ó
9­\c           @   sï  d  d l  m Z m Z m Z m Z m Z m Z m Z m Z m	 Z	 m
 Z
 m Z m Z m Z m Z m Z m Z m Z m Z m Z m Z m Z m Z m Z m Z m Z m Z m Z m Z m Z m Z m Z m  Z  m! Z! m" Z" m# Z# m$ Z$ m% Z% m& Z& m' Z' m( Z( m) Z) m* Z* m+ Z+ m, Z, m- Z- m. Z. m/ Z/ m0 Z0 m1 Z1 m2 Z2 m3 Z3 m4 Z4 m5 Z5 m6 Z6 m7 Z7 m8 Z8 m9 Z9 m: Z: m; Z; m< Z< m= Z= m> Z> d  d l? m@ Z@ d  d lA mB ZB d  d lC mD ZD mE ZE mF ZF d  d lG mH ZH mI ZI mJ ZJ mK ZK mL ZL mM ZM mN ZN mO ZO mP ZP mQ ZQ mR ZR mS ZS d  d lT mU ZU d  d lV mW ZW d  d lX mY ZY mZ ZZ m[ Z[ m\ Z\ m] Z] m^ Z^ d  d	 l_ m` Za d  d
 lb mc Zc md Zd me Ze mf Zf mg Zg mh Zh mi Zi mj Zj mk Zk ml Zl mm Zm mn Zn mo Zo d 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 „  Z d „  Z‚ d „  Zƒ d  „  Z„ d! „  Z… d" „  Z† d# „  Z‡ eY d$ „  ƒ Zˆ d% „  Z‰ d& „  ZŠ d' „  Z‹ d( „  ZŒ d) „  Z d* „  ZŽ d+ „  Z d, „  Z d- „  Z‘ d. „  Z’ d/ „  Z“ d0 „  Z” d1 „  Z• e[ d2 ƒ d3 „  ƒ Z– d4 „  Z— d5 „  Z˜ eY d6 „  ƒ Z™ eY d7 „  ƒ Zš eZ d8 „  ƒ Z› d9 „  Zœ d: „  Z d; „  Zž eY d< „  ƒ ZŸ d= „  Z  d> „  Z¡ d? „  Z¢ d@ „  Z£ dA „  Z¤ dB „  Z¥ dC „  Z¦ dD „  Z§ dE „  Z¨ dF „  Z© dG „  Zª dH „  Z« dI „  Z¬ dJ „  Z­ dK „  Z® dL „  Z¯ dM „  Z° dN „  Z± dO „  Z² dP „  Z³ dQ „  Z´ dR „  Zµ eY dS „  ƒ Z¶ eZ dT „  ƒ Z· dU „  Z¸ eZ dV „  ƒ Z¹ dW „  Zº dX „  Z» dY „  Z¼ dZ „  Z½ d[ „  Z¾ d\ „  Z¿ d] „  ZÀ d^ „  ZÁ d_ „  ZÂ d` „  ZÃ da „  ZÄ db „  ZÅ dc „  ZÆ dd „  ZÇ eY de „  ƒ ZÈ df „  ZÉ dg „  ZÊ dh „  ZË eY di „  ƒ ZÌ eY dj „  ƒ ZÍ dk „  ZÎ dl „  ZÏ eY dm „  ƒ ZÐ dn „  ZÑ do „  ZÒ dp „  ZÓ dq „  ZÔ dr „  ZÕ ds „  ZÖ dt „  Z× du „  ZØ dv „  ZÙ dw „  ZÚ eY dx „  ƒ ZÛ dy S(z   iÿÿÿÿ(>   t   Abst   Andt
   Derivativet   Dummyt   Eqt   Floatt   Functiont   Gtt   It   Integralt   LambertWt   Ltt   Matrixt   Ort   Polyt   Qt   Rationalt   St   Symbolt   Net   Wildt   acost   asint   atant   atanht   cost   cosht   difft   erft   erfinvt   erfct   erfcinvt   expt   imt   logt   pit   ret   sect   sint   sinht   solvet   solve_lineart   sqrtt   sstrt   symbolst   sympifyt   tant   tanht   roott   simplifyt   atan2t   argt   Mult   SparseMatrixt   askt   Tuplet   nsolvet   oot   Et   cbrtt   denomt   Add(   t   range(   t   nfloat(   t   solve_linear_systemt   solve_linear_system_LUt   solve_undetermined_coeffs(   t   _invertt   unradt   checksolt   posifyt   _ispowt	   det_quickt   det_permt	   det_minort   _simple_denst   check_assumptionst   denomst   failing_assumptions(   t   cm(   t   CRootOf(   t   slowt   XFAILt   SKIPt   raisest   skipt	   ON_TRAVIS(   t   verify_numerically(   t   at   bt   ct   dt   kt   ht   pt   xt   yt   zt   tt   qt   mi   c         K   s"   t  t |  ƒ j | |  d t ƒS(   Nt	   full_prec(   R+   R-   t   evalft   True(   t   et   nt   options(    (    s?   lib/python2.7/site-packages/sympy/solvers/tests/test_solvers.pyt   NS   s    c          C   s[  t  t d ƒ \ }  } |  t ƒ | t ƒ } } t | t d | | d g | t | ƒ i | d | 6| d t 6k s| t ‚ t | | t d | | g d t ƒd i d | 6d | 6k sÁ t ‚ t | | d t t | | g d t ƒi t | d t | 6g k st ‚ t |  d ƒ d t d g d t ƒi d t 6d |  d ƒ 6g k sWt ‚ d  S(	   Nt   fgi   i   i   t   dicti    i   iþÿÿÿ(   t   mapR   R_   R(   R`   t   AssertionErrorRg   (   t   ft   gt   fxt   gx(    (    s?   lib/python2.7/site-packages/sympy/solvers/tests/test_solvers.pyt   test_swap_back   s    (&EMc         C   s4   y t  |  | ƒ t SWn t t f k
 r/ t SXd  S(   N(   R(   Rg   t	   TypeErrort   NotImplementedErrort   False(   t   eqt   symbol(    (    s?   lib/python2.7/site-packages/sympy/solvers/tests/test_solvers.pyt   guess_solve_strategy)   s
    c           C   s\  t  t d ƒ t ƒ s t ‚ t  t t ƒ s0 t ‚ t  t t t ƒ sI t ‚ t  d t t ƒ sb t ‚ t  t t d ƒ t ƒ s t ‚ t  t d t d d ƒ t ƒ s§ t ‚ t  t d d t ƒ sÄ t ‚ t  t d d t ƒ sá t ‚ t  t t t t ƒ sþ t ‚ t  t t t ƒ t t ƒ s!t ‚ t  t t d t d t d t d ƒ t ƒ sXt ‚ d  S(   Ni   i   i   i   (	   Rz   R   R_   Ro   RX   R*   R   R`   R    (    (    (    s?   lib/python2.7/site-packages/sympy/solvers/tests/test_solvers.pyt   test_guess_poly1   s    &#c           C   s›   t  t t ƒ d t ƒ s t ‚ t  t t d d ƒ t t ƒ d t ƒ sO t ‚ t  d t d t t ƒ t ƒ sv t ‚ t  t d t t t ƒ s— t ‚ d  S(   Ni   i   i   (   Rz   R*   R_   Ro   R   R`   (    (    (    s?   lib/python2.7/site-packages/sympy/solvers/tests/test_solvers.pyt   test_guess_poly_cvA   s
    -'c           C   sž   t  t d t d d t ƒ s% t ‚ t  t t d t d t d t d ƒ t ƒ s\ t ‚ t  t t ƒ d t t d d ƒ t t ƒ d t ƒ sš t ‚ d  S(   Ni   i   i   (   Rz   R_   Ro   R`   R*   R   (    (    (    s?   lib/python2.7/site-packages/sympy/solvers/tests/test_solvers.pyt   test_guess_rational_cvL   s    %4c           C   sÌ   t  t t ƒ d t ƒ s t ‚ t  d t t ƒ t t ƒ sB t ‚ t  t t ƒ t t ƒ t t ƒ sl t ‚ t  d t d t ƒ s‰ t ‚ t  d t d t ƒ s§ t ‚ t  t t t t t ƒ sÈ t ‚ d  S(   Ni   i   i   i
   (   Rz   R    R_   Ro   R   R`   RX   RY   (    (    (    s?   lib/python2.7/site-packages/sympy/solvers/tests/test_solvers.pyt   test_guess_transcendentalW   s    #'c             sH	  i d t  6d t 6‰  t  d t d d t  d t d f ‰ t ‡  ‡ f d †  t t t t f Dƒ ƒ sm t ‚ t t	 ˆ Œ  t  t ƒ ˆ  k s‘ t ‚ t t t  d d ƒ ƒ t t
 d ƒ t
 d ƒ g ƒ k sÐ t ‚ t t  t d	 t  t d g ƒ i d t  6d
 t 6k st ‚ t t  t t  ƒ t  d t ƒt t  ƒ g k s@t ‚ t d ƒ t d t  ƒ k ofg  k n sqt ‚ t d d g ƒ g  k st ‚ t t  d	 t d f t  t t  ƒ i d	 t  6d t 6k sÌt ‚ t t d	 t t g ƒ ƒ d	 g k s÷t ‚ t t d	 t t  t g ƒ ƒ i d	 t 6g k s,t ‚ t t  t d	 t  t g ƒ d	 t t f g k sbt ‚ t t  t d	 t  t g d t ƒi d	 t t  6g k sŸt ‚ t t  t d	 ƒ i d	 t t  6g k sÍt ‚ t t t t  d t t g ƒ i d t 6d t 6k st ‚ t t t  t d d t t f }  t |  Œ  t d ƒ t d ƒ f t d ƒ t d ƒ f g k sot ‚ t d t |  Œ t t g t t d ƒ t d ƒ f t d ƒ t d ƒ f g ƒ f k sËt ‚ t d t |  Œ i t d ƒ t 6t d ƒ t 6i t d ƒ t 6t d ƒ t 6g k s%t ‚ t t  d t t  t t  t d d t t d t } t d t ƒ } t | t t t g d t t t g | i t t d d t t 6t d t t 6d d t t 6g k sÝt ‚ | j t d t ƒ ƒ t | t t t g d t t t g | i d t t t d d t t 6t d t t 6d d t t 6g k sjt ‚ t t t  t d t  d d	 t  d t  t t d t ƒi t d t  d	 t  d	 d t  d d t  d t  d t  d t 6g k sùt ‚ t d d t  t t t ƒ ƒ g  k s't ‚ t t d „  ƒ t t t t  ƒ t  g ƒ i t d ƒ t  6d t 6g k swt ‚ t t t  ƒ t  t t ƒ t f ƒ i t d
 ƒ t  6t d
 ƒ t 6g k sÈt ‚ t t t t  ƒ t  g t  t ƒ t d ƒ d f g k t t  d t t ƒ t  d g k s(t ‚ t g  t  g ƒ g  k sFt ‚ t t  t d d t  t d g ƒ i t d t  6g k s‡t ‚ t t  t d d t  d t d f ƒ i t d t  6k sÉt ‚ t t t t  d ƒ g t  g d t ƒi d t  6g k st ‚ t t t  t  ƒ t t  d ƒ t t  t  d ƒ g t  g d t ƒg  k sRt ‚ t t t  t  d ƒ t  d k  g t  ƒ st ‚ t t t  d ƒ t  d d k  g ƒ t t  d ƒ k s»t ‚ t t t  t  ƒ t t  t  d ƒ g t  ƒ g  k sòt ‚ t t t  ƒ g  k s	t ‚ t t  d t g t  g d t ƒg  t ƒ  f k sD	t ‚ d  S(   Niýÿÿÿi   i   i   i   i   c         3   s-   |  ]# } t  | ˆ ƒ t t ƒ ˆ  k Vq d  S(   N(   R(   R_   R`   (   t   .0t	   container(   t   anst   eqs(    s?   lib/python2.7/site-packages/sympy/solvers/tests/test_solvers.pys	   <genexpr>g   s    i   i   iÿÿÿÿt   impliciti*   iþÿÿÿRm   i    t   sett   excludeR1   i   i   c           S   s.   t  t t ƒ t t ƒ t t ƒ t t ƒ ƒ S(   N(   R(   R    R_   R&   R`   (    (    (    s?   lib/python2.7/site-packages/sympy/solvers/tests/test_solvers.pyt   <lambda>•   t    (   R_   R`   t   allt   tuplet   listR„   t	   frozensetRo   R(   R7   R   R    Rg   RX   RY   R*   RZ   R]   R^   R\   Rm   t   updateRw   RT   Rv   R
   R#   R   (   t   argsRx   t   flags(    (   R   R‚   s?   lib/python2.7/site-packages/sympy/solvers/tests/test_solvers.pyt   test_solve_argsc   sf    ($?<41=+56=.;#	;MK:'H'P9V.@N6*AB=L/:7c       	   C   sÄ  t  d t d t ƒ t d d ƒ g k s/ t ‚ t  t d t d ƒ t ƒ t d d ƒ g k sc t ‚ t t  t d d t ƒ ƒ t t d ƒ t d ƒ g ƒ k s¥ t ‚ t t  t t d d ƒ t ƒ ƒ t t d ƒ t d ƒ g ƒ k sì t ‚ t  t t d t ƒ t d g k st ‚ t t d ƒ }  t  t t d t ƒ |  |  d t	 d ƒ t
 |  d |  d t	 d ƒ t
 |  d g k s‡t ‚ t d ƒ \ } } } } } } t  | t | t | | t | t | g t t ƒ i | | | | | | | | t 6| | | | | | | | t 6k s/t ‚ i t j t 6t j t 6} t  t t t t f t t ƒ | k sut ‚ t  t t t t f t t f ƒ | k s¤t ‚ t  t t t t f t t g ƒ | k sÓt ‚ t t  t d d t d t ƒ ƒ t d d t d d ƒ t d ƒ d d t d d ƒ g ƒ k s;t ‚ t t  t d d d t t ƒ ƒ t t	 d t	 t ƒ ƒ t	 d t	 t ƒ ƒ t	 d t	 t ƒ ƒ t	 d t	 t ƒ ƒ g ƒ k sÀt ‚ d  S(   Ni   i   i   s   a11,a12,a21,a22,b1,b2i   i   iþÿÿÿ(   R(   R_   R   Ro   R   R„   R   R`   R0   R*   R   R,   t   ZeroRX   (   t   rxt   a11t   a12t   a21t   a22t   b1t   b2t   solution(    (    s?   lib/python2.7/site-packages/sympy/solvers/tests/test_solvers.pyt   test_solve_polynomial1±   s0    /4BG*N5#/,//%	&"*c           C   s   t  d t ƒ g  k s t ‚ d  S(   Ni   (   R(   R_   Ro   (    (    (    s?   lib/python2.7/site-packages/sympy/solvers/tests/test_solvers.pyt   test_solve_polynomial2Õ   s    c           C   sø   t  t t ƒ d t ƒ d g k s( t ‚ t  t t ƒ d t ƒ d g k sP t ‚ t  t t d d ƒ d t ƒ d g k s t ‚ t  t t d d ƒ d t ƒ d g k s® t ‚ t  t t ƒ t t d d ƒ t t d d ƒ t ƒ d g k sô t ‚ d S(	   sŽ   
    Test for solving on equations that can be converted to a polynomial equation
    using the change of variable y -> x**Rational(p, q)
    i   i   i   i   i   i   i    N(   R(   R*   R_   Ro   R   (    (    (    s?   lib/python2.7/site-packages/sympy/solvers/tests/test_solvers.pyt   test_solve_polynomial_cv_1aÙ   s
    ((//c           C   sŸ   t  t d t d t t t ƒ t ƒ ƒ t  t d ƒ d t d g ƒ k sQ t ‚ t  t t t t d ƒ d t ƒ ƒ t  t d ƒ t d ƒ g ƒ k s› t ‚ d  S(   Ni   i   i    i   i   i   (   R„   R(   R_   RX   R*   R   Ro   R0   (    (    (    s?   lib/python2.7/site-packages/sympy/solvers/tests/test_solvers.pyt   test_solve_polynomial_cv_1bå   s    Qc           C   s©   t  t d t d t ƒ t d d ƒ t t d ƒ d t d d ƒ t t d ƒ d g t d d ƒ t t d ƒ d t d d ƒ t t d ƒ d g g k s¥ t ‚ d S(   s‰   
