ó
~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¥ mŠ ZŠ m§ Z§ mš Zš m© Z© mª Zª m« Z« m¬ Z¬ m­ Z­ m® Z® m¯ Z¯ m° Z° m± Z± m² Z² m³ Z³ mŽ ZŽ mµ Zµ m¶ Z¶ m· Z· mž Zž m¹ Z¹ mº Zº m» Z» mŒ ZŒ mœ Zœ mŸ ZŸ m¿ Z¿ mÀ ZÀ mÁ ZÁ mÂ ZÂ mÃ ZÃ mÄ ZÄ mÅ ZÅ mÆ ZÆ mÇ ZÇ mÈ ZÈ mÉ ZÉ mÊ ZÊ mË ZË mÌ ZÌ mÍ ZÍ mÎ ZÎ mÏ ZÏ mÐ ZÐ mÑ ZÑ mÒ ZÒ mÓ ZÓ mÔ ZÔ mÕ ZÕ mÖ ZÖ m× Z× mØ ZØ mÙ ZÙ mÚ ZÚ mÛ ZÛ mÜ ZÜ mÝ ZÝ mÞ ZÞ mß Zß mà Zà má Zá mâ Zâ mã Zã mä Zä må Zå mæ Zæ mç Zç mè Zè mé Zé mê Zê më Zë mì Zì mí Zí mî Zî mï Zï mð Zð mñ Zñ mò Zò mó Zó mô Zô mõ Zõ mö Zö m÷ Z÷ mø Zø mù Zù mú Zú mû Zû mü Zü mý Zý mþ Zþ mÿ Zÿ m Z mZmZmZmZmZmZmZmZm	Z	m
Z
mZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZm Z m!Z!m"Z"m#Z#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¥mŠZŠm§Z§mšZšm©Z©mªZªm«Z«m¬Z¬mJZJm­Z­m®Z®m¯Z¯m°Z°m±Z±m²Z²m³Z³mŽZŽmµZµm¶Z¶m·Z·mžZžm¹Z¹mºZºm»Z»mŒZŒmœZœmŸZŸm¿Z¿mÀZÀmÁZÁmÂZÂmÃZÃmÄZÄmÅZÅmÆZÆmÇZÇmÈZÈmÉZÉmÂZÂmÊZÊmËZËmÌZÌmÍZÍmÎZÎmÏZÏmÐZÐmÑZÑmÒZÒmÓZÓmÔZÔmÕZÕmÖZÖm×Z×mØZØmÙZÙmÚZÚmÛZÛmÜZÜmÝZÝmÞZßmàZámâZâmãZãmäZäd d låmæZæmçZçmèZèméZémêZêmëZëmìZìmíZímîZîmïZïmðZðmñZñmòZòmóZómôZômõZõd d löm÷Z÷d d	 lømùZùmúZúd d
 lûmüZümýZýmþZþmÿZÿm Z mZmèZè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 låmZg  d D] Ze÷e ^ qç\ 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 ^ qœ\ 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eù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`.
iÿÿÿÿ(   t   import_modulet   matchpy(   t   doctest_depends_on(   t   Patternt   ReplacementRulet   CustomConstraintt   is_match(Ú  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   FactorRŸ  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   secRá  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          sá7 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 mB }B mC }C mD }D mE }E mF }F mG }G mH }H mI }I mJ }J mK }K mL }L mM }M mN }N mO }O mP }P mQ }Q mR }R mS }S mT }T mU }U mV }V mW }W mX }X mY }Y mZ }Z m[ }[ m\ }\ m] }] m^ }^ m_ }_ m` }` ma }a mb }b mc }c md }d me }e mf }f mg }g mh }h mi }i mj }j mk }k ml }l mm }m mn }n mo }o mp }p mq }q mr }r ms }s mt }t mu }u mv }v mw }w mx }x my }y mz }z 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¥ }¥ mŠ }Š m§ }§ mš }š m© }© mª }ª m« }« m¬ }¬ m­ }­ m® }® m¯ }¯ m° }° m± }± m² }² m³ }³ mŽ }Ž mµ }µ m¶ }¶ m· }· mž }ž m¹ }¹ mº }º m» }» mŒ }Œ mœ }œ mŸ }Ÿ m¿ }¿ mÀ }À mÁ }Á mÂ }Â mÃ }Ã mÄ }Ä mÅ }Å mÆ }Æ mÇ }Ç mÈ }È mÉ }É mÊ }Ê mË }Ë mÌ }Ì mÍ }Í mÎ }Î mÏ }Ï mÐ }Ð mÑ }Ñ mÒ }Ò mÓ }Ó mÔ }Ô mÕ }Õ mÖ }Ö m× }× mØ }Ø mÙ }Ù mÚ }Ú mÛ }Û mÜ }Ü mÝ }Ý mÞ }Þ mß }ß mà }à má }á mâ }â mã }ã mä }ä må }å mæ }æ mç }ç mè }è mé }é mê }ê më }ë mì }ì mí }í mî }î mï }ï mð }ð mñ }ñ mò }ò mó }ó mô }ô mõ }õ mö }ö m÷ }÷ mø }ø mù }ù mú }ú mû }û mü }ü mý }ý mþ }þ mÿ }ÿ 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.}.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mB}BmC}CmD}DmE}EmF}FmG}GmH}HmI}ImJ}JmK}KmL}LmM}MmN}NmO}OmP}PmQ}QmR}RmS}SmT}TmU}UmV}VmW}WmX}XmY}YmZ}Zm[}[m\}\m]}]m^}^m_}_m`}`ma}amb}bmc}cmd}dme}emf}fmg}gmh}hmi}imj}jmk}kml}lmm}mmn}nmo}omp}pmq}qmr}rms}smt}tmu}umv}vmw}wmx}xmy}ymz}zm{}{m|}|m}}}m~}~m}m}m}m}tttttd td   ttd td   td td   td td   t | | | | | | |  }  f d	   }t|| }ttttd
 td   tttd td   ttd td   td td   td td   t | | | |	 | | | | | 
 }  f d   }t|| }ttttd
 td   tttd td   td td   td td   td td   ttttd td   td td   ttd td   tt | | | | | | |	 | | | | | |
  }  f d   }t|| }ttttd td   td td   td td   td td   tttd td   td td   ttd td   t | | | | | | | | 	 }  f d   }t|| }ttttd td   td td   td td   td td   tttd td   td td   ttd td   t | | | | | | | | | 
 }  f d   }t|| }  f d   }ttttd td   td td   td td   td td   tttd td   td td   tt | | | | | | |  }t|| }  f d   }ttttd
 td   ttd td   td td   td td   td td   tttd td   td td   tt | | | | | |	 | | | 
 }t|| }  f d   }ttttd td   ttd td   td td   td td   td td   tttd td   td td   tt | | | | | | | | | 
 }t|| }  f d   }ttttd td   ttd
 td   ttd td   td td   td td   td td   tttd td   td td   tt | | | | | | | | | 
 }t|| }tttd td   tttd td   td td   tt | | | | | |  }  f d   }t|| } ttttd
 td   td td   tttd td   td td   td td   t | | | | | |  }¡  f d   }¢t|¡|¢ }£ttttd td   ttd td   tttd td   td td   td td   t | | | | |	 | | | 	 }€  f d   }¥t|€|¥ }Štttd td   tttd td   td td   ttd td   td td   td td   td td   t | | | | | | |  }§  f d   }št|§|š }©ttttd
 td   ttd td   tttd td   td td   ttd td   td td   td td   t | | | | | | | | 	 }ª  f d   }«t|ª|« }¬ttttd td   tttd td   tttd td   td td   ttd td   td td   td td   t | | | | | |	 | | | |  }­  f d   }®t|­|® }¯ttttd td   td td   td td   tttd td   td td   td td   t | | | | | | | | 	 }°  f d    }±t|°|± }²ttttd
 td   tttd td   td td   td td   tttd td   td td   t | | | | | | | | | 
 }³  f d!   }Žt|³|Ž }µttttd td   ttttd td   td td   td td   tttd td   td td   t | | | | | | | | | |  }¶  f d"   }·t|¶|· }žttttt |	 | |  }¹  f d#   }ºt|¹|º }»ttttd
 td   ttd td   t |	 | |  |!  }Œ  f d$   }œt|Œ|œ }Ÿttttd
 td   ttd td   ttd td   t |	 | | |" |#  }¿  f d%   }Àt|¿|À }Áttttd
 td   ttd td   ttd td   ttd& td   t |	 | | | |$ |%  }Â  f d'   }Ãt|Â|Ã }Ättttt | |& |'  }Å  f d(   }Æt|Å|Æ }Çttttd
 td   ttd td   t |	 | | |( |)  }È  f d)   }Ét|È|É }Êttttd
 td   ttd td   ttd td   t |	 | | |  |* |+  }Ë  f d*   }Ìt|Ë|Ì }Íttttd td   ttd& td   t | | |, |-  }Î  f d+   }Ït|Î|Ï }Ðttttt | |. |/  }Ñ  f d,   }Òt|Ñ|Ò }Óttttd td   ttd td   td
 td   t | |	 | |. |/  }Ô  f d-   }Õt|Ô|Õ }Öttttd td   ttd& td   t | | |0 |1 |2  }×  f d.   }Øt|×|Ø }Ùttttd td   ttd& td   ttd
 td   t |	 | | |0 |1 |2  }Ú  f d/   }Ût|Ú|Û }Üttttd
 td   ttd td   ttd& td   t |	 | | |3 |1 |4 |5  }Ý  f d0   }Þt|Ý|Þ }ßttttd td   ttd& td   ttd
 td   ttd td   t |	 | | | |6 |1 |7 |8 	 }à  f d1   }át|à|á }âttttt | |9 |:  }ã  f d2   }ät|ã|ä }åttttd td   ttd
 td   t |	 | |9 |:  }æ  f d3   }çt|æ|ç }èttttt | |; |<  }é  f d4   }êt|é|ê }ëttttd td   ttd td   td
 td   t | |	 | |; |<  }ì  f d5   }ít|ì|í }îttttd& td   ttd td   t | | |. |= |>  }ï  f d6   }ðt|ï|ð }ñttttd& td   ttd td   t | | |. |? |@  }ò  f d7   }ót|ò|ó }ôttttd td   ttd
 td   ttd& td   t |	 | | |A |; |B  }õ  f d8   }öt|õ|ö }÷ttttd td   ttd
 td   ttd& td   t |	 | | |A |. |C  }ø  f d9   }ùt|ø|ù }úttttt | |D |E  }û  f d:   }üt|û|ü }ýttttd td   ttd
 td   t |	 | |D |E  }þ  f d;   }ÿt|þ|ÿ } ttttd td   tt | |A |D |F |G  }  f d<   }t|| }ttttd td   ttd
 td   tt |	 | |A |D |F |G  }  f d=   }t|| }ttttd
 td   tttd td   td> td   ttd& td   td td   ttd td   td? td   tttd td   td td   td@  dA t | | | | |L |M |	 | |H |I |J |K  }  f dB   }t|| }	tttttd
 td   tttd td   td> td   ttd& td   td td   ttd td   td? td   tttd td   td td   td@  dA t | | | | | |L |M |	 | |J |H |I |K  }
  f dC   }t|
| }  f dD   }tttttd td   ttttd td   tt | | | |	 |N | |O  }t|| }tttttd
 td   ttttd td   td td   t | | |	 | | |P |Q |R 	 }  f dE   }t|| }ttttttd td   td td   tt | | |N |S |T  }  f dF   }t|| }tttttd td   td
 td   tttd td   td td   td td   t | | | |	 | |N |U  }  f dG   }t|| }ttttttd td   td td   td td   t | | | |N |U  }  f dH   }t|| }tttttd
 td   ttttd td   td td   t | | |	 | | |V |  }  f dI   }t|| }ttttttd
 td   ttttd td   td td   t | | | |	 | | |V | 	 }  f dJ   } t||  }!tttttd
 td   ttttd td   tt | | |	 | |N |W |X |Y 	 }"  f dK   }#t|"|# }$tttttd td   td
 td   tttd td   td td   tt | | | |	 | | |N |Z 	 }%  f dL   }&t|%|& }'ttttttd td   td td   tt | | | | |N |Z |[  }(  f dM   })t|(|) }*  f dN   }+tttttd
 td   tttd td   td td   tt | | |N |\ |] |^ |_  },t|,|+ }-  f dO   }.tttttd td   td
 td   tttd td   td td   tt | | | |	 |N |` |X |^ 	 }/t|/|. }0  f dP   }1ttttttd td   td td   tt | | |N |` |X |^  }2t|2|1 }3dQ   }4tttttttd td   tt | | |N |\ |X |Y t|4  }5  f dR   }6t|5|6 }7ttttttd td   td td   tt | | |N |\ |X |Y |a  }8  f dS   }9t|8|9 }:tttttdT  td? td   ttd@  td td   ttd td   tttdT  td td   td@  dA t | | | | | |L |b  };  f dU   }<t|;|< }=tttttdT  td? td   ttd@  td td   tttdT  td td   td@  dA t | | | | |L |b  }>  f dV   }?t|>|? }@tttttdT  td? td   ttd td   tttdT  td td   td@  dA t | | | | |L |b  }A  f dW   }Bt|A|B }CttttdA  ttdT  td> td   ttd td   td td   tttdT  td td   td@  dA t | | | | |M |c  }D  f dX   }Et|D|E }FttttdA  ttdT  td> td   td td   tttdT  td td   td@  dA t | | | |M |c  }G  f dY   }Ht|G|H }ItttttdZ  td> td   ttdT  td? td   ttd@  td td   ttdA  td td   tttdT  td td   td@  dA t | | | | | |L |M |c |b 
 }J  f d[   }Kt|J|K }LtttttdZ  td> td   ttdT  td? td   ttdA  td td   tttdT  td td   td@  dA t | | | | |L |M |c |b 	 }M  f d\   }Nt|M|N }Od]   }Pttttttd td   td td   tt | | |N |\ |X |Y t|P  }Q  f d^   }Rt|Q|R }S  f d_   }Tttttttttd td   td td   tt | | |N |\ |X |Y |d  }Ut|U|T }Vd`   }Wtttttd
 td   ttttd td   tt | | | |V |\ | t|W  }X  f da   }Yt|X|Y }Ztttttdb td   tttd@  td td   t | | |f |g |e  }[  f dc   }\t|[|\ }]  f dd   }^tttttdb td   tttd@  td td   t | | |f |g |h |i  }_t|_|^ }`  f de   }atttttdb td   tttd@  td td   t | | |f |g |h |j  }bt|b|a }ctttttdA  tdf td   ttdb td   tttd@  td td   t | | |f |g |m |k |l  }d  f dg   }et|d|e }f  f dh   }gttttdA  tdf td   ttdb td   tdi td   tttd@  td td   t | | |f |g |m |n  }ht|h|g }i  f dj   }jttttttdf td   tttd@  td td   t | | |g |m |o  }kt|k|j }l  f dk   }mtttttdA  tdf td   tttd@  td td   t | | |f |m |p  }nt|n|m }o  f dl   }pttttdA  tdf td   ttdb td   tdi td   tttd@  td td   t | | |f |g |m |q  }qt|q|p }r  f dm   }sttttttdf td   tttd@  td td   t | | |g |m |r  }tt|t|s }u  f dn   }vtttttdA  tdf td   tttd@  td td   t | | |f |m |s  }wt|w|v }x  f do   }yttttdA  tdf td   ttdb td   tdi td   tttd@  td td   t | | |f |g |m |t  }zt|z|y }{  f dp   }|ttttttdf td   tttd@  td td   t | | |g |m |u  }}t|}|| }~  f dq   }tttttdA  tdf td   tttd@  td td   t | | |f |m |v  }t|| }  f dr   }ttttdA  tdf td   ttdb td   tdi td   tttd@  td td   t | | |f |g |m |w  }t|| }  f ds   }ttttttdf td   tttd@  td td   t | | |g |m |x  }t|| }  f dt   }tttttdA  tdf td   tttd@  td td   t | | |f |m |y  }t|| }  f du   }ttttdA  tdf td   ttdb td   tdi td   tttd@  td td   t | | |f |g |m |z  }t|| }  f dv   }ttttttdf td   tttd@  td td   t | | |g |m |{  }t|| }  f dw   }tttttdA  tdf td   tttd@  td td   t | | |f |m ||  }t|| }  f dx   }ttttdA  tdf td   ttdb td   tdi td   tttd@  td td   t | | |f |g |m |}  }t|| }  f dy   }ttttttdf td   tttd@  td td   t | | |g |m |~  }t|| }  f dz   }ttttdA  tdf td   tdi td   tttd@  td td   t | | |f |m |  }t|| }  f d{   }ttttdA  tdf td   ttdb td   tdi td   tttd@  td td   t | | |f |g |m |  }t|| }  f d|   } ttttttdf td   tttd@  td td   t | | |g |m |  }¡t|¡|  }¢  f d}   }£tttttdA  tdf td   tttd@  td td   t | | |f |m |  }€t|€|£ }¥  f d~   }ŠttttdA  tdf td   ttdb td   tdi td   tttd@  td td   t | | |f |g |m |  }§t|§|Š }š  f d   }©ttttttdf td   tttd@  td td   t | | |g |m |  }ªt|ª|© }«  f d   }¬ttttdA  tdf td   tdi td   tttd@  td td   t | | |f |m |  }­t|­|¬ }®ttttdA  tdf td   ttdb td   tdi td   tttd@  td td   t | | |f |g |m |  }¯  f d   }°t|¯|° }±ttttttdf td   tttd@  td td   t | | |g |m |  }²  f d   }³t|²|³ }ŽtttttdA  tdf td   tttd@  td td   t | | |f |m |  }µ  f d   }¶t|µ|¶ }·  f d   }žttttdA  tdf td   ttdb td   tdi td   tttd@  td td   t | | |f |g |m |  }¹t|¹|ž }º  f d   }»tttttdf td   tdb td   tttd@  td td   t | | |g |m |  }Œt|Œ|» }œ  f d   }ŸtttttdA  tdf td   tttd@  td td   t | | |f |m |  }¿t|¿|Ÿ }À  f d   }ÁttttdA  tdf td   ttdb td   tdi td   tttd@  td td   t | | |f |g |m |  }Ât|Â|Á }Ã  f d   }Ättttttdf td   tttd@  td td   t | | |g |m |  }Åt|Å|Ä }Æ  f d   }ÇtttttdA  tdf td   tttd@  td td   t | | |f |m |  }Èt|È|Ç }Éd   }ÊttttdA  tdf td   ttdb td   tdi td   tttd@  td td   t | | |f |g |m |h | | t|Ê 
 }Ë  f d   }Ìt|Ë|Ì }Íd   }Îttttttdf td   tttd@  td td   t | | |g |m | | t|Î  }Ï  f d   }Ðt|Ï|Ð }Ñd   }ÒtttttdA  tdf td   tttd@  td td   t | | |f |m | | t|Ò  }Ó  f d   }Ôt|Ó|Ô }Õd   }ÖttttdA  tdf td   ttdb td   tdi td   tttd@  td td   t | | |f |g |m |h | | t|Ö 
 }×  f d   }Øt|×|Ø }Ùd   }Úttttttdf td   tttd@  td td   t | | |g |m | | t|Ú  }Û  f d   }Üt|Û|Ü }Ýd   }ÞtttttdA  tdf td   tttd@  td td   t | | |f |m | | t|Þ  }ß  f d   }àt|ß|à }ád   }âtttttd td   td
 td   ttttd td   t | | | |	 |N | | t|â 	 }ã  f d   }ät|ã|ä }åd   }ætttttttd td   t | | |N | | t|æ  }ç  f d   }èt|ç|è }é  f d   }êtttttd td   ttttd@  td td    t | | | | | |  }ët|ë|ê }ì  f d   }ítttttd td   ttttd@  td td    t | | | | | |  }ît|î|í }ï  f d   }ðtttttd td   ttttd@  td td    t | | | | | |  }ñt|ñ|ð }ò  f d   }ótttttd td   ttttd@  td td    t | | | | | |  }ôt|ô|ó }õ  f d   }ötttttdT  td td   ttttdZ  td td    t | | | | |  }÷t|÷|ö }ø  f d   }ùtttttdT  td td   ttttdZ  td td    t | | | | |  }út|ú|ù }ûtttttdA  td td   ttttd   td td    t | | | | |  }ü  f d¡   }ýt|ü|ý }þtttttdA  td td   ttttd   td td    t | | | | |  }ÿ  f d¢   } t|ÿ|  }tttttttttd td    t | | |N |\ |  }  f d£   }t|| }  f d€   }tttttd td   td
 td   ttttd td   tt | | | |	 | |N | | 	 }t|| }  f d¥   }tttttttd td   tt | | | |N | |  }	t|	| }
tttttttd td   tt | | | |N |\ |   }  f dŠ   }t|| }tttttd td   td
 td   ttttd td   t | | | |	 |N |¡  }  f d§   }t|| }tttttttd td   t | | |N |¡  }  f dš   }t|| }d©   }tttttd td   tttttd td   tt | | | | |N |\ |¢ |£ |€ t|  }  f dª   }t|| }d«   }tttttd td   td
 td   ttttd td   tt | | | |	 | |N |\ t| 	 }  f d¬   }t|| }d­   }tttttttd td   tt | | | |N |\ t|  }  f d®   }t|| }  f d¯   } tttttd
 td   ttttd td   tt | | | |N |¥ |  }!t|!|  }"  f d°   }#tttttd td   td
 td   ttttd td   tt | | | | |N |¥ |Š  }$t|$|# }%  f d±   }&tttttd td   tttttd td   tt | | | |	 | |N |¥ |§ 	 }'t|'|& }(  f d²   })tttttd
 td   ttttd td   tt | | |	 | |N |š  }*t|*|) }+  f d³   },tttttttd td   tt | | | |N |š  }-t|-|, }.ttttttttttd td   tt | | | |	 | |N |š  }/  f dŽ   }0t|/|0 }1tttttd
 td   ttttd td   tt | | |	 | | |V |© |ª 	 }2  f dµ   }3t|2|3 }4ttttttttttd td   tt | | | |	 | | |V |© |ª 
 }5  f d¶   }6t|5|6 }7tttttd
 td   tdb td   ttttd td   td td   t | | |f |g |	 | | |W 	 }8  f d·   }9t|8|9 }:tttttd td   td
 td   ttttd td   td td   t | | | |	 | | |«  };  f dž   }<t|;|< }=tttttttd td   td td   t | | | | |«  }>  f d¹   }?t|>|? }@tttttd
 td   tttd td   td td   tt | | |	 | | |¬ |­  }A  f dº   }Bt|A|B }Cttttttd td   td td   tt | | | | |® |­  }D  f d»   }Et|D|E }Ftttttd td   td
 td   tttd td   tdŒ td   td td   tttd td   tdœ td   td td   t |± |² |³ |Ž | |	 | | |N |¯ |°  }G  f dŸ   }Ht|G|H }Ittttttd td   tdŒ td   td td   tttd td   tdœ td   td td   t |± |² |³ |Ž | | |N |¯ |° 
 }J  f d¿   }Kt|J|K }Ltttttd td   td
 td   tttd td   tdŒ td   td td   tttd td   tdœ td   td td   t |± |² |³ |Ž | |	 | | |N |¯  }M  f dÀ   }Nt|M|N }Ottttttd td   tdŒ td   td td   tttd td   tdœ td   td td   t |± |² |³ |Ž | | |N |¯ 	 }P  f dÁ   }Qt|P|Q }Rtttttd td   td td   td td   tttd td   td td   td td   tttd td   td td   ttd td   td? td   t | | | | | | |L | | | |µ |¶  }S  f dÂ   }Tt|S|T }Utttttd td   td td   td td   tttd td   td td   td td   tttd td   td? td   t | | | | | |L | | | |· |¶  }V  f dÃ   }Wt|V|W }Xttttd> td   td
 td   tttd td   td td   td td   tttd td   td td   td td   tttd td   td td   ttd td   td? td   t | | | | | | |L |M |	 | | | |ž |¹ |P  }Y  f dÄ   }Zt|Y|Z }[ttttd> td   td
 td   tttd td   td td   td td   tttd td   td td   td td   tttd td   td? td   t | | | | | |L |M |	 | | | |º |¹ |P  }\  f dÅ   }]t|\|] }^tttttd
 td   tdb td   ttttd td   td& td   tttd td   td td   td td   t | | | | |f |g |	 | | | |» |W  }_  f dÆ   }`t|_|` }a  f dÇ   }bttttd& td   tttd td   ttd td   td td   tt | | | | | |Œ |œ |Ÿ 	 }ct|c|b }dtttttd
 td   ttttd td   ttd td   td td   td td   t | | | |	 | | | |V |W 
 }e  f dÈ   }ft|e|f }gtttttd td   td
 td   tttd td   td td   ttd td   td td   td td   t | | | | |	 | | |N |¿ 
 }h  f dÉ   }it|h|i }jttttttd td   td td   ttd td   td td   td td   t | | | | | |N |¿  }k  f dÊ   }lt|k|l }mtttttd td   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td td   td td   t | | | | | | | | | |À |Á  }n  f dË   }ot|n|o }ptttttd td   td td   tttd td   td td   ttd td   td td   td td   t | | | | | | | | |· |Â  }q  f dÌ   }rt|q|r }sttttd? td   td
 td   tttd td   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td td   td td   t | | | | | | |L |	 | | | |Ã |Ä |P  }t  f dÍ   }ut|t|u }vttttd? td   td
 td   tttd td   td td   tttd td   td td   ttd td   td td   td td   t | | | | | |L |	 | | | |º |Â |P  }w  f dÎ   }xt|w|x }ytttttd td   td
 td   tttd td   td td   ttd td   td td   tt | | | | |	 | | | |N |Å |Æ  }z  f dÏ   }{t|z|{ }|ttttttd td   td td   ttd td   td td   tt | | | | | | |N |Å |Æ 
 }}  f dÐ   }~t|}|~ }tttttd
 td   ttttd td   ttd td   td td   tt | | | |	 | | | |V |Ç |  }  f dÑ   }t|| }ttttttd
 td   ttttd td   ttd td   td td   tt | | | | |	 | | | |V |Ç |  }  f dÒ   }t|| }tttttd td   td
 td   tttd td   td td   ttd td   td td   tt | | | | |	 | | | |N |Z  }  f dÓ   }t|| }ttttttd td   td td   ttd td   td td   tt | | | | | | |N |Z |[ 
 }  f dÔ   }t|| }ttttttd td   ttd td   td td   td td   ttttd td   ttd td   td td   ttdÕ td   td? td   t | | | | | | |L | | | |È |Ç |É |Ê  }  f dÖ   }t|| }tt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tdÕ td   td? td   t | | | | | |L | | | |È |Ç |Ë |Ì  }  f d×   }t|| }ttttttd td   ttd td   td td   td td   ttttd td   ttdÕ td   td? td   t | | | | | |L | | | |È |Ç |É |Í  }  f dØ   }t|| }tttttdÕ td   td? td   ttttd td   ttd td   td td   td td   t | | | | |L | | | |È |Ç |Ë |Î  }  f dÙ   }t|| }ttttd
 td   tttd& td   td td   ttd td   td? td   ttdÚ td   td> td   tttd td   td td   ttd td   td td   td@  dA t | | | | | |L |M |	 | | |Ï |Ð |Ñ |Ç |Ò |K  }  f dÛ   }t|| }tttttd
 td   tttd& td   td td   ttd td   td? td   ttdÚ td   td> td   tttd td   td td   ttd td   td td   td@  dA t | | | | | | |L |M |	 | | |Ï |Ð |Ñ |Ç |Ò |K  }  f dÜ   }t|| }dÝ   }tttttttd td   tttd td   tt | | | | |N |Ç |\ |X |Y t|  }  f dÞ   } t||  }¡tttttdT  td? td   ttd@  td td   ttd td   tttdT  td td   ttdA  td td   td@  dA t | | | | | | |L |Ç |Ó 
 }¢  f dß   }£t|¢|£ }€tttttdT  td? td   ttd@  td td   tttdT  td td   ttdA  td td   td@  dA t | | | | | |L |Ç |Ó 	 }¥  f dà   }Št|¥|Š }§tttttdT  td? td   ttd td   tttdT  td td   ttdA  td td   td@  dA t | | | | | |L |Ç |Ó 	 }š  f dá   }©t|š|© }ªttttdA  ttdT  td> td   ttdA  td? td   ttd td   td td   tttdT  td td   ttdA  td td   td@  dA t | | | | | |L |M |Ç |Ô |Õ  }«  f dâ   }¬t|«|¬ }­ttttdA  ttdT  td> td   ttdA  td? td   td td   tttdT  td td   ttdA  td td   td@  dA t | | | | |L |M |Ç |Ô |Õ 
 }®  f dã   }¯t|®|¯ }°tttttdZ  td> td   ttdT  td? td   ttd@  td td   ttdA  td td   tttdT  td td   ttdA  td td   td@  dA t | | | | | | |L |M |Ç |Ô |Ö  }±  f dä   }²t|±|² }³tttttdZ  td> td   ttd@  td td   ttdA  td td   tttdT  td td   ttdA  td td   td@  dA t | | | | | | |M |Ç |Ô |×  }Ž  f då   }µt|Ž|µ }¶dæ   }·tttttttd td   tttd td   tt | | | | |N |Ç |\ |X |Y t|·  }ž  f dç   }¹t|ž|¹ }ºdè   }»tttttttttd td   tttd td   tt | | | | |N |Ç |\ |X |Y |d t|»  }Œ  f dé   }œt|Œ|œ }Ÿdê   }¿tttttd
 td   ttttd td   tttd td   tt | | | | | |V |Ç |\ | t|¿  }À  f dë   }Át|À|Á }Âtttttd td   td
 td   ttttd td   ttd td   td td   t | | | | |	 | |V |Ç |\ |Ø  }Ã  f dì   }Ät|Ã|Ä }Åtttttttd td   ttd td   td td   t | | | | |V |Ç |\ |Ù 	 }Æ  f dí   }Çt|Æ|Ç }Èdî   }ÉttttttdA  td td   ttd td   tt | | | |N |Ç |Ú t|É  }Ê  f dï   }Ët|Ê|Ë }Ìdð   }ÍttttttdA  td td   ttd td   tt | | | |N |Ç |Û |Ü t|Í 	 }Î  f dñ   }Ït|Î|Ï }Ðdò   }ÑttttttdA  td td   ttd td   tt | | | |N |Ç |Û |Ý t|Ñ 	 }Ò  f dó   }Ót|Ò|Ó }Ôdô   }Õtttttd td   td
 td   ttttd td   ttd td   td td   tt | | | | |	 | | |V |Ç |\ t|Õ  }Ö  f dõ   }×t|Ö|× }Ødö   }Ùtttttttd td   ttd td   td td   tt | | | | | |V |Ç |\ t|Ù 
 }Ú  f d÷   }Ût|Ú|Û }Ü  f dø   }Ýtttttd td   td
 td   ttttd td   tttd td   tt | | | | |	 | | |N |Ç |\ |Þ  }Þt|Þ|Ý }ß  f dù   }àtttttttd td   tttd td   tt | | | | | |N |Ç |\ |Þ 
 }át|á|à }âtttttd td   td
 td   tttd td   td td   ttd td   td td   t | | | | |	 | |N |Ç |\ 
 }ã  f dú   }ät|ã|ä }åttttttd td   td td   ttd td   td td   t | | | | |N |Ç |\  }æ  f dû   }çt|æ|ç }è  f dü   }étttttd
 td   ttttd td   ttd td   td td   tt | | | | | |N |Ç |¥ | 
 }êt|ê|é }ë  f dý   }ìtttttd td   td
 td   ttttd td   ttd td   td td   tt | | | | | | |N |Ç |¥ |Š  }ít|í|ì }î  f dþ   }ïtttttd td   tttttd td   ttd td   td td   tt | | | | |	 | | |N |Ç |¥ |§  }ðt|ð|ï }ñ  f dÿ   }òtttttd
 td   ttttd td   ttd td   td td   tt | | | |	 | | |N |Ç |š 
 }ót|ó|ò }ô  f d   }õtttttttd td   ttd td   td td   tt | | | | | |N |Ç |š 	 }öt|ö|õ }÷ttttttttttd td   ttd td   td td   tt | | | | | | |N |Ç |š |ß  }ø  f d  }ùt|ø|ù }úttttttttttd td   ttd td   td td   tt | | | | | | |N |Ç |š |à  }û  f d  }üt|û|ü }ýttttttttttd td   ttd td   td td   tt | | | | |	 | | |N |Ç |š  }þ  f d  }ÿt|þ|ÿ } tttttd
 td   ttttd td   ttd td   td td   tt | | | |	 | | | |V |Ç |© |ª  }  f d  }t|| }ttttttttttd td   ttd td   td td   tt | | | | |	 | | |V |Ç |© |ª  }  f d  }t|| }  f d  }tttttd td   td
 td   tttd td   td td   ttd td   td td   t | | | | |	 | | |N |Ç 
 }t|| }	  f d  }
ttttttd td   td td   ttd td   td td   t | | | | | |N |Ç  }t||
 }tttttd td   td
 td   tttd td   td td   ttd td   td td   tt | | | | |	 | | |N |á 
 }  f d  }t|| }ttttttd td   td td   ttd td   td td   tt | | | | | |N |á  }  f d	  }t|| }tttttd td   td
 td   tttd td   td td   ttd td   td td   td td   t | | | | |	 | | | |« 
 }  f d
  }t|| }ttttttd td   td td   ttd td   td td   td td   t | | | | | | |«  }  f d  }t|| }tttttd
 td   ttttd td   ttd td   td td   td td   t | | | |	 | | | |¬ |­ 
 }  f d  }t|| }tttttttd td   ttd td   td td   td td   t | | | | | | |® |­ 	 }  f d  }t|| }ttttdtd   td td   ttd td   td td   tt | | |å | | |â |ã |ä 	 }  f d  } t||  }!ttttdtd   td td   ttd td   td td   tt | | |å | |â |ã |æ |X |Y 
 }"  f d  }#t|"|# }$ttttdtd   td td   ttd td   td td   tt | | |å | | |â |ã |æ |ç 
 }%  f d  }&t|%|& }'ttttdtd   td td   ttd td   td td   tt | | |â |è |é |^ |ê  }(  f d  })t|(|) }*ttttdtd   td td   ttd td   td td   tt | | |â |è |é |^ |ë  }+  f d  },t|+|, }-ttttdtd   td td   ttd td   td td   tt | | |â |è |é |Y |ì  }.  f d  }/t|.|/ }0ttttdtd   td td   ttd td   td td   tt | | |â |è |é |Y  }1  f d  }2t|1|2 }3ttttdtd   td td   ttd td   td td   tt | | |å | |í |ã |î  }4  f d  }5t|4|5 }6tttd  tttdA  td td   ttd td   td td    t | | | |ï  }7  f d  }8t|7|8 }9ttttdtd   td td   ttd td   td td   tt | | |å | |Û |ã |î  }:  f d  };t|:|; }<tttd  tttdtd   td td   ttd td   td td    t | | |ð |ñ  }=  f d  }>t|=|> }?ttttdtd   td td   ttd td   td td   tt | | |å | | |â |ã |ò 	 }@  f d  }At|@|A }Bttttdtd   td td   ttd td   td td   tt | | |å | | | |ó  }C  f d  }Dt|C|D }Ettttd
 td   tttd td   ttdtd   td td   tt | | |å |	 | | |â |ã |ô |W  }F  f d  }Gt|F|G }Httttd td   td
 td   ttdtd   td td   ttd td   td td   tt | | | |å |	 | | |â |ã |õ |ö  }I  f d  }Jt|I|J }Kttttd td   td
 td   ttdtd   td td   ttd td   td td   tt | | | |å |	 | |â |ã |÷ |X |Y |ö  }L  f d  }Mt|L|M }Nttttd td   td
 td   ttdtd   td td   ttd td   td td   tt | | | |å |	 | | |â |ã |÷ |ø |ù  }O  f d  }Pt|O|P }Qtttttd
 td   ttdtd   td td   ttd td   td td   tt | | | |å |	 | | |â |ã |÷  }R  f d   }St|R|S }Tttttd
 td   tttd td   ttdtd   td td   tt | | |å |	 | | |â |ã |ô | |ú  }U  f d!  }Vt|U|V }Wtttttd
 td   tttd td   ttdtd   td td   tt | | | |å |	 | | |â |ã |ô | |ú  }X  f d"  }Yt|X|Y }Zttttd td   tttdtd   td td   ttd td   td td   tt | | | |â |û |é |ù |^ |ü 
 }[  f d#  }\t|[|\ }]ttttd td   td
 td   ttdtd   td td   ttd td   td td   tt | | | |	 |â |è |é |ù |^ |ý  }^  f d$  }_t|^|_ }`ttttd td   td
 td   ttdtd   td td   ttd td   td td   tt | | | |â |û |é |ù |Y |þ 
 }a  f d%  }bt|a|b }cttttd td   td
 td   ttdtd   td td   ttd td   td td   tt | | | |	 |â |è |é |ù |Y 
 }d  f d&  }et|d|e }fttttd td   td
 td   ttdtd   td td   ttd td   td td   tt | | | |	 | |â |ð |é |ù |ÿ |ý  }g  f d'  }ht|g|h }ittttd td   td
