
~9\c           @   sx  d  Z  d d l m Z e d  Z d d l m Z e rkd d l m Z m Z m Z m	 Z	 d d l
 m Z m Z m Z m Z m Z m Z m Z m Z m Z m Z m Z m Z m Z m Z m Z m Z m Z m Z m Z m Z m Z m  Z  m! Z! m" Z" m# Z# m$ Z$ m% Z% m& Z& m' Z' m( Z( 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 mG ZG mH ZH mI ZI mJ ZJ mK ZK mL ZL mM ZM mN ZN mO ZO mP ZP mQ ZQ mR ZR mS ZS mT ZT mU ZU mV ZV mW ZW mX ZX mY ZY mZ ZZ m[ Z[ m\ Z\ m] Z] m^ Z^ m_ Z_ m` Z` ma Za mb Zb mc Zc md Zd me Ze mf Zf mg Zg mh Zh mi Zi mj Zj mk Zk ml Zl mm Zm mn Zn mo Zo mp Zp mq Zq mr Zr ms Zs mt Zt mu Zu mv Zv mw Zw mx Zx my Zy mz Zz 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 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 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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mGZGmHZHmIZImJZJmKZKmLZLmMZMmNZNmOZOmPZPmQZQmRZRmSZSmTZTmUZUmVZVmWZWmXZXmYZYmZZZm[Z[m\Z\m]Z]m^Z^m_Z_m`Z`maZambZbmcZcmdZdmeZemfZfmgZgmhZhmiZimjZjmkZkmlZlmmZmmnZnmoZompZpmqZqmrZrmsZsmtZtmuZumvZvmwZwmxZxmyZymzZz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mZmZmZmJZJ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mZmZmZmZmZmZmZmZd d lmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZd d lmZd d	 lmZmZd d
 lmZmZmZmZm Z mZmZmZd d lmZmZmZmZmZm	Z	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mZd d lmZg  d D] Zee ^ q\ ZZZZZZ Z!Z"Z#Z$Z%Z&Z'Z(Z)Z*Z+Z,Z-Z.Z/Z0Z1Z2Z3Z4Z5Z6Z7Z8Z9g  d d d d d d d d d d d d d d d d d d d d  d! d" d# d$ d% d& d' d( d) d* g D] Zee ^ q\ Z:Z;Z<Z=Z>Z?Z@ZAZBZCZDZEZFZGZHZIZBZCZJZKZLZMZNZOZPZQZRZSZTZUed+  \	 ZZVZWZXZYZZZ[Z\Z]e^Z_e^Z`eaZbn  d,   Zcd- S(.   s   
This code is automatically generated. Never edit it manually.
For details of generating the code see `rubi_parsing_guide.md` in `parsetools`.
i(   t   import_modulet   matchpy(   t   doctest_depends_on(   t   Patternt   ReplacementRulet   CustomConstraintt   is_match(  t   Intt   Sumt   Sett   Witht   Modulet   Scant   MapAndt   FalseQt   ZeroQt	   NegativeQt   NonzeroQt   FreeQt   NFreeQt   Listt   Logt	   PositiveQt   PositiveIntegerQt   NegativeIntegerQt   IntegerQt	   IntegersQt   ComplexNumberQt   PureComplexNumberQt   RealNumericQt   PositiveOrZeroQt   NegativeOrZeroQt   FractionOrNegativeQt   NegQt   Equalt   Unequalt   IntPartt   FracPartt	   RationalQt   ProductQt   SumQt   NonsumQt   Substt   Firstt   Restt   SqrtNumberQt   SqrtNumberSumQt   LinearQt   Sqrtt   ArcCosht   Coefficientt   Denominatort   Hypergeometric2F1t   Nott   Simplifyt   FractionalPartt   IntegerPartt   AppellF1t
   EllipticPit	   EllipticEt	   EllipticFt   ArcTant   ArcCott   ArcCotht   ArcTanht   ArcSint   ArcSinht   ArcCost   ArcCsct   ArcSect   ArcCscht   ArcSecht   Sinht   Tanht   Cosht   Secht   Cscht   Cotht	   LessEqualt   Lesst   Greatert   GreaterEqualt	   FractionQt   IntLinearcQt   Expandt   IndependentQt   PowerQt   IntegerPowerQt   PositiveIntegerPowerQt   FractionalPowerQt   AtomQt   ExpQt   LogQt   Headt   MemberQt   TrigQt   SinQt   CosQt   TanQt   CotQt   SecQt   CscQt   Sint   Cost   Tant   Cott   Sect   Csct   HyperbolicQt   SinhQt   CoshQt   TanhQt   CothQt   SechQt   CschQt   InverseTrigQt   SinCosQt	   SinhCoshQt	   LeafCountt	   Numeratort   NumberQt   NumericQt   Lengtht   ListQt   Imt   Ret   InverseHyperbolicQt   InverseFunctionQt   TrigHyperbolicFreeQt   InverseFunctionFreeQt   RealQt   EqQt   FractionalPowerFreeQt   ComplexFreeQt   PolynomialQt   FactorSquareFreet   PowerOfLinearQt   Exponentt
