ó
¡¼™\c        	   @   s  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> m? Z? m@ Z@ mA ZA mB ZB mC ZC mD ZD mE ZE mF ZF d  d lG mH ZH d  d lI mJ ZJ d  d lK mL ZL d  d lM mN ZN d  d lO mP ZP d  d lQ mR ZR mS ZS mT ZT mU ZU mV ZV d  d lW mX ZX d  d	 lY m" Z" eB d
 ƒ \	 ZZ Z[ Z\ Z] Z^ Z_ Z` Za Zb eA d d ec ƒZd e d ƒ Ze d „  Zf d „  Zg d „  Zh d „  Zi d „  Zj d „  Zk d „  Zl d „  Zm d „  Zn d „  Zo d „  Zp d „  Zq d „  Zr d „  Zs d „  Zt d „  Zu d „  Zv d „  Zw d  „  Zx d! „  Zy d" „  Zz d# „  Z{ d$ „  Z| d% „  Z} d& „  Z~ d' „  Z d( „  Z€ d) „  Z d* „  Z‚ d+ „  Zƒ d, „  Z„ d- „  Z… d. „  Z† d/ „  Z‡ d0 „  Zˆ d1 „  Z‰ d2 „  ZŠ d3 „  Z‹ d4 „  ZŒ d5 d6 „ Z eT d7 „  ƒ ZŽ d8 „  Z eR d9 „  ƒ Z d: „  Z‘ d; „  Z’ eR d< „  ƒ Z“ d= „  Z” d> „  Z• d? „  Z– d@ „  Z— dA „  Z˜ dB „  Z™ dC „  Zš dD „  Z› dE „  Zœ dF „  Z dG „  Zž dH „  ZŸ dI „  Z  dJ „  Z¡ dK „  Z¢ dL „  Z£ dM „  Z¤ dN „  Z¥ dO „  Z¦ dP „  Z§ dQ „  Z¨ dR „  Z© dS „  Zª dT „  Z« dU „  Z¬ dV „  Z­ dW „  Z® dX „  Z¯ dY „  Z° dZ „  Z± d[ „  Z² d\ „  Z³ d] „  Z´ d^ „  Zµ d_ „  Z¶ d` „  Z· da „  Z¸ db „  Z¹ eT dc „  ƒ Zº dd „  Z» de „  Z¼ df „  Z½ dg „  Z¾ dh „  Z¿ di „  ZÀ dj „  ZÁ dk „  ZÂ dl „  ZÃ dm „  ZÄ dn „  ZÅ do „  ZÆ dp „  ZÇ dq „  ZÈ dr „  ZÉ ds „  ZÊ dt „  ZË du „  ZÌ dv „  ZÍ dw „  ZÎ dx „  ZÏ dy „  ZÐ dz „  ZÑ d{ „  ZÒ d| „  ZÓ d} „  ZÔ eR d~ „  ƒ ZÕ d „  ZÖ d€ „  Z× d „  ZØ d‚ „  ZÙ dƒ „  ZÚ d„ „  ZÛ eT d… „  ƒ ZÜ eT d† „  ƒ ZÝ d‡ „  ZÞ dˆ „  Zß d‰ „  Zà dŠ „  Zá d‹ „  Zâ dŒ „  Zã d „  Zä dŽ „  Zå d „  Zæ d „  Zç d‘ „  Zè d’ „  Zé d“ „  Zê d” „  Zë d• „  Zì d– „  Zí d— „  Zî d˜ „  Zï d™ „  Zð dš „  Zñ d› „  Zò dœ „  Zó d „  Zô dž „  Zõ dŸ „  Zö d  „  Z÷ d¡ „  Zø d¢ „  Zù d£ „  Zú eT d¤ „  ƒ Zû d¥ S(¦   iÿÿÿÿ(F   t   Abst   acost   acosht   Addt   Andt   asint   asinht   atant   Cit   cost   sinht   cosht   tanht
   Derivativet   difft
   DiracDeltat   Et   Eit   Eqt   expt   erft   erfct   erfit
   EulerGammat   Exprt   factort   Functiont   gammat	   gammasimpt   It   Idxt   imt   IndexedBaset   Integralt	   integratet   Intervalt   Lambdat   LambertWt   logt   Matrixt   Maxt   meijergt   Mint   nant   Net   Ot   oot   pit	   Piecewiset
   polar_liftt   Polyt	   polygammat   Rationalt   ret   St   Sit   signt   simplifyt   sint   sinct   SingularityFunctiont   sqrtt   sstrt   Sumt   Symbolt   symbolst   sympifyt   tant   trigsimpt   Tuple(   t   periodic_argument(   t   floor(   t   NonElementaryIntegral(   t   units(   t   range(   t   XFAILt   raisest   slowt   skipt	   ON_TRAVIS(   t   verify_numerically(   R!   s   x y a t x_1 x_2 z s bt   nt   integert   fc             sØ  d t  ‰  t ˆ  t  t t f ƒ j ƒ  d k s5 t ‚ t ˆ  t t t f ƒ j ƒ  t t d t  ƒ k sn t ‚ t t ‡  f d †  ƒ t t ‡  f d †  ƒ d t  d d ‰ t ˆ t  t t f ƒ j ƒ  t	 d ƒ t
 d k sæ t ‚ t t ‡ f d †  ƒ d t  d d }  t |  t  t t f ƒ j ƒ  d k s9t ‚ t |  t  d d f ƒ j ƒ  t d ƒ k sjt ‚ t  t  d d } t | t  t t f ƒ j ƒ  d k s§t ‚ t | t  d d f ƒ j ƒ  d k sÑt ‚ t  d t  d d } t | t  t t f ƒ j ƒ  t k st ‚ t | t  d d f ƒ j ƒ  t d ƒ d	 k sGt ‚ d t  d d d t  d } t | t  t t f ƒ j ƒ  t
 d k s•t ‚ t | t  d d f ƒ j ƒ  t d ƒ t d ƒ d k sÔt ‚ d  S(
   Ni   i    c              s   t  ˆ  t ƒ j ƒ  S(   N(   R!   t   xt   principal_value(    (   t   g(    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyt   <lambda>   t    c              s   t  ˆ  ƒ j ƒ  S(   N(   R!   RU   (    (   RV   (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyRW      RX   i   c              s   t  ˆ  t t d f ƒ j ƒ  S(   Ni   (   R!   RT   R.   RU   (    (   t   l(    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyRW       RX   i   iþÿÿÿi   (   RT   R!   R.   RU   t   AssertionErrort   yR8   RL   t
   ValueErrorR=   R/   R&   R   (   t   dt   vt   sRS   (    (   RV   RY   sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyt   test_principal_value   s(    
+9:+1+*+50c         C   sX   |  j  } xH | D]@ } |  j | ƒ j ƒ  |  j ƒ  j | ƒ j ƒ  d k s t ‚ q W| S(   sº   Return the set of symbols, s, which were used in testing that
    i.diff(s) agrees with i.doit().diff(s). If there is an error then
    the assertion will fail, causing the test to fail.i    (   t   free_symbolsR   t   doitt   expandRZ   (   t   it   symsR_   (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyt	   diff_test2   s    	>c           C   sŽ   t  t t ƒ t d d f ƒ d k s* t ‚ t  t d t d t f ƒ d k sR t ‚ t  d d t t ƒ t d t f ƒ t d ƒ k sŠ t ‚ d  S(   Ni    i   iÿÿÿÿiþÿÿÿi   (   R"   R&   RT   RZ   R.   R   (    (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyt   test_improper_integral<   s    *(c          C   sŽ  t  t t ƒ }  |  j t t ƒ f k s- t ‚ t  t t f ƒ } | j t t ƒ f k s] t ‚ t  t t t d t f ƒ ƒ } | j t t ƒ f k s™ t ‚ t  t t t ƒ ƒ } | j t t ƒ f k sÌ t ‚ t  t t t d d ƒ f ƒ } | j t t d d ƒ f k st ‚ t  t t d k ƒ } | j t t d t	 ƒ f k sGt ‚ t  t t d k t d k  @ƒ } | j t t d d ƒ f k sŠt ‚ d  S(   Ni   i   i
   i   (
   R!   RQ   t   limitsRE   RZ   R?   RT   R[   R#   R.   (   t   s1t   s2t   s3t   s4t   s5t   s6t   s7(    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyt   test_constructorB   s    $$c          C   sC  t  d t ƒ d k s t ‚ t  t t d d f ƒ d k s? t ‚ t  t t ƒ t k sZ t ‚ t  t j t ƒ t j k s{ t ‚ t t  t t ƒ t ƒ d k sŸ t ‚ t t  t t d d f ƒ t ƒ d k sÌ t ‚ t t  t t ƒ t ƒ t k sð t ‚ t t  t t d t f ƒ t ƒ t k st ‚ t d d }  t t	 |  t d t f ƒ t ƒ t t  |  t d t f ƒ t ƒ j
 ƒ  j ƒ  k o’d t d j ƒ  k n st ‚ t t	 |  t d t f ƒ t ƒ t t  |  t d t f ƒ t ƒ k oêd k n sõt ‚ t t	 |  t d t f ƒ t ƒ t t  |  t d t f ƒ t ƒ k oBd k n sMt ‚ t t	 |  t ƒ t ƒ t t  |  t ƒ t ƒ k oˆd k n s“t ‚ t	 |  t t t f ƒ j t ƒ t  |  t t t f ƒ j t ƒ j
 ƒ  j ƒ  k sçt ‚ t  |  t t t f ƒ j t ƒ j
 ƒ  d t d k s"t ‚ t	 |  t t t f ƒ j t ƒ j
 ƒ  d t d j ƒ  k sdt ‚ t	 t d t t d t f ƒ j t ƒ d t d k s¡t ‚ t  t t ƒ j ƒ  t h k sÅt ‚ t  t t ƒ t d d f ƒ j ƒ  t d ƒ t d ƒ t h k s
t ‚ t t  t t d t f ƒ ƒ t h k s8t ‚ t t  t t d t f ƒ ƒ t t h k sit ‚ t	 t t t t f ƒ d k st ‚ t	 t t t t f ƒ d k s³t ‚ t	 t t t t ƒ t ƒ t t t d d t t ƒ k söt ‚ t  t ƒ j st ‚ t d d t ƒ} t  | t t ƒ j t k s?t ‚ d  S(   Ni    i   i   i   i   RQ   t   commutative(   R!   RT   RZ   R.   R6   t   NaNR   R[   t   tR"   Rb   Rc   t   at   atomsRS   Rf   R   t   is_commutativeR@   t   False(   t   eRQ   (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyt   test_basicsX   s@    $!$-$-2"::F6;B=$E.1$&Cc          C   s    d t  f d „  ƒ  Y}  |  ƒ  } t | d | ƒ | d d | k sJ t ‚ t | d | d d f ƒ t d ƒ d k s| t ‚ t t d „  ƒ t t d „  ƒ d  S(	   Nt   Testc           B   s   e  Z e Z e Z RS(    (   t   __name__t
   __module__t   Truet	   _diff_wrtRv   (    (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyRz   ‡   s   i   i   i    i   c           S   s   t  t d t d ƒ S(   Ni   (   R"   RT   (    (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyRW      RX   c           S   s   t  t d t d d d f ƒ S(   Ni   i    (   R"   RT   (    (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyRW      RX   (   R   R"   RZ   R6   RL   R\   (   Rz   Rs   (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyt   test_diff_wrt†   s    	+2c           C   s”  t  t t t d t d t f t t d t f ƒ ƒ t h k sE t ‚ t  t t t d t f t t d t f ƒ ƒ t h k sƒ t ‚ t  t t t d t f t t d t f ƒ ƒ t t h k sÄ t ‚ t  t t t t ƒ ƒ t t h k sî t ‚ t  t t t t t ƒ ƒ t t h k st ‚ t  t t t t t d t f ƒ ƒ t h k sPt ‚ t  t t t t t t f t t t f ƒ ƒ t t h k st ‚ d  S(   Ni   i   i   i   (   Rf   R!   RT   R[   RZ   (    (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyt   test_basics_multiple“   s    E>A*.4c          C   sh  t  d d t ƒ\ }  } t d d t ƒ} t |  | | f ƒ } | j ƒ  j ƒ  | j ƒ  j ƒ  k sj t ‚ | j ƒ  j ƒ  | j ƒ  j ƒ  k s” t ‚ | j	 ƒ  j ƒ  | j ƒ  j	 ƒ  k s¾ t ‚ t d d t ƒ} t |  | | f ƒ } | j ƒ  j ƒ  | j ƒ  j ƒ  k st ‚ | j ƒ  j ƒ  | j ƒ  j ƒ  k s:t ‚ | j	 ƒ  j ƒ  | j ƒ  j	 ƒ  k sdt ‚ d  S(   Ns   A BRq   RT   t   complext   real(
   RA   Rw   R@   R}   R!   t   adjointRb   RZ   t	   conjugatet	   transpose(   t   At   BRT   t   p(    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyt   test_conjugate_transposež   s    *****c          C   sØ  t  d t d t f ƒ d k s$ t ‚ t  d t d t f ƒ d t k sL t ‚ t  t t d t f ƒ t d d k sx t ‚ t  d t t d t f ƒ d t d d k s¬ t ‚ t  d t d t d t f ƒ t d k sÜ t ‚ t  d t t d t f ƒ t t ƒ k s
