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
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 „  Z. d „  Z/ d „  Z0 d „  Z1 d „  Z2 d „  Z3 d „  Z4 d „  Z5 d „  Z6 d „  Z7 d „  Z8 d „  Z9 d „  Z: d „  Z; d „  Z< d „  Z= d „  Z> d „  Z? d „  Z@ d „  ZA d „  ZB d „  ZC d  „  ZD d! „  ZE d" „  ZF d# „  ZG d$ „  ZH d% „  ZI d& „  ZJ d' „  ZK d( „  ZL d) „  ZM d* „  ZN d+ „  ZO d, „  ZP d- „  ZQ d. „  ZR d/ „  ZS d0 „  ZT d1 „  ZU d2 S(3   iÿÿÿÿ($   t   symbolst   Symbolt   sinht   nant   oot   zoot   pit   asinht   acosht   logt   sqrtt   cotht   It   cott   Et   tanht   tant   cosht   cost   St   sint   Rationalt   atanht   acotht   Integert   Ot   expt   secht   sect   cscht   asecht   acscht   acost   asint
   expand_mult   AccumBounds(   t   raisesc          C   sþ  t  d ƒ \ }  } t d d t ƒ} t t ƒ t k s< t ‚ t t ƒ t k sT t ‚ t t ƒ t k sl t ‚ t t ƒ t k s† t ‚ t d ƒ d k sž t ‚ t d ƒ t d ƒ k s¼ t ‚ t d ƒ t d ƒ k sÛ t ‚ t |  ƒ t |  ƒ k sù t ‚ t |  ƒ t |  ƒ k st ‚ t t ƒ t t ƒ k s7t ‚ t t ƒ t t ƒ k sWt ‚ t d t	 ƒ t d t	 ƒ k s}t ‚ t d t	 ƒ t d t	 ƒ k s¤t ‚ t t t
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 d ƒ t
 k s…t ‚ t t t
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 k sút ‚ d  S(   Ns   x,yt   kt   integeri    i   iÿÿÿÿi   i   iþÿÿÿiýÿÿÿi
   iI   i   ig   i   i   i   i   i   iûÿÿÿii   lE                                                                                                                                            lE                                                                                                                                            lE                                                                                                                                            l»ÿÿÿ                                                                                                                                         lE                                                                                                                                            l             Bgòm‹9luêZnD¤$]'tT l                 koõP³+!k·{3…5UWoÄ ½$ŽXÿ\Ñ,‹yÛ(   R    R   t   TrueR   R   t   AssertionErrorR   R   R   R   R   R   t   HalfR
   R   (   t   xt   yR%   (    (    sO   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_hyperbolic.pyt	   test_sinh	   sT      &'  $$ "$%161356'),,.0.& $c          C   su   t  d ƒ }  t |  ƒ j |  d d ƒ |  |  d d |  d d |  d d	 |  d
 d t |  d ƒ k sq t ‚ d  S(   NR*   i    i
   i   i   i   ix   i   i°  i	   i€‰ (   R   R   t   seriesR   R(   (   R*   (    (    sO   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_hyperbolic.pyt   test_sinh_seriesH   s    c          C   s­  t  d ƒ \ }  } t d d t ƒ} t t ƒ t k s< t ‚ t t ƒ t k sT t ‚ t t ƒ t k sl t ‚ t t ƒ t k s… t ‚ t d ƒ d k s t ‚ t d ƒ t d ƒ k s» t ‚ t d ƒ t d ƒ k sÙ t ‚ t |  ƒ t |  ƒ k s÷ t ‚ t |  ƒ t |  ƒ k st ‚ t t t	 ƒ t
 t ƒ k s8t ‚ t t t	 ƒ t
 t ƒ k s[t ‚ t d t ƒ t d t ƒ k st ‚ t d t ƒ t d t ƒ k s§t ‚ t t t	 d ƒ d k sÇt ‚ t t t	 d ƒ d k sèt ‚ t d	 d d t t	 d ƒ d k st ‚ t d d d t t	 d ƒ d k s@t ‚ t t t	 ƒ d k s\t ‚ t t t	 ƒ d k syt ‚ t d t t	 ƒ d k s™t ‚ t d t t	 ƒ d k s¹t ‚ t t t	 d ƒ t j k sÜt ‚ t d t t	 d ƒ t j k st ‚ t t t	 d ƒ t j t d ƒ k s1t ‚ t t t	 d ƒ t j t d ƒ k s_t ‚ t d t t	 d ƒ t j t d ƒ k s‘t ‚ t d	 t t	 d ƒ t j t d ƒ k sÃt ‚ t t t	 d ƒ t j t d ƒ k sðt ‚ t t t	 d ƒ t j t d ƒ k st ‚ t d t t	 d ƒ t j t d ƒ k sPt ‚ t d t t	 d ƒ t j t d ƒ k s‚t ‚ t t t	 d ƒ t
 t d ƒ k s¬t ‚ t t t	 d ƒ t
 t d ƒ k s×t ‚ t d d t	 ƒ t d d t	 ƒ k st ‚ t |  t	 ƒ t
 |  ƒ k s't ‚ t | t t	 ƒ t
 | t ƒ k sQt ‚ t d | t t	 ƒ t
 d | t ƒ k sƒt ‚ t | t ƒ t | t ƒ k s©t ‚ d  S(   Ns   x,yR%   R&   i    i   iÿÿÿÿi   i   iýÿÿÿi
   iI   i   ig   i   i   i   iþÿÿÿi   i   i   iûÿÿÿii   i   lE                                                                                                                                            lE                                                                                                                                            lE                                                                                                                                            l»ÿÿÿ                                                                                                                                         lE                                                                                                                                            l             Bgòm‹9luêZnD¤$]'tT l                 koõP³+!k·{3…5UWoÄ ½$ŽXÿ\Ñ,‹yÛ(   R    R   R'   R   R   R(   R   R   R   R   R   R   R   R)   R