   QuadraticQt   LinearPairQt   BinomialPartst   TrinomialPartst   PolyQt   EvenQt   OddQt   PerfectSquareQt   NiceSqrtAuxQt	   NiceSqrtQt   Togethert   PosAuxt   PosQt   CoefficientListt
   ReplaceAllt   ExpandLinearProductt   GCDt   ContentFactort   NumericFactort   NonnumericFactorst   MakeAssocListt   GensymSubstt   KernelSubstt   ExpandExpressiont   Apartt
   SmartApartt   MatchQt   PolynomialQuotientRemaindert   FreeFactorst   NonfreeFactorst   RemoveContentAuxt   RemoveContentt	   FreeTermst   NonfreeTermst   ExpandAlgebraicFunctiont   CollectReciprocalst   ExpandCleanupt   AlgebraicFunctionQt   Coefft   LeadTermt   RemainingTermst
   LeadFactort   RemainingFactorst   LeadBaset
   LeadDegreet   Numert   Denomt	   hypergeomt   Expont   MergeMonomialst   PolynomialDividet	   BinomialQt
   TrinomialQt   GeneralizedBinomialQt   GeneralizedTrinomialQt   FactorSquareFreeListt   PerfectPowerTestt   SquareFreeFactorTestt   RationalFunctionQt   RationalFunctionFactorst   NonrationalFunctionFactorst   Reverset   RationalFunctionExponentst   RationalFunctionExpandt   ExpandIntegrandt   SimplerQt   SimplerSqrtQt   SumSimplerQt   BinomialDegreet   TrinomialDegreet   CancelCommonFactorst   SimplerIntegrandQt   GeneralizedBinomialDegreet   GeneralizedBinomialPartst   GeneralizedTrinomialDegreet   GeneralizedTrinomialPartst	   MonomialQt   MonomialSumQt   MinimumMonomialExponentt   MonomialExponentt   LinearMatchQt   PowerOfLinearMatchQt   QuadraticMatchQt   CubicMatchQt   BinomialMatchQt   TrinomialMatchQt   GeneralizedBinomialMatchQt   GeneralizedTrinomialMatchQt   QuotientOfLinearsMatchQt   PolynomialTermQt   PolynomialTermst   NonpolynomialTermst   PseudoBinomialPartst   NormalizePseudoBinomialt   PseudoBinomialPairQt   PseudoBinomialQt   PolynomialGCDt   PolyGCDt   AlgebraicFunctionFactorst   NonalgebraicFunctionFactorst   QuotientOfLinearsPt   QuotientOfLinearsPartst   QuotientOfLinearsQt   Flattent   Sortt   AbsurdNumberQt   AbsurdNumberFactorst   NonabsurdNumberFactorst   SumSimplerAuxQt   Prependt   Dropt   CombineExponentst   FactorIntegert   FactorAbsurdNumbert   SubstForInverseFunctiont   SubstForFractionalPowert*   SubstForFractionalPowerOfQuotientOfLinearst"   FractionalPowerOfQuotientOfLinearst   SubstForFractionalPowerQt   SubstForFractionalPowerAuxQt   FractionalPowerOfSquareQt   FractionalPowerSubexpressionQt   Applyt   FactorNumericGcdt   MergeableFactorQt   MergeFactort   MergeFactorst   TrigSimplifyQt   TrigSimplifyt   TrigSimplifyRecurt   Ordert   FactorOrdert   Smallestt   OrderedQt   MinimumDegreet   PositiveFactorst   Signt   NonpositiveFactorst   PolynomialInAuxQt   PolynomialInQt   ExponentInAuxt
