
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Z
mZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZm Z m!Z!m"Z"m#Z#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      $      s  d d l  m } m } m } m } m } m } m } m } m	 }	 m
 }
 m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m  }  m! }! m" }" m# }# m$ }$ m% }% m& }& m' }' m( }( m) }) m* }* m+ }+ m, }, m- }- m. }. m/ }/ m0 }0 m1 }1 m2 }2 m3 }3 m4 }4 m5 }5 m6 }6 m7 }7 m8 }8 m9 }9 m: }: m; }; m< }< m= }= m> }> m? }? m@ }@ mA }A tB tC tD tE tF d tG d   tF d tG d   tF d tG d   tF d tG d   tE  | | | | |  }B   f d   }C tH |B |C  }D tB tC tD tE tF d	 tG d   tF d
 tG d   tE tF d tG d   tF d tG d   tF d tG d   tF d tG d   tE  | | | | | | |  }E   f d   }F tH |E |F  }G tB tC tE tF d	 tG d   tF d
 tG d   tE tF d tG d   tF d tG d   tF d tG d   tF d tG d   tF d tG d   tE  | | | | | | |  }H   f d   }I tH |H |I  }J tB tC tE tF d	 tG d   tF d
 tG d   tE tF d tG d   tF d tG d   tF d tG d   tF d tG d   tF d tG d   tE  | | | | | | |	  }K   f d   }L tH |K |L  }M tB tC tI tF d tG d   tI tF d tG d   tF d tG d   tF d tG d   tF d tG d   tE  | | |
  }N   f d   }O tH |N |O  }P tB tC tJ tK tF d tG d   tE  | | |  }Q   f d   }R tH |Q |R  }S tB tC tD tE  | |  }T   f d   }U tH |T |U  }V tB tC tD tL tE tF d
 tG d   tE  | | | |  }W   f d   }X tH |W |X  }Y tB tC tM tE   }Z   f d   }[ tH |Z |[  }\ tB tC tM tN tG d  tD  tE  | |  }]   f d   }^ tH |] |^  }_ tB tC tD tM tE  | |  }`   f d   }a tH |` |a  }b tB tC tM tE  |  }c   f d   }d tH |c |d  }e tB tC tI tF d tG d   tL tI tO tF d tG d   tE  | | |  }f   f d   }g tH |f |g  }h tB tC tI tF d tG d   tP tI tF d tG d   tO tF d tG d   tE  | | | | | |  }i   f d   }j tH |i |j  }k tB tC tI tF d tG d   tP tI tF d tG d   tO tF d tG d   tE  | | | | | |  }l   f d   }m tH |l |m  }n tB tC tI tF d tG d   tP tI tF d tG d   tO tF d tG d   tE  | | | | | | |  }o   f d   }p tH |o |p  }q tB tC tI tF d tG d   tP tI tF d tG d   tO tF d tG d   tE  | | | | | | |  }r   f d   }s tH |r |s  }t tB tC tD tI tF d tG d   tF d tG d   tQ tI tF d tG d   tF d tG d   tF d tG d   tE  | | | | | | | | 	 }u   f d    }v tH |u |v  }w tB tC tD tI tF d tG d   tP tQ tI tF d tG d   tO tF d tG d   tE  | | | | | | | | | 
 }x   f d!   }y tH |x |y  }z tB tC tD tI tF d tG d   tP tQ tI tF d tG d   tO tF d tG d   tE  | | | | | | | | 	 }{   f d"   }| tH |{ ||  }} tB tC tI tF d tG d   tP tI tG d#  tF d
 tG d   tI tF d tG d   tF d tG d   tE  | | | | |   }~   f d$   } tH |~ |  } tB tC tD tI tF d tG d   tP tI tG d#  tF d% tG d   tI tF d& tG d   tF d' tG d   tF d tG d   tE  | | |" |# |$ |! | |  	 }   f d(   } tH | |  } tB tC tD tE tF d tG d   tF d tG d   tF d tG d   tQ tE tF d) tG d   tF d tG d   tF d tG d   tF d tG d   tE  | | | | | | |% |& |' |(  }   f d*   } tH | |  } tB tC tD tE tF d tG d   tF d tG d   tF d tG d   tQ tE tR tF d tG d   tF d tG d   tF d tG d   tE  | | | | | | | | |) |* |+ |,  }   f d+   } tH | |  } tB tC tD tE tG d#  tF d
