ó
¡¼™\c           @   sž   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 d  d l m Z m Z d  d l m Z m Z m Z m Z d „  Z d „  Z d S(   iÿÿÿÿ(   t   symbolst   Mult   sint   Integralt   oot   Eqt   Sum(   t   Normalt   Poissont   variance(   t   probabilityt   expectation(   t
   Covariancet   Variancet   Probabilityt   Expectationc          C   sÙ
  t  d d d ƒ }  t  d d d ƒ } t d d ƒ } t d d ƒ } t d d	 t ƒ} t d
 ƒ \ } } } t |  d k ƒ j ƒ  t |  d k ƒ k s™ t ‚ t |  | k ƒ j ƒ  t |  | k ƒ k sÉ t ‚ t |  d k ƒ j t	 ƒ j
 ƒ  t |  d k ƒ k st ‚ t |  | k ƒ j t	 ƒ j
 ƒ  t |  | k ƒ k s;t ‚ t |  ƒ j ƒ  t |  ƒ k s_t ‚ t |  ƒ j t	 ƒ j
 ƒ  t |  ƒ k sŒt ‚ t |  d ƒ j ƒ  t |  d ƒ k s¸t ‚ t | |  ƒ j | |  f k sÞt ‚ t | |  ƒ j
 ƒ  | t |  ƒ k s
t ‚ t d |  d | | |  | ƒ j
 ƒ  d t |  ƒ d t | ƒ | t |  | ƒ k sjt ‚ t d |  d | | |  | ƒ j d |  d | | |  | f k s¸t ‚ t t |  ƒ ƒ t t |  ƒ ƒ j
 ƒ  k sèt ‚ t d | t |  ƒ | | |  d | |  | ƒ j
 ƒ  d | t t |  ƒ | ƒ | t |  d ƒ | t |  | ƒ k slt ‚ t | ƒ j | f k sŠt ‚ t | ƒ j
 ƒ  d k s¨t ‚ t |  ƒ j ƒ  t |  ƒ j t	 ƒ j
 ƒ  k oæt |  ƒ k n sñt ‚ t |  | ƒ j |  | f k st ‚ t |  | ƒ j
 ƒ  t |  ƒ k s?t ‚ t |  | ƒ j t |  | ƒ f k sjt ‚ t t |  | ƒ ƒ t k sŒt ‚ t | |  ƒ j
 ƒ  | d t |  ƒ k s¼t ‚ t |  | ƒ j
 ƒ  t |  ƒ t | ƒ d t |  | ƒ k sÿt ‚ t |  | | | ƒ j
 ƒ  t |  ƒ t | ƒ t | ƒ t | ƒ d t |  | ƒ d t |  | ƒ d t |  | ƒ d t | | ƒ d t | | ƒ d t | | ƒ k s³t ‚ t |  d ƒ j ƒ  t |  d ƒ k sßt ‚ t |  d ƒ t |  d ƒ k st ‚ t | |  d ƒ j
 ƒ  | d t |  d ƒ k s=t ‚ t t |  ƒ ƒ j t |  ƒ f k sgt ‚ t t |  ƒ ƒ j
 ƒ  t t |  ƒ ƒ k s—t ‚ t | t |  ƒ ƒ j
 ƒ  | d t t |  ƒ ƒ k sÓt ‚ t | | ƒ j | | f k s÷t ‚ t | | ƒ j
 ƒ  d k st ‚ t |  | ƒ j
 ƒ  d k s9t ‚ t | |  ƒ j
 ƒ  d k sZt ‚ t |  | ƒ j |  | f k s~t ‚ t t |  | ƒ ƒ t k sŸt ‚ t | |  d | ƒ j
 ƒ  | t |  | ƒ k sÕt ‚ t |  |  ƒ j |  |  f k sùt ‚ t |  |  ƒ j
 ƒ  t |  ƒ k s t ‚ t | |  d | | d ƒ j
 ƒ  | | t |  | ƒ k sbt ‚ t |  | ƒ t | |  ƒ k s†t ‚ t |  | | | ƒ j
 ƒ  t | |  ƒ t | | ƒ t |  | ƒ t | | ƒ k sßt ‚ t | |  | | | | | | ƒ j
 ƒ  | | t | |  ƒ | | t | | ƒ | | t |  | ƒ | | t | | ƒ k sh	t ‚ t | |  d | t | ƒ | | | d | | ƒ j