   ExponentInt   PolynomialInSubstAuxt   PolynomialInSubstt   Distribt   DistributeDegreet   FunctionOfPowert   DivideDegreesOfFactorst   MonomialFactort   FullSimplifyt   FunctionOfLinearSubstt   FunctionOfLineart   NormalizeIntegrandt   NormalizeIntegrandAuxt   NormalizeIntegrandFactort   NormalizeIntegrandFactorBaset   NormalizeTogethert   NormalizeLeadTermSignst   AbsorbMinusSignt   NormalizeSumFactorst   SignOfFactort   NormalizePowerOfLineart   SimplifyIntegrandt   SimplifyTermt   TogetherSimplifyt   SmartSimplifyt   SubstForExpnt   ExpandToSumt   UnifySumt
   UnifyTermst	   UnifyTermt	   CalculusQt   FunctionOfInverseLineart   PureFunctionOfSinhQt   PureFunctionOfTanhQt   PureFunctionOfCoshQt   IntegerQuotientQt   OddQuotientQt   EvenQuotientQt   FindTrigFactort   FunctionOfSinhQt   FunctionOfCoshQt   OddHyperbolicPowerQt   FunctionOfTanhQt   FunctionOfTanhWeightt   FunctionOfHyperbolicQt   SmartNumeratort   SmartDenominatort   SubstForAuxt   ActivateTrigt
   ExpandTrigt
   TrigExpandt   SubstForTrigt   SubstForHyperbolict   InertTrigFreeQt   LCMt   SubstForFractionalPowerOfLineart   FractionalPowerOfLineart   InverseFunctionOfLineart
   InertTrigQt   InertReciprocalQt   DeactivateTrigt   FixInertTrigFunctiont   DeactivateTrigAuxt   PowerOfInertTrigSumQt   PiecewiseLinearQt   KnownTrigIntegrandQt   KnownSineIntegrandQt   KnownTangentIntegrandQt   KnownCotangentIntegrandQt   KnownSecantIntegrandQt   TryPureTanSubstt   TryTanhSubstt   TryPureTanhSubstt   AbsurdNumberGCDt   AbsurdNumberGCDListt   ExpandTrigExpandt   ExpandTrigReducet   ExpandTrigReduceAuxt   NormalizeTrigt	   TrigToExpt   ExpandTrigToExpt
   TrigReducet   FunctionOfTrigt   AlgebraicTrigFunctionQt   FunctionOfHyperbolict   FunctionOfQt   FunctionOfExpnQt   PureFunctionOfSinQt   PureFunctionOfCosQt   PureFunctionOfTanQt   PureFunctionOfCotQt   FunctionOfCosQt   FunctionOfSinQt   OddTrigPowerQt   FunctionOfTanQt   FunctionOfTanWeightt   FunctionOfTrigQt   FunctionOfDensePolynomialsQt   FunctionOfLogt   PowerVariableExpnt   PowerVariableDegreet   PowerVariableSubstt   EulerIntegrandQt   FunctionOfSquareRootOfQuadratict   SquareRootOfQuadraticSubstt   Dividest   EasyDQt   ProductOfLinearPowersQt   Rtt   NthRoott	   AtomBaseQt   SumBaseQt   NegSumBaseQt   AllNegTermQt   SomeNegTermQt   TrigSquareQt   RtAuxt
   TrigSquaret   IntSumt   IntTermt   Map2t   ConstantFactort   SameQt   ReplacePartt   CommonFactorst   MostMainFactorPositiont   FunctionOfExponentialQt   FunctionOfExponentialt   FunctionOfExponentialFunctiont    FunctionOfExponentialFunctionAuxt   FunctionOfExponentialTestt   FunctionOfExponentialTestAuxt   stdevt	   rubi_testt   Ift   IntQuadraticQt   IntBinomialQt   RectifyTangentt   RectifyCotangentt
   Inequalityt	   Conditiont   Simpt   SimpHelpt   SplitProductt   SplitSumt   SubstForRF  t   FresnelSt   FresnelCt   Erfct   Erfit   Gammat   FunctionOfTrigOfLinearQt   ElementaryFunctionQt   Complext   UnsameQt   _SimpFixFactort   SimpFixFactort   _FixSimplifyt   FixSimplifyt   _SimplifyAntiderivativeSumt   SimplifyAntiderivativeSumt   _SimplifyAntiderivativet   SimplifyAntiderivativet   _TrigSimplifyAuxt   TrigSimplifyAuxt   Cancelt   Partt   PolyLogt   Dt   Distt   Sum_doitt   PolynomialQuotientt   Floort   PolynomialRemaindert   FactorR  t   CosIntegralt   SinIntegralt   LogIntegralt   SinhIntegralt   CoshIntegralt   Rulet   Erft	   PolyGammat   ExpIntegralEit   ExpIntegralEt   LogGammat   UtilityOperatort	   Factorialt   Zetat