 tG d   tE tF d tG d   tF d tG d   tF d tG d   tE  | | | |- |&  }   f d,   } tH | |  } tB tC tD tE tO tF d tG d   tE tF d- tG d   tF d
 tG d   tF d tG d   tF d tG d   tE  | | | | |. |- |&  }   f d.   } tH | |  } tB tC tS tE tF d/ tG d   tE tG d#  tF d
 tG d   tE tF d tG d   tF d tG d   tF d tG d   tE  | | | | |0 | |/  }   f d0   } tH | |  } tB tC tE tF d tG d   tF d tG d   tE tF d) tG d   tF d tG d   tF d tG d   tF d tG d   tE  | | | |2 | |1  }   f d1   } tH | |  } tB tC tE tF d tG d   tF d tG d   tE tF d) tG d   tF d tG d   tE tF d2 tG d   tF d
 tG d   tF d tG d   tF d tG d   tE  | | | | |2 |4 | |1 |3 
 }   f d3   } tH | |  } tB tC tE tF d tG d   tD tE tO tF d tG d   tE  | | | | |5  }   f d4   } tH | |  } tB tC tE tF d tG d   tD tE tO tF d tG d   tK tE  | | | | | |5 |6  }   f d5   } tH | |  } tB tC tE tF d tG d   tT tE tF d tG d   tF d6 tG d   tK tU tE tF d tG d   tF d7 tG d   tK tE  |9 |: |; |< | | | |7 |8 |6  }   f d8   } tH | |  } d9   } tB tC tV tJ tF d tG d   tF d tG d   tF d tG d   tF d tG d   tE  | | | | | |= tW |   }   f d:   } tH | |  } d;   } tB tC tV tJ tF d tG d   tF d tG d   tJ tF d- tG d   tF d
 tG d   tF d tG d   tF d tG d   tE  | | | | | |. | |= tW |  
 }   f d<   } tH | |  } d=   } tB tC tX tP tY tK tF d tG d   tE  |> |? |@ |A tW |   }   f d>   } tH | |  } d?   } tB tC tX tY tK tF d tG d   tE  |? |@ |A tW |   }   f d@   } tH | |  } |D |G |J |M |P |S |V |Y |\ |_ |b |e |h |k |n |q |t |w |z |} | | | | | | | | | | | | | | | | g$ S(A   Ni(A   t   cons1t   cons2t   cons3t   cons4t   cons5t   cons6t   cons7t   cons8t   cons9t   cons10t   cons11t   cons12t   cons13t   cons14t   cons15t   cons16t   cons17t   cons18t   cons19t   cons20t   cons21t   cons22t   cons23t   cons24t   cons25t   cons26t   cons27t   cons28t   cons29t   cons30t   cons31t   cons32t   cons33t   cons34t   cons35t   cons36t   cons37t   cons38t   cons39t   cons40t   cons41t   cons42t   cons43t   cons44t   cons45t   cons46t   cons47t   cons48t   cons49t   cons50t   cons51t   cons52t   cons53t   cons54t   cons55t   cons56t   cons57t   cons58t   cons59t   cons60t   cons61t   cons62t   cons63t   cons64t   cons65t   ni   t   bt   pt   uc            s*     j  d  t | | | | |  |  S(   Ni   (   t   appendR   (   Rm  Rn  Rl  t   aRk  t   x(   t   rubi(    sR   lib/python2.7/site-packages/sympy/integrals/rubi/rules/integrand_simplification.pyt   replacement1   s    t   jt   cc            s@     j  d  t | | | | | | t d  | |  |  S(   Ni   (   Ro  R   R  (   Rm  Rn  Rt  Rl  Ru  Rk  Rp  Rq  (   Rr  (    sR   lib/python2.7/site-packages/sympy/integrals/rubi/rules/integrand_simplification.pyt   replacement2   s    Rp  i    c            s8     j  d  t | | | | t d  | |  |  S(   Ni   i   (   Ro  R   R  (   Rm  Rn  Rt  Rl  Rp  Ru  Rk  Rq  (   Rr  (    sR   lib/python2.7/site-packages/sympy/integrals/rubi/rules/integrand_simplification.pyt   