ó
~9­\c           @   sk  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# 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/ m0 Z0 m1 Z1 d  d l2 m3 Z3 e d ƒ \ Z4 Z5 Z6 Z7 Z8 Z9 e d d e: ƒZ; d „  Z< d	 „  Z= d
 „  Z> d „  Z? e1 d „  ƒ Z@ e1 d „  ƒ ZA d „  ZB d „  ZC d „  ZD e1 d „  ƒ 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+ „  Z_ d, „  Z` d- „  Za d. „  Zb d/ „  Zc d0 „  Zd d1 „  Ze d2 „  Zf d3 „  Zg d4 „  Zh d5 „  Zi d6 „  Zj d7 „  Zk d8 „  Zl d9 „  Zm d: „  Zn d; „  Zo d< „  Zp d= S(>   iÿÿÿÿ(,   t   adjointt   Andt   Basict	   conjugatet   difft   expandt   Eqt   Functiont   It   ITEt   Integralt	   integratet   Intervalt   lambdifyt   logt   Maxt   Mint   oot   Ort   pit	   Piecewiset   piecewise_foldt   Rationalt   solvet   symbolst	   transposet   cost   sint   expt   Abst   Net   Nott   Symbolt   St   sqrtt   Tuplet   zoot   factor_termst
   DiracDeltat	   Heavisidet   Addt   Mult	   factorialt   Ge(   t   srepr(   t   raisest   slow(   t	   Undefineds	   a:d, x, yt   zt   nonzeroc          C   s‹  t  t t d k  f d t f ƒ t  t t d k  f d t f ƒ k sH t ‚ t  t t d k  f d t f d t f ƒ t  t t d k  f d t f ƒ k s™ t ‚ t  t t d k  f d t f d d d k f ƒ t  t t d k  f ƒ k sç t ‚ t  t t d k  f d t d k  f d t f ƒ t  t t d k  f d t f ƒ k s>t ‚ t  t t d k  f d t d k  f d t f ƒ t  t t d k  f d t f ƒ k s•t ‚ t  t t d k  f t t d k  f d t f ƒ t  t t t d k  t d k  ƒ f d t f ƒ k sût ‚ t  t t d k  f t t d k  f t t f ƒ t k s7t ‚ t  t t f ƒ t k sUt ‚ t t d „  ƒ t  d t t d k  f t t f ƒ t  d t t d k  f t t f d t ƒk oÖt  d t t d k  f ƒ k n sát ‚ t  t t f ƒ t k sÿt ‚ t t d „  ƒ t  t d f ƒ t k s-t ‚ t t d „  ƒ t t d	 „  ƒ t t d
 „  ƒ t  d t f ƒ t	 d d ƒ k s„t ‚ t  d t d k  f d t f ƒ t
 k  }  t  d |  f ƒ t  d t t d k  t
 d k t
 d k ƒ f ƒ k sót ‚ t  d t d k f d t t d k t d k ƒ f ƒ t  d t d k f d t d k f ƒ k sVt ‚ t  d t d k  f t d t d k  f t t ƒ t d k f ƒ } t  d t d d k  f t d t d d k  f t t d ƒ t d d k f ƒ } | j t t d ƒ | k st ‚ | j t d ƒ d k s&t ‚ | j t d ƒ d k sDt ‚ | j t d ƒ t d ƒ k sht ‚ t  d t t k  f d t d t k  f d t d t k f ƒ } t  d t t d ƒ f d t t f ƒ } t  d t t d ƒ f d d t d k f ƒ } | j t d ƒ d k st ‚ | j t d ƒ d k s8t ‚ | j t d ƒ d k sVt ‚ | j t d ƒ d k stt ‚ | j t d ƒ d k s’t ‚ t d d t ƒ\ } } } t  | t ƒ t d k  f | t ƒ | t ƒ d t d k f ƒ }	 t  | t ƒ t d k  f | t ƒ | t ƒ d t d k f ƒ }
 |
 j | | ƒ |	 k sMt ‚ t  d t t d ƒ f d t f ƒ j t d ƒ d k s‰t ‚ t  d t t d ƒ f d t f ƒ j t d ƒ d k sÅt ‚ t  d t t t
 ƒ f d t f ƒ j t t
 ƒ d k st ‚ t  d t t t ƒ f d t f ƒ j t t ƒ d k s=t ‚ t  d t t t ƒ t t ƒ ƒ f d t f ƒ j t t ƒ t  d t t t ƒ t t ƒ ƒ f d t f ƒ k s¯t ‚ t  d t t t ƒ t
 d ƒ f d t f ƒ } | j t
 d ƒ t  d t t t ƒ d ƒ f d t f ƒ k s	t ‚ t  d t
 d k  f d t d k  f d t t d ƒ f d t f ƒ j t d ƒ t  d t
 d k  f d t f ƒ k s”	t ‚ t  d t t d d ƒ f d t d k  f ƒ j t t ƒ d k sÚ	t ‚ t  t t d k f ƒ } t d d t ƒ} | j t | ƒ t k s"
t ‚ | j ƒ  | k s:
t ‚ | j d i d t 6ƒ d k s_
t ‚ | j d i d t 6ƒ d k s„
t ‚ | j d i d t 6ƒ t d ƒ k s¯
t ‚ | j d i d t 6ƒ t k sÔ
t ‚ t  t t t d d f ƒ t d k  f ƒ } | j ƒ  t  t d ƒ d t d k  f ƒ k s2t ‚ t } t | } t  d t d k  f d t t d k  f d t t d k f ƒ } t | | } t | t ƒ | k s©t ‚ t | | t ƒ | k sÈt ‚ t | | k sÞt ‚ t | | | t | k s t ‚ | | | | k st ‚ | | | | k s4t ‚ | | | | k sOt ‚ t  d t d k  f d t d t d k  f d t d t d k f ƒ } | d | k s«t ‚ t t
 d } t t
 d d } t  | t d k  f | t d k f ƒ } | j t d ƒ | j t d ƒ | j t d ƒ | j t d ƒ } | j t d d ƒ d k sUt ‚ | j t d d ƒ | k svt ‚ t  | t d k  f | t f ƒ } | j t d d ƒ d k s¸t ‚ | j t d d ƒ | k sÚt ‚ | j t d d ƒ | j t d ƒ | j t d ƒ k st ‚ | j t d d ƒ | k s8t ‚ | j t d  d ƒ | j t d ƒ k set ‚ | j t d d  ƒ | j t d ƒ k s“t ‚ | j ƒ  t  t t d k  f t d d t d ƒ d t d k  f t t t ƒ t t d ƒ d t f ƒ k st ‚ t  t t d k  f t d d t k f t d t k  f ƒ } t | t d d f ƒ d d k sjt ‚ t | t d d f ƒ d d k s’t ‚ t  d t d k  f d t d k  f d t d k  f d t d k  f d t f ƒ } t | t t t f ƒ d k st ‚ t  t t d k  f t d t d k f t d t k  f ƒ } t | t d d f ƒ t k sct ‚ t  | t  ƒ r| j! t k s‡t ‚ d  S(   Ni   i    iÿÿÿÿi   c           S   s   t  ƒ  S(   N(   R   (    (    (    sN   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_piecewise.pyt   <lambda>"   t    t   evaluatec           S   s
   t  t ƒ S(   N(   R   t   x(    (    (    sN   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_piecewise.pyR2   (   R3   c           S   s   t  t d f ƒ S(   Ni   (   R   R5   (    (    (    sN   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_piecewise.pyR2   *   R3   c           S   s   t  t t d f ƒ S(   Ni   (   R   R5   (    (    (    sN   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_piecewise.pyR2   +   R3   c           S   s   t  d g t f ƒ S(   Ni   (   R   t   True(    (    (    sN   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_piecewise.pyR2   ,   R3   i   iûÿÿÿi
   g        s   f,g,ht   clst   nt   negativet   subsiþÿÿÿi   i   g      @iöÿÿÿ(   i   i   ("   R   R5   R6   t   AssertionErrort   FalseR   R-   t	   TypeErrorR/   R#   t   yR	   R   R   R:   R   R   R   R   R0   R   R   R   t   evalfR
   t   doitR!   R   t   _eval_intervalt   NoneR   R   t
   isinstancet   is_commutative(   t   condt   pt   p_x2t   p2t   p3t   p4t   ft   gt   ht   pft   pgt   p5t   p6R8   t   f_intt   fpt   dpt   fp_dxt   dp2t   f1t   f2t   pevalt   peval_intervalt   peval2(    (    sN   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_piecewise.pyt   test_piecewise   sÔ    H'*-!-*-*-9<"0*''930@P"$>(.AA<<<<99.BB3F%%+%*4