   ProductLogt   DerivativeDividest   HypergeometricPFQt   IntHidet   OneQt   Nullt   rubi_expt   rubi_logt   Discriminantt   Negativet   Quotient(   t   Integralt   St   sqrtt   Andt   Ort   Integert   Floatt   Modt   It   Abst   simplifyt   Mult   Addt   Powt   signt
   EulerGamma(   t   WC(   t   symbolst   Symbol(   t   sint   cost   tant   cott   csct   secR  t   erf(   t   acosht   asinht   atanht   acotht   acscht   asecht   cosht   sinht   tanht   cotht   secht   csch(   t   atant   acsct   asint   acott   acost   asect   atan2(   t   pit   ABCFGHabcdefghijklmnpqrtuvswxyzt   a1t   a2t   b1t   b2t   c1t   c2t   d1t   d2t   n1t   n2t   e1t   e2t   f1t   f2t   g1t   g2t   n3t   Pqt   Pmt   Pxt   Qmt   Qrt   Qxt   jnt   mnt   non2t   RFxt   RGxs   i ii Pqq Q R r C k uc   d         sT  d d l  m } m } m } m } m } m } m } m } m	 }	 m
 }
 m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m }   f d   } t t t t d t d   t   | |  } t! | |  } d   } t t t" t t   | t# |   }   f d   }  t! | |   }! d   }" t t t" t$ t t   | | | | t# |"   }#   f d	   }$ t! |# |$  }% d
   }& t t t d  t t" t   | t# |&   }'   f d   }( t! |' |(  }) d   }* t t t d  t t% t"  t   | t# |*   }+   f d   }, t! |+ |,  }- d   }. t t t d  t t% t"  t   | t# |.   }/   f d   }0 t! |/ |0  }1 d   }2 t t t" t$ t t   | | | t# |2   }3   f d   }4 t! |3 |4  }5 d   }6 t t t" t$ t t   | | t# |6   }7   f d   }8 t! |7 |8  }9 d   }: t t t d  t% t  t% t"  t   | t# |:   };   f d   }< t! |; |<  }= d   }> t t t d  t% t  t% t"  t   | t# |>   }?   f d   }@ t! |? |@  }A d   }B t t t t& t" t$ t   | | | |	 |
 t# |B   }C   f d   }D t! |C |D  }E d   }F t t t t& t" t d t d   t   | | | |
 | t# |F   }G   f d   }H t! |G |H  }I d   }J t t t t& t" t d t d   t   | | | | | | | t# |J  	 }K   f d   }L t! |K |L  }M d   }N t t t t& t" t$ t   | | | | t# |N   }O   f d    }P t! |O |P  }Q d!   }R t t t t& t" t$ t   | | | | t# |R   }S   f d"   }T t! |S |T  }U d#   }V t t t t& t" t$ t   | | | t# |V   }W   f d$   }X t! |W |X  }Y d%   }Z t t t t& t" t$ t   | | | t# |Z   }[   f d&   }\ t! |[ |\  }]   f d'   }^ t t t t d t d   t' t  t d( t d   t d) t d*    t   | | | | | |  }_ t! |_ |^  }`   f d+   }a t t t t d t d   t  t d( t d   t d) t d*   t d t d   t' t  t d( t d   t d) t d*    t   | | | | | | | |
 	 }b t! |b |a  }c | |! |% |) |- |1 |5 |9 |= |A |E |I |M |Q |U |Y |] |` |c g S(,   Ni(   t   cons1090t   cons21t   cons1091t   cons87t   cons88t   cons1092t   cons89t   cons23t   cons72t   cons66t   cons4t   cons1093t   cons214t   cons683t   cons100t   cons101t   cons1094t   cons1095t   cons31t   cons94t   cons356t   cons1096t   cons18t   cons1097t   cons2t   cons3c            sO   t  | |   }   j d  t t d  | t t |  | |   |  |  |   S(   NiZ  i   (   R  t   appendR  R  R*   R   (   t   xt   mt   ut   c(   t   rubi(    sJ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/piecewise_linear.pyt   With1882   s    RF  i   c         S   s^   t  | t t t t f  r t St | |  } t |  |  } t | |  | |  rZ t St S(   N(	   t