replacement3   s    c            s.     j  d  t | | | | | |  |  S(   Ni   (   Ro  R   (   Rm  Rn  Rt  Rl  Rp  Ru  Rk  Rq  (   Rr  (    sR   lib/python2.7/site-packages/sympy/integrals/rubi/rules/integrand_simplification.pyt   replacement4   s    t   wc            s.     j  d  t | |  | | | | |  S(   Ni   (   Ro  R   (   t   vRy  Rm  Rn  Rl  Rp  Rq  (   Rr  (    sR   lib/python2.7/site-packages/sympy/integrals/rubi/rules/integrand_simplification.pyt   replacement5   s    c            s"     j  d  t | | | |   S(   Ni   (   Ro  R   (   Rq  Rm  R   Rn  (   Rr  (    sR   lib/python2.7/site-packages/sympy/integrals/rubi/rules/integrand_simplification.pyt   replacement6   s    c            s     j  d  t | |  |   S(   Ni   (   Ro  R  (   Rq  Rp  (   Rr  (    sR   lib/python2.7/site-packages/sympy/integrals/rubi/rules/integrand_simplification.pyt   replacement7   s    c            s>     j  d  t | | | |  t d  t d  | |   S(   Ni   i   (   Ro  R  R  (   Rq  Ru  Rl  Rp  (   Rr  (    sR   lib/python2.7/site-packages/sympy/integrals/rubi/rules/integrand_simplification.pyt   replacement8   s    c            s,     j  d  t t d  t | |   |   S(   Ni	   i(   Ro  R  R  R   (   Rq  Rn  (   Rr  (    sR   lib/python2.7/site-packages/sympy/integrals/rubi/rules/integrand_simplification.pyt   replacement9   s    c            s5     j  d  t t t d  |  t | |   |   S(   Ni
   i    (   Ro  R  R  R  R   (   Rq  Rp  Rn  (   Rr  (    sR   lib/python2.7/site-packages/sympy/integrals/rubi/rules/integrand_simplification.pyt   replacement10   s    c            s&     j  d  t | t | |   |   S(   Ni   (   Ro  R  R   (   Rq  Rp  Rn  (   Rr  (    sR   lib/python2.7/site-packages/sympy/integrals/rubi/rules/integrand_simplification.pyt   replacement11   s    c            s#     j  d  t t | |   |   S(   Ni   (   Ro  R  R  (   Rq  Rn  (   Rr  (    sR   lib/python2.7/site-packages/sympy/integrals/rubi/rules/integrand_simplification.pyt   replacement12   s    t   mc            s;     j  d  t | | t | | |  | | |  |  S(   Ni   (   Ro  R  R   (   Rz  Rn  R  Rl  Rk  Rq  (   Rr  (    sR   lib/python2.7/site-packages/sympy/integrals/rubi/rules/integrand_simplification.pyt   replacement13   s    c            sv     j  d  t | | t d  d | | t d  d t | |   t | |   t | |  | | |  |  S(   Ni   i   i   i(   Ro  R  R  R  R   (   Rz  Rn  R  Rl  Rp  Rk  Rq  (   Rr  (    sR   lib/python2.7/site-packages/sympy/integrals/rubi/rules/integrand_simplification.pyt   replacement14   s    c            sv     j  d  t | | t d  d | | t d  d t | |   t | |   t | |  | | |  |  S(   Ni   ii   i   (   Ro  R  R  R  R   (   Rz  Rn  R  Rl  Rp  Rk  Rq  (   Rr  (    sR   lib/python2.7/site-packages/sympy/integrals/rubi/rules/integrand_simplification.pyt   replacement15   s    c            sS     j  d  t | | | | |  | | |  | t | |  | | |  |  S(   Ni   (   Ro  R  R   (   Rz  Rn  R  Rl  