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 Z
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 eD ƒZF e d d eD ƒZG e d d eD ƒZH e d d eD ƒZI e d d eD d eD ƒ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 d, „  Zd d- „  Ze d. „  Zf d/ „  Zg d0 „  Zh d1 „  Zi d2 „  Zj d3 „  Zk d4 „  Zl d5 „  Zm d6 „  Zn d7 „  Zo d8 „  Zp d9 „  Zq d: „  Zr d; „  Zs d< „  Zt d= „  Zu d> „  Zv d? „  Zw d@ „  Zx dA „  Zy dB „  Zz dC „  Z{ dD „  Z| dE „  Z} e9 dF „  ƒ Z~ e: dG „  ƒ Z e: dH „  ƒ Z€ dI „  Z dJ „  Z‚ dK „  Zƒ dL „  Z„ dM „  Z… dN „  Z† dO „  Z‡ dP „  Zˆ dQ „  Z‰ dR „  ZŠ dS „  Z‹ dT „  ZŒ dU „  Z dV „  ZŽ dW „  Z dX „  Z dY S(Z   iÿÿÿÿ(5   t   symbolst   Symbolt   nant   oot   zoot   It   sinht   sint   pit   atant   acost   Rationalt   sqrtt   asint   acott   cotht   Et   St   tant   tanht   cost   cosht   atan2t   expt   logt   asinht   acotht   atanht   Ot   cancelt   Matrixt   ret   imt   Floatt   Powt   gcdt   sect   csct   cott   difft   simplifyt	   Heavisidet   argt	   conjugatet   seriest	   FiniteSett   asect   acsct   Mult   sinct   jnt   Productt   AccumBounds(   t   range(   t   XFAILt   slowt   raises(   t   Net   Eq(   t	   Piecewises   x y zt   rt   realt   kt   integert   pt   positivet   nt   negativet   at	   algebraict   nat   nonzeroc          C   s“  t  d ƒ \ }  } t j t d ƒ k s- t ‚ t t ƒ t k sE t ‚ t t ƒ t k s] t ‚ t t ƒ t d d ƒ k s~ t ‚ t t ƒ t t ƒ t d d ƒ k s© t ‚ t t t	 ƒ t t	 k sÉ t ‚ t t t	 ƒ t t	 k së t ‚ d t t ƒ t
 j k s
t ‚ d t t ƒ t
 j k s)t ‚ d t t ƒ t d d ƒ k sNt ‚ d t t ƒ t d d	 ƒ k sst ‚ t d ƒ d k s‹t ‚ t t |  ƒ ƒ |  k s©t ‚ t t |  ƒ ƒ |  t d |  d ƒ k sÙt ‚ t t |  ƒ ƒ t d |  d ƒ k st ‚ t t |  ƒ ƒ d t d d |  d ƒ |  k s=t ‚ t t |  ƒ ƒ d |  k s_t ‚ t t |  ƒ ƒ t d d |  d ƒ k st ‚ t t | |  ƒ ƒ | t |  d | d ƒ k sÆt ‚ t t t	 ƒ t t ƒ t	 k sìt ‚ t t t	 ƒ t t ƒ t	 k st ‚ t d t	 ƒ t d ƒ t	 k s;t ‚ t t ƒ d k sSt ‚ t t ƒ d k slt ‚ t d t ƒ d k sˆt ‚ t d t ƒ d k s¤t ‚ t d
 d) t ƒ d k sÄt ‚ t d d* t ƒ d k sät ‚ t t d ƒ d k s t ‚ t t d ƒ d k st ‚ t d t d ƒ d k s=t ‚ t d t d ƒ d k s]t ‚ t  d d t d t ƒ} t  d d t ƒ} t t | d ƒ d | d t
 j k s¶t ‚ t t t d ƒ j t k sÙt ‚ t t | d ƒ d k sùt ‚ t t t ƒ d k st ‚ t t t ƒ j t d ƒ t t t d ƒ j t d	 ƒ k sWt ‚ t t d ƒ t
 j t d ƒ k s€t ‚ t d t d ƒ t
 j t d ƒ k s®t ‚ t t d ƒ t
 j t d ƒ k s×t ‚ t t d ƒ t
 j t d ƒ k st ‚ t d t d ƒ t
 j t d ƒ k s/t ‚ t d
 t d ƒ t
 j t d ƒ k s]t ‚ t t d	 ƒ t
 j k s|t ‚ t t d	 ƒ t
 j k st ‚ t d t d	 ƒ t
 j k sÁt ‚ t d t d	 ƒ t
 j k såt ‚ t d t d ƒ t d t d ƒ d ƒ k st ‚ t d t d ƒ t d t d ƒ d ƒ k sMt ‚ t d t d ƒ t d t d ƒ k s{t ‚ t d t d ƒ t d t d ƒ k s©t ‚ t d	 t d ƒ t d t d ƒ k sØt ‚ t d t d ƒ t d t d ƒ k st ‚ t d t d ƒ t d t d ƒ k s6t ‚ t t d ƒ t d t d ƒ d ƒ k sft ‚ t t d ƒ t
 d ƒ d t d ƒ d k s›t ‚ t t d ƒ t d ƒ d t d	 ƒ d k sÐt ‚ t d t d ƒ t d ƒ d t d	 ƒ d k s	t ‚ t d t d ƒ t d ƒ d t d	 ƒ d k sA	t ‚ t d t d ƒ t d ƒ d t d	 ƒ d k sy	t ‚ t d t d ƒ t t d ƒ k s£	t ‚ t d t d ƒ t t d ƒ k sÎ	t ‚ t d t d ƒ t t d ƒ k sù	t ‚ t d t d ƒ t t d ƒ k s#
t ‚ t |  t	 ƒ t |  ƒ t	 k sI
t ‚ t t t ƒ d k se
t ‚ t d t t ƒ d k s…
t ‚ t t t t	 ƒ t t t ƒ t	 k s³
t ‚ t t ƒ j t k sÎ
t ‚ t d d  t ƒj sé
t ‚ t t ƒ j d  k st ‚ t t! ƒ j t k st ‚ t" d! d" t ƒ} t t | ƒ j sJt ‚ t" d# d" t d$ t ƒ} t | ƒ j# t k s}t ‚ t | ƒ j# d  k s˜t ‚ t$ t t% |  ƒ t& | ƒ ƒ t ƒ t k sÉt ‚ t$ t t% |  ƒ t& | ƒ ƒ t ƒ t k sût ‚ x‘ t' t( d d% ƒ ƒ d& d' g D]p } xg t( d | d d ƒ D]N } | t | }  t) t* t |  ƒ ƒ t t* |  ƒ ƒ ƒ } | d( k  s9t ‚ q9WqWd  S(+   Ns   x yi   iÿÿÿÿiþÿÿÿi   i    i   i   i   iýÿÿÿi
   iI   i   ig   t   neR?   t   event   ei   i   iûÿÿÿi   iûÿÿi   iùÿÿÿiõÿÿÿih   ii   ij   i˜ÿÿÿi–ÿÿÿt   evaluatet   qt   rationalt   qnRG   i   i<   iU   gê-™—q=l             Bgòm‹9luêZnD¤$]'tT l                 koõP³+!k·{3…5UWoÄ ½$ŽXÿ\Ñ,‹yÛ(+   R    R   t   nargsR-   t   AssertionErrorR   R   R   R4   R   R   t   ZeroR   R	   R   R
   R   R/   R.   R   R   R   t   Truet   Falset   HalfR>   t   funct   subsR<   t   is_realt   is_algebraicRD   t   NoneRF   R   t   is_rationalt
   isinstanceR   R    t   listR5   t   abst   float(   t   xt   yRH   RJ   RL   RN   t   dRB   (    (    sR   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_trigonometric.pyt   test_sin   s®    !+ "%%0,8"07&('    /# B).)+-.!$$44..///055898*++*& .12&(c          C   sL  xEd d d d d d d d d	 d
 d d d d d g D]}  xt  d |  |  d ƒ D]î } | t |  } t | t d ƒ t | ƒ k sœ t d | |  f ƒ ‚ t | t d ƒ t | ƒ k sÓ t d | |  f ƒ ‚ t | ƒ t | t d ƒ k s	t d | |  f ƒ ‚ t | ƒ t | t d ƒ k sR t d | |  f ƒ ‚ qR Wq4 Wd  S(   Ni   i   i   i   i   i   i
   i   i   i   i   i   i(   i<   ix   iþÿÿÿs   fails for %d*pi/%d(   R5   R   R   R   RP   (   Ra   RB   R_   (    (    sR   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_trigonometric.pyt   test_sin_cosˆ   s    :676c           C   s]   t  t ƒ j t d d ƒ t t d d t d d t d d t t d ƒ k sY t ‚ d  S(	   Ni    i	   i   i   i   ix   i   i°  (   R   R_   R,   R   RP   (    (    (    sR   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_trigonometric.pyt   test_sin_series’   s    c           C   s®  t  t ƒ j t ƒ t t t t ƒ t t t ƒ d k sC t ‚ t  t ƒ j t ƒ d t t d ƒ d t t d ƒ d k sˆ t ‚ t  t ƒ j t ƒ d t t d ƒ d t t d ƒ d k sÍ t ‚ t  t t ƒ ƒ j t ƒ j	 t d ƒ j
 ƒ  t  t ƒ j t ƒ j	 t t d ƒ ƒ j
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 ƒ  k smt ‚ t  t t ƒ ƒ j t ƒ j	 t d ƒ j
 ƒ  t  t ƒ j t ƒ j	 t t d ƒ ƒ j
 ƒ  k sÍt ‚ t  t t ƒ ƒ j t ƒ t t t d t t t d k st ‚ t  t ƒ j t ƒ d t t ƒ k s<t ‚ t  t ƒ j t ƒ t t t d d t ƒk sqt ‚ t  t ƒ j t ƒ d t t t d d t ƒk sªt ‚ d  S(   Ni   i   i   RK   (   R   R_   t   rewriteR   R   RP   R   R&   R   RV   RB   R   R   R   R   R   R"   R%   R   RS   R$   (    (    (    sR   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_trigonometric.pyt   test_sin_rewrite—   s.    CEENNNNNNNND+5c           C   s8  t  t t ƒ j d t ƒ t  t ƒ t t ƒ t t ƒ t  t ƒ k sL t ‚ t  t t ƒ j d t ƒ t  t ƒ t t ƒ t t ƒ t  t ƒ k s˜ t ‚ t  t t ƒ j d t ƒ t t ƒ t  t ƒ t  t ƒ t t ƒ k sä t ‚ t  d t ƒ j d t ƒ d t  t ƒ t t ƒ k s t ‚ t  d t ƒ j d t ƒ d t  t ƒ d d t  t ƒ k sdt ‚ t  d t ƒ j d t ƒ d t  t ƒ d t t ƒ d t  t ƒ t t ƒ k s¼t ‚ t  d ƒ j d t ƒ d t  d ƒ t d ƒ k sôt ‚ t  d ƒ j d t ƒ d t  d ƒ d d t  d ƒ k s4t ‚ d  S(   Nt   trigi   i   iüÿÿÿi   iøÿÿÿi   (   R   R_   R`   t   expandRR   R   RP   (    (    (    sR   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_trigonometric.pyt   test_sin_expansion±   s    LLL<DX8c           C   sï  t  t t t ƒ ƒ t d d ƒ k s+ t ‚ t  t d t ƒ ƒ t d d ƒ k sU t ‚ t  t t d ƒ ƒ t d d ƒ k s€ t ‚ t  t d d t j ƒ ƒ t d d ƒ k s± t ‚ t  t d d t j d ƒ ƒ t d d ƒ k sæ t ‚ t  t d t j d d t j d ƒ ƒ t d t  d t j d ƒ ƒ k s7t ‚ t  t t j d t j d ƒ ƒ t t  t j d ƒ t  t j d ƒ ƒ k s‰t ‚ t  t d t j d d t j d	 ƒ ƒ t t  d t j d	 ƒ t  d t j d ƒ ƒ k sët ‚ d  S(
