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 d  d l m Z m  Z  m! Z! m" Z" m# Z# m$ Z$ d  d l% m& Z& m' Z' m( Z( e d ƒ \ Z) Z* Z+ e d d e, ƒ\ Z- Z. Z/ e d ƒ e d ƒ Z0 Z1 d	 „  Z2 d
 „  Z3 d „  Z4 d „  Z5 d „  Z6 d „  Z7 e( d „  ƒ Z8 e( d „  ƒ Z9 d „  Z: d „  Z; d „  Z< d „  Z= d „  Z> e' d „  ƒ Z? e' d „  ƒ Z@ d „  ZA d „  ZB d S(   iÿÿÿÿ(   t   symbolst	   factorialt   sqrtt   Rationalt   atant   It   logt   fpst   Ot   Sumt   oot   St   pit   cost   sint   Functiont   expt
   Derivativet   asint   airyait   acost   acosht   gammat   erft   asecht   Addt   Integralt   Mult	   integrate(   t   rational_algorithmt   FormalPowerSeriest   rational_independentt   simpleDEt   exp_ret   hyper_re(   t   raisest   XFAILt   slows   x y zs   n m kt   integert   ft   rc          C   sð  d t  d d t  d }  t |  t  t ƒ d t d d t t d ƒ t t ƒ d d f k sg t ‚ d t  t  d t  d t  d t  d }  t |  t  t ƒ d d t d d t  d d f k sÍ t ‚ t t t t t  t t  t  d }  t |  t  t ƒ t t d t t t t t d t t t d d f k sIt ‚ t  d t  t  d }  t |  t  t ƒ d  k s}t ‚ t |  t  t d t	 ƒt
 d d ƒ t d ƒ d t d t d ƒ d	 t
 d d ƒ t d ƒ d t
 d d ƒ t d t d ƒ d	 t
 d d ƒ d d f k s't ‚ d t  d d t  d }  t |  t  t ƒ d  k s_t ‚ t |  t  t d t	 ƒt d
 t t d d t d
 t t d d d d f k sºt ‚ t d t  ƒ }  t |  t  t ƒ d
 t t d d f k sût ‚ t t  ƒ }  t |  t  t ƒ d  k s%t ‚ t |  t  t d t	 ƒt t t d t t t d t d d f k sut ‚ t  t t  ƒ t d t  d ƒ d }  t |  t  t ƒ d  k s¹t ‚ t |  t  t d t	 ƒt t t d d t t t d d t t d d d f k st ‚ t d t  d t  ƒ d t t  ƒ }  t |  t  t ƒ d  k s]t ‚ t |  t  t d t	 ƒd
 t d t t t d t t t d t
 d d ƒ t d d f k sÈt ‚ t t t  ƒ t  t ƒ d  k sìt ‚ d  S(   Ni   i   i    i   iñÿÿÿi   t   fulli   i
   iÿÿÿÿ(   t   xR   t   kR   t   AssertionErrort   zt   yt   mt   Nonet   TrueR   R   R   R   R   R   (   R'   (    (    s=   lib/python2.7/site-packages/sympy/series/tests/test_formal.pyt   test_rational_algorithm   sL    >*-&G$$1F";&*!&0&c          C   s`  t  }  |  g  t ƒ g  k s! t ‚ |  t t ƒ t t ƒ g t ƒ t t ƒ t t ƒ g k s` t ‚ |  t d t t ƒ t t t ƒ t d g t ƒ t d t d t t t ƒ t t ƒ g k sÅ t ‚ |  t j t t t ƒ t t ƒ t t ƒ t t t ƒ t t ƒ t g t ƒ t d t t t ƒ t t ƒ t t ƒ t t t ƒ t t ƒ g k s\t ‚ d  S(   Ni   i   i   (   R   R*   R,   R   R   R   t   OneR   (   t   ri(    (    s=   