ó
¡¼™\c           @   sñ  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 d  d l m Z d  d l  m! Z! d  d l" m# Z# m$ Z$ d „  Z% d „  Z& d „  Z' d „  Z( d	 „  Z) d
 „  Z* d „  Z+ d „  Z, d „  Z- d „  Z. d „  Z/ d „  Z0 d „  Z1 d „  Z2 d „  Z3 d „  Z4 d „  Z5 d „  Z6 d „  Z7 d „  Z8 d „  Z9 d „  Z: d „  Z; d „  Z< e! d „  ƒ Z= d „  Z> d „  Z? d  S(!   iÿÿÿÿ(   t   symbolst   sint   simplifyt   cost   trigsimpt   radt   tant   exptrigsimpt   sinht   cosht   difft   cott   Subst   expt   tanhR   t   St	   integratet   It   Matrixt   Symbolt   cotht   pit   logt	   count_opst   sqrtt   Et   expandt	   Piecewiset   Rational(   t   long(   t   XFAIL(   t   xt   yc          C   só  t  d ƒ \ }  } t d t |  ƒ d ƒ t |  ƒ d k sB t ‚ t d t |  ƒ d ƒ t |  ƒ d k sr t ‚ t t |  ƒ d t |  ƒ d ƒ d k s¢ t ‚ t d t |  ƒ d ƒ d t |  ƒ d k sÖ t ‚ t d t |  ƒ d d ƒ t |  ƒ d k s
t ‚ t d t |  ƒ d t |  ƒ d ƒ d k s>t ‚ t d t |  ƒ d ƒ d t |  ƒ d k srt ‚ t d t |  ƒ d d ƒ d t |  ƒ d k sªt ‚ t d t |  ƒ d t |  ƒ d ƒ d k sÞt ‚ t d t |  ƒ d d t |  ƒ d ƒ d k st ‚ t d t |  d ƒ d d t |  d ƒ d ƒ d t |  ƒ d t d ƒ d k srt ‚ t t |  ƒ t |  ƒ ƒ t |  ƒ k s t ‚ t d t |  ƒ t |  ƒ ƒ d t |  ƒ k sÖt ‚ t t |  ƒ d t |  ƒ d ƒ t |  ƒ d k st ‚ t | t |  ƒ d t |  ƒ d ƒ | t |  ƒ d k sRt ‚ t t |  ƒ t |  ƒ ƒ d t |  ƒ k s„t ‚ t t |  | ƒ t |  | ƒ ƒ d t |  ƒ t | ƒ k sÈt ‚ t t |  | ƒ t |  | ƒ ƒ d t | ƒ t |  ƒ k st ‚ t t |  | ƒ t |  | ƒ ƒ d t |  ƒ t | ƒ k sPt ‚ t t |  | ƒ t |  | ƒ ƒ d t |  ƒ t | ƒ k s”t ‚ t t |  | ƒ t |  ƒ d t |  ƒ t | ƒ ƒ t | ƒ t | ƒ t |  ƒ t | ƒ k sýt ‚ t t |  | ƒ t |  | ƒ ƒ d t |  ƒ t	 | ƒ k sAt ‚ t t |  | ƒ t |  | ƒ ƒ d t | ƒ t	 |  ƒ k s…t ‚ t t	 |  | ƒ t	 |  | ƒ ƒ d t	 |  ƒ t	 | ƒ k sÉt ‚ t t	 |  | ƒ t	 |  | ƒ ƒ d t |  ƒ t | ƒ k st ‚ t t
 |  | ƒ t
 |  ƒ d t
 |  ƒ t
 | ƒ ƒ t | ƒ t | ƒ t
 |  ƒ t	 | ƒ k sut ‚ t t d ƒ d t d ƒ d ƒ d k s¥t ‚ d t |  ƒ d d t |  ƒ d } t t | ƒ ƒ t d ƒ k sït ‚ d  S(	   Ns   x,yi   i   i   i   i   iþÿÿÿg|ò°Pkš¿?(   R    R   R   R   t   AssertionErrorR   R   R   R   R	   R   R   (   R   R    t   e(    (    sA   lib/python2.7/site-packages/sympy/simplify/tests/test_trigsimp.pyt   test_trigsimp1   s@    0004444848\.6:B2DDDD54DDDD530&c           C   s  t  t d ƒ d t d ƒ t d ƒ t d ƒ d ƒ t d ƒ d t d ƒ t d ƒ k sb t ‚ t  t d ƒ d t d ƒ t d ƒ t d ƒ d ƒ t d ƒ d t d ƒ t d ƒ k sÄ t ‚ t  t d ƒ t d ƒ t d ƒ t d ƒ ƒ t d ƒ t d ƒ t d ƒ k st ‚ t  t d ƒ t d ƒ t d ƒ t d ƒ ƒ t d ƒ t d ƒ t d ƒ k spt ‚ t  t d ƒ t d ƒ t d ƒ t d ƒ ƒ t d ƒ t d ƒ t d ƒ k sÆt ‚ t  t d ƒ t d ƒ t d ƒ t d ƒ ƒ t d ƒ t d ƒ k st ‚ t  t d ƒ t d ƒ t d ƒ t d ƒ ƒ t	 d ƒ t d ƒ t d ƒ k sht ‚ t  t	 d ƒ t d ƒ t d ƒ t d ƒ ƒ t d ƒ t d ƒ t d ƒ k s¾t ‚ t  t