 td   ttdtd   td td   ttd td   td td   tt | | | |	 | |â |ð |é |ù |  }j  f d(  }kt|j|k }lttttd
 td   tttd td   ttdtd   td td   tt | | |å |	 | | |â |ã |ô |P |© |ª  }m  f d)  }nt|m|n }otttttd
 td   tttd td   ttdtd   td td   tt | | | |å |	 | | |â |ã |ô |P |© |ª  }p  f d*  }qt|p|q }rttttd td   td
 td   ttdtd   td td   ttd td   td td   tt | | | |å |	 | |í |ã ||ö  }s  f d+  }tt|s|t }uttttd
 td   tttdtd   td td   ttd td   td td    t | | |å | ||ã  }v  f d,  }wt|v|w }xttttd td   td
 td   ttdtd   td td   ttd td   td td   tt | | | |å |	 | |Û |ã ||ö  }y  f d-  }zt|y|z }{tttttd
 td   tttd td   ttdtd   td td   tt | | | |å |	 | | ||ã | }|  f d.  }}t|||} }~ttttd td   td
 td   ttdtd   td td   ttd td   td td   tt | | | |å |	 | | |â |ã |ò  }  f d/  }t|| }ttttd
 td   ttdtd   td td   ttd td   td td   td td   t | | |å |	 | | |¬  }  f d0  }t|| }ttttd
 td   ttttd td   td& td   tttd td   ttd1td   td td   tt | | | | |å ||	 | | | |â ||ô || |ú  }  f d2  }t|| }tttttd
 td   tttd td   td td   td& td   tttd td   ttd1td   td td   tt | | | | | |å ||	 | | | |â ||ô || |ú  }  f d3  }t|| }ttttd td   td
 td   tttd td   td td   ttd4td   td td   ttdtd   td td   tt | | | | | |å |	 | | ||â |» ||	|ø  }  f d5  }t|| }ttttd td   td
 td   tttd td   td td   ttd4td   td td   ttdtd   td td   tt | | | | | |å |	 | ||â |» |
|Y || }  f d6  }t|| }ttttd td   td
 td   tttd td   td td   ttd4td   td td   ttdtd   td td   tt | | | | | |å | ||â |» |||||ø | }  f d7  }t|| }ttttd td   td
 td   tttd td   td td   ttd4td   td td   ttdtd   td td   tt | | | | | |å |	 | | ||â |» || }  f d8  }t|| }ttttd
 td   tttd td   td td   td& td   tttd td   ttd1td   td td   tt | | | | |å ||	 | | | |â ||ô ||P |© |ª  }  f d9  }t|| }tttttd
 td   tttd td   td td   td& td   tttd td   ttd1td   td td   tt | | | | | |å ||	 | | | |â ||ô ||P |© |ª  }  f d:  }t|| }ttttd td   td
 td   tttd td   td td   td& td   ttd4td   td td   ttdtd   td td   tt | | | | | |å |	 | | | ||â |» | }  f d;  }t|| }  f d<  } ttttttd td   ttdtd   td td   tt | | |å | | |V |â |ã |ð |ô | }¡t|¡|  }¢tttttd
 td   tttd td   ttdtd   td td   tt | | |å |	 | | |V |â |ã |ô |  }£  f d=  }€t|£|€ }¥ttttttd
 td   tttd td   ttdtd   td td   tt | | | |å | | |V |â |ã |ô | |¢ | }Š  f d>  }§t|Š|§ }šttttttd
 td   tttd td   ttdtd   td td   tt | | | |å |	 | | |V |â |ã |ô |  }©  f d?  }ªt|©|ª }«d@  }¬tttttd
 td   tttd td   ttdtd   td td   tt | | | |V |â || t|¬ 	 }­  f dA  }®t|­|® }¯dB  }°tttttd td   td
 td   tttd td   ttdtd   td td   tt | | | |	 | |N |â ||t|°  }±  f dC  }²t|±|² }³tttttd
 td   tttd td   ttdtd   td td   tt | | |å |	 | | |V |â |ã |ô |© |ª  }Ž  f dD  }µt|Ž|µ }¶tttttttttd td   ttdtd   td td   tt | | | |å | | |V |â |ã |ô |© |ª |¢ | }·  f dE  }žt|·|ž }¹tttttttttd td   ttdtd   td td   tt | | | |å |	 | | |V |â |ã |ô |© |ª  }º  f dF  }»t|º|» }Œtttttd td   td
 td   tttd td   ttdtd   td td   tt | | | |å |	 | | |« |â |ã  }œ  f dG  }Ÿt|œ|Ÿ }¿ttttttd td   ttdtd   td td   tt | | |å | | |« |â |ã 	 }À  f dH  }Át|À|Á }Âttttd@  td td   ttd td   td td   tt | | | || }Ã  f dI  }Ät|Ã|Ä }Åttttd@  td td   ttd td   td td   tt | | | |¿ | }Æ  f dJ  }Çt|Æ|Ç }ÈdK  }Éttttd@  td td   ttd td   td td   tt | | | |Ú |t|É  }Ê  f dL  }Ët|Ê|Ë }Ì  f dM  }Íttttd@  td td   ttd td   td td   tt | | | |Ú | }Ît|Î|Í }Ïttttd@  td td   ttd td   td td   tt | | | | |â | }Ð  f dN  }Ñt|Ð|Ñ }ÒdO  }Óttttd@  td td   ttd td   td td   tt | | | | |â |t|Ó  }Ô  f dP  }Õt|Ô|Õ }Ö  f dQ  }×ttttd@  td td   ttd td   td td   tt | | | | |â | }Øt|Ø|× }Ùttttd td   td td   td
 td   ttd@  td td   ttd td   td td   tt | | | | | |	 ||	 }Ú  f dR  }Ût|Ú|Û }Üttttd td   td td   td
 td   ttd@  td td   ttd td   td td   tt | | | | | |	 |¿ |	 }Ý  f dS  }Þt|Ý|Þ }ßdT  }àttttd td   td td   td
 td   ttd@  td td   ttd td   td td   tt | | | | | |	 |Ú |t|à 
 }á  f dU  }ât|á|â }ã  f dV  }ättttd td   td td   td
 td   ttd@  td td   ttd td   td td   tt | | | | | |	 |Ú |	 }åt|å|ä }ættttd td   td td   td
 td   ttd@  td td   ttd td   td td   tt | | | | | |	 | |â |
 }ç  f dW  }èt|ç|è }édX  }êttttd td   td td   td
 td   ttd@  td td   ttd td   td td   tt | | | | | |	 | |â |t|ê  }ë  f dY  }ìt|ë|ì }í  f dZ  }îttttd td   td td   td
 td   ttd@  td td   ttd td   td td   tt | | | | | |	 | |â |
 }ït|ï|î }ðttttd@  td td   ttdA  td td   td td   tt | | | || }ñ  f d[  }òt|ñ|ò }óttttd@  td td   ttdA  td td   td td   tt | | | |¿ | }ô  f d\  }õt|ô|õ }öd]  }÷ttttd@  td td   ttdA  td td   td td   tt | | | |Ú |t|÷  }ø  f d^  }ùt|ø|ù }ú  f d_  }ûttttd@  td td   ttdA  td td   td td   tt | | | |Ú | }üt|ü|û }ýttttd@  td td   ttdA  td td   td td   tt | | | | |â | }þ  f d`  }ÿt|þ|ÿ } da  }ttttd@  td td   ttdA  td td   td td   tt | | | | |â |t|  }  f db  }t|| }  f dc  }ttttd@  td td   ttdA  td td   td td   tt | | | | |â | }t|| }ttttd td   td td   td
 td   ttd@  td td   ttdA  td td   td td   tt | | | | | |	 ||	 }  f dd  }	t||	 }
ttttd td   td td   td
 td   ttd@  td td   ttdA  td td   td td   tt | | | | | |	 |¿ |	 }  f de  }t|| }df  }ttttd td   td td   td
 td   ttd@  td td   ttdA  td td   td td   tt | | | | | |	 |Ú |t| 
 }  f dg  }t|| }  f dh  }ttttd td   td td   td
 td   ttd@  td td   ttdA  td td   td td   tt | | | | | |	 |Ú |	 }t|| }ttttd td   td td   td
 td   ttd@  td td   ttdA  td td   td td   tt | | | | | |	 | |â |
 }  f di  }t|| }dj  }ttttd td   td td   td
 td   ttd@  td td   ttdA  td td   td td   tt | | | | | |	 | |â |t|  }  f dk  }t|| }  f dl  }ttttd td   td td   td
 td   ttd@  td td   ttdA  td td   td td   tt | | | | | |	 | |â |
 }t|| }ttttd@  td td   ttdA  td td   ttd td   td td   tt | | | | ||| }  f dm  } t||  }!ttttd@  td td   ttdA  td td   ttd td   td td   tt | | | | |||  }"  f dn  }#t|"|# }$  f do  }%ttttd@  td td   ttdA  td td   ttd td   td td   tt | | | | ||!| }&t|&|% }'ttttd@  td td   ttdA  td td   ttd td   td td   tt | | | | |¿ |!|  }(  f dp  })t|(|) }*dq  }+ttttd@  td td   ttdA  td td   ttd td   td td   tt | | | | |Ú |!| t|+ 	 },  f dr  }-t|,|- }.ttttd@  td td   ttdA  td td   ttd td   td td   tt | | | | |Ú |!|  }/  f ds  }0t|/|0 }1ttttd@  td td   ttdA  td td   ttd td   td td   tt | | | | | |â ||	 }2  f dt  }3t|2|3 }4  f du  }5ttttd@  td td   ttdA  td td   ttd td   td td   tt | | | | | |â || 	 }6t|6|5 }7  f dv  }8ttttd@  td td   ttdA  td td   ttd td   td td   tt | | | | | |â |!|	 }9t|9|8 }:dw  };ttttd@  td td   ttdA  td td   ttd td   td td   tt | | | | | |â |!| t|; 
 }<  f dx  }=t|<|= }>  f dy  }?ttttd@  td td   ttdA  td td   ttd td   td td   tt | | | | | |â |!| 	 }@t|@|? }Attttt | |"|# }B  f dz  }Ct|B|C }Dttttd td   td td   td
 td   ttd@  td td   ttdA  td td   ttd td   td td   tt | | | | | | |	 ||| }E  f d{  }Ft|E|F }G  f d|  }Httttd td   td td   td
 td   ttd@  td td   ttdA  td td   ttd td   td td   tt | | | | | | |	 |||  }It|I|H }J  f d}  }Kttttd td   td td   td
 td   ttd@  td td   ttdA  td td   ttd td   td td   tt | | | | | | |	 ||!| }Lt|L|K }Mttttd td   td td   td
 td   ttd@  td td   ttdA  td td   ttd td   td td   tt | | | | | | |	 |¿ |!|  }N  f d~  }Ot|N|O }Pd  }Qttttd td   td td   td
 td   ttd@  td td   ttdA  td td   ttd td   td td   tt | | | | | | |	 |Ú |!| t|Q  }R  f d  }St|R|S }Tttttd td   td td   td
 td   ttd@  td td   ttdA  td td   ttd td   td td   tt | | | | | | |	 |Ú |!|  }U  f d  }Vt|U|V }Wttttd td   td td   td
 td   ttd@  td td   ttdA  td td   ttd td   td td   tt | | | | | | |	 | |â || }X  f d  }Yt|X|Y }Z  f d  }[ttttd td   td td   td
 td   ttd@  td td   ttdA  td td   ttd td   td td   tt | | | | | | |	 | |â ||  }\t|\|[ }]  f d  }^ttttd td   td td   td
 td   ttd@  td td   ttdA  td td   ttd td   td td   tt | | | | | | |	 | |â |!| }_t|_|^ }`d  }attttd td   td td   td
 td   ttd@  td td   ttdA  td td   ttd td   td td   tt | | | | | | |	 | |â |!| t|a  }b  f d  }ct|b|c }d  f d  }ettttd td   td td   td
 td   ttd@  td td   ttdA  td td   ttd td   td td   tt | | | | | | |	 | |â |!|  }ft|f|e }gttttd
 td   ttd td   t |	 | | |$|% }h  f d  }it|h|i }jttt ttdA  td? td   tttdA  td td   ttd td   ttttdT  td td   ttd@  td td   ttdA  td td   ttd td    t | | | | | | |L |&|'|( }k  f d  }lt|k|l }mttt ttdA  td? td   tttdA  td td   ttd td   ttttdT  td td   ttd@  td td   ttdA  td td   ttd td    t | | | | | | |L |&|'|) }n  f d  }ot|n|o }pttttdT  td td   ttd@  td td   ttdA  td td   ttd td   td td   tt | | | | | | |*|+|,
 }q  f d  }rt|q|r }sd  }tttttt | |-|.|+|,t|t  }u  f d  }vt|u|v }wtttttdT  td td   ttd@  td td   ttdA  td td   ttd td   td td   tt | | | | | | | |*|/
 }x  f d  }yt|x|y }zd  }{tttttt | | |-|.|/t|{  }|  f d  }}t|||} }~tttttdT  td td   ttd@  td td   ttdA  td td   ttd td   tt | | | | | |0|1 }  f d  }t|| }d  }ttttt | |-|.|1t|  }  f d  }t|| }  f d  }ttttd@  tdtd   ttdA  tdf td   ttdb td   tdi td   tttdT  td td   ttd@  td td   ttdA  td td   ttd td   t | | | |f |g |m |5|2|3|4 }t|| }  f d  }ttttd@  tdtd   ttdb td   tdi td   tttdT  td td   ttd@  td td   ttdA  td td   ttd td   t | | | |f |g |5|2|3|4
 }t|| }  f d  }ttttd
 td   ttd@  tdtd   ttdA  tdf td   ttdb td   tdi td   tttdT  td td   ttd@  td td   ttdA  td td   ttd td   t | | | |f |g |m |5|	 |2|3|4 }t|| }  f d  }ttttd
 td   ttd@  tdtd   ttdb td   tdi td   tttdT  td td   ttd@  td td   ttdA  td td   ttd td   t | | | |f |g |5|	 |2|3|4 }t|| }  f d  }ttttdA  tdf td   ttdb td   tdi td   tttdT  td td   ttd@  td td   ttdA  td td   ttd td   t | | | | | |f |g |m |6|7|8 }t|| }  f d  }ttttdA  tdf td   tdi td   tttdT  td td   ttd@  td td   ttdA  td td   ttd td   t | | | | | |f |m |9|:|; }t|| }  f d  }ttttdA  tdf td   ttdb td   tdi td   tttdT  td td   ttd@  td td   ttdA  td td   ttd td   t | | | | | |f |g |m |6|7|< }t|| }  f d  }ttttdA  tdf td   tdi td   tttdT  td td   ttd@  td td   ttdA  td td   ttd td   t | | | | | |f |m |9|:|= }t|| }ttttd@  tdtd   ttdA  tdf td   ttdb td   tdi td   tttdT  td td   ttd@  td td   ttdA  td td   ttd td   t | | | | | |f |g |m |5|>|? }  f d  }t|| } ttttd@  tdtd   ttdb td   tdi td   tttdT  td td   ttd@  td td   ttdA  td td   ttd td   t | | | | | |f |g |5|@|A }¡  f d  }¢t|¡|¢ }£ttttttd td   td td    td td   tttd td   td td    td td   t | | | | | | |» |B	 }€  f d  }¥t|€|¥ }Šttttttd td   td td    td td   tttd td   td td    td td   t | | | | | | |» |C	 }§  f d   }št|§|š }©ttttttd td   td td    td td   tttd td   td td    td td   t | | | | | | |D|E	 }ª  f d¡  }«t|ª|« }¬tttd td   ttd td   td td   tttd td   td td   td td    td td   t | | | | | |F|G }­  f d¢  }®t|­|® }¯ttttd
 td   ttd td   td td   tttd td   td td   td td    td td   t | | | | |	 | |F|H	 }°  f d£  }±t|°|± }²  f d€  }³tttd  tttd@  td td   tttdA  td td   ttd td   td td    t | | | | | |i  }Žt|Ž|³ }µ  f d¥  }¶tttd  tttd@  td td   tttdA  td td   td td    t | | | | |i  }·t|·|¶ }ž  f dŠ  }¹tttd  tttd@  td td   tttdA  td td   ttd td   td td    t | | | | | |j  }ºt|º|¹ }»  f d§  }Œtttd  tttd@  td td   tttdA  td td   td td    t | | | | |j  }œt|œ|Œ }Ÿtttd  tttd td   ttttdT  td td   ttdA  td td    t | | | | | |I }¿  f dš  }Àt|¿|À }Átttd  ttttdT  td td    tttd td   t | | | | |J }Â  f d©  }Ãt|Â|Ã }Ätttd  tttd td   tdA  ttttdT  td td   ttdA  td td    t | | | | | |K|L }Å  f dª  }Æt|Å|Æ }Çtttd  tttd td   tdA  ttttdT  td td   ttdA  td td    t | | | | | |K|M }È  f d«  }Ét|È|É }Êtttd  ttttdT  td td    tttd td   tdA  t | | | | |N }Ë  f d¬  }Ìt|Ë|Ì }ÍtttttdA  tdb td   tttdA  td td   ttttdT  td td   ttdA  td td    t | | | | | |f |g |O|P
 }Î  f d­  }Ït|Î|Ï }ÐtttttdA  tdb td   ttttdT  td td    tttdA  td td   t | | | | |f |g |O|P	 }Ñ  f d®  }Òt|Ñ|Ò }ÓtttttdT  tdb td   ttttdT  td td   ttdA  td td    tttdT  td td   ttdA  td td   t | | | | | | |f |g |Q|R }Ô  f d¯  }Õt|Ô|Õ }ÖtttttdT  tdb td   ttttdT  td td    tttdT  td td   ttdA  td td   t | | | | | |f |g |Q|R
 }×  f d°  }Øt|×|Ø }ÙtttttdT  tdb td   tttdT  td td   ttttdT  td td   ttdA  td td    t | | | | | |f |g |Q|R
 }Ú  f d±  }Ût|Ú|Û }ÜttttttdT  td td   ttdA  td td    tttdT  td td   t | | | | | |S|T }Ý  f d²  }Þt|Ý|Þ }ß  f d³  }àttttttdT  td td   ttdA  td td    tttdT  td td   t | | | | | |S|U }át|á|à }âtttd  tttd td   ttttdA  td td    ttttdA  td td    t | | | | | | |V }ã  f dŽ  }ät|ã|ä }åttttd> td   td? td   tttd td   tttdA  td td   ttd td   td td    td td   td td    t | | | | | | |L |M |W|X }æ  f dµ  }çt|æ|ç }èttttt td1td   tdtd   td td   td td   ttd> td   td? td   td
 td   t | |L |M |å ||	 | | |( |Y|Z }é  f d¶  }êt|é|ê }ëttttd td   tttdA  td td   ttd td   td td    td td   td td   ttd> td   td? td   td td   t | | | | | | |L |M | |[| }ì  f d·  }ít|ì|í }îttttd td   ttttdA  td td    td td   td td   ttd> td   td? td   td td   t | | | | | |L |M | |[| }ï  f dž  }ðt|ï|ð }ñttttt td td   ttd> td   td? td   td td   t | |L |M | | |( |) |\|
 }ò  f d¹  }ót|ò|ó }ôttttd td   tttdA  td td   td td    td td   td td   ttd> td   td? td   td
 td   t | | | | |L |M | |[| 
 }õ  f dº  }öt|õ|ö }÷ttttd td   t¡ttdA  td»td   td
 td   ttd td   ttttdA  td td    td td   td td   t | | | | |L |`| |[|]|^|_ }ø  f dŒ  }ùt|ø|ù }úttttd td   tttdA  td td   ttd td   td td    td td   td td   td td   ttdA  td»td   ttd> td   td? td   td
 td   t | | | | | | |L |M |`| |[|]|a|b|_ }û  f dœ  }üt|û|ü }ýttt¡ttdA  td»td   td
 td   ttd td   ttttdA  td td    td td   td td   td td   t | | | | | |L |`| |[|]|b|_ }þ  f dŸ  }ÿt|þ|ÿ } ttttd td   tttdA  td td   ttd td   td td    td td   td td   td td   ttdA  td»td   ttd> td   td? td   td
 td   t | | | | | | |L |M |`| |[|]|a|ß |c }  f d¿  }t|| }ttt¡ttdA  td»td   td
 td   ttd td   ttttdA  td td    td td   td td   td td   t | | | | | |L |`| |[|]|ß |c }  f dÀ  }t|| }ttttd td   tttdA  td td   ttd td   td td    td td   td td   td td   ttdA  td»td   ttd> td   td? td   td
 td   t | | | | | | |L |M |`| |[|]|a|à |c }  f dÁ  }t|| }	ttt¡ttdA  td»td   td
 td   ttd td   ttttdA  td td    td td   td td   td td   t | | | | | |L |`| |[|]|à |c }
  f dÂ  }t|
| }ttttd
 td   ttt td1td   tdtd   td td   td td   t | |å ||	 | | |d|e|f
 }  f dÃ  }t|| }tttd  tttd td   td td   tttdA  td td   tttd td   td td   td td   td td    t | | | | | |g }  f dÄ  }t|| }ttttttttdA  td td    td td    t | | | | |h }  f dÅ  }t|| }tttttdA  td td   tttttdA  td td    td td    tttttdA  td td    t | | | | |i|j }  f dÆ  }t|| }ttttttd td   ttttdA  td td    td td   td td    tttttdA  td td    t | | | | | |i|k }  f dÇ  }t|| }tttttdA  td td   ttttdT  td td    td td    ttttdT  td td    t | | | | |l }  f dÈ  }t|| }ttttd td   td td   td
 td   tttdA  td td   ttttdT  td td     ttttdT  td td    t | | | | |	 |m|n }  f dÉ  } t||  }!  f dÊ  }"tttd  ttttd@  td td    tttd td   t | | | | | |o }#t|#|" }$  f dË  }%tttd  ttttd@  td td    tttd td   t | | | | | |p }&t|&|% }'  f dÌ  }(tttd  ttttd@  td td    tttd td   t | | | | | |o })t|)|( }*  f dÍ  }+tttd  ttttd@  td td    tttd td   t | | | | | |p },t|,|+ }-dÎ  }.tttttd td   ttttd@  td td    tttd td   t | | | | | | | |ot|. 
 }/  f dÏ  }0t|/|0 }1dÐ  }2ttttd td   td td   ttttd@  td td    tttd td   t | | | | | | | |ot|2 
 }3  f dÑ  }4t|3|4 }5dÒ  }6tttttd td   ttttd@  td td    tttd td   t | | | | | | | |pt|6 
 }7  f dÓ  }8t|7|8 }9dÔ  }:ttttd td   td td   ttttd@  td td    tttd td   t | | | | | | | |pt|: 
 };  f dÕ  }<t|;|< }=dÖ  }>tttttd td   ttttd@  td td    tttd td   t | | | | | | | |ot|> 
 }?  f d×  }@t|?|@ }AdØ  }Bttttd td   td td   ttttd@  td td    tttd td   t | | | | | | | |ot|B 
 }C  f dÙ  }Dt|C|D }EdÚ  }Ftttttd td   ttttd@  td td    tttd td   t | | | | | | | |pt|F 
 }G  f dÛ  }Ht|G|H }IdÜ  }Jttttd td   td td   ttttd@  td td    tttd td   t | | | | | | | |pt|J 
 }K  f dÝ  }Lt|K|L }Mttttd
 td   ttttd td   tttttd td    td td   t | | | | | |	 | |q| 
 }N  f dÞ  }Ot|N|O }Ptttd td   ttttd td   tttttd td    td td   t | | | | | | |q }Q  f dß  }Rt|Q|R }Sttttttdb td   tttdA  td td   tttd td   tttd td   t | | | | |f |g | | |ï |r|s }T  f dà  }Ut|T|U }Vttttd
 td   tttd td   tdb td   ttttd td   ttd1td   td td   ttd td   td td   t | | | | |f |g |	 | | |t|u|v }W  f dá  }Xt|W|X }Yttttttd td   tttd td   ttt¡tt¢tttd td   tttd td   t | | | | | | |L | | |È |Ç |á  }Z  f dâ  }[t|Z|[ }\ttttttd td   tttd td   tttttd td   tttd td   t | | | | | | | | |Ç |á  }]  f dã  }^t|]|^ }_ttttttd td   tttd td   ttt¡tt¢tttd td   t | | | | | |L | | |È |Ç |á  }`  f dä  }at|`|a }bttttttd td   tttd td   ttt¡tt¢tttd td   t | | | | | |L | | |È |Ç |á  }c  f då  }dt|c|d }ettttttd td   ttttd td   tttd td   tt | | | | | | | |Ç |á 
 }f  f dæ  }gt|f|g }htttt¡tt¢ttttd td   tttd td   tt | | | | |L | | |È |Ç |á  }i  f dç  }jt|i|j }kttttttd td   ttt¡tt¢tttd td   tttd td   t | | | | | |L | | |È |á  }l  f dè  }mt|l|m }nttttttd td   tttttd td   tttd td   t | | | | | | | |á 	 }o  f dé  }pt|o|p }qttttttd td   ttt¡tt¢tttd td   t | | | | |L | | |È |á 
 }r  f dê  }st|r|s }t  f dë  }uttttdT  td td   ttdA  td td   td td   tttdZ  td? td   ttdT  td td   ttdA  td td   t | | | | | | |L |w|x|y|z|{|| }vt|v|u }w  f dì  }xttttdT  td td   td td   tttdZ  td? td   ttdT  td td   ttdA  td td   t | | | | | |L |}|~|y| }yt|y|x }zdí  }{tttttt |X |Y | |-|||t|{ 	 }|  f dî  }}t|||} }~|||||||||| |£|Š|©|¬|¯|²|µ|ž|»|Ÿ|Á|Ä|Ç|Ê|Í|Ð|Ó|Ö|Ù|Ü|ß|â|å|è|ë|î|ñ|ô|÷|ú|ý| |||	||||||||!|$|'|*|-|0|3|7|:|=|@|C|F|I|L|O|S|V|Z|]|`|c|f|i|l|o|r|u|x|{|~||||||||||||¢|¥|š|«|®|±|Ž|·|º|œ|À|Ã|Æ|É|Í|Ñ|Õ|Ù|Ý|á|å|é|ì|ï|ò|õ|ø|û|þ||||
|||||||"|%|(|+|.|1|4|7|:|=|@|C|F|I|L|O|R|U|X|[|^|a|d|g|j|m|p|s|v|y||||||||||||||¡|€|§|ª|­|°|³|¶|º|Ÿ|Â|Å|È|Ì|Ð|Ô|Ø|Ü|ß|â|å|è|ë|î|ñ|ô|÷|ú|ý| |||	||||||||!|$|'|*|-|0|3|6|9|<|?|B|E|H|K|N|Q|T|W|Z|]|`|c|f|i|l|o|r|u|x|{|~||||||||||||¢|¥|š|«|¯|³|¶|¹|Œ|¿|Â|Å|È|Ì|Ï|Ò|Ö|Ù|Ü|ß|ã|æ|é|í|ð|ó|ö|ú|ý| |||
|||||||!|$|'|*|.|1|4|7|:|>|A|D|G|J|M|P|T|W|Z|]|`|d|g|j|m|p|s|w|z|~||||||||||| |£|Š|©|¬|¯|²|µ|ž|»|Ÿ|Á|Ä|Ç|Ê|Í|Ð|Ó|Ö|Ù|Ü|ß|â|å|è|ë|î|ñ|ô|÷|ú|ý| |||	||||||||!|$|'|*|-|1|5|9|=|A|E|I|M|P|S|V|Y|\|_|b|e|h|k|n|q|t|w|z|~gS(ï  Niÿÿÿÿ(  t   cons798t   cons2t   cons3t   cons7t   cons50t   cons4t   cons5t   cons17t   cons21t   cons799t   cons27t   cons48t   cons125t   cons52t   cons800t   cons25t   cons801t   cons802t   cons149t   cons803t   cons500t   cons804t   cons648t   cons805t   cons806t   cons18t   cons46t   cons807t   cons808t   cons68t   cons809t   cons810t   cons811t   cons812t   cons813t   cons814t   cons815t   cons816t   cons817t   cons818t   cons819t   cons820t   cons821t   cons452t   cons822t   cons823t   cons824t   cons825t   cons826t   cons827t   cons828t   cons829t   cons830t   cons831t   cons832t   cons833t   cons834t   cons835t   cons836t   cons837t   cons838t   cons839t   cons840t   cons841t   cons842t   cons843t   cons844t   cons845t   cons846t   cons847t   cons848t   cons849t   cons850t   cons851t   cons852t   cons208t   cons209t   cons64t   cons853t   cons66t   cons854t   cons855t   cons464t   cons856t   cons857t   cons858t   cons53t   cons13t   cons137t   cons859t   cons860t   cons148t   cons244t   cons163t   cons861t   cons521t   cons862t   cons863t   cons864t   cons84t   cons865t   cons34t   cons35t   cons866t   cons468t   cons469t   cons867t   cons868t   cons36t   cons869t   cons870t   cons871t   cons872t   cons873t   cons874t   cons875t   cons876t   cons877t   cons878t   cons879t   cons880t   cons881t   cons882t   cons883t   cons884t   cons885t   cons886t   cons887t   cons888t   cons889t   cons890t   cons891t   cons892t   cons893t   cons894t   cons895t   cons896t   cons897t   cons898t   cons899t   cons900t   cons901t   cons902t   cons903t   cons904t   cons674t   cons905t   cons481t   cons906t   cons907t   cons482t   cons908t   cons909t   cons910t   cons911t   cons912t   cons913t   cons914t   cons915t   cons916t   cons85t   cons31t   cons94t   cons917t   cons196t   cons367t   cons356t   cons489t   cons541t   cons23t   cons918t   cons554t   cons919t   cons552t   cons55t   cons494t   cons57t   cons58t   cons59t   cons60t   cons920t   cons921t   cons922t   cons923t   cons924t   cons595t   cons71t   cons925t   cons586t   cons87t   cons128t   cons926t   cons927t   cons928t   cons929t   cons930t   cons45t   cons314t   cons226t   cons931t   cons932t   cons933t   cons934t   cons935t   cons936t   cons937t   cons938t   cons939t   cons940t   cons941t   cons942t   cons943t   cons944t   cons945t   cons946t   cons282t   cons947t   cons63t   cons719t   cons948t   cons949t   cons950t   cons73t   cons951t   cons702t   cons147t   cons952t   cons953t   cons796t   cons954t   cons955t   cons956t   cons957t   cons958t   cons959t   cons960t   cons961t   cons962t   cons963t   cons964t   cons965t   cons966t   cons69t   cons967t   cons968t   cons969t   cons970t   cons971t   cons972t   cons973t   cons974t   cons975t   cons512t   cons976t   cons977t   cons978t   cons979t   cons980t   cons667t   cons981t   cons982t   cons797t   cons983t   cons984t   cons985t   cons986t   cons987t   cons988t   cons93t   cons88t   cons989t   cons990t   cons991t   cons992t   cons993t   cons994t   cons995t   cons996t   cons997t   cons998t   cons38t   cons999t   cons1000t   cons1001t   cons1002t   cons1003t   cons1004t   cons1005t   cons1006t   cons1007t   cons1008t   cons1009t   cons1010t   cons383t   cons1011t   cons1012t   cons1013t   cons1014t   cons1015t   cons1016t   cons1017t   cons1018t   cons357t   cons1019t   cons246t   cons1020t   cons1021t   cons1022t   cons1023t   cons1024t   cons1025t   cons1026t   cons1027t   cons1028t   cons1029t   cons1030t   cons1031t   cons1032t   cons1033t   cons1034t   cons1035t   cons1036t   cons1037t   cons1038t   cons1039t   cons1040t   cons1041t   cons1042t   cons1043t   cons297t   cons1044t   cons1045t   cons1046t   cons1047t   cons1048t   cons705t   cons382t   cons1049t   cons1050t   cons697t   cons709t   cons153t   cons1051t   cons1052t   cons1053t   cons1054t   cons1055t   cons1056t   cons1057t   cons1058t   cons1059t   cons224t   cons1060t   cons515t   cons1061t   cons1062t   cons1063t   cons1064t   cons1065t   cons1066t   cons1067t   cons1068t   cons1069t   cons1070t   cons1071t   cons43t   cons479t   cons480t   cons1072t   cons1073t   cons1074t   cons1075t   cons1076t   cons1077t   cons1078t   cons1079t   cons1080t   cons1081t   cons1082t   cons1083t   cons1084t   cons1085t   cons1086t   cons1087t   cons1088t   cons1089t   ci   t   bt   ai    t   pc      	      sw     j  d  t | | | | t d  | t t | | | | | |  |  | | | | t d  |  |  S(   NiÁ  i   (   t   appendRÀ  Rà  R*   R   (   R¯  R­  R¬  R®  t   nt   xt   q(   t   rubi(    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1473   s    t   mc      
      s     j  d  t | | t d  | | | | t d  | t t | | | | | | | |  |  | | | | t d  |  |  S(   NiÂ  i   (   R°  RÀ  Rà  R*   R   (   R¯  R¶  R­  R¬  R®  R±  R²  R³  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1474   s    R±  t   rt   et   dt   fc            sÀ     j  d  t | | | |
 | | |  | |	 | |
 | | | | | |
 | |  | |	 | |
 | | | t |
 | | | |
 | |  | |	 | |
 | | | |
  |
  S(   NiÃ  (   R°  RÀ  R   (   R¯  R³  R¶  R»  R­  Rž  Rº  R®  R±  R¬  R²  t   sR¹  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1475   s    t   uc	   	         s2     j  d  t | | | |  t | |  |  S(   NiÄ  (   R°  RÀ  R   (	   R¯  RŸ  R­  Rº  R®  R±  R¬  R²  R¹  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1476   s    c	   	         sG     j  d  t | | | | | | |  | | | | |  |  S(   NiÅ  (   R°  R   (	   R¯  RŸ  R­  Rº  R®  R±  R¬  R²  R¹  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1477£   s    c   	   
      sú   t  |   }   j d  t | | | | | | | t t | | |  t d  t d  | | | | | t d  t d  | | | | | | t d  t d  | |  | | | | | | | | | | t d  |  |  S(   NiÆ  i   iÿÿÿÿ(   R3   R°  RÀ  R*   R   Rà  (	   R¯  R­  Rº  R®  R±  R¬  R²  R¹  R³  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   With1478§   s    c	   
   