    Test for solving on equations that can be converted to a polynomial equation
    multiplying both sides of the equation by x**m
    i   i   i   N(   R(   R_   R   R   R*   Ro   (    (    (    s?   lib/python2.7/site-packages/sympy/solvers/tests/test_solvers.pyt   test_solve_polynomial_cv_2ê   s    ?c          C   sG  t  d d t  d d t  d d t  d }  t |  d t ƒ} xA | D]9 } |  j t  | j ƒ  ƒ j ƒ  } t | d	 ƒ sG t ‚ qG Wt  d d
 t  d d t  d d t  d }  t |  ƒ } x# | D] } | j t k sÅ t ‚ qÅ Wt	 t t  d d t  d d ƒ d	 d t ƒt t  d d t  d d d	 ƒ j ƒ  k sCt ‚ d  S(   Ni   in   i   i7   i   i	  iÓ  t   checki    i   i
   i   i   t   exponent(
   R_   R(   Rw   t   subsRi   t   tnRo   t   funcRP   R?   (   Rp   t   sR0   t   res(    (    s?   lib/python2.7/site-packages/sympy/solvers/tests/test_solvers.pyt   test_quintics_1ô   s    ..	-c          C   sN   t  t d d t d ƒ }  t d „  |  Dƒ ƒ rD t |  ƒ d k sJ t ‚ d  S(   Ni   i   c         s   s   |  ] } t  | t ƒ Vq d  S(   N(   t
   isinstanceRP   (   R   t   i(    (    s?   lib/python2.7/site-packages/sympy/solvers/tests/test_solvers.pys	   <genexpr>  s    (   R(   R_   Rˆ   t   lenRo   (   t   sol(    (    s?   lib/python2.7/site-packages/sympy/solvers/tests/test_solvers.pyt   test_highorder_poly  s    c          C   sÐ   t  d d t  d }  t |  d t ƒ} xA | D]9 } |  j t  | j ƒ  ƒ j ƒ  } t | d ƒ s/ t ‚ q/ Wt  d d t  d d t  d d t  d	 }  t |  ƒ } x# | D] } | j t k s­ t ‚ q­ Wd  S(
   Ni   i   i   Rž   i    i   i   i
   i   (	   R_   R(   Rw   R    Ri   R¡   Ro   R¢   RP   (   Rp   R£   R0   R¤   (    (    s?   lib/python2.7/site-packages/sympy/solvers/tests/test_solvers.pyt   test_quintics_2  s    .c           C   sH   t  t t d t d t d t d ƒ t ƒ t d g k sD t ‚ d S(   s!   Test solve for rational functionsi   i   i   N(   R(   R_   R`   R*   Ro   (    (    (    s?   lib/python2.7/site-packages/sympy/solvers/tests/test_solvers.pyt   test_solve_rational  s    c           C   s
  t  t d t d t t d t ƒi t t 6i t t 6g k sE t ‚ t  t d t d t t ƒ t t d t ƒi d t t d ƒ t 6g k s— t ‚ t  t d t d t t ƒ t t d t ƒi t t t t ƒ ƒ t 6i t t t t ƒ ƒ t 6g k st ‚ d  S(   Ni   Rm   (   R(   R_   R`   Rg   Ro   R    R
   R*   (    (    (    s?   lib/python2.7/site-packages/sympy/solvers/tests/test_solvers.pyt   test_solve_nonlinear#  s    ERFc          C   sˆ   t  d ƒ }  t t |  d d |  d d d d |  d d ƒ |  ƒ g  k sT t ‚ t t |  d |  d |  ƒ |  ƒ g  k s„ t ‚ d  S(   NR_   i   i   i   (   R,   R(   R   Ro   (   R_   (    (    s?   lib/python2.7/site-packages/sympy/solvers/tests/test_solvers.pyt   test_issue_8666*  s    Hc           C   sJ   t  d d t d d t d t ƒ t d d ƒ t j g k sF t ‚ d  S(   Ni   i   i   i   (   R(   R_   R   R   t   HalfRo   (    (    (    s?   lib/python2.7/site-packages/sympy/solvers/tests/test_solvers.pyt   test_issue_72280  s    c           C   s@   t  t t d ƒ t t d ƒ t ƒ t d ƒ g k s< t ‚ d  S(   Ni   i
   (   R(   R"   R_   R*   Ro   (    (    (    s?   lib/python2.7/site-packages/sympy/solvers/tests/test_solvers.pyt   test_issue_71904  s    c          C   s-  t  d ƒ \ }  } } } } t |  d |  | |  d | | d g |  | g ƒ g  k s\ t ‚ t |  d |  | |  d | |  d g |  | g ƒ g  k s t ‚ t |  d |  d |  | |  d | g |  | g ƒ g  k sÞ t ‚ t |  d | d d |  d | d g |  | ƒ i d |  6d | 6k s,t ‚ t d d | | d | d d d g | d | d d	 | d | d d g d
 d d d d g g ƒ } t | |  | | | ƒ i | | | |  6| | | | 6d | 6k sÞt ‚ t |  | | | | | g |  | | | ƒ i | |  6| | 6k s)t ‚ d  S(   Ns   x, y, z, t, ni   i   i   iýÿÿÿi   i   i    iþÿÿÿiÿÿÿÿ(   R,   R(   Ro   R   R@   (   R_   R`   Ra   Rb   Ri   t   M(    (    s?   lib/python2.7/site-packages/sympy/solvers/tests/test_solvers.pyt   test_linear_system8  s    AAAN%'6c          C   sÙ   t  d ƒ }  t |  d d ƒ |  d d ƒ |  d d ƒ |  d d ƒ |  d d ƒ |  d d ƒ g |  d d ƒ |  d d ƒ |  d d ƒ |  d d ƒ ƒ i |  d d ƒ |  d d ƒ 6|  d d ƒ |  d d ƒ 6k sÕ t ‚ d  S(   NRX   i    i   (   R   R(   Ro   (   RX   (    (    s?   lib/python2.7/site-packages/sympy/solvers/tests/test_solvers.pyt   test_linear_system_functionL  s    Sc          C   sÆ   t  d ƒ }  t d d d d g d d d |  d g d d |  d d g g ƒ } t | t t t g ƒ i d |  d d	 |  t 6d d
 |  |  d d	 |  t 6d |  |  d d	 |  t 6k sÂ t ‚ d  S(   NRi   i   i   i    i   i   iÿÿÿÿiýÿÿÿi   i   i   (   R   R   RA   R_   R`   Ra   Ro   (   Ri   R²   (    (    s?   lib/python2.7/site-packages/sympy/solvers/tests/test_solvers.pyt   test_linear_systemLUR  s
    A/c             s6  d d l  m }  m } t t t ƒ d t ƒ t d ƒ g k sD t ‚ t t |  t | t t ƒ d t ƒ ƒ t | |  t d ƒ g ƒ k s’ t ‚ t t	 t ƒ t
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 t t t ƒ t t
 ƒ t t ƒ g k s2t ‚ d  S(#   Niÿÿÿÿ(   RX   RY   i   i   iýÿÿÿi   i   i   iûÿÿÿi   i    i Øÿÿi   iëÿÿÿi   i   iüÿÿÿc         3   s3   |  ]) } ˆ  j  t | ƒ j d  t ƒ d k Vq d S(   t   chopi    N(   R    R_   Ri   Rg   (   R   RX   (   Rx   (    s?   lib/python2.7/site-packages/sympy/solvers/tests/test_solvers.pys	   <genexpr>„  s    i   i	   ia	  i
   Rp   c              s#   t  ˆ  t t ƒ ˆ  d d ƒ t ƒ S(   Ni   i   (   R(   R_   R`   (    (   Rp   (    s?   lib/python2.7/site-packages/sympy/solvers/tests/test_solvers.pyR†   ±  R‡   c              s'   t  ˆ  t t ƒ ˆ  d t d ƒ t ƒ S(   Ni   (   R(   R_   R`   (    (   Rp   (    s?   lib/python2.7/site-packages/sympy/solvers/tests/test_solvers.pyR†   ²  R‡   c              s$   t  ˆ  t t ƒ ˆ  d t ƒ t ƒ S(   Ni   (   R(   R_   R`   (    (   Rp   (    s?   lib/python2.7/site-packages/sympy/solvers/tests/test_solvers.pyR†   ³  R‡   c              s    t  ˆ  t t ƒ ˆ  d ƒ t ƒ S(   Ni   (   R(   R_   R`   (    (   Rp   (    s?   lib/python2.7/site-packages/sympy/solvers/tests/test_solvers.pyR†   ´  R‡   c           S   s>   t  t t ƒ t t t ƒ ƒ t t ƒ t t t ƒ ƒ d ƒ S(   Ni   (   R(   R'   R_   R   (    (    (    s?   lib/python2.7/site-packages/sympy/solvers/tests/test_solvers.pyR†   º  s    c           S   s   t  t d t t d t ƒ S(   Ni   i   (   R(   R_   R`   (    (    (    s?   lib/python2.7/site-packages/sympy/solvers/tests/test_solvers.pyR†   ¾  R‡   s   a, bt   realt   negativeg      à?sP   [2.0 - 0.318309886183791*acos(1.0 - 2.0*a), 0.318309886183791*acos(1.0 - 2.0*a)]("   t	   sympy.abcRX   RY   R(   R    R_   R"   Ro   R„   R   R`   R   R#   R   R&   R*   R   R
   R¨   t   expandR0   R   R   Rˆ   Ra   R   R   RT   Rv   t
   ValueErrorR,   Rg   Rw   t   str(   RX   RY   R   t   result(    (   Rx   Rp   s?   lib/python2.7/site-packages/sympy/solvers/tests/test_solvers.pyt   test_solve_transcendental_  s˜    .N@LB*#)%+'<.3.5##='L*@&ACW4K,*O!LT 6>7P>P6660347UX6BJ.2.-c          C   s3  t  d ƒ }  t d ƒ |  ƒ } t d ƒ |  ƒ } t d ƒ \ } } } } } } t | | | | | | | | | | g | | ƒ }	 |	 i | | | | | | | | | 6| | | | | | | | | 6k sÞ t ‚ t | d | ƒ d g k s t ‚ t d | d | ƒ t d d ƒ g k s/t ‚ t | | j |  ƒ | | j |  ƒ | | | j |  ƒ | | j |  ƒ | g | j |  ƒ | j |  ƒ ƒ }	 |	 i | | | | | | | | | j |  ƒ 6| | | | | | | | | j |  ƒ 6k st ‚ t | j |  ƒ d | j |  ƒ ƒ d g k s;t ‚ t d | j |  ƒ d | j |  ƒ ƒ t d d ƒ g k s|t ‚ t d | d d | d f ƒ }
 t |
 t | | f ƒ ƒ i t d d ƒ | 6d | 6k sÜt ‚ t  d ƒ } t d	 ƒ } | d | | ƒ d d | d } t | j | ƒ t | | ƒ | ƒ ƒ | d | | ƒ g k s]t ‚ t  d ƒ } t d ƒ |  ƒ } t | | | | j |  ƒ | | | | | j |  ƒ | g | | j |  ƒ ƒ }	 |	 i | | | | | | | | | j |  ƒ 6| | | | | | | | | 6k s/t ‚ d  S(
   NRb   R_   R`   s   a11,a12,a21,a22,b1,b2i   i   i   i   Rp   (   R   R   R,   R(   Ro   R   R   R„   (   Rb   R_   R`   R’   R“   R”   R•   R–   R—   t   solnt   eqnsRp   t   F(    (    s?   lib/python2.7/site-packages/sympy/solvers/tests/test_solvers.pyt$   test_solve_for_functions_derivativesÌ  s8    8#/"/(F284A">$E42c          C   s–   t  d ƒ }  t d |  t ƒ d d t d } | j t ƒ } t | |  t ƒ j t ƒ ƒ d t |  t ƒ g t d |  t ƒ g g k s’ t ‚ d  S(   NRp   i   i   i   (   R   R_   R   R(   Ro   (   Rp   RÁ   Rh   (    (    s?   lib/python2.7/site-packages/sympy/solvers/tests/test_solvers.pyt   test_issue_3725ô  s    $c          C   sš  t  d ƒ \ }  } } } t d d |  | | | g ƒ } t d d d d d d g ƒ } t d d d d d d g ƒ } t | | | |  | | | g ƒ i d |  6t d ƒ d | 6d | 6d | 6k sÈ t ‚ t | | | g |  | | | g ƒ i d |  6t d ƒ d | 6d | 6d | 6k s!t ‚ t t | | | ƒ |  | | | g ƒ i d |  6t d ƒ d | 6d | 6d | 6k s|t ‚ t | | | | g |  | | | g ƒ i | |  6t d ƒ d | | 6k sÏt ‚ t | | | | g |  | | | g ƒ i | | |  6t d ƒ d | | 6k s%t ‚ t | | | | | | | | g |  | | | g ƒ i | |  6d | 6d | 6k st ‚ t t | | | | ƒ g |  | | | g ƒ i | |  6t d ƒ d | | 6k s×t ‚ t t | | | | ƒ g |  | | | g ƒ i | | |  6t d ƒ d | | 6k s2t ‚ t t | | | | ƒ t | | | | ƒ g |  | | | g ƒ i | |  6d | 6d | 6k s–t ‚ d  S(	   Ns   a b c di   i    iýÿÿÿi   i   i   iÿÿÿÿ(   R,   R   R(   R   Ro   R   (   RX   RY   RZ   R[   t   At   Bt   C(    (    s?   lib/python2.7/site-packages/sympy/solvers/tests/test_solvers.pyt   test_issue_3870û  s    VY[SVZX[c          C   sR  t  d ƒ }  t t t ƒ d k s' t ‚ t t d t g ƒd k sH t ‚ t t d |  g ƒd k si t ‚ t t t d t ƒ t t d f t d t f g k s¦ t ‚ t t t d t d t g ƒt d t f k sÜ t ‚ t d t t d ƒ t t d f t d t f g k st ‚ t d t t d t g ƒ t t d f k sLt ‚ t d t t d t g ƒ t d t f k st ‚ t t d t d ƒ t t d f k s¬t ‚ t |  t ƒ |  t f t |  f g k sÙt ‚ t t t ƒ d t t ƒ d d t ƒ t d t t ƒ d t t ƒ d f k s3t ‚ t t t ƒ d t t ƒ d d t d t g ƒd k stt ‚ t t t d ƒ ƒ t d f k s›t ‚ t d d t d ƒ d k s¿t ‚ t t d t t ƒ d t g ƒt d	 f k sõt ‚ t t d t t ƒ d t g ƒt d t t ƒ d f k s8t ‚ t t t t d ƒ d t g ƒt d f k snt ‚ t d t d ƒ d t d d f k sœt ‚ t d d t d ƒ t d f k sÆt ‚ t t t ƒ d t t t ƒ d t } t | ƒ d k st ‚ t t ƒ d t t ƒ d } t | ƒ d k s>t ‚ t	 t
 d