>"F'B!!!!"=!-.%4:((N%:$c          C   sC   t  t t d k  f t t f ƒ }  |  j t t t h k s? t ‚ d  S(   Ni    (   R   R5   t   aR>   R6   t   free_symbolsR;   (   RK   (    (    sN   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_piecewise.pyt   test_piecewise_free_symbolsž   s    !c          C   s  t  d d t d t ƒ\ }  } t |  d d |  d k f d t f ƒ } t | |  d d f ƒ t d d	 ƒ k st t ‚ t |  d
 d
 |  d k f | t f ƒ } t | |  d d f ƒ t d d	 ƒ k sÊ t ‚ t | |  d d
 f ƒ t d d ƒ k s÷ t ‚ | t |  d
 d
 |  d k f | |  d k  f ƒ k s2t ‚ t |  d
 d
 d |  k f | |  d k  f ƒ } t | |  d d f ƒ t d d	 ƒ k sŽt ‚ t | |  d d
 f ƒ t d d ƒ k s¼t ‚ | t |  d
 d
 d |  k f | t f ƒ k sñt ‚ t |  d
 d
 d |  k f d | t f ƒ } t | |  d d f ƒ d t d d	 ƒ k sOt ‚ t | |  d d
 f ƒ t d d ƒ k s}t ‚ d  S(   Ns   x yt   realt   finitei   i    i   iþÿÿÿi   i   i   i   i+   i   i½  i¡  (   R   R6   R   R   R   R;   (   R5   R>   RK   RL   (    (    sN   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_piecewise.pyt   test_piecewise_integrate1£   s    )-)--;/-.5-1c          C   s4  t  d t d k f d t t d ƒ f d t d k  f ƒ }  t |  t d d f ƒ d k s] t ‚ t  d t t d k  f d t f ƒ }  t |  t t d f ƒ t d t ƒ k s± t ‚ |  j	 t d ƒ j t t d f ƒ d k sâ t ‚ t |  t d t f ƒ t d t ƒ k st ‚ t |  t d t f ƒ t
 d t ƒ t k sBt ‚ t |  t t d f ƒ t d t ƒ d k sut ‚ t |  t t t f ƒ t t k sŸt ‚ t  d t d k  f t t d k f d t f ƒ }  |  j t t d f ƒ } |  j t d t f ƒ } xz d t j d f D]f } |  j t | d f ƒ | j	 t | ƒ k sHt ‚ |  j t d | f ƒ | j	 t | ƒ k st ‚ qW| t  t d t
 d t ƒ ƒ d d t d ƒ d t d k  f t d t f ƒ k s×t ‚ | t  t d t
 d t ƒ ƒ d d t d ƒ d t d k  f t d t f ƒ k s0t ‚ d  S(   Ni   i    iÿÿÿÿiýÿÿÿi   i*   i   (   R   R5   R   R   R;   R>   R6   R   R   R:   R   R!   t   Half(   RL   t   gy1t   g1yt   yy(    (    sN   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_piecewise.pyt   test_piecewise_integrate1bº   s*    9$%/1.23*00487c          C   s÷  t  d d t ƒ}  t d t t d d ƒ j t ƒ f d t t d d ƒ j t ƒ f d t f ƒ } | j t |  d f ƒ } | j t d |  f ƒ } | j t d d f ƒ | j |  d ƒ k sÂ t ‚ | j t d d f ƒ | j |  d ƒ k sò t ‚ | j t d d f ƒ | j |  d ƒ k s"t ‚ | j t d d f ƒ | j |  d ƒ k sRt ‚ | j t d d f ƒ | j |  d ƒ j	 ƒ  k sˆt ‚ | j t d d f ƒ | j |  d ƒ j	 ƒ  k s¾t ‚ t
 | j t ƒ ƒ t d |  d k f |  d d |  t d ƒ d |  d k f |  d d |  t d ƒ d |  d k  f d t f ƒ k sMt ‚ t
 | j t ƒ ƒ t d |  d k f |  d d |  t d ƒ d |  d k f |  d d |  t d ƒ d |  d k  f d t f ƒ k sÜt ‚ | j	 ƒ  t t d t d |  ƒ ƒ d d t d t d |  ƒ ƒ t d t d |  ƒ ƒ d t d ƒ d |  d k  f d t f ƒ k sht ‚ | j	 ƒ  t t d t d |  ƒ ƒ d d t d t d |  ƒ ƒ t d t d |  ƒ ƒ d t d ƒ d |  d k  f d t f ƒ k sót ‚ d  S(   NR>   R`   i   i    iÿÿÿÿiþÿÿÿi   (   R   R6   R   R5   R   t   containsR   R:   R;   t   simplifyR   t   rewriteR!   R   R   (   R>   RL   Rd   Re   (    (    sN   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_piecewise.pyt   test_piecewise_integrate1caÓ   s>    000066*))*hgc          C   sÖ  t  d d t ƒ}  t d t t d k t d k ƒ f d t t d k f d t t f ƒ } | j t |  d f ƒ } | j t d |  f ƒ } | j t d d f ƒ | j |  d ƒ k s¹ t ‚ | j t d d f ƒ | j |  d ƒ k sé t ‚ | j t d d f ƒ | j |  d ƒ k st ‚ | j t d d f ƒ | j |  d ƒ k sIt ‚ | j t d d f ƒ | j |  d ƒ k syt ‚ | j t d d f ƒ | j |  d ƒ k s©t ‚ t | j	 t ƒ ƒ t d |  d k f |  d d |  t
 d ƒ d |  d k f |  d d |  t
 d ƒ d |  d k  f d t f ƒ k s8t ‚ t | j	 t ƒ ƒ t d |  d k f |  d d |  t
 d ƒ d |  d k f |  d d |  t
 d ƒ d |  d k  f d t f ƒ k sÇt ‚ | t t d t d |  ƒ ƒ d d t d t d |  ƒ ƒ t d t d |  ƒ ƒ d t
 d ƒ d |  d k  f d t f ƒ k sMt ‚ | t t d t d |  ƒ ƒ d d t d t d |  ƒ ƒ t d t d |  ƒ ƒ d t
 d ƒ d |  d k  f d t f ƒ k sÒt ‚ d  S(   NR>   R`   i    iÿÿÿÿi   iþÿÿÿi   (   R   R6   R   R   R5   R   R:   R;   R   Rj   R!   R   R   (   R>   RL   Rd   Re   (    (    sN   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_piecewise.pyt   test_piecewise_integrate1cb  s>    000000*))*hgc       
   C   sw  d d l  m }  t t t t ƒ } t d t t k  f d t t k f d t	 f ƒ } | j
 | ƒ } | t t d t d t t t t t ƒ ƒ t t t t t t ƒ ƒ t t k  f d t t d t t t t t ƒ ƒ t t t t t t ƒ ƒ t	 f ƒ k st ‚ xk |  d ƒ D]] } t t t t t t f | ƒ ƒ } | j | ƒ j
 | j | ƒ ƒ | j | ƒ k st ‚ qWd  S(	   Niÿÿÿÿ(   t   permutationsi   i   i   iþÿÿÿi   (   i   i   i   i   (   t	   itertoolsRm   R#   R5   t   ct   dR   R]   t   bR6   R   R   R   R;   t   dictt   zipR:   (   Rm   t   limRF   t   qt   vt   r(    (    sN   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_piecewise.pyt   test_piecewise_integrate20  s    0KS!c           C   sC   t  d t d k  f d t f ƒ j t t d f ƒ d k s? t ‚ d  S(   Ni   i   i    iýÿÿÿ(   R   R5   R6   R   R   R;   (    (    (    sN   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_piecewise.pyt   test_meijer_bypass=  s    c          C   s»  d d l  m }  t d d f } d } t d t t k f d t t k f d t f ƒ } | j | ƒ } xn |  | d
 d ƒD]Z \ } } t t	 t t f | | f ƒ ƒ } | j
 | ƒ | j
 | ƒ j | ƒ k sw t ‚ qw W| j
 t d ƒ j
 t d ƒ d d d k st ‚ t d t t k f d t t k  f d t f ƒ } | j | ƒ } xn |  | d
 d ƒD]Z \ } } t t	 t t f | | f ƒ ƒ } | j
 | ƒ | j
