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 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$ Z$ d „  Z% d „  Z& d „  Z' d „  Z( d „  Z) d „  Z* d	 „  Z+ d
 „  Z, d „  Z- d „  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# S($   iÿÿÿÿ(    t   symbolst   logt   lnt   Floatt   nant   oot   zoot   It   pit   Et   expt   Symbolt   LambertWt   sqrtt   Rationalt
   expand_logt   St   signt	   conjugatet   refinet   sint   cost   sinht   cosht   tanht	   exp_polart   ret   Functiont   simplifyt   AccumBoundst   MatrixSymbolt   Pow(   t   xt   yt   zc          C   sÊ  t  d d t ƒ}  t t ƒ t k s* t ‚ t t ƒ t k sB t ‚ t t ƒ d k s[ t ‚ t d ƒ d k ss t ‚ t d ƒ t k s‹ t ‚ t d t ƒ j ƒ  t	 j
 t d f k sº t ‚ t d t ƒ j ƒ  t	 j
 t d f k sé t ‚ t t t d ƒ t k s	t ‚ t t t ƒ d k s%t ‚ t d t t d ƒ t k sJt ‚ t d t t ƒ d k sjt ‚ t t t t d |  ƒ ƒ d k s”t ‚ t t t t d |  t d d ƒ ƒ ƒ d k sËt ‚ t t t t d |  t d d ƒ ƒ ƒ t k st ‚ t t t t d |  t d d ƒ ƒ ƒ t k s:t ‚ t t t ƒ ƒ t k sXt ‚ t d t t ƒ ƒ t d k s~t ‚ t t t t ƒ ƒ t t k s¤t ‚ t d	 t t ƒ t t t ƒ ƒ t d	 t t k sàt ‚ t t t t ƒ ƒ t t k st ‚ t t t ƒ t t ƒ ƒ t k s.t ‚ t d t t ƒ t t ƒ t t t ƒ t d k sjt ‚ t d t t ƒ t t ƒ d t t ƒ ƒ t d t d t t ƒ t t ƒ ƒ k sÆt ‚ d  S(
   Nt   kt   integeri    i   iÿÿÿÿi   i   i   i   (   R   t   TrueR
   R   t   AssertionErrorR   R	   R    t   as_base_expR   t   Exp1R   R   R   R   R   R!   R   (   R#   (    (    sP   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_exponential.pyt   test_exp_values	   s0    // % *778&&<&(<c          C   sÜ   t  d d t ƒ}  t t |  ƒ ƒ |  k s0 t ‚ t t |  ƒ ƒ |  k sN t ‚ t |  ƒ j ƒ  t k sl t ‚ t |  ƒ j ƒ  t k sŠ t ‚ t  d d t ƒ} t t t ƒ ƒ t k sº t ‚ t t | ƒ ƒ | k sØ t ‚ d  S(   NR    t   realR!   t   polar(   R   R%   R   R
   R&   t   inverseR   R"   (   R    R!   (    (    sP   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_exponential.pyt   test_exp_log-   s    c          C   s®   t  t t d ƒ ƒ d t t t d ƒ ƒ t ƒ }  |  j ƒ  d k sL t ‚ t  t t ƒ t  t ƒ t  t ƒ k sx t ‚ t  t t ƒ j ƒ  t  t ƒ t  t ƒ k sª t ‚ d  S(   Ni   i   (   R
   R   R   R    t   expandR&   R!   (   t   e(    (    sP   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_exponential.pyt   test_exp_expand9   s    4,c           C   sC  t  t ƒ j ƒ  t t f k s$ t ‚ t  d t ƒ j ƒ  t d t f k sP t ‚ t  t t ƒ j ƒ  t t t f k s| t ‚ t  t ƒ j ƒ  t t f k s¢ t ‚ t t t  t ƒ k s¾ t ‚ t d t t  d t ƒ k sâ t ‚ t t t t  t t ƒ k st ‚ t  t ƒ j t j k s$t ‚ t  t ƒ j  t k s?t ‚ d  S(   Ni   (	   R
