ó
¡¼™\c           @   sÅ  d  d l  m Z m Z m Z 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& d  d l' m( Z( d  d l) m* Z* d  d l+ m, Z, d  d l- m. Z. m/ Z/ m0 Z0 m1 Z1 m2 Z2 m3 Z3 m4 Z4 m5 Z5 m6 Z6 m7 Z7 m8 Z8 d  d l9 m: Z: d  d	 l; m< Z< m= 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 d  „  ZT d! „  ZU d" „  ZV d# „  ZW d$ „  ZX d% „  ZY d& „  ZZ d' „  Z[ d( „  Z\ d) „  Z] d* „  Z^ d+ S(,   iÿÿÿÿ(   t   QQt   EXt   RR(   t   ring(    t   _invert_monomst   rs_integratet   rs_trunct   rs_mult	   rs_squaret   rs_powt   _has_constant_termt   rs_hadamard_expt   rs_series_from_listt   rs_expt   rs_logt	   rs_newtont   rs_series_inversiont   rs_compose_addt   rs_asint   rs_atant   rs_atanht   rs_tant   rs_cott   rs_sint   rs_cost
   rs_cos_sint   rs_sinht   rs_cosht   rs_tanht   _tan1t   rs_funt   rs_nth_roott   rs_LambertWt   rs_series_reversiont   rs_is_puiseuxt	   rs_series(   t   raises(   t   range(   t   symbols(   t   sint   cost   expt   tant   cott   atant   asint   atanht   tanht   logt   sqrt(   t   Rational(   t   expandt   Sc         C   s&   d } t  |  | ƒ | k  s" t ‚ d  S(   Ni
   iöÿÿÿg»½×Ùß|Û=(   t   abst   AssertionError(   t   at   bt   tol(    (    sA   lib/python2.7/site-packages/sympy/polys/tests/test_ring_series.pyt   is_close   s    c          C   sÍ  t  d t ƒ \ }  } | d d | d d | d } t | ƒ d | d d | d d | d k so t ‚ t | ƒ | d d | d d d | d k s§ t ‚ t  d t ƒ \ }  } | d d | d d | d } t | | ƒ | d d | d d d | d d d | k s%t ‚ t  d t ƒ \ }  } } | d | d | d } t | | ƒ | d | d d | d d | k s’t ‚ t | | ƒ | d | d d | | | k sÉt ‚ d  S(	   Nt   xi   i   i   i   i   i   s   x, y(   R   R    R   R6   R   R   (   t   RR;   t   pt   y(    (    sA   lib/python2.7/site-packages/sympy/polys/tests/test_ring_series.pyt   test_ring_series1   s    "88"G;c          C   s‰   t  d t ƒ \ }  } } } | | | d } t | | d ƒ } | | d d | d | | d | d | d | d k s… t ‚ d  S(   Ns   x, y, ti   i   i   i   (   R   R    R   R6   (   R<   R;   R>   t   tR=   t   p1(    (    sA   lib/python2.7/site-packages/sympy/polys/tests/test_ring_series.pyt
   test_trunc"   s    c             sÕ  t  d t ƒ \ }  ‰ } } d | ˆ | | ‰  x) t d ƒ D] } t ˆ  ˆ  | d ƒ ‰  q> Wˆ  d ˆ d | d d ˆ | | d d | d | d d ˆ | d | | d k sÃ t ‚ d | ˆ | | | d ˆ | ‰  t ˆ  ˆ  | d ƒ } | d d | ˆ d | | k s(t ‚ t  d t ƒ \ } ‰ ‡ ‡ f d	 †  ‰ t t ‡  ‡ f d
 †  ƒ d d ˆ d ˆ d } d ˆ d } t | | ˆ d ƒ d ˆ d d ˆ d d ˆ d k sÑt ‚ d  S(   Ns   x, y, ti   i   i   i   i   i   t   zc            s   t  |  ˆ ˆ  d ƒ } d  S(   Ni   (   R   (   R=   t   p2(   R;   RC   (    sA   lib/python2.7/site-packages/sympy/polys/tests/test_ring_series.pyt   test13   s    c              s
   ˆ ˆ  ƒ S(   N(    (    (   R=   RE   (    sA   lib/python2.7/site-packages/sympy/polys/tests/test_ring_series.pyt   <lambda>5   t    i   (   R   R    R%   R   R6   R$   t
   ValueError(   R<   R>   R@   t   iRA   t   R1RD   (    (   R=   RE   R;   RC   sA   lib/python2.7/site-packages/sympy/polys/tests/test_ring_series.pyt   test_mul_trunc(   s    f&*c          C   sÊ   t  d t ƒ \ }  } } } d | | | | d } t | | | d ƒ } t | | d ƒ } | | k sn t ‚ d | | d | d } t | | d ƒ d | d d | d d | d k sÆ t ‚ d  S(   Ns   x, y, ti   i   i   i   (   R   R    R   R   R6   (   R<   R;   R>   R@   R=   RA   RD   (    (    sA   lib/python2.7/site-packages/sympy/polys/tests/test_ring_series.pyt   test_square_trunc;   s    c    	      C   s²  t  d t ƒ \ }  } } } | | | } | d } xP | | | f D]? } t | | d ƒ } t | d | d ƒ } | | k sC t ‚ qC Wd | } t | d | d ƒ } | d d | k s¿ t ‚ t | d | d ƒ d k sà t ‚ t | d | d ƒ d d | k s	t ‚ | | } t | d | d ƒ | d d | d | d | | d k sXt ‚ t d | t d d ƒ | d	 ƒ d	 | d d
 | d d d | d d k s®t ‚ d  S(   Ns   x, y, zi   i   i   i   i   i    iþÿÿÿi   iQ   i	   (   R   R    R   R	   R6   R2   (	   R<   R;   R>   RC   t   p0R=   t   xxRA   RD   (    (    sA   lib/python2.7/site-packages/sympy/polys/tests/test_ring_series.pyt   test_pow_truncD   s    

!)
