ó
¡¼™\c           @   s  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 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- m. Z. m/ Z/ m0 Z0 m1 Z1 m2 Z2 m3 Z3 m4 Z4 m5 Z5 m6 Z6 m7 Z7 m8 Z8 m9 Z9 m: Z: m; Z; m< Z< m= Z= m> Z> m? Z? m@ Z@ mA ZA m# Z# d  d lB mC ZC mD ZD mE ZE mF ZF d  d lG mH ZH mI ZI d  d lJ mK ZK mL ZL mM ZM mN ZN mO ZO mP ZP e d ƒ \ ZQ ZR ZS d „  ZT d „  ZU d	 „  ZV eD eC d
 „  ƒ ƒ ZW d „  ZX eD d „  ƒ ZY eD d „  ƒ ZZ eD d „  ƒ Z[ eD d „  ƒ Z\ eD d „  ƒ Z] d „  Z^ d „  Z_ d „  Z` d „  Za d „  Zb d „  Zc d „  Zd d „  Ze d „  Zf d „  Zg d „  Zh d „  Zi d „  Zj d „  Zk d S(    iÿÿÿÿ(   t   mellin_transformt   inverse_mellin_transformt   laplace_transformt   inverse_laplace_transformt   fourier_transformt   inverse_fourier_transformt   sine_transformt   inverse_sine_transformt   cosine_transformt   inverse_cosine_transformt   hankel_transformt   inverse_hankel_transformt   LaplaceTransformt   FourierTransformt   SineTransformt   CosineTransformt   InverseLaplaceTransformt   InverseFourierTransformt   InverseSineTransformt   InverseCosineTransformt   IntegralTransformError(,   t   gammat   expt   oot	   Heavisidet   symbolst   Symbolt   ret	   factorialt   pit   argt   cost   St   Abst   Andt   Ort   sint   sqrtt   It   logt   tant   hyperexpandt   meijergt
   EulerGammat   erft   erfct   besseljt   besselyt   besselit   besselkt	   exp_polart
   polar_liftt
   unpolarifyt   Functiont   expintt
   expand_mult	   gammasimpt   trigsimpt   atant   sinht   cosht   Net   periodic_argumentt   atan2R!   (   t   XFAILt   slowt   skipt   raises(   t   Matrixt   eye(   t   xt   st   at   bt   ct   ds   nu beta rhoc          C   sô   d d l  m }  m } |  d ƒ } t | t ƒ t t ƒ | | t ƒ t t ƒ k sX t ‚ t | t ƒ t t ƒ t t ƒ | | t ƒ t t ƒ t t ƒ d t	 f t
 f k s² t ‚ t d | t ƒ t t ƒ d t | t ƒ t t ƒ k sð t ‚ d  S(   Niÿÿÿÿ(   R5   t   MellinTransformt   fi    i   (   t   sympyR5   RL   R    RF   RG   t   AssertionErrorR   R   R   t   TrueR   R   (   R5   RL   RM   (    (    sD   lib/python2.7/site-packages/sympy/integrals/tests/test_transforms.pyt   test_undefined_function   s    6 :c          C   s{   d d l  m }  |  d ƒ } t | t ƒ t t ƒ j t h k sF t ‚ t | t ƒ t t t ƒ j t t h k sw t ‚ d  S(   Niÿÿÿÿ(   R5   RM   (   RN   R5   R    RF   RG   t   free_symbolsRO   RH   (   R5   RM   (    (    sD   lib/python2.7/site-packages/sympy/integrals/tests/test_transforms.pyt   test_free_symbols!   s    *c          C   s  d d l  m }  m } |  d ƒ } t | t ƒ t t ƒ j d ƒ | t t d | t ƒ t d t f ƒ k ss t ‚ t	 | t ƒ t t ƒ j d ƒ | | t ƒ t
 d t t t t ƒ t t t f ƒ k sÓ t ‚ t | t ƒ t t ƒ j d ƒ | | t ƒ t
 t t ƒ t d t f ƒ k s't ‚ t d t t t | t ƒ t t t t f ƒ j d ƒ ƒ d	 k sot ‚ t d t t t | t ƒ t t ƒ j d ƒ ƒ d
 k s®t ‚ t | t ƒ t t ƒ j d ƒ | | t ƒ t
 d t t t t ƒ t t t f ƒ k st ‚ d  S(   Niÿÿÿÿ(   R5   t   IntegralRM   RT   i   i    iþÿÿÿi   s1   Integral(x**(-s)*f(s), (s, _c - oo*I, _c + oo*I))s2   Integral(f(s)*exp(s*x), (s, _c - oo*I, _c + oo*I))(   RN   R5   RT   R    RF   RG   t   rewriteR   RO   R   R   R&   R   R   t   strR   RH   RI   R   R   (   R5   RT   RM   (    (    sD   lib/python2.7/site-packages/sympy/integrals/tests/test_transforms.pyt   test_as_integral(   s    3B690c          C   sd  t  d ƒ t }  t d d t ƒ} t d d t ƒ} t t t d ƒ t t t t t d ƒ } |  | j t | ƒ t t	 ƒ d t d d t d t	 | t d t	 d t