   isinstancet   intR  t   floatR  t   FalseR  R   t   True(   t   vRE  RG  t   at   b(    (    sJ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/piecewise_linear.pyt   With1883   s    c            su   t  | |  } t  |  |  }   j d  t | |  | | | t t d  | |  |  t | | | |  S(   Ni[  i   (   R  RD  R  R   R  R  (   RP  RE  RG  RQ  RR  (   RI  (    sJ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/piecewise_linear.pyt   replacement1883   s    c         S   s^   t  | t t t t f  r t St | |  } t |  |  } t | |  | |  rZ t St S(   N(	   RK  RL  R  RM  R  RN  R  R   RO  (   RP  RE  t   nRG  RQ  RR  (    (    sJ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/piecewise_linear.pyt   With1884   s    c            s   t  | |  } t  |  |  }   j d  t | |  | | | t |  | t d  | |  |  t |  | | | |  S(   Ni\  i(   R  RD  R  R   R  R  (   RP  RE  RU  RG  RQ  RR  (   RI  (    sJ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/piecewise_linear.pyt   replacement1884   s    c         S   s^   t  | t t t t f  r t St | |  } t |  |  } t | |  | |  rZ t St S(   N(	   RK  RL  R  RM  R  RN  R  R   RO  (   RP  RE  RG  RQ  RR  (    (    sJ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/piecewise_linear.pyt   With1885   s    c            s   t  | |  } t  |  |  }   j d  t | | |  | | t t d  | |  |  t | | |  | | t t d  |  |  |  S(   Ni]  i   (   R  RD  R  R   R  (   RP  RE  RG  RQ  RR  (   RI  (    sJ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/piecewise_linear.pyt   replacement1885   s    c         S   s~   t  | t t t t f  r t St | |  } t |  |  } t t | |  | |  t	 | |  | | |   rz t
 St S(   N(   RK  RL  R  RM  R  RN  R  R  R   R   RO  (   RP  RE  RG  RQ  RR  (    (    sJ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/piecewise_linear.pyt   With1886   s    9c            s   t  | |  } t  |  |  }   j d  t t d  t t |   t | |  | | | t d    | t | |  | | | t d   |  S(   Ni^  i   (   R  RD  R  R  R=   R  R  (   RP  RE  RG  RQ  RR  (   RI  (    sJ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/piecewise_linear.pyt   replacement1886   s    c         S   s~   t  | t t t t f  r t St | |  } t |  |  } t t | |  | |  t	 | |  | | |   rz t
 St S(   N(   RK  RL  R  RM  R  RN  R  R  R   R!   RO  (   RP  RE  RG  RQ  RR  (    (    sJ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/piecewise_linear.pyt   With1887   s    9c            s   t  | |  } t  |  |  }   j d  t t d  t t |   t | |  | | | t d    | t | |  | | | t d   |  S(   Ni_  i   (   R  RD  R  R  R  R  R  (   RP  RE  RG  RQ  RR  (   RI  (    sJ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/piecewise_linear.pyt   replacement1887   s    c         S   s^   t  | t t t t f  r t St | |  } t |  |  } t | |  | |  rZ t St S(   N(	   RK  RL  R  RM  R  RN  R  R   RO  (   RP  RE  RU  RG  RQ  RR  (    (    sJ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/piecewise_linear.pyt   With1888   s    c            s   t  | |  } t  |  |  }   j d  t | | |  | | t |  | t d  | |  |  t |  | t d  | t d  | |  | | |  S(   Ni`  i   (   R  RD  R  R   R  R  (   RP  RE  RU  RG  RQ  RR  (   RI  (    sJ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/piecewise_linear.pyt   replacement1888   s    c         S   s^   t  | t t t t f  r t St | |  } t |  |  } t | |  | |  rZ t St S(   N(	   RK  RL  R  RM  R  RN  R  R   RO  (   RP  RE  RU  RG  RQ  RR  (    (    sJ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/piecewise_linear.pyt   With1889   s    c      
