ó
¡¼™\c           @   sç   d  d l  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 m Z d  d l m Z d  d l m Z m Z d „  Z e d „  ƒ Z d „  Z d	 „  Z d
 „  Z d „  Z d „  Z d S(   iÿÿÿÿ(   t   Symbolt   expt   logt   oot   St   It   sqrt(   t   singularitiest   is_increasingt   is_strictly_increasingt   is_decreasingt   is_strictly_decreasingt   is_monotonic(   t   Intervalt	   FiniteSet(   t   XFAIL(   t   xt   yc          C   sˆ  t  d ƒ }  t |  d |  ƒ t j k s. t ‚ t |  |  d d |  d |  ƒ t d d ƒ k sf t ‚ t d |  d d |  ƒ t t t ƒ k s— t ‚ t |  |  d d |  ƒ t d d t d ƒ t d d t d ƒ t d ƒ k sî t ‚ t d t d d t t d t ƒ t t t d ƒ t t t d ƒ t ƒ k sHt ‚ t  d d t	 ƒ}  t d |  d d |  ƒ t j k s„t ‚ d  S(   NR   i   i   iþÿÿÿiÿÿÿÿi   t   real(
   R    R   R   t   EmptySett   AssertionErrorR   R   R   R   t   True(   R   (    (    sF   lib/python2.7/site-packages/sympy/calculus/tests/test_singularities.pyt   test_singularities   s    "81?$6c          C   sp   t  d d t ƒ}  t t d |  ƒ |  ƒ t d ƒ k s= t ‚ t t |  d d ƒ |  ƒ t d ƒ k sl t ‚ d  S(   NR   R   i   i    i   (   R    R   R   R   R   R   R   (   R   (    (    sF   lib/python2.7/site-packages/sympy/calculus/tests/test_singularities.pyt   test_singularities_non_rational   s    +c          C   s2  t  d d t ƒ}  t t d d t d d t t j ƒ sB t ‚ t t d t t d ƒ ƒ sf t ‚ t t d t d t ƒ ƒ sŠ t ‚ t d t d d t d d t d	 t d
 d ƒ ƒ sÉ t ‚ t t d t	 t d t ƒ t ƒ sò t ‚ t t d |  t d t ƒ t ƒ st ‚ t d ƒ s.t ‚ d S(   s1   Test whether is_increasing returns correct value.t   at   negativei   i   i   i    i   iH   i   iþÿÿÿi   N(
   R    R   R   R   R   t   RealsR   R   R   R   (   R   (    (    sF   lib/python2.7/site-packages/sympy/calculus/tests/test_singularities.pyt   test_is_increasing%   s    0$$?)*c           C   s   t  d t d d t d d t d t j t d ƒ ƒ sB t ‚ t  d t d d t d d t d t j d t ƒ ƒ sƒ t ‚ t  d t d d t d d t d t j d d ƒ ƒ sÅ t ‚ t  t d t d t ƒ ƒ sé t ‚ t d	 ƒ sü t ‚ d
 S(   s:   Test whether is_strictly_increasing returns correct value.i   i   i   i   iH   i   iþÿÿÿi    i   N(	   R	   R   R   t   RopenR   R   t   Lopent   openR   (    (    (    sF   lib/python2.7/site-packages/sympy/calculus/tests/test_singularities.pyt   test_is_strictly_increasing2   s    ?>?$c          C   s  t  d d t ƒ}  t d t d d t t j d d ƒ ƒ sC t ‚ t d t d d t t j d t ƒ ƒ st t ‚ t d t d d t t j	 t t
 d ƒ d ƒ ƒ s± t ‚ t t d t t d ƒ ƒ sÖ t ‚ t t d |  t t d ƒ t ƒ st ‚ d S(	   s1   Test whether is_decreasing returns correct value.t   bt   positivei   i   i   g      ø?i    N(   R    R   R
   R   R   R   R   R   R   R   R   (   R    (    (    sF   lib/python2.7/site-packages/sympy/calculus/tests/test_singularities.pyt   test_is_decreasing>   s    11=%c           C   sÛ   t  d t d d t t j d t ƒ ƒ s1 t ‚ t  d t d d t t j t t d ƒ d ƒ ƒ sn t ‚ t  t d t t d ƒ ƒ s“ t ‚ t  d ƒ s¦ t ‚ t  d t d d t t j d d ƒ ƒ s× t ‚ d S(   s:   Test whether is_strictly_decreasing returns correct value.i   i   i   i    g      ø?N(	   R   R   R   R   R   R   R   R   R   (    (    (    sF   lib/python2.7/site-packages/sympy/calculus/tests/test_singularities.pyt   test_is_strictly_decreasingI   s    1:%c           C   sá   t  d t d d t t j d d ƒ ƒ s1 t ‚ t  d t d d t t j d t ƒ ƒ sb t ‚ t  t d d t d d t t j ƒ s’ t ‚ t  t d t j ƒ s° t ‚ t  t d t	 d t d d ƒ t ƒ sÝ t ‚ d S(   s0   Test whether is_monotonic returns correct value.i   i   i   g      ø?i   N(
   R   R   R   R   R   R   R   R   R   R   (    (    (    sF   lib/python2.7/site-packages/sympy/calculus/tests/test_singularities.pyt   test_is_monotonicS   s
    110N(   t   sympyR    R   R   R   R   R   R   t   sympy.calculus.singularitiesR   R   R	   R
   R   R   t
   sympy.setsR   R   t   sympy.utilities.pytestR   t	   sympy.abcR   R   R   R   R   R   R"   R#   R$   (    (    (    sF   lib/python2.7/site-packages/sympy/calculus/tests/test_singularities.pyt   <module>   s   4.					