 „  ƒ d  S(   Nt   wi    i   R…   R,   i   i   iþÿÿÿiÿÿÿÿc           S   s   t  t t d ƒ d ƒ S(   Ni   (   R)   R   R_   (    (    (    s?   lib/python2.7/site-packages/sympy/solvers/tests/test_solvers.pyR†   (  R‡   (   i    i   (   i    i   (   i    i   (   i    i   (   i    i    (   i    i   (   i    i   (   R   R)   R_   Ro   R`   R   R&   R   R    RT   R»   (   RÈ   Rx   (    (    s?   lib/python2.7/site-packages/sympy/solvers/tests/test_solvers.pyt   test_solve_linear  s4    !!=6=33--)1A'$6C6.**c           C   sb  t  t t d t t d t t d t t t d t t t g t ƒ i d t 6d t 6d t 6k sl t ‚ t  t t t t d d t d t d t t t g t ƒ i d t 6d t 6k sÆ t ‚ t  t d t t d t d t t d t d t t t d d t t t d d t d t t t g t ƒ i d t 6d t 6d t 6k s^t ‚ d  S(   Ni   i   iþÿÿÿiÿÿÿÿ(   RB   RX   R_   RY   RZ   Ro   (    (    (    s?   lib/python2.7/site-packages/sympy/solvers/tests/test_solvers.pyt   test_solve_undetermined_coeffs+  s    H$=qc       
   C   sy  t  d ƒ }  t t d ƒ |  k  |  t k  ƒ } t |  d d k ƒ | k sO t ‚ t |  d d k g ƒ | k st t ‚ t |  d d k g |  ƒ | k sœ t ‚ t |  d d k g |  g ƒ | k sÇ t ‚ t |  d d d ƒ t |  d d d ƒ g } t | ƒ t t t t t	 d ƒ |  ƒ t |  d ƒ ƒ t t d |  ƒ t |  t	 d ƒ ƒ ƒ ƒ t
 d d ƒ ƒ k skt ‚ t  d d t ƒ}  t |  d d d ƒ t |  d d d ƒ g } t | ƒ t t t t	 d ƒ |  ƒ t |  d ƒ ƒ t t d |  ƒ t |  t	 d ƒ ƒ ƒ ƒ k st ‚ t |  d |  d d k  |  ƒ t t d |  ƒ t |  d ƒ ƒ k sWt ‚ t |  |  d d k |  ƒ t t t |  ƒ t |  d ƒ ƒ k sœt ‚ t t |  ƒ t j k ƒ t t d |  k  |  d	 t d k  ƒ k sät ‚ t t
 t |  d k  ƒ ƒ t d ƒ |  k |  t k  @k s!t ‚ t t
 t |  d k  ƒ ƒ t |  k  |  d k  @k sYt ‚ t t
 |  d k  t ƒ ƒ t d ƒ |  k |  t k  @k s–t ‚ t t
 |  d k  t ƒ ƒ t |  k  |  d k  @k sÎt ‚ t t
 t |  ƒ ƒ t k sït ‚ t t
 t |  ƒ ƒ t k st ‚ t t
 t |  ƒ ƒ t k s2t ‚ t t
 t |  ƒ ƒ t k sTt ‚ t t t |  ƒ ƒ t k sut ‚ d  S(
   NR_   i    i   i   iÿÿÿÿR·   i   i   i   (   R   R   R   R9   R(   Ro   R   R   R   R*   R   Rg   R&   R¯   R#   Rw   R   (   R_   R©   t   system(    (    s?   lib/python2.7/site-packages/sympy/solvers/tests/test_solvers.pyt   test_solve_inequalities7  s4    !"%(+.	+B.	[HEH=8=8!!""c       	      sŒ  t  d t ƒ g  k s t ‚ t  t d d t ƒ d g k sC t ‚ t  t t t ƒ d ƒ d g k sl t ‚ t  d t d t d d d t ƒ g  k s¡ t ‚ t  t d d t t d d d ƒ g  k sÖ t ‚ t  t t d d d ƒ g  k sþ t ‚ t  t t t d d ƒ t ƒ d g k s.t ‚ t  t t ƒ t t ƒ t t ƒ g k s\t ‚ t  t t ƒ ƒ g  k szt ‚ t  t d t t t ƒ d t t ƒ d d t ƒ d d g d d g g k sÏt ‚ d d d t d d	 ‰  t  ˆ  t ƒ }  t	 |  ƒ d k r&t
 ‡  f d
 †  |  Dƒ ƒ s,t ‚ t  t t d ƒ t d t t ƒ t t d t ƒt t g t t t t ƒ t t d ƒ ƒ f t t t t ƒ t t d ƒ ƒ f h f k s¿t ‚ t  t d t d t d t d ƒ i t t 6i t t 6i d t 6g k st ‚ t  t d d d t d ƒ g  k s>t ‚ t  t t t t t ƒ d g k sht ‚ t t d „  ƒ t t d „  ƒ d  S(   Ni   i   i   i   iþÿÿÿi    iÿÿÿÿi   i   c         3   s3   |  ]) } ˆ  j  t | ƒ j d  t ƒ d k Vq d S(   R¶   i    N(   R    R_   Ri   Rg   (   R   RX   (   Rx   (    s?   lib/python2.7/site-packages/sympy/solvers/tests/test_solvers.pys	   <genexpr>h  s    R„   c           S   s   t  t t ƒ t t ƒ t ƒ S(   N(   R(   R"   R_   R    (    (    (    s?   lib/python2.7/site-packages/sympy/solvers/tests/test_solvers.pyR†   o  R‡   c           S   s   t  d t t t ƒ d ƒ S(   Ni   i   (   R(   R_   R    (    (    (    s?   lib/python2.7/site-packages/sympy/solvers/tests/test_solvers.pyR†   p  R‡   (   R(   R_   Ro   R*   R    R`   R"   R&   R   R¨   Rˆ   Rg   Ra   RT   Rv   (   R   (    (   Rx   s?   lib/python2.7/site-packages/sympy/solvers/tests/test_solvers.pyt   test_issue_4793[  s*    ')55(0.U41	YS,*c       	   C   su  t  t t ƒ ƒ t  t t d ƒ ƒ k o6 d g k n sA t ‚ t  t t d ƒ ƒ d g k sf t ‚ t d ƒ }  t  d |  t t ƒ t ƒ g  k s› t ‚ t  d t t d d t ƒ d g k sÉ t ‚ t t  t d d t j t ƒ ƒ ƒ t t d ƒ t d ƒ g ƒ k st ‚ t d	 ƒ } t  d d
 t | t ƒ | t ƒ | t ƒ ƒ d
 t d g k sht ‚ t  d t	 d
 t d
 ƒ d t ƒ d t d ƒ g k s¥t ‚ t  t t ƒ t t t ƒ ƒ d ƒ t j
 t d ƒ d d g k sðt ‚ t t  t t t t ƒ ƒ t t t ƒ ƒ d ƒ ƒ ƒ t t t d ƒ d d ƒ t t d ƒ d d ƒ g ƒ t d t t d ƒ d ƒ d t t d ƒ d ƒ g ƒ t t d t d ƒ d ƒ t d t d ƒ d ƒ g ƒ g k sÜt ‚ t t  t t t ƒ t t ƒ d ƒ ƒ ƒ t t t d ƒ d ƒ t t d ƒ d ƒ g ƒ k sBt ‚ t t  t t t d t d t ƒ ƒ t t j
 t d
 ƒ d d t t j
 t d
 ƒ d d t g ƒ k s·t ‚ t  t t t ƒ t t t ƒ d t ƒ t t t d ƒ g k s t ‚ t  t t t t d t ƒ t d ƒ t t ƒ t t ƒ g t d ƒ t t t ƒ g g k set ‚ t j } t  t d t ƒ t d ƒ t ƒ d t | t j
 t d ƒ t d ƒ t | t j
 t d ƒ t d ƒ g d t | d t d ƒ | t d ƒ t | d t d ƒ | t d ƒ g g k s7t ‚ t d d t ƒ} t  d | d | d ƒ g  k sqt ‚ d  S(   Ni   i    i   RX   iýÿÿÿi   i   i   Rp   i   i	   i´~ûÿi©æ  i   i   iüÿÿÿR^   t   positive(   R(   R*   R_   Ro   R   R„   R   R   R   R0   R¯   R   R    R"   R`   Ra   t   Exp1R   Rg   (   RX   Rp   R:   R^   (    (    s?   lib/python2.7/site-packages/sympy/solvers/tests/test_solvers.pyt   test_PR1964s  s6    A%).KH=K688F*<&OIb	 L]c          C   sc  t  d d t ƒ}  t |  d d |  ƒ g  k s5 t ‚ t  d d t d t ƒ} t | d | d d | d | ƒ d g k sƒ t ‚ t  d d t ƒ}  t  d ƒ } t |  d	 | d d
 |  d | d g |  | ƒ g  k sá t ‚ t |  | | | d d |  | ƒ t d ƒ t d ƒ f g k s)t ‚ t  d d t ƒ} t |  d | d t |  ƒ | |  d t ƒi |  t |  d ƒ | 6g k st ‚ t |  d | d t |  ƒ |  | d t ƒi d t | d ƒ |  6g k sßt ‚ t d d t ƒ\ }  } } t | d |  d | d | d t |  ƒ | |  | d t ƒi |  t |  d ƒ | 6g k s_t ‚ d  S(   NR_   R·   i   i   Ri   t   integerRÎ   R`   i   iýÿÿÿi   i   Rm   s   x y z(   R   Rg   R(   Ro   R*   R    R
   R,   (   R_   Ri   R`   Ra   (    (    s?   lib/python2.7/site-packages/sympy/solvers/tests/test_solvers.pyt   test_issue_5197   s    #6@HRRc           C   sÿ   t  t t t t t t d t ƒƒ t  t t ƒ t d ƒ t t ƒ g ƒ k sU t ‚ t  t t t t t t d t ƒƒ t  t t ƒ t t ƒ g ƒ k s¡ t ‚ t d d t d d t d d f ƒ g  k s× t ‚ t d d t d ƒ g  k sû t ‚ d  S(   NRž   i    i   i   i   (	   R„   R(   R_   R`   Rw   R*   R   Ro   Rg   (    (    (    s?   lib/python2.7/site-packages/sympy/solvers/tests/test_solvers.pyt   test_checking³  s
    RL6c       	   C   sƒ  t  t t d d ƒ d ƒ t d ƒ t d ƒ g t d ƒ t d ƒ g f k sV t ‚ t  d t t d t ƒ d t d d t ƒ t t t t d ƒ ƒ t t d ƒ t t ƒ ƒ t t t t d ƒ ƒ t t d ƒ t t ƒ ƒ g k sø t ‚ t	 d ƒ \ }  } t
 d ƒ } t  |  | t d t | t ƒ ƒ | t ƒ ƒ t t d |  t d | ƒ g k sqt ‚ t d ƒ } t j } t  d t | d t d ƒ t ƒ t | | ƒ d t | | ƒ d g t | | ƒ d t | | ƒ d g f k st ‚ t  t | d	 t d ƒ | t ƒ t d
 | d	 ƒ t d
 | d	 ƒ g t d
 | d	 ƒ t d
 | d	 ƒ g f k s„t ‚ t  d t | d t d ƒ t ƒ t | | ƒ d t | | ƒ d g t | | ƒ d t | | ƒ d g f k st ‚ t t  | d d t | t ƒ t | t ƒ t ƒ ƒ t t d | d t d | g ƒ k skt ‚ t  d t | t ƒ t | t ƒ t ƒ t d ƒ | g k s¯t ‚ t t  d t | t ƒ t | t ƒ d t ƒ ƒ t t d t d ƒ ƒ | t t d ƒ d ƒ | t t d ƒ d ƒ | t d t d ƒ ƒ | g ƒ k sTt ‚ t  t t ƒ d ƒ t d ƒ g k st ‚ d  S(   Ni   i   i   i   s   C1 C2Rp   RX   i   iýÿÿÿiÿÿÿÿi   iþÿÿÿ(   R(   R*   R_   Ro   R    R`   R"   R   R#   R,   R   R   R   RÏ   R„   R&   R   R'   R   R   R.   (   t   C1t   C2Rp   RX   R:   (    (    s?   lib/python2.7/site-packages/sympy/solvers/tests/test_solvers.pyt   test_issue_4671_4463_4467½  s4    1%.2B[	"(7"&5"(7`D22Ac       	   C   sƒ  t  d ƒ \ }  } t t |  t d t d t | ƒ t t g t t g ƒ ƒ t t |  t | ƒ d ƒ d t |  t | ƒ d ƒ t | ƒ f t |  t | ƒ d ƒ t |  t | ƒ d ƒ t | ƒ f g ƒ k sÞ t ‚ t t	 t ƒ t
 t ƒ d t d g t t g ƒ t t
 t d ƒ d ƒ ƒ t d ƒ d f g k sFt ‚ t t	 t ƒ t
 t ƒ d t	 t ƒ d g t t g ƒ t t
 t d ƒ ƒ ƒ t d ƒ f g k s®t ‚ t t t	 t ƒ t
 t ƒ t d d g t t g ƒ ƒ t t t
 d ƒ ƒ t d ƒ f t t
 d ƒ ƒ t d ƒ f g ƒ k s1t ‚ t	 t ƒ d t
 t ƒ t d d t	 t ƒ d g } t | d t ƒt t g t t t t d t
 t d ƒ ƒ ƒ ƒ t d ƒ f t t d t
 t d ƒ ƒ ƒ d t d ƒ f g ƒ f k søt ‚ t | t t d t ƒt t g t t d t
 t ƒ ƒ d t f t t t d t
 t ƒ ƒ ƒ t f h f k sot ‚ t t | t t ƒ ƒ t t t t d t
 t d ƒ ƒ ƒ ƒ t d ƒ f t t d t
 t d ƒ ƒ ƒ d t d ƒ f g ƒ k sút ‚ t t | t t ƒ ƒ t t d ƒ t t	 d t ƒ t
 t d ƒ ƒ ƒ f t d ƒ t t	 d t ƒ t
 t d ƒ ƒ ƒ f g ƒ k s‡t ‚ t	 t ƒ d t
 t ƒ t d t	 t ƒ d g } t | d t ƒt t g t t t t t
 t d ƒ ƒ ƒ ƒ t d ƒ f t t t
 t d ƒ ƒ ƒ d t d ƒ f g ƒ f k sBt ‚ t | t t d t ƒt t g t t t t
 t ƒ ƒ ƒ t f t t t
 t ƒ ƒ d t f h f k s±t ‚ t t | t t ƒ ƒ t t t t t
 t d ƒ ƒ ƒ ƒ t d ƒ f t t t
 t d ƒ ƒ ƒ d t d ƒ f g ƒ k s4t ‚ t | t t ƒ t	 d t ƒ t
 t d ƒ ƒ t d ƒ f g k s}t ‚ t t t d t d ƒ t d ƒ t t d f d t ƒt t g t t d ƒ t d ƒ f t d ƒ t d ƒ f g ƒ f k st ‚ t t t t d t d ƒ t d ƒ t t d f t t ƒ ƒ t t d ƒ t d ƒ f t d ƒ t d ƒ f g ƒ k st ‚ d  S(	   Ns   r,ti   iÿÿÿÿi   i   i   R„   i
   (   R,   R„   R(   R_   R`   R.   R*   R   Ro   R    R&   R"   R   Ra   Rg   (   t   rRb   R‚   (    (    s?   lib/python2.7/site-packages/sympy/solvers/tests/test_solvers.pyt   test_issue_5132ß  sV    <@M08626M62D	Y2A2C2.@	Q.=:9K?c          C   så   t  d ƒ \ }  } } d } d } |  d t | d t d t | t d t | d t d t d t | t t t | g } t t | g } t t | | d t d t ƒƒ d k sÀ t ‚ t t | | ƒ ƒ d k sá t ‚ d  S(   Ns   lam a0 concg{®Gázt?gÌ«¢Ã;Êç?i   i   t   manualt   minimal(   R,   R`   R_   R¨   R(   Rg   Ro   (   t   lamt   a0t   concRX   RY   R‚   t   sym(    (    s?   lib/python2.7/site-packages/sympy/solvers/tests/test_solvers.pyt   test_issue_5335  s    /#-t   Hangsc          C   s¾   t  d ƒ \ }  } } d } d } |  d t | d t d t | t d t | d t d t d t | t t t | g } t t | g } t t | | d t ƒƒ d k sº t ‚ d  S(   Ns   lam a0 concg{®Gázt?gÌ«¢Ã;Êç?i   i   t   rational(   R,   R`   R_   R¨   R(   Rw   Ro   (   RÛ   RÜ   RÝ   RX   RY   R‚   RÞ   (    (    s?   lib/python2.7/site-packages/sympy/solvers/tests/test_solvers.pyt   _test_issue_5335_float  s    /#c           C   s`   t  t t d t d g t g ƒ ƒ t  t t d ƒ f t t d ƒ f g ƒ k s\ t ‚ d  S(   Ni   i   (   R„   R(   R_   R`   R*   Ro   (    (    (    s?   lib/python2.7/site-packages/sympy/solvers/tests/test_solvers.pyt   test_issue_5767)  s    $c           C   s4  t  t t d d t d t t d g t t g ƒ ƒ t  t d ƒ t d ƒ f d t d ƒ d t d ƒ f d t d ƒ d t d ƒ f g ƒ k sš t ‚ t t d t d t d t g ƒ g  k sÌ t ‚ t t d t d t t d g t t f ƒ t t d t d t t d g t t f ƒ k s0t ‚ d  S(   Ni   i   i   i   i   (   R„   R(   R_   R`   R   R*   Ro   (    (    (    s?   lib/python2.7/site-packages/sympy/solvers/tests/test_solvers.pyt   test_polysys.  s    65/2/c    	   