t ‚ t  d t d t d t f ƒ d t d k s>t ‚ t  t d d t d t d t f ƒ t d d d t d d d t k s’t ‚ t  t d t ƒ t d d k s¹t ‚ t  d t t d t ƒ d t d t d d k sôt ‚ t d	 ƒ }  t d
 ƒ } t  t t t d t f ƒ t t d d k s@t ‚ t  t t d t d t f ƒ t t d d k sxt ‚ t  t t d |  t | t d t f ƒ t t d d |  t d d | t k sÔt ‚ d  S(   Ni    i   i   i   iÿÿÿÿi   i   i   t   bt   ci   (   R"   Rs   RT   RZ   R&   R@   Rt   (   RŠ   R‹   (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyt   test_integration®   s    $(,40.4T';48c           C   sR  t  t d t d t d d f t d d f ƒ t d ƒ k sB t ‚ t  t d t d t t ƒ t d d ƒ t d t d k s… t ‚ t  d t d d t d t ƒ t d ƒ d t d t ƒ t d ƒ d t d t ƒ t d d t d t d k st ‚ t  t t t ƒ t t d d f t d d f ƒ t d ƒ d k sNt ‚ d  S(	   Ni   i    i   iÿÿÿÿi	   i   i   i   (   R"   RT   R[   R4   RZ   R6   R&   R:   (    (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyt   test_multiple_integrationÁ   s
    BC `c           C   s/   t  t t ƒ t d t f ƒ d k s+ t ‚ d  S(   Ni    i   (   R"   R   RT   R.   RZ   (    (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyt   test_issue_3532É   s    c           C   s¡   t  t t ƒ d t ƒ d t t ƒ d d k s7 t ‚ t  t t ƒ t ƒ d t t ƒ d d k sj t ‚ t  d t t ƒ d t ƒ d t t ƒ k s t ‚ d  S(   Ni   i   i   i   iþÿÿÿ(   R"   R=   RT   RZ   (    (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyt   test_issue_3560Í   s    73c          C   s,  t  t t d t t d t t ƒ }  t |  t ƒ } t |  t ƒ } t | t  ƒ t k s_ t ‚ t | t  ƒ t k sz t ‚ | j t t f k s• t ‚ | j t t f k s° t ‚ | j ƒ  t d d t d t d t t d k sì t ‚ | j ƒ  t t t d t d d t d d k s(t ‚ d  S(   Ni   i   i   (	   R2   RT   R[   R"   t
   isinstanceR}   RZ   t   genst   as_expr(   Rˆ   t   qxt   qy(    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyt   test_integrate_polyÓ   s    &<c          C   s-  t  t t d t t d t t ƒ }  t |  t d d f ƒ } t |  t d t f ƒ } t | t  ƒ t k sq t ‚ t | t  ƒ t k sŒ t ‚ | j t f k s¤ t ‚ | j t f k s¼ t ‚ | j	 ƒ  t
 d d ƒ t d t d k sí t ‚ | j	 ƒ  t d d t t t d t d d k s)t ‚ d  S(   Ni   i   i    i   i   (   R2   RT   R[   R"   R/   R   R}   RZ   R‘   R’   R4   (   Rˆ   t   Qxt   Qy(    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyt   test_integrate_poly_definedã   s    &1c              sV   t  d ƒ ‰  t t ƒ t d d k s, t ‚ t t d „  ƒ t t ‡  f d †  ƒ d  S(   NR[   i   c           S   s
   t  d ƒ S(   Ni   (   R"   (    (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyRW   ø   RX   c              s   t  t ˆ  ƒ S(   N(   R"   RT   (    (   R[   (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyRW   ù   RX   (   R@   R"   RT   RZ   RL   R\   (    (    (   R[   sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyt   test_integrate_omit_varó   s     c          C   s‚   t  d ƒ }  t t t |  ƒ t ƒ t d t |  ƒ d k sC t ‚ t t d t |  ƒ t ƒ t d t |  ƒ d k s~ t ‚ d  S(   NR[   i   iè  ié  (   R@   R"   RT   R:   RZ   (   R[   (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyt   test_integrate_poly_accuratelyü   s    7c          C   sg   t  d ƒ }  t t d |  ƒ t d |  k s3 t ‚ t t d |  d d f ƒ d t d k sc t ‚ d  S(   NR[   i   iÿÿÿÿi   (   R@   R"   RT   RZ   (   R[   (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyt   test_issue_3635  s    'c          C   sÅ   t  d d t ƒ}  t t |  t d d ƒt |  d |  d k sG t ‚ t t |  ƒ t d |  d t |  ƒ t d d ƒt |  ƒ t |  ƒ t d |  d t |  ƒ d t |  ƒ k sÁ t ‚ d  S(   NR[   t   positivet   condst   nonei   i   (   R@   R}   R"   RT   RZ   R   R:   (   R[   (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyt   test_integrate_linearterm_pow  s    52c           C   s¦   t  t t t ƒ t ƒ d t t t ƒ d d k s; t ‚ t  t t t ƒ t t t ƒ d t ƒ d t t t ƒ d d d t t t ƒ d d k s¢ t ‚ d  S(   Ni   i   i   (   R"   R/   R=   RT   RZ   R   (    (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyt   test_issue_3618  s    ;(c           C   su  t  t t d t ƒ t ƒ t t t t d ƒ t d t t d d ƒ f t t f ƒ k sa t ‚ t  t t d t ƒ t ƒ t t t t d ƒ t d t t d d ƒ f t t f ƒ k sÂ t ‚ t  t t d t ƒ t t d t ƒ t ƒ t t t t d ƒ t d t t d d ƒ f t t f ƒ t t t t d ƒ t d t t d d ƒ f t t f ƒ k sqt ‚ d  S(   Ni   i    (	   R"   R	   RQ   RT   R0   R:   R,   R}   RZ   (    (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyt   test_issue_3623  s    DD,;c          C   sÓ   t  d d t d t ƒ}  t d d t t |  t t d ƒ t d d g ƒ d t t |  ƒ t |  k sp t ‚ t t d ƒ d t t |  t t d ƒ t d d g ƒ d t t |  ƒ t |  k sÏ t ‚ d  S(	   NRQ   RR   t   nonzerog      ð¿i   iþÿÿÿi    i   (	   R@   R}   R"   RT   R:   R/   R	   RZ   R4   (   RQ   (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyt   test_issue_3664&  s
    3%:c           C   sB   t  t d t d d t d t d d f ƒ ƒ d k s> t ‚ d  S(   Ni   i   i   i   i   s   1.10714871779409(   t   NSR!   RT   RZ   (    (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyt   test_issue_3679.  s    c          C   sw   d d l  m }  m } |  t t t d ƒ t ƒ ƒ t d ƒ t t ƒ | t d ƒ t t t ƒ ƒ d k ss t ‚ d  S(   Niÿÿÿÿ(   t   expand_funct   fresnelsi   (	   t   sympyR¦   R§   R"   R:   RT   R=   R/   RZ   (   R¦   R§   (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyt   test_issue_36863  s    c          C   sR   t  j }  t  j } t t |  | t d | d | f ƒ d |  | k sN t ‚ d  S(   Ni   i   i   (   RI   t   mR_   R"   RT   RZ   (   Rª   R_   (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyt   test_integrate_units8  s    		c           C   sN   t  t d t ƒ t ƒ t t t d t ƒ t t d t ƒ k sJ t ‚ d  S(   Ni   (   R"   R%   RT   RZ   (    (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyt   test_transcendental_functions>  s    c           C   s~   t  t d t ƒ t t d d f ƒ t d d k s; t ‚ t  t t ƒ d t d t d d f ƒ t d d k sz t ‚ d  S(   Ni   i    i   i   iÿÿÿÿ(   R"   R&   RT   R/   RZ   (    (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyt   test_log_polylogC  s    ;c          C   s~   d t  t ƒ d t  t ƒ d }  t t |  t ƒ t ƒ } t |  j t d ƒ j ƒ  | j t d ƒ j ƒ  ƒ d k  sz t ‚ d  S(   Ni   i   i*   g»½×Ùß|Û=(   R&   RT   R   R"   t   abst   subst   evalfRZ   (   RS   t   fid(    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyt   test_issue_3740H  s    "c           C   s1   t  d d t d t ƒ t t ƒ k s- t ‚ d  S(   Ni   i   (   R"   RT   R   RZ   (    (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyt   test_issue_3788N  s    c              sH   t  t ƒ ‰  t ˆ  t ƒ t t ƒ k s. t ‚ t t ‡  f d †  ƒ d  S(   Nc              s   t  ˆ  d t ƒ S(   Ni   (   R"   RT   (    (   RS   (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyRW   U  RX   (   R:   RT   R"   R	   RZ   RL   R\   (    (    (   RS   sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyt   test_issue_3952R  s    "c           C   sA   t  d t d t t ƒ d t t d ƒ t d k s= t ‚ d  S(   Ni   (   R"   RT   R&   RZ   (    (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyt   test_issue_4516X  s    c          C   s\   t  t d t t ƒ t d t f ƒ }  t |  ƒ t j k rR t |  ƒ t j k sX t	 ‚ d  S(   Ni   i    (