 t t	 ƒ t
 d t d t	 ƒ t
 d t	 ƒ t t ƒ t t ƒ d t d ƒ d f t f k st ‚ t t t d ƒ t t } |  | j t | ƒ t t	 ƒ d t d t	 t | t d t	 t
 t d t	 ƒ t
 t t	 ƒ t
 t	 d ƒ t t ƒ t t ƒ d f t f k sÒt ‚ |  | j i | t 6d t 6ƒ t t	 ƒ | d t	 d t
 t	 ƒ t
 t	 t d ƒ d ƒ d t t ƒ d t d ƒ d f t f k s`t ‚ d  S(   Ns   Risch takes forever.RI   t   positivet   negativei   iÿÿÿÿi   (   RB   R    R   RP   R%   RF   RI   RH   t   subsRG   R   R   R    RO   R   (   t   MTt   bpost   bnegt   expr(    (    sD   lib/python2.7/site-packages/sympy/integrals/tests/test_transforms.pyt   test_mellin_transform_fail;   s    
.a;S-'Ac          C   s‘  d d l  m }  m } t } t d d t ƒ} | t t t t d ƒ t t	 ƒ d t t	 t
 t t ƒ f t f k s} t ‚ | t t t d t ƒ t t	 ƒ d t t	 t t ƒ t
 f t f k sË t ‚ | d t t d t d t ƒ t t	 ƒ t t ƒ t t	 ƒ t t t	 ƒ d t
 f t t ƒ d k f k s<t ‚ | t d t d t t d ƒ t t	 ƒ t t ƒ t d t t	 ƒ t d t	 ƒ t
 t t ƒ d f t t ƒ d k f k sÁt ‚ | d t t t t	 ƒ t t	 ƒ t t t	 ƒ t t ƒ d t t ƒ f t f k st ‚ | t d t ƒ t t t	 ƒ d t t t d ƒ t d t ƒ t t t d t	 ƒ t t	 ƒ t t t	 ƒ t d t t ƒ f t t t ƒ d d k  t t ƒ d k  ƒ f k sÔt ‚ | d t t d t d t ƒ t t d t d t t d ƒ t t	 ƒ } | d set | d d t t ƒ d f t t ƒ d k f k ƒ ‚ | t t t t t t t t	 ƒ d t t t t	 d t t t ƒ t t t	 ƒ t t t t	 ƒ k sÙt ‚ | t t | t t | t t	 ƒ t | t t	 d t t t ƒ t t t	 ƒ t t t t	 ƒ |  t t ƒ d ƒ | d t t ƒ d ƒ f t f k s{t ‚ t t t d ƒ t t } | | j t | ƒ t t	 ƒ t d | t d t	 t t	 ƒ t t d t	 ƒ t t t	 d ƒ d t t ƒ d f t f k s t ‚ t t t d ƒ t t t t t d ƒ } | | j t | ƒ t t	 ƒ d t d t	 | t d t	 d t t	 ƒ t d t d t	 ƒ t d t t	 ƒ d t t ƒ d t d ƒ d f t f k sòt ‚ | t t ƒ t t	 ƒ t t	 ƒ d t
 f t f k s,t ‚ | t d t ƒ t t	 ƒ t t	 ƒ t
 d f t f k skt ‚ | t t ƒ d t d t ƒ t t	 ƒ d	 t	 d
 d t
 f t f k s¸t ‚ | t t ƒ d t t d ƒ t t	 ƒ d t	 d t
 d f t f k st ‚ | t t d ƒ t t	 ƒ t t	 t t t	 ƒ d t f k sIt ‚ | t d t d ƒ t t	 ƒ t t	 t t t	 ƒ d t f k st ‚ | t t d t ƒ ƒ t t	 ƒ t t	 t t t	 ƒ d t f k sÙt ‚ | t t d d t ƒ ƒ t t	 ƒ t t	 t t t	 ƒ d t f k s&t ‚ | t t t ƒ ƒ t t	 ƒ t t	 t d ƒ d ƒ t t ƒ t	 t d ƒ d d f t f k st ‚ d  S(   Niÿÿÿÿ(   t   Maxt   MinRI   RX   i   i    i   i   i   i   i   i   (   iÿÿÿÿi    (   i    i   (   iÿÿÿÿi    (   i    i   (   RN   R`   Ra   R    R   RP   RF   t   nuR   RG   R   R   RO   t   betaR   t   rhot   absR$   R   R   R"   RH   RI   R%   RZ   R    R   R'   R(   R,   (   R`   Ra   R[   R\   t   mtR^   (    (    sD   lib/python2.7/site-packages/sympy/integrals/tests/test_transforms.pyt   test_mellin_transformY   sV    !.!-)H))3BUF .C'M#A>H&.U4:?MNCGIMc          C   s8  t  }  |  t t ƒ t d t t ƒ } | d d t f k sB t ‚ t | d d t ƒj t ƒ sh t ‚ |  t t ƒ d t d t t ƒ } | d d t f k s¨ t ‚ t | d d t ƒj t ƒ sÎ t ‚ |  t t ƒ t d d t t ƒ } | d d t f k st ‚ t | d d t ƒj t ƒ s4t ‚ d  S(   Ni   i    t   allow_hyperi   (   i    i   (   i    i   (   i    i   (	   R    R'   RF   RG   RP   RO   R)   t   hasR*   (   R[   Rf   (    (    sD   lib/python2.7/site-packages/sympy/integrals/tests/test_transforms.pyt   test_mellin_transform2›   s     &$&$c       	   C   s  d d l  m }  t } | t t d t t ƒ ƒ t t ƒ t t d t ƒ t t d t d ƒ t	 t ƒ d t
