…t ‚ t ˆ d ˆ ˆ ˆ ˆ ƒ ˆ t t f d t ƒˆ d d ˆ ˆ d k sØt ‚ t ˆ ˆ ˆ ˆ ƒ ˆ ˆ | | ƒ ˆ t t f ˆ t t f d t ƒd k s,t ‚ t ˆ ˆ ˆ ˆ ˆ ƒ ˆ ˆ | | ƒ ˆ t t f ˆ t t f d t ƒˆ k s„t ‚ t ˆ ˆ ˆ ˆ ˆ ƒ ˆ ˆ | | ƒ ˆ t t f ˆ t t f d t ƒ| k sÜt ‚ t ˆ ˆ ˆ ˆ ˆ ˆ ƒ ˆ ˆ | | ƒ ˆ t t f ˆ t t f d t ƒˆ | k s<t ‚ t ˆ ˆ d ˆ ˆ ˆ ˆ ƒ ˆ ˆ | | ƒ ˆ t t f ˆ t t f d t ƒd ˆ | k s¤t ‚ t ˆ ˆ d ˆ ˆ ˆ ˆ ƒ ˆ ˆ | | ƒ ˆ t t f ˆ t t f d t ƒd ˆ | k st ‚ t ˆ d ˆ ˆ ˆ ˆ ƒ ˆ ˆ | | ƒ ˆ t t f ˆ t t f d t ƒ} | j | ƒ srt ‚ t | ƒ ˆ d ˆ d k s–t ‚ t ˆ d ˆ ˆ ˆ ˆ ƒ ˆ ˆ | | ƒ ˆ t t f ˆ t t f d t ƒ| d | d k sþt ‚ t ˆ ˆ ˆ ƒ ˆ d t f d t ƒd k s1t ‚ t ˆ ˆ ˆ ˆ ƒ ˆ d t f d t ƒd ˆ k slt ‚ t ˆ d ˆ ˆ ˆ ƒ ˆ d t f d t ƒd ˆ d k s¯t ‚ ‡  ‡ ‡ ‡ ‡ ‡ ‡ ‡ f d †  }	 |	 d ƒ d k sët ‚ |	 ˆ ˆ ƒ ˆ ˆ k st ‚ |	 ˆ ˆ d ƒ ˆ d ˆ ˆ d ˆ k s?t ‚ ˆ d d ˆ d }
 t |	 ˆ ˆ d d ƒ |	 ˆ ˆ d ƒ d ƒ |
 k s•t ‚ t |	 ˆ ˆ d d ƒ |	 ˆ ˆ d ƒ d ƒ |
 k sÕt ‚ t |	 ˆ ˆ d ƒ |	 ˆ ˆ ƒ d ƒ |
 k st ‚ |  d d	 t ƒ\ } } ˆ | d d ˆ | | t | | ƒ t | ƒ t | ƒ } t | ˆ d t f d t ƒd k st ‚ t ˆ | ˆ d t f d t d d ƒ} | | d ƒ | d f | | d d | k  f k sòt ‚ t ˆ d | ˆ d t f d t d d ƒ} | d d | d k  k s>t ‚ | | d | d d ƒ | | d | | d | d d k s†t ‚ |  d d	 t ƒ\ } } ˆ | d ˆ d | d t | | ƒ t | ƒ t | ƒ } t t | ˆ d d f d t ƒƒ d k s	t ‚ t t ˆ | ˆ d d f d t ƒƒ | | | k sK	t ‚ t t ˆ d | ˆ d d f d t ƒƒ | | d | | | | d k sŸ	t ‚ t t ˆ ˆ | ˆ d d f d t ƒƒ t | | ƒ t | ˆ ƒ t | ƒ t | | ˆ ƒ k s
t ‚ | d d t d	 t ƒ} d d | d ˆ | d t ˆ d d ƒ t | d ƒ } | t | ˆ d t f d t ƒƒ d k s’
t ‚ t t ˆ | ˆ d t f d t ƒƒ t d ƒ t | d d ƒ t | d ƒ k sì
t ‚ t t ˆ d | ˆ d t f d t ƒƒ | k s$t ‚ d | d t | d ƒ ˆ | d d t ˆ d ƒ } | t | ˆ d t f d t ƒƒ d k st ‚ t t ˆ | ˆ d t f d t ƒƒ | k sÄt ‚ t t ˆ d | ˆ d t f d t ƒƒ | | d k st ‚ | t ˆ | t d | ƒ d | ˆ d t f d t ƒƒ d t d ƒ t | ƒ k sbt ‚ |  d d	 t ƒ\ } } } | | ˆ ˆ | | | d ˆ | | | | d } t t | ˆ d t f d t ƒƒ d k sçt ‚ ˆ | } t t | ˆ d t f d t d d ƒƒ | | t d d | ƒ t | d d | ƒ | | d t | ƒ k sit ‚ t t ˆ | ˆ d t f d t d d ƒƒ | | d t d d | ƒ t | d d | ƒ | | d t | ƒ k sét ‚ |  d d	 t ƒ\ } } t | ˆ | | | | ˆ | | | ƒ ˆ t | d ƒ t | d ƒ t | | d ƒ } t t | ˆ d t f d t ƒƒ d k s“t ‚ t t ˆ | ˆ d t f d t d d ƒƒ | | d k sÕt ‚ t t ˆ d | ˆ d t f d t d d ƒƒ | d | d | | d | d k s3t ‚ |  d d	 t ƒ\ } } t | d t ƒ ˆ t d ƒ d t | ˆ | d ˆ d | d ƒ } d „  } | t | ˆ d t f ƒ ƒ d k sÌt ‚ | t ˆ | ˆ d t f ƒ ƒ | k