 | ƒ j | ƒ k sYt ‚ qYWd  S(   Niÿÿÿÿ(   t   cartesi    i   iþÿÿÿi   i   i   i   t   repeati   i   (   iþÿÿÿiÿÿÿÿi    i   i   i   i   i   i   (   t   sympy.utilities.iterablesRz   R5   R   R]   Rq   R6   R   Rr   Rs   R:   R;   (   Rz   Rt   t   NRF   t   anst   it   jt   reps(    (    sN   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_piecewise.pyt/   test_piecewise_integrate3_inequality_conditionsC  s    0!120!c          C   sÆ  t  d d t d t ƒ}  t  d d t d t ƒ} t  d d t d t ƒ} t  d d t d t ƒ} t d t | |  k  | | k ƒ f d t f ƒ } t d | |  k  f d | | k f d t f ƒ } t d | | k f d | |  k  f d t f ƒ } t d | |  k  f d | | k  f d t f ƒ } t d | | k f d | |  k f d t f ƒ } t d t |  | k  | | k  ƒ f d t f ƒ }	 t | t | ƒ }
 xè | | | | | |	 f D]Î } | j |
 ƒ } x¶ t d	 ƒ D]¨ } i d |  6d
 | 6| | 6} | j	 | ƒ | j	 | ƒ j |
 j	 | ƒ ƒ k s%t
 ‚ i d
 |  6d | 6| | 6} | j	 | ƒ | j	 | ƒ j |
 j	 | ƒ ƒ k sÎt
 ‚ qÎWq¬Wt | | t ƒ }
 xè | | | | | |	 f D]Î } | j |
 ƒ } x¶ t d	 ƒ D]¨ } i d |  6d
 | 6| | 6} | j	 | ƒ | j	 | ƒ j |
 j	 | ƒ ƒ k s"t
 ‚ i d
 |  6d | 6| | 6} | j	 | ƒ | j	 | ƒ j |
 j	 | ƒ ƒ k sËt
 ‚ qËWq©Wt d | t |  | ƒ k f | t |  | ƒ | | k f | t |  | ƒ t f ƒ } x5 | | | | f D]! } | j | ƒ | k sát
 ‚ qáW| j | ƒ t d | |  k  f |  | | t |  | ƒ k f |  t |  | ƒ t f ƒ k sgt
 ‚ |	 j | ƒ t d | |  k f |  | | t |  | ƒ k f |  t |  | ƒ t f ƒ k sÈt
 ‚ t d | |  k  f d | | k f d t f ƒ } t d | | k f d | |  k  f d t f ƒ } t d | |  k  f d | | k  f d t f ƒ } t d | | k f d | |  k f d t f ƒ } t d t |  | k  | | k  ƒ f d | | k f d t f ƒ }	 t | t | ƒ }
 xå | | | | |	 f D]Î } | j |
 ƒ } x¶ t d	 ƒ D]¨ } i d |  6d
 | 6| | 6} | j	 | ƒ | j	 | ƒ j |
 j	 | ƒ ƒ k sit
 ‚ i d
 |  6d | 6| | 6} | j	 | ƒ | j	 | ƒ j |
 j	 | ƒ ƒ k st
 ‚ qWqðWd  S(   NR]   R`   Ra   Rq   R5   R>   i    i   i   i   g      à?(   R    R6   R   R   R   R#   R   R   t   rangeR:   R;   R   R   (   R]   Rq   R5   R>   t   p0t   p1RH   RI   RJ   RP   Rt   RF   R~   R   R   (    (    sN   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_piecewise.pyt-   test_piecewise_integrate4_symbolic_conditions]  sj    0000006>6>&&0000?6c          C   sr   t  d t t d ƒ f t t t f ƒ }  t |  t d d f ƒ t  d t t d ƒ f d t t f ƒ k sn t ‚ d  S(   Ni    i   i   i   (   R   R   R>   R5   R6   R   R;   (   RF   (    (    sN   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_piecewise.pyt0   test_piecewise_integrate5_independent_conditionsž  s    (c       	   C   s¼  t  t d d t d t t d t t d d ƒ f d t d t f ƒ }  |  j ƒ  t  t t t d ƒ f d t d t f ƒ k sŠ t ‚ t  t t t t d ƒ t t t	 d ƒ ƒ f d t f ƒ j ƒ  t  d t t t d ƒ t t	 d ƒ ƒ f d t f ƒ k st ‚ t  d t t
 t ƒ t
 t ƒ t
 t t ƒ t t d ƒ t t t d ƒ @f d t
 t ƒ t
 t ƒ t
 t t ƒ t t d ƒ t t t d ƒ @f d t f ƒ j ƒ  t  d t t t t d ƒ t t d ƒ ƒ f d t t t d ƒ t t d ƒ ƒ f d t f ƒ k st ‚ d t t t d ƒ t t d ƒ ƒ f t t f f } t  | Œ  j ƒ  t  | Œ  k skt ‚ d t t d ƒ f t t ƒ t t f f } t  | Œ  j ƒ  t  | Œ  k sºt ‚ t  d t t t t d ƒ t t d ƒ ƒ f t t f ƒ j ƒ  t k st ‚ t d t t d ƒ f t t ƒ d t t f ƒ } t t t ƒ d } t d ƒ } t  | Œ  j ƒ  | k svt ‚ t  | j t | t ƒ ƒ Œ  j ƒ  | j t | t ƒ ƒ k s¸t ‚ d  S(   Ni   i   i    iÿÿÿÿRK   (   R   R5   R   R6   Ri   R$   R;   R]   R   Rq   R*   R>   R+   R   R#   R   R:   (   RF   t   argsR~   RK   (    (    sN   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_piecewise.pyt   test_piecewise_simplify£  s4    5	5:<-><($3$+$=2c             st  t  t t d k f t t d k f ƒ }  |  j t t d ƒ ‰  t ˆ  t ƒ d g k s\ t ‚ t ˆ  d t ƒ d d g k s t ‚ t  t d d t d k f d t f ƒ ‰  t ˆ  t ƒ d g k sÈ t ‚ t  t d d t d k f ˆ  t f ƒ } t | t ƒ d d g k st ‚ t  t d d t d k f ˆ  t d k  f ƒ } t | t ƒ d d g k sbt ‚ t  t d d t d k f ˆ  t d k  f ƒ } t | t ƒ d g k s¯t ‚ t  t d d t d k f ˆ  t f ƒ } t | t ƒ d g k söt ‚ t  t d d t d k f ˆ  t f d t f ƒ } t | t ƒ d g k sFt ‚ t  t d d t d k f t d t d d k f t d t d d k f ƒ } t | t ƒ d g k s³t ‚ t t  t d t d k f d t t f ƒ d ƒ d d g k søt ‚ t  t d d t d k f d t f ƒ ‰  t t ‡  f d	 †  ƒ d
 „  } t  t d d t t	 k  f t d t f ƒ } t | t ƒ } | g  | D] } | j t	 d ƒ ^ q†ƒ d g k s¶t ‚ | g  | D] } | j t	 d ƒ ^ qÀƒ d d g k sót ‚ | g  | D] } | j t	 d ƒ ^ qýƒ d d g k s0t ‚ | t  d t	 d k f t
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 d ƒ t d k f ƒ } t | t	 t ƒ t  t	 d t	 d k  f t
 j t f ƒ t  t	 d t	 d k f t
 j t f ƒ g k sSt ‚ t d d t ƒ} t | | t ƒ | d | d g k s“t ‚ t d ƒ ‰  t t ˆ  t ƒ t  d t d k f d t f ƒ ƒ ˆ  t ƒ ƒ t  d t d k f d t f ƒ g k s	t ‚ t  d t d t t
 d ƒ t k  t d k  ƒ f d t f ƒ ‰  t ˆ  d ƒ d t d ƒ g k spt ‚ d  S(   Ni    i   i   i   i   i   i
   iÿÿÿÿc              s   t  ˆ  t ƒ S(   N(   R   R5   (    (   RK   (    sN   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_piecewise.pyR2   â  R3   c         S   s   t  t d „  |  ƒ ƒ S(   Nc         S   s   |  t  j k	 S(   N(   R!   t   NaN(   R5   (    (    sN   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_piecewise.pyR2   å  R3   (   t   listt   filter(   R~   (    (    sN   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_piecewise.pyt   nonaä  s    iþÿÿÿRF   t   positiveRK   (   R   R5   R:   R   R;   R6   R<   R-   t   NotImplementedErrorR>   R!   RŠ   R    R   R   R   R"   (   t   abs2RL   R   RF   R~   R   t   absxm3(    (   RK   sN   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_piecewise.pyt   test_piecewise_solveÂ  sZ    (%))!/!/)25E)	-:==!!0#'4.=->c          C   sO  t  t t d k  f d d t k f ƒ }  t t |  ƒ t  t d t d k  f t d t k f ƒ k sh t ‚ t |  |  ƒ t  d t t d k  f d d t k f ƒ k s© t ‚ t t  d t d k  f d t f ƒ t  d t d k  f d t f ƒ ƒ t  d t d k  f d t f ƒ k st ‚ t  d t d k  f t t d k f d t f ƒ } t  d t d k  f d t t d k f d t f ƒ } d | d | }  t t |  ƒ t t t f ƒ t d t d t d d f ƒ k sÑt ‚ t t  d t d k f t  d t d k f ƒ t f ƒ ƒ t  d t d k f d	 t d k f ƒ k s8t ‚ t t  t t t d k t d k  t d k ƒ f ƒ ƒ t  t t d k t d k  Bt d k t d k B@f ƒ k sªt ‚ t  d t	 t d ƒ f d t f ƒ t  t t	 t t d ƒ f d t	 t t d ƒ f d t f ƒ } } t t