Rp  Rk  Rq  (   Rr  (    sR   lib/python2.7/site-packages/sympy/integrals/rubi/rules/integrand_simplification.pyt   replacement16   s    c            st     j  d  t | t |  | t |  | |  t |  | |  t |  t | | |  | | |  |  S(   Ni   (   Ro  R  R$   R%   R   (   Rz  Rn  R  Rl  Rp  Rk  Rq  (   Rr  (    sR   lib/python2.7/site-packages/sympy/integrals/rubi/rules/integrand_simplification.pyt   replacement17   s    t   dc	   	         sB     j  d  t | | | t | | | |  | | |  |  S(   Ni   (   Ro  R  R   (	   Rz  Rn  R  Rl  R  Rp  Rk  Ru  Rq  (   Rr  (    sR   lib/python2.7/site-packages/sympy/integrals/rubi/rules/integrand_simplification.pyt   replacement18   s    c	   	         sB     j  d  t | | | t | | | |  | | |  |  S(   Ni   (   Ro  R  R   (	   Rz  Rn  R  Rl  R  Rp  Ru  Rk  Rq  (   Rr  (    sR   lib/python2.7/site-packages/sympy/integrals/rubi/rules/integrand_simplification.pyt   replacement19   s    c	   	         sW     j  d  t | | |  | | | |  | t | | | |  | | |  |  S(   Ni   (   Ro  R  R   (	   Rz  Rn  R  Rl  R  Rp  Ru  Rk  Rq  (   Rr  (    sR   lib/python2.7/site-packages/sympy/integrals/rubi/rules/integrand_simplification.pyt   replacement20   s    i   c            sR     j  d  t t d  | t | | |  | t d  | | |  |  |  S(   Ni   i   (   Ro  R  R  R   (   Rz  Rn  R  Rl  Ru  Rp  Rq  (   Rr  (    sR   lib/python2.7/site-packages/sympy/integrals/rubi/rules/integrand_simplification.pyt   replacement21   s    t   Ct   Bt   Ac	   	         so     j  d  t | t d  t | | | | | t d  t |  | | | | | | |  |  |  S(   Ni   ii   (   Ro  R  R  R   R  (	   R  Rz  R  Rn  R  Rl  Rp  Rq  R  (   Rr  (    sR   lib/python2.7/site-packages/sympy/integrals/rubi/rules/integrand_simplification.pyt   replacement22   s    t   qc
   
         sS     j  d  t | | |  t | | | |  | | | | | |  |  |  S(   Ni   (   Ro  R  R   (
   Rm  Rn  R  Rl  R  Rp  Rk  Ru  Rq  R  (   Rr  (    sR   lib/python2.7/site-packages/sympy/integrals/rubi/rules/integrand_simplification.pyt   replacement23   s    c
   
         sN     j  d  t | t d  | | t | | | |	 | | |	  |	  S(   Ni   i   (   Ro  R  R  R   (
   Rm  Rn  Rt  R  Rl  R  Rp  Rk  Ru  Rq  (   Rr  (    sR   lib/python2.7/site-packages/sympy/integrals/rubi/rules/integrand_simplification.pyt   replacement24  s    c            s`     j  d  t t d  t d  |  | |  | | t d  | | t d  |  |  S(   Ni   i   (   Ro  R   R  (   Rm  Rn  Rl  Ru  Rp  Rq  (   Rr  (    sR   lib/python2.7/site-packages/sympy/integrals/rubi/rules/integrand_simplification.pyt   replacement25  s    R  c            sS     j  d  t | |  t | | t d  | | | t d  |  |  |  S(   Ni   i   (   Ro  R  R   R  (   Rm  Rn  Rl  R  Ru  Rp  Rk  Rq  (   Rr  (    sR   lib/python2.7/site-packages/sympy/integrals/rubi/rules/integrand_simplification.pyt   replacement26  s    t   ec      
