ó
¡¼™\c           @   sZ  d  Z  d d l m Z m Z m Z m Z m Z m Z m Z m	 Z	 m
 Z
 m Z m Z m Z m Z m Z m Z m Z m Z m Z m Z m Z m Z m Z m Z m Z m Z m Z m Z m Z m Z m Z d d l  m! Z! m" Z# m$ Z$ m% Z& m' Z' m( Z( d d l) m* Z* d d l+ m, Z, d d l- m. Z. d d l/ m0 Z0 m1 Z1 d d l2 m3 Z3 m4 Z4 m5 Z5 e j6 ƒ  Z7 d	 „  Z8 d
 „  Z9 d „  Z: d „  Z; d „  Z< d „  Z= d „  Z> d „  Z? d „  Z@ d „  ZA d „  ZB d „  ZC d „  ZD d „  ZE d „  ZF d „  ZG e5 d „  ƒ ZH d „  ZI d „  ZJ d „  ZK d „  ZL d „  ZM e5 d „  ƒ ZN d  „  ZO d! „  ZP d" „  ZQ d# S($   sF   Tests for tools for solving inequalities and systems of inequalities. iÿÿÿÿ(   t   Andt   Eqt	   FiniteSett   Get   Gtt   Intervalt   Let   Ltt   Net   oot   It   Ort   St   sint   cost   tant   sqrtt   Symbolt   Uniont   Integralt   Sumt   Functiont   Polyt   PurePolyt   pit   roott   logt   expt   Dummyt   Abs(   t   reduce_inequalitiest   solve_poly_inequalityt   reduce_rational_inequalitiest   solve_univariate_inequalityt   reduce_abs_inequalityt   _solve_inequality(   t   rootof(   t   solve(   t   solveset(   t   xt   y(   t   raisest   slowt   XFAILc           C   s’   t  t d t ƒ d ƒ t j g k s* t ‚ t  t d t ƒ d ƒ t j g k sT t ‚ t  t t d t ƒ d ƒ t d t	 t
 t ƒ g k sŽ t ‚ d  S(   Ni    s   ==i   t   >iÿÿÿÿ(   t   psolveR   R'   R   t   Realst   AssertionErrort   EmptySetR   R   R	   t   Truet   False(    (    (    sD   lib/python2.7/site-packages/sympy/solvers/tests/test_inequalities.pyt   test_solve_poly_inequality   s    **c       	   C   s  t  t t d d ƒ g g t d t ƒt d ƒ k s: t ‚ t  t t d d ƒ g g t d t ƒt d ƒ k st t ‚ t  t t d d ƒ g g t d t ƒt j	 k s« t ‚ t j
 rå t  t t d d ƒ g g t d t ƒt j k n t t t ƒ sû t ‚ t  t t d d ƒ g g t d t ƒt d ƒ j t j ƒ k sAt ‚ t  t t d d ƒ g g t d t ƒt d ƒ j t j ƒ k s‡t ‚ t  t t d d ƒ g g t d t ƒt d d ƒ k sÄt ‚ t  t t d d ƒ g g t d t ƒt d d ƒ k st ‚ t  t t d d ƒ g g t d t ƒt d d t t ƒ k sDt ‚ t  t t d d ƒ g g t d t ƒt t t d ƒ t d t ƒ ƒ k s”t ‚ t  t t d d ƒ g g t d t ƒt d d ƒ j t j ƒ k sÝt ‚ t  t t d d ƒ g g t d t ƒt d d ƒ j t j ƒ k s&t ‚ t  t t d d ƒ g g t d t ƒt d d ƒ j ƒ  k sit ‚ t  t t d d ƒ g g t d t ƒt d d ƒ k s¦t ‚ t  t t d d ƒ g g t d t ƒt d d t t ƒ k sét ‚ t  t t d d ƒ g g t d t ƒt t t d ƒ t d t ƒ ƒ k s9t ‚ t  t t d d ƒ g g t d t ƒt t t d d t ƒt d t d	 t ƒƒ k s•t ‚ t  t t d d ƒ g g t d t ƒt d d ƒ j t j ƒ k sÞt ‚ t d ƒ }  t  t t d d d ƒ t