 d ƒ d f t f k s t ‚ | t t t ƒ ƒ t t t t ƒ ƒ t t ƒ d t t d t t
 d ƒ d ƒ t t d t t
 d ƒ d ƒ t t d t d ƒ t t d t d ƒ t	 t ƒ d t
 d ƒ d t
 d ƒ d f t f k skt ‚ | t t t ƒ ƒ t t t t ƒ ƒ t t ƒ d t t t d t ƒ t d t t
 d ƒ d ƒ t t d t t
 d ƒ d ƒ t t d t d ƒ t	 t ƒ d t
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 }	 | d d t ƒ}
 | d d t ƒ} t |  t ƒ t t ƒ t t ƒ t d t f t f k s§ t ‚ t t t ƒ t t t d t f ƒ j | ƒ j ƒ  |  t ƒ k sí t ‚ t | t t ƒ t t ƒ t t ƒ t t d | d | t ƒ d ƒ t f t f k sHt ‚ | t t t t ƒ |
 t d t t d |
 t f ƒ j | ƒ j d	 t ƒ ƒ ƒ | |
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 d
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 ƒ t | d ƒ j ƒ  | t | ƒ ƒ k sct ‚ t | t ƒ t t ƒ t d t d
 ƒ d
 t d t f k s§t ‚ t | t t ƒ t t ƒ | t t t t ƒ d t ƒ d | t ƒ t d ƒ k f k st ‚ t | d t ƒ t t ƒ t t d ƒ t d t f k sAt ‚ t | d
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 t t | ƒ j ƒ  t | ƒ | | ƒ k sÒt ‚ t t t d ƒ t t t ƒ j | ƒ t t ƒ |  t ƒ k st ‚ t t t t d ƒ t d
 t t ƒ j | ƒ j ƒ  | d
 t ƒ t t ƒ j |	 ƒ j | ƒ j ƒ  k s…t ‚ d  S(   Niÿÿÿÿ(
   t   E1R6   R`   R   t   lerchphiR   t   simplifyt   Sit   Cit   EiRH   RY   t   ut   polari    i   Rk   i   i   (   iÿÿÿÿi    (   iÿÿÿÿi    (   i    i   (   i    i   (    RN   Ro   R6   R`   R   Rp   R   Rq   Rr   Rs   Rt   RP   R    RF   RG   R   R   RO   R   RU   Rl   RH   R4   R%   R   R    R   R'   R2   R&   R   R   (   Ro   R6   R`   R   Rp   R   Rq   Rr   Rs   Rt   t   anegRu   (    (    sD   lib/python2.7/site-packages/sympy/integrals/tests/test_transforms.pyt   test_expint  sH    F=0C+.0KV=-DD>.,&c       
      sç  d d l  m }  m ‰ m } m } m } m ‰ m ‰  m } m	 } t
 } | t t ƒ t t d t f ƒ t t ƒ k sz t ‚ | t t ƒ t t t d f ƒ t d t ƒ k s³ t ‚ ˆ | t d t d d t t d t f ƒ ƒ t d d t d t ƒ d t k st ‚ | d t d d t t d ƒ t t t d ƒ d t t d ƒ d t k set ‚ | d t d d t t d ƒ t t t d ƒ d t t d ƒ d t k s¼t ‚ | t t ƒ t t d ƒ t t d t f ƒ t d t t ƒ t k s
t ‚ t d d t ƒ} | d t d d t t t ƒ d  t f ƒ j t | ƒ j |  ƒ j ƒ  |  | ƒ t d t | ƒ ƒ k sŒt ‚ t d	 d
 t ƒ\ } }	 | |	 t | t t | ƒ t t t d t f ƒ t |	 t | ƒ k sõt ‚ | t | |	 t |	 ƒ | t t t | t f ƒ t | t t |	 ƒ k sJt ‚ ‡  ‡ ‡ f d †  }
 t d d t d t ƒ} | d | t t t t d  f ƒ t | t t d ƒ k s¹t ‚ | d | t t t d  t f ƒ t | t d t ƒ k sút ‚ |
 | t t ƒ t t ƒ t t t ƒ t t d t f ƒ ƒ d t t d t d t ƒ k s_t ‚ |
 | t t ƒ t d t t ƒ t d t ƒ t t t d  f ƒ ƒ t d t d t t d ƒ k sÍt ‚ |
 | t t ƒ t t t ƒ t t ƒ t t d ƒ ƒ d t d t k st ‚ |