 | | d
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 | | d
 t ƒƒ k sKt ‚ d  S(   Ni   i   i    i
   iöÿÿÿi   iøÿÿÿi   iþÿÿÿR4   (   R   R5   R   R;   R6   R   R   R>   R	   R   R)   R<   (   RF   R…   RH   R]   Rq   (    (    sN   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_piecewise.pyt   test_piecewise_fold  s(    'AA!"*04B403?!Dc    
      C   sd  t  t t ƒ t d k  f d t f ƒ }  t  d t |  d ƒ f |  t |  ƒ t f ƒ } t | ƒ } | j t t d ƒ d k s„ t	 ‚ | j t d ƒ d k s¢ t	 ‚ | j t t d ƒ d k sÅ t	 ‚ t  d t |  d ƒ f d t f ƒ } t | ƒ } xA t
 d d ƒ D]0 } | j t | ƒ | j t | ƒ k st	 ‚ qWd t  d t d k  f d t f ƒ k  } t | ƒ } x> t
 d ƒ D]0 } | j t | ƒ | j t | ƒ k syt	 ‚ qyWt  d t d k  f d t f ƒ } t  d t d k  f d t f ƒ } t  d | | k  f d t f ƒ }	 t |	 ƒ } xA t
 d d ƒ D]0 } | j t | ƒ |	 j t | ƒ k s,t	 ‚ q,Wd  S(	   Ni    i   g        i   i   g      ð?iÿÿÿÿi   (   R   R   R5   R6   R   R   R   R:   R   R;   Rƒ   (
   R…   RH   RI   RJ   R~   R   t   r1RP   RQ   t   p7(    (    sN   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_piecewise.pyt%   test_piecewise_fold_piecewise_in_cond"  s(    '.##$.'.!!!c          C   s¸   t  t t ƒ t d k  f d t f ƒ }  t  d t |  d ƒ f d |  t f ƒ } t  d t d k t t t ƒ d ƒ Bf d t t ƒ t d k  f t t f ƒ } t | ƒ | k s´ t ‚ d  S(   Ni    i   (   R   R   R5   R6   R   R$   R   R;   (   R…   RH   RI   (    (    sN   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_piecewise.pyt'   test_piecewise_fold_piecewise_in_cond_2;  s    '("c          C   s²   t  d t d d t t ƒ j t ƒ f d t f ƒ }  t t d t |  ƒ ƒ } | t  d t t d k t d k  @f d t f ƒ k sˆ t ‚ | t t d t |  ƒ ƒ k s® t ‚ d  S(   Ni   i    (	   R   R   R<   R6   Rh   R5   R   R   R;   (   R…   RH   (    (    sN   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_piecewise.pyt   test_piecewise_fold_expandE  s    3;c          C   sY   t  t t d k  f t d t d k f t d t k  f ƒ }  |  t  |  j Œ  k sU t ‚ d  S(   Niöÿÿÿi   iÿÿÿÿi   (   R   R5   Rˆ   R;   (   RF   (    (    sN   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_piecewise.pyt   test_piecewise_duplicateM  s    :c          C   s´   t  t t d k  f t d d t k f t d t k  f ƒ }  t  t t d k  f t d t ƒ d t k f t d t k  f ƒ } | j ƒ  |  k s’ t ‚ | j d t ƒ | k s° t ‚ d  S(   Ni   i   iÿÿÿÿi   t   deep(   R   R5   R
   R@   R;   R<   (   R…   RH   (    (    sN   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_piecewise.pyt	   test_doitR  s    :@c          C   s  t  t t d d ƒ j t ƒ f d t f ƒ }  |  j t d ƒ d k sK t ‚ |  j t d ƒ d k si t ‚ |  j t ƒ t  d t d d ƒ j t ƒ f d t f ƒ k s« t ‚ t |  t ƒ t  d t d k f t d d t d k f t	 d ƒ d t f ƒ k st ‚ d  S(   Ni    i   g      à¿g      à?i   (
   R   R5   R   Rh   R6   R:   R;   R   R   R!   (   R…   (    (    sN   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_piecewise.pyt   test_piecewise_intervalY  s    -Bc       
   C   s*  t  t t f ƒ t k s t ‚ t d k  }  t  t |  f t d |  f ƒ t  t |  f ƒ k sa t ‚ t  t |  f t d |  j f ƒ t  t |  f ƒ k s› t ‚ t d k  } d „  } x`d |  f t  d |  f d | f ƒ | f f d |  f t  d |  f d | j f ƒ | f f d |  f t  d |  f d | f ƒ | f d t f f d |  f t  d |  f d | f d t f ƒ | f f d |  f t  d |  f d | f d t f ƒ | f d t f f g D]_ } xV d D]N } | t  d	 t | Œ j t | ƒ ƒ | t  | Œ  j t | ƒ ƒ k s½t ‚ q½Wq°Wt d
 ƒ \ } } } } t | k  }  t | k  } t | k  }	 t | k  }
 t  d |  f t  d |  f d | f d |	 f ƒ | f d |	 f ƒ t  d |  f d | f d |	 f ƒ k sÇt ‚ t  d |  f t  d |  f d | f d |	 f d t f ƒ |	 f d |
 f ƒ t  d |  f t  d | f d |	 f ƒ |	 f d |
 f ƒ k sQt ‚ t  d t |  |
 ƒ f t  d |
 f d | f d |	 f ƒ | f d |	 f ƒ t  d t |  |
 ƒ f t  d |
 f d | f ƒ | f d |	 f ƒ k sät ‚ t  d |	 f d |	 f d t	 j
 f ƒ t  d |	 f d t	 j
 f ƒ k s0t ‚ t  d |	 f d t |	 | ƒ f d t f ƒ t  d |	 f d | f d t f ƒ k sˆt ‚ t  d |	 f d t |	 | ƒ f d t f ƒ j t t | | | | t f d ƒ ƒ ƒ d k sét ‚ t  d |	 f d |	 f ƒ t  d |	 f d t f ƒ k s&t ‚ d  S(   Ni   i   c         S   s    t  |  t ƒ r t |  j Œ  S|  S(   N(   RC   R   Rˆ   (   R   (    (    sN   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_piecewise.pyt	   canonicalj  s    i   i   i   i    i
   R4   s   r1:5i   g      @(   i    i   i