   R"   R   R   RT   R.   R5   R6   t   HalfR   RZ   (   t   ans(    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyt   test_issue_7450\  s    'c        	   C   sæ   t  d t d t ƒ d d t d t ƒ t d t f ƒ t d t d ƒ t d k s_ t ‚ t  d t d t ƒ d d t d t ƒ ƒ t d t d ƒ t t d ƒ t t ƒ ƒ t t t t d t ƒ d k sâ t ‚ d  S(   Ni   i   i   i    i   (	   R"   R	   RT   R/   R=   RZ   R   RC   RG   (    (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyt   test_issue_8623a  s    _5c           C   s°   t  d d t t ƒ t d t f ƒ t t d ƒ k s< t ‚ t  d d t t ƒ ƒ d t d ƒ t t d ƒ t t d ƒ ƒ t t t d t d t ƒ d k s¬ t ‚ d  S(   Ni   i   i    i   (	   R"   R	   RT   R/   R=   RZ   R   RC   RG   (    (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyt   test_issue_9569g  s    <c           C   s´   t  d d t t ƒ t d t f ƒ t t d ƒ k s< t ‚ t  d d t t ƒ ƒ d t d ƒ t t d ƒ t t d ƒ d ƒ t t t d t d t ƒ d k s° t ‚ d  S(   Ni   i   i    i   (	   R"   R	   RT   R/   R=   RZ   R   RC   RG   (    (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyt   test_issue_13749l  s    <c          C   st   t  d d d „  ƒ }  t |  t ƒ t  t t ƒ t d t ƒ g t d t ƒ t d t ƒ g g ƒ k sp t ‚ d  S(   Ni   c         S   s"   |  | d t  |  | d t ƒ S(   Ni   (   R:   RT   (   Rd   t   j(    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyRW   r  RX   i   (   R'   R"   RT   R	   RZ   (   t   M(    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyt   test_matricesq  s    c           C   sø   t  t t ƒ t ƒ t t t ƒ t ƒ k s0 t ‚ t  t t ƒ t d d f ƒ t t t ƒ t d d f ƒ k sr t ‚ t  t t ƒ t t t ƒ t ƒ t ƒ t t ƒ d d k s´ t ‚ t  t t t ƒ t ƒ t t ƒ t ƒ t t t ƒ ƒ k sô t ‚ d  S(   Ni    i   i   (   R"   RS   RT   R!   RZ   R   R&   (    (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyt   test_integrate_functionsz  s    0BBc           C   s»   t  t t t ƒ t ƒ t ƒ t t ƒ k s0 t ‚ t  t t t ƒ t ƒ t ƒ t t t t ƒ t ƒ k sm t ‚ t  t t t ƒ t ƒ d t ƒ t t t t ƒ t ƒ d t ƒ k s· t ‚ d  S(   Ni   (   R"   R   RS   RT   RZ   R[   R!   (    (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyt   test_integrate_derivatives‚  s    0=c          C   sW  t  t d d t d d f ƒ }  t } d t d } |  j ƒ  |  j | | ƒ j ƒ  k s^ t ‚ |  j | | ƒ j | | ƒ |  k sˆ t ‚ d t d } t } |  j | | ƒ j | | ƒ |  k sÆ t ‚ t  t d t ƒ t d d f ƒ }  |  j t d t ƒ t  t t ƒ t d t d t f ƒ k s*t ‚ |  j t d t ƒ j t d t ƒ |  k s\t ‚ t  t t d ƒ t t t f ƒ }  |  j t d t ƒ t  d t d t d ƒ t t t f ƒ k sÇt ‚ t  t t ƒ j t |  t ƒ j ƒ  t  t |  d t ƒ j ƒ  k st ‚ t	 d ƒ } t  t t d | f ƒ j t d t ƒ j ƒ  t  d t d t t d | f ƒ j ƒ  k s{t ‚ t  t t d | f ƒ j t d t ƒ t  t d t d | t f ƒ k sÉt ‚ t  t t t d d f t d d f ƒ } | j t t d t t f ƒ j ƒ  | j t t d t
 t f ƒ j ƒ  k oHd k n sSt ‚ d  S(   Ni   i   iÿÿÿÿi   i    iüÿÿÿiýÿÿÿ(   R!   RT   R[   Rb   t	   transformRZ   R:   R.   R   R6   t   z(   Rt   t   fxt   fyt   _3Rd   (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyt   test_transform‰  s.     ***"B2$G"&,4%)(#c          C   s†   t  d ƒ d t t ƒ t t d t d ƒ d }  t t t t ƒ ƒ t ƒ |  k s[ t ‚ t t t t ƒ ƒ t ƒ |  k s‚ t ‚ d  S(   Ni   i   (	   R6   R   RT   R=   R"   R	   RZ   R:   R   (   RS   (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyt   test_issue_4052¥  s    4'i   c         K   s"   t  t |  ƒ j | |  d t ƒS(   Nt	   full_prec(   R>   RB   R°   R}   (   Rx   RQ   t   options(    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyR¤   ¬  s    c          C   sÐ  t  t t t d d f ƒ d ƒ d k s- t ‚ t t t d ƒ t t t f ƒ }  t  |  d ƒ d k sl t ‚ t  |  d t t t d d. ƒ d ƒ d/ k s  t ‚ t	 d ƒ } d t
 d ƒ d d | d } d t
 d ƒ d | d t
 d | d | d ƒ d } d | d d d | d d | d d } t
 d ƒ d | d d | d d | d d | d d } | | | | } t  t | | d d f ƒ d ƒ t  d t
 d ƒ d t d t t
 d ƒ ƒ d d ƒ k sæt ‚ t  t t t d t ƒ ƒ d t t d t d d f ƒ d ƒ t  d d ƒ k s<t ‚ t  t t t
 t d d ƒ ƒ t
 t d d ƒ t d d t d d f ƒ d ƒ t  d t d d d ƒ k s°t ‚ t  t t t t t ƒ t t t ƒ t d d t d t f ƒ d ƒ t  d d ƒ k st ‚ t  t t t t t ƒ t t ƒ ƒ ƒ t t d t d f ƒ d d t ƒt  d d ƒ k sot ‚ t  d t t d t t d ƒ ƒ t t t f ƒ d d t ƒt  d d ƒ k sÄt ‚ t  d t t d t t d ƒ ƒ t t t f ƒ d d t ƒt  d d ƒ k st ‚ t  d t t d t t d ƒ ƒ t t t f ƒ d d t ƒt  d d ƒ k snt ‚ t  t d t d  t d d f ƒ d d! d" d t ƒd0 k s¯t ‚ t t t ƒ t d t d t f ƒ j d! d ƒ } d% | k  oød& k  n st ‚ t  t t t ƒ t d t d t f ƒ d' d( ƒd) k sAt ‚ t  t t t t d ƒ t t t d* f ƒ d' d( ƒd+ k s„t ‚ t  t t t ƒ ƒ d, k s¥t ‚ t  t t t t f ƒ ƒ d- k sÌt ‚ d  S(1   Ni   i   i   s   10.5000000000000s   1.77245385090552i   i
   i   s   2.71828182845904e-20s   2.71828182845905e-20Rs   i   i   i   i   i   iù   i6   iA   i    i2   i1   i¢   i   s*   pi/sqrt(3) * log(2*pi**(5/6) / gamma(1/6))i`   s   log(2)/2-1/4t   chops   pi/4*log(4*pi**3/gamma(1/4)**4)i   i   s   sqrt(1-x**2)t   maxni   s   0.0t   0g\Âõ(\ß?gR¸…ëQà?t   quadt   oscs   0.504067061906928iÿÿÿÿs   0.276374705640365s   Integral(x, x)s   Integral(x, (x, y))l      Fµx:^V (   s   2.71828182845904e-20s   2.71828182845905e-20(   s   0.0RÌ   (   R¤   R!   RT   RZ   R   R.   R/   R   R4   R@   R=   R   R&   R:   R	   R}   R°   R[   (   t   gaussRs   Rt   RŠ   R‹   R]   RS   (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyt   test_evalf_integrals°  sJ    -$  :.@B>>6FHRRR52";=!c           C   sµ   t  t d t d d t ƒ j t d ƒ d t ƒd
 k s? t ‚ t  t d t d d t d d f ƒ ƒ d	 k su t ‚ t  t d t d d t d d f ƒ d t ƒd	 k s± t ‚ d  S(   Ni   i   i   RÊ   s   -0.000976138910649103s   0.965906660135753s   1.93278945918216i   s   0.0144361088886740(   s   -0.000976138910649103s   0.965906660135753s   1.93278945918216(   R¤   R"   RT   R¯   R}   RZ   R!   (    (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyt   test_evalf_issue_939ä  s
    06c           C   s’   t  t t t ƒ t t t d d f t d d f ƒ d ƒ d k sG t ‚ t  t t t t t ƒ t d d f t d d f ƒ d ƒ d k sŽ t ‚ d  S(   Ni   i   iÿÿÿÿi   s   2.43790283299492s   0.0(   R¤   R!   R=   RT   R[   RZ   R:   (    (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyt   test_failing_integralsó  s    Ac    	      C   sf  t  t t d ƒ t  t d d ƒ }  t  t t d ƒ d t  t d d ƒ } t |  t ƒ | k sc t ‚ d t  t d d ƒ d t  t d d ƒ } d t  t d d	 ƒ d t  t d d ƒ } t | t ƒ | k sÒ t ‚ d
 t d
 t d t  t d d ƒ d
 t  t d d ƒ } d
 t d t d d
 t t  t d d ƒ d t  t d d ƒ d } t d
 t d
 d t t  t d d ƒ d
 t  t d d ƒ } t | t ƒ | k s«t ‚ t | t ƒ | k sÆt ‚ t | t ƒ t | t ƒ k sêt ‚ t | t ƒ j ƒ  | k st ‚ d t  t d d ƒ d
 t  t d d ƒ } d t  t d d ƒ d d
 t  t d d ƒ } t | t t t f ƒ | k sˆt ‚ t t  t d d ƒ t ƒ t  t d d ƒ k s»t ‚ t t  t d d ƒ t t t f ƒ d	 k sìt ‚ t d t  t d d ƒ t t t f ƒ d k s!t ‚ t t  t d d ƒ t	 t ƒ t t t f ƒ t	 d ƒ k sbt ‚ d  S(   Ni   i   iÿÿÿÿi   i    i
   iúÿÿÿiþÿÿÿi   i   iüÿÿÿi   i   (
   R<   RT   Rt   R"   RZ   R[   R!   Rb   R.   RS   (	   t   in_1t   out_1t   in_2t   out_2t   in_3t   out_3_1t   out_3_2t   in_4t   out_4(    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyt"   test_integrate_SingularityFunctioný  s(    "&**:F>$!*.%315c          C   s  t  t t ƒ t t ƒ t t t f ƒ t d ƒ k s; t ‚ t  t t ƒ d t t t f ƒ t d ƒ k sp t ‚ t  t  d d t t t d t t t ƒ t t d ƒ t d d f ƒ t d d f ƒ d k sÖ t ‚ t t d t d ƒ t }  t  |  t t d t ƒ t t t f t t t f ƒ t  |  t t d t ƒ t t t f t t t f ƒ k oöt  |  t d t t ƒ t t t f t t t f ƒ k oöt  |  t d t t ƒ t t t f t t t f ƒ k oöd t	 d t ƒ k n st ‚ d  S(   Ni    i   i   i   i
   ie   (
   R"   R   RT   RS   R.   RZ   R[   R   R/   R=   (   Rˆ   (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyt   test_integrate_DiracDelta  s    ;5`5===c           C   sd   t  t  t  t t t t ƒ t d t f ƒ t d d f ƒ t d d f ƒ t d ƒ d k s` t ‚ d  S(   Ni    i   i   (   R"   R   RT   R[   RÂ   R.   R6   RZ   (    (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyt   test_integrate_DiracDelta_fails*  s    	c           C   s  t  t t t ƒ t t t d t d t t d ƒ f t t ƒ t f ƒ k sS t ‚ t  t t t ƒ t t t t t ƒ t t t ƒ d ƒ f t t f ƒ k s¤ t ‚ t  t t	 t ƒ t ƒ t t t	 t ƒ t	 t t	 d ƒ f t t f ƒ k sõ t ‚ t  t t t	 t ƒ t ƒ t t	 t d t t	 t ƒ t	 d t t	 d d ƒ f t d d t f ƒ k sft ‚ t  t t	 t t ƒ t t t	 t d t	 t d t t	 t d ƒ f t t ƒ t f ƒ k sÉt ‚ t  t t	 t t ƒ t t t	 t t	 t t ƒ t t	 t t ƒ d ƒ f t t f ƒ k s*t ‚ t  t
 t	 t ƒ t ƒ t t t	 t ƒ t	 t t	 d ƒ f t t f ƒ k s{t ‚ t  t
 t	 t ƒ d t ƒ t t	 t d t t	 t ƒ t
 t	 t ƒ d t	 t t	 d ƒ f t t f ƒ k sît ‚ t  t t
 t	 t ƒ t ƒ t t t t	 t ƒ t	 t
 t	 t ƒ t	 d t t	 d ƒ f t d d t f ƒ k set ‚ t  t t	 t ƒ t ƒ t t
 t	 t ƒ t	 t t	 d ƒ f d t f ƒ k s·t ‚ t  t t	 t ƒ d t ƒ t t	 t d t t	 t ƒ t
 t	 t ƒ d t	 t t	 d ƒ f d t f ƒ k s*t ‚ t  t t t	 t ƒ t ƒ t t t
 t	 t ƒ t	 t t	 t ƒ t	 d t t	 d ƒ f d t f ƒ k sšt ‚ t  t t t ƒ t d t f ƒ t t t t ƒ t d t t t k t t k  @t t d ƒ @f t t f ƒ k st ‚ d  S(   Ni   iÿÿÿÿi    i   (   R"   RT   R[   R0   R,   R&   R}   RZ   R   RQ   R	   R:   RÂ   R.   (    (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyt    test_integrate_returns_piecewise1  s4    @>8TLJ8VZ9VS"c          C   sç  t  d d t ƒ}  t t |  d ƒ |  d d f ƒ d k s? t ‚ t t |  d |  d ƒ |  d d f ƒ t d ƒ d k s~ t ‚ t t t |  ƒ t |  ƒ ƒ d |  ƒ t t d |  ƒ d |  d k f d	 t d