 | t t t t d |  t t ƒ t t ƒ t t t ƒ t d t ƒ t d t t ƒ t t t | t t ƒ d ƒ | d t t ƒ d ƒ f ƒ ƒ t t t t t t k sÜt ‚ ˆ | d t t ƒ t d t t ƒ t d t d t ƒ t t d t ƒ t d t t ƒ t t d t t ƒ d f ƒ ƒ d t t d ƒ t k s~t ‚ ˆ | d t d t t  t d t d t t ƒ t d t d t ƒ t d t t ƒ t t d t t ƒ d d f ƒ ƒ t  t d t d t t  d ƒ d t d t  d t d t t  d ƒ t  d t t  d t k slt ‚ ˆ | d t d t t t  t d t t t ƒ t t d t ƒ t t t d ƒ t t d t t ƒ d f ƒ ƒ t  t t d t t  d ƒ d t k st ‚ | d t d t t d t f ƒ t! t ƒ d t d t ƒ k s^t ‚ | | d t d t t t d f ƒ d t ƒt! t ƒ d t t d ƒ k s²t ‚ | t t |  t t ƒ t t d ƒ t! t d ƒ k sït ‚ | t t |  t t d ƒ t t d ƒ t! t d d ƒ k s4	t ‚ | t t |  d t t ƒ t t t" d ƒ d d f ƒ t! t t ƒ d ƒ k sŒ	t ‚ | t t |  t t ƒ t t d ƒ t! d d t ƒ k sÍ	t ‚ ‡  f d †  } | | | t t t# t t ƒ t t d ƒ ƒ ƒ t! d t ƒ t d t ƒ t! t d ƒ t t d ƒ t! t ƒ t t d ƒ t! d d t ƒ t t d ƒ t! t d ƒ t t d ƒ g k s§
t ‚ | | t | t t ƒ t t t d ƒ ƒ t! d t d ƒ t d t ƒ t! d d t ƒ t t d ƒ t! t ƒ t t d ƒ t! d d t ƒ t t d ƒ t! t d ƒ t t d ƒ g k svt ‚ | t t t" d ƒ d ƒ t t ƒ t t t t" d ƒ d d f ƒ t$ t t ƒ ƒ k s×t ‚ ˆ | t t d t ƒ t t d t d ƒ t t t t ƒ d t" d ƒ d f ƒ ƒ t% t d t t ƒ ƒ k sPt ‚ ˆ | d t t t" d ƒ d d t ƒ t t t d d ƒ t d t t d ƒ t d d t t ƒ t t t t ƒ d d t" d ƒ d f ƒ ƒ |  t t ƒ ƒ t% t t t ƒ ƒ k st ‚ ˆ | d t t t d t ƒ t t" d ƒ d d t ƒ t t" d ƒ d t t d ƒ t d d t t ƒ t t t t ƒ d t" d ƒ d f ƒ ƒ | t t ƒ ƒ t% t t t ƒ ƒ k sàt ‚ ˆ | t t t ƒ t t" d ƒ d t ƒ t t ƒ t d t ƒ t d t t ƒ t t t t ƒ t" d ƒ d f ƒ ƒ t% t t t ƒ ƒ d k s}t ‚ ˆ | t t ƒ t t" d ƒ d t ƒ t t ƒ t d t t ƒ t d t t ƒ t t d t" d ƒ d f ƒ ƒ t% t t t ƒ ƒ t% t t t ƒ ƒ k s#t ‚ ˆ | d t t d t d ƒ t t d t  d t ƒ t t d t  d t d ƒ t t d t  d t d ƒ t t d t  d t d ƒ t t t t ƒ t t  ƒ d t" d ƒ d f ƒ ƒ t% t t t ƒ ƒ t% t  t t ƒ ƒ k st ‚ ˆ | d d t | t t d t t  d t t ƒ t d t d ƒ t t d t  d t ƒ t t d t  d t ƒ t t t d t  d t d ƒ t t d t  d t d ƒ t t | t t ƒ d t t  ƒ d t t ƒ d t t  ƒ d ƒ t" d ƒ d f ƒ ƒ t% t t t ƒ ƒ t% t  t t ƒ ƒ t% t  t t ƒ ƒ | t t  ƒ |  t t  ƒ k s–t ‚ | t | t t ƒ t t d t" d ƒ d f ƒ t t ƒ t d k sãt ‚ d  S(   Niÿÿÿÿ(	   R$   Rq   R`   Ra   Rl   t   powsimpR2   R   t   coti    i   i   i   t   rt   reals   a bRX   c            s.   ˆ ˆ t  |  d t ƒd t ƒƒ j ˆ  t ƒ S(   Nt   deept   force(   R7   t   FalseRP   t   replaceR   (   R^   (   R2   Ry   Rq   (    sD   lib/python2.7/site-packages/sympy/integrals/tests/test_transforms.pyt	   simp_pows[  s    Rb   t   finitei   i   i   R~   i   iþÿÿÿc            sV   d d l  m } m } m } | | | |  d t ƒd t d t ƒd t ƒj ˆ  t ƒ S(   Niÿÿÿÿ(   Rl   t
   logcombineRy   R~   R}   (   RN   Rl   Rƒ   Ry   RP   R€   R   (   R^   Rl   Rƒ   Ry   (   R2   (    sD   lib/python2.7/site-packages/sympy/integrals/tests/test_transforms.pyt   mysimp†  s    $(   iÿÿÿÿN(   Ni   (   i    N(   iÿÿÿÿi    (   iþÿÿÿi    (   i    i   (   iÿÿÿÿi    (   i    i   (&   RN   R$   Rq   R`   Ra   Rl   Ry   R2   R   Rz   R   R   RG   RF   R   R   RO   R   t   NoneR   RP   RZ   RU   R   Rc   Rd   RK   RJ   R   R   R%   RH   RI   R'   R    R(   R,   R.   (   R$   R`   Ra   Rl   R   Rz   t   IMTR{   t   _at   _bR   Rb   R„   (    (   R2   Ry   Rq   sD   lib/python2.7/site-packages/sympy/integrals/tests/test_transforms.pyt   test_inverse_mellin_transform<  s¶    @49.-99N.*QUBA<)/)6]8#[ !yot1G-'=EXA07>&*?@&FW"e..k*.O&"O23[41x@Tbc          C   s§  d d l  m }  m } t } t d d t ƒ\ } } } t d ƒ } t d ƒ } t d ƒ } t | | ƒ | | ƒ t | | ƒ | | ƒ k s‘ t	 ‚ t
 | | ƒ | | d d	 ƒt | | ƒ | | d	 ƒ k sÐ t	 ‚ t d