   (   R*   R+   R%   (    (    sO   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_hyperbolic.pyt	   test_coshN   sP    "#&& !,,  #(-.22-.22*+."*2c          C   su   t  d ƒ }  t |  ƒ j |  d d ƒ d |  d d |  d d |  d d	 |  d
 d t |  d ƒ k sq t ‚ d  S(   NR*   i    i
   i   i   i   i   i   iÐ  i   i€  (   R   R   R-   R   R(   (   R*   (    (    sO   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_hyperbolic.pyt   test_cosh_series‹   s    c          C   sò  t  d ƒ \ }  } t d d t ƒ} t t ƒ t k s< t ‚ t t ƒ t k sT t ‚ t t ƒ d k sl t ‚ t t ƒ d k s… t ‚ t d ƒ d k s t ‚ t d ƒ t d ƒ k s» t ‚ t d ƒ t d ƒ k sÚ t ‚ t |  ƒ t |  ƒ k sø t ‚ t |  ƒ t |  ƒ k st ‚ t t ƒ t t ƒ k s6t ‚ t t ƒ t t ƒ k sVt ‚ t d t	 ƒ t d t	 ƒ k s|t ‚ t d t	 ƒ t d t	 ƒ k s£t ‚ t t t
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 d ƒ t
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 d ƒ t
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 t t
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 d ƒ t
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 k s t ‚ t d d t
 ƒ t d d t
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 ƒ t |  ƒ t
 k stt ‚ t | t t
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 ƒ d k s¸t ‚ t | t t
 d ƒ t | t d ƒ t
 k sît ‚ d  S(   Ns   x,yR%   R&   i   iÿÿÿÿi    i   i   iþÿÿÿiýÿÿÿi
   iI   i   ig   i   i   i   i   i   iûÿÿÿii   lE                                                                                                                                            lE                                                                                                                                            lE                                                                                                                                            l»ÿÿÿ                                                                                                                                         lE                                                                                                                                            l             Bgòm‹9luêZnD¤$]'tT l                 koõP³+!k·{3…5UWoÄ ½$ŽXÿ\Ñ,‹yÛ(   R    R   R'   R   R   R(   R   R   R   R   R   R
   R   (   R*   R+   R%   (    (    sO   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_hyperbolic.pyt	   test_tanh‘   sT      &'  $$.066*. "$$*,...0.& $c          C   s   t  d ƒ }  t |  ƒ j |  d d ƒ |  |  d d d |  d d d |  d	 d
 d |  d d t |  d ƒ k s} t ‚ d  S(   NR*   i    i
   i   i   i   i   i   i   i;  i>   i	   i  (   R   R   R-   R   R(   (   R*   (    (    sO   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_hyperbolic.pyt   test_tanh_seriesÐ   s    c          C   s¹  t  d ƒ \ }  } t d d t ƒ} t t ƒ t k s< t ‚ t t ƒ t k sT t ‚ t t ƒ d k sl t ‚ t t ƒ d k s… t ‚ t d ƒ t d ƒ k s£ t ‚ t d ƒ t k s» t ‚ t d ƒ t d ƒ k sÙ t ‚ t d ƒ t d ƒ k sø t ‚ t |  ƒ t |  ƒ k st ‚ t |  ƒ t |  ƒ k s6t ‚ t t t	 ƒ t	 t
 t ƒ k s]t ‚ t t t	 ƒ t
 t ƒ t	 k s„t ‚ t d t ƒ t d t ƒ k sªt ‚ t d t ƒ t d t ƒ k sÑt ‚ t t t	 ƒ t	 t
 t ƒ k søt ‚ t t t	 ƒ t	 t
 t ƒ k st ‚ t d t t	 ƒ t	 t
 d t ƒ k sNt ‚ t d	 t t	 ƒ t	 t
 d t ƒ k s|t ‚ t d
 d t t	 ƒ t	 t
 d d t ƒ k s²t ‚ t d d t t	 ƒ t	 t
 d d t ƒ k sét ‚ t t t	 d ƒ d k s	t ‚ t t t	 d ƒ d k s*t ‚ t d t t	 d ƒ d k sNt ‚ t d t t	 d ƒ d k srt ‚ t t t	 d ƒ t	 t d ƒ k st ‚ t d	 t t	 d ƒ t	 t d ƒ k sÌt ‚ t t t	 d ƒ t	 k sít ‚ t t t	 d ƒ t	 k st ‚ t d t t	 d ƒ t	 k s3t ‚ t d
 t t	 d ƒ t	 k sXt ‚ t t t	 d ƒ t d ƒ t	 k sƒt ‚ t t t	 d ƒ t d ƒ t	 k s®t ‚ t d t t	 d ƒ t d ƒ t	 k sÝt ‚ t d t t	 d ƒ t d ƒ t	 k st ‚ t t t	 d ƒ t
 t d ƒ t	 k s;t ‚ t t t	 d ƒ t
 t d ƒ t	 k sjt ‚ t d d t	 ƒ t d d t	 ƒ k s˜t ‚ t |  t	 ƒ t
 |  ƒ t	 k s¿t ‚ t | t t	 ƒ t
 | t ƒ t	 k sît ‚ t d | t t	 ƒ t
 d | t ƒ t	 k s%t ‚ t | t t	 ƒ t
 | t ƒ t	 k sTt ‚ t t t d ƒ ƒ ƒ t t t d ƒ ƒ ƒ k s‹t ‚ t d t	 t d ƒ t d ƒ k sµt ‚ d  S(   Ns   x,yR%   R&   i   iÿÿÿÿi    i   i   iþÿÿÿiýÿÿÿi
