ó
¡¼™\c           @   sð  d  d l  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 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( d  d l) m* Z* d  d l+ m, Z, d  d l- m. Z. d  d l/ m0 Z0 d  d l1 m2 Z2 m3 Z3 d  d	 l4 m5 Z5 d  d
 l6 m7 Z7 d  d l8 m9 Z9 m: Z: m; Z; m< Z< e d d e= d e= ƒ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 e2 d „  ƒ ZO d  „  ZP d! „  ZQ e2 d" „  ƒ ZR d# „  ZS d$ „  ZT d% „  ZU d& „  ZV d' „  ZW d( „  ZX d) „  ZY d* „  ZZ d+ „  Z[ d, „  Z\ d- „  Z] d. „  Z^ d/ „  Z_ e2 d0 „  ƒ Z` d1 „  Za d2 „  Zb d3 „  Zc d4 „  Zd d5 „  Ze d6 „  Zf d7 „  Zg d8 „  Zh d9 „  Zi d: „  Zj d; „  Zk d< „  Zl d= „  Zm d> „  Zn d? „  Zo d@ „  Zp dA „  Zq dB „  Zr dC „  Zs dD „  Zt dE „  Zu dF „  Zv dG „  Zw dH „  Zx dI „  Zy dJ „  Zz dK „  Z{ dL „  Z| dM S(N   iÿÿÿÿ(   t   product(#   t   limitt   expt   oot   logt   sqrtt   Limitt   sint   floort   cost   ceilingt   atant   gammat   Symbolt   St   pit   Integralt   Rationalt   It
   EulerGammat   tant   cott	   integratet   Sumt   signt   Functiont   subfactorialt   symbolst   binomialt   simplifyt   fract   Floatt   sect   zoot   fresnelct   fresnels(   t   AccumBounds(   t   Add(   t   Mul(   t
   heuristics(   t   Order(   t   XFAILt   raises(   t   GoldenRatio(   t	   fibonacci(   t   xt   yt   zt   kt   nt   integert   positivec           C   s*  t  t t t ƒ t k s t ‚ t  t t t ƒ t k s> t ‚ t  t t t ƒ t k s^ t ‚ t  t d t t ƒ t k s t ‚ t  t d t t ƒ t k s¥ t ‚ t  t t t ƒ t d d d ƒd k sÓ t ‚ t  d t t t ƒ d k sõ t ‚ t  t t ƒ t t ƒ t k st ‚ t  t t ƒ t t ƒ t k s?t ‚ t  t t ƒ t t t ƒ t k sgt ‚ t  d t t t ƒ t t ƒ d k s”t ‚ t  t d t t t ƒ t k sºt ‚ t  t t d t t ƒ t k sát ‚ t  d t d t d ƒ t d ƒ d k st ‚ t  d t t t d ƒ t k s7t ‚ t  d t t t d d d ƒd k sct ‚ t  d t t t t d d d ƒd t t k s›t ‚ t  t t t t ƒ t d ƒ t t t ƒ k sÒt ‚ t  t	 t t ƒ t t d ƒ t t	 t ƒ ƒ t k st ‚ t  t
 d t d ƒ t t ƒ d k s:t ‚ t  t j t t ƒ t j k s_t ‚ t  t d ƒ t t t j ƒ t j k st ‚ t  d t d t d d d ƒt k s¹t ‚ t  d t d t d d d ƒt k sæt ‚ t  d d t d t d d d ƒt k st ‚ t  d d t d t d d d ƒt k sGt ‚ t  d t t ƒ t t d d ƒt k svt ‚ t  d t t ƒ t t d d ƒt k s¤t ‚ t  d t	 t ƒ t t d d d ƒt k s×t ‚ t  d t	 t ƒ t t d d d ƒt k s	t ‚ t  d t t d ƒ t d t t d ƒ d d d ƒt k sMt ‚ t  d t t d ƒ t d t t d ƒ d d d ƒt k s’t ‚ t  d t t ƒ d t d t d d d ƒt k sÍt ‚ t  d t t ƒ d t d t d d d ƒt k st ‚ t  t t ƒ t t d d d	 ƒd k s5t ‚ t  t d t d d d	 ƒd k s]t ‚ t  d t d t d d d	 ƒt k s‰t ‚ t t d
 „  ƒ t  d d t t d ƒ t k s¿t ‚ t  d d t t d d d ƒt k sìt ‚ t  t d t d d d ƒt k st ‚ t  t d t d d d ƒt k s=t ‚ t  d t t ƒ t d d d ƒt t k spt ‚ t  t d t d d d ƒd k s˜t ‚ t  t t ƒ t d d d ƒd k sÂt ‚ t  t t t d d d ƒt t d t ƒ k sút ‚ t  d t	 t ƒ t t d ƒ t k s&t ‚ d  S(   Ni   i    t   dirt   +i   t   -i   i   s   +-c           S   s   t  d t t d d d ƒS(   Ni   i    R4   s   +-(   R   R-   (    (    (    s=   lib/python2.7/site-packages/sympy/series/tests/test_limits.pyt   <lambda>@   t    iþÿÿÿiýÿÿÿiÿÿÿÿ(   R   R-   R   t   AssertionErrorR   R   R   R.   R   R	   R   R   t   NaNR(   R   R   R   R   R*   t