 d ƒ t d ƒ t d ƒ t d ƒ ƒ t d ƒ t d ƒ t d ƒ k st ‚ t  t	 d ƒ t d ƒ t d ƒ t d ƒ ƒ t d ƒ t d ƒ t d ƒ k sjt ‚ t  t
 d ƒ t d ƒ t d ƒ t d ƒ ƒ t d ƒ t d ƒ t d ƒ k sÀt ‚ t  t
 d ƒ t d ƒ t d ƒ t	 d ƒ ƒ t d ƒ t d ƒ k st ‚ d  S(   Ni   i   (   R   R   R   R   R   R!   R   R   R	   R   R   (    (    (    sA   lib/python2.7/site-packages/sympy/simplify/tests/test_trigsimp.pyt   test_trigsimp1a7   s    bbVVVLVVVVVc          C   s  t  d ƒ \ }  } t t |  ƒ d t | ƒ d t |  ƒ d t | ƒ d t |  ƒ d d t ƒd k sr t ‚ t t |  ƒ d t | ƒ d t |  ƒ d t | ƒ d t |  ƒ d d t ƒd k sÒ t ‚ t t |  |  t | ƒ d t | ƒ d ƒ ƒ t |  |  d ƒ k st ‚ d  S(   Ns   x,yi   t	   recursivei   (   R    R   R   R   t   TrueR!   R   (   R   R    (    (    sA   lib/python2.7/site-packages/sympy/simplify/tests/test_trigsimp.pyt   test_trigsimp2F   s    KKc          C   sR   t  d ƒ }  t t d t |  ƒ d d t |  ƒ d ƒ d ƒ d k  sN t ‚ d  S(   NR   g       @i   g»½×Ùß|Û=(   R   t   absR   R   R   R!   (   R   (    (    sA   lib/python2.7/site-packages/sympy/simplify/tests/test_trigsimp.pyt   test_issue_4373P   s    c          C   sÔ  t  d ƒ \ }  } t t |  ƒ t |  ƒ ƒ t |  ƒ k s@ t ‚ t t |  ƒ d t |  ƒ d ƒ t |  ƒ d k sz t ‚ t t |  ƒ d t |  ƒ d ƒ t |  ƒ d k s´ t ‚ t t |  ƒ d t |  ƒ d ƒ t |  ƒ d k sî t ‚ t t |  ƒ t |  ƒ ƒ d t |  ƒ k s t ‚ t t |  ƒ d t |  ƒ d ƒ d t |  ƒ d k s^t ‚ t t |  ƒ d t |  ƒ d ƒ d t |  ƒ d k sœt ‚ t t |  ƒ ƒ t t |  ƒ t |  ƒ ƒ k sÐt ‚ d  S(   Ns   x,yi   i   i
   i   (   R    R   R   R   R   R!   (   R   R    (    (    sA   lib/python2.7/site-packages/sympy/simplify/tests/test_trigsimp.pyt   test_trigsimp3U   s    .:::2>>c          C   s¿  t  d ƒ \ }  } } d t | ƒ d d t | ƒ d d t | ƒ d } t | ƒ d k se t ‚ t | ƒ d d t | ƒ d t | ƒ d d t | ƒ d t | ƒ d d t | ƒ d } t | ƒ d d t | ƒ d } t | | ƒ d k st ‚ t d	 t | ƒ d t | ƒ d t | ƒ d ƒ d k sHt ‚ t | ƒ d
 d t | ƒ t | ƒ d