   iI   i   i   ig   i   i   i   i   iûÿÿÿii   lE                                                                                                                                            lE                                                                                                                                            lE                                                                                                                                            l»ÿÿÿ                                                                                                                                         lE                                                                                                                                            l             Bgòm‹9luêZnD¤$]'tT l             Bgòm‹9luêZnD¤$]'tT l                 koõP³+!k·{3…5UWoÄ ½$ŽXÿ\Ñ,‹yÛl                 koõP³+!k·{3…5UWoÄ ½$ŽXÿ\Ñ,‹yÛ(   R    R   R'   R   R   R(   R   R   R   R   R   R   R
   R	   R   R   (   R*   R+   R%   (    (    sO   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_hyperbolic.pyt	   test_cothÖ   sZ     ''&'''/.67 !$$+/!!%%++////.'/7/7c          C   sy   t  d ƒ }  t |  ƒ j |  d d ƒ d |  |  d |  d d d |  d d	 |  d
 d t |  d ƒ k su t ‚ d  S(   NR*   i    i   i   i   i-   i   i   i±  i   iu  (   R   R   R-   R   R(   (   R*   (    (    sO   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_hyperbolic.pyt   test_coth_series  s    c          C   s€  t  d ƒ \ }  } t d d t ƒ} t d d t ƒ} t t ƒ t k sN t ‚ t t ƒ t k sf t ‚ t t ƒ d k s~ t ‚ t t ƒ d k s— t ‚ t d ƒ t k s¯ t ‚ t d ƒ t d ƒ k sÎ t ‚ t |  ƒ t |  ƒ k sî t ‚ t t ƒ t t ƒ k st ‚ t d t	 ƒ t d t	 ƒ k s5t ‚ t t t
 ƒ t k sQt ‚ t t t
 ƒ t k snt ‚ t d	 t t
 ƒ t k sŽt ‚ t d t t
 ƒ t k s®t ‚ t d d t t
 ƒ t k sÒt ‚ t d d t t
 ƒ t k söt ‚ t t t
 d	 ƒ t
 k st ‚ t t t
 d	 ƒ t
 k s8t ‚ t d t t
 d	 ƒ t
 k s]t ‚ t d t t
 d	 ƒ t
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 d ƒ d t d ƒ t
 k s¯t ‚ t d t t
 d ƒ d	 t d ƒ t
 k sát ‚ t t t
 d ƒ t d	 ƒ t
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 k s7t ‚ t d t t
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 k set ‚ t d t t
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 k s“t ‚ t t t
 d ƒ d t
 k s·t ‚ t t t
 d ƒ d	 t
 k sÜt ‚ t d t t
 d ƒ d	 t
 k st ‚ t d t t
 d ƒ d t
 k s,t ‚ t d t t
 d ƒ d	 t
 k sTt ‚ t t t
 d ƒ d t t d ƒ t
 k s†t ‚ t t t
 d ƒ d t t d ƒ t
 k s¹t ‚ t |  t
 ƒ d t |  ƒ t
 k sãt ‚ t | t t
 ƒ t k st ‚ t d | t t
 ƒ t k s't ‚ t | t t
 d	 ƒ d t | t d	 ƒ t
 k sat ‚ t | ƒ j t k s|t ‚ d  S(   Ns   x,yR%   R&   t   nt   positivei    iÿÿÿÿi   i   i   iþÿÿÿiýÿÿÿi
   iI   i   ig   i   i   i   i   iùÿÿÿiûÿÿÿii   i   lE                                                                                                                                            l»ÿÿÿ                                                                                                                                         lE                                                                                                                                            l             Bgòm‹9luêZnD¤$]'tT l                 koõP³+!k·{3…5UWoÄ ½$ŽXÿ\Ñ,‹yÛ(   R    R   R'   R   R   R(   R   R   R   R   R   R
   R   t   is_real(   R*   R+   R%   R5   (    (    sO   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_hyperbolic.pyt	   test_csch  sP      '  $$!!%$.2++..$%(((23* $:c          C   s‘   t  d ƒ }  t |  ƒ j |  d d ƒ d |  |  d d |  d d d	 |  d
 d d |  d d d |  d d t |  d ƒ k s t ‚ d  S(   NR*   i    i
   i   i   i   i   ih  i   i   i;  i   i€:	 iI   i	   i 54 (   R   R   R-   R   R(   (   R*   (    (    sO   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_hyperbolic.pyt   test_csch_seriesX  s    c          C   s  t  d ƒ \ }  } t d d t ƒ} t d d t ƒ} t t ƒ t k sN t ‚ t t ƒ t k sf t ‚ t t ƒ d k s~ t ‚ t t ƒ d k s— t ‚ t d ƒ d k s¯ t ‚ t d ƒ t d ƒ k sÍ t ‚ t |  ƒ t |  ƒ k sì t ‚ t t t	 ƒ t
 t ƒ k st ‚ t t t	 ƒ t