      sh"  t  t d „  ƒ t  t d „  ƒ t d d t ƒ‰ ‡ f d †  }  ‡ f d †  ‰ |  t t t ƒ ƒ t g  f ƒ sw t ‚ |  t t t ƒ d ƒ t d g  f ƒ s¦ t ‚ |  t t t ƒ t t d ƒ d	 ƒ ˆ d ˆ d	 d	 ˆ ˆ d
 t g f ƒ sü t ‚ |  t t t ƒ t t d ƒ d	 ƒ t d d g  f ƒ s<t ‚ |  t t t ƒ t d t	 d d ƒ ƒ t d t d d	 g  f ƒ sˆt ‚ |  t t t ƒ t t d ƒ t d	 t ƒ ƒ d t d	 ƒ t d	 t d g  f ƒ såt ‚ |  t t t ƒ t t d ƒ d	 ƒ d t d g  f ƒ s&t ‚ |  t t t ƒ t t d ƒ t d t ƒ ƒ d t d	 d t g  f ƒ syt ‚ |  t t
 t t ƒ t t t ƒ t t t ƒ t t t ƒ ƒ t
 t t ƒ t t t ƒ d	 t t t ƒ t t t ƒ d	 g  f ƒ s
t ‚ |  t t t ƒ t d t ƒ ƒ d	 t d g  f ƒ sGt ‚ |  t t t ƒ t d t ƒ d ƒ t d	 t d g  f ƒ sŒt ‚ |  t t t ƒ t d t ƒ t d	 t ƒ ƒ d t d	 d	 t d g  f ƒ sãt ‚ t t t ƒ t d t ƒ t d	 t ƒ d ƒ d t d d t d d t d	 d t d g  f d t d d t d
 d t d d t d	 d g  f g k st ‚ t t t ƒ t d t ƒ t d	 t ƒ t d d	 t ƒ ƒ d t d d t d d t d	 d t d g  f k st ‚ |  t t t ƒ t t d ƒ ƒ t d ƒ g  f ƒ sHt ‚ t t ƒ t t d ƒ t d t t ƒ ƒ } |  t | ƒ d t d	 d t g  f ƒ s§t ‚ t t | d t ƒƒ t t d  ƒ t d ƒ d g ƒ k sçt ‚ t | ƒ g  k sÿt ‚ t t t t ƒ t t d ƒ t d t t ƒ ƒ ƒ ƒ t t j t d ƒ d g ƒ k s^t ‚ |  t t t ƒ t t d d ƒ d	 t t ƒ t ƒ t d! ƒ g  f ƒ s­t ‚ |  t t t d t ƒ t d t	 d d ƒ ƒ t d t d t d d	 t d	 t d g  f ƒ st ‚ |  t t t d t ƒ d	 t t ƒ t ƒ d t t t d t g  f ƒ smt ‚ |  t t t ƒ t d t ƒ d	 t ƒ t d	 t d g  f ƒ sµt ‚ t t t t t d
 ƒ ƒ ƒ d g k sãt ‚ t t t t t d ƒ d ƒ ƒ d g k st ‚ t t d t t d	 t d ƒ ƒ ƒ g  k sHt ‚ t t t t d t d
 ƒ d	 t ƒ ƒ ƒ t t d ƒ t d	 ƒ g ƒ k sšt ‚ t t t t d	 t d ƒ t t d ƒ d	 ƒ ƒ ƒ t t d ƒ t d" ƒ g ƒ k sõt ‚ t t t t d# ƒ d	 t d t ƒ ƒ ƒ d$ g k s1	t ‚ t d	 t d t	 d d ƒ d ƒ d g k se	t ‚ t t t d t t d d t d t d ƒ ƒ ƒ t t d ƒ d	 t d ƒ d g ƒ k sÊ	t ‚ t t t d	 t d	 d# ƒ d t ƒ ƒ t t d ƒ t d	 ƒ g ƒ k s
t ‚ t t d	 t d ƒ t t d ƒ t t d ƒ ƒ d  g k s`
t ‚ t t t d ƒ t d	 t d ƒ d t t d ƒ ƒ d g k s©
t ‚ t t t ƒ t t d# ƒ d% ƒ d g k sÜ
t ‚ t t t d ƒ t t ƒ d ƒ d g k st ‚ t t d t d	 d ƒ d t d	 ƒ d  g k sHt ‚ t t t ƒ d	 d ƒ d& g k sqt ‚ t t t d ƒ t t ƒ d ƒ g  k s¡t ‚ t t t d ƒ t d# ƒ d' g k sÎt ‚ t t t d	 ƒ d ƒ d( g k s÷t ‚ t t d) t t t d	 d ƒ ƒ d# ƒ d g k s2t ‚ t t t ƒ t t d ƒ t t t ƒ ƒ ƒ g  k snt ‚ t d	 t d ƒ t t ƒ t d	 d t ƒ } t | ƒ d  } t | ƒ g  k sÆt ‚ t | ƒ g  k sÞt ‚ t | d
 t ƒ t d ƒ d* g k st ‚ t | d
 t ƒ g  k s,t ‚ t t t d d ƒ t t d ƒ ƒ t d t d d t d	 d t d g  f k sˆt ‚ |  t t t t d ƒ t t d ƒ d	 t t ƒ t ƒ ˆ d ˆ d	 ˆ t t ƒ ˆ ˆ d t g f ƒ süt ‚ |  t t t ƒ t t d ƒ t ƒ ˆ d ˆ d	 t ˆ ˆ d
 t g f ƒ sRt ‚ t t t ƒ t t d ƒ d	 ƒ d g k s„t ‚ t  t d+ „  ƒ t  t d, „  ƒ t t t t t d ƒ ƒ t t t d ƒ t ƒ t t t d ƒ d t t d ƒ d	 g k s
t ‚ |  t t t ƒ t t d d ƒ t t d	 ƒ d	 ƒ ˆ d' d ˆ d d- ˆ d
 d% ˆ d d. ˆ d d ˆ d d/ ˆ d	 d0 ˆ d1 ˆ ˆ d	 t g f ƒ sºt ‚ t t d d ƒ t t d ƒ } t | ƒ d	 t d g  f k s t ‚ t t ƒ t t d ƒ t d t ƒ d
 t d ƒ d } |  t | ƒ d2 t d d3 t d d4 t d	 d5 t d6 g  f ƒ s‡t ‚ |  t t t d ƒ t t d ƒ d d ƒ ˆ d ˆ d ˆ ˆ d t g f ƒ sàt ‚ |  t t t d	 ƒ t t d	 ƒ d d ƒ t d d	 t d	 t d g  f ƒ s7t ‚ t t d7 ƒ d  k sSt ‚ |  t t t t t d ƒ t t t d ƒ d ƒ ˆ d ˆ t ˆ ˆ d t t g f ƒ s¸t ‚ |  t t t t t d ƒ t t t d ƒ d t ƒ ˆ d ˆ t ˆ ˆ d t t g f ƒ s t ‚ |  t t t t t d ƒ t t t d ƒ d t ƒ ˆ d ˆ d ˆ t ˆ ˆ d t t g f ƒ st ‚ |  t t t d d ƒ t t d d ƒ t d	 d ƒ ƒ ˆ d d d	 t d ƒ d ˆ d ˆ d d' d	 t d	 ƒ d ˆ d d' d	 t d ƒ d ˆ d	 d d	 t d ƒ d ˆ d ˆ ˆ d t d g f ƒ srt ‚ t  t d8 „  ƒ t t t d ƒ t t d ƒ d	 ƒ d g k s·t ‚ t t ƒ t t d ƒ t d t ƒ d
 t d ƒ d } |  t | ƒ d t d d9 t d d: t d	 d; t d< g  f ƒ s>t ‚ t d= ƒ ‰  t | ƒ ˆ  k sbt ‚ |  t t t t t d d ƒ ƒ t t d d ƒ d	 ƒ ˆ d ˆ d	 d ˆ d ˆ ˆ d t d g f ƒ sÙt ‚ t t d	 d d ƒ t t d	 d d ƒ d	 } |  t | ƒ ˆ d d' ˆ d d> ˆ d d? ˆ d	 d? ˆ d@ ˆ ˆ d t d	 d g f ƒ stt ‚ t t t t d d	 ƒ ƒ t t d d ƒ d	 } |  t | ƒ ˆ d
 d	 ˆ d d# ˆ d d ˆ d dA ˆ d	 d ˆ d ˆ ˆ d t d g f ƒ st ‚ |  t | dB t ƒˆ d
 dC ˆ d dD ˆ d dE ˆ d dF ˆ d	 dG ˆ dH ˆ ˆ d	 t t t d ƒ g f ƒ sœt ‚ |  t t t t t t d ƒ d ƒ ƒ t t d
 ƒ d	 ƒ ˆ d% d	 ˆ d d ˆ d# d ˆ d
 ˆ d d ˆ d dI ˆ d	 dJ ˆ d) ˆ ˆ d
 t g f ƒ sMt ‚ t  t dK „  ƒ t t dL ƒ ƒ d  k s{t ‚ |  t t dL ƒ t ƒ ˆ d	 t ˆ d ˆ ˆ d t t g f ƒ sÇt ‚ t t t t ƒ t t d d t ƒ ƒ d k sþt ‚ t t dM t d dN t d	 t d ƒ d t d	 dO t d	 t d	 ƒ d t d t dP t dQ t ƒƒ d k syt ‚ t dR ƒ } t | t ƒ d d	 t d	 ƒ d d( t d( t t d	 ƒ t d ƒ d dS t d ƒ d	 t d ƒ t d	 dT t dU t dV t dU t dW ƒ dU d	 ƒ d	 t dX ƒ dU t d ƒ d d d d	 t d	 ƒ d d( t d( t t d	 ƒ t d ƒ d dS t d ƒ d	 t d ƒ t d	 dT t dU t dV t dU t dW ƒ dU d	 ƒ d	 t dX ƒ dU t d ƒ d d d d	 t d	 ƒ d d( t d( t t d	 ƒ t d ƒ d dS dT t dU t dV t dU t dW ƒ dU d	 ƒ d	 t dX ƒ dU t d ƒ d d g k s¡t ‚ t t d d ƒ t t d ƒ t t d ƒ } |  t | ƒ d ˆ d" d ˆ d* ˆ d d ˆ ˆ dY t g f ƒ st ‚ |  t | d	 ƒ d ˆ d" d ˆ d* d
 ˆ d' ˆ d d% ˆ d d
 ˆ d
 d% ˆ d d% ˆ d d# ˆ ˆ dY t g f ƒ s¬t ‚ |  t t t d ƒ t t d d ƒ d	 t t d	 d ƒ ƒ dZ ˆ d" d[ ˆ d% d\ ˆ d* ˆ d' d] ˆ d ˆ ˆ d t d g f ƒ sBt ‚ |  t t t d ƒ t t d d ƒ t t d	 d ƒ d	 ƒ dU ˆ d" d^ ˆ d% dN ˆ d* d_ ˆ d' d` ˆ d da ˆ d d] ˆ d# db ˆ d dc ˆ d dd ˆ ˆ ˆ d t d g f ƒ st ‚ |  t t t d ƒ d	 t t d d ƒ t t d	 d ƒ ƒ dd ˆ d" dc ˆ d% d] ˆ d* d_ ˆ d' db ˆ d da ˆ d dN ˆ d# d` ˆ d d^ ˆ d dU ˆ ˆ ˆ d t d g f ƒ sæt ‚ |  t t t d ƒ d	 t t d d ƒ t t d	 d ƒ d	 ƒ dd ˆ d" de ˆ d% df ˆ d' dg ˆ d dh ˆ d di ˆ d# dj ˆ d
 dk ˆ d dl ˆ d dm ˆ d dn ˆ d	 do ˆ dp ˆ ˆ d t d g f ƒ sØt ‚ t t t ƒ t t d ƒ t d t ƒ t d	 t ƒ ƒ ‰  t ˆ  ƒ d k r@t ˆ  d  ƒ d  dq k sFt ‚ t dr ƒ } | d	 t d	 t t t d	 t d	 ƒ } d	 | d# t d	 ƒ | dC ‰  t | t d t ƒ} xt t | ƒ D]Z } t t t j t | ƒ j t ƒ t ds t d t ƒ} t  ‡  f dt †  | Dƒ ƒ rÀPqÀqÀWd  s* t ‚ t t t d ƒ t t d ƒ d	 ƒ t du ƒ k sc t ‚ t t t t d ƒ ƒ t t	 d d ƒ d	 ƒ t dv ƒ k s¦ t ‚ t t t ƒ t t t ƒ d d ƒ d	 ƒ t dw ƒ k så t ‚ t dx ƒ } |  t | ƒ ˆ ˆ d
 t d ƒ ˆ d
 t dy d	 t d	 ƒ d d t d ƒ d ˆ d dz d% t d ƒ d ˆ d d{ d	 t d	 ƒ d d t d ƒ d
 ˆ d t d| ˆ d d| t d ƒ ˆ d t d} d~ t d ƒ d ˆ d	 d d t d ƒ t ˆ ˆ d d€ t t d ƒ t d t d	 d‚ t dƒ ƒ d„ g f ƒ sL"t ‚ t | ƒ g  k sd"t ‚ d  S(…   Nc           S   s6   t  t t ƒ t t d ƒ t d t t ƒ ƒ d ƒ S(   Ni   i   (   RD   R*   R_   (    (    (    s?   lib/python2.7/site-packages/sympy/solvers/tests/test_solvers.pyR†   :  s    c           S   s3   t  t t ƒ t d t d d ƒ d t t ƒ ƒ S(   Ni   i   i   (   RD   R*   R_   R   R`   (    (    (    s?   lib/python2.7/site-packages/sympy/solvers/tests/test_solvers.pyR†   <  s    R£   t   clsc            s‚   t  |  d ƒ t  | d ƒ k s& t ‚ | d r= ˆ  |  | ƒ S|  d j ƒ  } | d j ƒ  } | | | g k o |  d | d k S(   Ni   i    (   t   boolRo   Rº   (   t   rvR   Rh   RX   (   t   s_check(    s?   lib/python2.7/site-packages/sympy/solvers/tests/test_solvers.pyRž   C  s    &
c            s  t  |  ƒ }  |  d j t ƒ } t  t | ˆ  g t | ƒ ƒ ƒ } |  d j | ƒ j ƒ  |  d d j | ƒ |  d d j | ƒ g f }  | d j | ƒ j ƒ  | d d j | ƒ | d d j | ƒ g f } t |  d ƒ t | d ƒ t | d ƒ g k ot |  d ƒ t | d ƒ k S(   Ni    i   (   RŠ   t   atomsR   t   zipR¨   R    Rº   R¼   (   Rç   R   R[   t   reps(   R£   (    s?   lib/python2.7/site-packages/sympy/solvers/tests/test_solvers.pyRè   K  s    "GG1i   i   i   i   i   i@   iþÿÿÿi   i	   i   i   ix  iè  ià  i  i   iÜ  iæ	  i¼  i©   i)   i(   iè   i    Rž   i    s3   2*sqrt(x)*(x + 1)**(1/3) + x - 4*y + (x + 1)**(2/3)i   i   iúÿÿÿi   i1   i
   i   i   i   c           S   s2   t  t t ƒ t t d ƒ t t d d ƒ d ƒ S(   Ni   i   i   i   (   R(   R*   R_   R0   (    (    (    s?   lib/python2.7/site-packages/sympy/solvers/tests/test_solvers.pyR†   ²  s    c           S   s   t  t d ƒ t t ƒ t ƒ S(   Ni   (   R(   R*   R   R_   (    (    (    s?   lib/python2.7/site-packages/sympy/solvers/tests/test_solvers.pyR†   µ  R‡   i   i   iÔ   iÀ   i8   i	=  iÈ£ im i { i  g      à?c           S   sE   t  t t d ƒ t t d ƒ t t d ƒ j t t d t d ƒ ƒ S(   Ni   i   i   i   i   (   RD   R0   R_   R    (    (    (    s?   lib/python2.7/site-packages/sympy/solvers/tests/test_solvers.pyR†   Ï  s    i5  iì  iÀ‰ i D s¥   
        [4/5, -1484/375 + 172564/(140625*(114*sqrt(12657)/78125 +
        12459439/52734375)**(1/3)) +
        4*(114*sqrt(12657)/78125 + 12459439/52734375)**(1/3)]i'   iP   i   i   t   _reversei   iI   i»   i  iä   iY   i   i    c           S   s9   t  t t t ƒ t ƒ t t d d ƒ t t ƒ d ƒ S(   Ni   i   (   RD   R*   R   R_   R0   (    (    (    s?   lib/python2.7/site-packages/sympy/solvers/tests/test_solvers.pyR†   õ  s    s!   (x+y)**(2*y/3) + (x+y)**(1/3) + 1i þÿÿi@  i˜  i®  t   _unrads9   -x + (7*y/8 - (27*x/2 + 27*sqrt(x**2)/2)**(1/3)/3)**3 - 1i   i åÿÿiW  i Êÿÿi 6  i   i   i   iÀ  i0   iÀ  iX  i   i+  iÐ  i¥  iØ   iÙ  iÚ  i@H  i¥ú iúí iÀê i Z	 iÕë2 i ` iÀÞl i@HM i©9  iÒ s   0.73RÁ   R1   c         3   s"   |  ] } | ˆ  j  ƒ  j Vq d  S(   N(   Rº   t   is_zero(   R   RX   (   R   (    s?   lib/python2.7/site-packages/sympy/solvers/tests/test_solvers.pys	   <genexpr>/  s    s_   
        [(-11/(9*(47/54 + sqrt(93)/6)**(1/3)) + 1/3 + (47/54 +
        sqrt(93)/6)**(1/3))**3]s<  
        [(-sqrt(-2*(-1/16 + sqrt(6913)/16)**(1/3) + 6/(-1/16 +
        sqrt(6913)/16)**(1/3) + 17/2 + 121/(4*sqrt(-6/(-1/16 +
        sqrt(6913)/16)**(1/3) + 2*(-1/16 + sqrt(6913)/16)**(1/3) + 17/4)))/2 +
        sqrt(-6/(-1/16 + sqrt(6913)/16)**(1/3) + 2*(-1/16 +
        sqrt(6913)/16)**(1/3) + 17/4)/2 + 9/4)**3]s]   
        [(-(81/2 + 3*sqrt(741)/2)**(1/3)/3 + (81/2 + 3*sqrt(741)/2)**(-1/3) +
        2)**2]s  
        -x + (1/2 - sqrt(3)*I/2)*(3*x**3/2 - x*(3*x**2 - 34)/2 + sqrt((-3*x**3
        + x*(3*x**2 - 34) + 90)**2/4 - 39304/27) - 45)**(1/3) + 34/(3*(1/2 -