 d t ƒ}	 | t | ƒ | |	 ƒ d  d |	 d d f k st	 ‚ | | | | t | | | ƒ t | | ƒ | t ƒ t | | d t | t ƒ t | d ƒ | t f k s“t	 ‚ | | | | t ƒ t | d t | d ƒ d	 t f k sÕt	 ‚ | t | ƒ | t ƒ d t d	 t f k st	 ‚ | t | | ƒ | t ƒ t | t ƒ t d	 t f k sFt	 ‚ | d t | | ƒ | t ƒ | t | t d	 t f k sˆt	 ‚ | t d | ƒ d t | | ƒ t | ƒ d | t d t ƒt | ƒ t d d k sêt	 ‚ | t | ƒ | t ƒ d  d t d d f k s t	 ‚ | t d | ƒ | t ƒ d  d t d d f k sZt	 ‚ | t | | ƒ | t ƒ d  d t | | f k s”t	 ‚ | t | | ƒ | t ƒ t | t ƒ t t d d	 t f k sÛt	 ‚ | t | ƒ | t ƒ t t d ƒ t t d d ƒ t d	 t f k s(t	 ‚ | t | | ƒ | t ƒ | | d t d d	 t f k sit	 ‚ | t | | ƒ | t ƒ t | d t d d	 t f k sªt	 ‚ | t | | ƒ t | | ƒ | t ƒ | | d | t d | t f k sÿt	 ‚ | t | | ƒ t | | ƒ | t ƒ | t | d | t d | t f k sXt	 ‚ | t d	 | ƒ | t ƒ d t d t d ƒ d	 t f k sšt	 ‚ | t d | ƒ | t ƒ d d t d d t d ƒ d	 t f k sät	 ‚ | t | ƒ t | ƒ | t ƒ d  t d t d d t d t f t d t d d d t f g k sVt	 ‚ t |  | ƒ | t ƒ t t d d t ƒ |  t t ƒ t t d d t ƒ d t t d d t ƒ | t t ƒ t t d d t ƒ d t d	 t f k s t	 ‚ t | | ƒ | t ƒ d t t d d t ƒ | t t ƒ d t t d d t ƒ |  t t ƒ t d ƒ t t d d t t d ƒ d t d	 t f k s©t	 ‚ t d t d ƒ t d	 ƒ t t t t t ƒ ƒ ƒ t t ƒ d k  @}
 | t t | ƒ | t | ƒ g | t | ƒ t | ƒ g g ƒ | t ƒ t d t d d t f t d d d	 t f g t d d d	 t f d t d d t f g g ƒ k s£t	 ‚ d  S(   Niÿÿÿÿ(   t   fresnelst   fresnelcs   a b cRX   t   tt   wRM   t   planei    RG   i   i   t   nocondsi   iþÿÿÿ(   RN   RŠ   R‹   R   R   RP   R   R5   R   RO   R   R   R   R   RG   R   R'   R+   R,   R-   R$   R   R.   R%   R   R   R=   R    R!   R>   RD   (   RŠ   R‹   t   LTRH   RI   RJ   RŒ   R   RM   t   spost   cond(    (    sD   lib/python2.7/site-packages/sympy/integrals/tests/test_transforms.pyt   test_laplace_transformÄ  sX    6<68CB1@B@"6::GMAAU(1BJ#"-•”6I+c          C   sƒ  t  }  |  t t ƒ t t ƒ d t d d d t f k s? t ‚ |  t t ƒ t t ƒ t t d d d t f k sx t ‚ |  t t d ƒ t t ƒ t t d t d ƒ d t d ƒ t d t d d d t f k sÞ t ‚ |  t t ƒ t t ƒ t t ƒ d t d d d t t d d ƒ f k s.t ‚ |  t	 t d ƒ t t ƒ t t	 d ƒ t
 d ƒ t d d d t f k st ‚ d  S(   Ni   i   i   i   iýÿÿÿi   i    (   R   R;   RF   RG   RP   RO   R<   R   R=   R   R$   (   R   (    (    sD   lib/python2.7/site-packages/sympy/integrals/tests/test_transforms.pyt   test_issue_8368_7173  s    99M1c             sü  d d l  m }  m } m } m } m } m ‰  t } t d d t	 d t	 ƒ\ } } } t d ƒ }	 ‡  f d †  }
 | d t
 t
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 d
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 | t
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 t d	 ƒ t d d g d d	 g g ƒ j ƒ  t
 |	 ƒ t t |	 ƒ t |	 ƒ d g d t d	 |	 ƒ t |	 ƒ g g ƒ k søt ‚ d  S(   Niÿÿÿÿ(   R;   R<   R.   R0   Rq   t   factor_termss   a b cRX   R‚   RŒ   c            s   ˆ  t  |  ƒ ƒ j t ƒ S(   N(   R7   RU   R$   (   R^   (   R•   (    sD   lib/python2.7/site-packages/sympy/integrals/tests/test_transforms.pyt   simp_hyp   s    i   i   i   i   i   i    (   RN   R;   R<   R.   R0   Rq   R•   R   R   RP   RG   R   RO   R   R$   R   R   R%   RU   R,   RE   RD   t   inv(   R;   R<   R.   R0   Rq   t   ILTRH   RI   RJ   RŒ   R–   (    (   R•   sD   lib/python2.7/site-packages/sympy/integrals/tests/test_transforms.pyt   test_inverse_laplace_transform  s>    .!(087NBBHHUV"3,*B&?&FF;c          C   sr  d d l  m }  t } t d ƒ } | d t | ƒ d |  | ƒ k sJ t ‚ | d t d t ƒ d t d t ƒ t | ƒ d |  | d ƒ d |  | d ƒ k s¨ t ‚ t t d ƒ d ƒ } | | t d	 t ƒ t | ƒ | |  | d ƒ k sø t ‚ | t d t ƒ t | ƒ |  | d ƒ k s*t ‚ t	 d