      s  t  |   }	   j d  t | |	 | | | | | t t | |	 |  t d  t d  | | | | |	 t d  | t d  | | | | | |	 t d  | t d  | |  | | | | | | | | | | t d  |	  |  S(   NiÇ  i   iÿÿÿÿ(   R3   R°  RÀ  R*   R   Rà  (
   R¯  R¶  R­  Rº  R®  R±  R¬  R²  R¹  R³  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   With1479­   s    c
            s_  t  |   }
   j d  t |	 |
 | | | | | t t t | |
 |  t d  t d  | |	 | | |
 t d  t d  | | |	 | | |
 t d  t d  | t | t | | |	 | | |
 t d  | | |	 | | |
 t d  |   | |  |  | |	 | | | | | | | | t d  |
  |  S(   NiÈ  i   iÿÿÿÿ(	   R3   R°  RÀ  R*   R   R,  Rà  R   RË  (   R¯  RŸ  R­  Rž  Rº  R®  R±  R¬  R²  R¹  R³  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   With1480³   s    c            sg  t  |   }   j d  t |
 | | | | | | t t t |	 | |  t d  t d  | |
 | |	 | t d  | t d  | | |
 | |	 | t d  | t d  | t | t |	 | |
 | |	 | t d  | | |
 | |	 | t d  |   | |	  |	  |	 |
 | | |	 | | | |	 | t d  |  |	  S(   NiÉ  i   iÿÿÿÿ(	   R3   R°  RÀ  R*   R   R,  Rà  R   RË  (   R¯  RŸ  R¶  R­  Rž  Rº  R®  R±  R¬  R²  R¹  R³  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   With1481¹   s    c            sU     j  d  t | t t | | | | |  | t d  |  | | |  |  S(   NiÊ  i   (   R°  RÀ  R*   R   Rà  (   R¯  R­  R¬  R®  R±  R²  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1482À   s    c      	      sh     j  d  t | | t d  t t | | t d  | | | | |  |  | | |  |  S(   NiË  i   iþÿÿÿ(   R°  RÀ  Rà  R*   R   (   R¯  R¶  R­  R¬  R®  R±  R²  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1483Å   s    c      	      sr     j  d  t | | | | | | | t t | | t d  | | | | |  |  | | |  |  S(   NiÌ  iþÿÿÿ(   R°  RÀ  R*   R   Rà  (   R¯  R¶  R­  Rº  R¬  R®  R±  R²  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1484Ê   s    R  c      	      sk     j  d  t | t t | | | | | | t d  | |  | t d  |  | | |  |  S(   NiÍ  i   (   R°  RÀ  R*   R   Rà  (   R¯  R­  R  Rº  R®  R¬  R±  R²  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1485Ï   s    c	   	   
      s~     j  d  t | | t d  t t | | t d  | | | | | | t d  | |  |  | | |  |  S(   NiÎ  i   iþÿÿÿi   (   R°  RÀ  Rà  R*   R   (	   R¯  R¶  R­  R  Rº  R¬  R®  R±  R²  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1486Ô   s    c
   