   R    R'   R	   R&   R!   t   baseR   R(   (    (    (    sP   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_exponential.pyt   test_exp__as_base_exp@   s    $,,&$$c           C   s   t  t t ƒ t k s t ‚ t t  t t ƒ ƒ t k s> t ‚ t t  t t ƒ ƒ t k sa t ‚ t  t t t ƒ t k s t ‚ t  t ƒ t k s™ t ‚ d  S(   N(   R
   R   R!   R   R&   R   R   R   (    (    (    sP   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_exponential.pyt   test_exp_infinityO   s
    "# c          C   sµ  t  d ƒ }  t d t |  ƒ d t ƒ} | j |  d t d ƒ | k sN t ‚ | j |  d d ƒ | k sp t ‚ |  d j |  d t ƒ t d t d ƒ k s¤ t ‚ t t |  ƒ t |  d ƒ ƒ j t t |  ƒ ƒ t ƒ t t t |  d ƒ ƒ k sü t ‚ t |  ƒ j t t ƒ t |  k s$t ‚ t	 d d t
 ƒ}  t d |  ƒ j t d |  ƒ t ƒ t t d d ƒ k sut ‚ t d |  d ƒ j t d |  ƒ t ƒ t t d d ƒ t d ƒ k sÂt ‚ t	 d d t
 ƒ}  t d t |  ƒ ƒ j |  d t ƒ t t d d ƒ k st ‚ t t |  t ƒ ƒ j t d ƒ d d |  t k sMt ‚ t t |  t ƒ ƒ j t d ƒ d d |  d k s‡t ‚ t d ƒ j t t ƒ t d ƒ k s±t ‚ d  S(	   NR    i   t   evaluatei   i   R*   i   t   positive(   R   R
   R   t   Falset   subsR!   R&   R   R	   R    R%   R   R   (   R    R/   (    (    sP   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_exponential.pyt   test_exp_subsW   s    &"4X(?M?::c           C   s.   t  t t ƒ ƒ t t  t ƒ ƒ k s* t ‚ d  S(   N(   R   R
   R    R&   (    (    (    sP   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_exponential.pyt   test_exp_conjugatej   s    c          C   sÎ  d d l  m }  t t ƒ j t ƒ t t ƒ t t ƒ k sA t ‚ t t t	 ƒ j t
 ƒ t
 t ƒ t	 t t ƒ k sz t ‚ t d ƒ j t
 ƒ t d ƒ t d ƒ k s« t ‚ t d ƒ j t ƒ t d ƒ t d ƒ k sÜ t ‚ t d ƒ j t ƒ t d ƒ t d ƒ k st ‚ t t ƒ j t ƒ d t t d ƒ d t t d ƒ k sNt ‚ t t t	 d ƒ j t ƒ t d ƒ d t d ƒ t	 d k s“t ‚ t t t	 d ƒ j t ƒ t d ƒ d t d ƒ t	 d k sØt ‚ t t t t ƒ ƒ j t ƒ t t k st ‚ t t t ƒ t t ƒ ƒ j t ƒ t t t ƒ t t t ƒ g k sRt ‚ t t t t ƒ ƒ t ƒ j t ƒ t t ƒ t k st ‚ t d d t ƒ} |  t t t	 d ƒ d | | d	 t f ƒ j t ƒ j ƒ  t d ƒ d
 d t	 d
 k sþt ‚ |  t t t	 d ƒ d | | d	 t f ƒ j t ƒ j ƒ  d d t d ƒ d t	 d k sat ‚ |  t t t	 d ƒ d | | d	 t f ƒ j t ƒ j ƒ  d t d ƒ d t d ƒ t	 d k sÊt ‚ d  S(   Niÿÿÿÿ(   t   Sumi   i   i   i   t   nR$   i    i   (   t   sympy.concrete.summationsR:   R
   R    t   rewriteR   R   R   R&   R   R   R   R   R   R   R   R!   R   R   R%   R   t   doit(   R:   R;   (    (    sP   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_exponential.pyt   test_exp_rewriten   s     19111AEE/K;_cc           C   s   t  t ƒ j t ƒ d k s! t ‚ t  d t ƒ j t ƒ t  d t ƒ k sP t ‚ t  d t ƒ j t ƒ t  d ƒ k s{ t ‚ d  S(   Ni   i   (   R