Ec          C   sŸ   t  d t ƒ \ }  } } } | | | } t | | ƒ s> t ‚ | | d } t | | ƒ sb t ‚ d | | d } t | | ƒ s‰ t ‚ | | | | } d  S(   Ns   x, y, zi   i   (   R   R    R
   R6   (   R<   R;   R>   RC   R=   (    (    sA   lib/python2.7/site-packages/sympy/polys/tests/test_ring_series.pyt   test_has_constant_termV   s    c             s^  t  d t ƒ \ }  ‰ d ˆ d ˆ d ‰  d } t ˆ  ˆ | ƒ } t ˆ  | ˆ | ƒ d k se t ‚ t  d t ƒ \ }  ‰ } d ˆ d ˆ d | ˆ ˆ d | ‰  t ˆ  ˆ | ƒ } t ˆ  | ˆ | ƒ d k sÛ t ‚ t  d t ƒ \ }  ‰ } d ˆ | ‰  ‡ f d †  ‰ t t ‡  ‡ f d †  ƒ |  j ‰  ‡ f d †  ‰ t t ‡  ‡ f d	 †  ƒ d  S(
   NR;   i   i   i   s   x, yc            s   t  |  ˆ  d ƒ } d  S(   Ni   (   R   (   R=   RA   (   R;   (    sA   lib/python2.7/site-packages/sympy/polys/tests/test_ring_series.pyt   test2m   s    c              s
   ˆ ˆ  ƒ S(   N(    (    (   R=   RQ   (    sA   lib/python2.7/site-packages/sympy/polys/tests/test_ring_series.pyRF   o   RG   c            s   t  |  ˆ  d ƒ } d  S(   Ni   (   R   (   R=   RA   (   R;   (    sA   lib/python2.7/site-packages/sympy/polys/tests/test_ring_series.pyt   test3q   s    c              s
   ˆ ˆ  ƒ S(   N(    (    (   R=   RR   (    sA   lib/python2.7/site-packages/sympy/polys/tests/test_ring_series.pyRF   s   RG   (	   R   R    R   R   R6   R$   t   NotImplementedErrort   zerot   ZeroDivisionError(   R<   t   nRA   R>   (    (   R=   RQ   RR   R;   sA   lib/python2.7/site-packages/sympy/polys/tests/test_ring_series.pyt   test_inversion`   s     "*"	c          C   sº   t  d t ƒ \ }  } } t | | d ƒ } t | | d | ƒ t | | d ƒ k sW t ‚ t | | d ƒ } t | | d | ƒ d | d d d | d d | d d	 | k s¶ t ‚ d  S(
   Ns   x, yi
   i   i   i   ip   i   i(   i   (   R   R    R   R!   R   R6   R   (   R<   R;   R>   R=   (    (    sA   lib/python2.7/site-packages/sympy/polys/tests/test_ring_series.pyt   test_series_reversionv   s    -c          C   sá  t  d t ƒ \ }  } d d | | d d | d } d d d d d g } t | | | d ƒ } |  j t t | ƒ ƒ ƒ } t | j | | ƒ | d ƒ } | | k s¬ t ‚ t  d t ƒ \ }  } } d d d d	 g } t | | | | d d
 d ƒ} t d d | | d | | d d	 | | d | d ƒ }	 | |	 k sEt ‚ t  d t ƒ \ }  } d }
 t	 | | |
 ƒ d } t | | | |
 ƒ } d }	 x7 t
 | ƒ D]) \ } } |	 | t | | | |
 ƒ 7}	 qžW| |	 k sÝt ‚ d  S(   NR;   i   i   i   i    i   i   s   x, yi   t   concuri   (   R   R    R   t	   from_listt   listt   reversedR   t   composeR6   R   t	   enumerateR	   (   R<   R;   R=   t   ct   rt   pct   r1R>   RA   RD   t   hRI   t   cx(    (    sA   lib/python2.7/site-packages/sympy/polys/tests/test_ring_series.pyt   test_series_from_list€   s(    ">!c          C   s  t  d t ƒ \ }  } d | } t | | d ƒ | d } | t d ƒ d | t d ƒ d | d k so t ‚ d | d | d d } t | | d ƒ } | d | d	 d
 d | d d d | d d | d d d | d d | d d | d d | k st ‚ t | | d ƒ } t | | d ƒ } | | k sHt ‚ t  d t ƒ \ }  } } d | d | | d } t | | d ƒ } | d | d | d d | d | d | d | d | d d d | d | | d d d | d | | d d d | d | | d d | k s6t ‚ t d ƒ } t  d t ƒ \ }  } } t | | | d ƒ t d d | d ƒ | d t d d | d ƒ | d t d d | d ƒ | d t d | ƒ | t t | ƒ ƒ k sõt ‚ t | | d | | | d ƒ t | d ƒ | d | t d d | d ƒ | d t d | ƒ | d | t d d | d ƒ | d t d | ƒ | t t | ƒ ƒ k s²t ‚ | | d d } t | | d ƒ j	 | d ƒ t t d ƒ t d ƒ d ƒ k st ‚ d  S(   NR;   i   i   i   i   iÿÿÿÿi	   iïÿÿÿi   iˆ  i   i   i½   i   i   i¢   i   i-   i$   s   x, yR7   iþÿÿÿi