   
      s     j  d  t | | | | |	 | | t t | | t d  | | | | | | t d  | |  |  | | |  |  S(   NiÏ  iþÿÿÿi   (   R°  RÀ  R*   R   Rà  (
   R¯  R¶  R­  R  Rº  R¬  R®  R±  R²  R¹  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1487Ù   s    c      	      s~     j  d  t | t t | | | | | | t d  | | t d  | |  | t d  |  | | |  |  S(   NiÐ  i   (   R°  RÀ  R*   R   Rà  (   R¯  R­  R  Rº  R¬  R®  R±  R²  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1488Þ   s    c	   	   
      s     j  d  t | | t d  t t | | t d  | | | | | | t d  | | t d  | |  |  | | |  |  S(   NiÑ  i   iþÿÿÿi   (   R°  RÀ  Rà  R*   R   (	   R¯  R¶  R­  R  Rº  R¬  R®  R±  R²  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1489ã   s    c
   
   
      s     j  d  t | | | | |	 | | t t | | t d  | | | | | | t d  | | t d  | |  |  | | |  |  S(   NiÒ  iþÿÿÿi   (   R°  RÀ  R*   R   Rà  (
   R¯  R¶  R­  R  Rº  R¬  R®  R±  R²  R¹  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1490è   s    c            s'     j  d  t t | |   | |   S(   NiÓ  (   R°  R   R1  (   R²  R¶  RŸ  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1491í   s    c            s8     j  d  t t | |  | t |  |  | |  S(   NiÔ  (   R°  R   R1  (   t   vRŸ  R¶  R±  R²  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1492ò   s    c            sI     j  d  t t | |  | t |  |  | t | |  | |  S(   NiÕ  (   R°  R   R1  (   RÏ  t   wR¯  RŸ  R¶  R±  R²  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1493÷   s    R³  c	   	         sZ     j  d  t t | |  | t |  |  | t | |  | t | |  | |  S(   NiÖ  (   R°  R   R1  (	   RÏ  t   zRÑ  R¯  RŸ  R¶  R±  R²  R³  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1494ü   s    c            s'     j  d  t t | |   | |   S(   Ni×  (   R°  R   R1  (   R²  R¯  RŸ  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1495  s    c            s8     j  d  t t | |  | t |  |  | |  S(   NiØ  (   R°  R   R1  (   RÏ  R¯  RŸ  R¶  R²  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1496  s    c            sI     j  d  t t | |  | t |  |  | t | |  | |  S(   NiÙ  (   R°  R   R1  (   RÏ  RÑ  R¯  RŸ  R¶  R±  R²  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1497  s    c            s8     j  d  t t | |  | t |  |  | |  S(   NiÚ  (   R°  R   R1  (   RÏ  R¯  RŸ  R²  R³  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1498  s    c            s'     j  d  t t | |   | |   S(   NiÛ  (   R°  R   R1  (   R²  R¯  RŸ  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1499  s    c            s3     j  d  t | | | t | |  |  |  S(   NiÜ  (   R°  R   R1  (   R¯  RŸ  R¶  R¬  R²  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1500  s    c            s8     j  d  t t | |  | t |  |  | |  S(   NiÝ  (   R°  R   R1  (   RÏ  R¯  RŸ  R²  R³  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1501  s    c            s@     j  d  t | | t | |  | t |  |  | |  S(   NiÞ  (   R°  R   R1  (   RÏ  R¯  RŸ  R¶  R²  R³  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1502$  s    c            sI     j  d  t t | |  | t |  |  | t | |  | |  S(   Niß  (   R°  R   R1  (   RÏ  RÑ  R¯  RŸ  R¶  R²  R³  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1503)  s    c            sQ     j  d  t | | t | |  | t |  |  | t | |  | |  S(   Nià  (   R°  R   R1  (   RÏ  RÓ  R¯  RŸ  R¶  Rž  R²  R³  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1504.  s    c            s'     j  d  t t | |   | |   S(   Niá  (   R°  R   R1  (   R²  R¯  RŸ  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement15053  s    c            s/     j  d  t |  | t | |   | |   S(   Niâ  (   R°  R   R1  (   R²  R¶  R¯  RŸ  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement15068  s    c            s'     j  d  t t | |   | |   S(   Niã  (   R°  R   R1  (   R²  R¯  RŸ  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1507=  s    c            s3     j  d  t | | | t | |  |  |  S(   Niä  (   R°  R   R1  (   R¯  RŸ  R¶  Rº  R²  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1508B  s    c            s8     j  d  t t | |  | t |  |  | |  S(   Niå  (   R°  R   R1  (   RÏ  R¯  RŸ  R²  R³  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1509G  s    c            s8     j  d  t t | |  | t |  |  | |  S(   Niæ  (   R°  R   R1  (   RÏ  R¯  RŸ  R²  R³  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1510L  s    c            s@     j  d  t | | t | |  | t |  |  | |  S(   Niç  (   R°  R   R1  (   RÓ  R¯  RŸ  R¶  R²  R³  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1511Q  s    c            s@     j  d  t | | t | |  | t |  |  | |  S(   Niè  (   R°  R   R1  (   RÓ  R¯  RŸ  R¶  R²  R³  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1512V  s    c            s'     j  d  t t | |   | |   S(   Nié  (   R°  R   R1  (   R²  R¯  RŸ  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1513[  s    c            s/     j  d  t |  | t | |   | |   S(   Niê  (   R°  R   R1  (   R²  R¶  R¯  RŸ  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1514`  s    c            s4     j  d  t t | |   | t | |   |   S(   Nië  (   R°  R   R1  (   R²  RÓ  R¯  RŸ  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1515e  s    c            s<     j  d  t | | t | |  | t |  |  |  S(   Niì  (   R°  R   R1  (   RÓ  R¯  RŸ  R¶  R²  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1516j  s    t   ht   gi   i   c            s     j  d  t t d  | | t d  | | | | t d  t d  | | | | t d  | | | t | | | |  |  S(   Nií  i   i   (   R°  R€  Rà  Rá  (   R¶  R»  Rì  Rž  R¬  R±  R®  R²  Rë  R³  R¹  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1517o  s    c      
      s     j  d  t | |  | | |  t | |  | | | | t d  | | t d  | t d  |	 | | | | | | t d  d |  |  S(   Niî  i   i   i   (   R°  RÀ  R   Rà  (   R¶  R»  Rì  Rž  Rº  R¬  R±  R®  R²  Rë  R³  R¹  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1518t  s    c            s¶   t  |   }   j d  t | | t t | | |  | t d  | | | | | | | | t | t | | | | | |   |  | | | | t d  |  |  S(   Niï  iÿÿÿÿi   (   R3   R°  RÀ  R*   R   Rà  R   RË  (   R¯  R¶  R­  R  R¬  R®  R²  R±  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   With1519x  s    c            s     j  d  t t d  | t d  t t | | | | | t d  |  t | | t d  | |  |  | | | t d   |  S(   Nið  i   (   R°  RÀ  Rà  R*   R   Rš  (   R¯  R¶  R­  R  R®  R±  R²  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1520  s    c            sº     j  d  t | | | | |  t | | | t d  t | | | t d   |  |  t | | | | |  t d  t | | | t d   | | |  t d  |  S(   Niñ  iÿÿÿÿi   (   R°  R   R1  Rà  R°   R€  (   R¯  R­  R  R®  R±  R²  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1521  s    c            sC     j  d  t t | | | | | | | | |  |  |  S(   Niò  (   R°  R   RÊ   (   R¯  R¶  R­  R  R¬  R±  R®  R²  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1522  s    c            s7     j  d  t t | | | | | |  |  |  S(   Nió  (   R°  R   RÊ   (   R¯  R­  R  R®  R±  R²  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1523  s    c      	      s     j  d  t t d  | t t | t d  | t d  | | | | |  t | | | |  |  | | |  |  S(   Niô  i   iÿÿÿÿ(   R°  RÀ  Rà  R*   R   Rš  (   R¯  R¶  R­  R  R®  R±  R²  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1524  s    c            sm     j  d  t | t |  | t |  | | t |  t | | | | | | | |  |  |  S(   Niõ  (   R°  RÀ  R$   R%   R   (   R¯  R¶  R­  R  R¬  R®  R±  R²  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1525  s    c            s«     j  d  t t d  | | |  t d  t | | | | |  t d  t | |  |  |  t | | | | | |  t d  | | |  t d  |  S(   Niö  i   (   R°  RÀ  Rà  R   R¿  R€  (   R¯  R¶  R­  R  R®  R±  R²  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1526  s    c            sg     j  d  t t d  | t | | | t d  | | | | |  t | | |  |  |  S(   Ni÷  i   (   R°  RÀ  Rà  R   R1  (   R¯  R¶  R­  R  Rº  R®  R±  R²  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1527¢  s    c            s?     j  d  t | | | | | |  t | | |  |  S(   Niø  (   R°  R   R1  (   R¯  R­  R  R®  R±  R²  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1528§  s    c      
      s­   t  | | | |  }   j d  t | | |  t | | | | | | | |  t d  t | | | t d  |  |  |  t | | | | | |  |  S(   Niù  iÿÿÿÿ(   R×  R°  RÀ  R   Rà  R1  R€  (   R¯  R¶  R­  R  R®  R±  R²  RŸ  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   With1529«  s    c   
   