   Niÿÿÿÿi   i    i   i   i   i   i   i   (   R   R4   R   RP   R   t   Pi(    (    (    sR   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_trigonometric.pyt   test_sin_AccumBounds¾   s    +*+15QRc           C   s  t  t ƒ t  t ƒ k s  t ‚ t t ƒ t t ƒ k s? t ‚ t t ƒ t t ƒ k s_ t ‚ t t ƒ t t ƒ k s t ‚ t  t t ƒ t  t ƒ k s¢ t ‚ t  t d t ƒ t  t ƒ k sÈ t ‚ t  t d t ƒ t  t ƒ k sï t ‚ t  t d t ƒ t  t ƒ k st ‚ t  t d t ƒ t  t ƒ k s<t ‚ t t t ƒ t t ƒ k s_t ‚ t t d t ƒ t t ƒ k s…t ‚ t t d t ƒ t t ƒ k s¬t ‚ t t d t ƒ t t ƒ k sÒt ‚ t t d t ƒ t t ƒ k sùt ‚ t t t ƒ t t ƒ k st ‚ t t d t ƒ t t ƒ k sAt ‚ t t t ƒ t t ƒ k sct ‚ t t d t ƒ t t ƒ k s‰t ‚ t  t d t ƒ t t ƒ k s¯t ‚ t  d t d t ƒ t t ƒ k sÚt ‚ t  d t d t ƒ t t ƒ k st ‚ t t d t ƒ t  t ƒ k s*t ‚ t d t d t ƒ t  t ƒ k sUt ‚ t d t d t ƒ t  t ƒ k st ‚ t t d t ƒ t t ƒ k s¥t ‚ t d t d t ƒ t t ƒ k sÏt ‚ t d t d t ƒ t t ƒ k sùt ‚ t t d t ƒ t t ƒ k st ‚ t d t d t ƒ t t ƒ k sIt ‚ t d t d t ƒ t t ƒ k sst ‚ t  t d t ƒ t t ƒ k s™t ‚ t t d t ƒ t  t ƒ k sÀt ‚ t t d t ƒ t t ƒ k sçt ‚ t t d t ƒ t t ƒ k st ‚ d  S(   Ni   i   i   i   (   R   R_   RP   R   R   R&   R   (    (    (    sR   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_trigonometric.pyt   test_trig_symmetryÉ   sD       #&'&'#&'&'"&"&&+*&+*&**&**&''c          C   sÊ
  t  d ƒ \ }  } t j t d ƒ k s- t ‚ t t ƒ t k sE t ‚ t t ƒ t d d ƒ k sf t ‚ t t ƒ t t ƒ t d d ƒ k s‘ t ‚ t t t ƒ t k s­ t ‚ t t t ƒ t k sÊ t ‚ t t	 ƒ t k sâ t ‚ t d ƒ d k sú t ‚ t t
 |  ƒ ƒ |  k st ‚ t t |  ƒ ƒ d t d |  d ƒ k sHt ‚ t t |  ƒ ƒ t d |  d ƒ k stt ‚ t t |  ƒ ƒ d t d d |  d ƒ k s¨t ‚ t t |  ƒ ƒ t d d |  d ƒ k sØt ‚ t t |  ƒ ƒ d |  k sút ‚ t t | |  ƒ ƒ |  t |  d | d ƒ k s1t ‚ t t t ƒ t t ƒ k sSt ‚ t t t ƒ t t ƒ k svt ‚ t d t ƒ t d ƒ k s˜t ‚ t t d ƒ d k s´t ‚ t t d ƒ d k sÑt ‚ t t d ƒ d k sít ‚ t t d ƒ d k s
t ‚ t d d% d t d ƒ d k s2t ‚ t d
 d& d t d ƒ d k sZt ‚ t  d d t d t ƒ} t  d d t ƒ} t t | d ƒ d k s¤t ‚ t t | d ƒ d | d k sÌt ‚ t t ƒ d k sät ‚ t t ƒ d k sýt ‚ t d t ƒ d k st ‚ t d t ƒ d k s5t ‚ t d t ƒ d k sQt ‚ t t d ƒ t j k spt ‚ t d t d ƒ t j k s”t ‚ t t d ƒ t j t d ƒ k s½t ‚ t t d ƒ t j t d ƒ k sçt ‚ t d t d ƒ t j t d ƒ k st ‚ t d t d ƒ t j t d ƒ k sCt ‚ t t d ƒ t j t d ƒ k slt ‚ t t d ƒ t j t d ƒ k s–t ‚ t d
 t d ƒ t j t d ƒ k sÄt ‚ t d t d ƒ t j t d ƒ k sòt ‚ t d t d ƒ t d ƒ d d k s t ‚ t d t d ƒ t d ƒ d d k sNt ‚ t d t d ƒ t d t d ƒ k s}t ‚ t d t d ƒ t d t d ƒ k s¬t ‚ t d t d ƒ t d t d ƒ k sÛt ‚ t d t d ƒ t d t d ƒ k s	t ‚ t d t d ƒ t d t d ƒ k s8t ‚ t t d ƒ t d t d ƒ d ƒ k sht ‚ t t d ƒ t d ƒ d t d ƒ d k sœt ‚ t d t d ƒ t d ƒ d t d ƒ d k sÕt ‚ t d
 t d ƒ t d ƒ d t d ƒ d k st ‚ t d t d ƒ t d ƒ d t d ƒ d k sFt ‚ t d t d ƒ t t d ƒ k sqt ‚ t d t d ƒ t t d ƒ k sœt ‚ t d t d ƒ t t d ƒ k sÇt ‚ t d t d ƒ t t d ƒ k sòt ‚ t |  t ƒ t |  ƒ k s	t ‚ t t t t ƒ t t t ƒ k s>	t ‚ t t ƒ j t k sY	t ‚ t d d t ƒj st	t ‚ t t ƒ j d  k s	t ‚ t t ƒ j t k sª	t ‚ t d d  t ƒ} t t | ƒ j sÕ	t ‚ t d t d
 ƒ j sò	t ‚ t t t ƒ d t k s
t ‚ t d t t ƒ d k s2
t ‚ x‘ t  t! d d! ƒ ƒ d" d# g D]p } xg t! d d | d ƒ D]N } | t | }  t" t# t |  ƒ ƒ t t# |  ƒ ƒ ƒ } | d$ k  sp
t ‚ qp
WqR
Wd  S('   Ns   x yi   iÿÿÿÿiþÿÿÿi   i    iýÿÿÿi
   iI   i   ig   RB   R?   RI   RJ   i   i   i   i   i   i   iûÿÿÿiûÿÿi   ih   ii   ij   i˜ÿÿÿi–ÿÿÿRK   RL   RM   i   i<   iU   gê-™—q=l             Bgòm‹9luêZnD¤$]'tT l                 koõP³+!k·{3…5UWoÄ ½$ŽXÿ\Ñ,‹yÛ($   R    R   RO   R-   RP   R   R   R4   R   R   R
   R	   R   R   R   R/   R.   R   R   R   RR   RS   R   RT   R>   R<   RW   RX   RD   RY   RF   R   R\   R5   R]   R^   (   R_   R`   RB   RJ   RL   Ra   (    (    sR   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_trigonometric.pyt   test_cosî   s˜    !+0,40"7"#"(( ($)*..)*....///./04989++++"*  &(c          C   s¢   t  d d ƒ }  xŒ t t t t g D]x } | |  t ƒ | t d ƒ k sN t ‚ | d t ƒ | t d ƒ k st t ‚ | d t ƒ | d t ƒ k s" t ‚ q" Wd  S(	   Ns!   123456789012345678901234567890.25t    i   g     €@i   gÍÌÌÌÌÌ@i   ghfffffæ?(   R!   R   R   R   R&   R   RP   (   t   ct   cls(    (    sR   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_trigonometric.pyt   test_issue_6190S  s
    &&c           C   si   t  t ƒ j t d d ƒ d t d d t d d t d d t d	 d
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 ƒ  k sÕt ‚ t  t t ƒ ƒ j t ƒ t t d t t d k st ‚ t  t ƒ j t ƒ d t t ƒ k s<t ‚ t  t ƒ j t ƒ t t t d d t ƒk sqt ‚ t  t ƒ j t ƒ d t t t d d t ƒk s«t ‚ d  S(   Ni   i   i   RK   (   R   R_   Re   R   R   RP   R   R&   R   RV   RB   R   R   R   R   R   R"   R$   R   RS   R%   (    (    (    sR   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_trigonometric.pyt   test_cos_rewrite`  s.    BIJNNNNNNNN<+5c           C   s(  t  t t ƒ j d t ƒ t  t ƒ t  t ƒ t t ƒ t t ƒ k sL t ‚ t  t t ƒ j d t ƒ t  t ƒ t  t ƒ t t ƒ t t ƒ k s˜ t ‚ t  t t ƒ j d t ƒ t  t ƒ t  t ƒ t t ƒ t t ƒ k sä t ‚ t  d t ƒ j d t ƒ d t  t ƒ d d k st ‚ t  d t ƒ j d t ƒ d t  t ƒ d d t  t ƒ k sbt ‚ t  d t ƒ j d t ƒ d t  t ƒ d d t  t ƒ d d k s®t ‚ t  d ƒ j d t ƒ d t  d ƒ d d k sät ‚ t  d ƒ j d t ƒ d t  d ƒ d d t  d ƒ k s$t ‚ d  S(   NRg   i   i   i   i   i   (   R   R_   R`   Rh   RR   R   RP   (    (    (    sR   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_trigonometric.pyt   test_cos_expansionz  s    LLL:DL6c           C   s  t  t t t ƒ ƒ t d d ƒ k s+ t ‚ t  t d t ƒ ƒ t d d ƒ k sU t ‚ t  t t d ƒ ƒ t d d ƒ k s€ t ‚ t  t d d t j ƒ ƒ t d d ƒ k s± t ‚ t  t t j d t j d ƒ ƒ t t  t j d ƒ d ƒ k sø t ‚ t  t d t j d d t j d ƒ ƒ t d t  d t j d ƒ ƒ k sIt ‚ t  t d t j d d t j d ƒ ƒ t t  d t j d ƒ t  d t j d ƒ ƒ k s«t ‚ t  t t j d t j d ƒ ƒ t t  t j d ƒ t  t j d ƒ ƒ k sýt ‚ d  S(   Niÿÿÿÿi   i    i   i   i   i   (   R   R4   R   RP   R   Rj   (    (    (    sR   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_trigonometric.pyt   test_cos_AccumBounds…  s    +*+1GQbc           C   sm
  t  t ƒ t k s t ‚ t  t ƒ t k s0 t ‚ t  t ƒ t t t ƒ k sR t ‚ t  t ƒ t  t ƒ t t t ƒ k s~ t ‚ t  j t d ƒ k s™ t ‚ t  t t ƒ t k sµ t ‚ t  t t ƒ t k sÓ t ‚ t  d ƒ d k së t ‚ t  t	 t
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 k st ‚ t  t t ƒ t t ƒ t k sBt ‚ t  t t ƒ t t ƒ t k sjt ‚ t  d t ƒ t d ƒ t k s‘t ‚ t  t ƒ d k s©t ‚ t  t ƒ d k sÂt ‚ t  d t ƒ d k sÞt ‚ t  d t ƒ d k sút ‚ t  d d t ƒ d k st ‚ t  t d ƒ t k s6t ‚ t  d t d ƒ t k sVt ‚ t  t d ƒ t d ƒ k sxt ‚ t  d t d ƒ t d ƒ k sžt ‚ t  t d	 ƒ t j k s½t ‚ t  t d	 ƒ t j k sÞt ‚ t  d