 ƒ  | | t | |  d ƒ | | t t | ƒ | ƒ | | t | | d |  d ƒ | | t | | d t | ƒ ƒ k s'
t ‚ t |  |  d ƒ j
 ƒ  t |  |  d ƒ k sY
t ‚ t |  t |  ƒ ƒ j
 ƒ  t t |  ƒ |  ƒ k s
t ‚ t |  d t |  ƒ | ƒ j
 ƒ  t t |  ƒ | |  d ƒ k sÕ
t ‚ d  S(   Nt   Xi   i   t   Yi   t   Zt   Wt   xt   reals   y, w, zi    (   R   R   R    t   TrueR   t   evaluate_integralR
   t   AssertionErrort   rewriteR   t   doitR   R   t   argsR   R   R	   R   t   typeR   (   R   R   R   R   R   t   yt   wt   z(    (    sJ   lib/python2.7/site-packages/sympy/stats/tests/test_symbolic_probability.pyt   test_literal_probability   sn    0099$-,&,`N0„I&(+"0C™,&8*0<$!!!$!6$'B$Y*_<ƒ26c    
      C   su  t  d d d ƒ }  t  d d d ƒ } t d d ƒ } t d d ƒ } t d ƒ \ } } } } t | ƒ j t ƒ d	 k s{ t ‚ t |  ƒ j t ƒ t |  d ƒ t |  ƒ d k s´ t ‚ t |  d
 | ƒj t ƒ t |  d | ƒ t |  | ƒ d k sù t ‚ t |  | ƒ t |  d ƒ t |  ƒ d k s,t ‚ t |  | ƒ j t ƒ t |  | d ƒ t |  | ƒ d k sqt ‚ t |  | ƒ j t ƒ t |  d | d ƒ t |  | ƒ d k sºt ‚ t | |  ƒ j t ƒ | t |  ƒ t | |  ƒ k s÷t ‚ t |  | ƒ j t ƒ t |  | ƒ t |  ƒ t | ƒ k s9t ‚ t |  | d
 | ƒj t ƒ t |  | | ƒ t |  | ƒ t | | ƒ k sŠt ‚ t d ƒ \ } } } t t	 |  | ƒ ƒ } t t	 | | ƒ ƒ }	 t |  ƒ j t ƒ t
 | | | t t f ƒ k st ‚ t | ƒ j t ƒ t | |	 | d	 t f ƒ k s8t ‚ t |  ƒ j t ƒ t
 | d | | t t f ƒ t
 | | | t t f ƒ d k s“t ‚ t | ƒ j t ƒ t | d |	 | d	 t f ƒ t | |	 | d	 t f ƒ d k sìt ‚ t |  d
 | ƒj t ƒ t
 | d t t	 |  | ƒ | ƒ | t t f ƒ t
 | t t	 |  | ƒ | ƒ | t t f ƒ d k sqt ‚ d  S(   NR   i   i   R   i   R   R   s
   x, y, w, zi    t	   conditions   W, x, z(   R   R   R    R   R   R   R   R   R   R   R   R   R   (
   R   R   R   R   R   R   R   R   t   pxt   pz(    (    sJ   lib/python2.7/site-packages/sympy/stats/tests/test_symbolic_probability.pyt   test_probability_rewriteF   s.    !9E3EI=BQ87[YHN(   t   sympyR    R   R   R   R   R   R   t   sympy.statsR   R   R	   t   sympy.stats.rvR
   R   R   R   R   R   R    R$   (    (    (    sJ   lib/python2.7/site-packages/sympy/stats/tests/test_symbolic_probability.pyt   <module>   s
   4"	?