 |  ƒ d t f ƒ k sî t ‚ t  d d t ƒ} t t | |  ƒ t |  d ƒ |  t	 t	 f ƒ } t | t |  d ƒ |  t	 | f ƒ } t |  t |  d ƒ |  | t	 f ƒ } | | | k oØt
 t ƒ | t | ƒ d t
 t ƒ | d t | d ƒ d k n sãt ‚ d  S(   NRT   R‚   i   i    i   i   i1   i   i   iþÿÿÿR‹   (   RA   R}   R"   R*   RZ   R(   R6   R   R0   R.   R=   R/   R   (   RT   R‹   t   int1t   int2t   int3(    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyt   test_integrate_max_minM  s    -?)G1('c          C   sP  t  t t ƒ t d d f ƒ t d ƒ d k s4 t ‚ t  t t ƒ t d d f ƒ t d ƒ d k sh t ‚ t  t t d ƒ t d d f ƒ t d ƒ d k s  t ‚ t  t t d d ƒ t d d f ƒ d k sÒ t ‚ t  t t d d t ƒ t d d	 f ƒ d
 k st ‚ t  t t ƒ t d d f ƒ d k s2t ‚ t  t t ƒ t t ƒ t t t f ƒ d k sgt ‚ t  t t d ƒ t d t d d f ƒ t d ƒ d k s§t ‚ t d d t	 ƒ\ }  } t  t |  ƒ |  ƒ t
 |  d d |  d k f |  d d t	 f ƒ k st ‚ t  t d |  d ƒ |  ƒ t
 |  d d |  |  d k f |  d d |  d t	 f ƒ k smt ‚ t  t |  | d ƒ |  d d f ƒ d | d t d | d ƒ d | d t d | d ƒ d d k sÝt ‚ t  t t |  ƒ ƒ |  ƒ t
 t |  ƒ |  d k f d t |  ƒ t	 f ƒ k s1t ‚ t  t d |  d ƒ |  ƒ t
 |  |  d k  f |  d t	 f ƒ k szt ‚ t  d |  t |  d d ƒ |  ƒ t
 |  d |  d k  f |  d d |  d k  f |  d t	 f ƒ k sæt ‚ t  t |  ƒ |  | d f ƒ t
 | d | d d k f | d | d d k  f d t	 f ƒ k sLt ‚ d  S(   Niþÿÿÿi   i   i   i    i   i   iñÿÿÿi   iÓ  iÿÿÿÿi   s   t sR‚   i   i   (   R"   R    RT   R6   RZ   R8   R:   R/   RA   R}   R0   R®   R*   R   (   Rs   R_   (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyt   test_integrate_Abs_sign\  s.    44826*5@8D#M8,%Gc          C   s4  t  t t t ƒ t ƒ }  |  j t d ƒ t  t t d ƒ t ƒ k sJ t ‚ t  t t t ƒ t d d f ƒ }  |  j t d ƒ t  t t d ƒ t d d f ƒ k s¦ t ‚ t t t t d ƒ ƒ } t  | t t ƒ | t ƒ t t t f ƒ } | j i d t 6ƒ t  t d t d ƒ t t t f ƒ k s0t ‚ d  S(   Ni   i    i   i   iþÿÿÿ(   R!   R   RT   R[   R¯   RZ   R$   R.   (   Rx   RS   t   conv(    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyt
   test_subs1w  s    1":-c          C   sj  t  t t t ƒ t t ƒ }  |  j t d ƒ t  t t d ƒ t t ƒ k sP t ‚ t  t t t ƒ t d d f t d d f ƒ }  |  j t d ƒ t  t t d ƒ t d d f t d d f ƒ k sÄ t ‚ t t t t d ƒ ƒ } t  | t t ƒ | t ƒ t t t f t d d f ƒ } | j i d t 6ƒ t  t d t d ƒ t t t f t d d f ƒ k sft ‚ d  S(   Ni   i    i   i   iþÿÿÿ(	   R!   R   RT   R[   Rs   R¯   RZ   R$   R.   (   Rx   RS   Rå   (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyt
   test_subs2  s    4.F9c          C   s  t  t t t ƒ t d t f t t d f ƒ }  |  j t d ƒ t  t t d ƒ t d d f t d d f ƒ k st t ‚ t t t t d ƒ ƒ } t  | t t ƒ | t ƒ t t t f t t d f ƒ } | j i d t 6ƒ t  t d t d ƒ t t t f t d d f ƒ k st ‚ d  S(   Ni    i   i   i   iþÿÿÿ(	   R!   R   RT   R[   Rs   R¯   RZ   R$   R.   (   Rx   RS   Rå   (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyt
   test_subs3‹  s
    .F9c          C   s  t  t t ƒ t d t f t t d f ƒ }  |  j t d ƒ t  t t ƒ t d d f t d d f ƒ k sl t ‚ t t t t d ƒ ƒ } t  | t ƒ | t ƒ t t t f t t d f ƒ } | j i d t 6ƒ t  t d t d ƒ t t t f t d d f ƒ k s
t ‚ d  S(   Ni    i   i   i   iþÿÿÿ(	   R!   R   RT   R[   Rs   R¯   RZ   R$   R.   (   Rx   RS   Rå   (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyt
   test_subs4“  s
    *B5c          C   sZ  t  t t d ƒ t t t f ƒ }  |  j t d ƒ |  k sB t ‚ t  t t d t ƒ t ƒ }  |  j t d ƒ t  t t d d ƒ t ƒ k s– t ‚ t  t t d t ƒ t t f ƒ }  |  j t d ƒ t  t t t d ƒ t d f ƒ k sõ t ‚ |  j t d ƒ t  t t d d ƒ t ƒ k s+t ‚ t  t t d t ƒ t t t f t t t f ƒ }  |  j t d ƒ |  k s~t ‚ |  j t d ƒ |  k sœt ‚ t  t t d ƒ t t f ƒ }  |  j t d ƒ t  t t d ƒ t d f ƒ k sôt ‚ t  t t ƒ t ƒ }  |  j t d ƒ |  j t d ƒ t  t t ƒ t d d f ƒ j ƒ  j sVt ‚ d  S(   Ni   i   i   i    (	   R!   R   RT   R.   R¯   RZ   R[   Rb   t   is_zero(   Rx   (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyt
   test_subs5›  s    $6$;65 8c          C   sB  t  d ƒ \ }  } t t t t t t ƒ t t ƒ f ƒ } | j t d ƒ t t t t t d ƒ t t ƒ f ƒ k sz t ‚ | j t d ƒ t t t t t ƒ t d ƒ f ƒ k s¶ t ‚ t t t t t t ƒ t t ƒ f t t t ƒ t t ƒ f ƒ } | j t d ƒ t t t t t d ƒ t t ƒ f t t d ƒ t t ƒ f ƒ k sNt ‚ | j t d ƒ t t t t t t ƒ t t ƒ f t t t ƒ t d ƒ f ƒ k s¦t ‚ t t t t t t ƒ t |  ƒ f t t t ƒ t |  ƒ f ƒ } | j |  d ƒ t t t t t t ƒ t d ƒ f t t t ƒ t d ƒ f ƒ k s>t ‚ d  S(   Ns   a bi   (   RA   R!   RT   R[   RS   R¯   RZ   (   Rt   RŠ   Rx   (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyt
   test_subs6®  s    (@<@XX@c          C   s  t  t t d t f t d d f ƒ }  |  j i d t 6d t 6ƒ |  k sM t ‚ t  t t ƒ t t ƒ t t t ƒ t t ƒ f t d d f ƒ }  |  j t t ƒ d ƒ |  k s± t ‚ |  j t t ƒ d ƒ t  t t ƒ t t ƒ t d t t ƒ f t d d f ƒ k s	t ‚ d  S(   Ni   i   (   R!   RT   R[   R¯   RZ   R:   (   Rx   (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyt
   test_subs7º  s    $).$=c          C   s€   t  t t ƒ t t d ƒ t d t f ƒ }  |  j ƒ  t  t t ƒ t d t f ƒ t  t t d ƒ t d t f ƒ k s| t ‚ d  S(   Ni   i   (   R!   RS   RT   R[   Rc   RZ   (   Rx   (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyt   test_expandÃ  s    ,c           C   s$   t  t d „  ƒ t  t d „  ƒ d  S(   Nc           S   s   t  t t d ƒ d ƒ S(   Ni   i   (   R!   R   RT   (    (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyRW   È  RX   c           S   s"   t  t t d ƒ d t t f ƒ S(   Ni   i   (   R!   R   RT   R.   (    (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyRW   É  RX   (   RL   R\   (    (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyt   test_integration_variableÇ  s    c           C   s	  t  t t d ƒ t t d ƒ d t d d f ƒ j ƒ  t  t t d ƒ t t d ƒ t d d f ƒ t  t t d ƒ t d d f ƒ k s t ‚ t  t t d ƒ t t d ƒ d t ƒ j ƒ  t  t t d ƒ t t d ƒ t ƒ t  t t d ƒ t ƒ k st ‚ d  S(   Ni   i   i    (   R!   R	   RT   R:   Rc   RZ   (    (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyt   test_expand_integralÌ  s    7-,.$c              s¹  t  t t d d ƒ t d d f ƒ ‰  ˆ  j d d d ƒd t d ƒ k sQ t ‚ ˆ  j d d d ƒd	 t d
 ƒ d t d ƒ k sŠ t ‚ ˆ  j d d d ƒd t d ƒ d d t d ƒ d d t d ƒ d k sÝ t ‚ ˆ  j d	 d d ƒd t d ƒ d	 t d ƒ d	 t d ƒ d t d ƒ k s2t ‚ t ˆ  j d	 d d ƒj ƒ  ˆ  j ƒ  ƒ d k  sit ‚ t  t t d t d ƒ t d d f t d d f ƒ ‰  t t	 ‡  f d †  ƒ d  S(   Ni   i   i   i
   t   methodt   midpointi   iÙ   i   iA   i   i9   i	  i   iIÎ  iÚ  i   iV   i   i   g      à?i    c              s   ˆ  j  d ƒ S(   Ni   (   t   as_sum(    (   Rx   (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyRW   à  RX   (
   R!   R=   RT   Ró   RZ   R®   RQ   R[   RL   t   NotImplementedError(    (    (   Rx   sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyt   test_as_sum_midpoint1Õ  s    &+9AC76c          C   s}  t  t t d t d d f ƒ }  t d d t d t ƒ} |  j d d d ƒj ƒ  t d ƒ d	 t t d k su t ‚ |  j d d d ƒj ƒ  t d
 ƒ d t t d k s² t ‚ |  j d d d ƒj ƒ  t d ƒ d t t d k sï t ‚ |  j d	 d d ƒj ƒ  t d ƒ d t t d k s,t ‚ |  j | d d ƒj ƒ  t d t t d ƒ d d d | d k syt ‚ d  S(   Ni   i    i   RQ   Rœ   RR   Rñ   Rò   i   i   i   i   i#   il   i   i@   i   (	   R!   RT   R[   R@   R}   Ró   Rc   R6   RZ   (   Rx   RQ   (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyt   test_as_sum_midpoint2ã  s     ====c          C   s¥  t  t t d t d d f ƒ }  |  j d d d ƒj ƒ  t d k sK t ‚ |  j d d d ƒj ƒ  t d ƒ d t d t d k sŒ t ‚ |  j d d d ƒj ƒ  t d ƒ d	 d t d t d k sÑ t ‚ |  j d
 d d ƒj ƒ  t d ƒ d d t d
 t d k st ‚ |  j t d d ƒj ƒ  t d t t d ƒ d t t d d t d d t d k swt ‚ |  j d d d d t ƒj	 t
 ƒ s¡t ‚ d  S(   Ni   i    i   Rñ   t   lefti   i   i   i   i   i   i    i   i
   t   evaluate(   R!   RT   R[   Ró   Rc   RZ   R6   RQ   Rw   t   hasR?   (   Rx   (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyt   test_as_sum_leftî  s     +AEEIc          C   s‹  t  t t d t d d f ƒ }  |  j d d d ƒj ƒ  d d t t d k sW t ‚ |  j d d d ƒj ƒ  t d ƒ d d t d t d k sœ t ‚ |  j d d d ƒj ƒ  t d	 ƒ d