 t d	 ƒ t j k st ‚ t  d t d	 ƒ t j k s$t ‚ t  t d ƒ d t d ƒ k sJt ‚ t  t d ƒ d t d ƒ k sqt ‚ t  d t d ƒ d t d ƒ k s›t ‚ t  d t d ƒ d t d ƒ k sÅt ‚ t  t d ƒ j ƒ  d t d ƒ k sñt ‚ t  d t d ƒ j ƒ  d t d ƒ k s!t ‚ t  d t d ƒ j ƒ  d t d ƒ k sQt ‚ t  d t d ƒ j ƒ  d t d ƒ k st ‚ t  t d ƒ t d ƒ d k s¨t ‚ t  d t d ƒ t d ƒ d k sÒt ‚ t  d t d ƒ t d ƒ d k sýt ‚ t  d t d ƒ t d ƒ d k s't ‚ t  t d ƒ j ƒ  d t d ƒ t d ƒ t d ƒ k sgt ‚ t  d t d ƒ j ƒ  d t d ƒ t d ƒ t d ƒ k s«t ‚ t  d t d ƒ j ƒ  d t d ƒ t d ƒ t d ƒ k sït ‚ t  d t d ƒ j ƒ  d t d ƒ t d ƒ t d ƒ k s3t ‚ t  d t d ƒ j ƒ  d t d ƒ t d ƒ t d ƒ k swt ‚ t  d
 t d ƒ j ƒ  d t d ƒ t d ƒ t d ƒ k s»t ‚ t  d t d ƒ j ƒ  d t d ƒ t d ƒ t d ƒ k sÿt ‚ t  d t d ƒ j ƒ  d t d ƒ t d ƒ t d ƒ k sCt ‚ d t  d t d ƒ t d t d ƒ t d t d ƒ j ƒ  k st ‚ t  t
 t ƒ t t
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 t t ƒ d k sït ‚ t  t t t ƒ t t t ƒ t k s	t ‚ t  t ƒ j t k s8	t ‚ t  d d t  ƒj! sS	t ‚ t  t" ƒ j! d  k sn	t ‚ t  t$ ƒ j! t  k s‰	t ‚ t  d t d ƒ t  d t d ƒ k s·	t ‚ t  d t d ƒ t  d t d ƒ k sæ	t ‚ t  d t d ƒ t  d t d ƒ k s
t ‚ t  d t d ƒ t  t d ƒ k s>
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t ‚ d  S(   Ni   i    i   iþÿÿÿiýÿÿÿi
   iI   i   i   i   i   iÿÿÿÿi   iûÿÿÿi   i   i   i   i   i   i   i   i   RK   iõÿÿÿi   iñÿÿÿl             Bgòm‹9luêZnD¤$]'tT (%   R   R   RP   R   R   R4   RO   R-   R   R	   R_   R   R   R
   R   R/   R.   R   R`   R   R   R   t   OneRh   t   radsimpR   R   t   ratsimpR>   R<   RW   RR   RS   RX   RD   RY   RF   (    (    (    sR   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_trigonometric.pyt   test_tan  s‚    ",00"84%&('  "&!##&'**,000'*+*@DDDDDDDJ& ../.*c           C   se   t  t ƒ j t d d ƒ t t d d d t d d d t d d	 t t d ƒ k sa t ‚ d  S(
   Ni    i	   i   i   i   i   i   i   i;  (   R   R_   R,   R   RP   (    (    (    sR   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_trigonometric.pyt   test_tan_seriesè  s    c          C   s±  t  t t ƒ t  t t ƒ }  } t t ƒ j t  ƒ t |  | |  | k sS t ‚ t t ƒ j t ƒ d t t ƒ d t d t ƒ k s t ‚ t t ƒ j t ƒ t t t j	 d d t
 ƒt t ƒ k sÒ t ‚ t t ƒ j t ƒ d t t ƒ k sý t ‚ t t t ƒ ƒ j t  ƒ j t d ƒ j ƒ  t t ƒ j t  ƒ j t t d ƒ ƒ j ƒ  k s]t ‚ t t t ƒ ƒ j t  ƒ j t d ƒ j ƒ  t t ƒ j t  ƒ j t t d ƒ ƒ j ƒ  k s½t ‚ t t t ƒ ƒ j t  ƒ j t d ƒ j ƒ  t t ƒ j t  ƒ j t t d ƒ ƒ j ƒ  k st ‚ t t t ƒ ƒ j t  ƒ j t d ƒ j ƒ  t t ƒ j t  ƒ j t t d ƒ ƒ j ƒ  k s}t ‚ t t t ƒ ƒ j t  ƒ j t d ƒ j ƒ  t t ƒ j t  ƒ j t t d ƒ ƒ j ƒ  k sÝt ‚ t t t ƒ ƒ j t  ƒ j t d ƒ j ƒ  t t ƒ j t  ƒ j t t d ƒ ƒ j ƒ  k s=t ‚ t t t ƒ ƒ j t  ƒ j t d ƒ j ƒ  t t ƒ j t  ƒ j t t d ƒ ƒ j ƒ  k st ‚ t t t ƒ ƒ j t  ƒ j t d ƒ j ƒ  t t ƒ j t  ƒ j t t d ƒ ƒ j ƒ  k sýt ‚ t t t ƒ ƒ j t ƒ t t t t t t t t t k sFt ‚ d t t d ƒ t t d ƒ t t d ƒ j t ƒ k s‡t ‚ d t t d ƒ t t d ƒ t t d ƒ j t ƒ k sÈt ‚ t t d ƒ j t ƒ t t d ƒ k s÷t ‚ t d	 t d ƒ j t ƒ t d	 t d ƒ k s.t ‚ t t ƒ j t ƒ t t ƒ t t t d d t
 ƒk smt ‚ t t ƒ j t ƒ t t t d d t
 ƒt t ƒ k s­t ‚ d  S(
   Ni   RK   i   i   i    i"   i   i   i   (   R   R_   R   R   Re   RP   R   R   R   Rj   RS   R&   R   RV   RB   R   R   R   R   R"   R   t   powR   R$   R%   (   t   neg_expt   pos_exp(    (    sR   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_trigonometric.pyt   test_tan_rewriteí  s8    "1=B+NNNNNNNNIAA/7?c           C   s²   t  t ƒ j t  t ƒ t ƒ t k s* t ‚ t  t ƒ j t t ƒ t  t ƒ k sT t ‚ t  t ƒ j t t j d ƒ t k s t ‚ t  t ƒ j t d t j d ƒ t k s® t ‚ d  S(   Ni   i   (   R   R_   RV   R`   RP   R   Rj   R   (    (    (    sR   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_trigonometric.pyt   test_tan_subs  s    **+c           C   sp  t  t t ƒ j d t ƒ t  t ƒ t  t ƒ d t  t ƒ t  t ƒ j ƒ  k sV t ‚ t  t t ƒ j d t ƒ t  t ƒ t  t ƒ d t  t ƒ t  t ƒ j ƒ  k s¬ t ‚ t  t t t ƒ j d t ƒ t  t ƒ t  t ƒ t  t ƒ t  t ƒ t  t ƒ t  t ƒ d t  t ƒ t  t ƒ t  t ƒ t  t ƒ t  t ƒ t  t ƒ j ƒ  k sVt ‚ d t  d t ƒ j d t ƒ j t  ƒ j t  t ƒ t	 d d ƒ f g ƒ d d k s°t ‚ d t  d t ƒ j d t ƒ j t  ƒ j t  t ƒ t	 d d ƒ f g ƒ d	 d
 k s
t ‚ d t  d t t
 d ƒ j d t ƒ j t  ƒ j t  t ƒ t	 d d ƒ f g ƒ d d k slt ‚ d  S(   NRg   i   i    i   i   i   i   i   i7   i%   i   iï   (   R   R_   R`   Rh   RR   RP   t   zRe   RV   R   R   (    (    (    sR   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_trigonometric.pyt   test_tan_expansion  s    VV;RZZc           C   s¿   t  t t t ƒ ƒ t t t ƒ k s, t ‚ t  t t j d d t j d ƒ ƒ t t t ƒ k si t ‚ t  t t j d t j d ƒ ƒ t t  t j d ƒ t  t j d ƒ ƒ k s» t ‚ d  S(   Ni   i   i   (   R   R4   R   RP   R   Rj   (    (    (    sR   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_trigonometric.pyt   test_tan_AccumBounds  s    ,=c          C   s¢
  t  t ƒ t k s t ‚ t  j t d ƒ k s3 t ‚ t  t t ƒ t k sP t ‚ t  t t ƒ t k sm t ‚ t  t ƒ t k s… t ‚ t  d ƒ t k s t ‚ t  d t ƒ t k s¹ t ‚ t  t	 t
 ƒ ƒ t
 k s× t ‚ t  t t
 ƒ ƒ d t
 k sù t ‚ t  t t
 ƒ ƒ t d t
 d ƒ t
 k s)t ‚ t  t t
 ƒ ƒ t
 t d t
 d ƒ k sYt ‚ t  t t
 ƒ ƒ t d d t
 d ƒ t
 k st ‚ t  t t
 ƒ ƒ d t d d t
 d ƒ t
 k sÅt ‚ t  t t t
 ƒ ƒ t
 t k sêt ‚ t  t t ƒ t t ƒ t k st ‚ t  t t ƒ t t ƒ t k s8t ‚ t  d t ƒ t d ƒ t k s^t ‚ t  t ƒ t  d t ƒ k ot  d t ƒ k n sšt ‚ t  t ƒ t  d t ƒ k oÌt  d t ƒ k n s×t ‚ t  t d ƒ d k sót ‚ t  t d ƒ d k st ‚ t  d t d ƒ d k s0t ‚ t  d t d ƒ d k sPt ‚ t  t d ƒ d t d ƒ k svt ‚ t  d t d ƒ d t d ƒ k s t ‚ t  t d	 ƒ t j k s¿t ‚ t  t d	 ƒ t j k sàt ‚ t  d
 t d	 ƒ t j k st ‚ t  d t d	 ƒ t j k s&t ‚ t  t d ƒ t d ƒ k sHt ‚ t  t d ƒ t d ƒ k slt ‚ t  d t d ƒ t d ƒ k s’t ‚ t  d t d ƒ t d ƒ k s¸t ‚ t  t d ƒ j ƒ  d t d ƒ k sät ‚ t  d t d ƒ j ƒ  d t d ƒ k st ‚ t  d t d ƒ j ƒ  d t d ƒ k sDt ‚ t  d t d ƒ j ƒ  d t d ƒ k stt ‚ t  t d ƒ t d ƒ d k sšt ‚ t  d t d ƒ t d ƒ d k sÅt ‚ t  d t d ƒ t d ƒ d k sït ‚ t  d t d ƒ t d ƒ d k st ‚ t  t d ƒ j ƒ  t d ƒ t d ƒ d t d ƒ k sZt ‚ t  d t d ƒ j ƒ  t d ƒ t d ƒ d t d ƒ k sŸt ‚ t  d t d ƒ j ƒ  t d ƒ t d ƒ d t d ƒ k sät ‚ t  d t d ƒ j ƒ  t d ƒ t d ƒ d t d ƒ k s(t ‚ t  d t d ƒ j ƒ  t d ƒ t d ƒ d t d ƒ k smt ‚ t  d
 t d ƒ j ƒ  t d ƒ t d ƒ d t d ƒ k s±t ‚ t  d t d ƒ j ƒ  t d ƒ t d ƒ d t d ƒ k sõt ‚ t  d t d ƒ j ƒ  t d ƒ t d ƒ d t d ƒ k s:t ‚ d t  d	 t d ƒ t d	 t d ƒ t d	 t d ƒ j ƒ  k s„t ‚ t  t
 t ƒ t t
 ƒ t k s«t ‚ t  t t t ƒ t t t ƒ t k sÚt ‚ t  t ƒ j t k sõt ‚ t  t ƒ j  d  k s	t ‚ t  t" ƒ j  t# k s+	t ‚ t  d t d ƒ t  d t d ƒ k sY	t ‚ t  d t d ƒ t  d t d ƒ k sˆ	t ‚ t  d t d ƒ t  d t d ƒ k s¶	t ‚ t  d t d ƒ t  d t d ƒ k sä	t ‚ t  d t d ƒ t  d t d ƒ k s
t ‚ t  t
 ƒ j$ d  k s.