        sqrt(3)*I/2)*(3*x**3/2 - x*(3*x**2 - 34)/2 + sqrt((-3*x**3 + x*(3*x**2
        - 34) + 90)**2/4 - 39304/27) - 45)**(1/3))i™   i3   if   iT  i06  i   i`2 i2  iìy  ix… i,ð  i*  (!   RT   Rv   R,   R   RD   R*   R_   Ro   R0   R   RX   RY   RZ   R`   R[   R   R„   R(   Rw   R   R   RF   R   t   NoneRb   Rg   R¨   Rk   R   t   reversedR    R   t   any(	   Rž   Rx   Ra   R^   Rh   RÁ   t   Xt   xit   Y(    (   R   R£   Rè   s?   lib/python2.7/site-packages/sympy/solvers/tests/test_solvers.pyt   test_unrad18  sv   #3#'%./$.%@Q $!.)/5H=A;.%@7(4/=+)'!.23R[<441QEI339)0-);<0. #97=#32065{ &:A*/*-23535;7«5:A	8?07(2C$C.:w77uA¶uAc-C;7$;;?³92, 4'1-	èMc          C   sp   t  d t  d d t d ƒ ƒ t d t  d d t  d d t d ƒ ƒ }  t |  ƒ t j g k sl t ‚ d  S(   Ni   i   i   (   R*   R_   R(   R   R¯   Ro   (   Rx   (    (    s?   lib/python2.7/site-packages/sympy/solvers/tests/test_solvers.pyt   test_unrad_slowN  s    Nc           C   sÏ   t  t t d d t d d ƒ d t ƒ t d ƒ d g k sF t ‚ t  t t d d ƒ t t d d d ƒ d ƒ d d t t d t d d t d d t d d t d d	 ƒ d g k sË t ‚ d  S(
   Ni   i   i   i   iÿÿÿÿi   i   i
   i    (   R(   R0   R_   R   Ro   RP   (    (    (    s?   lib/python2.7/site-packages/sympy/solvers/tests/test_solvers.pyt   test_unrad_failV  s    F/c             s²  t  d ƒ \ ‰  }  } } | ˆ  d |  d } i t | ƒ t t | ƒ d d ƒ |  6t | ƒ t | ƒ t t | ƒ d d ƒ ˆ  6} t | | ƒ t k s¥ t ‚ t t ˆ  t ƒ i t ˆ  6ƒ t k sÐ t ‚ t t ˆ  t ƒ i t ˆ  6ƒ t k sû t ‚ t t ˆ  d k  t ƒ i d ˆ  6ƒ t k s,t ‚ t t ˆ  d k  t ƒ i d ˆ  6ƒ t k s]t ‚ t t ˆ  d k  t ƒ i d ˆ  6ƒ t k sŽt ‚ t t ˆ  d k  t ƒ i d ˆ  6ƒ t k s¿t ‚ t t ˆ  d ˆ  d d ƒ i d ˆ  6ƒ t k söt ‚ t ˆ  d ˆ  d d g ˆ  d ƒ t k s&t ‚ t ˆ  d ˆ  d d g ˆ  d ƒ t k sVt ‚ t t	 ˆ  d d ƒ ˆ  d ƒ t k s‚t ‚ t
 t ‡  f d †  ƒ t
 t ‡  f d †  ƒ d  S(   Ns
   x, y, r, ti   i   i    c              s   t  ˆ  d ƒ S(   Ni   (   RE   (    (   R_   (    s?   lib/python2.7/site-packages/sympy/solvers/tests/test_solvers.pyR†   o  R‡   c              s   t  g  ˆ  d ƒ S(   Ni   (   RE   (    (   R_   (    s?   lib/python2.7/site-packages/sympy/solvers/tests/test_solvers.pyR†   p  R‡   (   R,   R*   R.   RE   Rg   Ro   R   Rw   R   R   RT   R»   (   R`   R×   Rb   Rx   t   dict_var_soln(    (   R_   s?   lib/python2.7/site-packages/sympy/solvers/tests/test_solvers.pyt   test_checksol_  s"    )3++1111700,c           C   sÝ   t  t d ƒ d t f k s" t ‚ t  d ƒ d k s: t ‚ t  t d t ƒ d t ƒ d t d ƒ t f k ss t ‚ t  t d t t t ƒ d t ƒ t d t d ƒ t f k s¸ t ‚ t  t t ƒ t d f k sÙ t ‚ d  S(   Ni   i    i   i   (   i   i    (   RC   R_   Ro   R    R"   RX   (    (    (    s?   lib/python2.7/site-packages/sympy/solvers/tests/test_solvers.pyt   test__invertr  s
    "9Ec           C   sa  t  t t d t t t ƒ t ƒ t t d ƒ g k s? t ‚ t  t t t t d ƒ t ƒ d t t d ƒ g k s~ t ‚ t  t t ƒ g  k sš t ‚ t  t t d ƒ t t t d ƒ ƒ ƒ g k sÏ t ‚ t  t d t d t d t d ƒ d g k st ‚ t  t t t t d ƒ j t ƒ t ƒ d t t d ƒ t t ƒ d ƒ g k s]t ‚ d  S(   Ni   i   i   (	   R(   RX   R_   R"   R    Ro   R
   R   R*   (    (    (    s?   lib/python2.7/site-packages/sympy/solvers/tests/test_solvers.pyt   test_issue_4463z  s    ??57c          C   st  t  d ƒ \ }  } } } } } } } } }	 }
 } } } } } } } |  | | | | |
 | f } | | | | | | d | d | d | | | | | | d | d | d |	 | | | | | d | d | d | | | |
 | |
 d | d | d | | | | | | d | d | |
 | g } t t | | d t d t d t ƒƒ d k spt ‚ d  S(   Ns   a:ri   RÙ   Rž   R1   (   R,   R¨   R(   Rg   Rw   Ro   (   RX   RY   RZ   R[   Rh   Rp   Rq   R]   R§   t   jR\   t   lRd   Ri   t   oR^   Rc   R×   t   symsR‚   (    (    s?   lib/python2.7/site-packages/sympy/solvers/tests/test_solvers.pyt   test_issue_5114_solversƒ  s    B++++!c          C   s5  t  d ƒ \ }  } } } } } t  d ƒ \ } } } }	 }
 } |  | | | | | | | | |  | | d |  d | d | d | | d d | |	 | | d | d | d | |
 | d | d | | f	 } i | | |	 6d | d | d	 | d
 | d | 6| | | 6| | 6d | d | d | |
 6| | |  6| d d | d | d | 6g } |  | |
 | | | | |	 f } t | d t d t d t | Œ| k sºt ‚ t | d t | Œg  k sÛt ‚ g  | D] } | j | d ƒ ^ qâd d | | | | d d d d d g	 k s1t ‚ d  S(   Ns   I1:7s   dI1,dI4,dQ2,dQ4,Q2,Q4iþÿÿÿi   i   i   iüÿÿÿi   i   i   i   RÙ   Rž   Rm   i    (   R,   R(   Rg   Rw   Ro   R    (   t   I1t   I2t   I3t   I4t   I5t   I6t   dI1t   dI4t   dQ2t   dQ4t   Q2t   Q4Rh   R   t   vt   ei(    (    s?   lib/python2.7/site-packages/sympy/solvers/tests/test_solvers.pyt   test_issue_5849“  s0    +'&-!c          C   s’  t  d ƒ \ }  } } } } } t  d ƒ \ } } } }	 }
 } |  | | | | | | | | |  | | d |  d | d | d | | d d | |	 | | d | d | d | |
 | d | d | | f	 } t | |  | |
 | | | | |	 ƒ	 i | d | d | | 6d | d | d	 | d
 | d | 6| | 6| | |  6d | d | d | |
 6| | |	 6| | | 6k sŽt ‚ d S(   s4   Same as test_2750 but solved with the matrix solver.s   I1:7s   dI1,dI4,dQ2,dQ4,Q2,Q4iþÿÿÿi   i   i   iüÿÿÿi   i   i   i   N(   R,   R(   Ro   (   R  R  R  R  R  R  R  R  R	  R
  R  R  Rh   (    (    s?   lib/python2.7/site-packages/sympy/solvers/tests/test_solvers.pyt   test_issue_5849_matrix´  s&    +$'c       	      sF  t  t d ƒ \ ‰  }  } t d ƒ } t ˆ  t ƒ t ƒ } t |  | ƒ | ƒ } t ˆ  t ƒ ˆ  t ƒ j t ƒ ˆ  t ƒ ƒ | g k sŒ t ‚ t ˆ  t ƒ d ˆ  t ƒ ƒ d g k sº t ‚ t ˆ  t ƒ d ˆ  t ƒ j t ƒ ˆ  t ƒ ƒ d | g k sÿ t ‚ t ˆ  t ƒ d ˆ  t ƒ j t ƒ g ˆ  t ƒ ƒ i d | ˆ  t ƒ 6k sQt ‚ t ˆ  t ƒ d ˆ  t ƒ j t ƒ ˆ  t ƒ d t d g ˆ  t ƒ t ƒ i d | ˆ  t ƒ 6d | d d t 6g k sÑt ‚ t ˆ  | ƒ d |  | ƒ d ˆ  | ƒ d | | ƒ d |  | ƒ j | ƒ | | ƒ |  | ƒ d t	 ƒ|  | ƒ g t
 t | | ƒ d ˆ  | ƒ d | ƒ ˆ  | ƒ f t | | ƒ d ˆ  | ƒ d | ƒ ˆ  | ƒ f g ƒ f k sÃt ‚ ˆ  t ƒ j t d ƒ ˆ  t ƒ |  t ƒ |  t ƒ d d ˆ  t ƒ |  t ƒ g } t
 t | Œ  ƒ t
 t d ƒ t d ƒ f t d ƒ t d ƒ f g ƒ k sft ‚ ˆ  t ƒ d |  t ƒ d ˆ  t ƒ j t ƒ |  t ƒ d d g } t | ˆ  t ƒ |  t ƒ d t	 ƒˆ  t ƒ |  t ƒ g t
 t d | d ƒ t d ƒ f t d | d ƒ t d ƒ f t d | d ƒ t d ƒ f t d | d ƒ t d ƒ f g ƒ f k sqt ‚ t t ‡  f d †  ƒ t ˆ  t ƒ ˆ  t ƒ j t ƒ d	 t g ƒˆ  t ƒ t ˆ  t ƒ t ƒ d
 f k sàt ‚ t ˆ  t ƒ t t t t f ƒ d	 t g ƒˆ  t ƒ t t t t f ƒ d
 f k s9t ‚ t ˆ  t ƒ t t t t f ƒ t d	 t g ƒt ˆ  t ƒ t t t t f ƒ d
 f k sšt ‚ t ˆ  t ƒ t t t t f ƒ t d	 t g ƒt ˆ  t ƒ t t t t f ƒ f k søt ‚ t t ˆ  t ƒ | ˆ  t ƒ d
 | d	 t g ƒt d
 | f k sCt ‚ t t t d t t ƒ ƒ t d f k srt ‚ t t t t t ƒ d	 t g ƒt d f k s¦t ‚ t t t t t ƒ d d	 t g ƒt d t d
 f k sæt ‚ t
 t t t t ƒ d t t ƒ ƒ ƒ t
 t t ƒ t t ƒ g ƒ k s6t ‚ t t t t ƒ t d t	 ƒt t ƒ g k skt ‚ t t t ƒ t t ƒ t d t	 ƒg  k sœt ‚ t t t t ƒ t d t	 ƒt t ƒ g k sÐt ‚ t t d t d t d t	 ƒt d d g k s	t ‚ t t d t d t d d t	 ƒt d g k sBt ‚ d  S(   Nt   fghRX   i   i   i   i	   R„   c              s2   t  ˆ  t ƒ ˆ  t ƒ j t ƒ d ˆ  t ƒ g ƒS(   NR,   (   R)   R_   R   (    (   Rp   (    s?   lib/python2.7/site-packages/sympy/solvers/tests/test_solvers.pyR†   ò  R‡   R,   i   iþÿÿÿi    Rƒ   (   Rn   R   R   R   R_   R(   R   Ro   R`   Rg   R„   R*   R   RT   R»   R)   R	   R    R   R&   (   Rq   R]   RX   t   Dt   GR   R‚   (    (   Rp   s?   lib/python2.7/site-packages/sympy/solvers/tests/test_solvers.pyt   test_issue_5901Î  st    +/2 J6N3GSAE!3+.+./2//2#&*1"c          C   s  t  t t d t d d t ƒƒ t  t d ƒ d t d ƒ d t d ƒ d t d ƒ d g ƒ k sm t ‚ t t d t d d t ƒ}  t |  ƒ d k r³ t	 d „  |  Dƒ ƒ s¹ t ‚ t t d t d ƒ }  t |  ƒ d k rù t	 d „  |  Dƒ ƒ sÿ t ‚ d  S(	   Ni   gš™™™™™¹?Rá   i   i#   i
   c         s   s   |  ] } | j  Vq d  S(   N(   t	   is_Number(   R   RX   (    (    s?   lib/python2.7/site-packages/sympy/solvers/tests/test_solvers.pys	   <genexpr>  s    c         s   s   |  ] } | j  Vq d  S(   N(   R  (   R   RX   (    (    s?   lib/python2.7/site-packages/sympy/solvers/tests/test_solvers.pys	   <genexpr>  s    (
   R„   R(   R_   Rg   R   R*   Ro   Rw   R¨   Rˆ   (   R   (    (    s?   lib/python2.7/site-packages/sympy/solvers/tests/test_solvers.pyt   test_issue_5912  s    !L.c          C   sH  d „  }  t  t d d t ƒd j s, t ‚ t  t d d t ƒd j sO t ‚ t  t t j d t ƒd j su t ‚ t  t d d d  ƒd j s˜ t ‚ t  t t j d d  ƒd j s¾ t ‚ |  t
 d d t ƒ d d t ƒ sé t ‚ xm t t t g D]\ } t
 | d d t g ƒ ƒ } t | ƒ | k rO|  t | ƒ d d d t ƒ sù t ‚ qù Wt t
 i d d t g d t 6ƒ j ƒ  ƒ d \ } } |  | d t ƒ r¿|  | d d d t ƒ sÅt ‚ |  t
 t d t ƒ ƒ t d t ƒ ƒ sôt ‚ |  t
 d	 t d ƒ d
 t d ƒ st ‚ |  t
 d	 t d d t ƒd
 t d ƒ sPt ‚ |  t
 t d t ƒ ƒ t d t ƒ ƒ st ‚ |  t
 t d	 ƒ t d
 ƒ s¢t ‚ |  t
 t d d t t t d ƒ d	 ƒ d ƒ t d d t d ƒ sñt ‚ d t t t } t  d t | d d t | d t | d f ƒ g  k sDt ‚ d  S(   Nc         S   s(   t  |  j t ƒ ƒ t  | j t ƒ ƒ k S(   N(   R¨   Ré   R   (   t   e1t   e2(    (    s?   lib/python2.7/site-packages/sympy/solvers/tests/test_solvers.pyt   test  s    g      à?Rá   i    i   i   g      ð?g       @i   g      @RŸ   i   g!ÌÈ,‹ÿ?id   gffffffæ?g333333ã?gš™™™™™É?g333333Ó?gš™™™™™¹?(   R(   R_   Rg   t   is_RationalRo   Rw   t   is_FloatR   R¯   Rï   R?   RŠ   R‰   R„   t   typet   itemsR   R    RZ   Ra   Rb   (   R  t   containR   R\   R  t   tot(    (    s?   lib/python2.7/site-packages/sympy/solvers/tests/test_solvers.pyt   test_float_handling  s*    	##&#&+=84/+1/#0c              sz   t  d d t ƒ‰  t ˆ  d d ƒ d g k s5 t ‚ t d ˆ  ƒ t k sP t ‚ t t ‡  f d †  ƒ t t d „  ƒ d  S(   NR_   RÎ   i   i   c              s   t  d ˆ  ˆ  d t ƒS(   Ni   RÎ   (   RL   Rg   (    (   R_   (    s?   lib/python2.7/site-packages/sympy/solvers/tests/test_solvers.pyR†   8  R‡   c           S   s   t  d d ƒ S(   Ni   (   RL   (    (    (    s?   lib/python2.7/site-packages/sympy/solvers/tests/test_solvers.pyR†   9  R‡   (   R,   Rg   R(   Ro   RL   RT   Ru   (    (    (   R_   s?   lib/python2.7/site-packages/sympy/solvers/tests/test_solvers.pyt   test_check_assumptions4  s
    #c          C   s”   t  d d t d t ƒ}  t  d ƒ } t d |  | |  j  i
 d  d 6d  d 6d  d 6d  d 6d  d 6d  d	 6d  d