      s   t  | |  } t  |  |  }   j d  t |  | t d  t t d  | t d  | t d  | |  | |  | |  | t d  | |  | | |  S(   Nia  i   i   (   R  RD  R  R  R4   (   RP  RE  RU  RG  RQ  RR  (   RI  (    sJ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/piecewise_linear.pyt   replacement1889   s    c         S   sq   t  | t t t t f  r t St | |  } t |  |  } t t | |  | |  t	 | |   rm t
 St S(   N(   RK  RL  R  RM  R  RN  R  R  R   R   RO  (   RP  RE  RG  RQ  RR  (    (    sJ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/piecewise_linear.pyt   With1890  s    ,c            s   t  | |  } t  |  |  }   j d  t t d  t t |  t | | t d   | t |    t | | t d   |  S(   Nib  i   (   R  RD  R  R  R  R  R  (   RP  RE  RG  RQ  RR  (   RI  (    sJ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/piecewise_linear.pyt   replacement1890  s    c         S   sq   t  | t t t t f  r t St | |  } t |  |  } t t | |  | |  t	 | |   rm t
 St S(   N(   RK  RL  R  RM  R  RN  R  R  R   R!   RO  (   RP  RE  RG  RQ  RR  (    (    sJ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/piecewise_linear.pyt   With1891  s    ,c            s   t  | |  } t  |  |  }   j d  t t d  t t |  t | | t d   | t |    t | | t d   |  S(   Nic  i   (   R  RD  R  R  R=   R  R  (   RP  RE  RG  RQ  RR  (   RI  (    sJ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/piecewise_linear.pyt   replacement1891  s    c         S   s^   t  | t t t t f  r t St | |  } t |  |  } t | |  | |  rZ t St S(   N(	   RK  RL  R  RM  R  RN  R  R   RO  (   RP  RG  RF  RU  RE  RQ  RR  (    (    sJ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/piecewise_linear.pyt   With1892$  s    c            sx   t  | |  } t  |  |  }   j d  t | | t d  |  | t d  | t d  | |  | | |  S(   Nid  i   (   R  RD  R  R  (   RP  RG  RF  RU  RE  RQ  RR  (   RI  (    sJ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/piecewise_linear.pyt   replacement1892-  s    c         S   s^   t  | t t t t f  r t St | |  } t |  |  } t | |  | |  rZ t St S(   N(	   RK  RL  R  RM  R  RN  R  R   RO  (   RP  RG  RF  RU  RE  RQ  RR  (    (    sJ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/piecewise_linear.pyt   With18934  s    RU  c            s   t  | |  } t  |  |  }   j d  t | | | | t d  t | | t d  |  | t d  |  |  t | | t d  |  | | | t d  |  S(   Nie  i   i(   R  RD  R  R  R   R  (   RP  RG  RF  RU  RE  RQ  RR  (   RI  (    sJ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/piecewise_linear.pyt   replacement1893=  s    c         S   s^   t  | t t t t f  r t St | |  } t |  |  } t | |  | |  rZ t St S(   N(	   RK  RL  R  RM  R  RN  R  R   RO  (   RP  RG  RF  RU  RE  RQ  RR  (    (    sJ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/piecewise_linear.pyt   With1894D  s    c            s   t  | |  } t  |  |  }   j d  t | | |  | | | | | t d  t | | |  | t d  |  |  t | | t d  |  | | | | t d  |  S(   Nif  i   i(   