lib/python2.7/site-packages/sympy/series/tests/test_formal.pyt   test_rational_independentA   s    ?05Jc          C   sÚ  xS t  t t ƒ t t ƒ D]9 }  |  t t ƒ t t t ƒ t ƒ d f k sQ t ‚ Pq WxU t  t t ƒ t t ƒ D]; }  |  t t ƒ t t t ƒ t t ƒ d f k s© t ‚ Pqo Wxj t  t d t ƒ t t ƒ D]L }  |  t d t t t ƒ t d ƒ t t t ƒ t ƒ d f k st ‚ PqË Wxn t  t t ƒ t t ƒ D]T }  |  t t t t ƒ t ƒ t d d t t t ƒ t t ƒ d f k s‡t ‚ Pq4Wxw t  t t ƒ t t ƒ t t ƒ D]S }  |  d t t ƒ d t t t ƒ ƒ t t t ƒ t t ƒ d f k st ‚ Pq¯Wxp t  d t d t t	 t t ƒ D]L }  |  d t	 t t ƒ t d d t t t ƒ t ƒ d f k stt ‚ Pq)WxZ t  t
 t ƒ t t ƒ D]@ }  |  t t t ƒ t t t ƒ t t ƒ d f k sÑt ‚ Pq’Wd  S(   Ni   i   (   R    R   R*   R'   R   R,   R   R   R   t   nR   (   t   DE(    (    s=   lib/python2.7/site-packages/sympy/series/tests/test_formal.pyt   test_simpleDEK   s,    24#E;)L)E9c          C   sû  t  t ƒ t t  t ƒ t ƒ }  t |  t t ƒ t t ƒ t t d ƒ k sS t ‚ t  t ƒ t t  t ƒ t t ƒ }  t |  t t ƒ t t ƒ t t d ƒ k s§ t ‚ t  t ƒ t t  t ƒ t ƒ t t  t ƒ t t ƒ }  t |  t t ƒ t t ƒ t t d ƒ t t d ƒ k st ‚ t t  t ƒ t ƒ t t  t ƒ t t ƒ }  t |  t t ƒ t t ƒ t t d ƒ k syt ‚ t t  t ƒ t d ƒ t t  t ƒ t d ƒ t t  t ƒ ƒ }  t |  t t ƒ t t ƒ t t d ƒ t t d ƒ k s÷t ‚ d  S(   Ni   i   i   i   (   R'   R*   R   R!   R(   R+   R,   (   t   d(    (    s=   lib/python2.7/site-packages/sympy/series/tests/test_formal.pyt   test_exp_ree   s     3"25@+2>c          C   s_  t  t ƒ t t  t ƒ t t ƒ }  t |  t t ƒ t t ƒ t d t d t t d ƒ k sd t ‚ t t  t ƒ t t  t ƒ t t ƒ }  t |  t t ƒ t d t d t t d ƒ t t ƒ k sÍ t ‚ d t  t ƒ d t t  t ƒ t ƒ t t  t ƒ t t ƒ }  t |  t t ƒ d t d t t d ƒ t d t d t t d ƒ d t t ƒ k sjt ‚ d t t  t ƒ t d d t t  t ƒ t ƒ }  t |  t t ƒ t t t ƒ d t t t d ƒ t d t t d ƒ k sòt ‚ t d d t t  t ƒ t ƒ t t d d t t  t ƒ t t ƒ }  t |  t t ƒ t t d t t t ƒ d t t d t d d t t d ƒ k s—t ‚ t d d t t  t ƒ t d ƒ d t t t  t ƒ t t ƒ t t  t ƒ t ƒ }  t |  t t ƒ t t d t d d t t d t t t ƒ t t d t d t t d ƒ k s[t ‚ d  S(	   Ni   i   i   iþÿÿÿi
   i   i	   i(   (   R'   R*   R   R"   R(   R+   R,   R6   (   R9   (    (    s=   lib/python2.7/site-packages/sympy/series/tests/test_formal.pyt   test_hyper_rev   s$    "B'B=Q3FGO?1c          C   sW  t  d ƒ d k s t ‚ t  d t ƒ d k s3 t ‚ t  d t d d ƒd k sT t ‚ t  d t d d ƒd k su t ‚ t  t d t d ƒ t d t d k s¥ t ‚ t  d t d t d ƒ d t d t d k sÝ t ‚ t  t d t ƒ d t d t ƒt d t ƒ k st ‚ t  t d t ƒ ƒ }  t |  t ƒ s@t ‚ |  j t d t ƒ k s_t ‚ |  j t t	 ƒ |  k s}t ‚ |  d  d	 t t d d t d