      s<  t  | |  } t d  }	   j d  t | | |  t | | | | | | | |  t d  t | |	 t | | |	  |	 | | |  t d  t |	 t d  |   |  |  t	 | | | | | | | |  t | |	 t d  t | | |	  |	 | | |  t d  t |	 t d  |   |  S(   Nt   iiú  iÿÿÿÿi   i    (
   Rº   Rñ  R°  RÀ  R   Rà  RÁ  R°   R   R€  (
   R¯  R¶  R­  R  R¬  R±  R®  R²  R³  Rú  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   With1530±  s    c      
      s  t  | |  } t d  }   j d  t | | |  t | | | | |  t d  t | | t | | |  | | |  t d  t | t d  |   |  |  t	 | | | | |  t | | t d  t | | |  | | |  t d  t | t d  |   |  S(   NRú  iû  iÿÿÿÿi   i    (
   Rº   Rñ  R°  RÀ  R   Rà  RÁ  R°   R   R€  (   R¯  R­  R  R®  R±  R²  R³  Rú  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   With1531ž  s    c         S   s[   t  | t t t t f  r t St | |  } t d  } t | | t	 d   rW t
 St S(   NRú  iÿÿÿÿ(   t
   isinstancet   intRä  t   floatRå  t   FalseRº   Rñ  R"   Rà  t   True(   R¯  R­  R  R®  R±  R²  R³  Rú  (    (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   With1532¿  s    c            sV  t  | |  } t d  }   j d  t t d  | | |  t d  t | | | | |  t d  t | | | | |  t d  t d  t | | |  t | t d  | t d    |  |  t	 | | | | |  t d  | t | | |  | | t
 | | | t | | |  |  | | | |  t d  |  S(   NRú  iü  i   i    iÿÿÿÿ(   Rº   Rñ  R°  RÀ  Rà  R   RÁ  R°   R   R€  R1  (   R¯  R­  R  R®  R±  R²  R³  Rú  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1532È  s    c      	      sÑ     j  d  t t d  | | |  t d  t | | | | |  t d  t | | |  t d  t | | |  |  |  |  t | | | | | | |  t d  | | |  t d  |  S(   Niý  i   (   R°  RÀ  Rà  R   R1  R¿  R€  (   R¯  R­  R  R®  R±  R²  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1533Ð  s    i   c      	      s     j  d  t t d  | |  t d  | | | t d  | | | t d  t d  | | t | | | t d   |  S(   Niþ  i   i   (   R°  R€  Rà  Rá  (   R»  R­  Rì  Rº  R®  R²  R¹  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1534Õ  s    c      	      sW     j  d  t |  t d  | | t d  | t | | | t d   |  S(   Niÿ  i   i   (   R°  R€  Rà  Rá  (   R»  R­  Rì  Rº  R®  R²  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1535Ú  s    c      	      sg     j  d  t | t d  | |  | | | t d  | | t | | | t d   |  S(   Ni   i   i   (   R°  R€  Rà  Rá  (   Rì  R­  Rº  R®  R²  R¹  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1536ß  s    c      	      sa     j  d  t |  t d  | | t d  t d  | t | | | t d   |  S(   Ni  i   i   i   (   R°  R€  Rà  Rá  (   R»  R­  R®  R²  Rë  R¹  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1537ä  s    c      	      sH     j  d  t | | t d  |  t | |  | t d   |  S(   Ni  i   i   (   R°  R€  Rà  Rá  (   R­  R®  R²  Rë  R¹  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1538é  s    i   c      	      s     j  d  t | |  t d  | | | t d  t d  | | | t d  | | t | | | t d   |  S(   Ni  i   i   i   (   R°  R€  Rà  Rá  (   R»  R­  Rì  Rº  R®  R²  Rë  R¹  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1539î  s    c      	      s\     j  d  t | | | | t d  | | | | t | | | t d   |  S(   Ni  i   i   (   R°  R€  Rà  Rá  (   Rì  R­  Rº  R®  R²  Rë  R¹  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1540ó  s    c   	      S   sÍ   t  | t t t t f  r t St | |  } t | | t | t	 d  |  t	 d  | | | | |  } t
 | | t | t	 d  |  t	 d  | | | | |  } t | |  rÉ t St S(   Niÿÿÿÿi   (   Rý  Rþ  Rä  Rÿ  Rå  R   Rº   RÂ  RÃ  Rà  RÄ  RQ   R  (	   R¯  R­  R  R®  R±  R²  R³  t   Qt   R(    (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   With1541÷  s    DDc   	   	      s  t  | |  } t | | t | t d  |  t d  | | | | |  } t | | t | t d  |  t d  | | | | |  }   j d  t | t | d |  d | | |  d t | | | | |  d t | | | |  d | | |  d t	 | | |  |  |  |  t
 | | t | d |  d | | | | | |  d | | |  d |  S(   Niÿÿÿÿi   i  (   Rº   RÂ  RÃ  Rà  RÄ  R°  RÀ  R   R1  R¿  R€  (	   R¯  R­  R  R®  R±  R²  R³  R  R  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1541  s
    DDc   
         sß  t  | |  } t | | | t | t d  |  t d  | | | | | | |  } t | | | t | t d  |  t d  | | | | | | |  }	   j d  t | t | d |  d | | |  d t | | | | | | |  d t | | | | |  d t	 | t
 | t
 | |  d d t |	 | t
  | t t
 d | d   |  |  |  t |	 | t | d |  d | | | | | |  d | d | |  d |  S(   Niÿÿÿÿi   i  i    i   (   Rº   RÂ  RÃ  Rà  RÄ  R°  RÀ  R   R1  RÁ  Rú  R°   R   R€  (
   R¯  R¶  R­  R  R®  R±  R²  R³  R  R  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   With1542	  s
    PPc         S   sU   t  | t t t t f  r t St | t d  |  } t | t d   rQ t	 St S(   Ni   (
   Rý  Rþ  Rä  Rÿ  Rå  R   R   Rà  R#   R  (   R¯  R¶  R­  R  R®  R±  R²  Rì  (    (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   With1543  s    c            s±   t  | t d  |  }   j d  t t d  | t t | t d  | t d  | | | | | | |  t | t | | t d  |   |  | | |  |  S(   Ni   i  iÿÿÿÿ(   R   Rà  R°  RÀ  R*   R   R   RË  (   R¯  R¶  R­  R  R®  R±  R²  Rì  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1543  s    t   Bc      	      sp     j  d  t |  t d  | t t d  | t d  | |  | |  t d  | t d  |  |  S(   Ni  i   i   i   (   R°  RÀ  Rà  R   (   R  R­  R®  R²  t   A(   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1544   s    c      	      s-  t  t | | t d    } t t | | t d    }   j d  t | t d  | | t | t d  | | |  | | | | | |  | | t d  | | | | t d  | t d  |  |  t | | | |  | t d  | | t t d  | | | |  |  S(   Ni   i	  i   i   (   Rw   R  Rà  R3   R°  RÀ  R   (   R  R­  R®  R²  R  Rž  RŒ  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   With1545$  s    c      	      s/  t  t | | t d    } t t | | t d    }   j d  t | t d  | | t | t d  | | |  | | | | | |  | | t d  | | | | t d  | t d  |  |  t | | | |  | t d  | | t t d  | | | |  |  S(   Ni   i
  i   i   (   Rw   R  Rà  R3   R°  RÀ  R   (   R  R­  R®  R²  R  Rž  RŒ  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   With1546+  s      t   Cc            sG     j  d  t | t d  | t t d  |  | | |  |  S(   Ni  i   i   (   R°  RÀ  Rà  R   (   R  R  R­  R®  R²  R  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement15473  s    c      	      s­   | t  d  d | t  d  d }   j d  t | | t t  d  | | |  |  t |  | | | t t  d  | t  d  | | | t  d  |  |  S(   Ni   i   i  i   (   Rà  R°  RÀ  R   (   R  R  R­  R®  R²  R  R³  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   With15487  s    &R  c      	      s­   | t  d  d | t  d  d }   j d  t | | t t  d  | | |  |  t |  | | | t t  d  | t  d  | | | t  d  |  |  S(   Ni   i   i  i   (   Rà  R°  RÀ  R   (   R  R  R­  R®  R²  R³  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   With1549=  s    &c      	      s©   | t  d  d | t  d  d }   j d  t |  | t t  d  | | |  |  t |  | | t t  d  | t  d  | | | t  d  |  |  S(   Ni   i   i  i   (   Rà  R°  RÀ  R   (   R  R­  R®  R²  R  R³  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   With1550C  s    &c      	      s¯   | t  d  d | t  d  d }   j d  t | | t t  d  | | |  |  t |  | | | t t  d  | t  d  | | | t  d  |  |  S(   Ni   i   i  i   (   Rà  R°  RÀ  R   (   R  R  R­  R®  R²  R  R³  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   With1551I  s    (c      	      s¯   | t  d  d | t  d  d }   j d  t | | t t  d  | | |  |  t |  | | | t t  d  | t  d  | | | t  d  |  |  S(   Ni   i   i  i   (   Rà  R°  RÀ  R   (   R  R  R­  R®  R²  R³  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   With1552O  s    (c      	      s«   | t  d  d | t  d  d }   j d  t |  | t t  d  | | |  |  t |  | | t t  d  | t  d  | | | t  d  |  |  S(   Ni   i   i  i   (   Rà  R°  RÀ  R   (   R  R­  R®  R²  R  R³  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   With1553U  s    (c      	      s¯   | t  d  d | t  d  d }   j d  t | | t t  d  | | |  |  t |  | | | t t  d  | t  d  | | | t  d  |  |  S(   Ni   i   i  i   (   Rà  R°  RÀ  R   (   R  R  R­  R®  R²  R  R³  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   With1554[  s    'c      	      s¯   | t  d  d | t  d  d }   j d  t | | t t  d  | | |  |  t |  | | | t t  d  | t  d  | | | t  d  |  |  S(   Ni   i   i  i   (   Rà  R°  RÀ  R   (   R  R  R­  R®  R²  R³  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   With1555a  s    'c      	      s«   | t  d  d | t  d  d }   j d  t |  | t t  d  | | |  |  t |  | | t t  d  | t  d  | | | t  d  |  |  S(   Ni   i   i  i   (   Rà  R°  RÀ  R   (   R  R­  R®  R²  R  R³  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   With1556g  s    'c      	      s¯   | t  d  d | t  d  d }   j d  t | | t t  d  | | |  |  t |  | | | t t  d  | t  d  | | | t  d  |  |  S(   Ni   i   i  i   (   Rà  R°  RÀ  R   (   R  R  R­  R®  R²  R  R³  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   With1557m  s    'c      	      s¯   | t  d  d | t  d  d }   j d  t | | t t  d  | | |  |  t |  | | | t t  d  | t  d  | | | t  d  |  |  S(   Ni   i   i  i   (   Rà  R°  RÀ  R   (   R  R  R­  R®  R²  R³  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   With1558s  s    'c      	      s«   | t  d  d | t  d  d }   j d  t |  | t t  d  | | |  |  t |  | | t t  d  | t  d  | | | t  d  |  |  S(   Ni   i   i  i   (   Rà  R°  RÀ  R   (   R  R­  R®  R²  R  R³  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   With1559y  s    'c      	      s   | | t  d  d }   j d  t | | t t  d  | | |  |  t |  | | | t t  d  | t  d  | | | t  d  |  |  S(   Ni   i   i  i   (   Rà  R°  RÀ  R   (   R  R  R­  R®  R²  R  R³  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   With1560  s    c      	      s   | | t  d  d }   j d  t | | t t  d  | | |  |  t |  | | | t t  d  | t  d  | | | t  d  |  |  S(   Ni   i   i  i   (   Rà  R°  RÀ  R   (   R  R  R­  R®  R²  R³  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   With1561  s    c      	      s   | | t  d  d }   j d  t |  | t t  d  | | |  |  t |  | | t t  d  | t  d  | | | t  d  |  |  S(   Ni   i   i  i   (   Rà  R°  RÀ  R   (   R  R­  R®  R²  R  R³  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   With1562  s    c      	      s    t  | | t d   }   j d  t | | t t d  | | |  |  t |  | | | t t d  | t d  | | | t d  |  |  S(   Ni   i  i   i   (   R  Rà  R°  RÀ  R   (   R  R  R­  R®  R²  R  R³  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   With1563  s    c      	      s    t  | | t d   }   j d  t | | t t d  | | |  |  t |  | | | t t d  | t d  | | | t d  |  |  S(   Ni   i  i   i   (   R  Rà  R°  RÀ  R   (   R  R  R­  R®  R²  R³  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   With1564  s    c      	      s   t  | | t d   }   j d  t |  | t t d  | | |  |  t |  | | t t d  | t d  | | | t d  |  |  S(   Ni   i  i   i   (   R  Rà  R°  RÀ  R   (   R  R­  R®  R²  R  R³  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   With1565  s    c      	      s¡   | | t  d  d }   j d  t | | t t  d  | | |  |  t |  | | | t t  d  | t  d  | | | t  d  |  |  S(   Ni   i   i  i   (   Rà  R°  RÀ  R   (   R  R  R­  R®  R²  R  R³  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   With1566£  s    c      	      s¡   | | t  d  d }   j d  t | | t t  d  | | |  |  t |  | | | t t  d  | t  d  | | | t  d  |  |  S(   Ni   i   i  i   (   Rà  R°  RÀ  R   (   R  R  R­  R®  R²  R³  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   With1567©  s    c      	      s   | | t  d  d }   j d  t |  | t t  d  | | |  |  t |  | | t t  d  | t  d  | | | t  d  |  |  S(   Ni   i   i   i   (   Rà  R°  RÀ  R   (   R  R­  R®  R²  R  R³  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   With1568¯  s    c      	      s¢   t  | | t d   }   j d  t | | t t d  | | |  |  t |  | | | t t d  | t d  | | | t d  |  |  S(   Ni   i!  i   i   (   R  Rà  R°  RÀ  R   (   R  R  R­  R®  R²  R  R³  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   With1569µ  s    c      	      s¢   t  | | t d   }   j d  t | | t t d  | | |  |  t |  | | | t t d  | t d  | | | t d  |  |  S(   Ni   i"  i   i   (   R  Rà  R°  RÀ  R   (   R  R  R­  R®  R²  R³  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   With1570»  s    c      	      s   t  | | t d   }   j d  t |  | t t d  | | |  |  t |  | | t t d  | t d  | | | t d  |  |  S(   Ni   i#  i   i   (   R  Rà  R°  RÀ  R   (   R  R­  R®  R²  R  R³  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   With1571Á  s    c      	      sq     j  d  t | t | t d  | | | t d  |  |  t | |  | | | | t d  |  S(   Ni$  i   i   (   R°  RÀ  R   Rà  (   R  R  R­  R®  R²  R  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1572È  s    c      
      su     j  d  t |  t | | | | t d  |  |  t | t | t d  | | | t d  |  |  S(   Ni%  i   i   (   R°  RÀ  R   Rà  (   R  R  R­  R®  R²  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1573Í  s    c      
      s{     j  d  t | t t d  | | | t d  |  |  t |  t | t d  | | | t d  |  |  S(   Ni&  i   i   i   (   R°  RÀ  R   Rà  (   R  R­  R®  R²  R  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1574Ò  s    c            s|   | | t  d  d }   j d  t | t  d  | t | | | | | t  d  | | | t  d  |  |  S(   Ni   i   i'  i   (   Rà  R°  RÀ  R   (   R  R  R­  R®  R²  R  R³  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   With1575Ö  s    c            st   | | t  d  d }   j d  t | | t  d  | t | | t  d  | | | t  d  |  |  S(   Ni   i   i(  i   (   Rà  R°  RÀ  R   (   R  R  R­  R®  R²  R³  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   With1576Ü  s    c            s|   | | t  d  d }   j d  t | t  d  | t | |  | | | t  d  | | | t  d  |  |  S(   Ni   i   i)  i   (   Rà  R°  RÀ  R   (   R  R­  R®  R²  R  R³  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   With1577â  s    c            s{   | | t  d  d }   j d  t | | t | | | | |  | | t  d  | | | t  d  |  |  S(   Ni   i   i*  i   (   Rà  R°  RÀ  R   (   R  R  R­  R®  R²  R  R³  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   With1578è  s    c            su   | | t  d  d }   j d  t |  | t  d  | t | | t  d  | | | t  d  |  |  S(   Ni   i   i+  i   (   Rà  R°  RÀ  R   (   R  R  R­  R®  R²  R³  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   With1579î  s    c            so   | | t  d  d }   j d  t | | | t | | | t  d  | | | t  d  |  |  S(   Ni   i   i,  i   (   Rà  R°  RÀ  R   (   R  R­  R®  R²  R  R³  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   With1580ô  s    c         S   se   t  | t t t t f  r t S| | t d  d } t | |  | | | t d   ra t St S(   Ni   i   i   (	   Rý  Rþ  Rä  Rÿ  Rå  R   Rà  R   R  (   R  R  R­  R®  R²  R  R³  (    (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   With1581ú  s    &c      
      s  | | t  d  d }   j d  t | t  d  | t | t  d  | |  | | | t  d  | | |  | t  d  | | t  d  | t  d  | | | t  d  |  |  t | | |  | | | t  d  t  d  | t t  d  | | |  |  S(   Ni   i   i-  i   (   Rà  R°  RÀ  R   (   R  R  R­  R®  R²  R  R³  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1581  s    c         S   sa   t  | t t t t f  r t S| | t d  d } t |  | | | t d   r] t St S(   Ni   i   i   (	   Rý  Rþ  Rä  Rÿ  Rå  R   Rà  R   R  (   R  R  R­  R®  R²  R³  (    (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   With1582  s    "c      
      s  | | t  d  d }   j d  t | t  d  | t | |  | | | t  d  | |  | t  d  | | t  d  | t  d  | | | t  d  |  |  t | |  | | | t  d  t  d  | t t  d  | | |  |  S(   Ni   i   i.  i   (   Rà  R°  RÀ  R   (   R  R  R­  R®  R²  R³  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1582  s    c         S   s]   t  | t t t t f  r t S| | t d  d } t | |  | t d   rY t St S(   Ni   i   i   (	   Rý  Rþ  Rä  Rÿ  Rå  R   Rà  R   R  (   R  R­  R®  R²  R  R³  (    (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   With1583  s    c      
      sÿ   | | t  d  d }   j d  t | t  d  | t | t  d  | |  | t  d  | | t  d  |  | t  d  | t  d  | | | t  d  |  |  t | | |  | t  d  t  d  | t t  d  | | |  |  S(   Ni   i   i/  i   (   Rà  R°  RÀ  R   (   R  R­  R®  R²  R  R³  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1583  s    c         S   sf   t  | t t t t f  r t S| | t d  d } t | |  | | | t d   rb t St S(   Ni   i   i   (	   Rý  Rþ  Rä  Rÿ  Rå  R   Rà  R   R  (   R  R  R­  R®  R²  R  R³  (    (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   With1584$  s    &c      
      s  | | t  d  d }   j d  t | t  d  | t | t  d  | |  | | | t  d  | | |  | t  d  | | t  d  | t  d  | | | t  d  |  |  t | | |  | | | t  d  t  d  | t t  d  | | |  |  S(   Ni   i   i0  i   (   Rà  R°  RÀ  R   (   R  R  R­  R®  R²  R  R³  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1584,  s    c         S   sb   t  | t t t t f  r t S| | t d  d } t |  | | | t d   r^ t St S(   Ni   i   i   (	   Rý  Rþ  Rä  Rÿ  Rå  R   Rà  R   R  (   R  R  R­  R®  R²  R³  (    (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   With15852  s    "c      
      s  | | t  d  d }   j d  t | t  d  | t | |  | | | t  d  | |  | t  d  | | t  d  | t  d  | | | t  d  |  |  t | |  | | | t  d  t  d  | t t  d  | | |  |  S(   Ni   i   i1  i   (   Rà  R°  RÀ  R   (   R  R  R­  R®  R²  R³  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1585:  s    c         S   s^   t  | t t t t f  r t S| | t d  d } t | |  | t d   rZ t St S(   Ni   i   i   (	   Rý  Rþ  Rä  Rÿ  Rå  R   Rà  R   R  (   R  R­  R®  R²  R  R³  (    (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   With1586@  s    c      
      s   | | t  d  d }   j d  t | t  d  | t | t  d  | |  | t  d  | | t  d  |  | t  d  | t  d  | | | t  d  |  |  t | | |  | t  d  t  d  | t t  d  | | |  |  S(   Ni   i   i2  i   (   Rà  R°  RÀ  R   (   R  R­  R®  R²  R  R³  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1586H  s    c      
   S   sÍ   t  | t t t t f  r t St | t | | t |  | | t d  t	 | | t | t d   t	 | | t  | | | | t
 t t d  | t d  t d    } t |  rÉ t St S(   Ni   i    iÿÿÿÿ(   Rý  Rþ  Rä  Rÿ  Rå  R   RÁ  t   iiRà  R°   R   R(   R  (   R¶  R­  R  R¬  R®  R±  R²  RÏ  (    (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   With1587N  s    c      
      sŽ   t  | t | | t |  | | t d  t | | t | t d   t | | t  | | | | t t t d  | t d  t d    }   j d  t | |  S(   Ni   i    iÿÿÿÿi3  (   RÁ  RG  Rà  R°   R   R°  R   (   R¶  R­  R  R¬  R®  R±  R²  RÏ  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1587V  s    c      
   S   sŒ   t  | t t t t f  r t St | t | | t d  t	 | | t | t d   t	 | | t  | |  | | t
 t t d  | t d  t d    } t |  rž t St S(   Ni   i    iÿÿÿÿ(   Rý  Rþ  Rä  Rÿ  Rå  R   RÁ  RG  Rà  R°   R   R(   R  (   R­  R  R®  R±  R²  RÏ  (    (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   With1588\  s    c      
      s£   t  | t | | t d  t | | t | t d   t | | t  | |  | | t t t d  | t d  t d    }   j d  t | |  S(   Ni   i    iÿÿÿÿi4  (   RÁ  RG  Rà  R°   R   R°  R   (   R­  R  R®  R±  R²  RÏ  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1588d  s    c            sr  t  t |  | t d    } t t |  | t d    }   j d  t t d  | | t d  t | |  | t d   | | t d  | | | t d  t t d   |  t t d  t d  d | | t | t d  | t d  | | | | t d  | | | t d  t t d   t d   t t t d   t d   | | | t t | | | t t d   t d  | | | t d  t t d    t d  t d  t t d    | t d  t | | | | | | | t d  t t d   t d   t | |  | t d   |  S(   Ni   i5  i   i   i   iùÿÿÿ(	   R·   R  Rà  Rž   R°  R€  Rá  R;   R  (   R­  Rº  R¬  R®  R²  Rž  RŒ  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   With1589j  s    c            s  t  t |  | t d    } t t |  | t d    }   j d  t | | t | | | t t d   t d  t | |  | t d   |  |  t | | | | t t d   t d  | t t d  t | |  | t d   |  |  S(   Ni   i6  i   (   R·   R  Rà  Rž   R°  RÀ  R   Rá  (   R­  Rº  R¬  R®  R²  Rž  RŒ  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   With1590q  s    c            su  t  t |  | t d    } t t |  | t d    }   j d  t t d  | | t d  t | |  | t d   | | t d  | | | t t d   t d  |  t t d  t d  d | | t | t d  | t d  | | | | t d  | | | t t d   t d  t d   t t t d   t d   | | | t t | | | t d  t t d   | | | t t d   t d   t d  t d  t t d    | t d  t | | | | | | | t t d   t d  t d   t | |  | t d   |  S(   Ni   i7  i   i   i   iùÿÿÿ(	   R·   R  Rà  Rž   R°  R€  Rá  R;   R  (   R­  Rº  R¬  R®  R²  Rž  RŒ  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   With1591x  s    c            s  t  t |  | t d    } t t |  | t d    }   j d  t | | t | | | t d  t t d   t | |  | t d   |  |  t | | | | t d  t t d   | t t d  t | |  | t d   |  |  S(   Ni   i8  i   (   R·   R  Rà  Rž   R°  RÀ  R   Rá  (   R­  Rº  R¬  R®  R²  Rž  RŒ  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   With1592  s    c            sß  t  t |  | t d    } t t |  | t d    }   j d  t | | t d  | t d  t t d   t | |  | t d   t d  | | t d  | | t d  t d  t t d   | |  t t d  t d  d | | | t | t d  | t d  | | | t d  | t d  | | t d  t d  t t d   | t d   | | t d  | t t | | t d  t t d   t d  | | | t d  t d  t t d   |  t t d   t d  t d  d  t d  | t d  t | | t d  | | t d  | | | t d  t d  t t d   | t d   t | |  | t d   |  S(   Ni   i9  i   i   i   i   (	   R·   R  Rà  Rž   R°  R€  Rá  R;   R	  (   R­  Rº  R¬  R®  R²  Rž  RŒ  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   With1593  s    c            s9  t  |  | t d   }   j d  t | t d  | t d  t t d  | t d  | t d  t t d   t d  t | |  | t d   |  |  t t d  | | t d  | t t d   t d  t d  | t d  t t d  t | |  | t d   |  |  S(   Ni   i:  i   i   i   i   (   R  Rà  R°  RÀ  R   Rá  (   R­  Rº  R¬  R®  R²  R³  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   With1594  s    i   c      
      sÆ    j  d  t | | | t d  t | | | t d  t d  | | | t d   t | t d  | |  | t d  |  | t d  | t d   t t t t t d   | t d  t d  | | | t d  t t d   | t d  | t d  | | | t d   t d   t d  t d  t t d    t t t d   t d   t | |  | t d   | | | t d  |  S(   Ni;  i   i   i   i   iþÿÿÿ(   R°  R€  Rà  Rá  R<   R  (   R­  Rº  R¬  R®  R²  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1595  s    c            sH    j  d  t | t |  | t d   | t d  t |  | t d   t | t d  t |  | t d   t d  t | |  | t d   |  |  t | t |  | t d   | t d  t |  | t d   t | t d  t |  | t d   t d  t | |  | t d   |  |  S(   Ni<  i   i   i   i   (   R°  RÀ  R  Rà  R   Rá  (   R­  Rº  R¬  R®  R²  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1596  s    c      
      s     j  d  t t | | t d   t t d  | t | |  | |  |  |  t t | t | | t d   | |  t | |  | |  |  S(   Ni=  i    i   (   R°  RÀ  R°   Rà  R   Rá  R1  (   R­  R  R®  R±  R²  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1597  s    c            s	  t  | |  } t d  }	 t d  }
   j d  t t | |	 | | |	 | | | | | |  t | |
 | t d  t | | |	 |
 | t d   t |
 t d  t d  t d  |	 | |   t |	 t d  | t d  t d    |  S(   Nt   jt   ki>  i   i    i   iÿÿÿÿ(   Rº   Rñ  R°  R   RÁ  Rà  R°   R   (   R¯  R¶  R­  R  R¬  R®  R±  R²  R³  RU  RV  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   With1598¢  s
    c   	         sø   t  | |  } t d  } t d  }   j d  t t | | | | | | |  t | | | t d  t | | | | | t d   t | t d  t d  t d  | | |   t | t d  | t d  t d    |  S(   NRU  RV  i?  i   i    i   iÿÿÿÿ(   Rº   Rñ  R°  R   RÁ  Rà  R°   R   (	   R¯  R­  R  R®  R±  R²  R³  RU  RV  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   With1599ª  s
    c            sŽ     j  d  t t | | | t d   t | | t d  | | | | |  |  |  t | | | | |  t | | | t d  t | | | t d   |  |  S(   Ni@  iÿÿÿÿ(   R°  RÀ  R°   Rà  R   R1  (   R¯  R­  R  R®  R±  R²  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1600³  s    c            s?     j  d  t t | | | |  | | | | |  |  S(   NiA  (   R°  R   RÊ   (   R¶  R­  R  R¬  R®  R±  R²  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1601ž  s    c            s3     j  d  t t | | |  | | |  |  S(   NiB  (   R°  R   RÊ   (   R­  R  R®  R±  R²  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1602œ  s    c   	      S   sK   t  | t t t t f  r t St | | t d   } t |  rG t	 St S(   Ni    (
   Rý  Rþ  Rä  Rÿ  Rå  R   R°   Rà  R   R  (	   R¯  R¶  R­  R  R¬  R®  R±  R²  t   Pq0(    (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   With1603Á  s    c   	         sW  t  | | t d   }   j d  t t d  t d  | | | t d  t | | | t d  | | | | |  t t d  | | | | t d  | | |  t d  t d  t d  | | | | t d  | |  |  |  t | | | | t d  | | | | |  t d  | | | t d  |  S(   Ni    iC  i   i   iÿÿÿÿ(   R°   Rà  R°  RÀ  R   R1  R€  (	   R¯  R¶  R­  R  R¬  R®  R±  R²  R\  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1603É  s    c   
   