 d t d t d k sá t ‚ |  j d d d ƒj ƒ  t d ƒ d d t d t d k s&t ‚ |  j t d d ƒj ƒ  t d t t d ƒ d t t d d t d d t d k s‡t ‚ d  S(   Ni   i    i   Rñ   t   righti   i   i   i   i   i   i   i    i   (   R!   RT   R[   Ró   Rc   RZ   R6   RQ   (   Rx   (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyt   test_as_sum_rightø  s     7EEEc          C   s¥  t  t t d t d d f ƒ }  |  j d d d ƒj ƒ  t d t t d ƒ d k s] t ‚ |  j d d d ƒj ƒ  t d t t d ƒ d k sš t ‚ |  j d d d ƒj ƒ  t d t t d ƒ d	 k s× t ‚ |  j d
 d d ƒj ƒ  t d t t d ƒ d k st ‚ |  j t d d ƒj ƒ  t d t t d ƒ d d d t d k sat ‚ t  t t ƒ t d d f ƒ j d d ƒ t d ƒ d k s¡t ‚ d  S(   Ni   i    i   Rñ   t	   trapezoidi   i   i   i6   i   i   i    i   (	   R!   RT   R[   Ró   Rc   R6   RZ   RQ   R8   (   Rx   (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyt   test_as_sum_trapezoid  s     ====5c              sŒ   t  t t d t d d f ƒ ‰  t t ‡  f d †  ƒ t t ‡  f d †  ƒ t t d „  ƒ t t ‡  f d †  ƒ t t ‡  f d †  ƒ d  S(	   Ni   i    i   c              s   ˆ  j  d ƒ S(   Niÿÿÿÿ(   Ró   (    (   Rx   (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyRW     RX   c              s   ˆ  j  d ƒ S(   Ni    (   Ró   (    (   Rx   (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyRW     RX   c           S   s   t  t ƒ j d ƒ S(   Ni   (   R!   RT   Ró   (    (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyRW     RX   c              s   ˆ  j  t ƒ S(   N(   Ró   R.   (    (   Rx   (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyRW     RX   c              s   ˆ  j  d d d ƒS(   Ni   Rñ   t   xxxx2(   Ró   (    (   Rx   (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyRW     RX   (   R!   RT   R[   RL   R\   (    (    (   Rx   sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyt   test_as_sum_raises  s     c          C   sL   t  t  t t ƒ t ƒ }  t  t t t ƒ } |  j ƒ  | j ƒ  k sH t ‚ d  S(   N(   R!   RT   Rb   RZ   (   Rx   RS   (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyt   test_nested_doit  s    c          C   s˜  t  t d t d  d f ƒ }  t  t d t d d  f ƒ } |  j ƒ  t d d ƒ k sY t ‚ | j ƒ  t d d ƒ k sz t ‚ t  t t t d  t f ƒ j t t ƒ t  t t t d  t f ƒ k sÄ t ‚ t  t t t t d  f ƒ j t t ƒ t  t t t t d  f ƒ k st ‚ t	 t d t d  d f ƒ t d d ƒ k s?t ‚ t	 t d t d d  f ƒ t d d ƒ k spt ‚ t	 d d ƒ t d d ƒ k s”t ‚ d  S(	   Ni   i   i   iÿÿÿÿs   x**2RT   t   1(   RT   R  N(
   R!   RT   t   NoneRb   R4   RZ   R[   R¯   Rs   R"   (   Rx   RS   (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyt   test_issue_4665  s    !!JJ11c          C   s;   t  t d t d d f ƒ }  |  t  |  j Œ  k s7 t ‚ d  S(   Ni   iÿÿÿÿi   (   R!   RT   t   argsRZ   (   Rx   (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyt   test_integral_reconstruct(  s    c          C   sƒ  t  t  d t ƒ t d d f ƒ }  |  j ƒ  t d d ƒ k sC t ‚ |  j d t ƒ t d d ƒ k sj t ‚ t d ƒ } t  | t ƒ t d d f ƒ j ƒ  d k s¦ t ‚ t  d t d t  | t ƒ t ƒ f ƒ j ƒ  d k sß t ‚ t  t t d f ƒ j ƒ  d k st ‚ t d t t ƒ f t d f f } t  t | Œ j ƒ  t	 d ƒ d k sRt ‚ t  t t
 t | ƒ ƒ Œ j ƒ  d k st ‚ d  S(   Ni   i    i   i   t   deepRS   i   (   R!   RT   Rb   R4   RZ   Rw   R   Rt   R   R6   t   listt   reversed(   Rx   RS   Rh   (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyt   test_doit_integrals-  s    "!'09'!+c           C   s  t  t t ƒ d t ƒ t d t t ƒ t d d d d t t ƒ t d d d t t ƒ d t t d ƒ d k f d t t t ƒ t d d d d t t t ƒ t d d d t t t ƒ d t f ƒ k sæ t ‚ t  t t d t t ƒ ƒ t t k st ‚ d  S(   Ni   i   i   i   i   (	   R"   R=   RT   R0   R    R   R}   RZ   R&   (    (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyt   test_issue_4884<  s    IA,c       	   C   sÄ  d d l  m }  m } m } d d l m } m } t |  ƒ j t	 k sM t
 ‚ t d |  ƒ j t	 k sk t
 ‚ t d |  d f ƒ j t k s t
 ‚ t d |  d d f ƒ j t k s¶ t
 ‚ t d |  d | f ƒ j t	 k sÝ t
 ‚ t d |  | f ƒ j t	 k st
 ‚ t |  | ƒ j t	 k st
 ‚ t |  | d |  f ƒ j t	 k sFt
 ‚ t |  | d d f ƒ j t	 k smt
 ‚ t |  |  d d f ƒ j t k s”t
 ‚ t |  | d d f ƒ } | j t	 k rÍ| j ƒ  d k sÓt
 ‚ t |  | | | f ƒ } | j t	 k r| j ƒ  d k st
 ‚ t d | | | d f ƒ } | j t	 k rO| j ƒ  d k sUt
 ‚ t |  | |  d d f | d d f ƒ j t k sŒt
 ‚ t |  | |  d d f | d | f ƒ j t	 k sÃt
 ‚ t |  |  d f ƒ j t k sçt
 ‚ t |  |  d t | | d d f ƒ f ƒ j t k s t
 ‚ t t | | d d f ƒ |  d d f ƒ j t k sYt
 ‚ t | |  ƒ d | |  ƒ d d |  ƒ j t	 k s“t
 ‚ t t |  ƒ |  d d f ƒ j t k sÀt
 ‚ d  S(   Niÿÿÿÿ(   RT   R[   RÂ   (   R	   R:   i   i   i    i   (   t	   sympy.abcRT   R[   RÂ   R¨   R	   R:   R!   t	   is_numberRw   RZ   R}   RQ   R?   RS   (   RT   R[   RÂ   R	   R:   Rd   (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyt   test_is_numberF  s2    $''$''''''77$99:c          C   s  d d l  m }  m } m } t d |  ƒ j |  h k s= t ‚ t |  ƒ j |  h k s[ t ‚ t |  |  d  | f ƒ j | h k s… t ‚ t |  |  | d  f ƒ j | h k s¯ t ‚ t |  |  d | f ƒ j | h k sÙ t ‚ t |  |  | d f ƒ j | h k st ‚ t |  |  |  | f ƒ j |  | h k s0t ‚ t |  |  | ƒ j |  | h k sWt ‚ t |  |  d d f ƒ j t ƒ  k st ‚ t |  | d d f ƒ j |  h k s«t ‚ t |  | | | f ƒ j |  | h k sØt ‚ t |  | d d f | d  d  f ƒ j |  | h k st ‚ t |  | d d f |  d | f ƒ j | h k sGt ‚ t d | d d f | d |  f |  d d f ƒ j t ƒ  k s‰t ‚ t d | |  d f | d |  f |  d d f ƒ j t ƒ  k sËt ‚ t d |  d d f | |  d f | d d f ƒ j |  h k st ‚ d  S(   Niÿÿÿÿ(   RT   R[   RÂ   i    i   i   (	   R  RT   R[   RÂ   R!   Ra   RZ   R  t   set(   RT   R[   RÂ   (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyt   test_symbolsg  s$    !****-'**-96BB0c          C   s¹  d d l  m }  m } t d |  d |  f ƒ j s7 t ‚ t d |  d d f ƒ j sX t ‚ t d |  d d f t d f ƒ j t k sˆ t ‚ t |  | d f ƒ j s¦ t ‚ t |  | | d f ƒ j d  k sÎ t ‚ t | | d t	 |  ƒ f |  d f ƒ } | j d  k s
t ‚ t | |  d f | d t	 |  ƒ f ƒ j t
 k s@t ‚ t |  |  t t f ƒ j sat ‚ t |  |  t t f ƒ j s„t ‚ t t |  ƒ |  d d t f ƒ j d  k sµt ‚ d  S(   Niÿÿÿÿ(   RT   Rª   i    i   i   (   R  RT   Rª   R!   Rê   RZ   R[   Rw   R  R   R}   R.   R:   R/   (   RT   Rª   Rd   (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyt   test_is_zero}  s    !!0('6!#c          C   sŠ   d d l  m }  t t |  ƒ |  |  f ƒ } | j |  ƒ } | j |  d d ƒj ƒ  t g  t d ƒ D] } t	 | ƒ ^ qb Œ  k s† t
 ‚ d  S(   Niÿÿÿÿ(   RT   RQ   i   i   (   R  RT   R!   R	   t   lseriest   nseriest   removeOR   RJ   t   nextRZ   (   RT   Rd   Rx   R¼   (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyt   test_series  s    c          C   su   t  d ƒ }  t d t |  ƒ |  |  ƒ t |  ƒ t |  ƒ k sE t ‚ t t |  ƒ d |  |  ƒ j t ƒ sq t ‚ d  S(   NRT   i   i   (	   R@   R"   R:   R&   R7   RZ   R	   Rù   R   (   RT   (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyt!   test_trig_nonelementary_integrals—  s    9c          C   sh  t  d ƒ }  t  d ƒ } t  d d t ƒ} t t |  d | d ƒ |  ƒ | d t |  | ƒ d |  t |  d | d ƒ d k s‹ t ‚ t t |  d | d ƒ |  ƒ | d t |  | ƒ d |  t |  d | d ƒ d k sí t ‚ t  d d t ƒ}  t  d d t ƒ} t d |  d | d t d ƒ |  ƒ |  | d t |  d | d ƒ k sdt ‚ d  S(	   NRT   R[   RÂ   Rœ   i   R‚   i   s   3/2(   R@   R}   R"   R=   R   RZ   R   R6   (   RT   R[   RÂ   (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyt   test_issue_4403Ÿ  s    CD&c           C   sd   t  t t d d ƒ t ƒ d t t t d t d ƒ ƒ t t d t d ƒ d k s` t ‚ d  S(   Ni   i   iþÿÿÿiüÿÿÿ(   R"   R=   RT   R   RZ   (    (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyt   test_issue_4403_2°  s    c          C   sX   t  d d t ƒ}  t t |  d t d ƒ t d |  f ƒ t |  d d k sT t ‚ d  S(   Nt   RRœ   i   i    i   (   R@   R}   R"   R=   RT   R/   RZ   (   R  (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyt   test_issue_4100µ  s    c          C   sû  d d l  m }  m } m } m } t d ƒ } t t | | ƒ | ƒ | ƒ t | | ƒ | | ƒ k sj t ‚ t | | ƒ ƒ j | | ƒ t	 | ƒ f k s t ‚ t t | | ƒ ƒ ƒ j | | ƒ t	 | ƒ t	 | ƒ f k sß t ‚ t t | | ƒ ƒ | ƒ j | | ƒ t	 | ƒ t	 | ƒ f k s$t ‚ t t | | ƒ | ƒ | ƒ j | | ƒ t	 | ƒ t	 | ƒ f k slt ‚ t t t | | ƒ | ƒ | ƒ | ƒ j | | ƒ t	 | ƒ t	 | ƒ t	 | ƒ f k sÆt ‚ t
 t | | ƒ | ƒ | ƒ t | | ƒ | | ƒ k st ‚ t
 t | | ƒ | ƒ | ƒ | t | | ƒ | ƒ k s?t ‚ t
 t | | ƒ | ƒ | ƒ t | | | ƒ | ƒ | t | | ƒ | ƒ g k s•t ‚ t
 t d | ƒ | ƒ | d k s½t ‚ t