 d
 t d d g k s¼t ‚ |  j
 t ƒ t k s×t ‚ |  j d ƒ t t d d t d
 d
 t d d t d d k s"t ‚ |  j j d	 } |  j t d | t | | | d t f ƒ k skt ‚ |  j d d  ƒ |  d  } } x@ t | ƒ D]2 \ } } | d k r±Pn  | | | k s•t ‚ q•Wt t ƒ j  t ƒ }  t |  t ƒ sõt ‚ |  j ƒ  t t d
 d t d d t t d ƒ k s3t ‚ t t d „  ƒ t t d „  ƒ d  S(   Ni   i   t   dirt   +t   -t   hypert   rationali   i    i   i   i   iÿÿÿÿR6   ix   c           S   s   t  t t ƒ S(   N(   R   R.   R*   (    (    (    s=   lib/python2.7/site-packages/sympy/series/tests/test_formal.pyt   <lambda>®   t    c           S   s   t  t d d ƒS(   NR<   i    (   R   R*   (    (    (    s=   lib/python2.7/site-packages/sympy/series/tests/test_formal.pyRA   ¯   RB   (   R   R,   R*   R   t   Falset
   isinstanceR   t   functiont   subsR.   t   as_leading_termt
   polynomialt   akt	   variablest   infiniteR	   R
   t   truncateR0   t	   enumerateR   R   R#   t   NotImplementedErrort
   ValueError(   R'   R+   t   ftt   st   it   t(    (    s=   lib/python2.7/site-packages/sympy/series/tests/test_formal.pyt   test_fps   s4    !!088?K9>c          C   s’  t  d t ƒ d t k s  t ‚ t  t d t d t d d d ƒt d t d t d k sf t ‚ d t d d t d }  t  |  t ƒ j ƒ  t d d ƒ d t d d t d d	 d
 t d d d t d d d t d d t t d ƒ k st ‚ d t t d t d t d t d }  t  |  t ƒ j ƒ  t d d ƒ d t d d t d d	 d
 t d d d t d d d t d d t t d ƒ k s³t ‚ t d t t d }  t  |  t d t ƒj ƒ  t t d d t d d t d d t d t t d ƒ k s*t ‚ d t d d t d }  t  |  t d t ƒj ƒ  t d d ƒ t d t d d t d d	 t d d	 t t d ƒ k s®t ‚ t d t ƒ }  t  |  t ƒ j ƒ  t t d d t d d t d d t d d t t d ƒ k st ‚ t  |  t d d ƒj ƒ  t  |  t d d ƒj ƒ  k sYt ‚ t  |  t d ƒ j ƒ  t d ƒ t d d ƒ t d d d t d d d t d d d t d d d t d t t d d t d f ƒ k sót ‚ t  |  t d d d ƒj ƒ  t d ƒ t d d ƒ t d d d t d d d t d d d t d d d t d t t d d t d f ƒ k s—t ‚ t t ƒ }  t  |  t d t ƒj ƒ  t t d d t d d t t d ƒ k sðt ‚ t  |  t d t d d ƒj ƒ  t  |  t d t d d ƒj ƒ  k s8t ‚ t  |  t d d t ƒj ƒ  t d ƒ t d d ƒ d t d d d d t d d d d t d d d d t d d d t d t t d d t d f ƒ k sèt ‚ t  |  t d d t d d ƒj ƒ  t d ƒ t d d ƒ d t d d