 6d  d 6d  d 6d  d 6k s t ‚ d  S(   NR_   R·   RÎ   R`   i   t	   imaginaryt   complext	   hermitiant   nonpositivet   nonnegativet   nonzeroR¸   t   zero(   R   Rg   RN   t   assumptions0Rï   Ro   (   R_   R`   (    (    s?   lib/python2.7/site-packages/sympy/solvers/tests/test_solvers.pyt   test_failing_assumptions<  s    c       	   C   sÎ  t  t t d ƒ t t d ƒ d ƒ g  k s4 t ‚ t g  t  t t d ƒ t t d ƒ d ƒ D] }  t |  ƒ ^ q` ƒ t t d ƒ d t d t ƒ t d ƒ d t d t ƒ t d ƒ d t d t ƒ t d ƒ d t d t ƒ g ƒ k sý t ‚ t g  t  t t d ƒ t t d ƒ d d ƒ D] }  t |  ƒ ^ q-ƒ t t d ƒ d t d t ƒ t d ƒ d t d t ƒ t d ƒ d t d t ƒ t d ƒ d t d t ƒ g ƒ k sÊt ‚ d  S(   Ni   i   i   iÿÿÿÿ(   R(   R/   R_   Ro   R„   R1   R"   R   (   RÈ   (    (    s?   lib/python2.7/site-packages/sympy/solvers/tests/test_solvers.pyt   test_issue_6056D  s    4G.Kc          C   sy   t  t t t t t  ƒ ƒ ƒ t t t  ƒ ƒ ƒ }  t |  t  d ƒ t k sQ t ‚ t |  t  d d t ƒd  k su t ‚ d  S(   Ni   t	   numerical(	   R_   R    R
   R"   RE   Rg   Ro   Rw   Rï   (   Rx   (    (    s?   lib/python2.7/site-packages/sympy/solvers/tests/test_solvers.pyt   test_issue_5673R  s    3c    
   	   C   s,  t  d ƒ \ }  } } } } } } } t  d d t ƒ} | | | | d | | d |  | d | d | | | | | | | | | d |  | |  | | g }	 t |	 d | | |  ƒi | | |  | d d | |  | | 6| | 6d | | | |  | | 6| |  | | d	 | | | |  | | 6i d
 | 6d
 | 6d
 | 6d
 | 6g k sft ‚ t |	 d | | | g ƒi | | 6| d | d t | d | | | ƒ d | 6| d	 | t | d d | | d | d ƒ d | | | |  6| | | | | 6i | | 6| d | d t | d | | | ƒ d | 6| d	 | t | d d | | d | d ƒ d | | | |  6| | | | | 6g i | | 6| d | | | d | d | | 6| | | d | | d | | 6| | | | d | |  6g g k s(t ‚ d  S(   Ns$   R, C, Ri, Vout, V1, Vminus, Vplus, st   RfRÎ   iþÿÿÿi   iÿÿÿÿR…   i   i   i    i   i   (   R,   Rg   R(   Ro   R*   (
   t   RRÆ   t   Rit   Voutt   V1t   Vminust   VplusR£   R.  R‚   (    (    s?   lib/python2.7/site-packages/sympy/solvers/tests/test_solvers.pyt   test_excludeX  s@    $#('+1E1E'#c          C   sn   t  d d t  d d t  d t d ƒ d }  t t |  ƒ ƒ t t |  d d d ƒj ƒ  ƒ k sj t ‚ d  S(   Ni   i   i   i   i   t   domaint   ZZ(   R_   R   R„   R(   R   t	   all_rootsRo   (   R£   (    (    s?   lib/python2.7/site-packages/sympy/solvers/tests/test_solvers.pyt   test_high_order_roots€  s    0c          C   s  d „  }  |  t  t t t t t t t g d t d t ƒƒ d k sM t ‚ |  t  t t t t t t t g d t d t ƒƒ d k s‘ t ‚ |  t  t t t t t t g d t d t ƒƒ d k sÑ t ‚ |  t  t t t t t t g d t d t ƒƒ d k st ‚ d  S(   Nc         S   s/   t  g  |  j ƒ  D] } | d k r | ^ q ƒ S(   Ni    (   R¨   t   values(   t   dicR_   (    (    s?   lib/python2.7/site-packages/sympy/solvers/tests/test_solvers.pyt   count†  s    t
   particulart   quicki   i   i   (	   R(   R_   R`   Ra   RX   Rb   Rg   Ro   Rw   (   R<  (    (    s?   lib/python2.7/site-packages/sympy/solvers/tests/test_solvers.pyt   test_minsolve_linear_system…  s    	55@c          C   sD   t  d d t ƒ}  t t |  d |  d d ƒ ƒ d k s@ t ‚ d  S(   NR_   R·   i   i   i   (   R   Rg   R¨   R(   Ro   (   R_   (    (    s?   lib/python2.7/site-packages/sympy/solvers/tests/test_solvers.pyt   test_real_roots  s    c          C   s~   d t  d d t  d t d d d t  d d t  t d t d d	 g }  t t |  t t  d
 t ƒƒ d k sz t ‚ d  S(   NicË†i   iQÖAiTâkI1ûS   iýûa5iPQRiçäžI äT   Rž   i   (   R_   R`   R¨   R(   Rw   Ro   (   R‚   (    (    s?   lib/python2.7/site-packages/sympy/solvers/tests/test_solvers.pyt   test_issue_6528–  s    #-c          C   sÐ   t  d d t ƒ}  t d |  d ƒ d t d d |  ƒ d g } t | |  ƒ t j f g k sf t ‚ t | |  d	 t ƒt j f g k s t ‚ t | |  d	 t d
 t ƒt j f t d ƒ f g k sÌ t ‚ d  S(   NR_   R·   i   i   i   i   i   i   RÙ   Rž   (   R,   Rg   R    R(   R   R¯   Ro   Rw   (   R_   R‚   (    (    s?   lib/python2.7/site-packages/sympy/solvers/tests/test_solvers.pyt   test_overdeterminedŸ  s
    0$*c          C   sô   t  d ƒ }  t d |  d d |  d ƒ d d t t t d ƒ g k sP t ‚ t  d d t ƒ}  t d |  d d |  d ƒ d g k s‘ t ‚ t d ƒ t t d ƒ ƒ t t d ƒ ƒ } t d |  d d d |  ƒ | | g k sð t ‚ d  S(	   NR_   i   i   i   i    R·   i   i   (   R,   R(   R   R#   R"   Ro   Rg   R*   (   R_   RY   (    (    s?   lib/python2.7/site-packages/sympy/solvers/tests/test_solvers.pyt   test_issue_6605§  s    D/,c           C   s@   t  t d ƒ s t ‚ t  t ƒ s) t ‚ t  t ƒ s< t ‚ d  S(   Ni   (   RG   R_   Ro   Rg   (    (    (    s?   lib/python2.7/site-packages/sympy/solvers/tests/test_solvers.pyt   test__ispow±  s    c       	   C   s  t  t t d t d t t d ƒ d d ƒ t  t d d t  d t d d t d d t d ƒ d t d ƒ d d t d d t t  d t d d t d d t d ƒ d t d ƒ d d ƒ }  t |  t d t d t ƒ} t | ƒ d k s
t ‚ d  S(   Ni   i   i   i   R1   Rž   i   (   R*   Rd   Rc   R   R(   Rw   R¨   Ro   (   Rx   R©   (    (    s?   lib/python2.7/site-packages/sympy/solvers/tests/test_solvers.pyt   test_issue_6644·  s
    4LWc           C   s‚   t  t d t t t g t t g ƒ d d g k s9 t ‚ t  t d t t t t g t t g ƒ d t t f g k s~ t ‚ d  S(   Ni   iÿÿÿÿi    (   iÿÿÿÿiÿÿÿÿ(   i    i    (   i    i    (   R(   RX   RY   Ro   RZ   (    (    (    s?   lib/python2.7/site-packages/sympy/solvers/tests/test_solvers.pyt   test_issue_6752¿  s    9c           C   sÙ   t  t t d d t d t d t d ƒ d d d t t d t d d ƒ t t d t d d ƒ t t d t d d ƒ t t d t d d ƒ t t d t d d ƒ t t d t d d ƒ g	 k sÕ t ‚ d  S(	   Ni   i   i   iÿÿÿÿi    i   i   i   (   R(   R_   RP   Ro   (    (    (    s?   lib/python2.7/site-packages/sympy/solvers/tests/test_solvers.pyt   test_issue_6792Ä  s    -90c             s¿  t  d d t ƒ\ ‰  }  t t ˆ  d ƒ d t ˆ  d ƒ ƒ d d g k sR t ‚ t t ˆ  ƒ d t ˆ  ƒ t g ˆ  ƒ d d g k s t ‚ t t t ˆ  d ƒ d	 ƒ ƒ t t d ƒ t d
 ƒ g ƒ k sÒ t ‚ t t	 t
 ˆ  d ƒ t
 ˆ  d d ƒ d ƒ ˆ  ƒ t d ƒ d t d ƒ d t d ƒ d t d ƒ d g k sJt ‚ t d t ˆ  ƒ t ˆ  d ƒ ƒ d t d d ƒ g k s‰t ‚ t  d ƒ ‰  t t ˆ  ƒ d t ˆ  ƒ d g ˆ  ƒ i d t ˆ  ƒ 6d d t ˆ  6d t ˆ  ƒ 6g k söt ‚ t t ˆ  ƒ d t ˆ  ƒ d ƒ d } t | ƒ t | ˆ  ƒ k s?t ‚ t  d d t ƒ} t t | ƒ d ƒ d t d t g k st ‚ t t ‡  f d †  ƒ t  d d t ƒ} t d ˆ  | d |  | | ƒ t ˆ  |  | d | ƒ k sít ‚ t  d d t ƒ\ ‰  }  t ˆ  |  t d ƒ i d |  6d ˆ  6k s7t ‚ t ˆ  d t ƒ d g k sZt ‚ t  d d t ƒ\ ‰  }  t ˆ  |  t d d t ƒ i d t ˆ  6d t |  6k s´t ‚ t  d d t ƒ‰  t ˆ  |  d d t ƒ i d ˆ  6d t |  6k s t ‚ t d ƒ } t | ˆ  d ƒ | d ˆ  d ƒ ƒ d g k sCt ‚ t t ˆ  d ƒ t d ˆ  d ƒ ƒ d g k szt ‚ t  d ƒ ‰  t d ˆ  d ˆ  ƒ t t t d ƒ g k s»t ‚ d  S(   Ns   x yR·   i   i   i   i	   iþÿÿÿi   i   i   i=   iE   iÿÿÿÿR_   R§   R"  iýÿÿÿc              s   t  t ˆ  ƒ d ƒ S(   Ni   (   R(   t   abs(    (   R_   (    s?   lib/python2.7/site-packages/sympy/solvers/tests/test_solvers.pyR†   ã  R‡   RÈ   RÑ   i   i    Rp   (   iþÿÿÿ(   i   (   R,   Rg   R(   RH  Ro   R3   R#   R„   R   R   R    R*   R   R$   R!   R   RT   Rv   R   R"   (   R`   Rx   R§   RÈ   Rp   (    (   R_   s?   lib/python2.7/site-packages/sympy/solvers/tests/test_solvers.pyt$   test_issues_6819_6820_6821_6248_8692Ë  s:    :;E1G?&;(!0D2#B:77c          C   sŒ  t  d ƒ \ }  } } } } } |  d | | |  | |  | d | |  | | } t  d d t d t ƒ\ } } }	 | d d | |  |	 |  }
 | |
 j ƒ  } | t | ƒ j ƒ  9} t | |  ƒ } | j ƒ  } | | |	 g } t | | d t ƒ}  t |  ƒ d k st	 ‚ i | | | | | | 6| | | 6| | | | |	 6} x8 | D]0 } |  d | j ƒ  | | j ƒ  k sTt	 ‚ qTWd  S(	   Ns   s, tau_c, tau_1, tau_2, phi, Ki   i   s   K_C, tau_I, tau_DRÎ   R'  Rm   i    (
   R,   Rg   t   togetherR<   R1   R   t   coeffsR(   R¨   Ro   (   R£   t   tau_ct   tau_1t   tau_2t   phit   Kt   targett   K_Ct   tau_It   tau_Dt   PIDRx   RZ   t   varst   knownsolutiont   var(    (    s?   lib/python2.7/site-packages/sympy/solvers/tests/test_solvers.pyt   test_issue_14607ü  s$    7	c    
   	      sÍ  d d l  m }  m ‰  m ‰ d d l m } m } m } | t ˆ  d ˆ  t	 ˆ  ƒ ˆ ƒ ˆ  ƒ t
 ˆ  t	 ˆ  ƒ g ƒ k s t ‚ | ˆ  ˆ  ƒ g  k sœ t ‚ t ˆ  d d ˆ  d j ˆ  t ˆ  ƒ d ˆ  ƒ ƒ t d t j ƒ d g k sò t ‚ t ˆ  d d ˆ  d j ˆ  t ˆ  ƒ d ˆ  d d ƒ ƒ t d t	 t d ƒ ƒ ƒ d t d t	 t d ƒ ƒ ƒ d g k swt ‚ t ˆ  d d ˆ  d j ˆ  t ˆ  ƒ d ˆ  ƒ ƒ t d t	 d t d ƒ ƒ ƒ d t d t	 d t d ƒ ƒ ƒ d g k sût ‚ t ˆ  t ˆ  ƒ d ˆ  d ˆ  ƒ t	 d t t	 d ƒ ƒ ƒ g k sFt ‚ ˆ  t	 ˆ  ƒ d j ˆ  ˆ  t	 ˆ  ƒ ƒ } t | ƒ t d t	 t d ƒ ƒ ƒ g k s¢t ‚ t t ‡  ‡ f d †  ƒ t d ƒ d } t d	 ƒ d
 } t d	 ƒ d } |  d | t | ƒ | d } t d t |  d ˆ  d	 ƒ |  d ˆ  d	 ˆ  ƒ t |  d ƒ t d t | ƒ ƒ d t |  ƒ t d | d | t | ƒ t |  ƒ t d | d | t | ƒ t |  ƒ g k sÉt ‚ t d t d t d ƒ |  d	 | } t d t |  d ˆ  d	 ƒ t t |  d ˆ  d	 ƒ |  d ˆ  d	 ˆ  ƒ t | d t d ƒ t d ƒ t |  ƒ t | d t d ƒ t d ƒ t |  ƒ t t d t d t d ƒ |  d	 ƒ d t |  ƒ g k sÓt ‚ t d d t ƒ}	 d d d |	 d d |	 d } | | |	 | t | ƒ |	 ƒ ƒ t d ƒ d t d t d ƒ ƒ d t d ƒ g k sdt ‚ t |  ˆ  t	 ˆ  d ƒ j ˆ  d ƒ ˆ  ƒ d
 t t d d ƒ t |  d ƒ d ƒ g k sÄt ‚ t t ˆ  ƒ ˆ  j ˆ  ˆ  d d ƒ ƒ t t t d ƒ d ƒ t d t d ƒ ƒ g k s&t ‚ t ˆ  d d ˆ  ˆ  ƒ d d t t d ƒ d ƒ t d ƒ g k srt ‚ t ˆ  d d ˆ  ˆ  ƒ d d g k sŸt ‚ t ˆ  d d ˆ  ˆ  ƒ d d g k sÍt ‚ t d t ˆ  ƒ t ˆ  ƒ d ƒ t d ƒ t d t t d ƒ d ƒ t d ƒ ƒ g k s.t ‚ t
 t d t ˆ  ƒ ˆ  t d ƒ ƒ ƒ t
 d d t t d ƒ d ƒ t d ƒ g ƒ k st ‚ t t d ˆ  ƒ ˆ ˆ  ƒ ˆ t	 ˆ ƒ d g k sÉt ‚ d  S(   Niÿÿÿÿ(   RX   R_   R`   (   t   _filtered_genst   _lambertt   _solve_lamberti   i   i   iýÿÿÿc              s%   t  ˆ  t ˆ  ƒ t ˆ ˆ  ƒ ˆ  ƒ S(   N(   R(   R&   R"   (    (   R_   R`   (    s?   lib/python2.7/site-packages/sympy/solvers/tests/test_solvers.pyR†   )  R‡   i   i   iûÿÿÿiþÿÿÿR^   RÎ   i   iüÿÿÿ(   R¹   RX   R_   R`   t   sympy.solvers.bivariateRZ  R[  R\  R   R    R„   Ro   R(   R    R"   R
   R   RÏ   R*   RT   Rv   R   RY   R,   Rg   R   R0   R   R   (