   ValueErrorR   (    (    (    s=   lib/python2.7/site-packages/sympy/series/tests/test_limits.pyt   test_basic1   s^      #$."$&(-&'0&,87<,%.,-10/.32DE;:.(,&-()3(*8c           C   s]  t  t t t d d d ƒd k s( t ‚ t  t t ƒ d t t d ƒ d k sT t ‚ t  d d t t t ƒ d k sz t ‚ t  t d t ƒ t t ƒ d k s£ t ‚ t  t t t ƒ t t ƒ t k sÌ t ‚ t  t t t d ƒ t t ƒ t k sù t ‚ t  t t t t ƒ ƒ t t ƒ t k s(t ‚ t  d d t t t ƒ t t ƒ d k sYt ‚ d  S(   Ni    R4   R5   i   iÿÿÿÿi   i   (   R   R-   R9   R   R   (    (    (    s=   lib/python2.7/site-packages/sympy/series/tests/test_limits.pyt   test_basic2Q   s    (,&))-/c           C   sU   t  d t t d d d ƒt k s( t ‚ t  d t t d d d ƒt k sQ t ‚ d  S(   Ni   i    R4   R5   R6   (   R   R-   R   R9   (    (    (    s=   lib/python2.7/site-packages/sympy/series/tests/test_limits.pyt   test_basic3\   s    (c           C   s
  t  d t t t t d ƒ d k s* t ‚ t  d t t t t d ƒ d t k sX t ‚ t  d t d t t d t d ƒ d t d k s’ t ‚ t  t t d ƒ t t ƒ t t ƒ d k sÄ t ‚ t d t d d t d t f ƒ d t t d ƒ d	 k st ‚ d  S(
   Ni   i    i   i   iýÿÿÿiþÿÿÿi   i   i	   (   R   R-   R.   R9   R   R   R   R   (    (    (    s=   lib/python2.7/site-packages/sympy/series/tests/test_limits.pyt   test_basic4a   s
    *.:2c          C   sP   d t  f d „  ƒ  Y}  t |  t ƒ t t ƒ t |  t ƒ t t ƒ k sL t ‚ d  S(   Nt   myc           B   s   e  Z e d  „  ƒ Z RS(   c         S   s   | t  j k r t  j Sd  S(   N(   R   t   InfinityR:   (   t   clst   arg(    (    s=   lib/python2.7/site-packages/sympy/series/tests/test_limits.pyt   evalk   s    (   t   __name__t
   __module__t   classmethodRD   (    (    (    s=   lib/python2.7/site-packages/sympy/series/tests/test_limits.pyR@   j   s   (   R   R   R-   R   R   R9   (   R@   (    (    s=   lib/python2.7/site-packages/sympy/series/tests/test_limits.pyt   test_basic5i   s    c           C   s:   t  t t t t t d ƒ t t d t k s6 t ‚ d  S(   Ni   (   R   R-   R.   R/   R9   (    (    (    s=   lib/python2.7/site-packages/sympy/series/tests/test_limits.pyt   test_issue_3885r   s    c           C   s“   t  t t ƒ t t d ƒ d k s( t ‚ t  t t ƒ t t d ƒ j ƒ  d k sV t ‚ t  t t d d d ƒj t t d t d ƒ f k s t ‚ d  S(   Ni    i   R4   s   +-(   R   R   R-   R9   t   doitt   argsR   (    (    (    s=   lib/python2.7/site-packages/sympy/series/tests/test_limits.pyt
   test_Limitv   s    (.c           C   sØ  t  t t ƒ t d d ƒ d k s' t ‚ t  t t ƒ t d d ƒ d k sN t ‚ t  t t ƒ t d d ƒ d k su t ‚ t  t t ƒ t d d ƒ d k sœ t ‚ t  t t ƒ t d d ƒ d k sÃ t ‚ t  t t ƒ t d d ƒ d k sê t ‚ t  t t ƒ t d d ƒ d k st ‚ t  t t ƒ t d d ƒ d k s8t ‚ t  t t ƒ t d d ƒ d k s_t ‚ t  t t ƒ t d d ƒ d k s†t ‚ t  t t ƒ t d	 d ƒ d	 k s­t ‚ t  t t ƒ t d	 d ƒ d
 k sÔt ‚ d  S(   NiþÿÿÿR5   R6   iýÿÿÿiÿÿÿÿi    i   i   iø   i÷   (   R   R   R-   R9   (    (    (    s=   lib/python2.7/site-packages/sympy/series/tests/test_limits.pyt