      sT     j  d  t | | t t | |  |  | | | | | | t d   |  S(   Ni   i   (   Ro  R  R*   R   R  (   Rm  Rl  R  Ru  Rp  Rq  R  (   Rr  (    sR   lib/python2.7/site-packages/sympy/integrals/rubi/rules/integrand_simplification.pyt   replacement27  s    c            s?     j  d  t | | | |  | | | |  | | |  S(   Ni   (   Ro  R   (   Rm  Rn  R  Rl  Rp  Rq  R  (   Rr  (    sR   lib/python2.7/site-packages/sympy/integrals/rubi/rules/integrand_simplification.pyt   replacement28  s    t   rc	   	         sP     j  d  t | | | |  | | | |  | | | |  | | |  S(   Ni   (   Ro  R   (	   Rm  Rn  R  Rl  R  Rp  Ru  Rq  R  (   Rr  (    sR   lib/python2.7/site-packages/sympy/integrals/rubi/rules/integrand_simplification.pyt   replacement29  s    c            s=     j  d  t t t | | | | |   | | |  S(   Ni   (   Ro  R  R  R   (   R  Rl  Rp  Rk  Rq  (   Rr  (    sR   lib/python2.7/site-packages/sympy/integrals/rubi/rules/integrand_simplification.pyt   replacement30   s    c            sJ     j  d  t | | | | |  t d  | | |  t d  |  S(   Ni   i   (   Ro  R  R  (   Rm  R  Rl  Rp  Rk  Rq  (   Rr  (    sR   lib/python2.7/site-packages/sympy/integrals/rubi/rules/integrand_simplification.pyt   replacement31%  s    R  R  c            sv     j  d  t | | | | |  t d  | | | | |  t d  t d  | | | |  t d  |  S(   Ni    i   i   (   Ro  R  R  (   Rm  R  R  R  R  Rk  Rq  R  (   Rr  (    sR   lib/python2.7/site-packages/sympy/integrals/rubi/rules/integrand_simplification.pyt   replacement32*  s    c      
   S   s   t  | t t t t f  r t St | |  } t t t | |  | t	 d   t
 | | t | | |  t | | | t	 d   t | |    r t St S(   Ni(   t
   isinstancet   intR  t   floatR  t   FalseR   R  R"   R  R   R   R  t   True(   Rm  R   Rl  Rp  Rk  R"  Rq  R  (    (    sR   lib/python2.7/site-packages/sympy/integrals/rubi/rules/integrand_simplification.pyt   With33.  s    mc            s{   t  | |  }   j d  t t | | | t d   | t | | |  t t | | | | |  |  | |  |  S(   Ni!   i(   R   Ro  R  R   R  R*   R   (   Rm  R   Rl  Rp  Rk  R"  Rq  R  (   Rr  (    sR   lib/python2.7/site-packages/sympy/integrals/rubi/rules/integrand_simplification.pyt   replacement336  s    c	   
   
   S   s   t  | t t t t f  r t St | |  }	 t t t | |  |	 t	 d   t
 | |	 t | | |	  t | | |	 t	 d   t | |    r t St S(   Ni(   R  R  R  R  R  R  R   R  R"   R  R   R   R  R  (
   Rm  R   Rl  R  Ru  Rp  Rk  R"  Rq  R  (    (    sR   lib/python2.7/site-packages/sympy/integrals/rubi/rules/integrand_simplification.pyt   With34<  s    mc	   
   	      s   t  | |  }	   j d  t t | | |	 t d   |	 t | | |	  t t | | | | | | t d  | |  |  | |  |  S(   Ni"   ii   (   R   Ro  R  R   R  R*   R   (
   Rm  R   Rl  R  Ru  Rp  Rk  R"  Rq  R  (   Rr  (    sR   lib/python2.7/site-packages/sympy/integrals/rubi/rules/integrand_simplification.pyt   replacement34D  s    c         S   sO   t  | t t t t f  r t St | | |  } t | t d   rK t	 St S(   Ni(