 t ƒ k s1t ‚ t d t ƒ t d t ƒ k sWt ‚ t t t	 d	 ƒ t k swt ‚ t t t	 d	 ƒ t k s˜t ‚ t d d d t t	 d	 ƒ t k sÄt ‚ t d d d t t	 d	 ƒ t k sðt ‚ t t t	 ƒ d k st ‚ t t t	 ƒ d k s)t ‚ t d t t	 ƒ d k sIt ‚ t d t t	 ƒ d k sit ‚ t t t	 d ƒ d	 k s‰t ‚ t d t t	 d ƒ d k s­t ‚ t t t	 d ƒ t d	 ƒ k sÓt ‚ t t t	 d ƒ t d	 ƒ k sút ‚ t d t t	 d ƒ t d	 ƒ k s%t ‚ t d t t	 d ƒ t d	 ƒ k sPt ‚ t t t	 d ƒ d	 t d ƒ k szt ‚ t t t	 d ƒ d	 t d ƒ k s¥t ‚ t d t t	 d ƒ d t d ƒ k sÓt ‚ t d t t	 d ƒ d t d ƒ k st ‚ t t t	 d ƒ d t t d ƒ k s/t ‚ t t t	 d ƒ d t t d ƒ k s^t ‚ t |  t	 ƒ d t |  ƒ k s„t ‚ t | t t	 ƒ d t | t ƒ k s²t ‚ t d | t t	 ƒ d t d | t ƒ k sèt ‚ t | ƒ j t k st ‚ d  S(   Ns   x, yR%   R&   R5   R6   i    i   iÿÿÿÿi   i   iýÿÿÿi
   iI   i   ig   i   i   i   iþÿÿÿi   iûÿÿÿi   ii   i   lE                                                                                                                                            l»ÿÿÿ                                                                                                                                         lE                                                                                                                                            l             Bgòm‹9luêZnD¤$]'tT l                 koõP³+!k·{3…5UWoÄ ½$ŽXÿ\Ñ,‹yÛ(   R    R   R'   R   R   R(   R   R   R   R   R   R   R
   R   R7   (   R*   R+   R%   R5   (    (    sO   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_hyperbolic.pyt	   test_sech_  sJ    "#& !,,   $&'++*+.../&.6c          C   s   t  d ƒ }  t |  ƒ j |  d d ƒ d |  d d d |  d d d	 |  d
 d d |  d d t |  d ƒ k s} t ‚ d  S(   NR*   i    i
   i   i   i   i   i   i=   i   iÐ  i  i   i€  (   R   R   R-   R   R(   (   R*   (    (    sO   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_hyperbolic.pyt   test_sech_series—  s    c          C   s:  t  d ƒ \ }  } t |  ƒ t |  ƒ k s0 t ‚ t |  ƒ t |  ƒ k sP t ‚ t t ƒ t k sh t ‚ t d ƒ d k s€ t ‚ t d 
ƒ t t d ƒ d ƒ k s© t ‚ t d ƒ t t d ƒ d ƒ k sÑ t ‚ t t ƒ t t d k sñ t ‚ t t ƒ t t d k st ‚ t t d ƒ t t d k s7t ‚ t t d ƒ t t d k s]t ‚ t t ƒ t k sut ‚ t t ƒ t k st ‚ t t t ƒ t k s«t ‚ t t t ƒ t k sÉt ‚ t t	 ƒ t	 k sát ‚ t t t d ƒ d d t
 d ƒ d ƒ t t d k s!t ‚ t t t d ƒ d d t
 d ƒ d ƒ t t d k sct ‚ t t t d	 ƒ d d
 ƒ t t d k s•t ‚ t t t d	 ƒ d d
 ƒ t t d k sÉt ‚ t t t d	 ƒ d d
 ƒ d t t d k sÿt ‚ t t t d	 ƒ d d
 ƒ d t t d k s6t ‚ d  S(   Ns   x,yi    i   i   iÿÿÿÿi   i   i   i   i   i
   iýÿÿÿ(   R    R   R(   R   R	   R
   R   R   R   R   R   (   R*   R+   (    (    sO   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_hyperbolic.pyt
   test_asinh  s,     )( "$&@B246c          C   sI   t  d ƒ }  t |  ƒ j t ƒ t |  t |  d d ƒ ƒ k sE t ‚ d  S(   NR*   i   i   (   R   R   t   rewriteR	   R
   R(   (   R*   (    (    sO   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_hyperbolic.pyt   test_asinh_rewriteÁ  s    c          C   sÝ   t  d ƒ }  t |  ƒ j |  d d ƒ |  |  d d d |  d d d |  d d	 t |  d ƒ k sm t ‚ t |  ƒ j d |  ƒ } | d |  d d k s£ t ‚ t |  ƒ j d |  | d ƒ d
 |  d d	 k sÙ t ‚ d  S(   NR*   i    i   i   i   i   i(   i   ip   iûÿÿÿ(   R   R   R-   R   R(   t   taylor_term(   R*   t   t5(    (    sO   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_hyperbolic.pyt   test_asinh_seriesÆ  s    Ic          C   s  t  d ƒ }  t |  ƒ t |  ƒ k s, t ‚ t d ƒ d k sD t ‚ t d ƒ t t k s` t ‚ t d ƒ t t d k s€ t ‚ t t d d ƒ ƒ t t d k s© t ‚ t t d d ƒ ƒ d t t d k sÖ t ‚ t t ƒ t k sî t ‚ t t ƒ t k st ‚ t t t ƒ t t t d k s/t ‚ t t t ƒ t t t d k sXt ‚ t t ƒ t k spt ‚ t t ƒ t t d t	 d ƒ ƒ k sœt ‚ t t ƒ t t d t	 d ƒ ƒ k sÊt ‚ t t	 d ƒ d d t	 d ƒ ƒ d t t d k st ‚ t t	 d ƒ d d t	 d ƒ ƒ d	 t t d k sCt ‚ t t	 d ƒ d ƒ t t d
 k smt ‚ t t	 d ƒ d ƒ d t t d
 k sœt ‚ t t	 d ƒ d ƒ t t d k sÆt ‚ t t	 d ƒ d ƒ d t t d k sõt ‚ t t	 d t	 d ƒ ƒ d ƒ t t d k s)t ‚ t t	 d t	 d ƒ ƒ d ƒ d	 t t d k sbt ‚ t t	 d t	 d ƒ ƒ d ƒ d t t d k sšt ‚ t t	 d t	 d ƒ ƒ d ƒ d t t d k sÓt ‚ t d t	 d ƒ d t	 d ƒ ƒ t t d k st ‚ t d t	 d ƒ d t	 d ƒ ƒ d t t d k sHt ‚ t t	 d ƒ d d
 ƒ t t d k svt ‚ t t	 d ƒ d d
 ƒ d
 t t d k s©t ‚ t
 t d t ƒ j d ƒ ƒ d k sÔt ‚ t
 t d t ƒ j d ƒ ƒ d k sÿt ‚ d  S(   NR*   i   i    iÿÿÿÿi   i   i   i   i   i   i   i   i   s   2.31244 + 1.5708*Iiûÿÿÿs   2.31244 - 1.5708*I(   R   R   R(   R   R   R   R   R   R	   R
   t   strR5   (   R*   (    (    sO   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_hyperbolic.pyt
   test_acoshÏ  s<      )-(),.<=*/*/49898=.3+c          C   sS   t  d ƒ }  t |  ƒ j t ƒ t |  t |  d ƒ t |  d ƒ ƒ k sO t ‚ d  S(   NR*   i   (   R   R   R=   R	   R