   test_floor|   s    '''''''''''c           C   s|  t  t t t ƒ ƒ t d d ƒ d k s- t ‚ t  t t t ƒ ƒ t d d ƒ d k sZ t ‚ t  t t t ƒ ƒ t d d ƒ d k s‡ t ‚ t  t t t ƒ ƒ t d d ƒ d k s´ t ‚ t  t d t t ƒ ƒ t d d ƒ d k så t ‚ t  t d t t ƒ ƒ t d d ƒ d k st ‚ t  t d t t ƒ ƒ t d d ƒ d k sGt ‚ t  t d t t ƒ ƒ t d d ƒ d k sxt ‚ d  S(   Ni    R5   R6   iÿÿÿÿi   i   (   R   R   R   R-   R9   R	   (    (    (    s=   lib/python2.7/site-packages/sympy/series/tests/test_limits.pyt&   test_floor_requires_robust_assumptions‹   s    ----111c           C   sØ  t  t t ƒ t d d ƒ d k s' t ‚ t  t t ƒ t d d ƒ d k sN t ‚ t  t t ƒ t d d ƒ d k su t ‚ t  t t ƒ t d d ƒ d k sœ t ‚ t  t t ƒ t d d ƒ d k sÃ t ‚ t  t t ƒ t d d ƒ d k sê t ‚ t  t t ƒ t d d ƒ d k st ‚ t  t t ƒ t d d ƒ d k s8t ‚ t  t t ƒ t d d ƒ d k s_t ‚ t  t t ƒ t d d ƒ d k s†t ‚ t  t t ƒ t d	 d ƒ d
 k s­t ‚ t  t t ƒ t d	 d ƒ d	 k sÔt ‚ d  S(   NiþÿÿÿR5   iÿÿÿÿR6   i    i   i   i   iø   iù   (   R   R
   R-   R9   (    (    (    s=   lib/python2.7/site-packages/sympy/series/tests/test_limits.pyt   test_ceiling–   s    '''''''''''c           C   s|  t  t t t ƒ ƒ t d d ƒ d k s- t ‚ t  t t t ƒ ƒ t d d ƒ d k sZ t ‚ t  t t t ƒ ƒ t d d ƒ d k s‡ t ‚ t  t t t ƒ ƒ t d d ƒ d k s´ t ‚ t  t d t t ƒ ƒ t d d ƒ d k så t ‚ t  t d t t ƒ ƒ t d d ƒ d k st ‚ t  t d t t ƒ ƒ t d d ƒ d k sGt ‚ t  t d t t ƒ ƒ t d d ƒ d k sxt ‚ d  S(   Ni    R5   i   R6   i   i   (   R   R
   R   R-   R9   R	   (    (    (    s=   lib/python2.7/site-packages/sympy/series/tests/test_limits.pyt(   test_ceiling_requires_robust_assumptions¥   s    ----111c          C   sˆ   t  d d t ƒ}  t t |  ƒ t d |  ƒ |  d ƒ d k sD t ‚ t t |  ƒ t |  d ƒ t |  ƒ |  t ƒ t d k s„ t ‚ d  S(   NR-   t   reali   i    i   (	   R   t   TrueR   R   R   R9   R   R   R   (   R-   (    (    s=   lib/python2.7/site-packages/sympy/series/tests/test_limits.pyt	   test_atan°   s    2c           C   s°   t  t t ƒ t d ƒ d k s$ t ‚ t  t t t ƒ ƒ t d ƒ d k sN t ‚ t  t t t ƒ ƒ t d ƒ d k sx t ‚ t  t t t d ƒ ƒ t d ƒ t d ƒ k s¬ t ‚ d  S(   Ni    i   (   R   t   absR-   R9   R   R	   (    (    (    s=   lib/python2.7/site-packages/sympy/series/tests/test_limits.pyt   test_abs¶   s    $**c          C   s¢   t  d d t ƒ}  t t d |  ƒ t |  ƒ |  d d ƒ t d d ƒ k sP t ‚ t t d t	 t |  ƒ ƒ t	 t d |  ƒ ƒ ƒ |  d ƒ t d ƒ k sž t ‚ d  S(   NR-   RQ   i   i    R5   iÿÿÿÿi   (
   R   RR   R'   R   R   R$   R9   R   R   R   (   R-   (    (    s=   lib/python2.7/site-packages/sympy/series/tests/test_limits.pyt   test_heuristic½   s    >c          C   sk   t  d d t ƒ}  d |  t |  t ƒ } t | t t ƒ d k sI t ‚ | j t t ƒ d k sg t ‚ d  S(   NR/   R3   iÿÿÿÿi    (   R   RR   R   R-   R   R   R9   (   R/   t   f(    (    s=   lib/python2.7/site-packages/sympy/series/tests/test_limits.pyt   test_issue_3871Ã   s    c          C   s/  t  d ƒ }  t  d d t ƒ} t d | |  |  |  t ƒ t | ƒ k sN t ‚ t d | d |  |  |  t ƒ t | d ƒ k s† t ‚ t d | d |  d |  |  t ƒ t | d ƒ k sÂ t ‚ t | d | d | | t ƒ t d ƒ k sö t ‚ t d d d | | | t ƒ d t j k s+t ‚ d  S(   NR1   R-   RQ   i   i   iþÿÿÿ(   R   RR   R   R   R   R9   R   t   Exp1(   R1   R-   (    (    s=   lib/python2.7/site-packages/sympy/series/tests/test_limits.pyt   test_exponentialÊ   s    08<4c          C   sJ   t  d ƒ }  t d t |  t |  ƒ |  |  t ƒ t t ƒ k sF t ‚ d  S(   NR1   i   (   R   R   R-   R   R   R   R9   (   R1   (    (    s=   lib/python2.7/site-packages/sympy/series/tests/test_limits.pyt   test_exponential2Ô   s    c          C   sA   t  d t t ƒ }  t |  t t ƒ } | j ƒ  t k s= t ‚ d  S(   Ni   (   R   R-   R   R   RJ   R9   (   RW   t   l(    (    s=   lib/python2.7/site-packages/sympy/series/tests/test_limits.pyt	   test_doitÚ   s    c          C   sV  t  t t ƒ t t d ƒ t t ƒ t d d ƒ k s; t ‚ t  t t ƒ t t d ƒ d t t ƒ t d d ƒ k sz t ‚ t  t t ƒ t t ƒ t t ƒ t t ƒ t d d ƒ k s» t ‚ t t d ƒ d d d t d ƒ t	 t d d ƒ t d ƒ ƒ ƒ }  t  t