t ‚ t  t ƒ j$ d  k sI
t ‚ t% d d t ƒ}  t  |  ƒ j$ t k sv
t ‚ t  t
 ƒ j& t
 d t ƒ t k sž
t ‚ d  S(   Ni   i    i   iþÿÿÿi   iýÿÿÿi   i   i   i   i   iûÿÿÿi   iÿÿÿÿi   i   i   i   i   i   i   i
   iõÿÿÿi'   i"   i×ÿÿÿt   it	   imaginary('   R&   R   RP   RO   R-   R   R   R   R   R   R_   R	   R   R   R
   R/   R.   R   R`   R   R   Rv   Rh   Rw   R   R   Rx   R>   R<   RW   RR   RD   RX   RY   RF   RS   t	   is_finiteR   RV   (   Rƒ   (    (    sR   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_trigonometric.pyt   test_cot$  s‚    "0048%''&<=  &*!##"$&&,000&+*+@EEDEDDEJ'/./../c           C   sÎ   t  t ƒ j t d d ƒ d t t d t d d d t d d t d	 d
 t t d ƒ k si t ‚ t  t d t d ƒ j t d d ƒ t d d t d t d d t d t t ƒ k sÊ t ‚ d  S(   Ni    i	   i   i   i-   i   i   i±  i   iu  i   iüÿÿÿiþÿÿÿ(   R&   R_   R,   R   RP   (    (    (    sR   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_trigonometric.pyt   test_cot_series|  s    Q$c          C   s  t  t t ƒ t  t t ƒ }  } t t ƒ j t  ƒ t | |  | |  k sS t ‚ t t ƒ j t ƒ t d t ƒ d t t ƒ d k s t ‚ t t ƒ j t ƒ t t ƒ t t t d d t	 ƒk sÏ t ‚ t t ƒ j t
 ƒ d t
 t ƒ k sú t ‚ t t t ƒ ƒ j t  ƒ j t d ƒ j ƒ  t t ƒ j t  ƒ j t t d ƒ ƒ j ƒ  k sZt ‚ t t t ƒ ƒ j t  ƒ j t d ƒ j ƒ  t t ƒ j t  ƒ j t t d ƒ ƒ j ƒ  k sºt ‚ t t t ƒ ƒ j t  ƒ j t d ƒ j ƒ  t t ƒ j t  ƒ j t t d ƒ ƒ j ƒ  k st ‚ t t t ƒ ƒ j t  ƒ j t d ƒ j ƒ  t t ƒ j t  ƒ j t t d ƒ ƒ j ƒ  k szt ‚ t t t ƒ ƒ j t  ƒ j t d ƒ j ƒ  t t ƒ j t  ƒ j t t d ƒ ƒ j ƒ  k sÚt ‚ t t
 t ƒ ƒ j t  ƒ j t d ƒ j ƒ  t t ƒ j t  ƒ j t t
 d ƒ ƒ j ƒ  k s:t ‚ t t t ƒ ƒ j t ƒ t t t t t t t t t k s„t ‚ t d t d ƒ j t ƒ j ƒ  t d t d ƒ t d t d ƒ j t ƒ j ƒ  k sât ‚ t d t d ƒ j t ƒ t d t d ƒ t d t d ƒ j t ƒ k s4t ‚ t t d ƒ j t ƒ t t d ƒ k sct ‚ t t d ƒ j t ƒ t t d ƒ k s’t ‚ t t ƒ j t ƒ t t t d d t	 ƒt t ƒ k sÑt ‚ t t ƒ j t ƒ t t ƒ t t t d d t	 ƒk st ‚ d  S(	   Ni   RK   i   i   i   i"   i   i   (   R   R_   R   R&   Re   RP   R   R   R   RS   R   R   RV   RB   R   R   R   R   R"   R{   Rx   R   R$   R%   (   R|   R}   (    (    sR   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_trigonometric.pyt   test_cot_rewrite„  s0    "1=?+NNNNNNJ^R//?c           C   s£   t  t ƒ j t  t ƒ t ƒ t k s* t ‚ t  t ƒ j t t ƒ t  t ƒ k sT t ‚ t  t ƒ j t d ƒ t k sx t ‚ t  t ƒ j t t j ƒ t k sŸ t ‚ d  S(   Ni    (   R&   R_   RV   R`   RP   R   R   Rj   (    (    (    sR   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_trigonometric.pyt   test_cot_subsŸ  s    **$c           C   sÍ  t  t t ƒ j d t ƒ t  t ƒ t  t ƒ d t  t ƒ t  t ƒ j ƒ  k sV t ‚ t  t t ƒ j d t ƒ t  t ƒ t  t ƒ d t  t ƒ t  t ƒ j ƒ  k s­ t ‚ t  t t t ƒ j d t ƒ t  t ƒ t  t ƒ t  t ƒ t  t ƒ t  t ƒ t  t ƒ d t  t ƒ t  t ƒ t  t ƒ t  t ƒ t  t ƒ t  t ƒ j ƒ  k sWt ‚ t  d t ƒ j d t ƒ t  t ƒ d d t  t ƒ d t  t ƒ d d j ƒ  k s³t ‚ d t  d t ƒ j d t ƒ j t  ƒ j t  t ƒ t	 d d ƒ f g ƒ d d k st ‚ d t  d t ƒ j d t ƒ j t  ƒ j t  t ƒ t	 d d ƒ f g ƒ d	 d
 k sgt ‚ d t  d t t
 d ƒ j d t ƒ j t  ƒ j t  t ƒ t	 d d ƒ f g ƒ d d k sÉt ‚ d  S(   NRg   i   iÿÿÿÿi   i   i    i   i   i7   i%   i   i_  i¿   (   R&   R_   R`   Rh   RR   RP   R€   Re   RV   R   R   (    (    (    sR   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_trigonometric.pyt   test_cot_expansion¦  s    VW;R\ZZc           C   s¼   t  t t t ƒ ƒ t t t ƒ k s, t ‚ t  t t j d t j d ƒ ƒ t t t ƒ k sf t ‚ t  t t j d t j d ƒ ƒ t t  t j d ƒ t  t j d ƒ ƒ k s¸ t ‚ d  S(   Ni   i   (   R&   R4   R   RP   R   Rj   (    (    (    sR   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_trigonometric.pyt   test_cot_AccumBounds²  s    ,:c          C   s½  t  t t ƒ t ƒ s t ‚ t d d t ƒ}  t |  ƒ t j k sH t ‚ t t j ƒ t j	 k sf t ‚ t t j ƒ t j	 k s… t ‚ t t j
 ƒ t j
 k s£ t ‚ t t j ƒ t j
 k sÁ t ‚ t d d t d t ƒ} t | t ƒ t j	 k sø t ‚ t | t ƒ t j	 k st ‚ t t d ƒ d t k s8t ‚ t t d ƒ d t k sYt ‚ t d t d ƒ d d t k st ‚ t d t d ƒ d	 d t k s©t ‚ t t ƒ t t ƒ k sÈt ‚ t t ƒ j ƒ  t t t ƒ t t ƒ t d k st ‚ t t ƒ j ƒ  d
 t d d t d d t t d ƒ k sFt ‚ t t ƒ j t ƒ t d t ƒ k spt ‚ t t ƒ j t ƒ t t t ƒ t t t d ƒ f d
 t f ƒ k s¹t ‚ d  S(   Nt   st   zeroRB   R?   RG   i   i   i   iþÿÿÿi   i   i   ix   i    (   R[   R1   R_   RP   R   RR   R   Rv   t   InfinityRQ   t   NaNt   ComplexInfinityR   R'   R   R   R,   R   Re   R2   R;   R9   (   RŒ   RB   (    (    sR   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_trigonometric.pyt	   test_sinc¸  s&      !((:D*c           C   sX  t  t ƒ t k s t ‚ t  j t d ƒ k s3 t ‚ t  t ƒ t t k sP t ‚ t  t ƒ t t k sm t ‚ t  t ƒ t k s… t ‚ t  d ƒ d k s t ‚ t  d ƒ t d k s¹ t ‚ t  d ƒ t d k sÖ t ‚ t  t	 d ƒ d ƒ t d k sü t ‚ t  t	 d ƒ d ƒ t d k s$t ‚ t  t	 d ƒ d ƒ t d k sJt ‚ t  t	 d ƒ d ƒ t d k srt ‚ t  t	 d t	 d ƒ d ƒ ƒ t d k s¢t ‚ t  t	 d t	 d ƒ d ƒ ƒ t d k sÔt ‚ t  t
 d d ƒ ƒ t d	 k sùt ‚ t  t
 d d ƒ ƒ t d	 k s t ‚ t  t	 d t	 d ƒ ƒ d ƒ t d k sPt ‚ t  t	 d t	 d ƒ ƒ d ƒ t d k s‚t ‚ t  t	 d ƒ d d ƒ t d
 k s¬t ‚ t  t	 d ƒ d d ƒ t d
 k sØt ‚ t  t	 d ƒ d t	 d ƒ ƒ t d k st ‚ t  t	 d ƒ d t	 d ƒ ƒ t d k s:t ‚ t  t ƒ j t ƒ d t	 d t d ƒ k smt ‚ t  d ƒ j t k sˆt ‚ t  d ƒ j t k s£t ‚ t  t ƒ j d  k s¾t ‚ t  d t ƒ t t d ƒ k såt ‚ t  t
 d d ƒ d t ƒj t k st ‚ t  t
 d d ƒ d t ƒj t k s9t ‚ t  t ƒ j d  k sTt ‚ d  S(   Ni   i    i   iÿÿÿÿi   i   i   i   i   i
   i   gš™™™™™É?iþÿÿÿi   RK   i   i   (   R   R   RP   RO   R-   R   R   R   R   R   R   R_   R'   RW   RR   RS   R<   RY   R   t   is_positiveR@   (    (    (    sR   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_trigonometric.pyt	   test_asinÔ  s<    &(&(02%'02*,023'**c          C   sÑ   t  t ƒ j t d d ƒ t t d d d t d d d t d d t t d ƒ k sa t ‚ t  t ƒ j d t ƒ }  |  d t d d k s— t ‚ t  t ƒ j d t |  d ƒ d t d d k sÍ t ‚ d  S(	   Ni    i	   i   i   i   i(   i   ip   (   R   R_   R,   R   RP   t   taylor_term(   t   t5(    (    sR   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_trigonometric.pyt   test_asin_seriesü  s
    Ic        	   C   sZ  t  t ƒ j t ƒ t t t t t d t d ƒ ƒ k sB t ‚ t  t ƒ j t ƒ d t t d t d t d ƒ ƒ k sƒ t ‚ t  t ƒ j t ƒ t	 j
 d t t ƒ k sµ t ‚ t  t ƒ j t ƒ d t t t d d ƒ d t ƒ k s÷ t ‚ t  t ƒ j t ƒ t d t ƒ t d k s+t ‚ t  t ƒ j t ƒ t d t ƒ k sVt ‚ d  S(   Ni   i   (   R   R_   Re   R   R   R   RP   R	   R
   R   Rj   R   R.   R   R/   (    (    (    sR   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_trigonometric.pyt   test_asin_rewrite  s    BA2B4c           C   s®  t  t ƒ t k s t ‚ t  t ƒ t k s0 t ‚ t  j t d ƒ k sK t ‚ t  t ƒ t t k sg t ‚ t  t ƒ t t k s… t ‚ t  d ƒ t d k s¡ t ‚ t  t	 d d ƒ ƒ t d k sÆ t ‚ t  t	 d d ƒ ƒ d t d k sð t ‚ t  d ƒ d k st ‚ t  d ƒ t k s t ‚ t  t
 d ƒ d ƒ t d k sFt ‚ t  t
 d ƒ d ƒ d t d k sqt ‚ t  t ƒ j t ƒ d t
 d t d ƒ k s¤t ‚ t  d ƒ j t k s¿t ‚ t  d ƒ j t k sÚt ‚ t  t ƒ j d  k sõt ‚ t  t	 d d	 ƒ d
 t ƒj t k st ‚ t  t	 d d	 ƒ d
 t ƒj t k sIt ‚ t  t	 d d ƒ d
 t ƒj t k sst ‚ t  t ƒ j d  k sŽt ‚ t  d t ƒ j ƒ  t  d t ƒ k sºt ‚ t  d t ƒ j ƒ  t  d t ƒ k sæt ‚ t  t j d ƒ j ƒ  t  t j d ƒ k st ‚ t  t j d ƒ j ƒ  t  t j d ƒ k sLt ‚ t  t t t ƒ j ƒ  t  t t t ƒ k s€t ‚ t  t ƒ j ƒ  t  t t ƒ ƒ k sªt ‚ d  S(   Ni   i    i   i   iÿÿÿÿi   gš™™™™™É?iþÿÿÿi   RK   i
   iýÿÿÿ(   R
   R   RP   R   RO   R-   R   R   R   R   R   R_   R'   RW   RR   RS   R<   RY   R’   R@   R+   RB   R   Rv   R€   (    (    (    sR   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_trigonometric.pyt	   test_acos  s4    %*&+3***,,244c          C   s  t  t ƒ j t d d ƒ t d t t d d d t d d d t d d	 t t d ƒ k si t ‚ t  t ƒ j t d d ƒ t d t t ƒ j t d d ƒ k s­ t ‚ t  t ƒ j d t ƒ }  |  d