sút ‚ | t ˆ | d | ˆ d t f ƒ ƒ | d | k s8t ‚ | t ˆ | d | ˆ d t f ƒ ƒ d | d | d k s~t ‚ | d  d	 t ƒ} t t | d t ƒ t | d ˆ | ƒ ˆ | t d! ƒ ˆ | t f ƒ d k sët ‚ | | ˆ | d | | d d ˆ | | | d } t t | ˆ d t f ƒ ƒ d k sOt ‚ t t ˆ | ˆ d t f d d ƒƒ t | | | t | ƒ k s™t ‚ t t ˆ ˆ | ˆ d t f d d ƒƒ t | ˆ ˆ | | t ˆ | ƒ k sót ‚ | d d	 t ƒ} | d" d	 t ƒ}  | | ˆ | | d t ˆ | | ƒ } t t | ˆ d t f ƒ ƒ d k snt ‚ t t ˆ |  | ˆ d t f ƒ ƒ | |  t d |  | ƒ k s¶t ‚ d d# l m }! |  d$ d	 t ƒ\ }" }# ˆ |# d t ˆ d |" d d |# d ƒ |! d ˆ |" |# d ƒ }$ t |$ ˆ d t f d t ƒd k sRt ‚ | d% d t ƒ} | d& d	 t ƒ} t t ˆ | ƒ | ƒ d | }% t |% ˆ t t f d t ƒd k sÄt ‚ t ˆ |% ˆ t t f d t ƒ| k sót ‚ t ˆ d |% ˆ t t f d t ƒd | d | d k s6t ‚ | d d	 t ƒ} | ˆ  t t ˆ ƒ ˆ | d t ˆ ƒ t | ƒ ˆ d t f ƒ ƒ ƒ t d | ƒ k s¨t ‚ d  S('   Niÿÿÿÿ(   R#   R$   (   RN   Rj   t   Abst
   expand_mult	   gammasimpt   powsimpR   s   mu1 mu2RR   t   nonzerot   finites   sigma1 sigma2RO   t   lambdac         S   s9   d t  d t | d ƒ t |  | d d | d ƒ S(   Ni   i   (   R   R   R
   (   R#   R[   R\   (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_meijerint.pyt   normal~  s    c         S   s   | t  | |  ƒ S(   N(   R
   (   R#   t   rate(    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_meijerint.pyt   exponential  s    R    i   i   i   i    c            s²   t  |  ˆ ˆ ˆ ƒ ˆ ˆ ˆ ˆ ƒ ˆ d t f ˆ t t f d t ƒ} t  |  ˆ ˆ ˆ ƒ ˆ ˆ ˆ ˆ ƒ ˆ t t f ˆ d t f d t ƒ} ˆ  | ƒ ˆ  | ƒ k s® t ‚ | S(   Ni    R    (   R   R   R;   R-   (   R1   t   res1t   res2(   R‘   R™   t   mu1R—   R˜   t   sigma1R#   R$   (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_meijerint.pyt   E§  s    #%#%s
   alpha betaRb   t   separates   a bt   kRV   s   a b pRc   s   d1 d2i   s   lamda muc         S   s   t  |  j t ƒ ƒ S(   N(   R   t   rewriteR
   (   R1   (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_meijerint.pyt   <lambda>ÿ  t    i   R'   s   3/2RJ   (   Ra   s   nu sigmaR[   R&   (   t	   sympy.abcR#   R$   R6   RN   Rj   R   R‘   R’   R“   R   R;   R   R   R-   Rx   R   R   R
   R   R   R   Ra   RZ   R   R   (&   RN   Rj   R   R’   R“   R   t   mu2t   sigma2R]   Rž   t   ansRW   t   betat   betadistt   jR%   R&   R    t   chit