 t t t ƒ j t ƒ t d t f ƒ j ƒ  j t ƒ ƒ t t ƒ |  k sQt ‚ t t d ƒ d t	 t d d ƒ t d ƒ ƒ d t d ƒ d ƒ } t  t
 t t t ƒ j t ƒ t d t f ƒ j ƒ  j t ƒ ƒ t t ƒ | k sèt ‚ t  t t ƒ t t t ƒ t d t ƒ k st ‚ t  t t ƒ d d t t t ƒ t d t ƒ k sRt ‚ d  S(   Ni   iþÿÿÿi   iÿÿÿÿi   iýÿÿÿi    (   R   R   R0   R   R$   R9   R	   R&   R   R%   R   R   R1   t   rewriteR   RJ   R   R-   (   t   t1t   t2(    (    s=   lib/python2.7/site-packages/sympy/series/tests/test_limits.pyt   test_AccumBoundsà   s    ;?ABTCT1c          C   sG   t  d t t ƒ }  t |  t t ƒ } | j d t ƒ | k sC t ‚ d  S(   Ni   t   deep(   R   R-   R   R   RJ   t   FalseR9   (   RW   R\   (    (    s=   lib/python2.7/site-packages/sympy/series/tests/test_limits.pyt
   test_doit2ó   s    c           C   sÔ   t  d t t ƒ t d t t d ƒ d ƒ d d t t d ƒ d ƒ k sR t ‚ t  t t t d ƒ d ƒ t d ƒ t d t d ƒ ƒ k s” t ‚ t  t t t d ƒ d ƒ t d ƒ d t d ƒ k sÐ t ‚ d  S(   Ni   i   i   i    (   R   R	   R-   R   R9   R   RT   (    (    (    s=   lib/python2.7/site-packages/sympy/series/tests/test_limits.pyt   test_issue_3792û   s    RBc           C   sà   t  d t d t d ƒ t d ƒ d k s0 t ‚ t  d t t t d ƒ t d ƒ d t k sd t ‚ t  t t ƒ t d d t d ƒ t d ƒ d k sž t ‚ t  t t ƒ t d t t d ƒ t d ƒ d t k sÜ t ‚ d  S(   Ni   i   i   i   i   i   (   R   R-   R   R9   R   R   (    (    (    s=   lib/python2.7/site-packages/sympy/series/tests/test_limits.pyt   test_issue_4090  s    04:c           C   s\   t  t t ƒ t d d d ƒt k s* t ‚ t  t t ƒ t t d d d ƒd k sX t ‚ d  S(   Ni    R4   R5   i   (   R   R   R-   R   R9   R   (    (    (    s=   lib/python2.7/site-packages/sympy/series/tests/test_limits.pyt   test_issue_4547  s    *c           C   sÖ   t  t d t t ƒ t d k o+ t k n s6 t ‚ t  t d t d ƒ t d ƒ d k sb t ‚ t  t d t d ƒ d k s„ t ‚ t  t d t t ƒ d k s¦ t ‚ t  t d t d ƒ t d ƒ d k sÒ t ‚ d  S(   Ng      à?i   i    g      à¿i   (   R   R-   R   R9   R   (    (    (    s=   lib/python2.7/site-packages/sympy/series/tests/test_limits.pyt   test_issue_5164  s
    6,""c    
       C   s˜  t  t t t g d d g d d t d d ƒ t d d ƒ g d d g ƒ ƒ }  t t t t t t t t d t d d ƒ t d d d d d d d d t t t t t t t t t d t d d ƒ d d d d d d d d f  } t |  ƒ t | ƒ k s t ‚ x‘ t t	 |  | ƒ ƒ D]z \ } \ } } | \ } } } } | | | }	 y( t
 |	 t d d | ƒ| k sot ‚ Wqt k
 rd  st ‚ qXqWd  S(	   Niÿÿÿÿi   i   i   R6   R5   i    R4   (   t   listt   cartesR-   R   R   R   t   lenR9   t	   enumeratet   zipR   t   None(
   t   testst   resultst   iRK   t   resR.   t   st   et   dt   eq(    (    s=   lib/python2.7/site-packages/sympy/series/tests/test_limits.pyt   test_issue_5183  s     	!00((c          C   s  t  t t ƒ t t t ƒ d k s( t ‚ t  t t ƒ t t ƒ t d k sP t ‚ t  t t ƒ t t ƒ t k st t ‚ t  t t ƒ t t t ƒ d k sœ t ‚ t  t t ƒ t t	 d d ƒ ƒ t