   RX   RZ  R[  R\  Rx   t   _13t   _56t   _53RP  R^   (    (   R_   R`   s?   lib/python2.7/site-packages/sympy/solvers/tests/test_solvers.pyt   test_lambert_multivariate  sV    IV;J3QK*2 2/'6(C))D"?*6';L-.a*7c          C   s  d d l  m }  t d t |  ƒ |  t d ƒ |  ƒ d g k sF t ‚ t d ƒ d } t t |  | | |  ƒ ƒ t | | t t | ƒ | ƒ t | ƒ g ƒ k s¬ t ‚ t t d t	 |  ƒ t	 |  ƒ d ƒ ƒ t t
 d ƒ t
 d t t d ƒ d ƒ t d ƒ ƒ g ƒ k st ‚ d  S(   Niÿÿÿÿ(   R_   i   i   i   iýÿÿÿ(   R¹   R_   R(   R&   Ro   R   R„   R
   R"   R   R   (   R_   RX   (    (    s?   lib/python2.7/site-packages/sympy/solvers/tests/test_solvers.pyt   test_other_lambertR  s    68*c           C   s  t  t t ƒ t t ƒ ƒ d t t d t g k s9 t ‚ t  t t ƒ t t ƒ ƒ d t t j	 t
 d ƒ t
 d t
 d ƒ t ƒ d t
 d ƒ t d ƒ d t t j	 t
 d ƒ t
 d t
 d ƒ t ƒ d t
 d ƒ t d ƒ d t t j	 t
 d ƒ t
 d t
 d ƒ t ƒ d t
 d ƒ t d ƒ d t t j	 t
 d ƒ t d t
 d ƒ t
 d t
 d ƒ t ƒ d ƒ g k s‚t ‚ t  t t ƒ t t ƒ ƒ d t t g k s´t ‚ t  d t t ƒ t t ƒ t ƒ d t d t
 d ƒ ƒ d t d t
 d ƒ ƒ g k st ‚ d  S(   Ni    i   iþÿÿÿi   i   i   (   R(   R&   R_   R.   R#   Ro   R%   R   R   R¯   R*   R   R'   R/   R   (    (    (    s?   lib/python2.7/site-packages/sympy/solvers/tests/test_solvers.pyt   test_rewrite_trig]  s    9INHQ27c          C   s(  d d l  m }  t t t ƒ |  t ƒ ƒ d t t j t d ƒ d t d t d ƒ d ƒ d ƒ d t t j t d ƒ d t d t d ƒ d ƒ d ƒ d t t d ƒ d t j t d d t d ƒ ƒ d ƒ d t t d d t d ƒ ƒ d t d ƒ d t j ƒ g k s$t	 ‚ d  S(   Niÿÿÿÿ(   t   sechi   i   iþÿÿÿ(
   t   sympyRd  R(   R'   R_   R   R   R¯   R*   Ro   (   Rd  (    (    s?   lib/python2.7/site-packages/sympy/solvers/tests/test_solvers.pyt   test_rewrite_trighk  s    ;;;c          C   sî  t  t t ƒ t t t d t d t d ƒ }  t |  t d t ƒt t t t t  ƒ ƒ t t t t t  ƒ ƒ g k s‚ t ‚ t t t d ƒ t d d t ƒ d ƒ d t d t d ƒ ƒ t t	 d ƒ d ƒ d t d ƒ d t d t d ƒ ƒ t t	 d ƒ d ƒ d d t d ƒ d g d t d t d ƒ d	 d ƒ d t d ƒ d d t d t d ƒ d	 d ƒ d t d ƒ d g g k sŸt ‚ t t t d t ƒ d ƒ t t
 t ƒ d ƒ t d ƒ ƒ g  k sêt ‚ d  S(
   Niÿÿÿÿi   t   forcei   i   iýÿÿÿiôÿÿÿiÜÿÿÿi   (   Ra   R"   R_   R`   R(   Rg   R*   R    Ro   R   R/   (   Rx   (    (    s?   lib/python2.7/site-packages/sympy/solvers/tests/test_solvers.pyt   test_uselogcombinev  s    2P)=A2Dc           C   s=   t  t t d ƒ t d t ƒ d t d ƒ g k s9 t ‚ d  S(   Ni   i   (   R(   R2   R_   R#   R*   Ro   (    (    (    s?   lib/python2.7/site-packages/sympy/solvers/tests/test_solvers.pyt
   test_atan2‚  s    c           C   s¼   t  t t ƒ t t ƒ t t ƒ g k s. t ‚ t  t t ƒ t t ƒ t t ƒ g k s\ t ‚ t  t t ƒ t t ƒ t t ƒ g k sŠ t ‚ t  t t ƒ t t ƒ t t ƒ g k s¸ t ‚ d  S(   N(   R(   R   R_   R`   R   Ro   R   R   (    (    (    s?   lib/python2.7/site-packages/sympy/solvers/tests/test_solvers.pyt   test_errorinverses†  s    ...c       	   C   sµ  t  d ƒ }  t d ƒ |  t d |  d ƒ |  d t d ƒ t d |  d ƒ d } t | |  d t ƒd } | t t d ƒ d t d ƒ d t d ƒ t d t d ƒ d t d	 ƒ t d
 t d ƒ d d d
 t d ƒ d t d ƒ t d t d ƒ d t d	 ƒ t d
 t d ƒ d f t d ƒ d d d
 t d ƒ d t d	 ƒ t d
 t d ƒ d t d ƒ d t d	 ƒ t d
 t d ƒ d f g ƒ k s±t ‚ d  S(   NR/  i   i   R„   i   i   iû   i   io   i	   i(   (   R   R*   R(   Rg   R„   R   R   Ro   (   R/  Rx   R©   (    (    s?   lib/python2.7/site-packages/sympy/solvers/tests/test_solvers.pyt   test_issue_2725  s    J'c          C   sµ  t  d ƒ \ }  } } } } } } } } }	 }
 } } } } } } t |  | | | | g | d | d | d | | | | | g | | | d | d | d | | | g | | | d | d |
 d | |	 | g | | |	 d | d | d | | | g |	 | | d | d | g g ƒ } t | | |	 | |  | g ƒ } t t | ƒ t | ƒ d t ƒ} t g  | j ƒ  D] } | j ƒ  ^ qŠƒ d k s±t ‚ d  S(   Ns   b:ri   R1   i9
  (	   R,   R   R(   RŠ   Rw   t   sumR:  t	   count_opsRo   (   RY   RZ   R[   Rh   Rp   Rq   R]   R§   Rü   R\   Rý   Rd   Ri   Rþ   R^   Rc   R×   R‚   R  R   R£   (    (    s?   lib/python2.7/site-packages/sympy/solvers/tests/test_solvers.pyt   test_issue_5114_6611—  s    ?D^W!c          C   sä   t  d d t d ƒ ƒ }  |  j ƒ  t |  ƒ k s6 t ‚ d |  d <|  j ƒ  t |  ƒ k s^ t ‚ t  d d t t d ƒ ƒ ƒ }  |  j ƒ  t |  ƒ k sš t ‚ t d d d	 ƒ } t | ƒ t	 | ƒ k oÕ | j ƒ  k n sà t ‚ d  S(
   Ni   s   a:9i   i    i	   i   i   (   i    i    (   i   i   i   i   (
   R   R,   t   detRH   Ro   RŠ   R>   R5   RI   RJ   (   Rd   R£   (    (    s?   lib/python2.7/site-packages/sympy/solvers/tests/test_solvers.pyt   test_det_quick¨  s    
c          C   s»   t  d d t ƒ\ }  } t t |  d | d ƒ d |  ƒ t | d d ƒ t | d d ƒ g k sn t ‚ t  d d t ƒ\ }  } t t |  d | d ƒ d |  ƒ g  k s· t ‚ d  S(   Ns   a bR·   i   i   i	   R"  (   R,   Rg   R(   R*   Ro   (   RX   RY   (    (    s?   lib/python2.7/site-packages/sympy/solvers/tests/test_solvers.pyt   test_real_imag_splitting´  s
    "4c          C   sL   d t  d d t  d d t  d }  t d „  t |  ƒ Dƒ ƒ sH t ‚ d  S(   Niþÿÿÿi   i   i   i   c         s   s$   |  ] } t  t j | ƒ ƒ Vq d  S(   N(   R6   R   R·   (   R   R§   (    (    s?   lib/python2.7/site-packages/sympy/solvers/tests/test_solvers.pys	   <genexpr>¾  s    (   R_   Rñ   R(   Ro   (   R`   (    (    s?   lib/python2.7/site-packages/sympy/solvers/tests/test_solvers.pyt   test_issue_7110¼  s    &c           C   s3   t  d t d d t ƒ d t g k s/ t ‚ d  S(   Ni   i   (   R(   R_   RO   Ro   (    (    (    s?   lib/python2.7/site-packages/sympy/solvers/tests/test_solvers.pyt
   test_unitsÁ  s    c          C   sá   t  d ƒ \ }  } } t d | d | | d |  | d ƒ } t | d d | d ƒ } t |  d	 d | | d ƒ } t t t | | | ƒ |  | | g d ƒ ƒ } t | ƒ t t d g d g d g g ƒ ƒ k sÝ t ‚ d  S(   Ns   A,B,Vg®Gáz²ƒ@g     €C@i'   i    gÃõ(\Âõ?i
   i   g      @i   s   4442890172.68209s   4289299466.1432s   70.5389666628177i áõi † (   i    i    i    (   R,   R   R   R8   R7   R¼   Ro   (   RÄ   RÅ   t   Vt   eq1t   eq2t   eq3R©   (    (    s?   lib/python2.7/site-packages/sympy/solvers/tests/test_solvers.pyt   test_issue_7547Å  s    +-c          C   s;   t  d d t ƒ}  t t |  ƒ d ƒ d g k s7 t ‚ d  S(   NR×   R·   i   i   (   R,   Rg   R(   R*   Ro   (   R×   (    (    s?   lib/python2.7/site-packages/sympy/solvers/tests/test_solvers.pyt   test_issue_7895Ñ  s    c          C   sL  t  d d t ƒ\ }  } t |  d | d ƒ d t | d |  d d ƒ d } } d t d ƒ d t d ƒ d } } | | f | | f g } t | | f |  | f ƒ | k s» t ‚ t | | |  | f |  | f ƒ g  k sê t ‚ | d	 7} t | | f |  | f ƒ g  k st ‚ t | | f |  | f d
 t ƒ| k sHt ‚ d  S(   Ns   x yR·   i   i
   i   i¿   i   i‡  i   Rž   (   R,   Rg   R*   R   R(   Ro   Rw   (   R_   R`   R  R  RX   RY   R   (    (    s?   lib/python2.7/site-packages/sympy/solvers/tests/test_solvers.pyt   test_issue_2777Ö  s    >%'/
'c          C   s-   d }  t  t |  t ƒ d |  k s) t ‚ d  S(   Ng{[Rs±Ò8i    (   R(   R_   Ro   (   t   number(    (    s?   lib/python2.7/site-packages/sympy/solvers/tests/test_solvers.pyt   test_issue_7322ä  s    c           C   s4   t  t d „  ƒ t  t d „  ƒ t  t d „  ƒ d  S(   Nc           S   s   t  t d d d ƒS(   Niÿÿÿÿi   t   methodt   bisect(   iÿÿÿÿi   (   R8   R_   (    (    (    s?   lib/python2.7/site-packages/sympy/solvers/tests/test_solvers.pyR†   ê  R‡   c           S   s2   t  t t d t t t t f t t t f d ƒ S(   Ni   iÎÿÿÿi2   (   iÎÿÿÿi2   (   R8   R_   R`   Ra   (    (    (    s?   lib/python2.7/site-packages/sympy/solvers/tests/test_solvers.pyR†   ë  R‡   c           S   s   t  t t t t f d ƒ S(   Ni    i   (   i    i   (   R8   R_   R`   (    (    (    s?   lib/python2.7/site-packages/sympy/solvers/tests/test_solvers.pyR†   ì  R‡   (   RT   R»   Ru   (    (    (    s?   lib/python2.7/site-packages/sympy/solvers/tests/test_solvers.pyt   test_nsolveé  s    c          C   s1  t  t t t d t d t ƒ ƒ d k s1 t ‚ t  t t t d t d t ƒ ƒ d k sb t ‚ t t t d t d t ƒ g  k s t ‚ t t d „  ƒ t d t d }  t |  d d |  ƒ g  t d ƒ D] } t |  d | ƒ ^ qÑ k sù t ‚ t d }  t |  d d |  ƒ t	 j
 g k s-t ‚ d  S(   Ni   i   i   i   c           S   s#   t  t t d t d t d t ƒS(   Ni   i   t
   incomplete(   R(   RX   R_   Rw   (    (    (    s?   lib/python2.7/site-packages/sympy/solvers/tests/test_solvers.pyR†   ô  s    i   (   R¨   R(   RX   R_   Ro   RT   Rv   R>   RP   R   R¯   (   R[   R§   (    (    s?   lib/python2.7/site-packages/sympy/solvers/tests/test_solvers.pyt   test_high_order_multivariateï  s    11+J
c           C   sx   t  d t d ƒ d g k s# t ‚ t  d t d d ƒ d g k sJ t ‚ t  t d d t ƒƒ d d g k st t ‚ d  S(   Ni    i   i   s   x*(1/x**0 - x)t   evaluate(   R(   R_   Ro   R   Rw   (    (    (    s?   lib/python2.7/site-packages/sympy/solvers/tests/test_solvers.pyt   test_base_0_exp_0ÿ  s    #'c           C   s”   t  d t d t g ƒ t ƒ  k s) t ‚ t  d t t t g ƒ t t t g ƒ k s\ t ‚ t  d t t d ƒ t g ƒ t t g ƒ k s t ‚ d  S(   Ni   i    i   (   RK   R_   R„   Ro   R`   R0   (    (    (    s?   lib/python2.7/site-packages/sympy/solvers/tests/test_solvers.pyt   test__simple_dens  s    )3c           C   s¶   t  t t t ƒ t t d d t ƒ ƒ d k s7 t ‚ t  t d t d d t d t d ƒ d t d d t d t d ƒ d t d t d t d	 t ƒƒ d k s² t ‚ d  S(
   Ni   i   i þÿÿi@  i   i˜  i©   i®  Rí   (   R¨   R(   R*   R`   R_   Ro   R   Rw   (    (    (    s?   lib/python2.7/site-packages/sympy/solvers/tests/test_solvers.pyt   test_issue_8755  s    7c          C   sÎ  d }  d } d } d } d } d } d } d } t  t t f } t  |  d	 t | d	 | t d	 }	 | t  d	 | t d	 t d	 }
 t  | d	 t | d	 | t d	 } |	 |
 | f } t t  |  d	 t | d	 ƒ t | } |
 } t t  | d	 t | d	 ƒ t | } | | | f } t | | ƒ } t | | ƒ } t | | d
 t ƒ} g  | | | g D]5 } t g  | D] } t d „  | Dƒ ƒ ^ qtƒ ^ qd\ } } } | | k o¿| k n sÊt ‚ d  S(   Ni    i”ýÿÿi˜  i~   i  i3   iÍ   ih   i   RÙ   c         s   s   |  ] } | j  d  ƒ Vq d S(   i   N(   Rf   (   R   R§   (    (    s?   lib/python2.7/site-packages/sympy/solvers/tests/test_solvers.pys	   <genexpr>/  s    (	   R_   R`   Ra   R*   R(   Rg   R„   R‰   Ro   (   t   x1t   y1t   r1t   x2t   y2t   x3t   y3t   r3R  t   f1t   f2t   f3RÁ   t   g1t   g2t   g3R  RÄ   RÅ   RÆ   R/  Rü   R^   Rc   R×   (    (    s?   lib/python2.7/site-packages/sympy/solvers/tests/test_solvers.pyt   test_issue_8828  s,    &"&((Tc           C   sä  t  t d t ƒ t d t ƒ ƒ d t t d t d d t d d t d t t d ƒ t d t d ƒ t ƒ d t t d ƒ t d t d ƒ t ƒ d t t d ƒ t d	 t d ƒ t ƒ d t t d ƒ t d	 t d ƒ t ƒ d t t d ƒ t t d ƒ t ƒ d t t d ƒ t t d ƒ t ƒ d t t d ƒ t t d ƒ t ƒ d t t d ƒ t t d ƒ t ƒ d