   IK)A}   iè^— (
   R   R    R   R4   R6   R   R&   R   R0   R]   (   R<   R;   R=   RA   RD   t   p3R>   R7   (    (    sA   lib/python2.7/site-packages/sympy/polys/tests/test_ring_series.pyt   test_log—   s0    
6s§ˆžc    
      C   sl  t  d t ƒ \ }  } | | d } xd d d g D]V } t d | | | ƒ d } t | | | ƒ } t | | | ƒ } | | k s0 t ‚ q0 Wt | | d ƒ } | j | d ƒ t d d ƒ k sÄ t ‚ d	 } t d | | | ƒ } t | | | ƒ } | | d k st ‚ t d
 ƒ } t  d t t | ƒ | f ƒ \ }  } }	 t | | | d ƒ t | ƒ | d d t | ƒ | d d t | ƒ | d d t | ƒ | t | ƒ k s´t ‚ t | | d |	 | | d ƒ t | ƒ | d |	 d d t | ƒ | d |	 d t | ƒ | d d t | ƒ | d |	 t | ƒ | d d t | ƒ | d |	 t | ƒ | d d t | ƒ | t | ƒ k sœt ‚ t  d t	 ƒ \ }  } }	 t | | | d ƒ t	 t | ƒ d ƒ | d t	 t | ƒ d ƒ | d t	 t | ƒ d ƒ | d t	 t | ƒ ƒ | t	 t | ƒ ƒ k sJt ‚ t | | d |	 | | d ƒ t	 t | ƒ d ƒ | d |	 d t	 t | ƒ d ƒ | d |	 t	 t | ƒ d ƒ | d t	 t | ƒ ƒ | d |	 t	 t | ƒ d ƒ | d t	 t | ƒ ƒ | d |	 t	 t | ƒ d ƒ | d t	 t | ƒ ƒ | t	 t | ƒ ƒ k sht ‚ d  S(   NR;   i   i
   i   i   i   l   ÑOÄ$o¢bï®l      LÉeFS«Xi   R7   s   x, yi   i   i   i   i   (
   R   R    R   R   R   R6   t   coeffR&   R)   R   (
   R<   R;   R=   Rc   t   qRA   t   q1t   precR7   R>   (    (    sA   lib/python2.7/site-packages/sympy/polys/tests/test_ring_series.pyt   test_exp¶   s0    ((eÉƒc          C   sr   t  d t ƒ \ }  } | d d } t | | d ƒ } d d d g } | d | d d | d d k sn t ‚ d  S(   NR;   i   i   i   i    iþÿÿÿi   (   R   R    R   R6   (   R<   R;   R=   R`   t   f(    (    sA   lib/python2.7/site-packages/sympy/polys/tests/test_ring_series.pyt   test_newtonÖ   s
    c          C   s„   t  d t ƒ \ }  } | d d } | d d } t | | ƒ | d d | d d | d d | d d | d k s€ t ‚ d  S(	   NR;   i   i   i   i   i   i   i   (   R   R    R   R6   (   R<   R;   RA   RD   (    (    sA   lib/python2.7/site-packages/sympy/polys/tests/test_ring_series.pyt   test_compose_addÝ   s    c          C   sœ   t  d t ƒ \ }  } } | | | d | d | d | } t | t | d ƒ t | | d ƒ k sk t ‚ t | t | d ƒ t | | d ƒ k s˜ t ‚ d  S(   Ns   x, yi   i   i   i
   (   R   R    R   R   R6   R   (   R<   R;   R>   R=   (    (    sA   lib/python2.7/site-packages/sympy/polys/tests/test_ring_series.pyt   test_funã   s    &-c       	   C   s½  t  d t ƒ \ }  } } t d | d | d | d ƒ } t d | d | d | d ƒ d | d | d d d	 | d
 | d d d | d | d d | d | d d k s¾ t ‚ t d | | | d | d d | d ƒ | d | d
 d d | d | d d d | d | d d d | d | d d d | d | d d | d | d d | d | d d | | d d k s t ‚ t d | d | d ƒ d | t d d ƒ k sÖt ‚ t d | | d | d d | d ƒ | t d d ƒ d d | t d d ƒ k s1t ‚ t d | | d | | d d | d ƒ } | | t d	 d ƒ | d d | t d	 d ƒ d | t d d ƒ | d d | t d d ƒ k sÍt ‚ t d ƒ } t  d t ƒ \ }  } } t | | d | d ƒ t d d | t d d ƒ ƒ | d t d d | t d d ƒ ƒ | d t d d | t d d ƒ ƒ | t | t d d ƒ ƒ k sšt ‚ t | t d d ƒ | d | d d | d ƒ t t d ƒ d ƒ | t d d ƒ | t t d ƒ d ƒ | t d d ƒ t t d ƒ d ƒ | d | t t d ƒ d ƒ | d t t d ƒ d ƒ | t d d ƒ t t d ƒ d ƒ | t d d ƒ t t d ƒ ƒ k s¹t ‚ d  S(   Ns   x, yi   i   i   i