 t ƒ k sÏ t ‚ t d d t d t ƒ}  t  |  t d |  ƒ |  d ƒ d k st ‚ d  S(   Ni    i   i   t   rRQ   t   finite(   R   R   R-   R   R9   R   R   R   R	   R   R   R   RR   (   Rx   (    (    s=   lib/python2.7/site-packages/sympy/series/tests/test_limits.pyt   test_issue_5184-  s    (($(3c           C   s5   t  d t d t t j t d ƒ d k s1 t ‚ d  S(   Ni   i    (   R   R.   R   RY   R9   (    (    (    s=   lib/python2.7/site-packages/sympy/series/tests/test_limits.pyt   test_issue_52298  s    c    	      C   s<  t  t t t g t d d t d t d t d g d d g ƒ ƒ }  d d t t d d t t d d t t d d t t d d t t f } t |  ƒ t | ƒ k s© t ‚ xŒ t t	 |  | ƒ ƒ D]u \ } \ } } | \ } } } | t
 ƒ } y( t | t
 | d | ƒ| k st ‚ Wq¿ t k
 r3d  s4t ‚ q¿ Xq¿ Wd  S(   Ni   i    i   R6   R5   R4   (   Ri   Rj   R   R   R   R   Rk   R9   Rl   Rm   R-   R   Rn   (	   Ro   Rp   Rq   RK   Rr   RW   R\   Ru   Rv   (    (    s=   lib/python2.7/site-packages/sympy/series/tests/test_limits.pyt   test_issue_4546<  s    # '((c           C   sn   t  d t t d ƒ d t t d ƒ d k s4 t ‚ t  d d t d d t t t d ƒ d k sj t ‚ d  S(   Ni   i   i    i   (   R   R-   R   R9   (    (    (    s=   lib/python2.7/site-packages/sympy/series/tests/test_limits.pyt   test_issue_3934Q  s    4c           C   st   t  t t d ƒ d d t t d ƒ d t t ƒ d k sB t ‚ t  t d d t d t t ƒ d k sp t ‚ d  S(   NiM   i   i   gfffffFY@(   R   R-   R   R   R9   (    (    (    s=   lib/python2.7/site-packages/sympy/series/tests/test_limits.pyt   test_calculate_seriesV  s    Bc           C   sÇ   t  t d d t d t t ƒ d k s. t ‚ t  t d d t d t t ƒ d k s\ t ‚ t  t d d t d t t ƒ d k sŠ t ‚ t  t d t d d t t ƒ t t ƒ d k sÃ t ‚ d  S(   Ni   i   id   i]  iè  (   R   R-   R   R9   R   (    (    (    s=   lib/python2.7/site-packages/sympy/series/tests/test_limits.pyt   test_issue_5955]  s    ...c           C   sB   t  t d t t ƒ ƒ t t t ƒ ƒ t d ƒ d k s> t ‚ d  S(   Ni   i    (   R   R   R   R-   R   R9   (    (    (    s=   lib/python2.7/site-packages/sympy/series/tests/test_limits.pyt   test_newissued  s    c           C   s"  t  t t t t ƒ t k s# t ‚ t  t t t t ƒ t k sF t ‚ t  t d t d t t t ƒ t k su t ‚ t  d t t t ƒ t t d ƒ t k s¦ t ‚ t  t t t t ƒ t k sÈ t ‚ t  t t d t t t ƒ t k só t ‚ t  t t d t t d ƒ t k st ‚ d  S(   Ni   i   i   i    (   R   R-   R   R9   R   (    (    (    s=   lib/python2.7/site-packages/sympy/series/tests/test_limits.pyt   test_extended_real_lineh  s    ##/1"+c          C   sk   t  d d t d t ƒ}  t |  ƒ t t d |  ƒ k s= t ‚ t t |  d d |  t ƒ t k sg t ‚ d  S(   NR-   R3   Ry   i   i   i   (   R   RR   R(   R   R9   R   (   R-   (    (    s=   lib/python2.7/site-packages/sympy/series/tests/test_limits.pyt   test_order_oor  s    %c           C   s$   t  t d „  ƒ t  t d „  ƒ d  S(   Nc           S   s   t  t t t ƒ t t ƒ S(   N(   R   R   R-   R.   R   (    (    (    s=   lib/python2.7/site-packages/sympy/series/tests/test_limits.pyR7   z  R8   c           S   s   t  t t t ƒ t t ƒ S(   N(   R   R   R-   R.   