 d t | ƒ t d | ƒ t d | ƒ d } t | ƒ d k s»t ‚ d  S(   Ns   a x yiüÿÿÿi   i   i   i   i   iÿÿÿÿiþÿÿÿi   i    (   R    R   R   R   R!   R   (   t   aR   R    t   eqt   nt   d(    (    sA   lib/python2.7/site-packages/sympy/simplify/tests/test_trigsimp.pyt   test_issue_4661c   s    8b#B[c          C   s„   t  d ƒ \ }  } t |  ƒ d t | ƒ d t |  ƒ d t | ƒ d t |  ƒ d t |  ƒ d } t | ƒ d k s€ t ‚ d  S(   Ns   a bi   i   (   R    R   R   R   R   R!   (   R+   t   bR,   (    (    sA   lib/python2.7/site-packages/sympy/simplify/tests/test_trigsimp.pyt   test_issue_4494o   s    Vc          C   sk   t  d ƒ \ }  } } t t t t | ƒ t | ƒ d | ƒ | ƒ ƒ t | ƒ t | ƒ d k sg t ‚ d  S(   Ns   a x yi   (   R    R   R
   R   R   R   R!   (   R+   R   R    (    (    sA   lib/python2.7/site-packages/sympy/simplify/tests/test_trigsimp.pyt   test_issue_5948u   s    /c          C   s­   t  d ƒ \ }  } } t t | ƒ t | ƒ t | ƒ t | ƒ ƒ t | | ƒ k s[ t ‚ t t | ƒ t | ƒ t | ƒ t | ƒ d ƒ t | | ƒ d k s© t ‚ d  S(   Ns   a x yi   (   R    R   R   R   R!   (   R+   R   R    (    (    sA   lib/python2.7/site-packages/sympy/simplify/tests/test_trigsimp.pyt   test_issue_4775{   s    Fc          C   sW  t  d ƒ \ }  } } t t | ƒ d t | ƒ d t | ƒ d t | ƒ d t | ƒ d ƒ d k so t ‚ t |  d t | ƒ d |  d t | ƒ d t | ƒ d |  d t | ƒ d t | ƒ d ƒ |  d k så t ‚ t |  d t | ƒ d t | ƒ d |  d t | ƒ d t | ƒ d ƒ |  d t | ƒ d k sSt ‚ d  S(   Ns   a x yi   i   (   R    R   R   R   R!   (   R+   R   R    (    (    sA   lib/python2.7/site-packages/sympy/simplify/tests/test_trigsimp.pyt   test_issue_4280   s    Zvc       
   C   s›  t  d ƒ t d ƒ t  d ƒ t d ƒ t  d ƒ t  d ƒ t d ƒ t d ƒ t  d ƒ t d ƒ t  d ƒ t d ƒ t  d ƒ t  d ƒ t d ƒ t d ƒ t  d ƒ t  d ƒ t d ƒ t d ƒ t d ƒ t d ƒ t d ƒ t d ƒ t d ƒ t d ƒ t d ƒ t d ƒ t d ƒ f }  g  |  D] } t | ƒ ^ q)t  d ƒ t d ƒ t  d ƒ t d ƒ t d ƒ t d ƒ t d ƒ t d ƒ g k s—t ‚ d  S(   Ni   i   i   i   (   R   R   R   R	   R   R!   (   t   eqsR"   (    (    sA   lib/python2.7/site-packages/sympy/simplify/tests/test_trigsimp.pyt   test_issue_3210ˆ   s    '(''1'-		
		c          C   sL  t  d ƒ \ }  } } t t | ƒ d t | ƒ d t | ƒ ƒ t | ƒ k sU t ‚ t t t t | ƒ t | ƒ d | ƒ | ƒ ƒ t | ƒ t | ƒ d k s§ t ‚ t t t t | ƒ t | ƒ d | ƒ | ƒ ƒ t | ƒ t | ƒ d k sù t ‚ t | ƒ | t | ƒ | } t | ƒ | k s/t ‚ t | j | d ƒ ƒ t | ƒ d k s]t ‚ t | j | d ƒ ƒ t d ƒ | k s‹t ‚ t | ƒ d t | ƒ d t | ƒ d t | ƒ d j ƒ  d t | ƒ d t | ƒ d k sót ‚ t t | ƒ t | ƒ t | | ƒ t | | ƒ ƒ d t | ƒ t | | ƒ k sOt ‚ t d ƒ t d ƒ d d t d ƒ d d } t | ƒ | j	 ƒ  k st ‚ t t d ƒ t d ƒ d d t d ƒ d d ƒ t d ƒ t d ƒ d k sót ‚ t
 | ƒ j t | ƒ ƒ t k st ‚ t | ƒ d t | ƒ d d } t | ƒ d d t