 d t
 ƒ} | t | t ƒ t | ƒ |  | | ƒ k snt ‚ d  S(   Niÿÿÿÿ(   t
   DiracDeltaRŒ   i   i   i   iùÿÿÿi   iýÿÿÿR{   R|   (   RN   Rš   R   R   RG   RO   R   R   R$   R   RP   (   Rš   R˜   RŒ   RH   R{   (    (    sD   lib/python2.7/site-packages/sympy/integrals/tests/test_transforms.pyt$   test_inverse_laplace_transform_deltaJ  s    (//:2c    	      C   sÀ  d d l  m }  m } m } m } t } t d ƒ } t d d t ƒ} | t	 | t
 ƒ t
 | d t ƒ|  | | ƒ t f k s„ t ‚ t d ƒ } | t	 | t
 ƒ t
 | d t ƒ|  | | ƒ | | | ƒ d ƒ f k sÝ t ‚ xˆ t d d t ƒt d d	 t d
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 | d t ƒ} t | t ƒ rI| d n | } | j |  k st ‚ qW| d t
 t	 | t
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 t
 | d t ƒ| | ƒ | | | ƒ t f k s¼t ‚ d  S(   Niÿÿÿÿ(   Rš   t   Eqt   imR   RŒ   R{   R|   R   t   zi    t	   imaginaryt   zeroi   (   RN   Rš   Rœ   R   R   R   R   R   RP   R   RG   R   RO   t
   isinstancet   tupleRk   (	   Rš   Rœ   R   R   R˜   RŒ   R{   Rž   RM   (    (    sD   lib/python2.7/site-packages/sympy/integrals/tests/test_transforms.pyt)   test_inverse_laplace_transform_delta_condX  s    ">."+c    
         s•  d d l  m ‰ m ‰  m ‰ m }  m ‰ t } t } ‡  ‡ ‡ ‡ f d †  } d „  } t d d t	 ƒ} t
 d ƒ } t d d	 t	 ƒ} t d
 d	 t	 ƒ} t d d	 t	 ƒ}	 t | t ƒ t | ƒ t | t ƒ t | ƒ k sß t ‚ t | | ƒ | t ƒ t | | ƒ | t ƒ k st ‚ | | t d t d | t ƒ ƒ t | ƒ ƒ | | | ƒ | k s_t ‚ | | t d t | t ƒ ƒ d t | t ƒ t | ƒ ƒ | | | ƒ d | k s»t ‚ |  | t | t ƒ t t ƒ t | ƒ d t ƒd | d t t | k st ‚ | d | d t t t t |	 d t ƒt | |	 ƒ t	 f k sWt ‚ | d | d t t t t |	 d t ƒd t	 f k s–t ‚ | d | d t t t t t d d t	 ƒd t ƒd t	 f k sàt ‚ |  | t t | t ƒ t t ƒ t | ƒ d t ƒd | d t t | d k s;t ‚ | t | t ƒ t | t ƒ t t ƒ t | ƒ | | d | d t t | d k sœt ‚ | t | t d ƒ t | ƒ t t ƒ t t d | d | ƒ t | ƒ k sôt ‚ | t t | ƒ t t | d | ƒ | t ƒ t | t d ƒ k sBt ‚ | t | t t ƒ ƒ t | ƒ d | | d d t d | d k s‘t ‚ d  S(   Niÿÿÿÿ(   Rq   Rl   t   expand_complext   factort   expand_trigc            s   ˆ ˆ ˆ ˆ  |  ƒ ƒ ƒ ƒ S(   N(    (   RF   (   Rl   R¤   R¦   Rq   (    sD   lib/python2.7/site-packages/sympy/integrals/tests/test_transforms.pyt   simpp  s    c         S   s   t  t |  ƒ t |  S(   N(   R$   R   (   RF   (    (    sD   lib/python2.7/site-packages/sympy/integrals/tests/test_transforms.pyt   sincs  s    t   kR|   RM   RH   RX   RI   t   poski   i   t	   extensionR   i    RY   i   (   RN   Rq   Rl   R¤   R¥   R¦   R   R   R   RP   R5   RF   R   RO   R   R   Re   R   R&   R   R   R$   R%   (
   R¥   t   FTt   IFTR§   R¨   R©   RM   RH   RI   Rª   (    (   Rl   R¤   R¦   Rq   sD   lib/python2.7/site-packages/sympy/integrals/tests/test_transforms.pyt   test_fourier_transformk  s<    (	63J\0##&$/4'2/XNc          C   sß  d d l  m }  t d ƒ } t d ƒ } t d ƒ } t d ƒ } t | | ƒ | | ƒ t | | ƒ | | ƒ k sv t ‚ t | | ƒ | | ƒ t | | ƒ | | ƒ k s¬ t ‚ t d t	 | ƒ | | ƒ d t	 | ƒ k sÞ t ‚ t d t	 | ƒ | | ƒ d t	 | ƒ k st ‚ t d t	 | ƒ d | | ƒ d	 t	 | ƒ k sFt ‚ t | | | | ƒ d	 | t