   (   i   i   i   i   g      @(   R   R5   R6   R;   t   reversedR<   R:   R   R   R!   t   trueR   Rr   Rs   (   R]   Rq   R   Rˆ   R   R”   t   r2t   r3t   r4Ro   Rp   (    (    sN   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_piecewise.pyt   test_piecewise_collapsed  sN    7:	*-33F/0-9303%'+-.3c          C   sÌ   t  t d t d k  f t t d d t t ƒ j t ƒ f d t t d k f d t f ƒ }  t t |  ƒ } | d ƒ d k s€ t ‚ | d ƒ d k s˜ t ‚ | d ƒ d k s° t ‚ | d ƒ d k sÈ t ‚ d  S(	   Ni   i    i   g       Àg      @g        g      à?g       @(   R   R5   R   R<   R6   Rh   R   R;   (   RF   RK   (    (    sN   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_piecewise.pyt   test_piecewise_lambdify‘  s    !c          C   s·   d d l  m }  m } m } t |  t ƒ t d k  f | t ƒ t d k f ƒ } t t | t d ƒ t d k  f d | t d ƒ t d k f ƒ } | j t d d ƒ| k s³ t ‚ d  S(   Niÿÿÿÿ(   R   R   t   Oi    i   i   R8   (   t   sympyR   R   R¥   R   R5   t   nseriesR;   (   R   R   R¥   R…   RH   (    (    sN   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_piecewise.pyt   test_piecewise_series   s    3Cc          C   s  t  d t t d k f d t f ƒ }  t  t t d k f d t f ƒ } t  d t t d k f t t f ƒ } t  t t d k f d t t f ƒ } t  d t t d k f t t f ƒ } t  d t t d k  f t t f ƒ } t  t t d k  f d t t f ƒ } t  t t d k f d t t f ƒ } |  j t ƒ d k s?t ‚ | j t ƒ d k sZt ‚ | j t ƒ t k sut ‚ | j t ƒ d t k s”t ‚ | j t ƒ t k s¯t ‚ | j t ƒ d t k sÎt ‚ | j t ƒ t k sét ‚ | j t ƒ d t k st ‚ d  S(   Ni   i    (   R   R5   R6   t   as_leading_termR;   (   R…   RH   RI   RJ   RP   RQ   R•   t   p8(    (    sN   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_piecewise.pyt   test_piecewise_as_leading_term§  s     %!%%%%%%c          C   s½  t  d t d k  f d d t k f ƒ }  t  d t t d k  f t d t k f ƒ } t  t t t d k f d t t f ƒ } t  t t t ƒ t d k f d t t f ƒ } t |  ƒ |  k sÃ t ‚ t | ƒ t | ƒ k sâ t ‚ t | ƒ | k sú t ‚ |  j t k st ‚ |  j	 t k s$t ‚ | j t k s9t ‚ | j	 t k sNt ‚ | j d  k sct ‚ | j	 d  k sxt ‚ |  j ƒ  |  d f k s–t ‚ | j ƒ  d t | f k s¹t ‚ d  S(   Ni   i    i   (   R   R5   R   R6   R   R;   R   t   is_imaginaryR<   t   is_realRB   t   as_real_imag(   R…   RH   RI   RJ   (    (    sN   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_piecewise.pyt   test_piecewise_complexº  s    '+)0c          C   s:  t  d d t ƒ\ }  } t |  | d t d k f |  d | t f ƒ } | j ƒ  t t |  | d ƒ t d k f t |  d | ƒ t f ƒ k s˜ t ‚ | j ƒ  t t |  | d ƒ t d k f t |  d | ƒ t f ƒ k sç t ‚ | j ƒ  t t |  | d ƒ t d k f t |  d | ƒ t f ƒ k s6t ‚ d  S(   Ns   A Bt   commutativei   i    (	   R   R<   R   R5   R6   R    R;   R   R   (   t   At   BRF   (    (    sN   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_piecewise.pyt   test_conjugate_transposeÏ  s    1	F	F	c          C   s  t  t t f ƒ t k s t ‚ t  t t f d t ƒt k sB t ‚ t  t t f d t ƒ}  |  t k sl t ‚ |  j s{ t ‚ t d „  |  j Dƒ ƒ sš t ‚ t  d t d t ƒ f ƒ j d t t d ƒ f f k sÖ t ‚ t  d t d t ƒ f d t ƒj d t d t ƒ f f k st ‚ d  S(   NR4   c         s   s   |  ] } t  | t ƒ Vq d  S(   N(   RC   R   (   t   .0R   (    (    sN   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_piecewise.pys	   <genexpr>à  s    i   (	   R   R5   R6   R;   R<   t   is_Piecewiset   allRˆ   R   (   RF   (    (    sN   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_piecewise.pyt   test_piecewise_evaluateÚ  s    $<!c           C   sØ   t  t t d k f t t d k f ƒ j ƒ  t t d t t t ƒ f t t t d ƒ f g k sf t ‚ t  t d d t d k f d t f ƒ j ƒ  t d d t d t ƒ f d t t d t t ƒ f g k sÔ t ‚ d  S(   Ni    i   (   R   R5   t   as_expr_set_pairsR   R   R6   R;   (    (    (    sN   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_piecewise.pyt   test_as_expr_set_pairsæ  s    +;,c          C   sL   t  d t t d ƒ f d t f ƒ }  t t |  ƒ ƒ } |  | k sH t ‚ d  S(   Ni
   i    i   (   R   R   R5   R6   R!   R,   R;   (   RF   Ru   (    (    sN   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_piecewise.pyt   test_S_srepr_is_identityî  s    $c          C   s  t  d t d k f d t t d k t d k @ƒ f d t f ƒ }  |  j t d d f ƒ d k sd t ‚ t  d t d k f d t t k  f d t f ƒ }  t d	 d f } |  j | ƒ } xJ t d d ƒ D]9 } | j t | ƒ |  j t | ƒ j | ƒ k sÂ t ‚ qÂ Wd  S(
   Ni   i   i   i   iÿÿÿÿiûÿÿÿi   i   iýÿÿÿ(	   R   R5   R   R6   R   R;   R>   Rƒ   R:   (   RF   Rt   R~   R   (    (    sN   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_piecewise.pyt   test_issue_12587ô  s    @$0c          C   s  t  d t t t d d ƒ t d d f ƒ t d k s> t ‚ t d t t t d k  t d k ƒ t d k  ƒ f d t f ƒ j  t d d f ƒ d k s› t ‚ t d t d k f d t t d k f d t f ƒ j  t d d f ƒ d k sí t ‚ t d t d k f d t	 d t ƒ f d t f ƒ j  t d d f ƒ d k s>t ‚ t d t d t t d k t d k  ƒ f d t f ƒ j  t d d f ƒ d k s”t ‚ t d t d t t d k t d k  ƒ f d t f ƒ j  t d d f ƒ d k sêt ‚ t d t d k f d t t d k f d t f ƒ j  t d d f ƒ d k s<t ‚ t d t	 d t t d t d ƒ f d t f ƒ j  t d d f ƒ d k sŽt ‚ t d t t d k  t d k ƒ f d t d k f d t f ƒ j  t d d f ƒ d k sët ‚ t d t
 t d ƒ f d t f ƒ j  t d d f ƒ d k s-t ‚ t t t d k t d k  @f d t d k  f ƒ j  t d d f ƒ d k s|t ‚ t t t d k t d k  @f d t d k  f ƒ }  t } |  j  t d t f ƒ } | t t d t d k  f t d t ƒ d d t d t ƒ t d t ƒ t d ƒ d t t d t ƒ k f | t f ƒ k sMt ‚ |  j  t d d f ƒ | j t d ƒ k s}t ‚ |  j  t d d f ƒ d k s¡t ‚ |  j  t d d f ƒ | k sÅt ‚ t d t d k f d t t t d k t d k  ƒ ƒ f d t f ƒ }  |  j  t d d f ƒ d k s.t ‚ t d t d t k t d k ƒ f d t t d k  t d	 k ƒ f d t d
 k  f ƒ }  |  j  t d d f ƒ d k s¦t ‚ t d t d k  f d t t	 t d ƒ t d k ƒ f ƒ j  t d d f ƒ t j k s t ‚ t d t d k  f d t t	 t d ƒ t d k ƒ f d t f ƒ j  t d d f ƒ d	 k s`t ‚ t d t d k  f d t t	 t d ƒ t d k  ƒ f d t f ƒ j  t d d f ƒ d k sÀt ‚ t d t d k  f d t	 t d ƒ t t k  @f d t f ƒ j  t d d f ƒ d	 k st ‚ d  S(   Ni   i   i   i    i   i   i   iÿÿÿÿi   i   i