d d t d d d d t d d d d t d d d t d t t d d t d f ƒ k s¢t ‚ t t t ƒ t d t d ƒ d }  t  |  t d t ƒj ƒ  t d d t d d t t d ƒ k st ‚ t d t d t ƒ d t t ƒ }  t  |  t d t ƒj d d  ƒ d t d d d t d! d! t t d  ƒ k sŽt ‚ d  S("   Ni   i   i   R<   iÿÿÿÿi   i   i   i   i1   i   i   i    iA  i@   i   iq   iñ   R)   i   iQ   iD  i¿  i   i   iw  iq  i)   i	=  i   R6   i
   i   (	   R   R*   R,   RL   R   R   R1   R   R   (   R'   (    (    s=   lib/python2.7/site-packages/sympy/series/tests/test_formal.pyt   test_fps__rational²   sD     Fs*rIRM<…‰M*•!™&I&c          C   s¯  t  t ƒ }  t |  t ƒ j ƒ  t t d d t d d t t d ƒ k sS t ‚ t t ƒ }  t |  t ƒ j ƒ  d t d d t d d t t d ƒ k s¦ t ‚ t t ƒ }  t |  t ƒ j ƒ  d t t d d t d d t d d t d d t t d ƒ k st ‚ t t ƒ }  t |  t ƒ j ƒ  t t d d t d d t t d ƒ k sht ‚ t t	 t ƒ ƒ }  t |  t ƒ j ƒ  t t
 d ƒ t t t
 d ƒ t d t t
 d ƒ d t d t t
 d ƒ d d t d t t
 d ƒ d t d t t
 d ƒ d t t d ƒ k s1t ‚ t t t ƒ ƒ }  t |  t ƒ j ƒ  t t t t d d t t d d	 t t d ƒ k s–t ‚ t d t ƒ }  t |  t ƒ j ƒ  t
 d t t d d t d d t t d ƒ k sõt ‚ t t t ƒ t d t d ƒ d }  t |  t d
 t ƒj ƒ  t d d t d d t t d ƒ k sdt ‚ t d t ƒ }  t |  t d
 t ƒj ƒ  t t d d t d d t d d t d d t t d ƒ k sÙt ‚ t t d ƒ }  t |  t ƒ j ƒ  d t d d ƒ t t d d ƒ ƒ d t
 d t d d ƒ t d d t t d d ƒ ƒ t t d ƒ k spt ‚ t t ƒ t  t ƒ }  t |  t ƒ j ƒ  t t d t d d t d d t t d ƒ k sÕt ‚ t t ƒ t  t ƒ t }  t |  t ƒ j ƒ  d t t d d t d d t d d t t d ƒ k sFt ‚ t  t ƒ t t ƒ }  t |  t ƒ j ƒ  t d t d d d t d d t t d ƒ k s«t ‚ d  S(   Ni   i   i   ix   i   i   i   i   i   R@   i   i   iZ   i   (   R   R*   R   RL   R   R,   R   R   R   R   R   R   R   R   RC   R   R   R   (   R'   (    (    s=   lib/python2.7/site-packages/sympy/series/tests/test_formal.pyt   test_fps__hyperæ   s<    GGQG¥SO&IMuOWc          C   sÁ  t  d t t  ƒ }  t |  t  ƒ j ƒ  d t  d d d t  d t j d t  d d t  d d t t  d ƒ k s~ t ‚ t  d t t  ƒ }  t |  t  d	 t	 ƒj ƒ  t  d
 t  d d
 t t  d ƒ k s× t ‚ t
 t t  ƒ ƒ t  }  t |  t  ƒ j ƒ  t  t  d d t  d
 d t  d d t  d d t t  d ƒ k sLt ‚ t  d t
 t t  ƒ ƒ }  t |  t  ƒ j ƒ  t  d t  d