t d d d ƒ g g t d t ƒt j	 k s9t ‚ t  t t d d d ƒ t t d d d ƒ g g t d t ƒt d d ƒ k sŽt ‚ t  t t d d d ƒ t t d d d ƒ g g t d t ƒt t |  d t t ƒ t d |  t t ƒ ƒ k st ‚ t  t t d d d ƒ t t d d d ƒ g g t d t ƒt t |  d t t ƒ t d |  t t ƒ ƒ k svt ‚ t  t t d d d ƒ t t d d d ƒ g g t d t ƒt t |  d t t ƒ t d |  t t ƒ ƒ k sêt ‚ t  t t d d d ƒ t t d d d ƒ g g t d t ƒt t |  d t t ƒ t d |  t t ƒ ƒ k s^t ‚ t  t t d d d ƒ t t d d d ƒ g g t d t ƒt t |  d t t ƒ t d d t t ƒ t d |  t t ƒ ƒ k sät ‚ t  t t d d ƒ g g t ƒ t j k st ‚ d  S(
   Ni   i    t
   relationali   iÿÿÿÿg      ð?g      ð¿t
   right_opent	   left_open(   R    R   R'   R2   R   R/   R   R   R   R0   t   is_realR   R.   R   R	   R   t
   complementR   R1   R   t   evalft   infR   t   false(   t   s(    (    sD   lib/python2.7/site-packages/sympy/solvers/tests/test_inequalities.pyt+   test_reduce_poly_inequalities_real_interval   s„    774P"!"!::@"+"$"$=:="+"!$I;:7:7:7:7:(!c       
   C   sm  t  t t d d ƒ g g t d t ƒt t d ƒ k s= t ‚ t  t t d d ƒ g g t d t ƒt t d ƒ k sz t ‚ t  t t d d ƒ g g t d t ƒt k s® t ‚ t  t t d d ƒ g g t d t ƒt	 t t
 t ƒ t t t
 ƒ ƒ k sþ t ‚ t  t t d d ƒ g g t d t ƒt	 t t t
 ƒ t t t
 ƒ t t d ƒ ƒ k sZt ‚ t  t t d d ƒ g g t d t ƒt	 t t t
 ƒ t t t
 ƒ t t d ƒ ƒ k s¶t ‚ x°t d ƒ t d ƒ f D]–}  |  t
 } t  t t d |  ƒ g g t d t ƒt t t |  ƒ t t |  ƒ ƒ k s/t ‚ t  t t d |  ƒ g g t d t ƒt	 t	 t |  t ƒ t t |  ƒ ƒ ƒ k s…t ‚ t  t t d |  ƒ g g t d t ƒt	 t	 t |  t ƒ t t |  ƒ ƒ ƒ k sÛt ‚ t  t t d |  ƒ g g t d t ƒt	 t t	 t |  t ƒ t t | ƒ ƒ t	 t t |  ƒ t | t ƒ ƒ ƒ ƒ k sVt ‚ t  t t d |  ƒ g g t d t ƒt	 t t	 t | t ƒ t t |  ƒ ƒ t	 t |  t ƒ t t | ƒ ƒ ƒ ƒ k sÑt ‚ t  t t d |  ƒ g g t d t ƒt t	 t | t ƒ t t |  ƒ ƒ t	 t |  t ƒ t t |  ƒ ƒ t	 t |  t ƒ t t | ƒ ƒ ƒ k sÏt ‚ qÏWd  S(   Ni   i    R4   i   g      ð?(   R    R   R'   R1   R/   R   R   R2   R   R    R	   R   R   R   R   (   t   oneR:   (    (    sD   lib/python2.7/site-packages/sympy/solvers/tests/test_inequalities.pyt0   test_reduce_poly_inequalities_complex_relationalh   sH    ::1M"7"7
"+"1"1"V"V"#c           C   s&  t  g  t ƒ t k s t ‚ t  t d d t d t d d d k g g t d t ƒt t j t d ƒ t d d ƒ t j d	 t ƒ ƒ k s’ t ‚ t  d t d
 d t t d d t d d d k  g g t d t ƒt t j d d ƒ t j d d ƒ ƒ k st ‚ t  t d t d d k g g t d t ƒt j d d ƒ k sMt ‚ t  t d d	 t d t d d k g g t d t ƒt t j d d ƒ t j d t ƒ ƒ k s³t ‚ t  t d d t d d d k  g g t d t ƒt t j d d ƒ t j d d	 ƒ ƒ k st ‚ t  d t d t d	 d k g g t d t ƒt t j t d ƒ t j t	 d ƒ d t ƒ ƒ k s~t ‚ t  t d t d t k g g t d t ƒt t j