   R(   (   R*   (    (    sO   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_hyperbolic.pyt   test_acosh_rewriteù  s    c          C   s  t  d ƒ }  t |  ƒ j |  d d ƒ t |  t t d t |  d d d t |  d d d t |  d	 d
 t |  d ƒ k sŠ t ‚ t |  ƒ j d |  ƒ } | d t |  d d k sÄ t ‚ t |  ƒ j d	 |  | d ƒ d t |  d	 d
 k sþ t ‚ d  S(   NR*   i    i   i   i   i   i   i(   i   ip   iýÿÿÿiûÿÿÿ(   R   R   R-   R   R   R   R(   R?   (   R*   R@   (    (    sO   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_hyperbolic.pyt   test_acosh_seriesþ  s    f"c          C   sr  t  d ƒ }  t |  ƒ t |  ƒ k s, t ‚ t d ƒ d k sD t ‚ t d ƒ t t k s` t ‚ t d ƒ t k sx t ‚ t d ƒ t t d k s˜ t ‚ t d ƒ d t t d k s¼ t ‚ t t ƒ t t d k sÜ t ‚ t t ƒ t t d k sý t ‚ t t ƒ t t t d t d ƒ k s+t ‚ t t ƒ t d t	 d ƒ ƒ t t d k s_t ‚ t t ƒ t d t	 d ƒ ƒ t t d k s”t ‚ t t	 d ƒ t	 d ƒ ƒ d	 t t d
 k sÈt ‚ t t	 d d t	 d ƒ ƒ ƒ t t d k süt ‚ t t	 d d t	 d ƒ ƒ ƒ d t t d k s5t ‚ t d t	 d t	 d ƒ ƒ ƒ t t d k sit ‚ t d t	 d t	 d ƒ ƒ ƒ d t t d k s¡t ‚ t t	 d ƒ d ƒ t t d k sËt ‚ t d t	 d ƒ ƒ d t t d k sùt ‚ t t	 d d t	 d ƒ ƒ ƒ d t t d k s2t ‚ t t	 d ƒ ƒ t
 d t	 d ƒ ƒ k s`t ‚ t d t	 d ƒ ƒ t
 t	 d ƒ d ƒ k s’t ‚ t d t	 d t	 d ƒ ƒ ƒ t
 t	 d t	 d ƒ ƒ d ƒ k sØt ‚ t t d ƒ ƒ t
 d t d ƒ ƒ k st ‚ t t	 d ƒ ƒ t t d t	 d ƒ ƒ k s9t ‚ t d t	 d ƒ ƒ t t t	 d ƒ d ƒ k spt ‚ t t d ƒ ƒ t t t j ƒ k st ‚ t d t	 d ƒ ƒ t t t	 d ƒ d ƒ k sÔt ‚ t t t t	 d ƒ t	 d ƒ ƒ ƒ t	 d ƒ t	 d ƒ ƒ d k st ‚ t t t t	 d ƒ t	 d ƒ ƒ ƒ t	 d ƒ t	 d ƒ ƒ d k sdt ‚ t t t	 d d t	 d ƒ ƒ ƒ ƒ t	 d d t	 d ƒ ƒ j ƒ  d k s´t ‚ t t t	 d d t	 d ƒ ƒ ƒ ƒ t	 d d t	 d ƒ ƒ j ƒ  d k st ‚ t t t	 d d t	 d ƒ ƒ ƒ ƒ t	 d d t	 d ƒ ƒ j ƒ  d k sVt ‚ t t t d t	 d ƒ ƒ ƒ d t	 d ƒ ƒ d k s’t ‚ t t t d t	 d ƒ ƒ ƒ d t	 d ƒ ƒ d k sÎt ‚ t t t t	 d ƒ t	 d ƒ ƒ ƒ t	 d ƒ t	 d ƒ ƒ d k st ‚ t t d t ƒ j d ƒ ƒ d k sCt ‚ t t d t ƒ j d ƒ ƒ d k snt ‚ d  S(   NR*   i   i    iÿÿÿÿi   i   iþÿÿÿi   i   i   i   i
   i	   i   i   i   s   0.19869 - 1.5708*Iiûÿÿÿs   0.19869 + 1.5708*I(   R   R   R(   R   R   R   R   R#   R	   R
   R   R   R    R)   R"   R   t   simplifyRB   R5   (   R*   (    (    sO   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_hyperbolic.pyt
   test_asech  sL      $ !.4544948*.9.2F.37-7HHPRP<<J+c          C   s|   t  d ƒ }  t |  ƒ j d |  ƒ } | d |  d d k sB t ‚ t |  ƒ j d |  | d ƒ d |  d d k sx t ‚ d  S(	   NR*   i   iûÿÿÿi`   i   i    iÝÿÿÿi   (   R   R   t   expansion_termR(   (   R*   t   t6(    (    sO   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_hyperbolic.pyt   test_asech_series@  s    c          C   s_   t  d ƒ }  t |  ƒ j t ƒ t d |  t d |  d ƒ t d |  d ƒ ƒ k s[ t ‚ d  S(   NR*   i   (   R   R   R=   R	   R
   R(   (   R*   (    (    sO   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_hyperbolic.pyt   test_asech_rewriteG  s    c          C   sO  t  d ƒ }  t |  ƒ t |  ƒ k s, t ‚ t |  ƒ t |  ƒ k sL t ‚ t d ƒ t d t d ƒ ƒ k st t ‚ t d ƒ t d t d ƒ ƒ k s t ‚ t d ƒ t k sµ t ‚ t d ƒ t d t d ƒ d ƒ k sá t ‚ t d ƒ t d t d ƒ d ƒ k st ‚ t t ƒ t t d k s/t ‚ t t ƒ t t d k sPt ‚ t t t d ƒ t d ƒ ƒ t t d	 k s…t ‚ t t t d ƒ t d ƒ ƒ t t d	 k sºt ‚ t t d t d ƒ ƒ t t d
 k sét ‚ t t d t d ƒ ƒ t t d
 k st ‚ t t d t d t d ƒ ƒ ƒ t t d k sQt ‚ t t d t d t d ƒ ƒ ƒ t t d k sŠt ‚ t t d ƒ t t d k s¯t ‚ t t d ƒ t t d k sÔt ‚ t t t d d t d ƒ ƒ ƒ t t d k st ‚ t t t d d t d ƒ ƒ ƒ t t d k sFt ‚ t t t d ƒ ƒ t t d k sqt ‚ t t t d ƒ ƒ t t d k sœt ‚ t t t d ƒ d ƒ d t t d
 k sÏt ‚ t t t d ƒ d ƒ d t t d
 k st ‚ t t d t d ƒ ƒ t t d k s0t ‚ t t d t d ƒ ƒ t t d k s_t ‚ t t d t d t d ƒ ƒ ƒ d t t d k sœt ‚ t t d t d t d ƒ ƒ ƒ d t t d k sØt ‚ t t t d d t d ƒ ƒ ƒ d t t d k st ‚ t t t d d t d ƒ ƒ ƒ d t t d k sQt ‚ t t t d ƒ t d ƒ ƒ d t t d	 k sŠt ‚ t t t d ƒ t d ƒ ƒ d t t d	 k sÂt ‚ t t t d ƒ ƒ t t t d ƒ ƒ k sõt ‚ t t d t d ƒ ƒ t t t d ƒ d ƒ k s0t ‚ t t t d ƒ ƒ t t	 d t d ƒ ƒ k sht ‚ t t d t d ƒ ƒ t t	 t d ƒ d ƒ k s¥t ‚ t
 t t t t d ƒ t d ƒ ƒ ƒ t t d ƒ t d ƒ ƒ d k s÷t ‚ t
 t t t d t d ƒ ƒ ƒ t d t d ƒ ƒ d k s;t ‚ t t t t d d t d ƒ ƒ ƒ ƒ t t d d t d ƒ ƒ j ƒ  d k s“t ‚ t t t t d d t d ƒ ƒ ƒ ƒ t t d d t d ƒ ƒ j ƒ  d k sít ‚ t t d t d ƒ j d ƒ ƒ d k st ‚ t t d t d ƒ j d ƒ ƒ d k sKt ‚ d  S(   NR*   i   i   iÿÿÿÿi    i   iþÿÿÿi   i   i