 | ƒ d } d | | } t t | ƒ ƒ t d ƒ k st ‚ | | d | | } t | ƒ t j k sÁt ‚ t | d t ƒt j k sât ‚ t d ƒ j s÷t ‚ t t | ƒ d d t | ƒ d t | ƒ d t | ƒ d ƒ d k sHt ‚ d  S(   Ns   a x yi   i   i   i   R%   iÿÿÿÿ(   R    R   R   R   R!   R
   R   t   subsR   t   factorR   t   equalst   FalseR   t   NaNR&   t
   is_Integer(   R+   R   R    R"   R,   t   zt   z1R-   (    (    sA   lib/python2.7/site-packages/sympy/simplify/tests/test_trigsimp.pyt   test_trigsimp_issuesœ   s8    @/#/#..=+5'03#'""$!c          C   sy   t  d ƒ }  t |  t |  ƒ t |  ƒ ƒ |  t |  ƒ k sB t ‚ t t |  ƒ t |  ƒ t |  ƒ ƒ d k su t ‚ d  S(   NR   i    (   R   R   R   R   R   R!   (   R   (    (    sA   lib/python2.7/site-packages/sympy/simplify/tests/test_trigsimp.pyt   test_trigsimp_issue_2515Ê   s    6c           C   s<   t  t d t ƒ j d t ƒ ƒ t d t ƒ k s8 t ‚ d  S(   Ni   t   trig(   R   R   R   R   R&   R!   (    (    (    sA   lib/python2.7/site-packages/sympy/simplify/tests/test_trigsimp.pyt   test_trigsimp_issue_3826Ð   s    c          C   sŒ   t  d d t d t ƒ}  t d |  d t t |  d ƒ d d |  d d ƒ d |  d t t |  d ƒ d d |  d k sˆ t ‚ d  S(   NR-   t   integert   positivei   i   i   (   R   R&   R   R   R   R!   (   R-   (    (    sA   lib/python2.7/site-packages/sympy/simplify/tests/test_trigsimp.pyt   test_trigsimp_issue_4032Ô   s    7c           C   s0   t  t t d ƒ ƒ t t d ƒ k s, t ‚ d  S(   Ni   (   R   R	   R   R!   (    (    (    sA   lib/python2.7/site-packages/sympy/simplify/tests/test_trigsimp.pyt   test_trigsimp_issue_7761Ú   s    c          C   sT  t  d ƒ \ }  } t  d d t ƒ\ } } t | | t |  ƒ d ƒ | t |  ƒ d k sb t ‚ t | | t |  ƒ d ƒ | t |  ƒ d k sš t ‚ t | t |  ƒ d | t |  ƒ d ƒ | k sÒ t ‚ t | | t |  ƒ d ƒ | t |  ƒ d k s
t ‚ t | t |  ƒ d | ƒ | t |  ƒ d k sBt ‚ t | t |  ƒ d | t |  ƒ d ƒ | k szt ‚ t | | t |  ƒ d ƒ | t |  ƒ d k s²t ‚ t | t |  ƒ d | ƒ | t |  ƒ d k sêt ‚ t | t |  ƒ d | t |  ƒ d ƒ | k s"t ‚ t | | t |  ƒ d | | t |  ƒ d ƒ | | k sft ‚ t | t |  ƒ t |  ƒ ƒ | t |  ƒ k sœt ‚ t | t |  ƒ t |  ƒ ƒ | t |  ƒ k sÒt ‚ t | t |  ƒ d t |  ƒ d ƒ | t |  ƒ d k st ‚ t | | t |  ƒ d t |  ƒ d ƒ | | t |  ƒ d k s^t ‚ t | t |  ƒ t |  ƒ ƒ | t |  ƒ k s”t ‚ t | t |  | ƒ | t |  | ƒ ƒ d | t |  ƒ t | ƒ k sät ‚ t | t |  | ƒ | t |  | ƒ ƒ d | t | ƒ t |  ƒ k s4t ‚ t | t |  | ƒ | t |  | ƒ ƒ d | t |  ƒ t | ƒ k s„t ‚ t | t |  | ƒ | t |  | ƒ ƒ d | t |  ƒ t | ƒ k sÔt ‚ t | t |  | ƒ | t |  | ƒ ƒ d | t |  ƒ t	 | ƒ k s$t ‚ t | t |  | ƒ | t |  | ƒ ƒ d | t | ƒ t	 |  ƒ k stt ‚ t | t	 |  | ƒ | t	 |  | ƒ ƒ d | t	 |  ƒ t	 | ƒ k sÄt ‚ t | t	 |  | ƒ | t	 |  | ƒ ƒ d | t |  ƒ t | ƒ k st ‚ t | t d ƒ d | t d ƒ d ƒ d | k sPt ‚ d  S(	   Ns   x,ys   A,Bt   commutativei   i   iþÿÿÿg|ò°Pkš¿?g      ð?(