 t d d k sã t ‚ t  t ƒ j d t |  d ƒ d t d d	 k st ‚ d  S(   Ni    i   i   i   i   i   i(   i   ip   iýÿÿÿiûÿÿÿ(   R
   R_   R,   R   R   RP   R   R”   (   R•   (    (    sR   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_trigonometric.pyt   test_acos_series1  s    QDc        	   C   sÛ  t  t ƒ j t ƒ t d t t t t t d t d ƒ ƒ k sI t ‚ t  t ƒ j t ƒ t t d t d ƒ t ƒ t d d t t d t d ƒ k s¤ t ‚ t  d ƒ j t ƒ t	 j
 d k sÌ t ‚ t  d ƒ j t ƒ t  d ƒ j t ƒ k sü t ‚ t  t ƒ j t ƒ t	 j
 d t t ƒ k s.t ‚ t  t ƒ j t ƒ d t t t d d ƒ d t ƒ t d k sxt ‚ t  t ƒ j t ƒ t d t ƒ k s£t ‚ t  t ƒ j t ƒ t d t ƒ t d k s×t ‚ d  S(   Ni   i   i    g      à?iþÿÿÿ(   R
   R_   Re   R   R   R   R   RP   R	   R   Rj   R   R   R.   R/   (    (    (    sR   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_trigonometric.pyt   test_acos_rewrite:  s    II(02J+c           C   sÍ  t  t ƒ t k s t ‚ t  j t d ƒ k s3 t ‚ t  t ƒ t d k sO t ‚ t  t ƒ t d k sm t ‚ t  t ƒ t t d t d ƒ k s— t ‚ t  d ƒ d k s¯ t ‚ t  d ƒ t d k sË t ‚ t  t	 d ƒ ƒ t d k sí t ‚ t  t ƒ t d k s	t ‚ t  t
 ƒ j t
 ƒ d d t
 d k s6t ‚ t  t ƒ j t k sQt ‚ t  d t ƒ t t d ƒ k sxt ‚ t  t ƒ j t k s“t ‚ t  t ƒ j t k s®t ‚ t  t
 ƒ j d  k sÉt ‚ d  S(   Ni   i   i    i   i   iþÿÿÿ(   R	   R   RP   RO   R-   R   R   R   R4   R   R_   R'   R<   RW   RR   R   R   R@   R’   RB   RS   RY   (    (    (    sR   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_trigonometric.pyt	   test_atanF  s    *"-'c           C   s>  t  t ƒ j t ƒ t t d t t ƒ t d t t ƒ d k sI t ‚ t  t ƒ j t ƒ t d t t d d ƒ ƒ t d t t d ƒ t k s t ‚ t  t ƒ j t	 ƒ t t d ƒ t	 d t t d d ƒ ƒ t k sè t ‚ t  t ƒ j t
 ƒ t
 d t ƒ k st ‚ t  t ƒ j t ƒ t t d ƒ t t t d d ƒ ƒ t k sZt ‚ t  t ƒ j t ƒ t t t d d ƒ ƒ t d t t d ƒ t k sªt ‚ t  d t ƒ j ƒ  t  t ƒ j t ƒ j d i d t t 6ƒ k sòt ‚ t  d t ƒ j ƒ  t  t ƒ j t ƒ j d i d t t 6ƒ k s:t ‚ d  S(   Ni   i   iûÿÿÿRV   i   (   R	   R_   Re   R   R   RP   R   R   R   R
   R   R.   R/   t   evalf(    (    (    sR   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_trigonometric.pyt   test_atan_rewrite\  s    ITK+GPHc       	   C   s:  t  j t d ƒ k s t ‚ t  d d ƒ t j k s9 t ‚ t  d d ƒ d k sT t ‚ t  d d ƒ t d k ss t ‚ t  d d ƒ t d k s’ t ‚ t  d d ƒ d t d k sµ t ‚ t  d d ƒ t k sÐ t ‚ t  d d ƒ d t d k só t ‚ t  d d ƒ t d k st ‚ t  d d ƒ t d k s3t ‚ t d d	 t ƒ}  t d
 d t ƒ} t  | |  ƒ } t	 t
 |  t	 | t |  d | d ƒ ƒ } | d f |  t	 f f } | j | ƒ | j | ƒ k sÑt ‚ t d d t ƒ} t d d t ƒ} t  | | ƒ t | | ƒ t k st ‚ t d d t ƒ} t  | | ƒ t | | ƒ t k sYt ‚ t d ƒ } t  | | ƒ t  | | d t ƒk st ‚ t d d t ƒ} t  d | ƒ d k s¼t ‚ t d d t ƒ} t  d | ƒ t k sét ‚ t  | t ƒ d k st ‚ t  | t ƒ d t t t | ƒ ƒ t k s8t ‚ t  | | ƒ j t
 ƒ t	 t
 | t	 | t | d | d ƒ ƒ k s…t ‚ t  | | ƒ j t ƒ d t | | t | d | d ƒ ƒ k sÍt ‚ t  | | ƒ t | t	 | ƒ } | j i d | 6d | 6ƒ j t ƒ d k s t ‚ | j i d | 6d t	 | 6ƒ j t ƒ t t	 t
 t d ƒ t	 d ƒ k sst ‚ | j i d t	 | 6d | 6ƒ j t ƒ t d t	 t
 t d ƒ t	 ƒ k sÆt ‚ | j i d t	 | 6d t	 | 6ƒ j t ƒ t t d t d ƒ ƒ t d t d ƒ ƒ k s)t ‚ t d d	 t ƒ}  t d
 d t ƒ} t  |  | ƒ }	 |	 j t ƒ }
 i t	 |  6d | 6} |
 t	 t
 t t	 |  | ƒ t t |  d | d ƒ ƒ ƒ t t	 |  | t |  d | d ƒ ƒ k sît ‚ |	 |
 j | ƒ j d ƒ st ‚ t t  | | ƒ ƒ t  t | ƒ t | ƒ ƒ k sFt ‚ t t  | | ƒ | ƒ | | d | d k s{t ‚ t t  | | ƒ | ƒ | | d | d k s¯t ‚ t t t  | | ƒ j t
 ƒ | ƒ ƒ | | d | d k sót ‚ t t t  | | ƒ j t
 ƒ | ƒ ƒ | | d | d k s6t ‚ d  S(   Ni   i    i   i   iÿÿÿÿi   iýÿÿÿRƒ   R„   R<   R=   R_   RC   R`   t   nonnegativeRK   t   uRA   i   iþÿÿÿ(   R   RO   R-   RP   R   R   R   R    RR   R   R   R   RV   R   R	   RS   R   R)   R   Re   R*   R]   t   equalsR+   R'   R(   (   Rƒ   R<   t   eqt   anst   repsR_   R`   RŸ   t   exRJ   Re   (    (    sR   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_trigonometric.pyt
   test_atan2h  s`    ##  /$))*4MH!2SSco"654Dc           C   s,  t  t ƒ t k s t ‚ t  j t d ƒ k s3 t ‚ t  t ƒ d k sL t ‚ t  t ƒ d k sd t ‚ t  t ƒ d k s| t ‚ t  d ƒ t d k s˜ t ‚ t  d ƒ t d k s´ t ‚ t  t d ƒ d ƒ t d k sÚ t ‚ t  d t d ƒ ƒ t d k s t ‚ t  d t d ƒ ƒ t d k s't ‚ t  t	 ƒ j
 t	 ƒ d d t	 d k sTt ‚ t  t ƒ j t k sot ‚ t  t t ƒ t t t ƒ k s–t ‚ t  d t ƒ t t d ƒ k s¼t ‚ t  t	 ƒ j d  k s×t ‚ t  t ƒ j t k sòt ‚ t  t ƒ j t k st ‚ t  t ƒ j t k s(t ‚ d  S(   Ni   i    i   i   i   iÿÿÿÿiþÿÿÿ(   R   R   RP   RO   R-   R   R   R   R   R_   R'   R<   RW   RR   R   R   R’   RY   RB   RS   R@   (    (    (    sR   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_trigonometric.pyt	   test_acot£  s$    &&'-'&c           C   sh  t  t ƒ j t ƒ t t d t t ƒ t d t t ƒ d k sI t ‚ t  t ƒ j t ƒ t t t t d ƒ t t d d ƒ ƒ t d t t d ƒ k s© t ‚ t  t ƒ j t	 ƒ t t t d ƒ t	 t t d ƒ t t d d ƒ ƒ k s t ‚ t  t ƒ j t
 ƒ t
 d t ƒ k s+t ‚ t  t ƒ j t ƒ t t t d ƒ t t t d d t d ƒ ƒ k szt ‚ t  t ƒ j t ƒ t t t t d d t d ƒ ƒ t d t t d ƒ k sÒt ‚ t  t d ƒ j ƒ  t  t ƒ j t ƒ j d i t d t 6ƒ k st ‚ t  t d ƒ j ƒ  t  t ƒ j t ƒ j d i t d t 6ƒ k sdt ‚ d  S(   Ni   i   iþÿÿÿi   RV   (   R   R_   Re   R   R   RP   R   R   R   R
   R	   R.   R/   Rœ   (    (    (    sR   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_trigonometric.pyt   test_acot_rewrite»  s    I`W+OXJc           C   s"   t  t ƒ j t f k s t ‚ d  S(   N(   R   R_   t   argsRP   (    (    (    sR   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_trigonometric.pyt   test_attributesÇ  s    c           C   s•   t  t d t ƒ t t ƒ k s& t ‚ t  t t ƒ t  t ƒ k sH t ‚ t t d t ƒ t  t ƒ k sn t ‚ t t t ƒ t t ƒ k s‘ t ‚ d  S(   Ni   (   R   R   R_   R   RP   (    (    (    sR   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_trigonometric.pyt   test_sincos_rewriteË  s    &"&c         C   s   |  | ƒ j  d | k S(   sM   Checks that the expr has been rewritten using f(-x) -> f(x)
    arg : -x
    i    (   R¨   (   RU   R*   (    (    sR   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_trigonometric.pyt   _check_even_rewriteÒ  s    c         C   s   |  | ƒ j  j S(   sN   Checks that the expr has been rewritten using f(-x) -> -f(x)
    arg : -x
    (   RU   t   is_Mul(   RU   R*   (    (    sR   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_trigonometric.pyt   _check_odd_rewriteÙ  s    c         C   s   |  | ƒ j  d | k S(   s%   Checks that the expr is not rewritteni    (   R¨   (   RU   R*   (    (    sR   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_trigonometric.pyt   _check_no_rewriteà  s    c          C   sR  t  d ƒ }  t d ƒ } t  g } t t t t t t g } d d t t d t	 t
 t	 t
 g } xs | D]k } x# | D] } t | | ƒ su t ‚ qu Wt | |  | ƒ s­ t ‚ | t	 t
 ƒ | t
 t	 ƒ k sh t ‚ qh Wxt | D]l } x# | D] } t | | ƒ së t ‚ që Wt | |  | ƒ s#t ‚ | t	 t
 ƒ | t
 t	 ƒ k sÞ t ‚ qÞ Wd  S(   Ni   i   iÿÿÿÿi   ii   lE                                                                                                                                            l»ÿÿÿ                                                                                                                                         (   R   R   R   R&   R   R	   R   R   R   R_   R`   R«   RP   R®   R­   (   RD   t   bRI   t   oddt