   R    t   as_leading_termR&   (    (    (    sP   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_exponential.pyt   test_exp_leading_termƒ   s    !/c          C   sŒ   t  d ƒ }  t |  ƒ j d |  ƒ |  k s0 t ‚ t |  ƒ j d |  ƒ |  d d k s\ t ‚ t |  ƒ j d |  ƒ |  d d k sˆ t ‚ d  S(   NR    i   i   i   i   i   (   R    R
   t   taylor_termR&   (   R    (    (    sP   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_exponential.pyt   test_exp_taylor_termˆ   s    $,c          C   s1   t  d d d ƒ }  t |  ƒ j t ƒ s- t ‚ d  S(   Nt   Ai   (   R   R
   t   hasR&   (   RD   (    (    sP   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_exponential.pyt   test_exp_MatrixSymbol   s    c           C   s+  t  t ƒ t k s t ‚ t  t ƒ t k s0 t ‚ t  t ƒ t k sI t ‚ t  t ƒ t k sa t ‚ t  t ƒ t k sz t ‚ t  d ƒ t k s’ t ‚ t  d ƒ d k sª t ‚ t  d ƒ t t k sÆ t ‚ t  t ƒ d k sÞ t ‚ t  t ƒ j ƒ  d t t k st ‚ t  t ƒ t  t ƒ k s#t ‚ t  t ƒ j ƒ  t  t ƒ t t k sPt ‚ t  d ƒ t  d ƒ k snt ‚ t  d ƒ t  d ƒ t t k s”t ‚ t  t ƒ t t d k s´t ‚ t  t ƒ t t d k sÖt ‚ t  d t ƒ t t d t  d ƒ k st ‚ t  d t ƒ j ƒ  t t d t  d ƒ k s9t ‚ t  t t ƒ t k sUt ‚ t  t t ƒ t k srt ‚ t  d d ƒ t k st ‚ t  d d ƒ t k s¨t ‚ t	 t  d ƒ ƒ d d k sËt ‚ t  t
 j ƒ t  d ƒ k sít ‚ t  d	 ƒ j t  k st ‚ t  d d
 ƒ j t  k s't ‚ d  S(   Ni    i   iÿÿÿÿi   iïÿÿÿi   i   i   i   i	   (   R   R   R&   R   R   R   R   R	   R.   R
   R   t   Halft   func(    (    (    sP   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_exponential.pyt   test_log_values”   s4    '-& ".5#"c           C   s   t  d d ƒ d k s t ‚ t  d d ƒ d k s6 t ‚ t  d d ƒ t  d ƒ t  d ƒ k sa t ‚ t  d d ƒ d t  d ƒ t  d ƒ k s t ‚ t  d d ƒ d t  d ƒ t  d ƒ k s¿ t ‚ t  d d ƒ d k sÚ t ‚ t  d	 d ƒ d k sõ t ‚ t  d d ƒ t k st ‚ t  d d ƒ t k s+t ‚ t  t d d ƒ d ƒ t  t d ƒ d ƒ t  d ƒ k sit ‚ t  t d d ƒ t d d ƒ ƒ t  d ƒ t  d ƒ d k s«t ‚ t  t d d ƒ t d d ƒ ƒ t  t d ƒ d ƒ t  t d ƒ d ƒ k süt ‚ d  S(
   Ni   i   i    i   i   i   i
   i   i   (   R   R&   R   R   R   R   (    (    (    sP   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_exponential.pyt   test_log_base½   s    +//>Bc          C   s®  t  t t d ƒ ƒ t  t ƒ k s' t ‚ t  t t ƒ ƒ t k sE t ‚ t  t t d ƒ ƒ t  t ƒ k sl t ‚ t  t t ƒ t  t ƒ t  t ƒ k s˜ t ‚ t  t t ƒ j ƒ  t  t ƒ t  t ƒ k sÊ t ‚ t  t t ƒ j d t ƒ t  t ƒ t  t ƒ k st ‚ t  t t ƒ j ƒ  t t  t ƒ k s.t ‚ t  t t ƒ j d t ƒ t t  t ƒ k s`t ‚ t  t d ƒ t  t ƒ t  d ƒ k s‹t ‚ t  t d ƒ d t  d ƒ k s°t ‚ t d d t ƒ\ }  } t	 d d t ƒ} t  |  d ƒ d t  |  ƒ k s t ‚ t  |  d ƒ j ƒ  d t  |  ƒ k s,t ‚ t  t d ƒ j ƒ  d t  t ƒ k sXt ‚ t  |  | ƒ | t  |  ƒ k s~t ‚ t  t |  ƒ ƒ |  k sœt ‚ t  |  | ƒ t  |  ƒ t  | ƒ k sÈt ‚ t  |  | ƒ j ƒ  t  |  ƒ t  | ƒ k sút ‚ t  t