   i   (   R   R5   R"   R   R;   R   R   R   R6   R   R   R/   R>   R   R!   R:   R   RŠ   (   RF   t   nanR   (    (    sN   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_piecewise.pyt   test_issue_11045ÿ  s^    >?438844?$11<0$$E$$9!BB=c          C   sI  t  }  t d t d k  f ƒ j t ƒ t t t d k  f |  t f ƒ k sN t ‚ t d t t d k t d k  ƒ f ƒ j t ƒ t |  t d k  f t d t d k  f |  t f ƒ k s¸ t ‚ t d t t d k t d k  ƒ f ƒ j t d d f ƒ |  k sý t ‚ t d t t d k t d k  ƒ f ƒ j t d d f ƒ d k sBt ‚ t d ƒ \ } } t d d t ƒ\ } } t | t t d k  | d k  ƒ f | t t d k  | d k ƒ f ƒ j t ƒ t | t | d k f t | t t d k  f | t t d k  f |  t f ƒ | d k  f t | t t d k  f |  t f ƒ t f ƒ k sEt ‚ d  S(	   Ni   i   i    i   i   s   A Bs   a bRa   (	   R/   R   R5   R   R6   R;   R   R   R   (   R¼   R±   R²   R]   Rq   (    (    sN   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_piecewise.pyt
   test_holesI  s    !'0:EEE	Ac             s  d „  ‰  ‡  f d †  }  |  d ƒ d k s0 t  ‚ t d ƒ } ‡  f d †  } | | ƒ } | j | d ƒ d k su t  ‚ t d d t ƒ} | | ƒ } | j | d ƒ d k s± t  ‚ t d t d	 k  f d
 t d	 k f ƒ j ƒ  t d t d	 k  f d
 t d
 t f ƒ k st  ‚ d  S(   Nc         S   s6   t  d |  d k  f d |  d |  d k  f d t f ƒ S(   Ni    iÿÿÿÿi   i   (   R   R6   (   R5   (    (    sN   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_piecewise.pyRK   ^  s    c            s*   ˆ  t  ƒ ˆ  t  |  ƒ j t  d d f ƒ S(   Niÿÿÿÿi   (   R5   R   (   t   k(   RK   (    sN   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_piecewise.pyR2   `  s    gffffffþ?i    R¿   c            s,   d t  d ˆ  t  |  ƒ j t  d d f ƒ S(   Ni   i   iÿÿÿÿ(   R5   R   (   R¿   (   RK   (    sN   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_piecewise.pyR2   d  s    i   RŽ   i   i
   (   R;   R   R:   R6   R   R5   R   (   t   autocorrR¿   t   good_autocorrR]   (    (   RK   sN   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_piecewise.pyt   test_issue_11922]  s    	*c       	   C   sV  d t  d t d k  f d t d t d k  f t  d t d k f d	 t f ƒ t  d
 t d k f d t f ƒ t d k f d t d t d k  f d t f ƒ }  t |  t t t f ƒ } | t |  t t t f ƒ j ƒ  k sà t ‚ t | ƒ d k sø t ‚ t  d t t	 d k  f d t f ƒ j t	 ƒ t  d t	 t k f t t	 t f ƒ k sRt ‚ d  S(   Ngý©§J™¢j?i    gf'vb'6TÀgŠÈlAw¿g¶3Ø†Põ?i   g333333Ó?i{   gffffffæ?gš™™™™™Ù?g333333ã?gð%Ñ”½€¿g%JMã× @gš$I’$Éw@s   1.00195081676351i   (
   R   R5   R6   R   R   R
   R@   R;   t   strR>   (   RK   R   (    (    sN   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_piecewise.pyt   test_issue_5227o  s    "+%c    
      C   sL  t  d d t d t ƒ}  t  d d t d t ƒ} t  d d t d t ƒ} t  d d t d t ƒ} t d t | |  k  | | k ƒ f d t f ƒ } t d t |  | k | | k  ƒ f d t f ƒ } t | | | t f ƒ t | | | t f ƒ k sö t ‚ t d t d | k  | |  k  ƒ f d t f ƒ } t d t |  | k | d k ƒ f d t f ƒ } t | | ƒ } | t d | d k f | | t d |  ƒ k f t d |  ƒ t f ƒ k s³t ‚ t | | ƒ }	 |	 | k sÔt ‚ | j | d	 d
 f ƒ t	 d
 t d	 |  ƒ ƒ d	 k st ‚ | j | d	 d
 f ƒ t	 d
 t d	 |  ƒ ƒ d	 k sHt ‚ d  S(   NR]   R`   Ra   Rq   R5   R>   i    i   i   i   (
   R    R6   R   R   R   R   R;   R   R   R   (
   R]   Rq   R5   R>   R„   R…   RI   RJ   t   ip3t   ip4(    (    sN   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_piecewise.pyt   test_issue_10137}  s$    00600!:c             sÝ   d „  ‰  ‡  f d †  }  |  t  ƒ } | j t  d ƒ | j t  d ƒ k sN t ‚ | j t  d ƒ d k sl t ‚ t ˆ  t  t ƒ ˆ  t ƒ ƒ t d t d k t d k @t  t d k @t  t d k @f d t f ƒ k sÙ t ‚ d  S(	   Nc         S   s)   t  d |  d k |  d k @f d t f ƒ S(   Ni   iÿÿÿÿi    (   R   R6   (   R5   (    (    sN   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_piecewise.pyR2   “  R3   c            s,   t  ˆ  |  t ƒ ˆ  t ƒ t t t 
f ƒ S(   N(   R   R>   R   (   R5   (   RK   (    sN   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_piecewise.pyR2   ”  R3   g      ø¿g      ø?i   i    i   iÿÿÿÿ(   R5   R:   R;   R   R>   R   R6   (   t   Convt   cx(    (   RK   sN   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_piecewise.pyt   test_stackoverflow_43852159’  s    	* 5c          C   sç   t  d d t ƒ}  t  d d t d t ƒ} d „  } t | |  ƒ |  t t f ƒ t d k sb t ‚ t | |  ƒ t |  d ƒ } t | |  t t f ƒ t d d | | d d | d t | d	 ƒ f t d t f ƒ k sã t ‚ d
 S(   sD  
    # 3200 seconds to compute the fourier part of issue
    import sympy as sym
    x,y,z,t = sym.symbols('x y z t')
    k = sym.symbols("k", integer=True)
    fourier = sym.fourier_series(sym.cos(k*x)*sym.sqrt(x**2),
                                 (x, -sym.pi, sym.pi))
    assert fourier == FourierSeries(
    sqrt(x**2)*cos(k*x), (x, -pi, pi), (Piecewise((pi**2,
    Eq(k, 0)), (2*(-1)**k/k**2 - 2/k**2, True))/(2*pi),
    SeqFormula(Piecewise((pi**2, (Eq(_n, 0) & Eq(k, 0)) | (Eq(_n, 0) &
    Eq(_n, k) & Eq(k, 0)) | (Eq(_n, 0) & Eq(k, 0) & Eq(_n, -k)) | (Eq(_n,
    0) & Eq(_n, k) & Eq(k, 0) & Eq(_n, -k))), (pi**2/2, Eq(_n, k) | Eq(_n,
    -k) | (Eq(_n, 0) & Eq(_n, k)) | (Eq(_n, k) & Eq(k, 0)) | (Eq(_n, 0) &
    Eq(_n, -k)) | (Eq(_n, k) & Eq(_n, -k)) | (Eq(k, 0) & Eq(_n, -k)) |
    (Eq(_n, 0) & Eq(_n, k) & Eq(_n, -k)) | (Eq(_n, k) & Eq(k, 0) & Eq(_n,
    -k))), ((-1)**k*pi**2*_n**3*sin(pi*_n)/(pi*_n**4 - 2*pi*_n**2*k**2 +
    pi*k**4) - (-1)**k*pi**2*_n**3*sin(pi*_n)/(-pi*_n**4 + 2*pi*_n**2*k**2
    - pi*k**4) + (-1)**k*pi*_n**2*cos(pi*_n)/(pi*_n**4 - 2*pi*_n**2*k**2 +
    pi*k**4) - (-1)**k*pi*_n**2*cos(pi*_n)/(-pi*_n**4 + 2*pi*_n**2*k**2 -
    pi*k**4) - (-1)**k*pi**2*_n*k**2*sin(pi*_n)/(pi*_n**4 -
    2*pi*_n**2*k**2 + pi*k**4) +
    (-1)**k*pi**2*_n*k**2*sin(pi*_n)/(-pi*_n**4 + 2*pi*_n**2*k**2 -