 t d | ƒ | ƒ d | | k sét ‚ t d | | ƒ j t d | | ƒ j k st ‚ t | | ƒ | | | | ƒ j ƒ  | d t | | ƒ | | ƒ d k sgt ‚ t | | ƒ | d d f |  d | f | d | f ƒ j ƒ  | | d t | | ƒ | d d f ƒ | d t | | ƒ | d d f ƒ k s÷t ‚ d  S(   Niÿÿÿÿ(   t   wRT   R[   RÂ   RS   i   i   (   R  R  RT   R[   RÂ   R   R!   RZ   R  RE   R"   Rb   (   R  RT   R[   RÂ   RS   (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyt   test_issue_5167º  s$    "<3BEH'3<=V(,0N9c          C   sh  t  d d t ƒ}  t t t t ƒ d ƒ t ƒ t t ƒ t t d ƒ d ƒ t	 t t ƒ t d ƒ d ƒ d k sz t
 ‚ t t t t ƒ d ƒ t ƒ t t ƒ t t d ƒ d ƒ t t t ƒ t d ƒ d ƒ d k sâ t
 ‚ t t |  t t ƒ d ƒ t ƒ t t ƒ t d d |  ƒ t	 t |  ƒ t t ƒ d d t |  ƒ ƒ d t |  ƒ k sdt
 ‚ d  S(   NRÂ   Rœ   i   i   i   (   R@   R}   R"   R   R&   RT   R=   R/   R6   R   RZ   R   (   RÂ   (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyt   test_issue_4890Ñ  s    KL!c       	   C   s©   t  d d t d t ƒ}  t t |  t d |  d t d t j f ƒ |  d d d |  |  d |  d d |  d d d |  |  d d d |  ƒ d k s¥ t ‚ d  S(   NRQ   RR   Rœ   i   i    i   (   R@   R}   R9   R"   RT   R6   R¶   RZ   (   RQ   (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyt   test_issue_4376Û  s    +c           C   sl   t  t t ƒ t d t t d d ƒ t ƒ d t t d d ƒ d d t t d d ƒ d k sh t ‚ d  S(   Ni   i   i   i   i   (   R"   R=   RT   R4   RZ   (    (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyt   test_issue_4517á  s    +c       
   C   sA  t  d d t ƒ\ }  } t t |  t ƒ t | t ƒ t d t f ƒ j ƒ  t d t |  d ƒ t | d ƒ Bf t d t |  | ƒ f t d t |  | ƒ f d t f ƒ k } t t |  t ƒ t | t ƒ t f ƒ t d t	 t |  d ƒ t | d ƒ ƒ f t t | t ƒ d d t t
 | t ƒ d d t | t ƒ t
 | t ƒ d | t |  | ƒ f t t | t ƒ d d t t
 | t ƒ d d t | t ƒ t
 | t ƒ d | t |  | ƒ f | t |  t ƒ t
 | t ƒ |  d | d |  t | t ƒ t
 |  t ƒ |  d | d t f ƒ k s=t ‚ d  S(   Ns   k mRR   i    i   (   RA   R}   R"   R:   RT   R/   R9   R0   R   R   R	   RZ   (   t   kRª   R·   (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyt   test_issue_4527æ  s    3*$hf/c          C   sŠ   t  d d t ƒ}  t t t d t |  t ƒ t t t t f d d ƒt t t d t |  t ƒ t t t t f ƒ k s† t	 ‚ d  S(   NR[   Rœ   i   R   Rž   (
   R@   R}   R"   R   R   R/   RT   R.   R!   RZ   (   t   ypos(    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyt   test_issue_4199ö  s    7c          C   s  t  d d t d t ƒ\ }  } } } t t t d t | t ƒ t ƒ t t ƒ t | d d ƒ t t | d t ƒ d k sŠ t	 ‚ t t |  t d | t | ƒ t ƒ t t ƒ t | ƒ t | d d |  ƒ t
 t |  ƒ t | d t |  ƒ ƒ d t |  ƒ k st	 ‚ d d l m } d d l m } | t t t d ƒ t t | t ƒ t t t f ƒ ƒ t t ƒ t | d d ƒ k s›t	 ‚ t  d	 d t ƒ\ }  } | t t |  t d d | t ƒ t t t f ƒ ƒ t t ƒ t | d |  ƒ t |  ƒ k st	 ‚ d  S(
   Ns   a:dRœ   t   finitei   i   iÿÿÿÿ(   t
   expand_mul(   R!  s   a d(   RA   R}   R"   R   RT   R   R=   R/   R   RZ   R   R¨   R&  R  R!  R.   (   Rt   RŠ   R‹   R]   R&  R!  (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyt   test_issue_3940ý  s    $#C&j9(7c           C   sa   t  t t d t d t ƒ t t t t t ƒ d t t t t t ƒ d k s] t ‚ d  S(   Ni   (   R"   Rt   RT   R   R&   RZ   (    (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyt   test_issue_5413  s    c       
   C   sô  t  d ƒ \ }  } t d d t ƒ} |  t | ƒ } |  | t t t ƒ d t t ƒ d } t t ƒ d t t ƒ d } t t ƒ d t t ƒ d d } t	 | | | t ƒ | |  | t
 | t ƒ | |  t t | ƒ | |  | t
 | t ƒ | |  t t | ƒ | |  | t
 | t ƒ | |  t t | ƒ | |  | t
 | t ƒ | |  t t | ƒ |  | t |  | t
 t ƒ t | ƒ t | ƒ |  | t |  | t
 t ƒ t | ƒ t | ƒ g k sðt ‚ d  S(   Ns   A zR‹   R¢   i   i   (   RA   R@   R}   R   Rs   R:   RT   R	   R[   R"   R&   RZ   (   R†   RÂ   R‹   t   P1t   P2t   h1t   h2(    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyt   test_issue_4892a  s    +#22003c          C   sr   t  t ƒ t d d t t ƒ t d d t d d }  t t t |  t ƒ j t ƒ |  ƒ ƒ d k sn t ‚ d  S(   Ni   i   i   i    (	   R:   R[   RT   R	   RD   R   R"   R   RZ   (   t   expr(    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyt   test_issue_4892b)  s    	:c           C   s~   t  t t ƒ t t t ƒ t d t f t d t f t d t f ƒ d t t t t ƒ t d t f t d t f ƒ k sz t ‚ d  S(   Ni    i   (	   R"   R:   RT   RS   R[   RÂ   R/   R!   RZ   (    (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyt   test_issue_51786  s    @c          C   sÙ   t  t ƒ j t d d ƒ }  t d d t d d t d d t d d	 t d d
 t t d ƒ } t |  t ƒ | k s‚ t ‚ t t |  t ƒ t ƒ |  k s¦ t ‚ t t t d ƒ t ƒ t t d ƒ k sÕ t ‚ d  S(   Ni    i
   i   i   i   i   iÐ  i   i€  i _7 i   i   (   R:   RT   t   seriesR-   R"   RZ   R   (   RS   RV   (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyt   test_integrate_series;  s
    L$c          C   sT   d d l  m }  d d l m } | |  g  g  d g g  t ƒ t ƒ d  k sP t ‚ d  S(   Niÿÿÿÿ(   R)   (   t   heurischi   (   R¨   R)   t   sympy.integrals.heurischR3  RT   R  RZ   (   R)   R3  (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyt   test_atom_bugE  s    c          C   sÉ   t  d d t ƒ}  t t t t |  ƒ t d t f t d t f ƒ t |  d ƒ d t d t t ƒ d |  t t |  ƒ t t d |  d ƒ d t	 t d |  ƒ |  t t ƒ |  k sÅ t
 ‚ d  S(   NRÂ   t   zeroi    i   (   R@   Rw   R"   R:   RT   R[   R/   R&   R   R   RZ   (   RÂ   (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyt   test_limit_bugK  s    /c          C   s>   t  d ƒ }  t t t ƒ |  t ƒ t ƒ j t ƒ s: t ‚ d  S(   NRV   (   R   R"   R   RT   Rù   R!   RZ   (   RV   (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyt   test_issue_4703R  s    c          C   sA   t  d ƒ }  t |  t ƒ j t ƒ d t ƒ j t ƒ s= t ‚ d  S(   NRS   i   (   R   R"   RT   R   Rù   R!   RZ   (   RS   (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyt   test_issue_1888W  s    c          C   si   d d l  m }  t t t t ƒ t t d t d f t d t f ƒ d |  t d d ƒ k se t ‚ d  S(   Niÿÿÿÿ(   R7   i   i    (   R¨   R7   R"   R	   RT   R[   R/   RZ   (   R7   (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyt   test_issue_3558^  s    c           C   sC   t  d t d d t d ƒ t ƒ t t d ƒ d k s? t ‚ d  S(   Ni   i   i   i   (   R"   R=   RT   R   RZ   (    (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyt   test_issue_4422c  s    c          C   sm   d d l  m }  |  t t t d d t ƒ t ƒ ƒ t d t d ƒ d t d t d d k si t ‚ d  S(   Niÿÿÿÿ(   R9   i   i   i   i   (   R¨   R9   R"   RT   R=   RZ   (   R9   (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyt   test_issue_4493g  s    $c           C   se   t  t t ƒ t t t t f ƒ t k s/ t ‚ t  t t ƒ t t d t f ƒ t d k sa t ‚ d  S(   Ni    i   (   R"   R:   RT   R.   R/   RZ   (    (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyt   test_issue_4737m  s    /c          C   sœ   d d l  m }  m } m } m } t d d t ƒ} |  | t t t	 ƒ t
 t	 ƒ t	 | t	 d t f ƒ ƒ ƒ | | d | ƒ d | | ƒ k s˜ t ‚ d  S(   Niÿÿÿÿ(   R9   R¦   R3   R   Rt   Rœ   i    i   (   R¨   R9   R¦   R3   R   R@   R}   R"   R   RT   R&   R.   RZ   (   R9   R¦   R3   R   Rt   (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyt   test_issue_4992r  s    ":c          C   sW   d d l  m }  m } | t t t ƒ t t t ƒ ƒ |  t d t ƒ k sS t ‚ d  S(   Niÿÿÿÿ(   t
   lowergammaR9   i   (   R¨   R?  R9   R"   R   RT   R[   RZ   (   R?  R9   (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyt   test_issue_4487z  s    c          C   s<   t  d ƒ }  t d |  d |  d d f ƒ t k s8 t ‚ d  S(   NRT   i   i   iÿÿÿÿ(   R@   R"   R.   RZ   (   RT   (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyt   test_issue_4215  s    c          C   s¹   t  d d t d t ƒ}  t t |  t t ƒ t ƒ |  t t |  t t ƒ |  d d |  d t t |  t t ƒ |  d d |  d t t |  |  d d |  d k sµ t ‚ d  S(   NRQ   RR   Rœ   i   i   (   R@   R}   R"   RT   R&   RZ   (   RQ   (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyt   test_issue_4400„  s    Wc           C   so   t  t d t ƒ t d t ƒ d t t d t ƒt t t d ƒ t t d ƒ d t t ƒ k sk t ‚ d  S(   Ni   i   R)   (   R"   R=   RT   R}   R!   RZ   (    (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyt   test_issue_6253‹  s    2c           C   s  t  d d t t t t d d f t d d f t d d f ƒ d t d ƒ d t d ƒ d d t d ƒ d d t d ƒ d	 t d
 ƒ d t d ƒ d t d