 t t d t d	 ƒ d ƒ d
 t t d t d ƒ d ƒ d
 t t t t d ƒ t t t d ƒ ƒ d
 t t t t d ƒ t t t d ƒ ƒ d
 t t t t d ƒ t t t d ƒ ƒ d
 t t t t d ƒ t t t d ƒ ƒ d
 t t t	 d
 t t d ƒ ƒ d
 t t t	 t t d ƒ ƒ d
 t t t	 t t d ƒ ƒ d
 t t t	 d t t d ƒ ƒ g k st
 ‚ t  d t t ƒ d t d t ƒ ƒ d t t d t t d ƒ t t d ƒ t ƒ d t t d ƒ t t d ƒ t ƒ d t t d ƒ t t d ƒ t ƒ d t t d ƒ t t d ƒ t ƒ g k sàt
 ‚ d  S(   Ni   i   i    i   i	   i   i   iÿÿÿÿi   iþÿÿÿi   (   R(   R&   R_   R#   R   R"   R*   R   R   R    Ro   (    (    (    s?   lib/python2.7/site-packages/sympy/solvers/tests/test_solvers.pyt   test_issue_2840_81553  s    !PROKOQXSd%@Kc           C   s+   t  d d t d ƒ d g k s' t ‚ d  S(   Ni   i    (   R(   R_   Ro   (    (    (    s?   lib/python2.7/site-packages/sympy/solvers/tests/test_solvers.pyt   test_issue_9567E  s    c          C   sä  t  t t ƒ t g k s  t ‚ t  t d t ƒ t t t ƒ t t t ƒ g k s[ t ‚ t  t d d t ƒ t d t ƒ t d ƒ t t ƒ d t d ƒ t d ƒ t t t ƒ d t d ƒ t t ƒ d t d ƒ t d ƒ t t t ƒ d g k st ‚ t  t d t t g t t ƒ i d t 6t t 6k sBt ‚ t  t d d t t g t t ƒ d t t f d t t f g k sŽt ‚ t t d d }  t t d d t } t t  |  | g t t ƒ ƒ d k sàt ‚ d  S(   Ni   i   i   iüÿÿÿiþÿÿÿ(	   R(   R_   R:   Ro   R   R*   R;   R`   R¨   (   R  R  (    (    s?   lib/python2.7/site-packages/sympy/solvers/tests/test_solvers.pyt   test_issue_11538I  s     ;=L;!+c    	      C   sÂ  t  d ƒ \ }  } } } } } } d |  | | | d |  | | | d | | | | | |  d | d | | d | d | | d | d g } t | |  | | | | | | g d t ƒ} | i t | d d ƒ |  6t | d d ƒ | 6t | d d ƒ | 6| | 6| | 6d | 6i t | d d ƒ |  6t | d d ƒ | 6t | d d ƒ | 6| | 6| | 6d | 6i t d ƒ | d t | d d ƒ d |  6t d ƒ | d t | d d ƒ d | 6t | d d ƒ | 6| d t d | d d ƒ d | 6| d t d ƒ t | d d ƒ d | 6d | 6i t d ƒ | d t | d d ƒ d |  6t d ƒ | d t | d d ƒ d | 6t | d d ƒ | 6| d t d | d d ƒ d | 6| d t d ƒ t | d d ƒ d | 6d | 6i t d ƒ | d t | d d ƒ d |  6t d ƒ | d t | d d ƒ d | 6t | d d ƒ | 6| d t d | d d ƒ d | 6| d t d ƒ t | d d ƒ d | 6d | 6i t d ƒ | d t | d d ƒ d |  6t d ƒ | d t | d d ƒ d | 6t | d d ƒ | 6| d t d | d d ƒ d | 6| d t d ƒ t | d d ƒ d | 6d | 6g k s¾t ‚ d  S(	   Ns   a,b,c,d,e,f,gi   i   Rm   iÿÿÿÿi   iýÿÿÿi   (   R,   R(   Rg   R*   Ro   (	   RX   RY   RZ   R[   Rh   Rp   Rq   t   termsR£   (    (    s?   lib/python2.7/site-packages/sympy/solvers/tests/test_solvers.pyt   test_issue_12114Y  s0    !9?*4,/+0B&40C&4/C&4/D&c           C   sf   t  d t t ƒ g  k s  t ‚ t  t t t ƒ g  k s? t ‚ t  t t t t ƒ g  k sb t ‚ d  S(   Ni   (   R(   R9   R_   Ro   (    (    (    s?   lib/python2.7/site-packages/sympy/solvers/tests/test_solvers.pyt   test_infu  s     c          C   s³  t  d ƒ }  g  t d ƒ D] } |  | ƒ ^ q } t d ƒ } t t | | ƒ ƒ } | d  | d \ } } } } t g  t d ƒ D]P } | d | | | d | d | | d | d | | d | d ^ q€ | | | f ƒ }	 | d  | d \ } } } } t g  t d ƒ D]P } | d | | | d | d | | d | d | | d | d ^ q| | | f ƒ }
 |
 | d j | ƒ j ƒ  |	 | d j ƒ  k s¯t ‚ d  S(	   NRp   i   s   x:15i   i   i   i   i    (	   R   R>   R,   Rm   Rê   R(   t   xreplaceRm  Ro   (   Rp   R§   t   funRÞ   Rë   R_   R`   Ra   RZ   t   ssymt   sfun(    (    s?   lib/python2.7/site-packages/sympy/solvers/tests/test_solvers.pyt   test_issue_12448{  s    %ooc           C   s]  t  t d d t ƒ t d t g ƒ k s0 t ‚ t  t d d t t ƒ t t g ƒ k s` t ‚ t  t d d t t g ƒ t t g ƒ k s“ t ‚ t  d t d t d t t t g ƒ t t t g ƒ k sÔ t ‚ t  d t d t d t t t ƒ t t t g ƒ k st ‚ t  d t d t d t t t t g ƒ ƒ t t t g ƒ k sYt ‚ d  S(   Ni   i   (   RM   R_   R`   R„   Ro   Ra   (    (    (    s?   lib/python2.7/site-packages/sympy/solvers/tests/test_solvers.pyt   test_denoms  s    003A>c       &   C   s!  t  d ƒ \ }  } } } } } |  d |  |  | | |  | | |  | | |  | | |  | | |  | | |  d | d d | d | | | d | d | d | | | d | d | d | | d | d | d | | | |  | | | | | d | d | d |  d | d | d | d | d | d | d | | | d | d | d | d | | | d | d | d | | | |  | | | | | d | d | d | d | | | d | d | d | d |  d | d | d | d | d | d | d | d | | | d | | | |  | | | | d | d | d | | | d | d | d | d | d | | | d |  d d | d | d | | | |  | | | | | | | | | | | | | | |  | d |  d g% } i d |  6t d ƒ d | 6t d ƒ d | 6t d ƒ d | 6t d ƒ d | 6d | 6i d |  6t d ƒ d | 6t d ƒ d | 6d | 6d | 6d | 6i d |  6t d ƒ d | 6t d ƒ d | 6t d ƒ d | 6t d ƒ d | 6d | 6i d |  6d | 6d | 6d | 6d | 6d | 6i d |  6t d ƒ d | 6t d ƒ d | 6t d ƒ d | 6t d ƒ d | 6d | 6i d |  6t d ƒ d | 6t d ƒ d | 6t d ƒ d | 6t d ƒ d | 6d | 6g } t | ƒ | k st ‚ d  S(	   Ns   x0 x1 x2 x3 x4 x5i   i   i   i   i    iÿÿÿÿi   (   R,   R   R*   R(   Ro   (   t   x0R†  R‰  R‹  t   x4t   x5RÀ   t   sols(    (    s?   lib/python2.7/site-packages/sympy/solvers/tests/test_solvers.pyt   test_issue_12476–  s&    BFPOO50PQSGWBW-W]c          C   sO   t  d ƒ }  t |  t d ƒ t d ƒ t d ƒ |  f |  ƒ g  k sK t ‚ d  S(   NRb   i   i   (   R,   R(   R*   Ro   (   Rb   (    (    s?   lib/python2.7/site-packages/sympy/solvers/tests/test_solvers.pyt   test_issue_13849­  s    c          C   sP   d d l  m }  m } t d | |  t t t ƒ d |  t g k sL t ‚ d  S(   Niÿÿÿÿ(   t   newtont   kiloi   iÀàÿÿ(   t   sympy.physics.unitsR§  R¨  R(   R_   R`   Ro   (   R§  R¨  (    (    s?   lib/python2.7/site-packages/sympy/solvers/tests/test_solvers.pyt   test_issue_14860²  s    c       	   C   s¥  t  d ƒ \ }  } } } t d |  d d | d | d d | d d |  d d | d | d d | d | |  d g | |  | | ƒ d d | t d | d d ƒ | f d d | t d | d d ƒ | f g k së t ‚ t | | | d | d d | d d | d d g | | | ƒ | d t d ƒ d f | d t d ƒ d f g k skt ‚ t | | d d | | d d f ƒ g  k s¡t ‚ d  S(   Ns   :4iÿÿÿÿi   i   i    iþÿÿÿi	   (   R,   R(   R*   Ro   (   R\   R]   RX   RY   (    (    s?   lib/python2.7/site-packages/sympy/solvers/tests/test_solvers.pyt   test_issue_14721·  s    --&4A<c          C   s„   t  d d t ƒ}  t t |  d d |  d d ƒ t |  d d |  d d ƒ d t |  ƒ |  |  ƒ t d ƒ g k s€ t ‚ d  S(	   NR_   R·   i   i‚   i   iA  i  i`   (   R,   Rg   R(   R*   R    Ro   (   R_   (    (    s?   lib/python2.7/site-packages/sympy/solvers/tests/test_solvers.pyt   test_issue_14779Å  s    c          C   s[  t  t d t t d t d d t ƒf ƒ i d t 6d t 6i d t 6d t 6g k s[ t ‚ t  t d t d t d d t ƒf ƒ i d t 6d t 6k sž t ‚ t  t d t t d t d d t ƒf ƒ i d t 6d t 6k så t ‚ t d t d t d d	 t t ƒ }  t d
 t d d t d ƒ } t  |  | g ƒ i d t 6d t 6k sWt ‚ d  S(   Ni   i   R‚  iýÿÿÿi   iÿÿÿÿiá0  iÕW i¢éÿÿiþÿÿÿi   i(   i   iK   (   R(   R`   R4   R_   Rw   Ro   R=   R   (   Ru  Rv  (    (    s?   lib/python2.7/site-packages/sympy/solvers/tests/test_solvers.pyt   test_issue_15307Ë  s    *1&*'c           C   s  t  t d t ƒ d g k s" t ‚ t  t d g t ƒ i d t 6k sK t ‚ t  t t d t d d t d t ƒ t ƒ g  k s‡ t ‚ t  t t d t d d t d t ƒ g t ƒ g  k sÆ t ‚ t  t t d t d d t d t ƒ t t d ƒ g t ƒ g  k st ‚ d  S(   Ni   i   i   (   R(   R_   Ro   R   R`   (    (    (    s?   lib/python2.7/site-packages/sympy/solvers/tests/test_solvers.pyt   test_issue_15415Ö  s
    ")<?c          C   s  t  t t d d t d t d d t d d ƒ ƒ d d d d	 d
 d g k sW t ‚ t  t t d d ƒ d g k s~ t ‚ t  t t d d ƒ d g k s§ t ‚ t  t d d
 t d d d ƒ d d g k sÝ t ‚ t  t d d t d t d d d d d t d ƒ ƒ t d ƒ g k s0t ‚ t  t t t j d t d ƒ ƒ t d ƒ g k sjt ‚ t  t d d t d ƒ d g k s•t ‚ t  t d t d ƒ d d g k s¿t ‚ t  t d d t t d ƒ ƒ d d g k sót ‚ t  t t t j t d ƒ d ƒ t d ƒ d g k s1t ‚ t  t t d ƒ ƒ t d ƒ d t d ƒ t d t d ƒ d ƒ t t	 g k sŠt ‚ t  t d ƒ t t t d ƒ ƒ ƒ t d ƒ d g k sÉt ‚ t  t d ƒ t d t d ƒ ƒ d d t d ƒ d d t	 d d t t	 t d ƒ t d ƒ d d t	 d g k sJt ‚ t  t d ƒ t d t d ƒ ƒ d g k s}t ‚ t  t t d ƒ d g k s t ‚ t  d t t d t ƒ d g k sËt ‚ t  t d ƒ t d ƒ t d t d
 ƒ d	 t d ƒ d ƒ t d ƒ d g k s$t ‚ t
 d ƒ }  t  |  t |  d t ƒ d g k sZt ‚ t  |  t d |  t ƒ d g k s„t ‚ t  |  t |  t ƒ d g k sªt ‚ t
 d d t ƒ}  t  |  t |  d t ƒ d g k sæt ‚ t  |  t d |  t ƒ d g k st ‚ d  S(   Ni   i   i   i   i*   i   i   i   i   i   iþÿÿÿi   i   i	   RY   iÿÿÿÿRÎ   (   R(   R   R_   Ro   R*   R   R¯   R"   R   R#   R   Rg   (   RY   (    (    s?   lib/python2.7/site-packages/sympy/solvers/tests/test_solvers.pyt   test_issue_15731Þ  s2    W')6S:+*4>Y?%\3#+Y**&*N(Ü   Re  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.   R/   R0   R1   R2   R3   R4   R5   R6   R7   R8   R9   R:   R;   R<   R=   t   sympy.core.compatibilityR>   t   sympy.core.functionR?   t   sympy.solversR@   RA   RB   t   sympy.solvers.solversRC   RD   RE   RF   RG   RH   RI   RJ   RK   RL   RM   RN   R©  RO   t   sympy.polys.rootoftoolsRP   t   sympy.utilities.pytestRQ   RR   RS   RT   RU   RV   t   sympy.utilities.randtestRW   R¡   R¹   RX   RY   RZ   R[   R\   R]   R^   R_   R`   Ra   Rb   Rc   Rd   Rk   Rt   Rz   R{   R|   R}   R~   R   R™   Rš   R›   Rœ   R   R¥   Rª   R«   R¬   R­   R®   R°   R±   R³   R´   Rµ   R¾   RÂ   RÃ   RÇ   RÉ   RÊ   RÌ   RÍ   RÐ   RÒ   RÓ   RÖ   RØ   Rß   Râ   Rã   Rä   Rõ   Rö   R÷   Rù   Rú   Rû   R   R  R  R  R  R   R!  R*  R+  R-  R5  R9  R?  R@  RA  RB  RC  RD  RE  RF  RG  RI  RY  Ra  Rb  Rc  Rf  Rh  Ri  Rj  Rk  Rn  Rp  Rq  Rr  Rs  Rx  Ry  Rz  R|  R  R  Rƒ  R„  R…  R”  R•  R–  R—  R™  Rš  RŸ  R   R¥  R¦  Rª  R«  R¬  R­  R®  R¯  (    (    (    s?   lib/python2.7/site-packages/sympy/solvers/tests/test_solvers.pyt   <module>   sî   ÿ 	R.X	
						N	$				
											m	(					$		-		
	"	0			
ÿ 						!		C								(							
					1	9					
																											