R   (    (    (    s=   lib/python2.7/site-packages/sympy/series/tests/test_limits.pyR7   {  R8   (   R*   t   NotImplementedError(    (    (    s=   lib/python2.7/site-packages/sympy/series/tests/test_limits.pyt   test_issue_5436y  s    c           C   s$   t  t d „  ƒ t  t d „  ƒ d  S(   Nc           S   s   t  t t d d d ƒS(   Ni    R4   (   R   R-   (    (    (    s=   lib/python2.7/site-packages/sympy/series/tests/test_limits.pyR7     R8   c           S   s   t  t t d d d ƒS(   Ni    R4   t   0(   R   R-   (    (    (    s=   lib/python2.7/site-packages/sympy/series/tests/test_limits.pyR7   €  R8   (   R*   t	   TypeErrorR;   (    (    (    s=   lib/python2.7/site-packages/sympy/series/tests/test_limits.pyt   test_Limit_dir~  s    c           C   sq   t  t d d t d d d t t ƒ d k s6 t ‚ t  t d d t d d d t t ƒ d k sm t ‚ d  S(   Ni   iè  (   R   R-   R   R9   (    (    (    s=   lib/python2.7/site-packages/sympy/series/tests/test_limits.pyt   test_polynomialƒ  s    6c           C   s¡   t  d t d t t t t t t t t t ƒ t d t t k sN t ‚ t  d t d t t t t t t t t t ƒ t d t t k s t ‚ d  S(   Ni   (   R   R.   R-   R/   R   R9   (    (    (    s=   lib/python2.7/site-packages/sympy/series/tests/test_limits.pyt   test_rationalˆ  s    Nc           C   sL   t  t t ƒ t t d t ƒ t t d ƒ t t t t ƒ k sH t ‚ d  S(   Ni   i    (   R   R   R-   R/   R.   R   R   R9   (    (    (    s=   lib/python2.7/site-packages/sympy/series/tests/test_limits.pyt   test_issue_5740  s    c          C   sv   t  d d t d t ƒ}  |  d t |  d t |  d d t t d } t | t d ƒ j ƒ  |  d k sr t ‚ d  S(   NR1   R2   R3   i   i   (   R   RR   R-   R   R   R9   (   R1   Rx   (    (    s=   lib/python2.7/site-packages/sympy/series/tests/test_limits.pyt   test_issue_6366‘  s    2c          C   s"  d d l  m }  m } |  t ƒ } t | t t ƒ t k s@ t ‚ t t | t t ƒ d k sb t ‚ t | t d t t ƒ t | t t t ƒ d k sž t ‚ t | t t ƒ |  t ƒ k sÄ t ‚ t | t t d ƒ |  t d ƒ k sð t ‚ t | t t d ƒ |  t d ƒ k st ‚ d  S(   Niÿÿÿÿ(   t	   factorialt   Ei    i   i   (	   t   sympyRŒ   R   R-   R   R   R9   R   R   (   RŒ   R   RW   (    (    s=   lib/python2.7/site-packages/sympy/series/tests/test_limits.pyt   test_factorial—  s    "<&,c          C   sÀ   d t  d d d t  d t d t  d d t d ƒ d d t  d d d t  d d t d ƒ d d t d }  t |  t t ƒ d t  d d t  d d t  d d k s¼ t ‚ d  S(	   Ni   i   i   i   i   i#   i   i   (   R-   R.   R   R   R   R9   (   Rt   (    (    s=   lib/python2.7/site-packages/sympy/series/tests/test_limits.pyt   test_issue_6560¤  s    _c             si  t  d ƒ ‰ t  d d t ƒ}  t  d ƒ } t  d d t ƒ} t  d d t ƒ} d ˆ ˆ |  d	 ˆ |  ˆ |  d	 | |  d	 ˆ ˆ |  d ˆ |  ˆ |  d	 | ˆ ˆ | ˆ ‰  ˆ  j | | d	 ƒ ‰  t t ‡  ‡ f d
 †  ƒ t ˆ  j | | ƒ ˆ t ƒ d	 k st ‚ t ˆ  j | | ƒ ˆ t ƒ j ƒ  d | d	 |  d	 |  d	 | d	 k set ‚ d  S(   NR1   Rx   R3   t   ct   pt   mt   negativei   i   c              s   t  ˆ  ˆ t ƒ S(   N(   R   R   (    (   t   exprR1   (    s=   lib/python2.7/site-packages/sympy/series/tests/test_limits.pyR7   ³  R8   (	   R   RR   t   subsR*   Rƒ   R   R   R9   R   (   Rx   R‘   R’   R“   (    (   R•   R1   s=   lib/python2.7/site-packages/sympy/series/tests/test_limits.pyt   test_issue_5172ª  