 d ƒ ƒ t  t
 d ƒ ƒ t t k s-t ‚ t  t |  ƒ ƒ |  t t k sTt ‚ t  t t ƒ ƒ j ƒ  t t t k st ‚ t  t | ƒ ƒ j ƒ  | t t k s®t ‚ t  t t ƒ t t  t ƒ k sÔt ‚ t  t d	 ƒ d
 j ƒ  d
 t  t ƒ d k st ‚ t  |  d	 ƒ d
 j ƒ  d
 t  |  ƒ d k s<t ‚ t  t ƒ j t  k rmt  t ƒ j d t k sst ‚ t  |  ƒ j t  k r¤t  |  ƒ j d |  k sªt ‚ d  S(   Ni   t   forcei   s   p,qR5   t   rR*   i   iûÿÿÿiÿÿÿÿi   i    (   R   R    R
   R&   R!   R.   R%   R	   R    R   R   R   R   RH   t   args(   t   pt   qRL   (    (    sP   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_exponential.pyt   test_log_symbolicÍ   s8    '',28,2+%&,,&,23'--&447c          C   s  t  d d t ƒ}  t  d d t ƒ} xø t t f D]ê } | t ƒ j d  k sR t ‚ | t ƒ j d  k sm t ‚ | | ƒ j d  k sˆ t ‚ | | ƒ j d  k s£ t ‚ | |  ƒ j t k s¾ t ‚ | |  ƒ j t	 k sÙ t ‚ | t
 t ƒ ƒ j t k sú t ‚ | t
 t ƒ ƒ j t	 k s1 t ‚ q1 Wt d d t	 ƒj s:t ‚ t  d d t ƒ} t  d	 d t d
 t ƒ} t  d d t ƒ}  t  d d t d
 t ƒ} t | ƒ j d  k s©t ‚ t | ƒ j t	 k sÄt ‚ t t |  ƒ j d  k sãt ‚ t t | ƒ j t	 k st ‚ d  S(   NRL   R*   t   it	   imaginaryi    R4   t   at	   algebraict   ant   nonzerot   rationalt   rn(   R   R%   R
   R   R    t   is_realt   NoneR&   t   is_imaginaryR6   R   t   is_algebraicR   (   RL   RQ   R/   RS   RU   RX   (    (    sP   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_exponential.pyt   test_exp_assumptionsó   s(    !%c           C   s2   t  t d d ƒ ƒ t t t d ƒ k s. t ‚ d  S(   Ni   i   (   R
   R   R	   R&   (    (    (    sP   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_exponential.pyt   test_exp_AccumBounds  s    c          C   s™  t  d d t ƒ}  t  d d t ƒ} t  d d t ƒ} t  d d t d t ƒ} t | ƒ j t k si t ‚ t | ƒ j t k s„ t ‚ t d	 ƒ d
 k sœ t ‚ t d d t ƒj s· t ‚ t d | ƒ j sÐ t ‚ t |  ƒ j d  k së t ‚ t | ƒ j t k st ‚ t d ƒ j t k s!t ‚ t t	 |  ƒ d ƒ j s@t ‚ t d d t ƒj
 s[t ‚ t d d t ƒj
 t k s|t ‚ t d | ƒ j s•t ‚ d  S(   NRN   R5   R;   t   negativeR"   t   zeroR    t   infinitei   i    i   R4   g      à?i*   (   R    R%   R   t   is_positiveR6   R&   t   is_zeroRZ   t   is_negativeR