    pi*k**4) + (-1)**k*pi*k**2*cos(pi*_n)/(pi*_n**4 - 2*pi*_n**2*k**2 +
    pi*k**4) - (-1)**k*pi*k**2*cos(pi*_n)/(-pi*_n**4 + 2*pi*_n**2*k**2 -
    pi*k**4) - (2*_n**2 + 2*k**2)/(_n**4 - 2*_n**2*k**2 + k**4),
    True))*cos(_n*x)/pi, (_n, 1, oo)), SeqFormula(0, (_k, 1, oo))))
    R5   R`   R¿   t   integerRa   c         S   s&   t  |  |  d k f |  |  d k f ƒ S(   Ni    (   R   (   R5   (    (    sN   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_piecewise.pyR2   ¼  R3   i   iÿÿÿÿi    N(	   R   R6   R   R   R;   R   R"   R   R   (   R5   R¿   R   t   func(    (    sN   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_piecewise.pyt   test_issue_12557  s    	/c       	   C   sh  d d l  m }  t d ƒ \ } } } } t d | | k  f t t | | k | | k  ƒ f d | | k f ƒ } | j | ƒ } | t d | | k f | t | t | t | | ƒ k f | t t t | | ƒ t f ƒ k sã t	 ‚ x” |  t
 d ƒ ƒ D]€ } t t | | f | ƒ ƒ } x\ t
 d d ƒ D]K }	 | j | ƒ j | |	 ƒ | j | ƒ j | ƒ j | |	 ƒ k s't	 ‚ q'Wqö Wt | | | ƒ }
 | j |
 ƒ } t | t t t | t | | ƒ ƒ | | k f d t f ƒ } xt |  t
 d ƒ ƒ D]` } t t | | | f | ƒ ƒ } | j | ƒ j |
 j | ƒ ƒ } | | j | ƒ k sît	 ‚ qîW| | k sdt	 ‚ d  S(   Niÿÿÿÿ(   Rm   s
   t0, t1 T ti    i   i   (   Rn   Rm   R   R   R5   R   R   R   R6   R;   Rƒ   Rr   Rs   t   xreplaceR:   R#   R   (   Rm   t   t0t   t1t   Tt   tRK   RL   R   R   t   ttRt   R~   t   tru(    (    sN   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_piecewise.pyt   test_issue_6900Â  s.    E$.5.!c           C   st   t  t t ƒ t t d ƒ d d k t ƒ t t t t k  t d k  ƒ t t j t k  t t k  ƒ ƒ k sp t ‚ d  S(   Ni   i    (	   R   t   absR5   R   R   R   R!   t   OneR;   (    (    (    sN   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_piecewise.pyt   test_issue_10122Ü  s    *c          C   s/  t  d t d k f d t t k f t t t f ƒ }  |  |  j t t ƒ d t t d } t d t ƒ } t | t ƒ j ƒ  t  t  d t d k f t d t d t t d t t t d d t t	 t ƒ t d d t t	 t t ƒ t d t t d t | k f t d t d t t d | d t | d t t d t t	 t ƒ t d d t t	 t | ƒ t d t t d | t d t f ƒ t t k t d k @t d k t t
 k @Bf t  d t t t d k f t d t d t t d t d t t t d t t d t t d t d t t d t d t	 t ƒ t d t	 t t ƒ t d t t t d d t t	 t ƒ t d d t t	 t t ƒ t d t t d t | k f t d t d t t d | d t t t d t t d | t d t d t t d | d t	 t ƒ t d t	 t | ƒ t d t d t t	 t ƒ t d d t t	 t | ƒ t d t t d | t d t f ƒ t t k f t  t d t d t t d t t d k f t t d t t d t | k f t d t d t t d | t d t d t t d t d t t t d t t d | d t t t d t t d t t d t d t t d | t d t d t t d t t t d | t d t f ƒ t f ƒ k s+t ‚ d  S(   Ni    i   i   iÿÿÿÿ(   R   R5   R]   R6   R:   R>   R   R   R   R   R   R;   (   t   ut   et   M(    (    sN   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_piecewise.pyt   test_issue_4313á  s(    4&}•+Úô,#ëc           C   sÇ  t  t d t t d ƒ f ƒ j t ƒ g  k s4 t ‚ t  d t t d k f t  d t t d k  f ƒ d t d t d k  f d t f ƒ j t ƒ t t d d f g k s¯ t ‚ t  d t t t ƒ f d t f ƒ j t ƒ t t d d f g k sø t ‚ t  t	 t ƒ t
 t ƒ d k f t	 t ƒ t f ƒ j t ƒ d t t	 t ƒ d f t t t	 t ƒ d f g k smt ‚ t  d t t d ƒ d k f d t f ƒ j t ƒ d d t t d d f g k sÃt ‚ d  S(	   Ni   i   i   i    iþÿÿÿiÿÿÿÿ(   iÿÿÿÿi    i   i    (   i    i   i   i    (   R   R5   R   t
   _intervalsR;   R6   R   R   R   R   R   R   R   (    (    (    sN   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_piecewise.pyt   test__intervals  s    414*4A+c          C   s  d d d d d g \ }  } } } } t  | t d k f | t f ƒ t  |  t t d ƒ d k  f | t t d ƒ d k  f | t f ƒ } | j t ƒ j t ƒ t  | | t d k f |  | t d k f |  | t d k  f | | t d k  f | | t f ƒ k st ‚ d  S(   Ni   i   i   i   i   i    (   R   R5   R6   R   R   R   R;   (   R]   Rq   Ro   Rp   RÚ   RF   (    (    sN   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_piecewise.pyt   test_containment  s    $Ec          C   sñ   t  t d ƒ }  t |  t t t f ƒ d k s5 t ‚ t |  t d d f ƒ d k sY t ‚ t |  t t d ƒ f d t f ƒ j t ƒ d k s’ t ‚ t |  t d k  f d t f ƒ j t ƒ t t t d ƒ t d k  f d t f ƒ k sí t ‚ d  S(   Ni   i    i   (	   R&   R5   R   R   R;   R   R   R6   R'   (   t   d1(    (    sN   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_piecewise.pyt   test_piecewise_with_DiracDelta   s    %$9*c          C   sG  t  d t d k  f d t f ƒ j d  k s0 t ‚ t  d t d k  f d t f ƒ j t k s` t ‚ t d d t ƒ}  t  d t d k  f |  t f ƒ j sœ t ‚ t  d t d k  f |  t d k  f ƒ j d  k sÒ t ‚ t d ƒ }  t  d t d k  f |  t f ƒ j d  k st ‚ t  d t d k  f d t f ƒ j d  k s>t ‚ t  d t d k  f d t f ƒ j sht ‚ t  d t d k  f t	 t f ƒ j
 d  k s˜t ‚ t  d t d k  f d t f ƒ j
 sÂt ‚ t ƒ  } t  | t d k  f ƒ j
 d  k sòt ‚ t  d t d k  f d t f ƒ d k  } | t k s+t ‚ t | ƒ t k sCt ‚ d  S(   Ni    i   iÿÿÿÿR]   t   zeroi   i   (   R   R5   R6   t   is_zeroRB   R;   R<   R    t
   is_nonzeroR   t	   is_finiteR   R   (   R]   Rq   Ro   (    (    sN   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_piecewise.pyt   test_issue_10258,  s     00*600*0*	''c          C   sé   t  t t d k f d t f ƒ t  t t d k f d t f ƒ }  } |  | } t | ƒ } x8 d D]0 } | j t | ƒ | j t | ƒ k s` t ‚ q` W|  | } t | ƒ } x8 d D]0 } | j t | ƒ | j t | ƒ k s± t ‚ q± Wd  S(   Ni   i   i   i    i   (   i    i   i   (   i    i   i   (   R   R5   R6   R   R:   R;   (   R]   Rq   t   mRK   R   (    (    sN   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_piecewise.pyt   test_issue_10087A  s    C
.