   with_minusRU   t   expr(    (    sR   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_trigonometric.pyt   test_evenodd_rewriteå  s"    	('c           C   sê   t  t ƒ j t ƒ d t t d ƒ d t t d ƒ d k sE t ‚ t t ƒ j t ƒ d t t d ƒ d d t t d ƒ d k s t ‚ t t ƒ j t ƒ d t t ƒ k sº t ‚ t t ƒ j ƒ  d t t ƒ d k sæ t ‚ d  S(   Ni   i   iÿÿÿÿ(   R   R_   Re   R&   RP   R   R   t   fdiff(    (    (    sR   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_trigonometric.pyt   test_issue_4547ù  s    EJ+c           C   s  t  t ƒ j t ƒ t k s! t ‚ t t ƒ j t ƒ d k sB t ‚ t t ƒ j t ƒ t k sc t ‚ t t ƒ j t ƒ d t k sˆ t ‚ t t ƒ j t ƒ t k s© t ‚ t t ƒ j t ƒ t k sÊ t ‚ t	 t ƒ j t ƒ t k së t ‚ t
 t ƒ j t ƒ t k st ‚ d  S(   Ni   (   R   R_   t   as_leading_termRP   R   R   R&   R   R
   R	   R   (    (    (    sR   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_trigonometric.pyt   test_as_leading_term_issue_5272   s    !!!%!!!c          C   sr   xk t  t t t t t t t g D]K }  xB d t t	 j
 f D]- } |  | ƒ } | j t ƒ | k s9 t ‚ q9 Wq Wd  S(   Ni   (   R   R   R   R&   R   R
   R	   R   R_   R   RT   R¶   RP   (   RU   R*   R¡   (    (    sR   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_trigonometric.pyt   test_leading_terms  s    %c           C   s,  t  t t d t d ƒ j t ƒ t t d t d ƒ j t ƒ ƒ d k sQ t ‚ t  t t t ƒ j t d d ƒ t t t ƒ j t d d ƒ t d t ƒ t d ƒ ƒ t t d ƒ k s¿ t ‚ t  t t t ƒ j t d d ƒ t t t ƒ j t d d ƒ t t d ƒ t t ƒ ƒ t t d d t d f ƒ k s:t ‚ t  t t t t ƒ j t d d ƒ t t t t ƒ j t d d ƒ t d t d ƒ t d t ƒ ƒ t t d d t d f ƒ k sÅt ‚ t	 t t t ƒ g ƒ j
 t t g ƒ t	 t t d t d t t d t d g g ƒ k s(t ‚ d  S(   Ni   i   i    i   i   i   (   R   R   R_   R'   R	   RP   R`   R,   R   R   t   jacobian(    (    (    sR   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_trigonometric.pyt   test_atan2_expansion  s    Qkxˆ$c          C   sY   d „  }  |  t  d d d ƒ |  t  d d d ƒ |  t d d d ƒ |  t d d d ƒ d  S(   Nc         S   s[   t  |  d | ƒ j ƒ  |  d t ƒ j t d | ƒj ƒ  j t | ƒ ƒ | k  sW t ‚ d  S(   Ni   t   dir(   R]   Rœ   R_   R,   t   removeORV   RP   (   RB   t   vRa   RJ   (    (    sR   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_trigonometric.pyt   t  s    gš™™™™™¹?t   +gñhãˆµøä>gš™™™™™¹¿t   -(   R	   R   (   R¾   (    (    sR   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_trigonometric.pyt   test_aseries  s
    	c          C   s  t  d d t ƒ}  t  d d t ƒ} t  d d t ƒ} t d |  t ƒ d k sV t ‚ t d |  t ƒ d	 k sv t ‚ t d |  t ƒ d	 k s– t ‚ t d |  t ƒ t k s¶ t ‚ t d
 |  t ƒ t t |  ƒ k sà t ‚ t d
 |  t ƒ d	 k s t ‚ t d
 |  t ƒ d	 k s t ‚ t d
 |  t ƒ t k s@t ‚ t d |  t ƒ d k s`t ‚ t d |  t ƒ d	 k s€t ‚ t d |  t ƒ d	 k s t ‚ t d |  t ƒ t k sÀt ‚ t d |  t ƒ t t |  ƒ k sêt ‚ t d |  t ƒ d	 k s
t ‚ t d |  t ƒ d	 k s*t ‚ t d |  t ƒ t k sJt ‚ t d |  t ƒ t d t |  ƒ k sxt ‚ t d |  t ƒ t d t |  ƒ k s¦t ‚ t d |  t ƒ t d t |  ƒ k sÔt ‚ t d |  t ƒ t d t |  ƒ k st ‚ t d | t ƒ d k s"t ‚ t d | t ƒ d	 k sBt ‚ t d | t ƒ d	 k sbt ‚ t d | t ƒ t k s‚t ‚ t d
 | t ƒ d k s¢t ‚ t d
 | t ƒ d	 k sÂt ‚ t d
 | t ƒ d	 k sât ‚ t d
 | t ƒ t k st ‚ t d | t ƒ d k s"t ‚ t d | t ƒ d	 k sBt ‚ t d | t ƒ d	 k sbt ‚ t d | t ƒ t k s‚t ‚ t d | t ƒ d k s¢t ‚ t d | t ƒ d	 k sÂt ‚ t d | t ƒ d	 k sât ‚ t d | t ƒ t k st ‚ t d | t ƒ t d t | ƒ k s0t ‚ t d | t ƒ t d t | ƒ k s^t ‚ t d | t ƒ t d t | ƒ k sŒt ‚ t d | t ƒ t d t | ƒ k sºt ‚ t d | t ƒ d k sÚt ‚ t d | t ƒ d	 k sút ‚ t d | t ƒ d	 k st ‚ t d | t ƒ t k s:t ‚ t d
 | t ƒ d k sZt ‚ t d
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 | t ƒ t k sºt ‚ t d | t ƒ d k sÚt ‚ t d | t ƒ d	 k sút ‚ t d | t ƒ d	 k st ‚ t d | t ƒ t k s:t ‚ t d | t ƒ d k sZt ‚ t d | t ƒ d	 k szt ‚ t d | t ƒ d	 k sšt ‚ t d | t ƒ t k sºt ‚ t d | t ƒ t d t | ƒ k sèt ‚ t d | t ƒ t d t | ƒ k st ‚ t d | t ƒ t d t | ƒ k sDt ‚ t d | t ƒ t d t | ƒ k srt ‚ t d t	 t ƒ t d t t	 ƒ k s t ‚ t d t	 t ƒ t d t t	 ƒ k sÎt ‚ t d t	 t ƒ t d t t	 ƒ k süt ‚ t d t	 t ƒ t d t t	 ƒ k s*	t ‚ t d
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t ‚ t d t	 t ƒ t d t t	 ƒ k s>
t ‚ t d t	 t ƒ t d t t	 ƒ k sl
t ‚ t d t	 t ƒ t d t t	 ƒ k sš
t ‚ t d t	 t ƒ t d t t	 ƒ k sÈ
t ‚ t d t	 t ƒ t d t t	 ƒ k sö
t ‚ t d t	 t ƒ t d t t	 ƒ k s$t ‚ t d t	 t ƒ t d t t	 ƒ k sRt ‚ t d t	 t ƒ t d t t	 ƒ k s€t ‚ t d t	 t ƒ t d t t	 ƒ k s®t ‚ t d t	 t ƒ t d t t	 ƒ k sÜt ‚ t d t	 t ƒ t d t t	 ƒ k s
t ‚ d  S(   NRƒ   R?   RJ   RI   t   oR°   i   i   i    i   g      @g      @g      @g      à?iÿÿÿÿ(
   R   RR   R   R   RP   R   R   R&   R   R_   (   Rƒ   RJ   RÂ   (    (    sR   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_trigonometric.pyt   test_issue_4420(  s¦        *       *   ....                ....                .......................c           C   sø   t  t d „  ƒ t  t d „  ƒ t t ƒ j ƒ  t k s> t ‚ t t ƒ j ƒ  t k s\ t ‚ t  t d „  ƒ t  t d „  ƒ t	 t ƒ j ƒ  t
 k sš t ‚ t t ƒ j ƒ  t k s¸ t ‚ t t ƒ j ƒ  t k sÖ t ‚ t t ƒ j ƒ  t k sô t ‚ d  S(   Nc           S   s   t  t ƒ j ƒ  S(   N(   R   R_   t   inverse(    (    (    sR   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_trigonometric.pyt   <lambda>–  Rn   c           S   s   t  t ƒ j ƒ  S(   N(   R   R_   RÄ   (    (    (    sR   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_trigonometric.pyRÅ   —  Rn   c           S   s   t  t ƒ j ƒ  S(   N(   R%   R_   RÄ   (    (    (    sR   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_trigonometric.pyRÅ   š  Rn   c           S   s   t  t ƒ j ƒ  S(   N(   R$   R_   RÄ   (    (    (    sR   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_trigonometric.pyRÅ   ›  Rn   (   R8   t   AttributeErrorR   R_   RÄ   R	   RP   R&   R   R   R   R
   R   (    (    (    sR   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_trigonometric.pyt   test_inverses•  s    c          C   s„  t  d d t ƒ\ }  } |  | t } xWt t g D]I} t | ƒ j d | ƒ t |  ƒ t | ƒ t |  ƒ t | ƒ f k sƒ t	 ‚ t | ƒ j d | ƒ t |  ƒ t | ƒ t |  ƒ t | ƒ f k sÎ t	 ‚ t
 | ƒ j d | ƒ t d |  ƒ t d |  ƒ t d | ƒ t d | ƒ t d |  ƒ t d | ƒ f k sDt	 ‚ t | ƒ j d | ƒ t d |  ƒ t d |  ƒ t d | ƒ t d | ƒ t d |  ƒ t d | ƒ f k s¼t	 ‚ t |  ƒ j d | ƒ t |  ƒ d f k sìt	 ‚ t |  ƒ j d | ƒ t |  ƒ d f k st	 ‚ t
 |  ƒ j d | ƒ t
 |  ƒ d f k sLt	 ‚ t |  ƒ j d | ƒ t |  ƒ d f k s3 t	 ‚ q3 Wd  S(   Ns   a bR=   t   deepi   i    (   R    RR   R   RS   R   t   as_real_imagR   R   R   RP   R   R&   (   RD   R¯   R€   RÈ   (    (    sR   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_trigonometric.pyt   test_real_imag£  s    GH/G0H000c           C   s:   t  t ƒ t j k s t ‚ t t ƒ t j k s6 t ‚ d  S(   N(   R   R   R   R   RP   R   (    (    (    sR   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_trigonometric.pyt   test_sin_cos_with_infinityµ  s    c    	      C   sC  x”d d d d g D]€}  xwd d g D]i} | |  } xVt  d t | d d d d ƒ ƒ D]0} d t | | ƒ k r‹| t | } t | ƒ j t ƒ } t | ƒ j t ƒ } | j t t ƒ s× t	 d | | f ƒ ‚ | j t t ƒ s t	 d | | f ƒ ‚ d	 t
 t | j d ƒ ƒ | j d ƒ ƒ k sDt	 d | | f ƒ ‚ d	 t
 t | j d ƒ ƒ | j d ƒ ƒ k sˆt	 d | | f ƒ ‚ n  q[ Wq& Wq Wt t d