   R  R  R  R  R  R  R   R   R  R  (   Rm  Rn  R  R  R#  Rq  t   gcd(    (    sR   lib/python2.7/site-packages/sympy/integrals/rubi/rules/integrand_simplification.pyt   With35J  s    c            s`   t  | | |  }   j d  t | | |  | t | | |  | t | | |  |  |  S(   Ni#   (   R   Ro  R   R  (   Rm  Rn  R  R  R#  Rq  R  (   Rr  (    sR   lib/python2.7/site-packages/sympy/integrals/rubi/rules/integrand_simplification.pyt   replacement35R  s    c         S   sO   t  | t t t t f  r t St | | |  } t | t d   rK t	 St S(   Ni(
   R  R  R  R  R  R  R   R   R  R  (   Rm  Rn  R  R#  Rq  R  (    (    sR   lib/python2.7/site-packages/sympy/integrals/rubi/rules/integrand_simplification.pyt   With36X  s    c            sb   t  | | |  }   j d  t | |  t d  | t | | |  t | | |  |  |  S(   Ni$   i   (   R   Ro  R   R  R  (   Rm  Rn  R  R#  Rq  R  (   Rr  (    sR   lib/python2.7/site-packages/sympy/integrals/rubi/rules/integrand_simplification.pyt   replacement36`  s    (Z   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  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  R   R  t   a_t   x_R  R  R   t   v_t   Pm_t   p_t   b_t   u_R  t   n_t   m_t   c_t   j_t   d_t   a1_t   a2_t   Qm_R   t   Pq_t   Qr_(   Rr  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  t   pattern1Rs  t   rule1t   pattern2Rv  t   rule2t   pattern3Rw  t   rule3t   pattern4Rx  t   rule4t   pattern5R{  t   rule5t   pattern6R|  t   rule6t   pattern7R}  t   rule7t   pattern8R~  t   rule8t   pattern9R  t   rule9t	   pattern10R  t   rule10t	   pattern11R  t   rule11t	   pattern12R  t   rule12t	   pattern13R  t   rule13t	   pattern14R  t   rule14t	   pattern15R  t   rule15t	   pattern16R  t   rule16t	   pattern17R  t   rule17t	   pattern18R  t   rule18t	   pattern19R  t   rule19t	   pattern20R  t   rule20t	   pattern21R  t   rule21t	   pattern22R  t   rule22t	   pattern23R  t   rule23t	   pattern24R  t   rule24t	   pattern25R  t   rule25t	   pattern26R  t   rule26t	   pattern27R  t   rule27t	   pattern28R  t   rule28t	   pattern29R  t   rule29t	   pattern30R  t   rule30t	   pattern31R  t   rule31t	   pattern32R  t   rule32R  t	   pattern33R  t   rule33R  t	   pattern34R  t   rule34R  t	   pattern35R  t   rule35R  t	   pattern36R  t   rule36(    (   Rr  sR   lib/python2.7/site-packages/sympy/integrals/rubi/rules/integrand_simplification.pyt   integrand_simplification   s     t5<.Plloo}zV`			I	B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  t   logR  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_R  R  R  R  t   e_t   f_t   g_t   h_t   i_R  t   k_t   l_R  R  R  t   q_t   r_t   t_R  R  t   s_t   w_R  t   y_t   z_R  R  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_R  R  t   Px_R  R  t   Qx_t   jn_t   mn_t   non2_t   RFx_t   RGx_t   iit   Pqqt   Qt   RR  R  t   kRn  R  t	   _UseGammat	   ShowStepst   Nonet   StepCounterR  (    (    (    sR   lib/python2.7/site-packages/sympy/integrals/rubi/rules/integrand_simplification.pyt   <module>   s>   "           1nj:R4|'	