 d t  d d t  d d t t  d ƒ k s½t ‚ d  S(   Niûÿÿÿi   i   i   i   ix   i°  i€‰ R@   i   i   i   iÐ  i€  (   R*   R   R   RL   R   R3   R   R,   R   RC   R   R   (   R'   (    (    s=   lib/python2.7/site-packages/sympy/series/tests/test_formal.pyt   test_fps_shift  s    X-Mc          C   sâ  t  t t  ƒ t d t  d ƒ d }  t |  t  ƒ j ƒ  t  d d t  d d t t  d ƒ k si t ‚ t t  ƒ t t  ƒ t	 t  ƒ t d t  ƒ }  t |  t  ƒ j ƒ  t  d t  d d t  d d t  d d t t  d ƒ k sî t ‚ d t  t t  ƒ }  t |  t  ƒ j ƒ  d t  t  t  d d t  d d t t  d ƒ k sQt ‚ t t  ƒ t t  ƒ d t  d }  t |  t  ƒ j ƒ  d	 t  d d d
 t  d d d t  d d d t  d d t t  d ƒ k sÞt ‚ d  S(   Ni   i   i   i   i   i   i   ix   iþÿÿÿi   i   i   iw   (
   R*   R   R   R   RL   R   R,   R   R   R   (   R'   (    (    s=   lib/python2.7/site-packages/sympy/series/tests/test_formal.pyt   test_fps__Add_expr(  s    &C.WO"c          C   s  t  t ƒ }  t |  t t ƒ |  k s* t ‚ t |  t t ƒ j ƒ  t d t d t t f ƒ k sf t ‚ t t ƒ }  t |  t t ƒ j ƒ  d t d t d t t f ƒ k s± t ‚ t |  t t ƒ j ƒ  d t d t d t t f ƒ k sñ t ‚ t t ƒ }  t |  t t d t	 ƒj ƒ  d d t d d d t d d t t
 d t d t d t t f ƒ k snt ‚ t |  t t d t	 ƒj ƒ  d d t d d d t d d t t
 d t d t d t t f ƒ k sàt ‚ t d t ƒ }  t |  t t ƒ d d t d d d t d d d t d d d t d d t t d t ƒ t d t d t t f ƒ k s{t ‚ t |  t t ƒ d d t d d d t d d d t d d d t d d t t t
 t d t ƒ t d t d t t f ƒ k st ‚ d  S(	   Ni   i   iÿÿÿÿR)   i   i   i   i   (   R   R*   R   R
   R,   RL   R   R   R   R1   R   R   R   (   R'   (    (    s=   lib/python2.7/site-packages/sympy/series/tests/test_formal.pyt   test_fps__asymptotic7  s"    <?@VVU'c          C   s+  t  t t ƒ ƒ t }  t |  t ƒ j ƒ  d t t ƒ t t ƒ d t t d d ƒ d t t d d ƒ d t t d d ƒ d	 t t d
 d ƒ d t t d d ƒ d t t d ƒ k sÆ t ‚ t  t t ƒ ƒ t }  t |  t ƒ j ƒ  t t d d ƒ t t d d ƒ d t t d d ƒ d t t d
 d ƒ d t t d d ƒ d	 t t d ƒ k slt ‚ t t t ƒ ƒ t d }  t |  t ƒ j ƒ  t t d d ƒ t t d d ƒ d t t d d ƒ d t t d d ƒ d t t d d ƒ d
 t t d d ƒ d t t d
 d ƒ d t t d d ƒ d t t d ƒ k sUt ‚ t	 t t ƒ ƒ }  t |  t ƒ j ƒ  j
 ƒ  d t d t d d t d d t d d t d d t t ƒ t t d d ƒ d t t d d ƒ d t t d d ƒ d t t d
 d ƒ d	 t t d d ƒ d t t d ƒ k sGt ‚ t	 t t ƒ ƒ t }  t |  t ƒ j ƒ  j
 ƒ  t t d d t d d t d d t d d t t d d ƒ t t d d ƒ d t t d d ƒ d t t d