   R    R:   R   R   R   R!   R   R   R   R	   (   R   R    t   At   B(    (    sA   lib/python2.7/site-packages/sympy/simplify/tests/test_trigsimp.pyt   test_trigsimp_noncommutativeÞ   s4    888888888D66BJ6PPPPPPPPc          C   sŒ  t  d ƒ \ }  } t t |  ƒ d d ƒ t |  ƒ d k sB t ‚ t t |  ƒ d d ƒ t |  ƒ d k sr t ‚ t t |  ƒ d t |  ƒ d ƒ d k s¢ t ‚ t d t |  ƒ d ƒ d t |  ƒ d k sÖ t ‚ t d d t |  ƒ d ƒ t |  ƒ d k s
t ‚ t t |  ƒ d d t |  ƒ d ƒ d k s>t ‚ t t |  ƒ d d ƒ d t |  ƒ d k srt ‚ t d t |  ƒ d d ƒ d t |  ƒ d k sªt ‚ t t |  ƒ d d t |  ƒ d ƒ d k sÞt ‚ t d t |  ƒ d d t |  ƒ d ƒ d k st ‚ t d t |  d ƒ d d t |  d ƒ d ƒ d t |  ƒ d t d ƒ d k srt ‚ t t |  ƒ t |  ƒ ƒ t |  ƒ k s t ‚ t t |  ƒ ƒ t t |  ƒ t |  ƒ ƒ k sÔt ‚ t t |  ƒ t |  ƒ ƒ d t |  ƒ k st ‚ t d t |  ƒ t |  ƒ ƒ d t |  ƒ k s<t ‚ t t |  ƒ d t |  ƒ d ƒ t |  ƒ d k svt ‚ t | t |  ƒ d t |  ƒ d ƒ | t |  ƒ d k s¸t ‚ t t |  ƒ t |  ƒ ƒ d t |  ƒ k sêt ‚ x¼ t d t	 t d t	 t d t	 f D]“ } t t | ƒ t |  ƒ t | ƒ t |  ƒ ƒ t |  | ƒ k s^t ‚ t t | ƒ t |  ƒ t | ƒ t |  ƒ ƒ t |  | ƒ k st ‚ qWd t |  ƒ d d t |  ƒ d } t t
 | ƒ ƒ t
 d ƒ k sót ‚ t t |  ƒ d t | ƒ d t |  ƒ d t | ƒ d t |  ƒ d d	 t ƒd k sSt ‚ t t |  ƒ d t | ƒ d t |  ƒ d t | ƒ d t |  ƒ d d	 t ƒd k s³t ‚ t t d
 t |  ƒ d d
 t |  ƒ d ƒ d
 ƒ d k  sõt ‚ t t |  ƒ d t |  ƒ d ƒ t |  ƒ d k s/t ‚ t t |  ƒ d t |  ƒ d ƒ t |  ƒ d k sit ‚ t t |  ƒ d t |  ƒ d ƒ t |  ƒ d k s£t ‚ t t |  ƒ d t |  ƒ d ƒ d t |  ƒ d k sát ‚ t t |  ƒ t |  ƒ ƒ d t |  ƒ k st ‚ t t |  ƒ d t |  ƒ d ƒ d t |  ƒ d k sQt ‚ t t |  ƒ d t |  ƒ d ƒ d t |  ƒ d k st ‚ t |  t |  ƒ t |  ƒ ƒ |  t |  ƒ k sÅt ‚ t t |  ƒ t |  ƒ t |  ƒ ƒ d k søt ‚ t |  ƒ d t |  ƒ k st ‚ t t |  ƒ d t |  ƒ ƒ d k sFt ‚ t d t |  ƒ d d t |  ƒ d ƒ t |  ƒ d k sˆt ‚ d  S(   Ns   x,yi   i   i   i   i   i   i   R%   g       @g»½×Ùß|Û=i
   i    (   R    R   R   R	   R!   R   R   R   R   R   R   R&   R(   R   R   (   R   R    R+   R"   (    (    sA   lib/python2.7/site-packages/sympy/simplify/tests/test_trigsimp.pyt   test_hyperbolic_simp  sR    0004444848\.426:B2.FK&$KKB:::>2>>63",c          C   s©  d d l  m }  t t ƒ } t t ƒ } d | | d | d | d d | d d	 | d
 | | d d | | d