c          C   s³  t  d ƒ }  t  d ƒ } t |  d | d k  f |  d t f ƒ } t |  d | t d ƒ d k  f |  d t f ƒ } t | | | d d f ƒ |  d |  d d d |  d |  d d |  d |  d k sÔ t ‚ t d | d k  f d t f ƒ } t d | d k  f d t f ƒ } t | | | d d f ƒ d k s>t ‚ t  d	 d
 t ƒ} t  d d t ƒ\ } } }  } } t t d | | k | d k  B| |  k Bf | t f ƒ | d | f ƒ } | j ƒ  }	 |	 t d | |  k f | t | | ƒ | t d | ƒ t f ƒ k st ‚ x t t	 f D] }
 x† t
 d d ƒ D]u } xl t
 | d | ƒ D]W } | |  k |
 f | | f | | f g } |	 j | ƒ | j | ƒ j ƒ  k sLt ‚ qLWq2WqWd  S(   Ns   c:5R5   i   i   i   i   i    i   R>   RŽ   s	   a,b,c,x,zR`   (   R   R   R6   R!   R   R;   R
   R@   R   R<   Rƒ   R:   (   Ro   R5   RW   RX   R>   R]   Rq   R0   R   R~   RE   Rf   t   zzR   (    (    sN   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_piecewise.pyt   test_issue_8919M  s*    )3G!!(!#K'c          C   se  t  d ƒ }  t d t |  t ƒ d d ƒ f d t d d k  f d t f ƒ } | j t ƒ t | t ƒ k sq t ‚ | j t d d f ƒ t | t d d f ƒ k s§ t ‚ t | t d d f ƒ j |  t ƒ t d ƒ j	 ƒ  d k sç t ‚ | j t
 ƒ t t
 t |  t ƒ d ƒ t d k  t |  t ƒ d ƒ @Bf d t
 t t k t d k  @f d t f ƒ k sat ‚ d  S(   NRK   i   i    i   i
   i   (   R   R   R   R5   R6   R   R
   R;   R:   R8   R>   R   (   RK   RF   (    (    sN   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_piecewise.pyt   test_unevaluated_integralsf  s    A$6@5c          C   sˆ   t  d ƒ \ }  } } t t t t d k  t d k f t d k t f ƒ f ƒ t t t t d k t d k  t d k ƒ f ƒ k s„ t ‚ d  S(   Ns   a:ci   i    (   R   R   R5   R>   R6   R	   R;   (   R]   Rq   Ro   (    (    sN   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_piecewise.pyt%   test_conditions_as_alternate_booleansw  s    6c             ss  t  d ƒ \ ‰ ‰ }  } d „  ‰  ˆ  ˆ t d k  f ˆ t d k f ƒ t t d k  ˆ ˆ ƒ k sf t ‚ ˆ  ˆ t d k  f ˆ t t k  f ƒ t t d k  ˆ ˆ ƒ k s« t ‚ ˆ  ˆ t d k  f ˆ t t d k  t t k  ƒ f |  t d k f ƒ t t d k  ˆ ˆ ƒ k st ‚ ˆ  ˆ t d k  f ˆ t f ƒ t t d k  ˆ ˆ ƒ k sMt ‚ ˆ  ˆ t d k  f ˆ t d k  f |  t f ƒ t t d k  ˆ t t d k  ˆ |  ƒ ƒ k s­t ‚ ˆ  ˆ t d k  f ˆ t d k  f |  t f ƒ t t d k  ˆ t t d k  ˆ |  ƒ ƒ k st ‚ ˆ  ˆ t d k  f ˆ t t k  f |  t d k  f ƒ t t d k  ˆ ˆ ƒ k sat ‚ ˆ  ˆ t d k  f |  t d k  f ˆ t t k  f | t f ƒ t t d k  ˆ t t d k  |  ˆ ƒ ƒ k sÐt ‚ ˆ  ˆ t d k  f ˆ t t t k  t d k  ƒ f ƒ t t d k  ˆ ˆ ƒ k s$t ‚ t t	 ‡  f d †  ƒ t t
 ‡  ‡ f d †  ƒ t t ‡  ‡ ‡ f d †  ƒ d  S(	   Ns   a:dc          W   s   t  |  Œ  j t ƒ S(   N(   R   Rj   R	   (   Rˆ   (    (    sN   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_piecewise.pyt   _ITE€  s    i   i    i   c              s#   ˆ  t  d t  d k  f t  t f ƒ S(   Ni   (   R5   R6   (    (   Rí   (    sN   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_piecewise.pyR2   ’  R3   c              s%   ˆ  t  t  t k  f t t  ˆ k f ƒ S(   N(   R5   R>   (    (   Rí   R]   (    sN   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_piecewise.pyR2   –  R3   c              s%   ˆ  ˆ t  d k  f ˆ t  d k f ƒ S(   Ni   i   (   R5   (    (   Rí   R]   Rq   (    sN   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_piecewise.pyR2   —  R3   (   R   R5   R	   R;   R   R   R>   R6   R-   R=   R   t
   ValueError(   Ro   Rp   (    (   Rí   R]   Rq   sN   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_piecewise.pyt   test_Piecewise_rewrite_as_ITE}  s(    	EEB!?-3-33!<33!c           C   s8   t  t t t ƒ ƒ t d d t f ƒ d k s4 t ‚ d  S(   Ni    i   i   (   R   RÖ   R   R5   R   R;   (    (    (    sN   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_piecewise.pyt   test_issue_14052š  s    c          C   s©  t  t d t f d t f d t f ƒ t d t f d t f ƒ ƒ t d t f d t f d t f ƒ k sm t ‚ t  t d t f d	 t f d
 t f ƒ t d t f d t f ƒ ƒ t d t f d t f d t f ƒ k sÚ t ‚ t  t g  t d ƒ D]! }  t |  t f d t f ƒ ^ qí Œ  ƒ t d t f d t f ƒ k s;t ‚ t  t g  t d d ƒ D]! }  t |  t f d t f ƒ ^ qQŒ  ƒ t t	 d ƒ t f d t f ƒ k s¥t ‚ d  S(   Ni   i   i   i   i   i	   i   i   i   i   i   i   i   i!   i7   i(   i    i  i)   (
   R   R   R]   Rq   R6   R;   R(   Rƒ   R)   R*   (   R   (    (    sN   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_piecewise.pyt   test_issue_14240ž  s    !-!-7$:c          C   sY   t  d ƒ }  t |  |  d k  f t d ƒ d t f ƒ } t | j ƒ  ƒ d k sU t ‚ d  S(   NR5   i   i:   i   s/   Piecewise((x, x < 1), (8.28571428571429, True))(   R    R   R!   R6   RÃ   R?   R;   (   R5   RK   (    (    sN   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_piecewise.pyt   test_issue_14787°  s    +c          C   sv  t  d ƒ \ }  } t d t |  d ƒ f t |  ƒ t f ƒ } | j ƒ  t |  ƒ k sZ t ‚ t |  t |  d ƒ f d |  | d d t |  d ƒ t |  | d ƒ @f t |  ƒ t f ƒ } | j ƒ  t |  ƒ k sÕ t ‚ t |  d t |  d ƒ f d |  | d d t |  d ƒ t |  | d ƒ @f t |  ƒ t f ƒ } | j ƒ  t d t |  d ƒ f t |  ƒ t f ƒ k srt ‚ d  S(   Ns   x yi    i   i   i   iÿÿÿÿ(   R   R   R   R   R6   Ri   R;   (   R5   R>   R…   RH   RI   (    (    sN   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_piecewise.pyt   test_issue_8458¶  s    *]aN(q   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!   R"   R#   R$   R%   R&   R'   R(   R)   R*   R+   t   sympy.printingR,   t   sympy.utilities.pytestR-   R.   t$   sympy.functions.elementary.piecewiseR/   R]   Rq   Ro   Rp   R5   R>   R6   R0   R\   R_   Rb   Rg   Rk   Rl   Rx   Ry   R‚   R†   R‡   R‰   R’   R“   R–   R—   R˜   R™   R›   Rœ   R£   R¤   R¨   R«   R¯   R³   R·   R¹   Rº   R»   R½   R¾   RÂ   RÄ   RÇ   RÊ   RÍ   RÕ   RØ   RÜ   RÞ   Rß   Rá   Ræ   Rè   Rê   Rë   Rì   Rï   Rð   Rñ   Rò   Ró   (    (    (    sN   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_piecewise.pyt   <module>   sv   ÿ 				/.			A			C			
					-										J						%			#												