   i³ÿÿÿi   i   i   i   i   i€   i    i   i	   i   ió   iQ   i   i   R7   id   i€>  iÐ  iÈ   (   R   R    R   R6   R&   R   R1   (   R<   R;   R>   Rb   R`   R7   (    (    sA   lib/python2.7/site-packages/sympy/polys/tests/test_ring_series.pyt   test_nth_rooté   s     !g*¸6[-o“/c          C   s  t  d t ƒ \ }  } } t | | d ƒ | d d | d d | d d | k s[ t ‚ t | | | d | d | d ƒ d | d | d | d | d d | d | d | d | d d | d	 | d d | d	 | d | d | d | d | d d | d
 | d | d | d d | d | d | | k sYt ‚ t d ƒ } t  d t ƒ \ }  } } t | | | d ƒ t | d | | d d
 | d	 d	 | d
 d
 | d d ƒ | d
 t d | d d d | d	 d | d
 d | d d ƒ | d t | | d
 d | d d ƒ | d t d | d d ƒ | t t | ƒ ƒ k s€t ‚ t | | d | | | d
 ƒ t d | | d
 d | d d ƒ | d | t d | d d d | d	 d | d
 d | d d ƒ | d t d | d d ƒ | d | t | | d
 d | d d ƒ | d t d | d d ƒ | t t | ƒ ƒ k s™t ‚ d  S(   Ns   x, yi	   i   i   i   i   i   i   i   i   R7   i   (   R   R    R   R6   R&   R   R,   (   R<   R;   R>   R7   (    (    sA   lib/python2.7/site-packages/sympy/polys/tests/test_ring_series.pyt	   test_atan   s    C#Ûðc          C   s(  t  d t ƒ \ }  } } t | | | | d ƒ | d | d d | d | d d | d | d | d d | | | k sŠ t ‚ t | | | d | d | d ƒ | d | d d d | d | d d | d | d d | d | d d | d | d | | k s$t ‚ d  S(	   Ns   x, yi   i   i   i   i   i(   i   (   R   R    R   R6   (   R<   R;   R>   (    (    sA   lib/python2.7/site-packages/sympy/polys/tests/test_ring_series.pyt	   test_asin  s
    [#c          C   s  t  d t ƒ \ }  } } t | | d ƒ | d t d ƒ d | d t d ƒ d t d ƒ d	 | d
 | d k s| t ‚ t | | | d | d	 | d ƒ d | d | d d	 d | d | d d d | d | d d	 d | d | d d | d | d d	 d | d | d d	 | d | d d | d | d d | d | d | d	 | d	 d	 | d | d	 | | k sšt ‚ t d ƒ } t  d t t | ƒ | f ƒ \ }  } } t | | | d ƒ t | ƒ d d t | ƒ t d	 ƒ d	 d t | ƒ d	 | d t | ƒ d d t | ƒ d d	 t d ƒ d	 | d	 t | ƒ d	 t | ƒ | d t | ƒ d d | t | ƒ k sªt ‚ t | | d | | | d ƒ d t | ƒ d	 d t | ƒ | d	 | t | ƒ d t d ƒ d	 t | ƒ d t d ƒ d	 | d	 t | ƒ d d | d | t | ƒ d	 t | ƒ | d t | ƒ d d | t | ƒ k sžt ‚ t  d t ƒ \ }  } } t | | | d ƒ t t | ƒ d d t | ƒ d	 d	 d t | ƒ d	 ƒ | d t t | ƒ d d t | ƒ d d	 t d ƒ d	 ƒ | d	 t t | ƒ d	 t | ƒ ƒ | d t t | ƒ d d ƒ | t t | ƒ ƒ k sªt ‚ t | | d | | | d ƒ t d t | ƒ d	 d t | ƒ ƒ | d	 | t t | ƒ d d t | ƒ d d	 t d ƒ d	 ƒ | d	 t t | ƒ d d ƒ | d | t t | ƒ d	 t | ƒ ƒ | d t t | ƒ d d ƒ | t t | ƒ ƒ k s¼t ‚ | | d d } t | | d ƒ j	 | d ƒ t t
 d ƒ t d ƒ d ƒ k st ‚ d  S(   Ns   x, yi	   i   i   i;  i   i   i   i   iþÿÿÿiüÿÿÿi   i   i   i-   i   i   R7   i
   IPÈ®~†ð I“™àŒ›   (   R   R    R   R4   R6   R&   R*   R   R   R]   R,   (   R<   R;   R>   R7   R=   (    (    sA   lib/python2.7/site-packages/sympy/polys/tests/test_ring_series.pyt   test_tan  s&    M#û(ÉÕáó0c          C   s]  t  d t ƒ \ }  } } t | d | d | d ƒ | d | d | d | d | d	 | d
 d | | d | d | d | d d | d d d | d d k s¶ t ‚ t | | d | | d ƒ | d | d | d | d | d | d | d d | d | d | d | d | | d | d | | d