   S   sÅ   t  | t t t t f  r t St | |  } t | | |  }	 t t	 | | |  | t
 d   t | | t
 d   t t t
 d  |   t |  | t
 d  t
 d  |    rÁ t St S(   Ni   i    i   (   Rý  Rþ  Rä  Rÿ  Rå  R   Rº   R°   Râ  R   Rà  RQ   Rã  R   R  (
   R¯  R¶  R­  R  R¬  R®  R±  R²  R³  t   Pqq(    (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   With1604Ï  s    }c   
         s7  t  | |  } t | | |  }	   j d  t d | | | |  | d t | | | | | | | |  t |	 | | | | | | | d | | |	 | | | | |  | d |  |  |  t |	 | | | d | | | | | d | | | | |  d | | | |  | d |  S(   NiD  i   (   Rº   R°   R°  RÀ  R   R1  R€  (
   R¯  R¶  R­  R  R¬  R®  R±  R²  R³  R_  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1604Ø  s    c      
   S   sÁ   t  | t t t t f  r t St | |  } t | | |  } t t	 | |  | t
 d   t | | t
 d   t t t
 d  |   t |  | t
 d  t
 d  |    rœ t St S(   Ni   i    i   (   Rý  Rþ  Rä  Rÿ  Rå  R   Rº   R°   Râ  R   Rà  RQ   Rã  R   R  (   R¯  R­  R  R®  R±  R²  R³  R_  (    (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   With1605ß  s    yc            s  t  | |  } t | | |  }   j d  t d | | |  | d t | | | | |  t | | | | | | | d | | | | | | |  | d |  |  |  t | | | | d | | | | |  d | | |  | d |  S(   NiE  i   (   Rº   R°   R°  RÀ  R   R1  R€  (   R¯  R­  R  R®  R±  R²  R³  R_  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1605è  s    c            s   t  | |  }   j d  t t | | | t d  | | | | |  t | | t | t | t d  |   |  |  | t d  |  S(   NiF  iþÿÿÿi   (   Rº   R°  R*   R   Rà  R1  R   RË  (   R¯  R¶  R­  R  R®  R±  R²  R³  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   With1606ï  s    c   
         sÜ   t  |  } t | |  }	   j d  t | | t t | | | |	 t d  t d  | | | | | | | |  t | | |	 t | t	 | | | |   |  |  | | | t d  |  |  S(   NiG  i   iÿÿÿÿ(
   R3   Rº   R°  RÀ  R*   R   Rà  R1  R   RË  (
   R¯  R¶  R­  R  R¬  R®  R±  R²  Rì  R³  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   With1607õ  s    c   	         s¿   t  | |  }   j d  t | | | t d  | | t t | | | t d  | | | | |  t | | t | t | t d  |   |  |  | t d  |  |  S(   NiH  i   iþÿÿÿ(	   Rº   R°  RÀ  Rà  R*   R   R1  R   RË  (	   R¯  R¶  R­  R  R¬  R®  R±  R²  R³  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   With1608ü  s    c            s   t  |  }   j d  t | t t | | | t d  t d  | | | | | |  t | t | | |   |  | | t d  |  |  S(   NiI  i   iÿÿÿÿ(   R3   R°  RÀ  R*   R   Rà  R   RË  (   R¯  R¶  R­  R  R®  R±  R²  Rì  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   With1609  s    c            s   t  |  }   j d  t | t t | | t d  | | | | | |  t | t | | |   |  | | t d  |  |  S(   NiJ  iÿÿÿÿi   (   R3   R°  RÀ  R*   R   Rà  R   RË  (   R¯  R­  R  R®  R±  R²  Rì  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   With1610  s    c            sm     j  d  t | t |  | t |  | | t |  t | | | | | | | |  |  |  S(   NiK  (   R°  RÀ  R$   R%   R   (   R¯  R¶  R­  R  R¬  R®  R±  R²  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1611  s    c            sª     j  d  t t d  | t d  t t | | | | | t d  |  t t | | | |  t | | | | t d    |  | | | t d   |  S(   NiL  i   (   R°  RÀ  Rà  R*   R   R   Rš  RË  (   R¯  R¶  R­  R  R®  R±  R²  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1612  s    c            sm     j  d  t | t |  | t |  | | t |  t | | | | | | | |  |  |  S(   NiM  (   R°  RÀ  R$   R%   R   (   R¯  R¶  R­  R  R¬  R®  R±  R²  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1613  s    c      	      sg     j  d  t | t | | | | | |  |  t |  t | | | | | | | |  |  S(   NiN  (   R°  RÀ  R   (   R  R¯  R¶  R­  R®  R±  R²  R  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1614  s    c            sC     j  d  t t | | | | | | | | |  |  |  S(   NiO  (   R°  R   RÊ   (   R¯  R¶  R­  R  R¬  R®  R±  R²  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1615#  s    c            s7     j  d  t t | | | | | |  |  |  S(   NiP  (   R°  R   RÊ   (   R¯  R­  R  R®  R±  R²  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1616(  s    c	   	   	      s}     j  d  t | | |  | t |  | t d   t t | | | | | | | t |  | |  |  | |   |  S(   NiQ  i   (   R°  RÀ  R°   Rà  R*   R   Rš  (	   RÏ  R¯  RŸ  R¶  R­  R  R®  R±  R²  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1617-  s    c      	      sn     j  d  t t d  t |  | t d   t t | | | | | t |  | |  |  | |   |  S(   NiR  i   (   R°  RÀ  Rà  R°   R*   R   Rš  (   RÏ  R¯  R­  R  R®  R±  R²  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement16182  s    R  R  c
   
         sL     j  d  t | | | | |	 | | | | t d  | |  |  S(   NiS  i   (   R°  R   Rà  (
   R¯  R  R¶  R  R  R  R¬  R±  R²  R  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement16197  s    c            s@     j  d  t | | | | | | t d  | |  |  S(   NiT  i   (   R°  R   Rà  (   R¯  R  R  R  R  R±  R²  R  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1620<  s    c
   
   	      sµ     j  d  t |	 | | | t |   | | | | t |   |	 | | | | t d  | t |   t | | | | |	 | | | | t d  | |  |  |  S(   NiU  i   (   R°  RÀ  R%   Rà  R   (
   R¯  R  R¶  R  R  R  R¬  R±  R²  R  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1621A  s    c      	      s©     j  d  t | | | | t |   | | | | t |   | | | | | t d  | t |   t | | | | | | t d  | |  |  |  S(   NiV  i   (   R°  RÀ  R%   Rà  R   (   R¯  R  R  R  R  R±  R²  R  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1622F  s    c            sb     j  d  t |
 |	 | | |	 | |  t d  | | |	 | |  t d  | | |	  S(   NiW  i   (   R°  R€  Rà  (   R¯  R»  R­  Rì  R  Rº  R®  R±  R¬  R²  R¹  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1623K  s    c
   
         sb     j  d  t |	 | | | | | |  t d  | | | | |  t d  | | |  S(   NiX  i   (   R°  R€  Rà  (
   R¯  Rì  R­  R  Rº  R®  R±  R¬  R²  R¹  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1624P  s    c            s     j  d  t | | |
 | t d  | | |
 | |  t d  |	 | |
 | |  t d  | |	 | | t d  |
  S(   NiY  i   (   R°  R€  Rà  (   R¯  R¶  R»  R­  Rì  R  Rº  R®  R±  R¬  R²  Rë  R¹  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1625U  s    c            s     j  d  t | |
 |	 | t d  | | |	 | |  t d  | | |	 | |  t d  | | |
 | t d  |	  S(   NiZ  i   (   R°  R€  Rà  (   R¯  R¶  Rì  R­  R  Rº  R®  R±  R¬  R²  Rë  R¹  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1626Z  s    c      	      s     j  d  t |
 t | | | | | | | | | |	 |  |  t |  t | | | | | | | | | | | |	 |  |  S(   Ni[  (   R°  RÀ  R   (   R  R¯  R¶  R­  Rº  R®  R±  R¬  R²  R³  R  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1627_  s    c	   
         s²   t  |  }	   j d  t |	 | t t t | |	 t d  | | | |	 | |  t | t | | | | |	 |   | |  |  | | | | t d  |	  |  S(   Ni\  iÿÿÿÿi   (	   R3   R°  RÀ  R*   R   R,  Rà  R   RË  (
   R¯  R­  R!  Rº  R®  R¬  R±  R²  R³  RV  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   With1628c  s    c	   	   	      sr     j  d  t t d  | t t | | | | | t d  |  t | | | |  |  | | |  |  S(   Ni]  i   i   (   R°  RÀ  Rà  R*   R   Rš  (	   R¯  R¶  R­  R  R  R¬  R®  R±  R²  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1629j  s    c
   
         sY     j  d  t t | | |	 | | | |	 | | |	 t d  | |  |	  |	  S(   Ni^  i   (   R°  R   RÊ   Rà  (
   R¯  R¶  R­  R  R  Rº  R¬  R±  R®  R²  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1630o  s    c            sM     j  d  t t | | | | | | | t d  | |  |  |  S(   Ni_  i   (   R°  R   RÊ   Rà  (   R¯  R­  R  R  R¬  R±  R®  R²  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1631t  s    c
   
         sV     j  d  t | | | | | | | | t d  | |  t d  | |  S(   Ni`  i   i   (   R°  R€  Rà  (
   R¯  R»  R­  R  Rº  R¬  R±  R®  R²  R¹  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1632y  s    c	   	         sV     j  d  t | | | | | | | | t d  | |  t d  | |  S(   Nia  i   i   (   R°  R€  Rà  (	   R¯  R»  R­  R  Rº  R¬  R±  R®  R²  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1633~  s    c            sz     j  d  t | | |
 | t d  |	 | |
 | | |
 t d  | |  t d  |	 | | t d  |
  S(   Nib  i   i   (   R°  R€  Rà  (   R¯  R¶  Rì  R­  R  R»  Rº  R¬  R±  R®  R²  R¹  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1634  s    c            sz     j  d  t | | |
 | t d  |	 | |
 | | |
 t d  | |  t d  |	 | | t d  |
  S(   Nic  i   i   (   R°  R€  Rà  (   R¯  R¶  Rì  R­  R  R»  Rº  R¬  R±  R®  R²  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1635  s    c
   
         sÎ     j  d  t t d  | t |   | t d  | |	 | t d  t |   | | |	 | | |	 t d  | t |   t | | |	 | | t d  | |	 | t d  |  |	  |	  S(   Nid  i   i   (   R°  RÀ  Rà  R$   R%   R   (
   R¯  R¶  R­  R  R  Rº  R¬  R±  R®  R²  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1636  s    c            sÂ     j  d  t t d  | t |   | t d  | | | t d  t |   | | | | | | t d  | t |   t | | t d  | | | t d  |  |  |  S(   Nie  i   i   (   R°  RÀ  Rà  R$   R%   R   (   R¯  R­  R  R  R¬  R±  R®  R²  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1637  s    c	   	   
      s     j  d  t t d  | t t | t d  | t d  | | | | | | t d  |  t | | | |  |  | | |  |  S(   Nif  i   iÿÿÿÿi   (   R°  RÀ  Rà  R*   R   Rš  (	   R¯  R¶  R­  R  R  R¬  R®  R±  R²  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1638  s    c
   
   	      si     j  d  t |	 | | |	 | t | |	 | | | |	 | | |	 t d  | |  |	  |	  S(   Nig  i   (   R°  RÀ  R   Rà  (
   R¯  R¶  R­  R  R  Rº  R¬  R®  R±  R²  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1639  s    c
   
   	      s}     j  d  t t d  | t | |	 | t d  | | |	 | | |	 t d  | |  t | |	 |	  |	  |	  S(   Nih  i   i   (   R°  RÀ  Rà  R   R1  (
   R¯  R¶  R­  R  R  Rº  R¬  R±  R®  R²  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1640¡  s    c            sU     j  d  t | | | | | | | t d  | |  t | | |  |  S(   Nii  i   (   R°  R   Rà  R1  (   R¯  R­  R  R  R¬  R±  R®  R²  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1641Š  s    R  c            s¹     j  d  t |
 t d  | | |
 t d  | | t d  | | |  t d  | | | | |
 t d  | |
 t d  |  t d  t d  | t d  |
  S(   Nij  i   i   i   i   (   R°  R€  Rà  (   R¯  R»  R­  R  Rì  Rº  R  R¬  R®  R±  R²  R¹  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1642«  s    c            s°     j  d  t |
 t d  | | |
 t d  t d  | | |  t d  | | | | |
 t d  | |
 t d  |  t d  t d  | t d  |
  S(   Nik  i   i   i   i   (   R°  R€  Rà  (   R¯  R»  Rì  R  R­  Rº  R  R¬  R®  R±  R²  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1643°  s    c            s¹     j  d  t |	 t d  | | |	 t d  | |
 t d  | | |  t d  | | | | |	 t d  | |	 t d  |  t d  t d  | t d  |	  S(   Nil  i   i   i   i   (   R°  R€  Rà  (   R¯  Rì  R­  R  Rº  R  R¬  R®  R±  R²  R¹  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1644µ  s    c
   