s    n*!c          C   s<   t  d ƒ }  t t t t |  ƒ t t ƒ d k s8 t ‚ d  S(   Nt   ai   (   R   R   R   R-   R   R9   (   R˜   (    (    s=   lib/python2.7/site-packages/sympy/series/tests/test_limits.pyt   test_issue_7088¹  s    c          C   s„   t  d ƒ }  t d t d t ƒ t |  ƒ d t d t ƒ t |  ƒ d } t | t d ƒ j ƒ  d t d |  ƒ k s€ t ‚ d  S(   NR˜   i   i   i    (   R   R/   R   R   R	   R   R   R9   (   R˜   Rt   (    (    s=   lib/python2.7/site-packages/sympy/series/tests/test_limits.pyt   test_issue_6364¾  s    Bc          C   sÄ   t  d ƒ }  t |  t t d ƒ t t |  ƒ k s8 t ‚ t |  t t d ƒ t t |  ƒ k sf t ‚ t |  t t t ƒ t t |  ƒ k s” t ‚ t |  t t t ƒ t t |  ƒ k sÀ t ‚ d  S(   NR˜   i    (   R   R   R-   R   R   R9   (   R˜   (    (    s=   lib/python2.7/site-packages/sympy/series/tests/test_limits.pyt   test_issue_4099Ä  s
    ,..c          C   sx   t  d ƒ }  t t d t t |  ƒ ƒ t d t t ƒ ƒ |  |  d ƒ t t ƒ d t t t ƒ d ƒ k st t ‚ d  S(   Nt   dxi   i    i   (   R   R   R   R   R-   R9   (   Rœ   (    (    s=   lib/python2.7/site-packages/sympy/series/tests/test_limits.pyt   test_issue_4503Ì  s    ;c           C   s(   t  t t ƒ t t ƒ t k s$ t ‚ d  S(   N(   R   R   R-   R   R9   (    (    (    s=   lib/python2.7/site-packages/sympy/series/tests/test_limits.pyt   test_issue_8730Ò  s    c           C   s?   t  d t t t d t t ƒ d t t ƒ t k s; t ‚ d  S(   Ni   i   (   R   R0   R   R   R   R9   (    (    (    s=   lib/python2.7/site-packages/sympy/series/tests/test_limits.pyt   test_issue_10801Ö  s    c          C   sÄ   t  d ƒ \ }  } } t |  |  | ƒ j | h k s9 t ‚ t |  |  | d ƒ j | h k s` t ‚ t |  | |  | | ƒ j | h k sŒ t ‚ t |  d | |  d | ƒ j | | h k sÀ t ‚ d  S(   Ns   x, y, aR6   i   (   R   R   t   free_symbolsR9   (   R-   R.   R˜   (    (    s=   lib/python2.7/site-packages/sympy/series/tests/test_limits.pyt   test_issue_9205Û  s
    $',c           C   sH   t  t t t t t t t t d ƒ ƒ t t t d k sD t ‚ d  S(   Ni    i   (   R   R   R-   R.   R1   R9   (    (    (    s=   lib/python2.7/site-packages/sympy/series/tests/test_limits.pyt   test_issue_11879ã  s    c          C   s^   t  d ƒ }  t d |  |  t ƒ d k s. t ‚ t d d |  |  t ƒ t d ƒ k sZ t ‚ d  S(   NR0   g      ð?i   g333333Ó?(   R   R   R   R9   R   (   R0   (    (    s=   lib/python2.7/site-packages/sympy/series/tests/test_limits.pyt   test_limit_with_Floatç  s    "c           C   sQ   t  d t d t d t d d t d t t ƒ t d ƒ d k sM t ‚ d  S(   Ni   i   i   (   R   R-   R   R   R9   (    (    (    s=   lib/python2.7/site-packages/sympy/series/tests/test_limits.pyt   test_issue_10610í  s    c           C   s0   t  t t t ƒ t t t ƒ d k s, t ‚ d  S(   Ni   (   R   R1   R	   R   R9   (    (    (    s=   lib/python2.7/site-packages/sympy/series/tests/test_limits.pyt   test_issue_6599ñ  s    c           C   s…   t  d t d t d t d t t ƒ t t ƒ d k sA t ‚ t  d t d t d t d t t ƒ t t ƒ t k s t ‚ d  S(   Ni   i   i