   chisquaredt   pt   dagumRB   t   d1t   d2Rg   t   lamdaR[   t   distt   mysimpR'   t   distnRJ   Ra   t   nuR\   t   ricet   laplace(    (   R‘   R™   Rœ   R—   R˜   R   R#   R$   sC   lib/python2.7/site-packages/sympy/integrals/tests/test_meijerint.pyt   test_probabilityt  s
   4$		7,00#"2&2&2*6.:.#*&$*#3(,$ 4@@8A*(:, /A0%)+)C?0%58<04)2,:0
'/"+3"b0+//N	*.>F=*%%)1-*#%J*#+/$3c       	   C   sè  d d l  m }  m } m } m } m } m } m } m } m	 } m
 }	 m }
 m } t | t t t t ƒ t t t d t f d t d d ƒj |  ƒ j d t ƒ ƒ ƒ |  t t ƒ k s¿ t ‚ t t t t ƒ t t d t f d t d d ƒj |  ƒ j ƒ  |  d t ƒ k st ‚ t t t t ƒ t d t d t f d t d d ƒj |  ƒ j ƒ  |  d t ƒ j | ƒ j |  ƒ k sƒt ‚ t t t t ƒ t d	 t d t f d t d d ƒj |  ƒ j ƒ  |  d	 t ƒ j | ƒ j |  ƒ j ƒ  k söt ‚ | d
 d t ƒ} t | t ƒ t t | t f d t ƒj ƒ  | | ƒ k sIt ‚ t | t ƒ t t | t f d t ƒj ƒ  | | ƒ t d k s’t ‚ t | t ƒ t t d t f d t ƒ| t ƒ k sÌt ‚ t |	 t ƒ t t d t f d t ƒ| t ƒ k st ‚ t t t ƒ t t d t ƒj ƒ  j |  ƒ t t |  d t ƒ k sRt ‚ t t t ƒ t d t d t ƒj |  ƒ j ƒ  |  d t ƒ t t ƒ t t t k s±t ‚ | d d t ƒ} t | | ƒ | | d t ƒj ƒ  j | ƒ d | | ƒ k st ‚ t |
 | ƒ | | d t ƒj ƒ  j | ƒ d | | ƒ k sKt ‚ t |  d t ƒ t d t ƒj |  ƒ j ƒ  t |  d t ƒ t t ƒ k sœt ‚ t |  d t ƒ t d t ƒj |  ƒ j ƒ  t d |  d t ƒ d t t t ƒ d t t ƒ d k st ‚ t | t |  t t ƒ t d t ƒj |  ƒ j d t ƒ ƒ ƒ |  t d t ƒ k sft ‚ t | t ƒ t d t ƒt | t ƒ | t ƒ k s¡t ‚ t | | ƒ | d t ƒj ƒ  | | | ƒ | | ƒ k sât ‚ t | t ƒ t d t ƒt | t ƒ |
 t ƒ k st ‚ t | | ƒ | d t ƒj ƒ  | | | ƒ |	 | ƒ k s^t ‚ t | t ƒ t t ƒ t d t f d t ƒt d k st ‚ t |  d t ƒ | t ƒ t d t f d t ƒt d ƒ d k sät ‚ d S(   s%    Test various exponential integrals. iÿÿÿÿ(   t   expintt
   unpolarifyRj   t   Cit   Sit   Shit   ChiR   R   t   sinhR   t   Eii   R    Rb   Rc   t   funci   i   R*   RO   i    R:   R   i   N(   R6   R¹   Rº   Rj   R»   R¼   R½   R¾   R   R   R¿   R   RÀ   R   R   R
   R+   R#   R$   R   R;   R¡   RP   R-   R   R   t   as_independentR   (   R¹   Rº   Rj   R»   R¼   R½   R¾   R   R   R¿   R   RÀ   R*   R:   (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_meijerint.pyt   test_expint6  sT    R.0*.*.0A,::, 0///3G!;A;A?c          C   sY  d d l  m }  m } m } m } m } m } m } m } m	 } m
 }	 m }
 m } m } m } m } |  | t ƒ t t ƒ | t ƒ t d t d t f k s¤ t ‚ |  | t ƒ t t ƒ | t ƒ t d t f k sÛ t ‚ |  | t ƒ t t ƒ t t d ƒ t t d d t d ƒ d t d t f k s4t ‚ |  | t t ƒ t t ƒ d d | | t d ƒ t d ƒ d t d ƒ k | t d ƒ d t d ƒ k ƒ f k s¬t ‚ | | d t ƒ t t t d t ƒ| d d t t d t d ƒ d k f d | d	 t d t d d ƒ t f ƒ t d k f k s8t ‚ t | t ƒ | d t ƒ t d t f d