 d ƒ d	 | | d t | d	 d ƒ t | d d	 ƒ k s­t ‚ t d	 | t
 d ƒ d	 | | d t | d	 d ƒ t | d	 t
 d ƒ d	 ƒ | | ƒ | | k st ‚ t t | | ƒ | | ƒ t	 d	 ƒ | t	 t ƒ | d	 | d	 k skt ‚ t t	 d	 ƒ | t	 t ƒ | d	 | d	 | | ƒ t | | ƒ k s¸t ‚ t t | ƒ | | | ƒ t	 d	 ƒ t	 t ƒ t | d	 ƒ d	 |  d
 k st ‚ t | t | | d	 ƒ | | ƒ t	 d	 ƒ | t | d	 d
 | ƒ d
 | t
 d ƒ d	 k sst ‚ t t	 d	 ƒ | t | d	 d
 | ƒ d
 | t
 d ƒ d	 | | ƒ | t | | d	 ƒ k sÛt ‚ d  S(   Niÿÿÿÿ(   R+   RŒ   R   RH   RM   i   i   i   i   (   RN   R+   R   R5   R   R   RO   R   R   R%   R    R   R   R   R'   (   R+   RŒ   R   RH   RM   (    (    sD   lib/python2.7/site-packages/sympy/integrals/tests/test_transforms.pyt   test_sine_transform£  s2    63226SnJJPec          C   sw  d d l  m }  m } t d ƒ } t d ƒ } t d ƒ } t d ƒ } t | | ƒ | | ƒ t | | ƒ | | ƒ k s| t ‚ t | | ƒ | | ƒ t	 | | ƒ | | ƒ k s² t ‚ t d t
 | ƒ | | ƒ d t
 | ƒ k sä t ‚ t d t
 | ƒ | | ƒ d t
 | ƒ k st ‚ t d | d | d | | ƒ t
 d ƒ t
 t ƒ t | | ƒ d | k skt ‚ t | | | | ƒ d | t d ƒ d | | d t | d d ƒ t | d ƒ k sÎt ‚ t d | t d ƒ d | | d t | d t d ƒ d ƒ t | d ƒ | | ƒ | | k s;t ‚ t t | | ƒ | | ƒ t
 d ƒ | t
 t ƒ | d | d k sˆt ‚ t t
 d ƒ | t
 t ƒ | d | d | | ƒ t | | ƒ k sÕt ‚ t t | t
 | ƒ ƒ t | t
 | ƒ ƒ | | ƒ | t | d d | ƒ d | t d	 ƒ d k sEt ‚ t d | | | | ƒ t
 d ƒ d
 |  | | ƒ t t | | ƒ d t | | ƒ | | | ƒ t
 t ƒ k s¿t ‚ t t
 d ƒ t t d ƒ d d f d f t d ƒ d d d f t d ƒ d f f | d | d d ƒ d t | | ƒ d | | k sOt ‚ t d t
 | d | d ƒ | | ƒ t
 d ƒ t t d ƒ d f d f d t d ƒ d f f | d | d d ƒ d t
 t ƒ k sÝt ‚ t t
 d ƒ t t d ƒ d f d f d t d ƒ d f f | d | d d ƒ d t
 t ƒ | | ƒ d | t
 | d | d d ƒ k sst ‚ d  S(   Niÿÿÿÿ(   Rr   Rs   RŒ   R   RH   RM   i   i   i   iþÿÿÿi    i   (    (    (   i    i    (    (   i    i    (   RN   Rr   Rs   R   R5   R   R   RO   R	   R   R%   R   R   R    R   R   R$   R*   (   Rr   Rs   RŒ   R   RH   RM   (    (    sD   lib/python2.7/site-packages/sympy/integrals/tests/test_transforms.pyt   test_cosine_transformÈ  s:    6322O]jJJ Pc%ic          C   sp  d d l  m }  m } m } t d ƒ } t d ƒ } t d ƒ } t d ƒ } t d ƒ } t d | | | d	 ƒ d | k s t ‚ t d | | | d	 ƒ d | k sª t ‚ t d | | | | d	 ƒ d
 | d | | d
 |  | d
 d ƒ |  | d
 ƒ k s	t ‚ t d
 | d | | d
 |  | d
 d ƒ |  | d
 ƒ | | d	 ƒ | | k set ‚ t d | | | | | ƒ d
 d
 | | | d
 |  | d
 | d
 d ƒ |  | d
 | d
 ƒ k sÔt ‚ t d
 | d | | d
 |  | d
 | d
 d ƒ |  | d
 | d
 ƒ | | | ƒ | | k s@t ‚ t | | | | | ƒ | | | ƒ d
 | d | | | d | d
 | d
 d | t	 d ƒ d
 |  | t	 d ƒ d
 ƒ | t
 ƒ k sÖt ‚ t d
 | d | | | d | d
 | d
 d | t	 d ƒ d
 |  | t	 d ƒ d
 ƒ | t
 ƒ | | | ƒ | | | | | ƒ k slt ‚ d  S(   Niÿÿÿÿ(   R   R%   R   R{   R©   Rb   t   mRH   i   i    i   i   (   RN   R   R%   R   R   R   R