 t d ƒ t j
 d d	 ƒ ƒ k sÙt ‚ t  t t k  t d k t t k  g g t d t ƒt d t ƒ k s"t ‚ d  S(   Ni   i   i   i    R4   iüÿÿÿiþÿÿÿiÿÿÿÿi   i
   i   iûÿÿÿi   iýÿÿÿi   (   R    R'   R2   R/   R   R   t   openR	   t   RopenR   t   Lopen(    (    (    sD   lib/python2.7/site-packages/sympy/solvers/tests/test_inequalities.pyt1   test_reduce_rational_inequalities_real_relational   s2    7==0$00,0(;$1c             sd  t  t d ƒ d k  }  t t d t ƒ t t d ƒ ƒ } t |  ƒ | k sO t ‚ t |  t ƒ | k sj t ‚ t t  t d ƒ ƒ t t d ƒ k s• t ‚ t t  d t d ƒ d k ƒ t t t t	 d ƒ d t ƒ t t t
 ƒ ƒ t t t t	 d ƒ d ƒ t t
 t ƒ ƒ ƒ k st ‚ t t  t d ƒ t  d t d ƒ d k  ƒ t t t	 d ƒ d t ƒ t t d ƒ ƒ k sut ‚ t t  t d ƒ t  d t  t ƒ d ƒ d k  ƒ t t t	 d	 ƒ t k  t d
 k  ƒ t t	 d ƒ d t k  t d k  ƒ ƒ k søt ‚ t d d t ƒ‰  t t ‡  f d †  ƒ t t d k  d t ˆ  g ƒt t
 t k  t d k  ƒ k s`t ‚ d  S(   Ni   i   i   i   i   i   i   i   iþÿÿÿiÿÿÿÿt   nrt   realc              s   t  t ˆ  d ƒ d k  ƒ S(   Ni   i   (   R   t   abs(    (   RD   (    sD   lib/python2.7/site-packages/sympy/solvers/tests/test_inequalities.pyt   <lambda>Ã   t    t   symbols(   RF   R'   R    R   R   R/   R   R   R   R   R	   R   R2   R)   t	   TypeError(   t   et   ans(    (   RD   sD   lib/python2.7/site-packages/sympy/solvers/tests/test_inequalities.pyt   test_reduce_abs_inequalities´   s    !+E9L1Rc           C   s”   t  t t d ƒ t d ƒ ƒ t t d ƒ d t k t t k  ƒ k sJ t ‚ t  t t d t ƒ d k ƒ t t d ƒ t k  t t k  ƒ k s t ‚ d  S(   Ni   i   i    iÿÿÿÿ(	   R   R   R   R'   R    R	   R/   R   R   (    (    (    sD   lib/python2.7/site-packages/sympy/solvers/tests/test_inequalities.pyt    test_reduce_inequalities_generalÇ   s    Jc           C   sˆ   t  t t d d ƒ t g ƒ t t d ƒ k s4 t ‚ t  t t d d ƒ t g ƒ t k s_ t ‚ t  t d d k ƒ t j k s„ t ‚ d  S(   Ni   i    (   R   R   R'   R1   R/   R2   R   t   true(    (    (    sD   lib/python2.7/site-packages/sympy/solvers/tests/test_inequalities.pyt    test_reduce_inequalities_booleanÌ   s    1+c        
   C   sÅ   t  t t d d ƒ t t d d ƒ g ƒ t t t t d t ƒ t t t ƒ ƒ t t t d ƒ t t t ƒ ƒ ƒ t t t d t ƒ t t t ƒ ƒ t t t d ƒ t t t ƒ ƒ ƒ ƒ k sÁ t	 ‚ d  S(   Ni   i   iÿÿÿÿ(