         s°     j  d  t |	 t d  | | |	 t d  t d  | | |  t d  | | | | |	 t d  | |	 t d  |  t d  t d  | t d  |	  S(   Nim  i   i   i   i   (   R°  R€  Rà  (
   R¯  Rì  R­  R  Rº  R  R¬  R®  R±  R²  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1645º  s    RŒ  c      	      s    j  d  t t d  | |
 | | | t d  | | t d  | t d  |	 | | | t d  | |
 | t d  t d  |	 | | t d  | | t d  |	 | | t d  t |	 | |
 | | |
 t d  |  |
  S(   Nin  i   i   (   R°  R€  Rà  Rá  (   RŒ  R¶  R»  R­  R  Rì  Rž  R¬  R±  R®  R²  Rë  R³  R¹  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1646¿  s    c      
      s¿     j  d  t | | | | | t | | | | | |	 t d  | | t d  |	 t d  | | t d  |	 |
 | | |	 | | t d  |	 t d  d |  |  S(   Nio  i   i   (   R°  RÀ  R   Rà  (   RŒ  R¶  R»  R­  R  Rì  Rž  Rº  R¬  R±  R®  R²  Rë  R³  R¹  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1647Ä  s    c   
      S   s[   t  | t t t t f  r t St | |  } t d  }	 t | t	 d  |  rW t
 St S(   NRú  i   (   Rý  Rþ  Rä  Rÿ  Rå  R   Rº   Rñ  RO   Rà  R  (
   R¯  R­  R  R  R¬  R®  R±  R²  R³  Rú  (    (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   With1648È  s    c   
         s,  t  | |  } t d  }	   j d  t t d  | | |  t d  t d  | | | t d  t | | | | | | t d  | |  t d  t | | |	 | t d  | t | | |	 |  | t | | |	  |	 | t d  |  t d  t d  | |	 | | |	 t d  t | | |	 |  t d  | | |	 t d  | |  t d  t d  | t d  |	 | |  t d  t d  t | | |	  t |	 t d  | t d    |  |  t	 | | | | | | | t d  | |  t d  t | | |	 | t d  | t | | |	 |  | t | | |	  | |	 | | t | | |	 |  t d  | | | t d  t | | |	  t |	 t d  | t d    | | |  t d  t d  | | | t d  |  S(	   NRú  ip  i   i   i   i   i    iÿÿÿÿ(
   Rº   Rñ  R°  RÀ  Rà  R   RÁ  R°   R   R€  (
   R¯  R­  R  R  R¬  R®  R±  R²  R³  Rú  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1648Ñ  s    c      	      sß     j  d  t | | t d  | |  t d  | | | t d  | |  | | | | t d  | | | t d  | t d  | | | t d  t | | | t d  | | t d   |  S(   Niq  i   i   (   R°  R€  Rà  Rá  (   R»  R­  Rì  Rº  R¬  R®  R²  R¹  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1649Ù  s    c      	      sÂ     j  d  t t d  | | |  | | |  | t d  | | t d  | | | t d  | t d  | | | t d  t | | | t d  | | t d   |  S(   Nir  i   i   (   R°  R€  Rà  Rá  (   R»  R­  Rì  Rº  R¬  R®  R²  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1650Þ  s    c      	      sÉ     j  d  t | | | t d  | t d  | | t d  |  | t d  | | | t d  | t d  | | | t d  t | | | t d  | | t d   |  S(   Nis  i   i   (   R°  R€  Rà  Rá  (   Rì  R­  Rº  R¬  R®  R²  R¹  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1651ã  s    c      	      sâ     j  d  t t d  | t d  | |  | | | |  | t d  | | | t d  t d  | | | t d  | | t d  | | | t d  t | | | t d  | | t d   |  S(   Nit  i   i   i   (   R°  R€  Rà  Rá  (   R»  R­  Rì  R¬  R®  R²  Rë  R¹  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1652è  s    c      	      sZ     j  d  t | | t d  | t | | | t d  | | t d   |  S(   Niu  i   i   i   (   R°  R€  Rà  Rá  (   Rì  R­  R¬  R®  R²  Rë  R¹  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1653í  s    c	   	   	      s    j  d  t t d  | t d  | |  | | | |  | t d  | | | t d  t d  | | | t d  | | | t d  | | | t d  | | t d  | | | t d  t | | | t d  | | t d   |  S(   Niv  i   i   i   (   R°  R€  Rà  Rá  (	   R»  R­  Rì  Rº  R¬  R®  R²  Rë  R¹  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1654ò  s    c      	      s    j  d  t t d  | t d  | |  | | | |  | t d  | | | t d  t d  | | | t d  | | | t d  | | | t d  | | t d  | | | t d  t | | | t d  | | t d   |  S(   Niw  i   i   i   (   R°  R€  Rà  Rá  (   R»  R­  Rº  R¬  R®  R²  Rë  R¹  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1655÷  s    c         S   s  t  | t t t t f  r t St | |  } t | | | t | t	 d  |  t	 d  | | | | | | t	 d  | |  }	 t
 | | | t | t	 d  |  t	 d  | | | | | | t	 d  | |  }
 t | t	 d  |  rt St S(   Niÿÿÿÿi   i   (   Rý  Rþ  Rä  Rÿ  Rå  R   Rº   RÂ  RÃ  Rà  RÄ  RQ   R  (   R¯  R­  R  R  R¬  R®  R±  R²  R³  R  R  (    (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   With1656û  s    ^^c            s  t  | |  } t | | | t | t d  |  t d  | | | | | | t d  | |  }	 t | | | t | t d  |  t d  | | | | | | t d  | |  }
   j d  t | | t | d |  d | | |  d d | | | d t | | | | | | d | |  d t |	 | | |  d d | | | d t	 | | t
 | d | t |
 | t
 |  | t |
 | t
  t
 | d |  d d | t
 | | t
 d t |
 | t
 |  d | | t
 d | |  d d | d t
 | |  d d t |
 | t
  t t
 d | d   |  |  |  t | | | t | d |  d | | | | | | d | |  d t	 | | t
 | d | t |
 | t
 |  | t |
 | t
  | t
 | | t |
 | t
 |  d | | | d t |
 | t
  t t
 d | d   | | |  d d | | | d |  S(	   Niÿÿÿÿi   i   ix  iüÿÿÿiþÿÿÿi   i    (   Rº   RÂ  RÃ  Rà  RÄ  R°  RÀ  R   R1  RÁ  Rú  R°   R   R€  (   R¯  R­  R  R  R¬  R®  R±  R²  R³  R  R  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1656  s
    ^^c	         S   s#  t  | t t t t f  r t St | |  }	 t | | | | | | t |	 t	 d  |  t	 d  | | | | | | t	 d  | |  }
 t
 | | | | | | t |	 t	 d  |  t	 d  | | | | | | t	 d  | |  } t |	 t	 d  |  rt St S(   Niÿÿÿÿi   i   (   Rý  Rþ  Rä  Rÿ  Rå  R   Rº   RÂ  RÃ  Rà  RÄ  RQ   R  (   R¯  R¶  R­  R  R  R¬  R®  R±  R²  R³  R  R  (    (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   With1657  s    jjc	            sº  t  | |  }	 t | | | | | | t |	 t d  |  t d  | | | | | | t d  | |  }
 t | | | | | | t |	 t d  |  t d  | | | | | | t d  | |  }   j d  t | | t |	 d |  d | | |  d d | | | d t | | | | | | | | d | |  d t |
 | | | |  d d | | | d t	 | | t
 | | d t | | t
 |  | t | | t
  | t
 | d |  d d | t
 | | t
 d t | | t
 |  d | t
 d | |  d d | d t
 | |  d d | t | | t
  t t
 d | d   |  |  |  t | | | t |	 d |  d | | | | | | d | |  d t	 | | t
 | d | t | | t
 |  | t | | t
  | t
 | | t | | t
 |  d | | | d t | | t
  t t
 d | d   | d | |  d d | | | d |  S(	   Niÿÿÿÿi   i   iy  iüÿÿÿiþÿÿÿi   i    (   Rº   RÂ  RÃ  Rà  RÄ  R°  RÀ  R   R1  RÁ  Rú  R°   R   R€  (   R¯  R¶  R­  R  R  R¬  R®  R±  R²  R³  R  R  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1657  s
    jjc	   
      S   sU   t  | t t t t f  r t St | t d  |  }	 t |	 t d   rQ t	 St S(   Ni   (
   Rý  Rþ  Rä  Rÿ  Rå  R   R   Rà  R#   R  (
   R¯  R¶  R­  R  R  R¬  R®  R±  R²  Rì  (    (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   With1658  s    c	   
         sË   t  | t d  |  }	   j d  t t d  |	 t t | t d  | t d  |	 | | | | |	 | | t d  | |	 |  t | t | | t d  |	   |  | | |	  |  S(   Ni   iz  iÿÿÿÿi   (   R   Rà  R°  RÀ  R*   R   R   RË  (
   R¯  R¶  R­  R  R  R¬  R®  R±  R²  Rì  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1658'  s    c	   	         sU     j  d  t t | | | |  | | | | | | t d  | |  |  S(   Ni{  i   (   R°  R   RÊ   Rà  (	   R¶  R­  R  R  Rº  R¬  R±  R®  R²  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1659.  s    c            sI     j  d  t t | | |  | | | | t d  | |  |  S(   Ni|  i   (   R°  R   RÊ   Rà  (   R­  R  R  R¬  R±  R®  R²  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement16603  s    c         S   su   t  | t t t t f  r t St | |  } t | | |  } t t	 d  |  | t	 d  t	 d   rq t
 St S(   Ni   i   i    (   Rý  Rþ  Rä  Rÿ  Rå  R   Rº   R°   R"   Rà  R  (   R¯  R­  R  R¬  R®  R²  R³  R_  (    (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   With16617  s    -c            sè   t  | |  } t | | |  }   j d  t d d t | | | | | d |  t d | | | |  | d | | | | | | | d |  d |  |  |  t | | |  t | | | | | d  d |  S(   Ni}  i   i   (   Rº   R°   R°  RÀ  R   R1  R€  t   log(   R¯  R­  R  R¬  R®  R²  R³  R_  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1661@  s    c         S   su   t  | t t t t f  r t St | |  } t | | |  } t t	 d  |  | t	 d  t	 d   rq t
 St S(   Ni   i   i    (   Rý  Rþ  Rä  Rÿ  Rå  R   Rº   R°   R"   Rà  R  (   R¯  R­  R  R¬  R®  R²  R³  R_  (    (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   With1662G  s    -c            só   t  | |  } t | | |  }   j d  t | | | | | d |  t | | | |  d d | | | | | d |  d d |  |  t | | |  t | d | | d t | | | | | d  t | d   |  S(   Ni~  i   i   (	   Rº   R°   R°  R   R1  R€  Rû  Rá  R  (   R¯  R­  R  R¬  R®  R²  R³  R_  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1662P  s    c         S   su   t  | t t t t f  r t St | |  } t | | |  } t t	 d  |  | t	 d  t	 d   rq t
 St S(   Ni   i   i    (   Rý  Rþ  Rä  Rÿ  Rå  R   Rº   R°   R"   Rà  R  (   R¯  R­  R  R¬  R®  R²  R³  R_  (    (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   With1663W  s    -c            sö   t  | |  } t | | |  }   j d  t | | | | | d |  t | | | |  d d | | | | | d |  d d |  |  t | | |  t | d | | d t | | | | | d  t | d   |  S(   Ni  i   i   (	   Rº   R°   R°  R   R1  R€  R=   Rá  R  (   R¯  R­  R  R¬  R®  R²  R³  R_  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1663`  s    c
         S   s  t  |	 t t t t f  r t St | |	  }
 t | |	 |
  } t t	 |
 t
 d  |  t | t
 d  | |  |
 t
 d  t
 d   t t t
 d  |   t t | t
 d   t t
 d  |    t |  |
 t
 d  t
 d  |    rþ t St S(   Ni   i   i    i   (   Rý  Rþ  Rä  Rÿ  Rå  R   Rº   R°   Râ  RQ   Rà  R#   Rã  R   R"   R  (   R¯  R¶  R­  R  R  Rº  R¬  R±  R®  R²  R³  R_  (    (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   With1664g  s    ºc
            sr  t  | |	  }
 t | |	 |
  }   j d  t | |	 | | | |	 | | |	 d | |  t | | |	 |
 | | |	 d | |
 | d | |
 d | |	 | |
 | | |  d |
 d | | d | |  |
 d |	  |	  t | | d | |
 d | |	 | d | |
 d | | |	 | | |	 d | |  d | | d | |  |
 d |	  S(   Ni  i   iþÿÿÿi   (   Rº   R°   R°  R   R1  R€  (   R¯  R¶  R­  R  R  Rº  R¬  R±  R®  R²  R³  R_  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1664p  s    c   
      S   sþ   t  | t t t t f  r t St | |  } t | | |  }	 t t	 | t
 d  |  t t
 d  | |  | t
 d  t
 d   t t t
 d  |   t t | t
 d   t t
 d  |    t |  | t
 d  t
 d  |    rú t St S(   Ni   i   i    i   (   Rý  Rþ  Rä  Rÿ  Rå  R   Rº   R°   Râ  RQ   Rà  R#   Rã  R   R"   R  (
   R¯  R­  R  R  R¬  R±  R®  R²  R³  R_  (    (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   With1665w  s    ¶c   
   
      s:  t  | |  } t | | |  }	   j d  t | | | | | | d | |  t | |	 | | |	 | | d | | d | | d | | | | | |  d | d | d | |  | d |  |  t |	 | d | | d | | | | | | d | |  d | d | |  | d |  S(   Ni  i   iþÿÿÿi   (   Rº   R°   R°  R   R1  R€  (
   R¯  R­  R  R  R¬  R±  R®  R²  R³  R_  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1665  s    c
            s÷   t  | |	  }
 t d  } t d  }   j d  t t | | | |	 | | | | |	 | | |	 t d  | |  t |	 | | t | |	 | | |  t | t d  t d  | |
 |   t | t d  | t d    |	  S(   NRU  RV  i  i   i    i   iÿÿÿÿ(   Rº   Rñ  R°  R   RÁ  Rà  R°   R   (   R¯  R¶  R­  R  R  Rº  R¬  R®  R±  R²  R³  RU  RV  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   With1666  s
    c            sæ   t  | |  } t d  }	 t d  }
   j d  t t | |	 | | | | | | t d  | |  t | |
 | t | | |	 |
 |  t |
 t d  t d  |	 | |   t |	 t d  | t d    |  S(   NRU  RV  i  i   i    i   iÿÿÿÿ(   Rº   Rñ  R°  R   RÁ  Rà  R°   R   (   R¯  R­  R  R  R¬  R®  R±  R²  R³  RU  RV  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   With1667  s
    c	   	         sU     j  d  t t | | | |  | | | | | | t d  | |  |  S(   Ni  i   (   R°  R   RÉ   Rà  (	   R¶  R­  R  R  Rº  R¬  R±  R®  R²  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1668  s    c            sI     j  d  t t | | |  | | | | t d  | |  |  S(   Ni  i   (   R°  R   RÉ   Rà  (   R­  R  R  R¬  R±  R®  R²  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1669  s    c	   
         s°   t  | |  }	   j d  t t | | |	 t d  | | | | | | t d  | |  t | |	 t | t | t d  |   |  |  | t d  |  S(   Ni  iþÿÿÿi   i   (   Rº   R°  R*   R   Rà  R1  R   RË  (
   R¯  R¶  R­  R  R  R¬  R®  R±  R²  R³  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   With1670¡  s    c
            s
  t  |  }
 t | |	  }   j d  t |
 | t t |	 |
 | | t d  t d  | | | | |	 |
 | | | t d  | |	 t d  |
 | |  t |	 |
 | t | t	 |	 |	 |
 |   |	  |	  |	 | |	 t d  |
  |	  S(   Ni  i   iÿÿÿÿi   (
   R3   Rº   R°  RÀ  R*   R   Rà  R1  R   RË  (   R¯  R¶  R­  R  R  Rº  R¬  R®  R±  R²  Rì  R³  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   With1671§  s    c
            sÖ   t  | |	  }
   j d  t | |	 | t d  |	 | t t |	 | |
 t d  | | |	 | | |	 t d  | |  t |	 |
 t | t |	 t d  |	   |	  |	  |	 t d  |	  |	  S(   Ni  i   iþÿÿÿi   (	   Rº   R°  RÀ  Rà  R*   R   R1  R   RË  (   R¯  R¶  R­  R  R  Rº  R¬  R®  R±  R²  R³  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   With1672®  s    c	   
         sŽ   t  |  }	   j d  t |	 t t | |	 | t d  t d  | | | |	 | | | t d  |	 | |  t | t | | |	   |  | | t d  |	  |  S(   Ni  i   iÿÿÿÿi   (   R3   R°  RÀ  R*   R   Rà  R   RË  (
   R¯  R¶  R­  R  R  R¬  R®  R±  R²  Rì  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   With1673Ž  s    c   	         sŠ   t  |  }   j d  t | t t | | t d  | | | | | | | t d  | | |  t | t | | |   |  | | t d  |  |  S(   Ni  iÿÿÿÿi   i   (   R3   R°  RÀ  R*   R   Rà  R   RË  (	   R¯  R­  R  R  R¬  R®  R±  R²  Rì  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   With1674º  s    c
   
   	      s     j  d  t | | t d  d t | |	  t |	  t | |	 | | | |	 | | |	 t d  | |  |	  |	  S(   Ni  iÿÿÿÿi   (   R°  RÀ  Rà  Rá  R   (
   R¯  R¶  R­  R  R  Rº  R¬  R®  R±  R²  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1675Á  s    c
   
   	      s     j  d  t | | t d  d t |	  t | |	  t | |	 | | | |	 | | |	 t d  | |  |	  |	  S(   Ni  i   i   (   R°  RÀ  Rà  Rá  R   (
   R¯  R¶  R­  R  R  Rº  R¬  R®  R±  R²  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1676Æ  s    c
   
   	      si     j  d  t |	 | | |	 | t | |	 | | | |	 | | |	 t d  | |  |	  |	  S(   Ni  i   (   R°  RÀ  R   Rà  (
   R¯  R¶  R­  R  R  Rº  R¬  R®  R±  R²  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1677Ë  s    c	   	         sÎ     j  d  t t d  | t d  t t | | | | | t d  | | t d  | | t d  |  t t | | | |  t | | | | t d    |  | | | t d   |  S(   Ni  i   i   (   R°  RÀ  Rà  R*   R   R   Rš  RË  (	   R¯  R¶  R­  R  R  R¬  R®  R±  R²  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1678Ð  s    c
   
   	      si     j  d  t |	 | | |	 | t | |	 | | | |	 | | |	 t d  | |  |	  |	  S(   Ni  i   (   R°  RÀ  R   Rà  (
   R¯  R¶  R­  R  R  Rº  R¬  R®  R±  R²  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1679Õ  s    c	   
   	      sá   t  t d  | | | t d  t d   }	   j d  t t d  | |	 t | | | |  | t d  | | | |	 |  |  t t d  | |	 t | | | |  | t d  | | | |	 |  |  S(   Ni   i   i  (   R  Rà  R°  RÀ  R   (
   R¶  R­  R  R  Rº  R¬  R±  R®  R²  R³  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   With1680Ù  s    2c      	      sÉ   t  t d  | | |  t d  t d   }   j d  t t d  | | t | |  t d  | | | | |  |  t t d  | | t | |  t d  | | | | |  |  S(   Ni   i   i  (   R  Rà  R°  RÀ  R   (   R­  R  R  R¬  R±  R®  R²  R³  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   With1681ß  s    2c
   
         sY     j  d  t t | | |	 | | | |	 | | |	 t d  | |  |	  |	  S(   Ni  i   (   R°  R   RÊ   Rà  (
   R¯  R¶  R­  R  R  Rº  R¬  R±  R®  R²  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1682æ  s    c            sM     j  d  t t | | | | | | | t d  | |  |  |  S(   Ni  i   (   R°  R   RÊ   Rà  (   R¯  R­  R  R  R¬  R±  R®  R²  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1683ë  s    c
   