R  RD  R  R  R   R  (   RP  RG  RF  RU  RE  RQ  RR  (   RI  (    sJ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/piecewise_linear.pyt   replacement1894M  s    c         S   s^   t  | t t t t f  r t St | |  } t |  |  } t | |  | |  rZ t St S(   N(	   RK  RL  R  RM  R  RN  R  R   RO  (   RP  RG  RF  RU  RE  RQ  RR  (    (    sJ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/piecewise_linear.pyt   With1895T  s    c            s   t  | |  } t  |  |  }   j d  t | | |  | | | | | t d  t | | |  | t d  |  |  t | | t d  |  | | | | t d  |  S(   Nig  i   i(   R  RD  R  R  R   R  (   RP  RG  RF  RU  RE  RQ  RR  (   RI  (    sJ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/piecewise_linear.pyt   replacement1895]  s    c         S   s^   t  | t t t t f  r t St | |  } t |  |  } t | |  | |  rZ t St S(   N(	   RK  RL  R  RM  R  RN  R  R   RO  (   RP  RG  RF  RU  RE  RQ  RR  (    (    sJ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/piecewise_linear.pyt   With1896d  s    c            s   t  | |  } t  |  |  }   j d  t | | | t d  | t d  | |  | | t | | t d  |  | |  |  t | | t d  |  | t d  | t d  | |  | | |  S(   Nih  i   i   (   R  RD  R  R  R   R  (   RP  RG  RF  RU  RE  RQ  RR  (   RI  (    sJ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/piecewise_linear.pyt   replacement1896m  s    c         S   s^   t  | t t t t f  r t St | |  } t |  |  } t | |  | |  rZ t St S(   N(	   RK  RL  R  RM  R  RN  R  R   RO  (   RP  RG  RF  RU  RE  RQ  RR  (    (    sJ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/piecewise_linear.pyt   With1897t  s    c            s   t  | |  } t  |  |  }   j d  t | | | t d  | t d  | |  | | t | | t d  |  | |  |  t | | t d  |  | t d  | t d  | |  | | |  S(   Nii  i   i   (   R  RD  R  R  R   R  (   RP  RG  RF  RU  RE  RQ  RR  (   RI  (    sJ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/piecewise_linear.pyt   replacement1897}  s    c         S   s^   t  | t t t t f  r t St | |  } t |  |  } t | |  | |  rZ t St S(   N(	   RK  RL  R  RM  R  RN  R  R   RO  (   RP  RG  RF  RU  RE  RQ  RR  (    (    sJ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/piecewise_linear.pyt   With1898  s    c      
      s   t  | |  } t  |  |  }   j d  t | | |  | t d  | | | |  | | | t | | t d  | t d  | |  | |  | |  | | t d  |  S(   Nij  i   i   (   R  RD  R  R  R4   (   RP  RG  RF  RU  RE  RQ  RR  (   RI  (    sJ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/piecewise_linear.pyt   replacement1898  s    c            s   t  |  |  }   j d  t | | | t |  | t d  | | | t | | |  |  |  t |  | |  t |  | | | | t | | |  | |  S(   Nik  i(   R  RD  R  R   R  t   logR  (   RG  RR  RQ  RU  RE  RH  (   RI  (    sJ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/piecewise_linear.pyt   With1899  s    RR  RQ  i    c            s  t  |  |  }   j d  t | | | | t d  t |  | t d  | | | | t d  t | | |  |  |  t t d  | t d  t |  | | | | | |  |  t |  | | | | | t d  t | | |  | | t d  |  S(   Nil  i   i(   R  RD  R  R  R   Rt  R  (   RG  RF  RR  RQ  RU  RE  RH  (   RI  (    sJ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/piecewise_linear.pyt   With1900  s    ((   t    