 | d | d d | d d | d } d | d | d } d | d | } | | | | g } |  | ƒ | k sý t ‚ |  | | d t g ƒt t ƒ k s(t ‚ |  | | ƒ | | k sHt ‚ t | d | | | d d d ƒd | k s€t ‚ t | d | | | d d d d t ƒd | k s¾t ‚ |  | d d g ƒ| k sßt ‚ |  | d t	 d ƒ g ƒ| k st ‚ |  t t
 t ƒ t t
 t ƒ d t g ƒt
 t t ƒ k sIt ‚ |  t t ƒ t t ƒ d t t ƒ t t ƒ d t t t f g ƒt t t ƒ k s¥t ‚ d  S(   Niÿÿÿÿ(   t   trigsimp_groebneri   i   i   i   i   i   i   i   i   i   i%   i   i   i   t   hintst   methodt   groebnert
   polynomial(   t   sympy.simplify.trigsimpRL   R   R   R   R!   R   R   R&   R   R   R   R    (   RL   t   ct   st   ext   resnumt   resdenomt   results(    (    sA   lib/python2.7/site-packages/sympy/simplify/tests/test_trigsimp.pyt   test_trigsimp_groebner9  s(    7H+ !'C1c             s	  d „  }  d „  } t  d t  t t  ƒ d t t  ƒ d } t d g ƒ } t | g ƒ ‰  t ˆ  d d d |  ƒ| k s~ t ‚ t ˆ  d d d | ƒ| k s¢ t ‚ t j d ƒ ‰  t ‡  f d †  d	 j ƒ  Dƒ ƒ sÙ t ‚ d t	 t
 ƒ t
 } t | ƒ | k st ‚ d  S(
   Nc         S   s   t  t |  ƒ ƒ S(   N(   t   lent   str(   t   expr(    (    sA   lib/python2.7/site-packages/sympy/simplify/tests/test_trigsimp.pyt   <lambda>X  t    c         S   s   t  |  ƒ S(   N(   R   (   R[   (    (    sA   lib/python2.7/site-packages/sympy/simplify/tests/test_trigsimp.pyR\   Y  R]   i   i   RN   t   fut   measurec         3   s'   |  ] } t  ˆ  d  | ƒˆ  k Vq d S(   RN   N(   R   (   t   .0t   m(   t   M(    sA   lib/python2.7/site-packages/sympy/simplify/tests/test_trigsimp.pys	   <genexpr>c  s    s   fu matching groebner old(   R   R   R   R   R   R!   t   eyet   allt   splitR   R   R   (   t   measure1t   measure2R[   t   ansR,   (    (   Rb   sA   lib/python2.7/site-packages/sympy/simplify/tests/test_trigsimp.pyt    test_issue_2827_trigsimp_methodsW  s    		*$$c          C   s  t  t t d d ƒ ƒ t t d d ƒ ƒ d g ƒ }  t  t t d d ƒ ƒ t t d d ƒ ƒ d g ƒ } t  t t d d ƒ ƒ t t d d ƒ ƒ d g ƒ } |  j | ƒ } |  j | ƒ } t | ƒ t t d ƒ d ƒ k sß t ‚ t | ƒ t t d ƒ d ƒ k st ‚ d  S(   Ni   i2   i    i   i   (   R   R   R   R   t   dotR   R   R!   (   t   t1t   t2t   t3t   r1t   r2(    (    sA   lib/python2.7/site-packages/sympy/simplify/tests/test_trigsimp.pyt!   test_issue_15129_trigsimp_methodsi  s    333(c    	         sƒ  d „  ‰  t  t t ƒ t t ƒ ƒ d t t ƒ k s< t ‚ t  t t ƒ t t ƒ ƒ d t t ƒ k so t ‚ t  d t t ƒ d t t ƒ t t ƒ t t ƒ ƒ d t t ƒ k s¿ t ‚ t  d t d t ƒ d t d t ƒ d ƒ d t t ƒ k st ‚ t t ƒ t t	 t ƒ t t ƒ t t	 t ƒ t t ƒ t t ƒ t t ƒ t t ƒ g }  t t t ƒ t t t ƒ t t ƒ t t ƒ g } t