   R\   t   is_rational(   RN   R;   R"   R    (    (    sP   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_exponential.pyt   test_log_assumptions  s     !c          C   sp  t  t t t  ƒ ƒ k s t ‚ t t  ƒ t t t t  ƒ ƒ ƒ k sH t ‚ t t  ƒ t t t t  ƒ ƒ ƒ k sr t ‚ d t t t  ƒ t t t  ƒ ƒ ƒ }  |  j j t k s° t ‚ d t t t  ƒ t t t t  ƒ ƒ ƒ ƒ }  |  j j t k sô t ‚ t t t  ƒ ƒ }  |  j t k st ‚ t  j t k	 s0t ‚ t t t t  ƒ ƒ ƒ t t  ƒ k sZt ‚ |  t  k slt ‚ d  S(   Ni   (   R    R   R&   t   hashR1   RH   (   R/   (    (    sP   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_exponential.pyt   test_log_hashing&  s    **&,*c           C   s"   t  t d ƒ ƒ d k s t ‚ d  S(   Ni   i   (   R   R   R&   (    (    (    sP   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_exponential.pyt   test_log_sign7  s    c           C   sˆ   t  d t ƒ j d t ƒ t  d ƒ d t t d k s> t ‚ t  d t d ƒ ƒ j d t ƒ t  t d ƒ d ƒ t t k s„ t ‚ d  S(   Ni   t   complexi   i   (   R   R   R.   R%   R   R&   R   (    (    (    sP   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_exponential.pyt   test_log_expand_complex;  s    >c          C   s?   t  d ƒ t  d ƒ d j ƒ  }  |  j t d ƒ ƒ s; t ‚ d  S(   Ni   i   i   s   0.58496250072115618145373(   R   t   evalft
   epsilon_eqR   R&   (   t   value(    (    sP   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_exponential.pyt   test_log_apply_evalf@  s     c          C   sg  t  d d t ƒ}  t |  t d ƒ t d ƒ ƒ } | j ƒ  t d ƒ t d ƒ t |  ƒ k sd t ‚ t d d t ƒ\ } } } t | | | ƒ j d t ƒ t | ƒ t | | ƒ k s¿ t ‚ t t | d ƒ t | | ƒ ƒ j ƒ  t d t | ƒ t | ƒ d t | ƒ t | ƒ ƒ t t | ƒ t | ƒ t | ƒ t | ƒ ƒ t d ƒ t t | ƒ t | ƒ t | ƒ ƒ t d ƒ g k sŽt ‚ t | t | d ƒ ƒ j d t ƒ t | ƒ t | d ƒ k sÔt ‚ t | t | d ƒ ƒ j ƒ  d t | ƒ d k st ‚ t | | | ƒ | | s‡t t d t d	 t ƒ | t | ƒ | t | | ƒ | t | ƒ | t | | ƒ k ƒ ‚ t d
 ƒ \ } } t | | ƒ j d t ƒ t | ƒ t | ƒ k sÑt ‚ t | | ƒ j d t ƒ | t | ƒ k st ‚ t t | ƒ ƒ j d t ƒ | k s-t ‚ t d d ƒ j ƒ  d t d ƒ t d ƒ k sct ‚ d  S(   Nt   wR5   i   i   s   x,y,zt   muli   t   deepR   s   x,yRK   i	   (   R   R%   R   R.   R&   R    R6   R
   (   Rp   R/   R    R!   R"   (    (    sP   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_exponential.pyt   test_log_expandE  s"     2@AR<F:1H82*c          C   sa  t  d d t ƒ}  t |  d ƒ j ƒ  d t |  ƒ k s> t ‚ t t |  d t d ƒ ƒ ƒ d t d ƒ t |  ƒ k s~ t ‚ t  d ƒ } t t | ƒ ƒ j ƒ  t | ƒ d k s¸ t ‚ t t | t d ƒ d ƒ ƒ t d ƒ d t | ƒ k sø t ‚ t | d ƒ j ƒ  t | ƒ k s!t ‚ t | |  |  d ƒ j ƒ  |  t | ƒ |  d k s]t ‚ d  S(   NR    R5   i   R"   i   iÿÿÿÿ(   R   R%   R   R.   R&   R   R   (   R    R"   (    (    sP   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_exponential.pyt   test_log_simplify]  s    ,@.