   R   R   R'   R(   R    R   R   R   R	   R/   (    (    (    sD   lib/python2.7/site-packages/sympy/solvers/tests/test_inequalities.pyt%   test_reduce_inequalities_multivariateÓ   s    ,Cc           C   s$   t  t d „  ƒ t  t d „  ƒ d  S(   Nc           S   s   t  t t t ƒ t d ƒ ƒ S(   Ni   (   R   R   R   R'   (    (    (    sD   lib/python2.7/site-packages/sympy/solvers/tests/test_inequalities.pyRG   Ú   RH   c           S   s   t  t t d t t d ƒ ƒ S(   Ni   i   (   R   R   R'   R(   (    (    (    sD   lib/python2.7/site-packages/sympy/solvers/tests/test_inequalities.pyRG   Û   RH   (   R)   t   NotImplementedError(    (    (    sD   lib/python2.7/site-packages/sympy/solvers/tests/test_inequalities.pyt   test_reduce_inequalities_errorsÙ   s    c           C   sç   t  t t d k  d t g ƒt d t k  k s5 t ‚ t  t t d k d t g ƒt t k  t t d k @k su t ‚ t  t d t t ƒ d t g ƒt t t ƒ k s¬ t ‚ t  t d t t ƒ d t g ƒt t t ƒ k sã t ‚ d  S(   Ni   RI   i    (   R   R'   R(   R/   R	   R   R   (    (    (    sD   lib/python2.7/site-packages/sympy/solvers/tests/test_inequalities.pyt   test__solve_inequalitiesÞ   s    5@7c          C   s•   d t  d d d t  d t d ƒ d d k }  t |  ƒ t t  t d ƒ d t d ƒ d k  t d ƒ d t d ƒ d t  k  ƒ k s‘ t ‚ d  S(	   Niýÿÿÿi   i-   i   i!   i    i   i‘  (   R'   R   R   R    R   R/   (   t   eq(    (    sD   lib/python2.7/site-packages/sympy/solvers/tests/test_inequalities.pyt   test_issue_6343å   s    2	c          C   s  t  t d d d k  ƒ t t d ƒ t k  t t d ƒ k  ƒ k sG t ‚ t  t d d d k ƒ t t d ƒ t k t d k ƒ k sˆ t ‚ t  t d d d k ƒ t t t t k  t d k  ƒ t t t k  t d ƒ t k  ƒ ƒ k sè t ‚ t  t d d d k ƒ t t t t k  t t d ƒ k ƒ t t d ƒ t k t t k  ƒ ƒ k sNt ‚ t d t d }  t |  d k ƒ } t t t |  d ƒ t k t t k  ƒ t t t k  t t |  d ƒ k ƒ ƒ } | | k sÐt ‚ t t	 t d d ƒ d k  ƒ t t d ƒ t k  t d k  ƒ k st ‚ d  S(   Ni   i   i    iÿÿÿÿi   i	   (
   R   R'   R    R   R/   R   R	   R%   R$   R   (   RU   t   solt   tru(    (    sD   lib/python2.7/site-packages/sympy/solvers/tests/test_inequalities.pyt   test_issue_8235ë   s    0*IOLc          C   sô   t  t d ƒ t t t d t d d f ƒ d k t g ƒ t t t d t d d f ƒ d k k si t ‚ t d ƒ }  t |  t ƒ t d d f ƒ } t  t d ƒ t | t d k t g ƒ t t d t |  t ƒ t d d f ƒ k k sð t ‚ d  S(   Ni    i   i   i   t   f(   R   R   R'   R   R(   R/   R   R   (   RZ   RK   (    (    sD   lib/python2.7/site-packages/sympy/solvers/tests/test_inequalities.pyt   test_issue_5526þ   s    -0'c             s¢  t  t d d k t d t ƒt t t d ƒ t d t ƒ ƒ k sG t ‚ t  t d d k t ƒ t t t	 d t ƒ t