 ƒ j t ƒ t t t d ƒ d t j ƒ k s×t	 ‚ t t d ƒ j t ƒ j d ƒ t t d ƒ j d ƒ k st	 ‚ t d t d d d t ƒj t ƒ t t d t d ƒ d t j ƒ k slt	 ‚ t t d t t j d t ƒd t ƒj t ƒ d k s¨t	 ‚ t t d d ƒ } d t t d ƒ d ƒ t t d ƒ d ƒ d d t d ƒ t t d ƒ d ƒ d t t d ƒ d ƒ t d t d ƒ t t d ƒ d ƒ t d ƒ t t d ƒ d ƒ t d ƒ t t d ƒ d ƒ d t d ƒ d ƒ d t t d ƒ d ƒ t d t d ƒ t t d ƒ d ƒ t d ƒ t t d ƒ d ƒ t d ƒ t t d ƒ d ƒ d t d ƒ d ƒ d t d ƒ d t d ƒ t d t d ƒ t t d ƒ d ƒ t d ƒ t t d ƒ d ƒ t d ƒ t t d ƒ d ƒ d t d ƒ d ƒ d d t d ƒ t t d ƒ d ƒ d t d ƒ t t d ƒ d ƒ d d t d ƒ t t d ƒ d ƒ d t d ƒ t t d ƒ d ƒ t d t d ƒ t t d ƒ d ƒ t d ƒ t t d ƒ d ƒ t d ƒ t t d ƒ d ƒ d t d ƒ d ƒ d d t d ƒ d t d ƒ t t d ƒ t t d ƒ d ƒ t t d ƒ d t d ƒ t t d ƒ d ƒ d t d ƒ t d t d ƒ t t d ƒ d ƒ t d ƒ t t d ƒ d ƒ t d ƒ t t d ƒ d ƒ d t d ƒ d ƒ d t d ƒ d ƒ d d t d ƒ t t d ƒ d t d ƒ t t d ƒ d ƒ d t d ƒ t d t d ƒ t t d ƒ d ƒ t d ƒ t t d ƒ d ƒ t d ƒ t t d ƒ d ƒ d t d ƒ d ƒ d t d ƒ d ƒ t d t d ƒ t t d ƒ d ƒ t d ƒ t t d ƒ d ƒ t d ƒ t t d ƒ d ƒ d t d ƒ d ƒ d d t d ƒ t t d ƒ d ƒ t t d ƒ d t d ƒ t t d ƒ d ƒ d t d ƒ t d t d ƒ t t d ƒ d ƒ t d ƒ t t d ƒ d ƒ t d ƒ t t d ƒ d ƒ d t d ƒ d ƒ d t d ƒ d ƒ d t d ƒ t t d ƒ d t d ƒ t t d ƒ d ƒ d t d ƒ t d t d ƒ t t d ƒ d ƒ t d ƒ t t d ƒ d ƒ t d ƒ t t d ƒ d ƒ d t d ƒ d ƒ d t d ƒ d ƒ t d t d ƒ t t d ƒ d ƒ t d ƒ t t d ƒ d ƒ t d ƒ t t d ƒ d ƒ d t d ƒ d ƒ d t t d ƒ d t d ƒ t t d ƒ d ƒ d t d ƒ t d t d ƒ t t d ƒ d ƒ t d ƒ t t d ƒ d ƒ t d ƒ t t d ƒ d ƒ d t d ƒ d ƒ d t d ƒ d ƒ d t j t t d ƒ d ƒ t t d ƒ d t d ƒ t t d ƒ d ƒ d t d ƒ t d t d ƒ t t d ƒ d ƒ t d ƒ t t d ƒ d ƒ t d ƒ t t d ƒ d ƒ d t d ƒ d ƒ d t d ƒ d ƒ t d t d ƒ t t d ƒ d ƒ t d ƒ t t d ƒ d ƒ t d ƒ t t d ƒ d ƒ d t d ƒ d ƒ d t d ƒ t t d ƒ d ƒ t t d ƒ d t d ƒ t t d ƒ d ƒ d t d ƒ t d t d ƒ t t d ƒ d ƒ t d ƒ t t d ƒ d ƒ t d ƒ t t d ƒ d ƒ d t d ƒ d ƒ d t d ƒ d ƒ d ƒ d } | j t ƒ | k s¼t	 ‚ | j ƒ  | j ƒ  k sÚt	 ‚ t t d d ƒ j t ƒ t t d ƒ t d t d ƒ t t d ƒ t d t d ƒ k s?t	 ‚ d  S(   Ni   i   i   i   i   i   i
   s   fails for %d*pi/%dgü©ñÒMbP?i   i   i  i@   iñÿÿÿi   RK   i   iÿÿÿÿiýÿÿÿi"   i€   iøÿÿÿi   i    i   i   i	   (   R5   t   minR#   R   R   Re   R   R   t   hasRP   R]   Rœ   R   RT   RS   R0   RB   (	   R@   R¾   RB   Rƒ   R_   t   s1t   c1RJ   RD   (    (    sR   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_trigonometric.pyt   test_sincos_rewrite_sqrt½  sF    
+))DS@A6'ÿ ÿ ÿ +ÿ ÿ ÿ ÿ ÿ ÿ ÿ Äc          C   sÝ  xÖd d d d g D]Â}  x¹d d g D]«} | |  } x˜t  d t | d d d d ƒ ƒ D]r} d t | | ƒ k r[ | t | } d | | k r-d | d | k r-t | ƒ j t ƒ } | j t t ƒ sæ t	 d | | f ƒ ‚ d	 t
 t | j d
 ƒ ƒ | j d ƒ ƒ k s-t	 d | | f ƒ ‚ n  | d k rÍ| | k rÍt | ƒ j t ƒ } | j t t ƒ sƒt	 d | | f ƒ ‚ d	 t
 t | j d
 ƒ ƒ | j d ƒ ƒ k sÊt	 d | | f ƒ ‚ qÍq[ q[ Wq& Wq Wd  S(   Ni   i   i   i   i   i   i
   s   fails for %d*pi/%dgü©ñÒMbP?i   i   i    (   R5   RÌ   R#   R   R   Re   R   RÍ   R&   RP   R]   Rœ   (   R@   R¾   RB   Rƒ   R_   t   t1RÏ   (    (    sR   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_trigonometric.pyt   test_tancot_rewrite_sqrt  s    
+$)G)c          C   s  t  d d t ƒ}  t  d ƒ } t j t d ƒ k s9 t ‚ t t ƒ t k sQ t ‚ t d ƒ d k si t ‚ t t ƒ d k s t ‚ t t d ƒ t k s t ‚ t t d ƒ t k sº t ‚ t t d ƒ d t	 d	 ƒ d	 k sä t ‚ t t d	 ƒ d k s t ‚ t d
 t d ƒ t k s t ‚ t d t d ƒ t d t d ƒ k sOt ‚ t d	 t d ƒ t	 d ƒ k svt ‚ t t
 ƒ d t d ƒ k s˜t ‚ t |  t
 ƒ d t |  ƒ k s¾t ‚ t |  ƒ t |  ƒ k sÝt ‚ t t |  ƒ ƒ |  k sût ‚ t | ƒ j ƒ  t t | ƒ ƒ k s%t ‚ t | ƒ j ƒ  t t | ƒ ƒ t t | ƒ ƒ t t | ƒ ƒ d t t | ƒ ƒ d t t | ƒ ƒ d t t | ƒ ƒ d t t | ƒ ƒ t t | ƒ ƒ t t | ƒ ƒ d t t | ƒ ƒ d t t | ƒ ƒ d t t | ƒ ƒ d f k s!t ‚ t |  ƒ j d t ƒ d t |  ƒ k sOt ‚ t d |  ƒ j d t ƒ d d t |  ƒ d d k st ‚ t |  ƒ j t k s¨t ‚ t | ƒ j d  k sÃt ‚ t t ƒ j d  k sÞt ‚ t t ƒ j t k sùt ‚ t |  ƒ j ƒ  t |  ƒ k st ‚ t d ƒ j t k s8t ‚ t |  ƒ j d  k sSt ‚ t t d ƒ j t k srt ‚ t t |  ƒ |  d d d d ƒd |  d d d
 |  d d t |  d ƒ k sÉt ‚ t t	 t |  ƒ ƒ ƒ d |  d d d |  d d t |  d ƒ k st ‚ t t	 t |  ƒ ƒ |  d t d	 d d d ƒd t	 |  d	 t d ƒ |  d	 t d t d	 ƒ d d |  d	 t d t d ƒ d d t |  d	 t d d |  d	 t d f ƒ k s×t ‚ t |  ƒ j  |  ƒ t! |  ƒ t |  ƒ k st ‚ t | ƒ j" d | ƒ d
 | d d k s8t ‚ t | ƒ j" d | ƒ d | d d k sht ‚ t | ƒ j" d
 | ƒ d k sŒt ‚ d  S(   NR_   R=   R€   i   i    iÿÿÿÿi   i   i   i   i	   i   i   Rg   t   x0RB   i   i`   i   i    i=   iÐ  (#   R    RR   R$   RO   R-   RP   R   R   R   R   R   R   R.   R+   RÉ   R   R   R    R   R   Rh   RW   RY   RD   RX   RF   RS   R¶   R…   R,   R   R   R'   R   R”   (   R_   R€   (    (    sR   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_trigonometric.pyt   test_sec   sR    * /'"&*F)F8.>$WN,”100c           C   s  t  t ƒ j t ƒ d t t t ƒ d t t t ƒ d k sF t ‚ t  t ƒ j t ƒ d t t ƒ k sq t ‚ t  t ƒ j t ƒ t t d ƒ d d t t d ƒ d d k s» t ‚ t  t ƒ j t ƒ t  t ƒ k sâ t ‚ t  t ƒ j t	 ƒ t  t ƒ k s	t ‚ t  t
 ƒ j t ƒ t t
 d ƒ d d t t
 d ƒ d d k sRt ‚ t  t ƒ j t ƒ d t t t d d t ƒk s‹t ‚ t  t ƒ j t ƒ t t d ƒ d d t t d ƒ d d k sÕt ‚ t  t ƒ j t ƒ t t t d d t ƒk st ‚ d  S(   Ni   i   RK   (   R$   R_   Re   R   R   RP   R   R   R{   R   R€   R&   R   R   RS   R%   (    (    (    sR   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_trigonometric.pyt   test_sec_rewrite_  s    F+J''I9Jc          C   sj  t  d d t ƒ}  t  d ƒ } t d ƒ } d t d ƒ } | j | ƒ t k sU t ‚ | j | ƒ t k sp t ‚ t j t d ƒ k s‹ t ‚ t d ƒ t k s£ t ‚ t t	 ƒ t k s» t ‚ t t ƒ t
 k sÓ t ‚ t t	 d ƒ d k sï t ‚ t t	 d ƒ d k st ‚ t t	 d ƒ d k s(t ‚ t t	 d	 ƒ d t d	 ƒ d	 k sRt ‚ t d
 t	 d ƒ d k srt ‚ t d t	 d ƒ t d t	 d ƒ k s¡t ‚ t d	 t	 d ƒ t d ƒ k sÇt ‚ t t ƒ t t d ƒ k sêt ‚ t |  t ƒ t t |  ƒ k st ‚ t |  ƒ t |  ƒ k s1t ‚ t t |  ƒ ƒ |  k sOt ‚ t | ƒ j ƒ  t t | ƒ ƒ k syt ‚ t | ƒ j ƒ  t t | ƒ ƒ t t | ƒ ƒ t t | ƒ ƒ d t t | ƒ ƒ d t t | ƒ ƒ d t t | ƒ ƒ d t t | ƒ ƒ t t | ƒ ƒ t t | ƒ ƒ d t t | ƒ ƒ d t t | ƒ ƒ d t t | ƒ ƒ d f k svt ‚ t |  ƒ j d t ƒ d t |  ƒ k s¤t ‚ t d |  ƒ j d t ƒ d d t |  ƒ t |  ƒ k sät ‚ t |  ƒ j t k sÿt ‚ t | ƒ j d  k st ‚ t t ƒ j d  k s5t ‚ t t ƒ j t k sPt ‚ t |  ƒ j ƒ  t |  ƒ k stt ‚ t d ƒ j t k st ‚ t |  ƒ j d  k sªt ‚ t t	 d ƒ j t k sÉt ‚ t t |  ƒ |  d t	 d d d ƒd |  t	 d d d d
 |  t	 d d d t |  t	 d d |  t	 d f ƒ k sIt ‚ t t |  ƒ |  d d d d ƒd |  |  d d |  d	 d d |  d
 d t |  d ƒ k s°t ‚ t |  ƒ j  |  ƒ t! |  ƒ t |  ƒ k sât ‚ t |  ƒ j" d |  ƒ d k st ‚ t |  ƒ j" d	 |  ƒ d |  d	 d k s6t ‚ t |  ƒ j" d
 |  ƒ d |  d
 d k sft ‚ d  S(   NR_   R=   R€   i   i    i   iÿÿÿÿi   i   i   i	   i   i   Rg   RÓ   RB   i   ih  i   i;  (#   R    RR   R%   R   R    RP   RO   R-   R   R   R   R   R   R   R/   R+   RÉ   R   R   R    R   Rh   RW   RY   RD   RX   RF   RS   R¶   R…   R,   R   R'   R&   R”   (   R_   R€   t   cosecantt	   alternate(    (    sR   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_trigonometric.pyt   test_csck  sZ    * /&#' *F)G8.@$"^I2$0c          C   s»  t  d d t ƒ}  t |  ƒ t k s* t ‚ t t ƒ t k sB t ‚ t d ƒ d k sZ t ‚ t d ƒ t k sr t ‚ t t ƒ t d k sŽ t ‚ t t ƒ t d k s« t ‚ t t ƒ t d k sÇ t ‚ t t ƒ j	 t ƒ d t d t
 d d t d ƒ k st ‚ t t ƒ j t ƒ t t ƒ k s-t ‚ t t ƒ j t ƒ t t t
 d d t d ƒ t t ƒ t d k szt ‚ t t ƒ j t ƒ t d t ƒ t d k s®t ‚ t t ƒ j t ƒ t d t ƒ k sÙt ‚ t t ƒ j t ƒ d t t t
 t d d ƒ ƒ t d t
 t d ƒ t k s0t ‚ t t ƒ j t ƒ d t t t
 t d d ƒ ƒ t d t
 t d ƒ t k s‡t ‚ t t ƒ j t ƒ t t ƒ t d k s·t ‚ d  S(   NR€   R   i   i    iÿÿÿÿi   (   R   RR   R.   R   RP   R   R   R   R_   R'   R   R¶   R   Re   R   R   R
   R	   R   R/   (   R€   (    (    sR   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_trigonometric.pyt	   test_asec«  s     ?'M4+WWc          C   s¿   t  t d ƒ d ƒ j t k s% t ‚ t d d t d t ƒ}  t  |  ƒ j t k sX t ‚ t  t ƒ j d  k ss t ‚ t  t	 ƒ j d  k sŽ t ‚ t d d t ƒ} t  | ƒ j t k s» t ‚ d  S(   Ni   i   RB   RA   R?   R¾   R=   (