 k sYt ‚ d  S(   Ns   x, yi   i   i   iúÿÿÿiûÿÿÿiüÿÿÿiýÿÿÿiþÿÿÿiÿÿÿÿi   i   i   i   i   i   i-   (   R   R    R   R6   (   R<   R;   R>   (    (    sA   lib/python2.7/site-packages/sympy/polys/tests/test_ring_series.pyt   test_cot9  s
    ƒc          C   sú  t  d t ƒ \ }  } } t | | d ƒ | d t d ƒ d | d t d ƒ d t d ƒ d | d	 | d
 k s} t ‚ t | | | d | d | d ƒ | d | d d | d | d d | d | d d | d | d d | d | d d | d | d d | d | d d | d | d d | d | d d | d | d d | d | d | | k s‹t ‚ t d ƒ } t  d t t | ƒ t | ƒ | f ƒ \ }  } } t | | | d ƒ t | ƒ | d d t | ƒ | d d t | ƒ | d d t | ƒ | t | ƒ k s@t ‚ t | | d | | | d ƒ t | ƒ | d | d d t | ƒ | d | d t | ƒ | d d t | ƒ | d | t | ƒ | d d t | ƒ | d | t | ƒ | d d t | ƒ | t | ƒ k s)t ‚ t  d t ƒ \ }  } } t | | | d ƒ t t | ƒ d ƒ | d t t | ƒ d ƒ | d t t | ƒ d ƒ | d t t | ƒ ƒ | t t | ƒ ƒ k s×t ‚ t | | d | | | d ƒ t t | ƒ d ƒ | d | d t t | ƒ d ƒ | d | t t | ƒ d ƒ | d t t | ƒ ƒ | d | t t | ƒ d ƒ | d t t | ƒ ƒ | d | t t | ƒ d ƒ | d t t | ƒ ƒ | t t | ƒ ƒ k söt ‚ d  S(   Ns   x, yi	   i   i   i°  i   ix   i   iþÿÿÿiüÿÿÿi   i   i   i   iÐ  i   i   i   R7   (	   R   R    R   R4   R6   R&   R'   R(   R   (   R<   R;   R>   R7   (    (    sA   lib/python2.7/site-packages/sympy/polys/tests/test_ring_series.pyt   test_sinA  s     N#ë1eÊƒc          C   s#  t  d t ƒ \ }  } } t | | d ƒ | d t d ƒ d | d t d ƒ d | t d ƒ d | d	 t d ƒ d
 | d | d k s– t ‚ t | | | d
 | d | d ƒ | d | d d | d | d d | d | d d | d | d d | d | d d | d | d d | d | d d | d | d d | d | d d
 | d | d d | d | d | d
 | d
 d
 d k s´t ‚ t d ƒ } t  d t t | ƒ t | ƒ | f ƒ \ }  } } t | | | d ƒ t | ƒ | d d t | ƒ | d d t | ƒ | d
 d
 t | ƒ | t | ƒ k sit ‚ t | | d
 | | | d ƒ t | ƒ | d | d
 d
 t | ƒ | d | d
 t | ƒ | d d t | ƒ | d | t | ƒ | d d t | ƒ | d
 | t | ƒ | d
 d
 t | ƒ | t | ƒ k sRt ‚ t  d t ƒ \ }  } } t | | | d ƒ t t | ƒ d ƒ | d t t | ƒ d ƒ | d t t | ƒ d
 ƒ | d
 t t | ƒ ƒ | t t | ƒ ƒ k s t ‚ t | | d
 | | | d ƒ t t | ƒ d
 ƒ | d | d
 t t | ƒ d
 ƒ | d | t t | ƒ d ƒ | d t t | ƒ ƒ | d | t t | ƒ d ƒ | d t t | ƒ ƒ | d
 | t t | ƒ d
 ƒ | d
 t t | ƒ ƒ | t t | ƒ ƒ k st ‚ d  S(   Ns   x, yi	   i   i   i€  i   iÐ  i   iÿÿÿÿi   iýÿÿÿiûÿÿÿi   i   i
   i0   i   i   ix   i   R7   (	   R   R    R   R4   R6   R&   R'   R(   R   (   R<   R;   R>   R7   (    (    sA   lib/python2.7/site-packages/sympy/polys/tests/test_ring_series.pyt   test_cos[  s     g#û1eÊƒc          C   sÜ   t  d t ƒ \ }  } } t | | d ƒ \ } } | t | | d ƒ k sN t ‚ | t | | d ƒ k sl t ‚ t | | | | d ƒ \ } } | t | | | | d ƒ k s² t ‚ | t | | | | d ƒ k sØ t ‚ d  S(   Ns   x, yi	   i   (   R   R    R   R   R6   R   (   R<   R;   R>   R(   R'   (    (    sA   lib/python2.7/site-packages/sympy/polys/tests/test_ring_series.pyt   test_cos_sinu  s     &c          C   s  t  d t ƒ \ }  } } t | | d ƒ | d t d ƒ d | d t d ƒ d t d ƒ d | d | d	 k s| t ‚ t | | | d | d | d ƒ d | d
 | d | d
 | d d | d | d | d | d d | d | d d | d | d | d | d | d | d d | d | d | d | d d | d | d | | k szt ‚ t d ƒ } t  d t ƒ \ }  } } t | | | d ƒ t | d | | d