 t t ƒ ƒ t t	 t d ƒ t
 t t ƒ ƒ ƒ k s¬ t ‚ t  t d t d t d d k t d t ƒt t d d ƒ t d t ƒ ƒ k st ‚ t  t d t d t d d k t ƒ t t t	 d t ƒ t	 t d ƒ ƒ t t	 d t ƒ t
 t t ƒ ƒ ƒ k svt ‚ t  t d t d t d d k  t d t d d ƒ ƒt t t d ƒ t t d ƒ ƒ k sÕt ‚ t  t d d t d d k t d t ƒt t d	 t d
 ƒ d t d ƒ d t t ƒ t t d ƒ d t d
 ƒ d t t t ƒ ƒ k sdt ‚ t  t d t d t d d k t d t ƒt d t t ƒ k s«t ‚ t  t t t d t d k  t ƒ t t d ƒ k såt ‚ t  t d t d t t d t d d t d k  t ƒ t t t d ƒ t t d ƒ ƒ k sIt ‚ t  t d t d t t d t d d t t d d k t ƒ t t d ƒ k s£t ‚ t t d „  ƒ t  t d t d d k t ƒ t t t d t d d ƒ t k  t t k  ƒ k s
t ‚ t  d t d d k t ƒ t t d ƒ t k  t t k  ƒ k sNt ‚ t d t d j ƒ  }  t  t d |  d k t ƒ t t t t k  t d k  ƒ t t d ƒ t k  t d k  ƒ ƒ k sÉt ‚ t d ƒ ‰ t t ‡ f d †  ƒ t d d t ƒ‰  t t ‡  ‡ f d †  ƒ t d d t ƒ‰ t  ˆ ˆ  d k ˆ  ƒ ˆ d ˆ  k  k sXt ‚ t  ˆ ˆ  d k  ˆ  ƒ t k s}t ‚ t  ˆ ˆ  d k ˆ  ƒ t k s¢t ‚ t d ƒ d t d ƒ d d ‰ t t ‡ f d †  ƒ t t ‡ f d †  ƒ t t d „  ƒ t t d „  ƒ t t d „  ƒ t d t t t d ‰ t  ˆ d k  t d t ƒt j k sdt ‚ t  ˆ d k t d t ƒt j k sŽt ‚ t t d „  ƒ d  S(   Ni   i   R4   iþÿÿÿi   i   i    t   domainiÿÿÿÿi   c           S   s+   t  t d d t t d t d k  t ƒ S(   Ni   i   i    (   t   isolveR'   R
   (    (    (    sD   lib/python2.7/site-packages/sympy/solvers/tests/test_inequalities.pyRG     RH   i   t   nc              s   t  t t ƒ ˆ  k t d t ƒS(   NR4   (   R]   R   R'   R2   (    (   R^   (    sD   lib/python2.7/site-packages/sympy/solvers/tests/test_inequalities.pyRG   -  RH   t   c1t   positivec              s   t  ˆ ˆ  d k  ˆ  ƒ S(   Ni    (   R]   (    (   R_   R^   (    sD   lib/python2.7/site-packages/sympy/solvers/tests/test_inequalities.pyRG   /  RH   t   negativec              s   t  t d ˆ  k  t ƒ S(   Ni   (   R]   R'   (    (   t   zero(    sD   lib/python2.7/site-packages/sympy/solvers/tests/test_inequalities.pyRG   6  RH   c              s   t  t d ˆ  t k  t ƒ S(   Ni   (   R]   R'   R
   (    (   Rb   (    sD   lib/python2.7/site-packages/sympy/solvers/tests/test_inequalities.pyRG   7  s   c           S   s   t  d t t d k  t ƒ S(   Ni   i   (   R]   R'   R(   (    (    (    sD   lib/python2.7/site-packages/sympy/solvers/tests/test_inequalities.pyRG   9  RH   c           S   s   t  d t t d k  t ƒ S(   Ni   i    (   R]   R'   R(   (    (    (    sD   lib/python2.7/site-packages/sympy/solvers/tests/test_inequalities.pyRG   :  RH   c           S   s   t  t t d k  t ƒ S(   Ni    (   R]   R'   R