   (   R   R-   R   R   R9   (    (    (    s=   lib/python2.7/site-packages/sympy/series/tests/test_limits.pyt   test_issue_12555õ  s    Ac           C   sC  t  t d t t t ƒ t t ƒ t t ƒ t k s; t ‚ t  t d t t t ƒ t t ƒ t t ƒ t k su t ‚ t  t t t ƒ d j ƒ  t t ƒ t k s§ t ‚ t  t t t ƒ d j ƒ  t t ƒ t k sÙ t ‚ t  t t t ƒ d j ƒ  t t ƒ t k st ‚ t  t t t ƒ d j ƒ  t t ƒ t k s?t ‚ d  S(   Ni   (   R   R-   R   R	   R   R9   t   expand(    (    (    s=   lib/python2.7/site-packages/sympy/series/tests/test_limits.pyt   test_issue_12564ú  s    ;:223c           C   s$   t  t d „  ƒ t  t d „  ƒ d  S(   Nc           S   s   t  t t ƒ t t ƒ j ƒ  S(   N(   R   R   R-   R!   RJ   (    (    (    s=   lib/python2.7/site-packages/sympy/series/tests/test_limits.pyR7     R8   c           S   s"   t  t d t d t t ƒ j ƒ  S(   Ni   i   (   R   R-   R!   RJ   (    (    (    s=   lib/python2.7/site-packages/sympy/series/tests/test_limits.pyR7     R8   (   R*   Rƒ   (    (    (    s=   lib/python2.7/site-packages/sympy/series/tests/test_limits.pyt   test_issue_14456  s    c           C   sM   t  d t d t t t d ƒ t d t d t d ƒ t k sI t ‚ d  S(   Ni   i   i   i   (   R   R    R   R-   R   R9   (    (    (    s=   lib/python2.7/site-packages/sympy/series/tests/test_limits.pyt   test_issue_14411  s    c           C   sB   t  t t ƒ t t t d ƒ t d t t ƒ d k s> t ‚ d  S(   Ni   i   i    (   R   R   R-   R	   R   R9   (    (    (    s=   lib/python2.7/site-packages/sympy/series/tests/test_limits.pyt   test_issue_14574  s    c           C   s  t  t t ƒ t t ƒ t j k s' t ‚ t  d t t ƒ t t ƒ d t j k sV t ‚ t  d t t ƒ t t ƒ d t j k s… t ‚ t  t t ƒ t t ƒ t j k s¬ t ‚ t  t t ƒ t t ƒ t j k sÕ t ‚ t  d t t ƒ t t ƒ d k sþ t ‚ d  S(   Ni   i   i   iþÿÿÿ(   R   R#   R-   R   R   t   HalfR9   R"   (    (    (    s=   lib/python2.7/site-packages/sympy/series/tests/test_limits.pyt   test_issue_10102  s    '//')c           C   s   t  t d „  ƒ d  S(   Nc           S   s(   t  t t t ƒ t t t ƒ t t ƒ S(   N(   R   R   R   R-   R   R   R   (    (    (    s=   lib/python2.7/site-packages/sympy/series/tests/test_limits.pyR7     R8   (   R*   Rƒ   (    (    (    s=   lib/python2.7/site-packages/sympy/series/tests/test_limits.pyt   test_issue_14377  s    c           C   sG   t  t t t t ƒ d ƒ t t t d d ƒj ƒ  d k sC t ‚ d  S(   Ni   R4   R6   i    (   R   R-   R   R   R   RJ   R9   (    (    (    s=   lib/python2.7/site-packages/sympy/series/tests/test_limits.pyt   test_issue_15984  s    N(}   t	   itertoolsR    Rj   RŽ   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.calculus.utilR$   t   sympy.core.addR%   t   sympy.core.mulR&   t   sympy.series.limitsR'   t   sympy.series.orderR(   t   sympy.utilities.pytestR)   R*   t   sympy.core.numbersR+   t%   sympy.functions.combinatorial.numbersR,   t	   sympy.abcR-   R.   R/   R0   RR   R1   R<   R=   R>   R?   RH   RI   RL   RM   RN   RO   RP   RS   RU   RV   RX   RZ   R[   R]   Ra   Rd   Re   Rf   Rg   Rh   Rw   Rz   R{   R|   R}   R~   R   R€   R   R‚   R„   R‡   Rˆ   R‰   RŠ   R‹   R   R   R—   R™   Rš   R›   R   Rž   RŸ   R¡   R¢   R£   R¤   R¥   R¦   R¨   R©   Rª   R«   R­   R®   R¯   (    (    (    s=   lib/python2.7/site-packages/sympy/series/tests/test_limits.pyt   <module>   s’   Ü"	;																
															
																													