 d | d d | d d | d d ƒ | d t d | d d d | d d | d d | d d ƒ | d t | | d d | d d ƒ | d t d | d d ƒ | t t | ƒ ƒ k s t ‚ t | | d | | | d ƒ t d | | d d | d d ƒ | d | t d | d d d | d d | d d | d d ƒ | d t d | d d ƒ | d | t | | d d | d d ƒ | d t d | d d ƒ | t t | ƒ ƒ k s¸t ‚ | | d d } t | | d ƒ j | d ƒ t t d ƒ d t d ƒ ƒ k st ‚ d  S(   Ns   x, yi	   i   i   i   i   i   iþÿÿÿiüÿÿÿi   i   i   i   R7   i
   I×ùÕì› I Ð½.   (	   R   R    R   R4   R6   R&   R   R.   R]   (   R<   R;   R>   R7   R=   (    (    sA   lib/python2.7/site-packages/sympy/polys/tests/test_ring_series.pyt
   test_atanh~  s    d#Ûïù,c          C   sŽ  t  d t ƒ \ }  } } t | | d ƒ | d t d ƒ d | d t d ƒ d t d ƒ d | d	 | d
 k s| t ‚ t | | | d | d | d ƒ | d | d d | d | d d | d | d d | d | d d | d | d d | d | d d | d | d d | d | d d | d | d d | d | d d | d | d | | k sŠt ‚ d  S(   Ns   x, yi	   i   i   i°  i   ix   i   iþÿÿÿiüÿÿÿi   i   i   i   iÐ  i   i   i   (   R   R    R   R4   R6   (   R<   R;   R>   (    (    sA   lib/python2.7/site-packages/sympy/polys/tests/test_ring_series.pyt	   test_sinh•  s    d#c          C   s¸  t  d t ƒ \ }  } } t | | d ƒ | d t d ƒ d | d t d ƒ d | t d ƒ d | d	 t d ƒ d
 | d | d k s– t ‚ t | | | d
 | d | d ƒ | d | d d | d | d d | d | d d | d | d d | d | d d | d | d d | d | d d | d | d d | d | d d
 | d | d d | d | d | d
 | d
 d
 d k s´t ‚ d  S(   Ns   x, yi	   i   i   i€  i   iÐ  i   iÿÿÿÿi   iýÿÿÿiûÿÿÿi   i   i
   i0   i   i   ix   i   (   R   R    R   R4   R6   (   R<   R;   R>   (    (    sA   lib/python2.7/site-packages/sympy/polys/tests/test_ring_series.pyt	   test_cosh  s
    g#c          C   s[  t  d t ƒ \ }  } } t | | d ƒ | d t d ƒ d | d t d ƒ d t d ƒ d	 | d
 | d k s} t ‚ t | | | d | d	 | d ƒ d | d | d d	 d | d | d d d | d | d d	 d | d | d d | d | d d	 d | d | d d	 | d | d d | d | d d | d | d | d	 | d	 d	 | d | d	 | | k s›t ‚ t d ƒ } t  d t ƒ \ }  } } t | | | d ƒ t t | ƒ d d t | ƒ d	 d	 d t | ƒ d	 ƒ | d t t | ƒ d d t | ƒ d d	 t d d	 ƒ ƒ | d	 t t | ƒ d	 t | ƒ ƒ | d t t | ƒ d d ƒ | t t | ƒ ƒ k s´t ‚ t | | d | | | d ƒ } | j | d ƒ j | d ƒ t d t | ƒ d d t | ƒ d	 d t | ƒ d d	 d t | ƒ t d d	 ƒ ƒ k sWt ‚ d  S(   Ns   x, yi	   i   i   i;  i   i   i   i   iþÿÿÿiüÿÿÿi   i   i   i-   i   i   R7   i
   iüÿÿit'  i¦	  is'  i  (	   R   R    R   R4   R6   R&   R   R/   R]   (   R<   R;   R>   R7   R=   (    (    sA   lib/python2.7/site-packages/sympy/polys/tests/test_ring_series.pyt	   test_tanh¦  s    e#ûâ"c    
      C   sZ  t  t t t t t g }  t t t t	 t
 t g } t d t ƒ \ } } } t d ƒ } x‰ t |  | ƒ D]x \ } } | d | | d ƒ j | d ƒ } | d | ƒ j | d d ƒ j ƒ  }	 t | j ƒ  |	 j | d ƒ j ƒ  ƒ qd Wt d | d | d ƒ j | d ƒ } d | t d d ƒ j | d d ƒ j ƒ  }	 t | j ƒ  |	 j | d ƒ j ƒ  ƒ d  S(   Ns   x, yR7   i   i   i    i   (   R   R   R   R   R   R   R'   R(   R*   R+   R,   R/   R   R   R&   t   zipR]   t   seriest   removeOR:   t   as_exprt   subsRV   R   R    (
   t   rs_funcst   sympy_funcsR<   R;   R>   R7   t   rs_funct