   (    (    (    sD   lib/python2.7/site-packages/sympy/solvers/tests/test_inequalities.pyRG   ;  RH   c           S   s.   t  t t t ƒ d t t ƒ d d ƒ t ƒ S(   Ni   i   (   R]   R   R   R'   R   (    (    (    sD   lib/python2.7/site-packages/sympy/solvers/tests/test_inequalities.pyRG   B  s   (   R]   R'   R2   R   R   R	   R/   R   R    R   R   R   R   R   R   R1   R
   R)   t
   ValueErrorR$   t   expandR   RR   R   R   RJ   R0   R.   (   t   den(    (   R_   R^   Rb   sD   lib/python2.7/site-packages/sympy/solvers/tests/test_inequalities.pyt    test_solve_univariate_inequality  sV    ,F,*&N5*(.9,:dZ9DI0%%"**c           C   sß  t  t t ƒ t j k  t d t ƒt t d t d t t	 ƒ t d t d d t t	 t ƒ ƒ k sg t
 ‚ t  t t ƒ t j k t d t ƒt t d d t d t	 t	 ƒ k s² t
 ‚ t  t t ƒ t j k  t d t ƒt t d d t d t	 t	 ƒ k sý t
 ‚ t  t t ƒ t j k t d t ƒt t d t d ƒ t d t d d t ƒ ƒ k sXt
 ‚ t  t t ƒ t j k  t d t ƒt t j d t d ƒ t j t d t ƒ ƒ k s±t
 ‚ t  t t ƒ t j k t d t ƒt t t d ƒ ƒ t t d t ƒ ƒ k st
 ‚ t  t t ƒ t d ƒ k t d t ƒt j k s9t
 ‚ t  t t ƒ t d	 ƒ k  t d t ƒt j k sot
 ‚ t  t t ƒ t d
 ƒ k t d t ƒt j k s¥t
 ‚ t  t t ƒ t d ƒ k t d t ƒt j k sÛt
 ‚ d  S(   NR4   i    i   i   i   i   i   i   iþÿÿÿiÿÿÿÿ(   R]   R   R'   R   t   HalfR2   R   R   R   R1   R/   R   t   ZeroR   t   OneRA   RB   R   R.   R0   (    (    (    sD   lib/python2.7/site-packages/sympy/solvers/tests/test_inequalities.pyt   test_trig_inequalitiesF  s     !F!*!*!:!8!1666c           C   sÎ   t  t d d k t d t ƒt j k s. t ‚ t  t d d k t d t ƒt j j t ƒ k se t ‚ t  t d d k  t d t ƒt j k s“ t ‚ t  t d d k  t d t ƒt j j t ƒ k sÊ t ‚ d  S(   Ni   i    R4   (	   R]   R'   R2   R   R.   R/   R1   t   as_relationalR0   (    (    (    sD   lib/python2.7/site-packages/sympy/solvers/tests/test_inequalities.pyt   test_issue_9954]  s    .7.c          C   s™   t  t d t d d d ƒ }  t t t ƒ d t t d ƒ d k ƒ t t t d ƒ t k  t |  d k  ƒ t |  d t k  t t k  ƒ ƒ k s• t	 ‚ d  S(   Ni   i   i   i    i   i   (