 ƒ d t d ƒ d d t d ƒ d t d ƒ d d t d ƒ d t d ƒ d d t d ƒ d g k st ‚ d  S(   Ni   i    iôÿÿÿi   i   i   i   i   i   i   i   i   i/   (   R"   RT   R[   RÂ   R&   RZ   (    (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyt   test_issue_4153’  s    =MLc          C   sk   t  d ƒ \ }  } } t | t |  | | t |  d t d ƒ t |  | |  f ƒ j t ƒ sg t ‚ d  S(   Ns   R b hi   (   RA   R"   RT   R=   Rù   R+   RZ   (   R  RŠ   t   h(    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyt   test_issue_4326™  s    c           C   sK   t  d t d t t ƒ d t t d ƒ d t t d ƒ k sG t ‚ d  S(   Ni   i   (   R"   RT   R&   RZ   (    (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyt   test_powers   s    c           C   sO   t  t d „  ƒ t t d t ƒ t t d d f d t ƒj t ƒ sK t ‚ d  S(   Nc           S   s   t  d t t d t d t ƒS(   Ni   t   manualR)   (   R"   RT   R}   (    (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyRW   ¥  RX   i   i    RH  (	   RL   R\   R"   R&   RT   R}   Rù   R!   RZ   (    (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyt   test_manual_option¤  s    c           C   sJ   t  t d „  ƒ t t t ƒ t d t ƒt t t ƒ t ƒ k sF t ‚ d  S(   Nc           S   s   t  d t t d t d t ƒS(   Ni   R)   t   risch(   R"   RT   R}   (    (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyRW   «  RX   R)   (   RL   R\   R"   RC   RT   R}   R!   RZ   (    (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyt   test_meijerg_optionª  s    c           C   sÞ   t  t d „  ƒ t t t d ƒ t d t ƒt t t d ƒ t ƒ k sP t ‚ t t d t ƒ t	 t t	 d t ƒt	 d t t d t ƒ d t d k s¤ t ‚ t t
 t ƒ t d t ƒt t
 t ƒ t ƒ k sÚ t ‚ d  S(   Nc           S   s&   t  d t t ƒ t d t f d t ƒS(   Ni   i    RJ  (   R"   R&   RT   R.   R}   (    (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyRW   ²  RX   i   RJ  i   (   RL   R\   R"   R   RT   R}   RH   RZ   R&   R[   R   R!   (    (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyt   test_risch_option°  s    @Tc           C   sˆ  t  t d „  ƒ t t t d ƒ t d t ƒt t ƒ t t ƒ d k sO t	 ‚ t t t ƒ t t d t ƒt
 t t ƒ t t ƒ k s t	 ‚ t t t ƒ t t t ƒ ƒ t t d ƒ d t d t ƒd t t d ƒ d t t t ƒ ƒ d d	 t t d ƒ d t t t ƒ ƒ d d
 t t d ƒ d t t t ƒ ƒ d d t t d ƒ d t t t ƒ ƒ d t t ƒ k s„t	 ‚ d  S(   Nc           S   s   t  d t t d t d t ƒS(   Ni   RJ  R3  (   R"   RT   R}   (    (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyRW   º  RX   i   R3  i   i   i€ÿÿÿi   i!  ið   i   i   (   RL   R\   R"   R   RT   R}   R=   R/   R   RZ   R!   R&   R	   R6   Rw   R:   (    (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyt   test_heurisch_option¹  s    ?>:Sc          C   sM   d d t  d d }  t |  t  ƒ j t  ƒ } t |  | d d ƒsI t ‚ d  S(   Ni   gHáz®Gñ?i   g333333@t   tolgê-™—q=(   RT   R"   R   RP   RZ   (   RS   RV   (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyt   test_issue_6828Å  s    c          C   sw   t  d t d t d k  f d t d t d d t d t d k f ƒ }  t |  t d t f ƒ d t k ss t ‚ d  S(   Ni    g    @è}@gý›áW?j*@gÓç¯ÿVŒL?g×£p=
×ï?i   g    øÁÍ@(   R0   Rs   R/   R"   R.   RZ   (   RS   (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyt,   test_integrate_Piecewise_rational_over_realsÊ  s    1c          C   sn   t  d ƒ }  t t t t |  t t t ƒ ƒ t ƒ t t t |  t t ƒ ƒ t t ƒ t k sj t ‚ d  S(   Nt   x_max(	   R@   R"   R[   R/   R   RT   R	   Rt   RZ   (   RQ  (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyt   test_issue_4803Ó  s    )c           C   sR   t  d t d t t ƒ d ƒ ƒ t t ƒ t d t t ƒ d ƒ k sN t ‚ d  S(   Ni   i   (   R"   R=   RC   RT   RZ   (    (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyt   test_issue_4234Ù  s    c           C   s*  t  t t d t d t d ƒ t ƒ ƒ t t d t d d t d d t d t t d d ƒ t t d ƒ t d ƒ d t t d d ƒ d t t d ƒ d k  f d t d d t d d t d t t d d ƒ t t d ƒ t d ƒ d t t d d ƒ t	 f ƒ k s&t
 ‚ d  S(	   Ni   i   i   i   i   i   i   iþÿÿÿ(   R9   R"   RT   R=   R0   R   R   R    R   R}   RZ   (    (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyt   test_issue_4492Ý  s
    +Q0Nc          C   so  d t  t t t ƒ }  t |  t d d f ƒ } t |  t d d f ƒ j ƒ  | k sZ t ‚ t |  t t ƒ t d d f ƒ | t d ƒ t d ƒ k sœ t ‚ t d |  t t ƒ t d d f ƒ d | t d ƒ t d ƒ k sæ t ‚ t t d t	 t
 t t t t ƒ t d t f ƒ t t d t	 t
 t ƒ t d t	 t
 t d t ƒ t d t f ƒ k skt ‚ d  S(   Ni   i   i   g333333ó?i    g333333ó¿(   Rt   RÂ   R&   RH   R!   Rb   RZ   R"   R   RQ   R_   Rs   RT   (   RS   t
   integral_f(    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyt   test_issue_2708ä  s    *B#'46c           C   s¦  t  t t t ƒ t t ƒ t d t f ƒ t t t t t t d d t t d ƒ d k  f d t t d d t d t t d ƒ d k  f t	 t
 d ƒ d f d f d t
 d ƒ d f d f t t ƒ d ƒ t f ƒ t t t t t ƒ d t ƒ ƒ t k  t t t t t ƒ d t ƒ ƒ d ƒ t t t d ƒ ƒ d d k t t d d ƒ ƒ f t t t t ƒ t t ƒ t d t f ƒ t f ƒ k s™t ‚ t  t t t ƒ t t ƒ t d t f ƒ t d t d d d t d d t t d t d ƒ t t t t ƒ ƒ t d k  t t t t ƒ ƒ t d k t t t t t ƒ ƒ ƒ t t ƒ d d k ƒ f t t t t ƒ t t ƒ t d t f ƒ t f ƒ k s¢t ‚ d  S(   Ni    i   i   iþÿÿÿiÿÿÿÿ(   i    i    (   i    (   R"   R   R_   RT   R   R.   R0   R/   R    R)   R6   R1   R}   R   RF   R	   R=   R,   R!   RZ   R
   (    (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyt   test_issue_8368ñ  s8    *
"D** 2*c           C   s¨   t  t d t ƒ ƒ d t d t ƒ k s0 t ‚ t  t d t ƒ ƒ d t d t t d t ƒ d ƒ k sr t ‚ t  t t ƒ ƒ t t t t ƒ d ƒ k s¤ t ‚ d  S(   Ng      ð?i   (   R"   R
   RT   R   RZ   R   R&   (    (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyt   test_issue_8901  s    0Bc           C   sã   t  t t ƒ d t t d d f ƒ t d ƒ d d t d ƒ d k sO t ‚ t  t t ƒ d t t d t f ƒ t d k s… t ‚ t  t t ƒ d t d t ƒ t d t ƒ t d t ƒ d t d d t k sß t ‚ d  S(   Ni   i    i   i   i   (   R"   R:   RT   R7   RZ   R.   R/   R	   (    (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyt   test_issue_8945  s    O6c          C   s‡   t  r t d ƒ n  t d ƒ \ }  } } } t t |  t | ƒ d | | t j t ƒ } t t | t d | f ƒ j	 k sƒ t
 ‚ d  S(   Ns   Too slow for travis.s   i L a bi   i    (   RO   RN   RA   R	   R/   RT   t   rewriteR   R"   Ra   RZ   (   Rd   t   LRt   RŠ   t	   integrand(    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyt   test_issue_7130  s
    1c          C   s¦   t  d ƒ \ }  } } } t |  | | | g ƒ } t | | ƒ t | | ƒ j ƒ  k s[ t ‚ t | | ƒ t |  | d d g | | g | | g g ƒ k s¢ t ‚ d  S(   Ns   a b c ti   (   RA   R'   R"   R!   Rb   RZ   (   Rt   RŠ   R‹   Rs   t   vt(    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyt   test_issue_10567'  s    *c          C   sC   t  d ƒ }  t t t |  ƒ |  ƒ t t |  ƒ t k s? t ‚ d  S(   NRs   (   RA   R"   R;   R/   R7   RZ   (   Rs   (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyt   test_issue_11856-  s    c           C   si   t  d t t ƒ d t d t ƒ t d t ƒ t ƒ d t d t ƒ d t d t ƒ k se t ‚ d  S(   NiÄÿÿÿg3333333@i   g333333Ài   g      (@i   (   R"   R   RT   RZ   (    (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyt   test_issue_49501  s    6c           C   sd   t  t t t d ƒ ƒ ƒ t t d t t ƒ ƒ d d t t d t t ƒ ƒ d k s` t ‚ d  S(   Ni   i   (   R"   R:   R&   RT   R	   RZ   (    (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyt   test_issue_49686  s    c           C   së   t  d t d t t t f ƒ t k s- t ‚ t  d t d t d d f ƒ t k sY t ‚ t  d t d d t d d f ƒ t k s‰ t ‚ t  d t d t d d f ƒ t k s¶ t ‚ t  d t d d t d d f ƒ t k sç t ‚ d  S(   Ni   i   iÿÿÿÿiþÿÿÿ(   R"   RT   R.   RZ   (    (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyt   test_singularities9  s
    -,0-c          C   sè   t  d d t ƒ\ }  } t t |  |  |  | | ƒ |  t t | | ƒ t t | | ƒ f | t t ƒ t t ƒ f ƒ t t |  d | d ƒ |  t | d t ƒ t | d t ƒ f | t t ƒ t t ƒ f ƒ k sä t ‚ d  S(   Ns   x yR‚   i   i   (   RA   R}   R"   R:   R=   R/   R!   RZ   (   RT   R[   (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyt   test_issue_12645A  s    )+c           C   sI   t  t t ƒ t t ƒ d t d t d f ƒ t d d ƒ k sE t ‚ d  S(   Ni   i    i   i   (   R"   R:   RT   R	   R/   R4   RZ   (    (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyt   test_issue_12677J  s    c           C   s6   t  d t t ƒ t d t f ƒ t d k s2 t ‚ d  S(   Ni   i    i   (   R"   R   RT   R.   R/   RZ   (    (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyt   test_issue_14064M  s    c        