   sympy_funcR=   Ri   (    (    sA   lib/python2.7/site-packages/sympy/polys/tests/test_ring_series.pyt   test_RR¹  s    "%)%,c          C   sÓ   t  d t ƒ \ }  } } d d | | d d | d } t | | ƒ sP t ‚ | | t d d ƒ | } t | | ƒ s€ t ‚ t | | ƒ s– t ‚ | | d | t d d ƒ | } t | | ƒ sÏ t ‚ d  S(   Ns   x, yi   i   i   i   (   R   R    R"   R6   (   R<   R;   R>   R=   (    (    sA   lib/python2.7/site-packages/sympy/polys/tests/test_ring_series.pyt   test_is_regularÇ  s    "#c          C   s_	  t  d t ƒ \ }  } } | t d d ƒ | t d d ƒ | } t | | d ƒ } | t d d ƒ | t d d ƒ d | t d	 d ƒ | t d d ƒ d | t d
 d ƒ | t d d ƒ | t d d ƒ | t d d ƒ | t d d ƒ | t d d ƒ } | | k st ‚ t d | d | d ƒ } | | t d d ƒ d | t d d ƒ d | t d d ƒ d d k s„t ‚ t d | | d ƒ } | | t d d ƒ d | t d d ƒ | t d d ƒ k sàt ‚ t | | d ƒ } | | t d d ƒ | t d d ƒ | t d d ƒ k s4t ‚ | | t d d ƒ | } t | | d ƒ } | | t d d ƒ | d d | t d d ƒ | d d | t d d ƒ | d d | t d d ƒ | d k sßt ‚ t | | d ƒ } | | t d d ƒ | t d d ƒ | t d d ƒ | t d d ƒ d | | t d d ƒ | t d d ƒ k snt ‚ t | | d ƒ } | | t d d ƒ | d d | t d d ƒ | d | t d
 d ƒ | d
 d
 | t d
 d ƒ | d | | d d | | t d d ƒ | d d | t d d ƒ | k s@t ‚ t	 | | d ƒ } | | t d d ƒ d | t d d ƒ d | t d d ƒ d | t d d ƒ d | | t d d ƒ | t d d ƒ k sÚt ‚ t
 | | d ƒ } | | t d d ƒ | t d d ƒ d | t d	 d ƒ d | t d d ƒ d d | t d
 d ƒ d | t d d ƒ d | t d d ƒ | t d d ƒ | t d d ƒ | t d d ƒ k s½t ‚ t | | d ƒ } | d | t d d ƒ d | t d d ƒ | t d d ƒ d | t d
 d ƒ | t d d ƒ d | t d d ƒ | t d d ƒ d d k slt ‚ | d | t d d ƒ d | t d d ƒ d | t d d ƒ d | t d d ƒ d | | t d d ƒ | t d d ƒ k sùt ‚ t | | d ƒ } | | t d d ƒ | t d d ƒ | t d d ƒ | t d d ƒ d | | t d d ƒ | t d d ƒ k s‡t ‚ t | | d ƒ } | | t d d ƒ d | t d d ƒ d | t d d ƒ d | t d d ƒ d | | t d d ƒ | t d d ƒ k s!t ‚ t | | d ƒ } | | t d d ƒ d | t d d ƒ | t d d ƒ d | t d
 d ƒ | t d d ƒ d | t d d ƒ | t d d ƒ d d k sÌt ‚ t | | d ƒ } | | t d d ƒ | t d d ƒ | t d d ƒ | t d d ƒ d | | t d d ƒ | t d d ƒ k s[	t ‚ d  S(   Ns   x, yi   i   i   i   i   i   i   i   i   iþÿÿÿi	   i   i   i   i   i    i   i   i   (   R   R    R   R6   R   R   R    R   R   R   R   R   R   R   R   R   (   R<   R;   R>   R=   R`   Rb   RA   (    (    sA   lib/python2.7/site-packages/sympy/polys/tests/test_ring_series.pyt   test_puiseuxÓ  sX    (µRFB{z½…Î–†y…–c          C   sR  t  d t ƒ \ }  } t | | d ƒ | d } | | d d | d d | d d	 | d
 d t d d ƒ | d d | d k sŽ t ‚ t | | d ƒ } t | d
 | d ƒ } | d | t d d
 ƒ d | t d d
 ƒ d | t d d
 ƒ d | t d d
 ƒ d | t d d
 ƒ k s,t ‚ t | | d ƒ } t | d | d ƒ } t | d | d ƒ } | d | t d d ƒ d | t d d ƒ d d  | t d! d ƒ d" d | t d# d ƒ d$ | t d d ƒ k sçt ‚ t | t d d
 ƒ | d ƒ } | | t d# d
 ƒ d% | d d& | t d d
 ƒ d' | d d( | t d d
 ƒ d) | d d* | t d d
 ƒ d | d d+ | t d  d
 ƒ d | d d, | t d d
 ƒ d	 | d d- | t d d
 ƒ d | d. d/ | t d d
 ƒ d | d
 d0 | t d. d
 ƒ d | d
 | t d d
 ƒ d k sNt ‚ d  S(1   NR;   i   iûÿÿÿi   I Ì(s   i   i ai   i€‰ i   i°  i   ix   iþÿÿÿiüÿÿÿi
   i½ÿÿÿi   i øºi   i€^  i	   i   i   i   i   iŸÿÿÿi=   i€:ki/   iP@  i   i!   iÈ  i   i*   I  ‰“+°I  sÊì¾ I €Íî~C I €uw  I Xww0  I (;L   i üŒi _7 i€  i   iÐ  i   (   R   R    R   R6   R   R	   R   (   R<   R;   R`   R=   (    (    sA   lib/python2.7/site-packages/sympy/polys/tests/test_ring_series.pyRE     s     \t|c          C   sS  t  d t ƒ \ }  } t  d |  ƒ \ } } | | t d d ƒ | } t | | d ƒ } | | d d | d d | d | t d d ƒ | d	 d	 | d