 t ƒt d | d ƒ ƒ k s…t ‚ t | t ƒ | d t ƒ t d t f d
 t ƒt t d ƒ d | d ƒ d ƒ k sàt ‚ t d t | d t d ƒ t d
 t ƒ| |	 d t ƒ t t d ƒ d k f t |
 d t ƒ t f ƒ k sUt ‚ d  S(   Niÿÿÿÿ(   t   laplace_transformR¼   R½   R¾   t   atant	   Piecewiset   acotht   E1R`   t   acosht   asinRS   RT   t   fourier_transformR   i   i    i   iþÿÿÿt   nocondsi   iüÿÿÿR    (   R6   RÄ   R¼   R½   R¾   RÅ   RÆ   RÇ   RÈ   R`   RÉ   RÊ   RS   RT   RË   R   R#   R)   R   R;   R-   R   R%   R   RY   RZ   R   R   R   (   RÄ   R¼   R½   R¾   RÅ   RÆ   RÇ   RÈ   R`   RÉ   RÊ   RS   RT   RË   R   (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_meijerint.pyt
   test_messyl  s     d@7D\"(B..-(c           C   s[   t  t t t d ƒ t t t f d t ƒt t t ƒ t t t d ƒ k sW t ‚ d  S(   Ni   R    i   (	   R   R
   R   R#   R   R;   R   R   R-   (    (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_meijerint.pyt   test_issue_6122Œ  s    +c          C   sS   d t  t t t  t d ƒ d }  t |  t  d t ƒ} |  j t ƒ sO t ‚ d  S(   Ni   i   R    (	   R#   R%   R&   R   R   R;   Rx   R   R-   (   R1   t   anti(    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_meijerint.pyt   test_issue_6252‘  s    $c           C   sX   t  t t t ƒ d t d t t t f ƒ j ƒ  j t ƒ t t d ƒ k sT t ‚ d  S(   Ni   i   iÿÿÿÿ(	   R   R
   R   R#   R   R   R¡   R   R-   (    (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_meijerint.pyt   test_issue_6348™  s    ;c          C   sŒ   d d l  m }  m } t t t t t d d ƒ t ƒ ƒ |  t ƒ k sO t ‚ t t t	 t t d d ƒ t ƒ ƒ | t ƒ k sˆ t ‚ d  S(   Niÿÿÿÿ(   t   fresnelst   fresnelci   (
   R6   RÒ   RÓ   R   R   R   R   R#   R-   R   (   RÒ   RÓ   (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_meijerint.pyt   test_fresnelž  s    9c           C   s'   t  t t t t ƒ d  k s# t ‚ d  S(   N(   R   R#   R,   R-   (    (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_meijerint.pyt   test_issue_6860¥  s    c          C   sš   t  t t d t d ƒ t ƒ j ƒ  }  |  t d t d ƒ d t d t d d k s_ t ‚ |  j t t d ƒ t d ƒ ƒ t d ƒ d k s– t ‚ d  S(   Ni   i   i   iÿÿÿÿi   (   R   R#   R   t   togetherR-   t   _eval_intervalR   (   Rg   (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_meijerint.pyt   test_issue_7337©  s    '8c           C   sv   t  t t ƒ t t t ƒ t ƒ t d t t ƒ t d t t ƒ t t t ƒ d t d d k sr t ‚ d  S(   Ni   i   (   R   R   R#   R