   i   i   i   iýÿÿÿiûÿÿÿs   0.0391819 - 0.193363*Is   0.0391819 + 0.193363*I(   R   R   R(   R	   R
   R   R   R   R   R!   R"   R   RF   RB   R5   (   R*   (    (    sO   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_hyperbolic.pyt
   test_acschL  sT      (),-!!55//99%%99++32//=<=<983;8=RDXZ/c           C   sM   t  t ƒ d k s t ‚ t  t ƒ d k s1 t ‚ t  t ƒ d k sI t ‚ d  S(   Ni    (   R   R   R(   R   (    (    (    sO   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_hyperbolic.pyt   test_acsch_infinities†  s    c          C   sQ   t  d ƒ }  t |  ƒ j t ƒ t d |  t d |  d d ƒ ƒ k sM t ‚ d  S(   NR*   i   i   (   R   R   R=   R	   R
   R(   (   R*   (    (    sO   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_hyperbolic.pyt   test_acsch_rewriteŒ  s    c          C   sÚ  t  d ƒ }  t d ƒ d k s$ t ‚ t t ƒ t t d k sD t ‚ t t ƒ t t d k sf t ‚ t d ƒ t k s~ t ‚ t d ƒ t k s— t ‚ t t ƒ t t d k s¸ t ‚ t t ƒ t t d k sÙ t ‚ t t t ƒ t t d k sý t ‚ t t t ƒ t t d k s#t ‚ t t ƒ t t t d t d ƒ k sQt ‚ t |  ƒ t |  ƒ k sqt ‚ t t t d ƒ ƒ t t d k s›t ‚ t t t d ƒ ƒ t t d k sÇt ‚ t t t d ƒ ƒ t t d k sñt ‚ t t t d ƒ ƒ t t d k st ‚ t t d t d ƒ ƒ d t t d	 k sOt ‚ t t t d ƒ d ƒ t t d	 k s}t ‚ t t d t d ƒ ƒ t t d	 k s¬t ‚ t t d t d ƒ ƒ d
 t t d	 k sßt ‚ t t t d d t d ƒ ƒ ƒ d t t d k st ‚ t t t d d t d ƒ ƒ ƒ d t t d k sXt ‚ t t d t d ƒ ƒ t t d k s†t ‚ t t t d ƒ d ƒ t t d k sµt ‚ t t ƒ t t d k sÖt ‚ d  S(   NR*   i    i   i   iÿÿÿÿi   i   i   i   iýÿÿÿi   iþÿÿÿi   (	   R   R   R(   R   R   R   R   R#   R
   (   R*   (    (    sO   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_hyperbolic.pyt
   test_atanh‘  s2     "!!$&. *,*,2./3<=./c          C   sM   t  d ƒ }  t |  ƒ j t ƒ t d |  ƒ t d |  ƒ d k sI t ‚ d  S(   NR*   i   i   (   R   R   R=   R	   R(   (   R*   (    (    sO   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_hyperbolic.pyt   test_atanh_rewrite¶  s    c          C   su   t  d ƒ }  t |  ƒ j |  d d ƒ |  |  d d |  d d |  d d |  d d t |  d ƒ k sq t ‚ d  S(   NR*   i    i
   i   i   i   i	   (   R   R   R-   R   R(   (   R*   (    (    sO   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_hyperbolic.pyt   test_atanh_series»  s    c          C   sç  t  d ƒ }  t d ƒ t t d k s, t ‚ t t ƒ t t d k sM t ‚ t t ƒ t t d k sn t ‚ t d ƒ t k s† t ‚ t d ƒ t k sŸ t ‚ t t ƒ d k s· t ‚ t t ƒ d k sÐ t ‚ t t t ƒ d k sì t ‚ t t t ƒ d k s	t ‚ t t ƒ d k s!t ‚ t |  ƒ t |  ƒ k sAt ‚ t t t d ƒ ƒ t t d k slt ‚ t t t d ƒ ƒ t t d k s—t ‚ t t t d ƒ ƒ t t d k sÂt ‚ t t t d ƒ ƒ t t d k sít ‚ t t d t d ƒ ƒ t t d	 k st ‚ t t t d ƒ d ƒ t t d	 k sKt ‚ t t d t d ƒ ƒ d t t d	 k s}t ‚ t t t d ƒ d ƒ d
 t t d	 k s¯t ‚ t t t d d t d ƒ ƒ ƒ t t d k sèt ‚ t t t d d t d ƒ ƒ ƒ t t d k s!t ‚ t t d t d ƒ ƒ t t d k sPt ‚ t t d t d ƒ ƒ t t d k st ‚ t t d t d ƒ ƒ d t t d k s±t ‚ t t t d ƒ d ƒ d t t d k sãt ‚ d  S(   NR*   i    i   i   i   iÿÿÿÿi   i   i   iýÿÿÿi   i
   i   iûÿÿÿ(   R   R   R   R   R(   R   R   R
   (   R*   (    (    sO   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_hyperbolic.pyt
   test_acothÁ  s4     !! ++++//2299//2c          C   sU   t  d ƒ }  t |  ƒ j t ƒ t d d |  ƒ t d d |  ƒ d k sQ t ‚ d  S(   NR*   i   i   (   R   R   R=   R	   R(   (   R*   (    (    sO   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_hyperbolic.pyt   test_acoth_rewriteå  s    c          C   s   t  d ƒ }  t |  ƒ j |  d d ƒ t t d |  |  d d |  d d |  d d |  d d t |  d ƒ k s} t ‚ d  S(	   NR*   i    i
   i   i   i   i   i	   (   R   R   R-   R   R   R   R(   (   R*   (    (    sO   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_hyperbolic.pyt   test_acoth_seriesê  s    c              s4  t  d ƒ ‰  t ˆ  ƒ j ƒ  t k s* t ‚ t t ‡  f d †  ƒ t ˆ  ƒ j ƒ  t k s^ t ‚ t	 ˆ  ƒ j ƒ  t
 k s| t ‚ t ˆ  ƒ j ƒ  t k sš t ‚ t ˆ  ƒ j ƒ  t k s¸ t ‚ t ˆ  ƒ j ƒ  t k sÖ t ‚ t
 ˆ  ƒ j ƒ  t	 k sô t ‚ t ˆ  ƒ j ƒ  t k st ‚ t ˆ  ƒ j ƒ  t k s0t ‚ d  S(   NR*   c              s   t  ˆ  ƒ j ƒ  S(   N(   R   t   inverse(    (   R*   (    sO   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_hyperbolic.pyt   <lambda>ó  t    (   R   R   RU   R   R(   R$   t   AttributeErrorR   R   R   R   R   R   R   R   R   R   (    (    (   R*   sO   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_hyperbolic.pyt   test_inversesð  s    c          C   s•  t  d ƒ }  t |  ƒ j |  ƒ d k s- t ‚ t |  ƒ j |  ƒ d |  k sR t ‚ t |  ƒ j |  ƒ t t d k s{ t ‚ t |  ƒ j |  ƒ t t d k s¤ t ‚ x; t	 t