   R.   R   RW   RS   RP   R   RR   R_   RY   R<   (   RB   R¾   (    (    sR   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_trigonometric.pyt   test_asec_is_realÀ  s    %c           C   s}  t  t ƒ t k s t ‚ t  d ƒ t d k s4 t ‚ t  d ƒ t d k sQ t ‚ t  t ƒ d k si t ‚ t  t ƒ d k s‚ t ‚ t  t ƒ d k sš t ‚ t  t ƒ j t ƒ d t d t d d t d ƒ k sÙ t ‚ t  t ƒ j	 t ƒ t
 t ƒ k s t ‚ t  t ƒ j t
 ƒ t t
 t d d t d ƒ t t ƒ k sFt ‚ t  t ƒ j t ƒ t d t ƒ k sqt ‚ t  t ƒ j t ƒ t d t ƒ t d k s¥t ‚ t  t ƒ j t ƒ t t t d d ƒ ƒ t d t t d ƒ t k sõt ‚ t  t ƒ j t ƒ t d t t d d ƒ ƒ t d t t d ƒ t k sIt ‚ t  t ƒ j t ƒ t t ƒ t d k syt ‚ d  S(   Ni   i   iÿÿÿÿi    (   R/   R   RP   R   R   R   R_   R'   R   R¶   R   Re   R   R   R
   R	   R   R.   (    (    (    sR   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_trigonometric.pyt	   test_acscÊ  s    ?'F+4PTc           C   s¸  t  t ƒ j t ƒ t  t ƒ k s' t ‚ t  t ƒ j t ƒ t  t ƒ k sN t ‚ t  t ƒ j t ƒ d t t t t ƒ t t t ƒ k s t ‚ t  t ƒ j t ƒ d t t ƒ k s» t ‚ t  t ƒ j t	 ƒ t	 t d ƒ d d d t	 t d ƒ k s t ‚ t  t ƒ j t
 ƒ t
 t d ƒ d d d t
 t d ƒ k sEt ‚ t  t ƒ j t ƒ d t t t d d t ƒk s~t ‚ t  t ƒ j t ƒ t t t d d t ƒk s´t ‚ d  S(   Ni   i   RK   (   R%   R_   Re   R{   RP   R   R   R   R   R   R&   R   R   RS   R$   (    (    (    sR   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_trigonometric.pyt   test_csc_rewriteÝ  s    ''B+EE9c          C   sg   t  d d t ƒ}  t |  ƒ j d  k s- t ‚ t |  ƒ j d  k sH t ‚ t |  ƒ j d  k sc t ‚ d  S(   NRB   R?   (   R   RR   R   t   is_irrationalRY   RP   R   R   (   RB   (    (    sR   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_trigonometric.pyt   test_issue_8653é  s    c          C   s3   t  d d t d t ƒ}  t |  d ƒ j t k d  S(   NRB   R?   RA   i   (   R   RR   R	   t   is_nonnegative(   RB   (    (    sR   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_trigonometric.pyt   test_issue_9157ð  s    c             s  t  d ƒ \ ‰  }  t ˆ  ƒ j ƒ  d t k s4 t ‚ t ˆ  ƒ j ƒ  d t k sV t ‚ t ˆ  ƒ j ƒ  t k st t ‚ t ˆ  ƒ j ƒ  t k s’ t ‚ t ˆ  ƒ j ƒ  d t k s´ t ‚ t	 ˆ  ƒ j ƒ  d t k sÖ t ‚ t d ˆ  ƒ j ƒ  t k sø t ‚ t d ˆ  d ƒ j ƒ  t d k s"t ‚ t d ˆ  ƒ j ƒ  d t d k sLt ‚ t ˆ  |  ƒ j ˆ  ƒ d t t
 |  ƒ k st ‚ t d ˆ  |  d t ƒ j |  ƒ d t t
 d ˆ  ƒ k sÂt ‚ t d ˆ  ƒ j |  ƒ t j k sêt ‚ t t ‡  f d †  ƒ d  S(   Ns   x, yi   i   i   iýÿÿÿi   c              s   t  ˆ  d ƒ j ˆ  ƒ S(   Ni   (   R   t   period(    (   R_   (    sR   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_trigonometric.pyRÅ     Rn   (   R    R   Rá   R   RP   R   R   R&   R$   R%   R]   R   RQ   R8   t   NotImplementedError(   R`   (    (   R_   sR   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_trigonometric.pyt   test_trig_periodõ  s    """""**3C(c           C   sR   t  t ƒ j t ƒ t  t ƒ k s' t ‚ t  t ƒ j t ƒ t  t ƒ k sN t ‚ d  S(   N(   R   R_   Re   R   RP   R{   (    (    (    sR   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_trigonometric.pyt   test_issue_7171  s    'c          C   s«   t  d d t ƒ\ }  } t d t d t | d ƒ f t t | ƒ t | t f ƒ } t d t d t | d ƒ f t t | ƒ t f ƒ } | j t ƒ | k s§ t ‚ d  S(   Ns   w, kR=   i   i   i    (	   R    RR   R;   R:   R   R   R1   Re   RP   (   t   wR>   t   Ft   soln(    (    sR   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_trigonometric.pyt   test_issue_11864  s    >6c          C   sü  t  d d t ƒ}  t |  ƒ j d  k s- t ‚ t |  ƒ j d  k sH t ‚ t |  ƒ j t k sc t ‚ t |  ƒ j d  k s~ t ‚ t	 |  ƒ j d  k s™ t ‚ t
 |  ƒ j t k s´ t ‚ t t ƒ j d  k sÏ t ‚ t t ƒ j d  k sê t ‚ t t ƒ j d  k st ‚ t t ƒ j d  k s t ‚ t t ƒ j d  k s;t ‚ t t ƒ j d  k sVt ‚ t t ƒ j d  k sqt ‚ t t ƒ j d  k sŒt ‚ t t ƒ j t k s§t ‚ t t ƒ j t k sÂt ‚ t t ƒ j t k sÝt ‚ t t ƒ j t k søt ‚ d  S(   NR€   R=   (   R   RS   R   RW   RY   RP   R   R   R$   R%   R&   R   R@   RB   R.   R
   R/   R	   R’   RR   t   is_negativeR   (   R€   (    (    sR   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_trigonometric.pyt   test_real_assumptions  s&    c           C   sH  t  t d ƒ ƒ d t k ra t d d t k o@ t d k n ra t d ƒ t d t ƒ k sg t ‚ t  t d ƒ ƒ d t d k rÔ t d d t d k o¯ t d k n rÔ t d ƒ t d t d ƒ k sÚ t ‚ t t d ƒ ƒ t d d k rAd t d d k ot k n rAt d ƒ t t d d ƒ k sGt ‚ t t d ƒ ƒ d t d k r«d d t d k o†t k n r«t d ƒ t d t d ƒ k s±t ‚ t t d ƒ ƒ d d t k rd d d t k oðt k n rt d ƒ t d d t ƒ k st ‚ t t d	 ƒ ƒ d
 t d	 k rˆt d d
 t d	 k  oct d k  n rˆt d	 ƒ t d
 t d	 ƒ k sŽt ‚ t t d ƒ ƒ d
 t d k rût d d
 t d k  oÖt d k  n rût d ƒ t d
 t d ƒ k st ‚ t t d ƒ ƒ d d t d k rzt d d d t d k  oQt d k  n rzt d ƒ t d d t d ƒ k s€t ‚ t	 t d ƒ ƒ d
 t d k rít d d
 t d k  oÈt d k n rít d ƒ t d
 t d ƒ k sót ‚ t	 t d ƒ ƒ d d t d k rlt d d d t d k  oCt d k n rlt d ƒ t d d t d ƒ k srt ‚ t
 t d ƒ ƒ d d t k rÖd d d t k o±t k n rÖt d ƒ t d d t ƒ k sÜt ‚ t
 t d ƒ ƒ d d t d k rLd d d t d k o#t k n rLt d ƒ t d d t d ƒ k sRt ‚ t t d ƒ ƒ d t d k r¿t d d t d k ošt d k n r¿t d ƒ t d t d ƒ k sÅt ‚ t t d ƒ ƒ d t d d k r>t d d t d d k ot d k n r>t d ƒ t d t d d ƒ k sDt ‚ d  S(   Ni   iþÿÿÿi    i   iúÿÿÿi   iâÿÿÿi
   i   iûÿÿÿi   i   iôÿÿÿi   i   iíÿÿÿi   i   iõÿÿÿi   ióÿÿÿi	   i   iüÿÿÿiùÿÿÿ(   R   R   R   RP   R   R
   R	   R   R&   R   R.   R$   R%   R/   (    (    (    sR   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_trigonometric.pyt   test_issue_14320'  s    gsmjjsssjvsc          C   sx  t  d t d ƒ t  d ƒ k s& t ‚ t  d t d ƒ t  d ƒ k sL t ‚ t  t d ƒ t  d ƒ k so t ‚ t  t d ƒ t  d ƒ k s’ t ‚ t d t d ƒ t d ƒ k s¸ t ‚ t d t d ƒ t d ƒ k sß t ‚ t t d ƒ t d ƒ k st ‚ t t d ƒ t d ƒ k s$t ‚ t d ƒ }  t t d |  ƒ t  |  ƒ k sVt ‚ t t d |  ƒ t  |  ƒ k s|t ‚ t d t d |  ƒ t  |  ƒ k s§t ‚ t d t d |  ƒ t  |  ƒ k sÒt ‚ t  t d |  ƒ t |  ƒ k søt ‚ t  t d |  ƒ t |  ƒ k st ‚ t  d t d |  ƒ t |  ƒ k sIt ‚ t  d t d |  ƒ t |  ƒ k stt ‚ d  S(   Ni   i   i   R_   i   (   R$   R   RP   R%   R   (   R_   (    (    sR   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_trigonometric.pyt   test_issue_145439  s"    &&##&'#"&&++&'*c           C   s.   t  d t d ƒ d t d ƒ k s* t ‚ d  S(   Ni   i   i   i   (   R   R   R   RP   (    (    (    sR   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_trigonometric.pyt   test_issue_15959O  s    N(‘   t   sympyR    R   R   R   R   R   R   R   R   R	   R
   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R    R!   R"   R#   R$   R%   R&   R'   R(   R)   R*   R+   R,   R-   R.   R/   R0   R1   R2   R3   R4   t   sympy.core.compatibilityR5   t   sympy.utilities.pytestR6   R7   R8   t   sympy.core.relationalR9   R:   t$   sympy.functions.elementary.piecewiseR;   R_   R`   R€   RR   R<   R>   R@   RB   RD   RF   Rb   Rc   Rd   Rf   Ri   Rk   Rl   Rm   Rq   Rr   Rs   Rt   Ru   Ry   Rz   R~   R   R   R‚   R†   R‡   Rˆ   R‰   RŠ   R‹   R‘   R“   R–   R—   R˜   R™   Rš   R›   R   R¥   R¦   R§   R©   Rª   R«   R­   R®   R³   Rµ   R·   R¸   Rº   RÁ   RÃ   RÇ   RÊ   RË   RÐ   RÒ   RÔ   RÕ   RØ   RÙ   RÚ   RÛ   RÜ   RÞ   Rà   Rã   Rä   Rè   Rê   Rë   Rì   Rí   (    (    (    sR   lib/python2.7/site-packages/sympy/functions/elementary/tests/test_trigonometric.pyt   <module>   s¤   ÿ I	s	
					%	e						X						X							(				$						;													
	m		Q	?		@		
										