   R*   R-   (    (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_meijerint.pyt   test_issue_8368¯  s    !c          C   sŽ   d d l  m }  m } t d t t t d |  d ƒ d t d | f t d | f ƒ d t d | d |  d ƒ |  d |  k sŠ t ‚ d  S(   Niÿÿÿÿ(   t   ht   wi   i   i   i    (   R¤   RÚ   RÛ   R   R   R$   R#   R-   (   RÚ   RÛ   (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_meijerint.pyt   test_issue_10211´  s    ?c          C   s   d d l  m }  |  d d t ƒ\ } } t d t t d | d ƒ d t | | f ƒ d | | d t | d | d ƒ k s‰ t ‚ d  S(   Niÿÿÿÿ(   RN   s   y LRO   i   i   i   (   R6   RN   R;   R   R   R#   R-   (   RN   R$   t   L(    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_meijerint.pyt   test_issue_11806º  s    0c          C   sá   d d l  m }  d d l m } m } t | d | d | d d | d t ƒ} d d | d | d t d	 t d ƒ d f t d
 ƒ d f | d t	 d t
 t ƒ | d ƒ } |  j | | j ƒ  d d ƒ sÝ t ‚ d  S(   Niÿÿÿÿ(   t   RR(   t   RR8   i   g      à?R    g      ð?i   g      à¿i   gê-™—q=(   R6   Rß   R¤   Rà   R8   R   R;   R   R   R   R   R   t   almosteqRJ   R-   (   Rß   Rà   R8   Rg   RC   (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_meijerint.pyt   test_issue_10681À  s    -=(c          C   s\   d d l  m }  |  d d t d t ƒ} t d t d t t | f ƒ d | k sX t ‚ d  S(   Niÿÿÿÿ(   Rj   R%   RR   RO   i   i   (   R6   Rj   R;   R   R#   R   R-   (   Rj   R%   (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_meijerint.pyt   test_issue_13536È  s    N(P   R6   R    R   R   R   R   R   R   R   R   R	   R
   R   R   R   R   R   R   R   R   R   R   R   R   R{   R   R   R   R   R   R   R   t   sympy.utilitiesR   t   sympy.utilities.pytestR   t   sympy.utilities.randtestR    R!   R>   t   sympy.core.compatibilityR"   R¤   R#   R$   R%   R&   R'   R(   R)   R*   R+   R<   R=   RE   RH   RM   RQ   R_   Rd   Ri   Rq   Rs   R‹   RŽ   R   R¸   RÃ   RÍ   RÎ   RÐ   RÑ   RÔ   RÕ   RØ   RÙ   RÜ   RÞ   Râ   Rã   (    (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_meijerint.pyt   <module>   sD   ”4@	)					j	0			!	
	Â6	 										