 t t g D]' } | |  ƒ j |  ƒ |  k s· t ‚ q· Wxk t	 t t
 t t t t t g D]K } xB d |  t j f D]- } | | ƒ } | j |  ƒ | k st ‚ qWqWx> t t g D]0 } | t j ƒ } | j |  ƒ | k s]t ‚ q]Wd  S(   NR*   i   i   (   R   R   t   as_leading_termR(   R   R   R   R   R   R   R   R   R   R   R)   R   R   (   R*   t   funct   argt   eq(    (    sO   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_hyperbolic.pyt   test_leading_termþ  s    !%))%%#c          C   sÌ  t  d d t ƒ\ }  } |  | t } xL t t t t t t g D]2 } | | ƒ j	 ƒ  | |  | t ƒ k s? t
 ‚ q? WxPt t g D]B} t | ƒ j d t d | ƒ t |  ƒ t | ƒ t t |  ƒ t | ƒ k sÚ t
 ‚ t | ƒ j d t d | ƒ t |  ƒ t | ƒ t t |  ƒ t | ƒ k s,t
 ‚ t | ƒ j d t d | ƒ t |  ƒ t |  ƒ t | ƒ d t |  ƒ d t t | ƒ t | ƒ t | ƒ d t |  ƒ d k s¶t
 ‚ t | ƒ j d t d | ƒ t |  ƒ t |  ƒ t | ƒ d t |  ƒ d t t | ƒ t | ƒ t | ƒ d t |  ƒ d k s@t
 ‚ t | ƒ j d t d | ƒ t | ƒ t |  ƒ t | ƒ d t |  ƒ d t | ƒ d t |  ƒ d t t | ƒ t |  ƒ t | ƒ d t |  ƒ d t | ƒ d t |  ƒ d k st
 ‚ t | ƒ j d t d | ƒ t | ƒ t |  ƒ t | ƒ d t |  ƒ d t | ƒ d t |  ƒ d t t | ƒ t |  ƒ t | ƒ d t |  ƒ d t | ƒ d t |  ƒ d k s‚ t
 ‚ q‚ Wd  S(   Ns   a,bt   realt   complext   deepi   (   R    R'   R   R   R   R   R   R   R   t	   conjugateR(   t   Falset   expandR   R   (   t   at   bt   zR[   Ra   (    (    sO   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_hyperbolic.pyt   test_complex  s&    0CCoo;O8;Oc          C   s€   t  d d t ƒ\ }  } xa t t g D]S } xJ t t t t g D]6 } | |  ƒ j d t d | ƒ | |  ƒ k s> t ‚ q> Wq% Wd  S(   Ns   a,bR_   R`   Ra   (	   R    R'   Rc   R   R   R   R   Rd   R(   (   Re   Rf   Ra   R[   (    (    sO   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_hyperbolic.pyt   test_complex_2899%  s    c          C   sP  t  d ƒ }  t t |  ƒ ƒ |  k s* t ‚ t t |  ƒ ƒ t |  d ƒ t |  d ƒ k s` t ‚ t t |  ƒ ƒ |  t d |  d ƒ k s t ‚ t t |  ƒ ƒ d t |  d ƒ t |  d ƒ k sÊ t ‚ t t |  ƒ ƒ t d |  d ƒ k sö t ‚ t t |  ƒ ƒ |  k st ‚ t t |  ƒ ƒ d t d |  d ƒ k sDt ‚ t t |  ƒ ƒ |  t |  d ƒ t |  d ƒ k s~t ‚ t	 t |  ƒ ƒ |  t d |  d ƒ k s®t ‚ t	 t |  ƒ ƒ t |  d ƒ t |  d ƒ |  k sèt ‚ t	 t |  ƒ ƒ |  k st ‚ t	 t |  ƒ ƒ d |  k s(t ‚ t
 t |  ƒ ƒ t d |  d ƒ |  k sXt ‚ t
 t |  ƒ ƒ |  t |  d ƒ t |  d ƒ k s’t ‚ t
 t |  ƒ ƒ d |  k s´t ‚ t
 t |  ƒ ƒ |  k sÒt ‚ t t |  ƒ ƒ d |  k sôt ‚ t t |  ƒ ƒ d t |  d ƒ t |  d ƒ k s.t ‚ t t |  ƒ ƒ t d |  d ƒ |  k s^t ‚ t t |  ƒ ƒ t |  d ƒ t |  d ƒ k s”t ‚ t t |  ƒ ƒ d t d |  d ƒ k sÄt ‚ t t |  ƒ ƒ d |  k sæt ‚ t t |  ƒ ƒ t d |  d ƒ k st ‚ t t |  ƒ ƒ t |  d ƒ t |  d ƒ |  k sLt ‚ d  S(   NR*   i   i   (   R   R   R   R(   R   R
   R   R   R   R   R   R   R   (   R*   (    (    sO   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_hyperbolic.pyt   test_simplifications,  s2    60:,0:0:"0:"":060",c           C   s<   t  t t d ƒ d ƒ ƒ t t d ƒ d ƒ k s8 t ‚ d  S(   Ni   i   i   i   (   R   R   R   R
   R(   (    (    (    sO   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_hyperbolic.pyt   test_issue_4136M  s    c          C   s%  t  d ƒ }  t |  ƒ j t ƒ t |  ƒ t |  ƒ d k oV t |  ƒ j d ƒ k n sa t ‚ t |  ƒ j t ƒ t t |  t t d ƒ k s™ t ‚ t t	 j
 |  ƒ } t |  ƒ j t ƒ d | d | d k sÝ t ‚ t t	 j
 |  ƒ } t |  ƒ j t ƒ d | | d d k s!t ‚ d  S(   NR*   i   t	   tractablei   (   R   R   R=   R   R(   R   R   R   R   R   R)   R   (   R*   t	   tanh_halft	   coth_half(    (    sO   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_hyperbolic.pyt   test_sinh_rewriteQ  s    2#81c          C   s%  t  d ƒ }  t |  ƒ j t ƒ t |  ƒ t |  ƒ d k oV t |  ƒ j d ƒ k n sa t ‚ t |  ƒ j t ƒ t t |  t t d ƒ k s™ t ‚ t t	 j
 |  ƒ d } t |  ƒ j t ƒ d | d | k sÝ t ‚ t t	 j
 |  ƒ d } t |  ƒ j t ƒ | d | d k s!t ‚ d  S(   NR*   i   Rl   i   (   R   R   R=   R   R(   R   R   R   R   R   R)   R   (   R*   Rm   Rn   (    (    sO   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_hyperbolic.pyt   test_cosh_rewrite\  s    2#8-c          C   s#  t  d ƒ }  t |  ƒ j t ƒ t |  ƒ t |  ƒ t |  ƒ t |  ƒ k og t |  ƒ j d ƒ k n sr t ‚ t |  ƒ j t ƒ t t |  ƒ t t t d |  ƒ k s³ t ‚ t |  ƒ j t ƒ t t t t d |  ƒ t |  ƒ k sô t ‚ t |  ƒ j t	 ƒ d t	 |  ƒ k st ‚ d  S(   NR*   Rl   i   i   (