@)c           C   s.   t  t d t ƒ ƒ t d d ƒ k s* t ‚ d  S(   Ni   i    (   R   R   R	   R&   (    (    (    sP   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_exponential.pyt   test_log_AccumBoundsi  s    c          C   s  t  d ƒ }  t t d ƒ t t ƒ k s- t ‚ t t d d t ƒt t ƒ k sT t ‚ t d ƒ d k sl t ‚ t t ƒ d k s„ t ‚ t d t ƒ d k s  t ‚ t t d ƒ d ƒ t d ƒ k sÊ t ‚ t t ƒ t k sâ t ‚ t d d ƒ t k sþ t ‚ t d d ƒ t k st ‚ t t d d ƒ t	 t d k sCt ‚ t d t d ƒ d k sbt ‚ t d t
 d ƒ d ƒ d k s‡t ‚ t t d ƒ j t ƒ d t t d ƒ t d t t d ƒ k sÐt ‚ t t |  ƒ j t ƒ t t |  ƒ t d t t |  ƒ k st ‚ t t d ƒ ƒ j d	 ƒ j t d
 d	 ƒ d ƒ sHt ‚ t t d d ƒ ƒ j ƒ  j t d ƒ ƒ sxt ‚ t d ƒ j t k s“t ‚ t d d t ƒj s®t ‚ t  d d t ƒ} t | d t ƒj sÛt ‚ t | d d t ƒj d  k s t ‚ t | d t j d t ƒj t k s-t ‚ t t j d d t ƒj t k sTt ‚ t t j d d d t ƒj szt ‚ t d d d t ƒj t k sžt ‚ t d d d t ƒj t k sÂt ‚ t d d t ƒj sÝt ‚ t  d d t d t ƒ} t | ƒ j t k st ‚ d  S(   NR#   i    R4   i   iÿÿÿÿi   i*   iþÿÿÿi   s    0.701338383413663009202120278965gG³¦þ^Zé9s   -0.834310366631110RN   R5   i
   iöÿÿÿt   naRV   RT   (   R   R   R    R&   R6   R	   R   R   R   R   R
   t   diffR   Rl   Rm   R   R   RY   R%   RZ   R   R(   RG   t   OneR\   (   R#   RN   Rv   (    (    sP   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_exponential.pyt   test_lambertwm  s>    !'*)%IB0%-'&$$c          C   s®   t  d ƒ }  |  j t k s! t ‚ |  j t k	 s6 t ‚ d d d t d ƒ } |  j t k	 sc t ‚ d t t t  t d ƒ ƒ ƒ t  t d ƒ ƒ ƒ } | j t k	 sª t ‚ d  S(   Niÿÿÿÿi   iüÿÿiþÿÿÿi   (	   R   t   is_comparableR6   R&   Rb   R%   R
   R   t
   is_nonzero(   R/   t   e2t   e3(    (    sP   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_exponential.pyt   test_issue_5673”  s    2c          C   sñ   t  d d t ƒ\ }  } } t |  | ƒ j ƒ  t |  | ƒ k sG t ‚ t |  | | ƒ j ƒ  t |  | | ƒ k s{ t ‚ t t t ƒ j ƒ  t t ƒ t t ƒ k s­ t ‚ t t t t ƒ j ƒ  t t ƒ t t ƒ t t ƒ k sí t ‚ d  S(   Ns   A,B,Ct   commutative(   R    R6   R
   R.   R&   R    R!   R"   (   RD   t   Bt   C(    (    sP   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_exponential.pyt   test_exp_expand_NCž  s
    ,42c          C   s°  t  d d t ƒ}  t t ƒ j ƒ  t t ƒ d f k s< t ‚ t t ƒ j ƒ  d t t ƒ f k sg t ‚ t d t ƒ j ƒ  d t d t ƒ f k s™ t ‚ t d ƒ j ƒ  d t d ƒ f k sÃ t ‚ t |  ƒ j ƒ  d t |  ƒ f k sî t ‚ t |  ƒ j ƒ  t |  ƒ d f k st ‚ t t t ƒ j ƒ  d t t t ƒ f k sMt ‚ t t |  ƒ j ƒ  d t t |  ƒ f k s€t ‚ t |  ƒ j ƒ  t |  ƒ d f k s¬t ‚ d  S(   NR;   R_   i   iþÿÿÿi   (   R    R%   R