   C   s±   t  d d t t t d ƒ d ƒ d t t ƒ t ƒ t t t d ƒ d ƒ t t t ƒ t t d ƒ d ƒ d t t d ƒ d ƒ ƒ t t d ƒ d ƒ t k s­ t ‚ d  S(   Ni   i   (   R"   R   RT   R6   R&   R   RZ   (    (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyt   test_issue_14027P  s    6c           C   s5   t  t t ƒ t d t d f ƒ t j k s1 t ‚ d  S(   Ni    i   (   R"   RC   RT   R/   R6   t   InfinityRZ   (    (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyt   test_issue_8170T  s    c           C   s^   t  d t t d d f ƒ t j k s+ t ‚ t  d t d t d d f ƒ t j k sZ t ‚ d  S(   Ni   iÿÿÿÿiþÿÿÿi   (   R"   RT   R6   Rr   RZ   (    (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyt   test_issue_8440_14040W  s    +c           C   sº   t  d t t d t d d f ƒ d t d d t k s@ t ‚ t  d d t t t d t d d f t d d f t d d f ƒ d t d ƒ d t d ƒ d t d	 ƒ k s¶ t ‚ d  S(
   Ni   i   i    iÿÿÿÿiüÿÿÿi   i   i	   i   (   R"   RT   R[   RZ   RÂ   R&   (    (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyt   test_issue_14096[  s    @Ac           C   sŒ   t  t d t d t d ƒ t d d f ƒ j ƒ  d ƒ d k  sF t ‚ t  t t d t d ƒ t d d f ƒ j ƒ  d ƒ d k  sˆ t ‚ d  S(   Ni   i   i    gQ£dVoö?gíµ ÷Æ°>g)“Ú ìê?(   R    R"   R=   RT   RQ   RZ   (    (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyt   test_issue_14144`  s    Fc           C   s6   t  t t t ƒ t t ƒ t ƒ j t ƒ s2 t ‚ d  S(   N(   R"   R   R   RT   R&   Rù   R   RZ   (    (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyt   test_issue_14375d  s    c          C   s‚   t  d ƒ t t t ƒ }  t |  t d d f t d d f t d d f ƒ t |  t d d f t d d f t d d f ƒ k s~ t ‚ d  S(   NRS   i    i   i   i   (   R   RT   R[   RÂ   R"   R!   RZ   (   RS   (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyt   test_issue_14437i  s    -c           C   ss   t  d t t t ƒ d ƒ t ƒ t d d t t t ƒ d ƒ ƒ t d d t t t ƒ d ƒ ƒ k so t ‚ d  S(   Ni   iÿÿÿÿ(   R"   R=   R   RT   R&   RZ   (    (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyt   test_issue_14470n  s     c          C   sÀ   t  d t  t d ƒ t d t d ƒ d t d t d t  t d ƒ t d }  t |  t ƒ t  d t d t t  t d ƒ d ƒ t t  d t d ƒ t  d t d ƒ k s¼ t ‚ d  S(   Ni   i   i   (   R   RT   R"   RZ   (   RS   (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyt   test_issue_14877r  s    Tc          C   s…   t  t d d ƒ t d t }  t |  t d d g ƒ t d k sK t ‚ t |  t d d g ƒ t d ƒ d t d k s t ‚ d  S(   Ni   i   iÿÿÿÿi   i    i   i   (   R=   RT   R"   R/   RZ   R6   (   RS   (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyt   test_issue_14782w  s    ")c          C   sH   t  t d ƒ d t t  ƒ }  t |  t  d t g ƒ t k sD t ‚ d  S(   Ni   i   i    (   RT   R6   R   R"   R.   RZ   (   RS   (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyt   test_issue_12081}  s     c          C   sV   d t  d }  d |  t d |  ƒ t  d } t | t  d d g ƒ d k sR t ‚ d  S(   Ni   i   iþÿÿÿi   i    (   RT   R   R"   RZ   (   R[   RS   (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyt   test_issue_15285‚  s     c           C   sÀ   t  t t t t ƒ t t ƒ t d t f ƒ j ƒ  t t t d ƒ t	 d t ƒ t t d ƒ t t
 t ƒ d d k f t t t t t ƒ t t ƒ t d t f ƒ t f ƒ k s¼ t ‚ d  S(   Ni    i   (   R"   RT   RQ   R   R&   R.   R   R0   R   R3   R5   R!   R}   RZ   (    (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyt   test_issue_15432ˆ  s    7Bc          C   s    t  d ƒ }  t d d t ƒ\ } } t t t t |  | |  | ƒ t d d ƒt t t t |  | ƒ t t t |  | ƒ |  | |  | k sœ t ‚ d  S(   Nt   omegas   m pt   clsR   Rž   (   R    RA   R   R"   R   RT   R   RZ   (   Ru  Rª   Rˆ   (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyt   test_issue_15124Ž  s    ,c           C   s»   t  t t ƒ j t ƒ t  t d d t t ƒ k s9 t ‚ t t  t t ƒ t ƒ t  t t t ƒ t t t ƒ ƒ k sx t ‚ t t  t t ƒ t ƒ j ƒ  t  t d d t t ƒ k s· t ‚ d  S(   Ni   (   R   RT   R[   R"   RZ   R!   Rb   (    (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyt   test_issue_15218•  s    9?c          C   s¦   t  t t d t d t ƒ ƒ t t d t d t ƒ ƒ t d t f ƒ }  t |  t ƒ sb t	 ‚ t
 |  t t ƒ d t t ƒ j t t d ƒ ƒ d k s¢ t	 ‚ d  S(   Ni   i    i   (   R"   R   RT   R	   Rs   R:   R.   R   R0   RZ   R   R=   R/   R¯   (   t   res(    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyt   test_issue_15292›  s    Mc           C   s=   t  t d t ƒ t t ƒ t ƒ d t t ƒ k s9 t ‚ d  S(   Ni   (   R"   R:   RT   RZ   (    (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyt   test_issue_4514¡  s    c          C   sF  t  d d t ƒ\ }  } } t t t |  d ƒ ƒ |  | | f ƒ } t t t |  d ƒ ƒ |  ƒ } | j i d | 6d | 6ƒ d d t k s“ t ‚ | j |  d ƒ | j |  d ƒ d d t k sÉ t ‚ | j i d | 6d | 6ƒ t d ƒ t d	 ƒ k st ‚ | j |  d ƒ | j |  d ƒ t d ƒ t d	 ƒ k sBt ‚ d  S(
   Ns   x a bR‚   i   i   i   iþÿÿÿiýÿÿÿiÿÿÿÿi   (   RA   R}   R"   R   R    R¯   R   RZ   (   RT   Rt   RŠ   t   definitet
   indefinite(    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyt   test_issue_15457¥  s    (16:c           C   se   t  t t t ƒ t t ƒ t ƒ t t t ƒ t t ƒ t t ƒ t t ƒ t t ƒ k sa t ‚ d  S(   N(   R"   RT   R   R&   R   RZ   (    (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyt   test_issue_15431¯  s     c          C   sT  t  t t  ƒ }  t d t t  ƒ ƒ } t |  t  ƒ | k rP | j t  ƒ |  k sV t ‚ t  d t t  ƒ d }  t  d t t  ƒ d t d t t  ƒ ƒ } t |  t  ƒ | k rÅ | j t  ƒ |  k sË t ‚ t t t  ƒ ƒ t  d }  t t ƒ t t t t  ƒ ƒ ƒ d t t t  ƒ ƒ t  } t |  t  ƒ | k rJ| j t  ƒ |  k sPt ‚ d  S(   Ni   i   i   (	   RT   R&   R   R"   R   RZ   R=   R/   R   (   RS   t   F(    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyt"   test_issue_15640_log_substitutions´  s    0-0;c          C   sÖ   d d l  m }  |  d ƒ } | j } t t t | t ƒ | t t f d t	 ƒt
 t t t t ƒ t t t t t ƒ t t t k t t k  @t t d ƒ @f t t t ƒ t t t ƒ t	 f ƒ k sÒ t ‚ d  S(   Niÿÿÿÿ(   t
   CoordSys3Dt   NR3  i    (   t   sympy.vectorR‚  RT   R"   R	   Rt   RŠ   t   x_1t   x_2R}   R0   R:   R.   R,   RZ   (   R‚  Rƒ  RT   (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyt   test_issue_15509¿  s    	,Pc          C   s  t  d ƒ }  t |  t d |  d ƒ |  ƒ t |  t d |  d ƒ |  ƒ k sT t ‚ t  d d t ƒ}  t |  t d |  d ƒ |  ƒ t |  d d d |  d d |  d k f |  d d d |  d d t d ƒ d |  d k f |  d d d |  d d t f ƒ k st ‚ d  S(	   NRT   i	   i   R‚   i   iýÿÿÿiQ   i   (   RA   R"   R®   R!   RZ   R}   R0   R6   (   RT   (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyt   test_issue_4311Ç  s    H!'6N(ü   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.   R/   R0   R1   R2   R3   R4   R5   R6   R7   R8   R9   R:   R;   R<   R=   R>   R?   R@   RA   RB   RC   RD   RE   t$   sympy.functions.elementary.complexesRF   t#   sympy.functions.elementary.integersRG   t   sympy.integrals.rischRH   t   sympy.physicsRI   t   sympy.core.compatibilityRJ   t   sympy.utilities.pytestRK   RL   RM   RN   RO   t   sympy.utilities.randtestRP   t   sympy.integrals.integralsRT   R[   Rt   Rs   R…  R†  RÂ   R_   RŠ   R}   RQ   RS   R`   Rf   Rg   Rp   Ry   R   R€   R‰   RŒ   R   RŽ   R   R•   R˜   R™   Rš   R›   RŸ   R    R¡   R£   R¥   R©   R«   R¬   R­   R²   R³   R´   Rµ   R¸   R¹   Rº   R»   R¾   R¿   RÀ   RÆ   RÇ   R¤   RÐ   RÑ   RÒ   RÜ   RÝ   RÞ   Rß   Rã   Rä   Ræ   Rç   Rè   Ré   Rë   Rì   Rí   Rî   Rï   Rð   Rõ   Rö   Rú   Rü   Rþ   R   R  R  R  R
  R  R  R  R  R  R  R  R  R  R  R  R  R   R"  R$  R'  R(  R-  R/  R0  R2  R5  R7  R8  R9  R:  R;  R<  R=  R>  R@  RA  RB  RC  RD  RF  RG  RI  RK  RL  RM  RO  RP  RR  RS  RT  RV  RW  RX  RY  R]  R_  R`  Ra  Rb  Rc  Rd  Re  Rf  Rg  Ri  Rj  Rk  Rl  Rm  Rn  Ro  Rp  Rq  Rr  Rs  Rt  Rw  Rx  Rz  R{  R~  R  R  R‡  Rˆ  (    (    (    sC   lib/python2.7/site-packages/sympy/integrals/tests/test_integrals.pyt   <module>   sD  ÿ ¯	('		
			.																		
																				4	
						
	
													
	
	
							
	!									
									
																												"																												
			