 d ƒ d t t d d ƒ d	 t t d ƒ k s't ‚ d  S(   Ni   i   i   i   ix   i   i°  i   i€‰ i	   i ai   I Ì(s   iýÿÿÿiÿÿÿÿi   i   i   iÐ  i   i€  i _7 (   R   R   R*   R   RL   R   R   R,   R   R   t   expand(   R'   (    (    s=   lib/python2.7/site-packages/sympy/series/tests/test_formal.pyt   test_fps__fractionalO  s    ž~½Èc          C   sæ   t  d d t ƒ }  t |  t ƒ t  t ƒ t t d d t d d t d d t d d t t d ƒ k sx t ‚ t |  t d t ƒt  t ƒ t t d d t d d t d d t d d t t d ƒ k sâ t ‚ d  S(   Ni   i   i   i   i   i   R@   (   R   R*   R   R   R,   RC   (   R'   (    (    s=   lib/python2.7/site-packages/sympy/series/tests/test_formal.pyt!   test_fps__logarithmic_singularityn  s
    Xc          C   se   t  t ƒ }  t |  t ƒ t d ƒ t t ƒ t d d d t d d t t d ƒ k sa t ‚ d  S(   Ni   i   i   i@   i   (   R   R*   R   R   R   R,   (   R'   (    (    s=   lib/python2.7/site-packages/sympy/series/tests/test_formal.pyt&   test_fps__logarithmic_singularity_failv  s    c          C   sí  t  t t t  d ƒ }  t |  t  ƒ j d ƒ t  d t  t t  d t  t d t t  t d t  ƒ k sq t ‚ t  t d t t  ƒ }  t |  t  ƒ j ƒ  t  t t d ƒ d t  d t  d t  t d t  d t  t d t t  t d t  ƒ k st ‚ t  t t	 d t  ƒ }  t |  t  ƒ } | j
 j d	 } | j t d
 | t  | t  t | | d t f ƒ k szt ‚ t  t d t t  ƒ t  t t t  ƒ }  t |  t  ƒ j ƒ  t  t d d t  d t  t  t d t  d t  t d d t  d t  t d t  d t  t d d t  d t  t d t t  t d t  ƒ k sVt ‚ t  d t t	 d t  ƒ }  t |  t  d ƒ j ƒ  t  d t t	 d ƒ t  d d t  d t d t  d d t  d t d t  d d t  d t d t  d d t  d t d t  d t d ƒ d t  d t t t  d t d t  d f ƒ k sYt ‚ t  t t t  ƒ }  t |  t  t ƒ j ƒ  t  t d t  d t  t d t  d t  t t d d t  t t  t d t  t f ƒ k sét ‚ d  S(   Ni   i   i   i   iþÿÿÿi   i   iÐ  i    iÿÿÿÿi   i   i   i(   i)   i°  i   iQ   iD  i¿  (   R*   R6   R   R   RL   R   R,   R   R   R   RI   RJ   RK   R	   R
   R   R   R   (   R'   t   fpR+   (    (    s=   lib/python2.7/site-packages/sympy/series/tests/test_formal.pyt   test_fps__symbolic|  s,    YF!;* §+@c          C   sy   t  t t  ƒ t d t  ƒ }  t |  t  ƒ j ƒ  d t  d d t  d t  d d t  d t t  d ƒ k su t ‚ d  S(   Ni   i   i   i   i   (   R*   R   R   R   RL   R   R,   (   R'   (    (    s=   lib/python2.7/site-packages/sympy/series/tests/test_formal.pyt   test_fps__slowž  s    c             s  t  t t ƒ ƒ t  t t ƒ ƒ ‰  }  ˆ  |  } | j t t ƒ t t ƒ k sT t ‚ | j ƒ  d t t d d t d d t d d t d d t t d ƒ k s® t ‚ ˆ  d } | j t t ƒ d k s× t ‚ | j ƒ  d t t d d t d d t t d ƒ k st ‚ d |  } | j t t ƒ d k sBt ‚ | j ƒ  d t d d t d d t t d ƒ k s€t ‚ ˆ  t t ˆ  t ƒ k sŸt ‚ |  j ƒ  d	 t d d t d d t t d ƒ k sÞt ‚ ˆ  ˆ  t	 j