 ‡  f d †  t g  |  D] } t  | ƒ ^ q¬| ƒ Dƒ ƒ s×t ‚ t t ƒ t	 t ƒ t t ƒ t	 t ƒ t t ƒ t t t ƒ t t ƒ t t t ƒ g } g  | D] } t  | ƒ | k ^ q8s\t ‚ g  } t t d ƒ d t t d ƒ t t t d ƒ t t t d ƒ t t t ƒ d t t t ƒ t t t t ƒ t t t t ƒ t t d t ƒ d t t d t ƒ g
 } xy d t t t t d t f D]Z } t | ƒ } t | d | | d | } | j t | ƒ ƒ | j t d | ƒ ƒ q.Wt
 ‡  f d †  t | | ƒ Dƒ ƒ s·t ‚ xÅ t d d ƒ D]´ } t | ƒ } | d | }  t |  ƒ } | t  |  ƒ k st ‚ ˆ  | d t | ƒ ƒ s*t ‚ | d | }  t |  ƒ } | t  |  ƒ k s\t ‚ ˆ  | d t | ƒ ƒ sÇt ‚ qÇWd  S(   Nc         S   s3   d d l  m } | |  | ƒ o( |  | k s/ t St S(   Niÿÿÿÿ(   t   verify_numerically(   t   sympy.utilities.randtestRq   R:   R&   (   R+   R0   t   tn(    (    sA   lib/python2.7/site-packages/sympy/simplify/tests/test_trigsimp.pyt   valids  s    i   i   c         3   s$   |  ] \ } } ˆ  | | ƒ Vq d  S(   N(    (   R`   t   it   j(   Rt   (    sA   lib/python2.7/site-packages/sympy/simplify/tests/test_trigsimp.pys	   <genexpr>€  s    c         3   s$   |  ] \ } } ˆ  | | ƒ Vq d  S(   N(    (   R`   Ru   Rv   (   Rt   (    sA   lib/python2.7/site-packages/sympy/simplify/tests/test_trigsimp.pys	   <genexpr>  s    i   (   R   R   R   R	   R!   R   R   R   R   R   Rd   t   zipR    R   t   appendR   t   range(	   R"   t   okt   eit   uet   resR+   t   wR,   RS   (    (   Rt   sA   lib/python2.7/site-packages/sympy/simplify/tests/test_trigsimp.pyt   test_exptrigsimpr  sB    	33PF.,42&4+AA,$+c          C   s²   t  d d t ƒ\ }  } t d d t ƒ} t |  | ƒ t t |  ƒ t | ƒ ƒ k s\ t ‚ t |  ƒ t | ƒ t | ƒ t |  ƒ } | t | ƒ k o£ d k n s® t ‚ d  S(   Ns   a bRG   R   i    (   R    R:   R   R&   R   R   R!   (   R+   R0   R   t   p(    (    sA   lib/python2.7/site-packages/sympy/simplify/tests/test_trigsimp.pyt   test_exptrigsimp_noncommutative  s
    2*c           C   s:   d t  d ƒ d d d t  d ƒ d d k s6 t ‚ d  S(   Ni   i   i   i   (   R   R!   (    (    (    sA   lib/python2.7/site-packages/sympy/simplify/tests/test_trigsimp.pyt   test_powsimp_on_numbers¤  s    c          C   sÖ   t  d ƒ \ }  } } } d d t | ƒ | d t d | ƒ | d t d | ƒ | d | |  d	 t | ƒ d t d | ƒ } t | ƒ d