   R   R   R=   R   R(   R   R   R   R   R   (   R*   (    (    sO   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_hyperbolic.pyt   test_tanh_rewriteg  s    C#AAc          C   s%  t  d ƒ }  t |  ƒ j t ƒ t |  ƒ t |  ƒ t |  ƒ t |  ƒ k og t |  ƒ j d ƒ k n sr t ‚ t |  ƒ j t ƒ t t t t d |  ƒ t |  ƒ k s´ t ‚ t |  ƒ j t ƒ t t |  ƒ t t t d |  ƒ k sö t ‚ t |  ƒ j t	 ƒ d t	 |  ƒ k s!t ‚ d  S(   NR*   Rl   i   i   (
   R   R   R=   R   R(   R   R   R   R   R   (   R*   (    (    sO   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_hyperbolic.pyt   test_coth_rewritep  s    C#BBc          C   s,  t  d ƒ }  t |  ƒ j t ƒ d t |  ƒ d t |  ƒ d k o^ t |  ƒ j d ƒ k n si t ‚ t |  ƒ j t ƒ t t |  t t d ƒ k s  t ‚ t t	 j
 |  ƒ } t |  ƒ j t ƒ d | d d | k sä t ‚ t t	 j
 |  ƒ } t |  ƒ j t ƒ | d d d | k s(t ‚ d  S(   NR*   i   i   Rl   (   R   R   R=   R   R(   R   R   R   R   R   R)   R   (   R*   Rm   Rn   (    (    sO   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_hyperbolic.pyt   test_csch_rewritey  s    :#71c          C   s,  t  d ƒ }  t |  ƒ j t ƒ d t |  ƒ d t |  ƒ d k o^ t |  ƒ j d ƒ k n si t ‚ t |  ƒ j t ƒ t t |  t t d ƒ k s  t ‚ t t	 j
 |  ƒ d } t |  ƒ j t ƒ d | d | k sä t ‚ t t	 j
 |  ƒ d } t |  ƒ j t ƒ | d | d k s(t ‚ d  S(   NR*   i   i   Rl   (   R   R   R=   R   R(   R   R   R   R   R   R)   R   (   R*   Rm   Rn   (    (    sO   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_hyperbolic.pyt   test_sech_rewrite„  s    :#7-c          C   sR  t  d ƒ }  t |  ƒ j |  ƒ t |  ƒ d k s8 t ‚ t |  ƒ j |  ƒ t |  ƒ k s_ t ‚ t |  ƒ j |  ƒ t |  ƒ k s† t ‚ t |  ƒ j |  ƒ t |  ƒ d d k s¶ t ‚ t |  ƒ j |  ƒ t |  ƒ t |  ƒ k sè t ‚ t |  ƒ j |  ƒ t |  ƒ t |  ƒ k st ‚ t	 |  ƒ j |  ƒ d |  d d k sHt ‚ t
 |  ƒ j |  ƒ d t |  d d ƒ k s{t ‚ t |  ƒ j |  ƒ d t |  d d ƒ k s®t ‚ t |  ƒ j |  ƒ d |  d d k sÜt ‚ t |  ƒ j |  ƒ d |  t d |  d ƒ k st ‚ t |  ƒ j |  ƒ d |  d t d |  d ƒ k sNt ‚ d  S(   NR*   iþÿÿÿi   i   iÿÿÿÿ(   R   R   t   diffR   R(   R   R   R   R   R   R   R
   R   R   R   R   (   R*   (    (    sO   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_hyperbolic.pyt   test_derivs  s    ,''022.33.7c          C   sò   t  d ƒ \ }  } t |  | ƒ j d t ƒ t |  ƒ t | ƒ t |  ƒ t | ƒ k s^ t ‚ t d |  ƒ j d t ƒ d t |  ƒ t |  ƒ k sš t ‚ t d |  ƒ j d t ƒ j ƒ  t |  ƒ d d t |  ƒ t |  ƒ d k sî t ‚ d  S(   Ns   x,yt   trigi   i   (   R    R   Rd   R'   R   R(   (   R*   R+   (    (    sO   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_hyperbolic.pyt   test_sinh_expansionŸ  s
    L<c          C   sö   t  d ƒ \ }  } t |  | ƒ j d t ƒ t |  ƒ t | ƒ t |  ƒ t | ƒ k s^ t ‚ t d |  ƒ j d t ƒ t |  ƒ d t |  ƒ d k sž t ‚ t d |  ƒ j d t ƒ j ƒ  d t |  ƒ d t |  ƒ t |  ƒ d k sò t ‚ d  S(   Ns   x,yRw   i   i   (   R    R   Rd   R'   R   R(   (   R*   R+   (    (    sO   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_hyperbolic.pyt   test_cosh_expansion§  s
    L@c          C   s¸   t  d d t ƒ}  t |  ƒ j d  k s- t ‚ t |  ƒ j d  k sH t ‚ t |  ƒ j d  k sc t ‚ t |  ƒ j d  k s~ t ‚ t	 |  ƒ j d  k s™ t ‚ t
 |  ƒ j d  k s´ t ‚ d  S(   NRg   R_   (   R   Rc   R   R7   t   NoneR(   R   R   R   R   R   (   Rg   (    (    sO   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_hyperbolic.pyt   test_real_assumptions®  s    c          C   sl  t  d d t ƒ}  t  d d t ƒ} t | ƒ j t k s? t ‚ t |  ƒ j t k sZ t ‚ t | ƒ j t k su t ‚ t |  ƒ j t k s t ‚ t | ƒ j t k s« t ‚ t |  ƒ j t k sÆ t ‚ t | ƒ j t k sá t ‚ t |  ƒ j t k sü t ‚ t	 | ƒ j t k st ‚ t	 |  ƒ j t k s2t ‚ t
 | ƒ j t k sMt ‚ t
 |  ƒ j t k sht ‚ d  S(   Nt   pR6   R5   t   negative(   R   R'   R   t   is_negativeR(   t   is_positiveR   R   R   R   R   (   R|   R5   (    (    sO   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_hyperbolic.pyt   test_sign_assumptions·  s    N(V   t   sympyR    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   R    R!   R"   R#   t   sympy.utilities.pytestR$   R,   R.   R/   R0   R1   R2   R3   R4   R8   R9   R:   R;   R<   R>   RA   RC   RD   RE   RG   RJ   RK   RL   RM   RN   RO   RP   RQ   RR   RS   RT   RY   R^   Rh   Ri   Rj   Rk   Ro   Rp   Rq   Rr   Rs   Rt   Rv   Rx   Ry   R{   R€   (    (    (    sO   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_hyperbolic.pyt   <module>   s`   â	?		=		?		A		;		8		$				*				9			:			%			$							!														