 | | t d	 d ƒ | d d | d | t d d ƒ | d d | d | t d d ƒ | d d d | | d | t d d ƒ d | | t d d ƒ k sOt ‚ d  S(   NR>   R;   i   i   i   i   i   i   i   i   i	   i   i   (   R   R    R   R6   (   R<   R>   R4   R;   R=   R`   (    (    sA   lib/python2.7/site-packages/sympy/polys/tests/test_ring_series.pyt   test_puiseux2,  s    c          C   sŸ  t  d ƒ \ }  } } } t | | d ƒ j ƒ  | k s< t ‚ t t | ƒ | d ƒ j ƒ  t | ƒ j | d d ƒ j ƒ  k s t ‚ t t | ƒ t | ƒ | d ƒ j ƒ  t | ƒ t | ƒ j | d d ƒ j ƒ  k sÚ t ‚ t t | ƒ t | ƒ | d ƒ j ƒ  t | ƒ t | ƒ j | d d ƒ j ƒ  k s3t ‚ t | ƒ | t | d ƒ | d d } t t | | d ƒ j ƒ  ƒ t | j | d d ƒ j ƒ  ƒ k s¢t ‚ t | d d | d ƒ t | d ƒ t | d ƒ d } t t | | d ƒ j ƒ  ƒ t | j | d d ƒ j ƒ  ƒ k s#t ‚ t |  d | ƒ t |  d d ƒ | | d } t t | | d ƒ j ƒ  ƒ t | j | d d ƒ j ƒ  ƒ k sšt ‚ t | d | d d ƒ d t	 | d | d ƒ } t t | | d ƒ j ƒ  ƒ t | j | d d ƒ j ƒ  ƒ k st ‚ t | | | ƒ } t t | | d ƒ j ƒ  ƒ t | j | d d ƒ j ƒ  ƒ k snt ‚ t
 t | d d ƒ | | ƒ } t t | | d	 ƒ j ƒ  ƒ t | j | d d	 ƒ j ƒ  ƒ k sÕt ‚ | t d d ƒ | t d d ƒ | } t t
 | ƒ | d ƒ } | j ƒ  | t d
 d ƒ | t d d ƒ | t d d ƒ | t d	 d ƒ d | | t d d ƒ | t d d ƒ k s—t ‚ t t	 | ƒ | d ƒ } | j ƒ  | t d d ƒ d | t d d ƒ | t d d ƒ d k sþt ‚ t t | ƒ | d ƒ } | j ƒ  | t d
 d ƒ d | t d d ƒ d | t d d ƒ d | t d	 d ƒ d	 | | t d d ƒ | t d d ƒ k s¥t ‚ t t | ƒ | d ƒ } | j ƒ  | t d d ƒ d	 | t d d ƒ | t d d ƒ d | t d d ƒ | t d d ƒ d | t d d ƒ | t d d ƒ d d k s\t ‚ t t | ƒ d | d ƒ j ƒ  t | ƒ d j | d d ƒ j ƒ  k s©t ‚ t t d |  ƒ |  d ƒ j ƒ  |  d d |  d d |  d d |  k süt ‚ t t d d |  ƒ |  d ƒ j ƒ  d |  d d |  d d d |  d d |  k sZt ‚ t t d |  |  d ƒ |  d ƒ j ƒ  d |  d
 d
 |  d d |  d d |  d	 d |  d d |  d d d |  d d |  d d |  k søt ‚ t t d |  | d ƒ |  d ƒ j ƒ  |  d	 | d d	 |  d | d d |  d | d d |  d | d	 d |  d | d d |  | d k s›t ‚ d  S(   Ns
   x, a, b, ci   i    i   i   i
   i   i   i   i	   i   i   i   i   i   i   i   i   iÀÿÿÿi@   iþÿÿÿi   (   R&   R#   R€   R6   R'   R~   R   R(   R3   R)   R*   R    R0   (   R;   R7   R8   R_   R=   R`   (    (    sA   lib/python2.7/site-packages/sympy/polys/tests/test_ring_series.pyt   test_rs_series6  s`    $-.+.+**<*2*6**"*(	yO	†	–54#;'w'N(_   t   sympy.polys.domainsR    R   R   t   sympy.polys.ringsR   t   sympy.polys.ring_seriesR   R   R   R   R   R	   R
   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R    R!   R"   R#   t   sympy.utilities.pytestR$   t   sympy.core.compatibilityR%   t   sympy.core.symbolR&   t   sympy.functionsR'   R(   R)   R*   R+   R,   R-   R.   R/   R0   R1   t   sympy.core.numbersR2   t
   sympy.coreR3   R4   R:   R?   RB   RK   RL   RO   RP   RW   RX   Re   Rg   Rl   Rn   Ro   Rp   Rq   Rr   Rs   Rt   Ru   Rv   Rw   Rx   Ry   Rz   R{   R|   R†   R‡   Rˆ   RE   R‰   RŠ   (    (    (    sA   lib/python2.7/site-packages/sympy/polys/tests/test_ring_series.pyt   <module>   sR   ÊL								
		
			 																				?		