 d t | ƒ t | ƒ | d | |  t | ƒ k sÒ t ‚ d  S(   Ns   xp, y, x, zi   iíÿÿÿi   i   i   i   i   i	   iþÿÿÿ(   R    R   R   R   R   R!   (   t   xpR    R   R=   R,   (    (    sA   lib/python2.7/site-packages/sympy/simplify/tests/test_trigsimp.pyt   test_issue_6811_fail¨  s    pc          C   sÆ   t  t  t t t  t }  t t  ƒ d t t  ƒ d } t t  t t t  ƒ } t |  ƒ } t | ƒ } t | ƒ } t t |  | | k  f | t f ƒ ƒ t |  | | k  f | t f ƒ k sÂ t	 ‚ d  S(   Ni   (
   R   R    R   R   R   R   R   R   R&   R!   (   t   e1t   e2t   e3t   s1t   s2t   s3(    (    sA   lib/python2.7/site-packages/sympy/simplify/tests/test_trigsimp.pyt   test_Piecewise³  s    $c          C   sã  t  d ƒ \ }  } t d t |  ƒ d d t ƒt |  ƒ d k sH t ‚ t d t |  ƒ d d t ƒt |  ƒ d k s~ t ‚ t t |  ƒ d t |  ƒ d d t ƒd k s´ t ‚ t d t |  ƒ d d t ƒd t |  ƒ d k sî t ‚ t d t |  ƒ d d d t ƒt |  ƒ d k s(t ‚ t d t |  ƒ d t |  ƒ d d t ƒd k sbt ‚ t d t |  ƒ d d t ƒd t |  ƒ d k sœt ‚ t d t |  ƒ d t |  ƒ d d t ƒd k sÖt ‚ t d t |  ƒ d d t |  ƒ d d t ƒd k st ‚ t t |  ƒ t |  ƒ d t ƒt |  ƒ k sHt ‚ t d t |  ƒ t |  ƒ d t ƒd t |  ƒ k s„t ‚ t t |  ƒ d t |  ƒ d d t ƒt |  ƒ d k sÄt ‚ t | t |  ƒ d t |  ƒ d d t ƒ| t |  ƒ d k st ‚ t t |  ƒ t |  ƒ d t ƒd t |  ƒ k sDt ‚ t t |  | ƒ t |  | ƒ d t ƒd t |  ƒ t | ƒ k sŽt ‚ t t |  | ƒ t |  | ƒ d t ƒd t | ƒ t |  ƒ k sØt ‚ t t |  | ƒ t |  | ƒ d t ƒd t |  ƒ t | ƒ k s"t ‚ t t |  | ƒ t |  | ƒ d t ƒd t |  ƒ t | ƒ k slt ‚ t t |  | ƒ t |  | ƒ d t ƒd t |  ƒ t	 | ƒ k s¶t ‚ t t |  | ƒ t |  | ƒ d t ƒd t | ƒ t	 |  ƒ k s t ‚ t t	 |  | ƒ t	 |  | ƒ d t ƒd t	 |  ƒ t	 | ƒ k sJt ‚ t t	 |  | ƒ t	 |  | ƒ d t ƒd t |  ƒ t | ƒ k s”t ‚ t t d ƒ d t d ƒ d d t ƒd k sÊt ‚ t t |  ƒ t |  ƒ d t d	 d
 ƒt |  ƒ k st ‚ t t |  ƒ t |  ƒ d t d	 d ƒt |  ƒ t |  ƒ k sHt ‚ t t |  ƒ t |  ƒ d t d	 d d t g ƒt |  ƒ k s‹t ‚ t d t t |  ƒ d t |  ƒ d ƒ d d t d t ƒt d ƒ d k sßt ‚ d  S(   Ns   x,yi   i   t   oldi   i   iþÿÿÿg|ò°Pkš¿?RN   t   combinedRO   RM   t   deep(
   R    R   R   R&   R   R!   R   R   R   R	   (   R   R    (    (    sA   lib/python2.7/site-packages/sympy/simplify/tests/test_trigsimp.pyt   test_trigsimp_old¿  s8    666:::::>4<@H8JJJJJJJJ6:DCN(@   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.core.compatibilityR   t   sympy.utilities.pytestR   t	   sympy.abcR   R    R#   R$   R'   R)   R*   R/   R1   R2   R3   R4   R6   R?   R@   RB   RE   RF   RJ   RK   RX   Ri   Rp   R   R   R‚   R„   R‹   R   (    (    (    sA   lib/python2.7/site-packages/sympy/simplify/tests/test_trigsimp.pyt   <module>   s<   ¾	)		
									.					#	8					+			