   R    t   as_numer_denomR&   R   (   R;   (    (    sP   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_exponential.pyt   test_as_numer_denom§  s    *+2*+,33c          C   sœ  t  d d t ƒ\ }  } t t t d ƒ ƒ d k s: t ‚ t t d ƒ ƒ d k sX t ‚ t t d d t ƒ ƒ t d ƒ k s„ t ‚ t t d ƒ j ƒ  t t d ƒ k s° t ‚ t t t	 ƒ ƒ t	 k sÎ t ‚ t |  | ƒ j
 ƒ  t |  ƒ t | ƒ k s t ‚ t |  t	 ƒ j
 ƒ  t	 t |  ƒ k s,t ‚ t d ƒ j d k sGt ‚ t d	 t t ƒ j d
 d ƒ j ƒ  d d k s}t ‚ t d ƒ j t k s˜t ‚ d  S(   Ns   x yR+   i   i   i    i   i   i
   g      ð?R;   i   (   R    R%   t   absR   R   R&   R
   R;   R   R"   R.   R   t   as_real_imagRe   (   R    R!   (    (    sP   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_exponential.pyt
   test_polar´  s    ",,2,6c          C   s}  d d l  m }  m } t d d t d t ƒ\ } } t d d t ƒ\ } } d d l m } m } t d ƒ t d	 ƒ } }	 t	 t
 | | | | d
 |  f ƒ ƒ ƒ | | t
 | ƒ | d
 |  f ƒ k sË t ‚ t	 t
 | | | | | | d
 |  f | d
 | f ƒ ƒ ƒ t
 | | | | | | d
 |  f | d
 | f ƒ ƒ k sCt ‚ t
 | d |  d d f ƒ ƒ }
 t	 |
 ƒ |
 k syt ‚ d  S(   Niÿÿÿÿ(   R;   t   ms   i,jR5   R$   s   x,y(   t   ProductR:   t   ft   gi   iþÿÿÿi    i   (   t	   sympy.abcR;   Rˆ   R    R%   t   sympy.concreteR‰   R:   R   R   R   R&   (   R;   Rˆ   RQ   t   jR    R!   R‰   R:   RŠ   R‹   t   expr(    (    sP   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_exponential.pyt   test_log_productÈ  s    P9?c          C   sZ  t  t t d d t ƒƒ t  t t d ƒ ƒ k s6 t ‚ t t t d d t ƒƒ t t t d ƒ ƒ k sl t ‚ t d d t ƒ}  t t |  ƒ t d ƒ ƒ } t t |  ƒ t d ƒ ƒ } t t |  ƒ t d ƒ d t ƒ} t t |  ƒ t d ƒ d t ƒ} t  t | | ƒ ƒ t  t | | ƒ ƒ k s&t ‚ t t | | ƒ ƒ t t | | ƒ ƒ k sVt ‚ d  S(   Ni
   R4   R!   R5   i   (	   R   R   R    R6   R&   R   R   R%   R
   (   R!   t   l1t   b1t   l2t   b2(    (    sP   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_exponential.pyt   test_issue_8866Ö  s    66!!0c          C   sR   t  d d t d t ƒ}  t |  ƒ j t k s3 t ‚ t |  ƒ j t k sN t ‚ d  S(   NR;   R5   R$   (   R   R%   R   t   is_nonnegativeR&   R   (   R;   (    (    sP   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_exponential.pyt   test_issue_9116ã  s    N(E   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   RŒ   R    R!   R"   R)   R-   R0   R2   R3   R8   R9   R?   RA   RC   RF   RI   RJ   RP   R]   R^   Rf   Rh   Ri   Rk   Ro   Rs   Rt   Ru   Ry   R~   R‚   R„   R‡   R   R•   R—   (    (    (    sP   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_exponential.pyt   <module>   sB   Ê	$											)		&											'	
						