 k s÷t ‚ ˆ  |  } | j t t ƒ t t ƒ k s&t ‚ | j ƒ  d	 t t d d t d d t d d t d d t t d ƒ k s€t ‚ ˆ  d } | j t t ƒ d k s©t ‚ | j ƒ  d	 t t d d t d d t t d ƒ k sët ‚ d |  } | j t t ƒ d k st ‚ | j ƒ  t d d t d d t t d ƒ k sOt ‚ t t ‡  f d
 †  ƒ t t ‡  f d †  ƒ ˆ  d } | j d t t ƒ k s¤t ‚ | j ƒ  d t t d d t d d t t d ƒ k sæt ‚ d |  } | j d t t ƒ k st ‚ | j ƒ  d d t d d t d d t t d ƒ k sQt ‚ ˆ  |  t ˆ  |  ƒ k spt ‚ ˆ  t t ˆ  t ƒ k st ‚ ˆ  j ƒ  } | j t t ƒ k s¶t ‚ | j ƒ  d t d d t d d t t d ƒ k sôt ‚ |  j ƒ  } | j t t ƒ k st ‚ | j ƒ  t t d d t d d t t d ƒ k s[t ‚ |  j ƒ  j ƒ  } | j t t ƒ k s‰t ‚ | j ƒ  d	 t d d t d d t t d ƒ k sÇt ‚ t  t t t ƒ ƒ ƒ } | j ƒ  } | j ƒ  j ƒ  d d t t ƒ t	 d ƒ d t d t d d t d d t d d t d d t t ƒ d t t	 d ƒ d d t t	 d ƒ d d t t	 d ƒ d d t t	 d ƒ d d t t	 d ƒ d d t t d ƒ k sçt ‚ ˆ  j t d d f ƒ t d ƒ d k st ‚ t ˆ  t d d f ƒ t d ƒ d k sEt ‚ t ˆ  t ƒ } | j t t ƒ k spt ‚ | j ƒ  d	 t d d t d d t t d ƒ k s®t ‚ |  j t ƒ } | j t t ƒ k sØt ‚ | j ƒ  t t d d t d d t t d ƒ k st ‚ d  S(   Ni   i   i   i   i   i   i   ix   iÿÿÿÿc              s   ˆ  t  t t ƒ d d ƒS(   NR<   iÿÿÿÿ(   R   R   R*   (    (   t   f1(    s=   lib/python2.7/site-packages/sympy/series/tests/test_formal.pyRA   Å  RB   c              s   ˆ  t  t t ƒ d d ƒS(   Nt   x0i   (   R   R   R*   (    (   Ra   (    s=   lib/python2.7/site-packages/sympy/series/tests/test_formal.pyRA   Æ  RB   i(   i   i   ið   i`'  i  i *Âi0   i   i   i ; i	   i ¾n i   i ø9i    (   R   R   R*   R   RE   R,   RL   R   R   R   t   ZeroR#   RO   R   t   diffR   R   RZ   R   (   t   f2t   fsumt   fsubt   fmt   fdt   f3t   fi(    (   Ra   s=   lib/python2.7/site-packages/sympy/series/tests/test_formal.pyt   test_fps__operations£  sp    %
%	Q
B
>?
%	Q
B
 :
B
B>?>Ó//>N(C   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   t   sympy.series.formalR   R   R   R    R!   R"   t   sympy.utilities.pytestR#   R$   R%   R*   R.   R-   R1   R6   R/   R+   R'   R(   R2   R5   R8   R:   R;   RT   RU   RV   RW   RX   RY   R[   R\   R]   R_   R`   Rl   (    (    (    s=   lib/python2.7/site-packages/sympy/series/tests/test_formal.pyt   <module>   s,   ¸.	2	
				"40					"	