   R$   R'   R%   R   R   R   R    R   R	   R/   (   t   r(    (    sD   lib/python2.7/site-packages/sympy/solvers/tests/test_inequalities.pyt   test_slow_general_univariated  s    &c          C   s•   d t  t d t  ƒ }  t t d t  ƒ t t  t ƒ ƒ } t |  d t  ƒ | k sW t ‚ d t  t d t  d ƒ }  t |  d k  ƒ | k s‘ t ‚ d  S(   Ni   t   <i   i    (	   R'   RF   R    R   R	   R"   R/   R   R   (   RU   RL   (    (    sD   lib/python2.7/site-packages/sympy/solvers/tests/test_inequalities.pyt   test_issue_8545k  s
    !c           C   ss   t  t t k  t ƒ t t t k  t t k  ƒ k s8 t ‚ t  t t k t ƒ t t t k  t t k  ƒ k so t ‚ d  S(   N(   R]   R	   R'   R    R/   (    (    (    sD   lib/python2.7/site-packages/sympy/solvers/tests/test_inequalities.pyt   test_issue_8974s  s    8c           C   s^  t  d d t d t d ƒ d k  ƒ t t t t k  t d k  ƒ t t d ƒ t k  t t d ƒ d k  ƒ ƒ k sx t ‚ t  t d t t ƒ ƒ d t ƒ t	 t d ƒ k s° t ‚ t
 d d t d d t ƒ d t ƒ t t t t k  t d k  ƒ t t d ƒ t k  t t d ƒ d k  ƒ t t d ƒ d t k  t t k  ƒ ƒ k sJt ‚ t t d	 „  ƒ d  S(
   Niÿÿÿÿi   i    i   iýÿÿÿRo   i   i   c           S   s,   t  d d t d d t t ƒ ƒ d t ƒ S(   Niýÿÿÿi   Ro   (   R"   RF   R   R'   (    (    (    sD   lib/python2.7/site-packages/sympy/solvers/tests/test_inequalities.pyRG     s   (   R   RF   R'   R   R    R	   R   R/   R   R   R"   R)   Rc   (    (    (    sD   lib/python2.7/site-packages/sympy/solvers/tests/test_inequalities.pyt   test_issue_10198x  s    %P8%Yc           C   s.   t  t t ƒ d k  ƒ t t k k s* t ‚ d  S(   Ni   (   R%   R   R'   R	   R/   (    (    (    sD   lib/python2.7/site-packages/sympy/solvers/tests/test_inequalities.pyt   test_issue_10047…  s    c           C   sI   t  t t ƒ d k  ƒ t t d ƒ t k  t t d ƒ k  ƒ k sE t ‚ d  S(   Niè  i    (   R%   R   R'   R    R   R   R/   (    (    (    sD   lib/python2.7/site-packages/sympy/solvers/tests/test_inequalities.pyt   test_issue_10268‹  s    c          C   se   t  d ƒ }  t t t ƒ |  k t d t ƒt t j |  d k  f t |  |  ƒ t	 f ƒ k sa t
 ‚ d  S(   NR^   R4   i    (   R   R]   R   R'   R2   t	   PiecewiseR   R0   R   R1   R/   (   R^   (    (    sD   lib/python2.7/site-packages/sympy/solvers/tests/test_inequalities.pyt   test_isolve_Sets  s    c          C   s»   t  t t ƒ t t d t ƒ ƒ t d t ƒ k s6 t ‚ t d d ƒ }  t  d t j t ƒ d k  t |  ƒ |  k sv t ‚ t  t	 t d ƒ t d k t t
 j ƒ t j d d ƒ k s· t ‚ d  S(   Ni    i   i
   i   i   (   R&   R   R(   R   R   R   R/   R'   t   diffR   R   R.   RB   (   t   i(    (    sD   lib/python2.7/site-packages/sympy/solvers/tests/test_inequalities.pyt   test_issue_10671_12466–  s