   RO   R   R    R   (   R   R%   R   R{   R©   Rb   R±   RH   (    (    sD   lib/python2.7/site-packages/sympy/integrals/tests/test_transforms.pyt   test_hankel_transformò  s(    ))\YUi%qc           C   s*   t  d d t t t ƒ d  k s& t ‚ d  S(   Ni   (   R    RF   RG   R…   RO   (    (    (    sD   lib/python2.7/site-packages/sympy/integrals/tests/test_transforms.pyt   test_issue_7181  s    c              s˜   t  t d d d t  d t d t d t  d ƒ t t t t ƒ t t t t d t  d ƒ d ƒ ƒ t t ƒ ‰  t	 t
 ‡  f d †  ƒ d  S(   Ni   i   i   c              s*   t  ˆ  t t d t f i t d 6t d 6 S(   Niÿÿÿÿt
   as_meijergt   needeval(   R   RG   RF   R   RP   (    (   t   F(    sD   lib/python2.7/site-packages/sympy/integrals/tests/test_transforms.pyt   <lambda>   s    (   RH   RG   R%   R   R&   R   R$   R:   R   RC   R   (    (    (   R¶   sD   lib/python2.7/site-packages/sympy/integrals/tests/test_transforms.pyt   test_issue_8882  s    ~c          C   s  d d l  m }  t d ƒ \ } } } } t t t t ƒ t t t ƒ t t ƒ } |  | ƒ \ } } | | t	 t ƒ f | t
 | ƒ f | t d f | t
 | t ƒ f g k s´ t ‚ | t d t d t d d | | k | | k  B| | k | | k  B@g k st ‚ d  S(   Niÿÿÿÿ(   t   cses   x:4i   iüÿÿÿi    (   RN   R¹   R   R   R;   RH   RF   R<   RG   R   R!   R   RO   (   R¹   t   x0t   x1t   x2t   x3t   ansR{   t   e(    (    sD   lib/python2.7/site-packages/sympy/integrals/tests/test_transforms.pyt   test_issue_7173%  s    *"c          C   s  d d l  m }  t d d t ƒ\ } } } t d d t ƒ} |  t d | t d | t | t | ƒ ƒ } | t t | t t	 d d	 | | | d ƒ d ƒ t
 t d
 | | | d ƒ ƒ | ƒ t | t t	 d d	 | | | d ƒ d ƒ t
 t d
 | | | d ƒ ƒ d | ƒ t | t t	 d d	 | | | d ƒ d ƒ t
 t d
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 | | | d ƒ ƒ d | ƒ t | | t t	 d d	 | | | d ƒ d ƒ t
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 d	 | | | d ƒ k s	t ‚ d  S(   Niÿÿÿÿ(   Rq   s   a b cRX   RŒ   i   i   i    iüÿÿÿi   (   RN   Rq   R   RP   R   RG   R&   R   R   R?   R%   R!   R$   RO   (   Rq   RH   RI   RJ   RŒ   t   ft(    (    sD   lib/python2.7/site-packages/sympy/integrals/tests/test_transforms.pyt   test_issue_85145  s    0c          C   sR   t  d d t ƒ\ }  } t t |  ƒ |  | ƒ t t |  ƒ |  | ƒ k sN t ‚ d  S(   Ns   x yR|   (   R   RP   R   R   R   RO   (   RF   t   y(    (    sD   lib/python2.7/site-packages/sympy/integrals/tests/test_transforms.pyt   test_issue_12591C  s    c          C   s   t  d d t ƒ}  t d t t |  t t ƒ t t t |  t ƒ t d |  t t t t	 d ƒ ƒ d t f k s{ t
 ‚ d  S(   NRI   RY   i   i   i    (   R   RP   R   R&   RF   RG   R   R6   R2   R   RO   (   RI   (    (    sD   lib/python2.7/site-packages/sympy/integrals/tests/test_transforms.pyt   test_issue_14692H  s    N(l   t   sympy.integrals.transformsR    R   R   R   R   R   R   R   R   R	   R
   R   R   R   R   R   R   R   R   R   R   RN   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/   R0   R1   R2   R3   R4   R5   R6   R7   R8   R9   R:   R;   R<   R=   R>   R?   t   sympy.utilities.pytestR@   RA   RB   RC   t   sympy.matricesRD   RE   t	   sympy.abcRF   RG   RH   RI   RJ   RK   Rb   Rc   Rd   RQ   RS   RW   R_   Rg   Rj   Rn   Rx   R‰   R“   R”   R™   R›   R£   R®   R¯   R°   R²   R³   R¸   RÀ   RÂ   RÄ   RÅ   (    (    (    sD   lib/python2.7/site-packages/sympy/integrals/tests/test_transforms.pyt   <module>   s>   ˆ	ÿ ".				Ba/ˆI		0			8	%	*						