sympy.integrals.rubi.constraintsR*  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  R   R  t   u_R  R  t   x_R   t   v_R   t   n_R  t   m_Rt  (d   RI  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  RJ  t   pattern1882t   rule1882RS  t   pattern1883RT  t   rule1883RV  t   pattern1884RW  t   rule1884RX  t   pattern1885RY  t   rule1885RZ  t   pattern1886R[  t   rule1886R\  t   pattern1887R]  t   rule1887R^  t   pattern1888R_  t   rule1888R`  t   pattern1889Ra  t   rule1889Rb  t   pattern1890Rc  t   rule1890Rd  t   pattern1891Re  t   rule1891Rf  t   pattern1892Rg  t   rule1892Rh  t   pattern1893Ri  t   rule1893Rj  t   pattern1894Rk  t   rule1894Rl  t   pattern1895Rm  t   rule1895Rn  t   pattern1896Ro  t   rule1896Rp  t   pattern1897Rq  t   rule1897Rr  t   pattern1898Rs  t   rule1898Ru  t   pattern1899t   rule1899Rv  t   pattern1900t   rule1900(    (   RI  sJ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/piecewise_linear.pyt   piecewise_linear   s    .	%	2	/	5	5	/	,	;	;	9	H	N	6	6	3	3jN(d  t   __doc__t   sympy.externalR    R   t   sympy.utilities.decoratorR   R   R   R   R   t%   sympy.integrals.rubi.utility_functionR   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$   R%   R&   R'   R(   R)   R*   R+   R,   R-   R.   R/   R0   R1   R2   R3   R4   R5   R6   R7   R8   R9   R:   R;   R<   R=   R>   R?   R@   RA   RB   RC   RD   RE   RF   RG   RH   RI   RJ   RK   RL   RM   RN   RO   RP   RQ   RR   RS   RT   RU   RV   RW   RX   RY   RZ   R[   R\   R]   R^   R_   R`   Ra   Rb   Rc   Rd   Re   Rf   Rg   Rh   Ri   Rj   Rk   Rl   Rm   Rn   Ro   Rp   Rq   Rr   Rs   Rt   Ru   Rv   Rw   Rx   Ry   Rz   R{   R|   R}   R~   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R  R  R  R  R  R  R  R  R	  R
  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R   R!  R"  R#  R$  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  RF  RG  RH  RI  RJ  RK  RL  RM  RN  RO  RP  RQ  RR  RS  RT  RU  RV  RW  RX  RY  RZ  R[  R\  R]  R^  R_  R`  Ra  Rb  Rc  Rd  Re  Rf  Rg  Rh  Ri  Rj  Rk  Rl  Rm  Rn  Ro  Rp  Rq  Rr  Rs  Rt  Ru  Rv  Rw  Rx  Ry  Rz  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  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  t   expR  Rt  R  R  R  t   sympyR  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  t   sympy.integrals.rubi.symbolR  t   sympy.core.symbolR  R  t   sympy.functionsR  R  R  R  R  R  R  t%   sympy.functions.elementary.hyperbolicR  R  R  R  R  R  R  R   R  R  R  R  t(   sympy.functions.elementary.trigonometricR  R  R  R  R	  R
  R  R  t   Pit   it   A_t   B_t   C_t   F_t   G_t   H_t   a_t   b_t   c_t   d_t   e_t   f_t   g_t   h_t   i_t   j_t   k_t   l_R|  R{  t   p_t   q_t   r_t   t_Rx  Rz  t   s_t   w_Ry  t   y_t   z_t   a1_t   a2_t   b1_t   b2_t   c1_t   c2_t   d1_t   d2_t   n1_t   n2_t   e1_t   e2_t   f1_t   f2_t   g1_t   g2_t   n3_t   Pq_t   Pm_t   Px_t   Qm_t   Qr_t   Qx_t   jn_t   mn_t   non2_t   RFx_t   RGx_t   iit   Pqqt   Qt   Rt   rt   Ct   kRG  RN  t	   _UseGammat	   ShowStepst   Nonet   StepCounterR  (    (    (    sJ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/piecewise_linear.pyt   <module>   s>   "           1nj:R4|'	