    61&c          C   so  xq t  t t t t t f D]W }  t |  t d ƒ t ƒ j t k sF t	 ‚ t |  t
 j t ƒ t ƒ j t k s t	 ‚ q Wt t d t d t ƒ t ƒ t t d ƒ k s© t	 ‚ t t
 j t ƒ } t | t ƒ | k sÖ t	 ‚ x’ t d t t ƒ t t ƒ t t ƒ t d t f D]\ } xS d	 D]K } d | | d k } t | t d t ƒ| | t
 d ƒ k k st	 ‚ qWqWt d t d d t d d k  t d t ƒt t d t
 j k  k s·t	 ‚ t t t t d ƒ t ƒ t t t d ƒ k sìt	 ‚ t d d t ƒ} t t t | d ƒ t ƒ t t d | ƒ k s3t	 ‚ t t | d k  t ƒ t | d k  k sbt	 ‚ t d d t ƒ} t | t d k t ƒ t
 j t k  t | k  @k s¬t	 ‚ t | t d k t d t ƒd t d | k k såt	 ‚ t d t t d t d ƒ } t | t ƒ t t d ƒ k s(t	 ‚ t t t d t d k  t ƒ t t
 j k  t t d ƒ @k skt	 ‚ d  S(
   Ni   i   i    t   lineart   nzt   nonzerot   aR`   (   i    i   (   R   R   R   R   R   R   R#   R'   t   lhsR/   R   Ri   R(   R   R   R   R1   Rg   R   Rh   (   t   opt   iet   fxt   cRK   R{   R}   (    (    sD   lib/python2.7/site-packages/sympy/solvers/tests/test_inequalities.pyt   test__solve_inequalityž  s.    '.5;', 55/89$c              sê  d d l  m ‰  ˆ  t t ƒ d k s, t ‚ ˆ  t d ƒ t d ƒ ƒ d k sS t ‚ ˆ  t d ƒ t ƒ ˆ  t t d ƒ ƒ k oˆ d k n s“ t ‚ ˆ  t d ƒ t ƒ ˆ  t t d ƒ ƒ k oÍ t j k n sØ t ‚ ˆ  t d ƒ t ƒ ˆ  t t d ƒ ƒ k ot j k n st ‚ ˆ  t d ƒ t ƒ ˆ  t t d ƒ ƒ k oSd k n s^t ‚ ˆ  t t ƒ ˆ  t t ƒ k o‹t d k n s–t ‚ ˆ  t t ƒ ˆ  t t ƒ k oÅt d k n sÐt ‚ t t ‡  f d †  ƒ d  S(	   Niÿÿÿÿ(   t   _pti    i   i   i   iþÿÿÿc              s   ˆ  t  d d t ƒt d ƒ ƒ S(   NRx   t   infinitei   (   R   R1   R   (    (   R„   (    sD   lib/python2.7/site-packages/sympy/solvers/tests/test_inequalities.pyRG   Ä  RH   (	   t   sympy.solvers.inequalitiesR„   R	   R/   R   Rg   R'   R)   Rc   (    (    (   R„   sD   lib/python2.7/site-packages/sympy/solvers/tests/test_inequalities.pyt   test__ptº  s    '@EDB8:N(R   t   __doc__t   sympyR    R   R   R   R   R   R   R   R   R	   R
   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R†   R   R   R-   R    R!   R]   R"   R#   t   sympy.polys.rootoftoolsR$   t   sympy.solvers.solversR%   t   sympy.solvers.solvesetR&   t	   sympy.abcR'   R(   t   sympy.utilities.pytestR)   R*   R+   R9   R:   R3   R=   R?   RC   RM   RN   RP   RQ   RS   RT   RV   RY   R[   Rf   Rj   Rl   Rn   Rp   Rq   Rr   Rs   Rt   Rv   Ry   Rƒ   R‡   (    (    (    sD   lib/python2.7/site-packages/sympy/solvers/tests/test_inequalities.pyt   <module>   sD   ¾.		K	(	$									
	>									