         sP     j  d  t | | |	 | | | |	 | | |	 t d  | |  |	  S(   Ni  i   (   R°  R   Rà  (
   R¯  R¶  R­  R  R  Rº  R¬  R±  R®  R²  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1684ð  s    c            sD     j  d  t | | | | | | | t d  | |  |  S(   Ni  i   (   R°  R   Rà  (   R¯  R­  R  R  R¬  R±  R®  R²  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1685õ  s    c      
      s     j  d  t | | |  | t |  |
 t d   t t |
 | | | |
 |	 | |
 t d  |	 | t |  | |
  |
  |
 |   |
  S(   Ni  i   i   (   R°  RÀ  R2   Rà  R*   R   Rš  (   RÏ  R¯  RŸ  R¶  R­  R  R  R¬  R®  R±  R²  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1686ú  s    c	   	   	      s     j  d  t t d  t |  | t d   t t | | | | | | t d  | | t |  | |  |  | |   |  S(   Ni  i   i   (   R°  RÀ  Rà  R2   R*   R   Rš  (	   RÏ  R¯  R­  R  R  R¬  R®  R±  R²  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1687ÿ  s    RU  c            sj     j  d  t | | t d  | | | | | | |  t d  | | | |  t d  |  S(   Ni  i   (   R°  R€  Rà  (   R¯  RU  R­  R®  R±  R²  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1688  s    c            sà     j  d  t | | |  | t d  | | | |  t d  t | | | | | | | | |  t d  |  |  t | | t d  | | | | | | |  t d  | | | |  t d  |  S(   Ni  i   (   R°  RÀ  Rà  R   R€  (   R¯  RU  R­  R®  R±  R²  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1689	  s    c            sÕ     j  d  t | | | |  | t d  | | |  t d  t | | | | | | | | | |  |  |  t | | t d  | | | | | | |  t d  | | |  t d  |  S(   Ni  i   (   R°  RÀ  Rà  R   R€  (   R¯  RU  R­  R®  R±  R²  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1690  s    c            s«     j  d  t | |  | | | |  t d  t | | | | | | | | |  t d  |  |  t | | | | | | | |  | |  t d  |  S(   Ni  i   iÿÿÿÿ(   R°  RÀ  Rà  R   R€  (   R¯  RU  R­  R®  R±  R²  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1691  s    c            sª     j  d  t | |  | | | |  t d  t | | | | | | | | |  t d  |  |  t | | | | | | | |  | |  t d  |  S(   Ni  i   iÿÿÿÿ(   R°  RÀ  Rà  R   R€  (   R¯  RU  R­  R®  R±  R²  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1692  s    c            sà     j  d  t | |  | | t d  | | | |  t d  t | | | | | | | | |  t d  |  |  t | | t d  | | | | | | |  t d  | | | |  t d  |  S(   Ni  i   (   R°  RÀ  Rà  R   R€  (   R¯  RU  R­  R®  R±  R²  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1693  s    c            sà     j  d  t | | |  | t d  | | | |  t d  t | | | | | | | | |  t d  |  |  t | | t d  | | | | | | |  t d  | | | |  t d  |  S(   Ni  i   (   R°  RÀ  Rà  R   R€  (   R¯  RU  R­  R®  R±  R²  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1694"  s    c            s     j  d  t | t | | | | | | | | |  t d  |  |  t | | | | | | | |  |  | | |  S(   Ni  iÿÿÿÿ(   R°  RÀ  R   Rà  R€  (   R¯  RU  R­  R®  R±  R²  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1695'  s    c            s     j  d  t t d  | t d  t t t d  | |  t d  t d  |   |  |  t | |  t d  | |  |   |   S(   Ni   i   i   (   R°  RÀ  Rà  R*   R   Rá  (   R²  R®  R±  R­  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1696,  s    c            sà     j  d  t | | |  | t d  | | | |  t d  t | | | | | | | | |  t d  |  |  t | | t d  | | | | | | |  t d  | | | |  t d  |  S(   Ni¡  i   (   R°  RÀ  Rà  R   R€  (   R¯  RU  R­  R®  R±  R²  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement16971  s    c      	      sÓ     j  d  t | |  t d  | t d  | | t d  t | |  | t | | |  | | |  |  |  t t d  | | t d  t | | |  | | |  | | t d  |  S(   Ni¢  i   iþÿÿÿi   (   R°  RÀ  Rà  R   Rá  R€  (   RU  R­  R®  R±  R²  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement16986  s    c      	      s     j  d  t | | t |   | | | | | t |   | | | | | | t |   t | | |  | | | | | |  |  |  S(   Ni£  (   R°  RÀ  R%   R   (   R¯  RU  R­  R®  R±  R²  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1699;  s    c            sf     j  d  t t d  t | | t d   t t | | | | | | |  |  | |  |  S(   Ni€  i   (   R°  RÀ  Rà  R2   R*   R   (   R¯  RŸ  RU  R­  R®  R±  R²  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1700@  s    c            sX     j  d  t t d  | t t | | | | | | |  |  | | |  |  S(   Ni¥  i   (   R°  RÀ  Rà  R*   R   (   R¯  RU  R¶  R­  R®  R±  R²  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1701E  s    c            s     j  d  t | | t d  | | | | t d  | | | | | | |  t d  | | | |  t d  |  S(   NiŠ  iÿÿÿÿi   (   R°  R€  Rà  (   R¯  RU  R¶  R­  R¬  R®  R±  R²  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1702J  s    c            s    j  d  t | | | | | |  | t d  | | | |  t d  t | | | | | | | | | | |  t d  |  |  t | | t d  | | | | t d  | | | | | | |  t d  | | | |  t d  |  S(   Ni§  i   iÿÿÿÿ(   R°  RÀ  Rà  R   R€  (   R¯  RU  R¶  R­  R¬  R®  R±  R²  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1703O  s    c            s    j  d  t | | | | | | | |  | t d  | | |  | t d  t | | | | | | | | | | | |  |  |  t | | t d  | | | | t d  | | | | | | |  t d  | | |  | t d  |  S(   Niš  i   iÿÿÿÿ(   R°  RÀ  Rà  R   R€  (   R¯  RU  R¶  R­  R¬  R®  R±  R²  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1704T  s    c            sq     j  d  t | t |  | t |  | | t |  t | | | | | | | | |  |  |  S(   Ni©  (   R°  RÀ  R$   R%   R   (   R¯  RU  R¶  R­  R®  R±  R¬  R²  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1705Y  s    c      	      sx     j  d  t t d  | t t | t d  | t d  | | | | | | | |  |  | | |  |  S(   Niª  i   iÿÿÿÿ(   R°  RÀ  Rà  R*   R   (   R¯  RU  R¶  R­  R®  R±  R²  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1706^  s    c            sq     j  d  t | t |  | t |  | | t |  t | | | | | | | | |  |  |  S(   Ni«  (   R°  RÀ  R$   R%   R   (   R¯  RU  R¶  R­  R¬  R®  R±  R²  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1707c  s    c            sÚ     j  d  t | | | |  | | | |  | t d  t | | | | | | | | | | |  t d  |  |  t | | | t d  | | | | | | |  | | |  | t d  |  S(   Ni¬  i   iÿÿÿÿ(   R°  RÀ  Rà  R   R€  (   R¯  RU  R¶  R­  R¬  R±  R®  R²  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1708h  s    c            sÙ     j  d  t | | | |  | | | | |  t d  t | | | | | | | | | | |  t d  |  |  t | | | t d  | | | | | | |  | | | |  t d  |  S(   Ni­  i   iÿÿÿÿ(   R°  RÀ  Rà  R   R€  (   R¯  RU  R¶  R­  R¬  R®  R±  R²  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1709m  s    c            s    j  d  t | | | |  | | | t d  | | | |  t d  t | | | | | | | | | | |  t d  |  |  t | | t d  | | | | t d  | | | | | | |  t d  | | | |  t d  |  S(   Ni®  i   iÿÿÿÿ(   R°  RÀ  Rà  R   R€  (   R¯  RU  R¶  R­  R¬  R®  R±  R²  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1710r  s    c            s    j  d  t | | | | | |  | t d  | | | |  t d  t | | | | | | | | | | |  t d  |  |  t | | t d  | | | | t d  | | | | | | |  t d  | | | |  t d  |  S(   Ni¯  i   iÿÿÿÿ(   R°  RÀ  Rà  R   R€  (   R¯  RU  R¶  R­  R¬  R®  R±  R²  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1711w  s    c            s    j  d  t | | | | | |  | | | t d  | | | |  t d  t | | | | | | | | | | | |  |  |  t | | t d  | | | | t d  | | | | | | |  t d  | | | |  t d  |  S(   Ni°  i   iÿÿÿÿ(   R°  RÀ  Rà  R   R€  (   R¯  RU  R¶  R­  R¬  R®  R±  R²  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1712|  s    c            s    j  d  t | | | | | | | |  | t d  | | |  | t d  t | | | | | | | | | | | |  |  |  t | | t d  | | | | t d  | | | | | | |  t d  | | |  | t d  |  S(   Ni±  i   iÿÿÿÿ(   R°  RÀ  Rà  R   R€  (   R¯  RU  R¶  R­  R¬  R®  R±  R²  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1713  s    c            s     j  d  t t d  | t d  t t | | | | t d  | | | | t d  |  |  | | | t d   |  S(   Ni²  i   (   R°  RÀ  Rà  R*   R   (   R¯  RU  R¶  R­  R®  R±  R²  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1714  s    c            sq     j  d  t | t |  | t |  | | t |  t | | | | | | | | |  |  |  S(   Ni³  (   R°  RÀ  R$   R%   R   (   R¯  RU  R¶  R­  R¬  R®  R±  R²  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1715  s    c            s­     j  d  t | | | t | | | | | | | | | | |  t d  |  |  t | | | t d  | | | | | | |  | |  | | |  S(   NiŽ  iÿÿÿÿi   (   R°  RÀ  R   Rà  R€  (   R¯  RU  R¶  R­  R¬  R®  R±  R²  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1716  s    c            s     j  d  t t d  |  | t t t d  | | t d  t d  |  | | |  t d  t | | |  | | |   |  S(   Niµ  i   i   (   R°  RÀ  Rà  R*   R   Rá  (   RU  R¶  R­  R®  R±  R²  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1717  s    c            s    j  d  t | | | | | |  | t d  | | | |  t d  t | | | | | | | | | | |  t d  |  |  t | | t d  | | | | t d  | | | | | | |  t d  | | | |  t d  |  S(   Ni¶  i   iÿÿÿÿ(   R°  RÀ  Rà  R   R€  (   R¯  RU  R¶  R­  R¬  R®  R±  R²  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1718  s    c            sq     j  d  t | t |  | t |  | | t |  t | | | | | | | | |  |  |  S(   Ni·  (   R°  RÀ  R$   R%   R   (   R¯  RU  R¶  R­  R¬  R®  R±  R²  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1719  s    c      	      sÆ     j  d  t | t |  | | t |   t |  | | t |  | | | | | t |   | | | | | | t |   t | | |  | | | | | | |  |  |  S(   Niž  (   R°  RÀ  R$   R%   R   (   R¯  RU  R¶  R­  R¬  R®  R±  R²  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1720€  s    c	   	   	      su     j  d  t | | |  | t |  | t d   t t | | | | | | | | | |  | |   |  S(   Ni¹  i   (   R°  RÀ  R2   Rà  R*   R   (	   RÏ  R¯  RŸ  RU  R¶  R­  R®  R±  R²  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1721©  s    RV  c      
      s     j  d  t t d  | t t |	 t d  | t d  | | | |	 |
 | |	 | | | |	 | | |  |	  |	 |	 |  |	  S(   Niº  i   iÿÿÿÿ(   R°  RÀ  Rà  R*   R   (   R¯  RU  RV  R¶  R­  Rº  R®  R¬  R±  R²  R³  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1722®  s    c            s     j  d  t | t |  |	 t |  | |	 t |  t |	 | | | |	 | |
 | |	 | | |	 | |  |	  |	  S(   Ni»  (   R°  RÀ  R$   R%   R   (   R¯  RU  RV  R¶  R­  Rº  R®  R±  R¬  R²  R³  R¹  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1723³  s    R%  c            s     j  d  t | |
 | t d  |
 |	 | | t d  | |	 | | |	 | | |  t d  | | |  | t d  |	  S(   NiŒ  iÿÿÿÿi   (   R°  R€  Rà  (   R¯  RU  R¶  R­  Rº  R®  R±  R%  R¬  R²  R¹  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1724ž  s    c      	      sK    j  d  t |
 | | | | |  | t d  | | | | |  | | t d  | | | |  t d  t |
 |	 | | | |	 | | |	 | | |  t d  |	  |	  t |
 | t d  |
 |	 | | t d  | | | | | |	 | | |	 | | |  t d  | | | |  t d  |	  S(   Niœ  i   iÿÿÿÿ(   R°  RÀ  Rà  R   R€  (   R¯  RU  R¶  R­  Rº  R®  R±  R%  R¬  R²  R¹  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1725œ  s    c      	      s3    j  d  t |
 | | | | |  | t d  | | | | |  | | t d  | | |  | t d  t |
 |	 | | | |	 | | |	 | | |  |	  |	  t | |
 | t d  |
 |	 | | t d  | |	 | | |	 | | |  t d  | | |  | t d  |	  S(   NiŸ  i   iÿÿÿÿ(   R°  RÀ  Rà  R   R€  (   R¯  RU  R¶  R­  Rº  R®  R±  R%  R¬  R²  R¹  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1726Â  s    c      	      s7    j  d  t | | | |  | t d  | | | | |  | | t d  | | | |  | | t d  t |
 |	 | | |	 | | |	 | | |  |	  |	  t | |
 | t d  |
 |	 | | t d  | |	 | | |	 | | |  t d  | | | |  | | t d  |	  S(   Ni¿  i   iÿÿÿÿ(   R°  RÀ  Rà  R   R€  (   R¯  RU  R¶  R­  Rº  R®  R±  R%  R¬  R²  R¹  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1727Ç  s    c            sª     j  d  t t d  | t d  t t | | |	 | | t d  |
 | |	 | | t d  | |	 | | t d  |  |	  |	 |	 | t d   |	  S(   NiÀ  i   (   R°  RÀ  Rà  R*   R   (   R¯  RU  RV  R¶  R­  Rº  R®  R±  R¬  R²  R³  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1728Ì  s    c            s     j  d  t | t |  |	 t |  | |	 t |  t |	 | | | |	 | |
 | |	 | | |	 | |  |	  |	  S(   NiÁ  (   R°  RÀ  R$   R%   R   (   R¯  RU  RV  R¶  R­  Rº  R®  R±  R¬  R²  R³  R¹  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1729Ñ  s    c            sÔ     j  d  t | t |  |	 | t |   t |  | |	 t |  | | |	 | t |   | |	 | | |	 | | t |   t |	 | |  | | | |	 | |  | | |	 | |
 |	  |	  S(   NiÂ  (   R°  RÀ  R$   R%   R   (   R¯  RU  R¶  R­  Rº  R®  R±  R%  R¬  R²  R³  R¹  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1730Ö  s    c            s¬   t  |  }   j d  t | t t | | t d  | | | | | | | | |  t t | | | |  t | | | |   |  | | t d  |  |  S(   NiÃ  iÿÿÿÿi   (	   R3   R°  RÀ  R*   R   Rà  R   Rš  RË  (   R¯  RU  R­  R  R®  R±  R²  Rº  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   With1731Ú  s    c      	      s     j  d  t t d  | t t | t d  | t d  | | | | | | | |  t | | | |  |  | | |  |  S(   NiÄ  i   iÿÿÿÿ(   R°  RÀ  Rà  R*   R   Rš  (   R¯  RU  R¶  R­  R  R®  R±  R²  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1732á  s    c	   	         s     j  d  t | t | t |   t |  | t | t |   | | t | t |   t | | | | | | | | | |  |  |  S(   NiÅ  (   R°  RÀ  RÞ  Rí  Ræ  R   (	   R¯  RU  R¶  R­  R  R®  R¬  R±  R²  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1733æ  s    c	   	         s[     j  d  t | | | | | t | | | | | | | | | |  |  |  S(   NiÆ  (   R°  RÀ  R   (	   R¯  RU  R¶  R­  R  R®  R¬  R±  R²  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1734ë  s    c   	      S   sU   t  | t t t t f  r t St | t d  |  } t | t d   rQ t	 St S(   Ni   (
   Rý  Rþ  Rä  Rÿ  Rå  R   R   Rà  R#   R  (	   R¯  RU  R¶  R­  R  R®  R±  R²  Rì  (    (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   With1735ï  s    c   	         sœ   t  | t d  |  }   j d  t t d  | t t | t d  | t d  | | | | | | | | | |  t | t | | t d  |   |  | | |  |  S(   Ni   iÇ  iÿÿÿÿ(   R   Rà  R°  RÀ  R*   R   R   RË  (	   R¯  RU  R¶  R­  R  R®  R±  R²  Rì  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1735÷  s    c	      
   S   sÍ   t  | t t t t f  r t St | |  }	 t | | |	  }
 t t	 |	 | t
 d   t | | |  |	 t
 d  t
 d   t t t
 d  |   t |  |	 t
 d  t
 d  |    rÉ t St S(   Niÿÿÿÿi   i    i   (   Rý  Rþ  Rä  Rÿ  Rå  R   Rº   R°   Râ  RP   Rà  R#   Rã  R   R  (   R¯  RU  R¶  R­  R  R¬  R®  R±  R²  R³  R_  (    (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   With1736ý  s    c	      	      s"  t  | |  }	 t | | |	  }
   j d  t | | | | | | | | | |  t | |
 | | | |	 | | |	 d | | | |  |	 d |
 | |	 |  |  t |
 | | |	 d | | | | |	 d | | | | | | |  d | | | |  |	 d |  S(   NiÈ  i   (   Rº   R°   R°  R   R1  R€  (   R¯  RU  R¶  R­  R  R¬  R®  R±  R²  R³  R_  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1736  s    c            sÀ     j  d  t t d  | t d  t t | | | | t d  | | | | t d  |  t t | | | |  t | | | | t d    |  | | | t d   |  S(   NiÉ  i   (   R°  RÀ  Rà  R*   R   R   Rš  RË  (   R¯  RU  R¶  R­  R  R®  R±  R²  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1737  s    c	   	         s     j  d  t | t | t |   t |  | t | t |   | | t | t |   t | | | | | | | | | |  |  |  S(   NiÊ  (   R°  RÀ  RÞ  Rí  Ræ  R   (	   R¯  RU  R¶  R­  R  R¬  R®  R±  R²  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1738  s    c	   	         s[     j  d  t | | | | | t | | | | | | | | | |  |  |  S(   NiË  (   R°  RÀ  R   (	   R¯  RU  R¶  R­  R  R¬  R®  R±  R²  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1739  s    c	   	         sK     j  d  t t | | | | | | | | | | |  |  |  S(   NiÌ  (   R°  R   RÊ   (	   R¯  RU  R¶  R­  R  R¬  R®  R±  R²  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1740  s    c            s?     j  d  t t | | | | | | | |  |  |  S(   NiÍ  (   R°  R   RÊ   (   R¯  RU  R­  R  R®  R±  R²  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1741"  s    c            s     j  d  t t d  t d  |  | t d  |  t t d  | | | |  t d  | t d  | | t d  |  |  |  S(   NiÎ  i   i   (   R°  RÀ  Rà  R   (   R¯  R­  Rº  R®  R²  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1742'  s    c            sA     j  d  t t | | | | | t d  |  |  |  S(   NiÏ  i   (   R°  R   R1  Rà  (   R¯  R­  Rº  R®  R²  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1743,  s    c         S   sb   t  | t t t t f  r t St | | | | | t d   } t t	 | |   r^ t
 St S(   Ni   (   Rý  Rþ  Rä  Rÿ  Rå  R   RÅ  Rà  R'   R§   R  (   R¯  R­  Rº  R®  R²  RŸ  (    (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   With17440  s    &c            sk   t  | | | | | t d   }   j d  t t | |  |  t t t | |  |   |  |  S(   Ni   iÐ  (   RÅ  Rà  R°  RÀ  RŠ   R   R  R§   (   R¯  R­  Rº  R®  R²  RŸ  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement17448  s    &c            sŽ  t  t d  | | t d  t d  t t d   | t t d  | t d  | t d  t d  | t d  |  t d   }   j d  t t d  t d  |  | t d  |  t t d  | | t d  t d  d t d  | | t d  t t d   t t d  t d  d | t d  t d  t t d   t t d  | |  t d  | | t d  t d  d t d  | | t d  t t d   t t d  t d  d | t d  t d  t t d   t t d  | |  t d  | | t d  t d  d t d  | | t d  t d  d | t d  t d  | |  |  |  S(   Ni   i   i   i   iÑ  i   i   (   R  Rà  Rá  R°  RÀ  R   Rç  (   R¯  R­  Rº  R®  R²  Rž  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   With1745>  s    c            sÒ     j  d  t t d  | | | |  t d  | t d  | | t d  |  | | | | | t d  |  t t d  | | | |  t d  | t d  | | t d  |  |  |  S(   NiÒ  i   i   (   R°  RÀ  Rà  R   (   R¯  R­  Rº  R®  R²  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1746E  s    c         S   sb   t  | t t t t f  r t St t | | | | | t d   |  } t	 |  r^ t
 St S(   Ni   (   Rý  Rþ  Rä  Rÿ  Rå  R   R§   RÅ  Rà  R'   R  (   R¯  R­  Rº  R®  R²  RŸ  (    (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   With1747I  s    /c            s   t  t | | | | | t d   |  }   j d  t | | | | | t d  |  t | |   t t | |   |  |  S(   Ni   iÓ  (   R§   RÅ  Rà  R°  RÀ  R  R   (   R¯  R­  Rº  R®  R²  RŸ  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1747Q  s    /c            s  t  t d  | | t d  t d  t t d   | t t d  | t d  | t d  t d  | t d  |  t d   }   j d  t t d  | | t d  t d  d t d  | | t d  t t d   t t d  t d  d | t d  t d  t t d   t t d  | |  t d  | | t d  t d  d t d  | | t d  t t d   t t d  t d  d | t d  t d  t t d   t t d  | |  t d  | | t d  t d  d t d  | | t d  t d  d | t d  t d  | |  | | | | | t d  |  t t d  | | t d  t d  d t d  | | t d  t t d   t t d  t d  d | t d  t d  t t d   t t d  | |  t d  | | t d  t d  d t d  | | t d  t t d   t t d  t d  d | t d  t d  t t d   t t d  | |  t d  | | t d  t d  d t d  | | t d  t d  d | t d  t d  | |  |  |  S(   Ni   i   i   i   iÔ  i   i   (   R  Rà  Rá  R°  RÀ  Rç  R   (   R¯  R­  Rº  R®  R²  Rž  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   With1748W  s    c            s¢     j  d  t t d  t d  |  | t d  |  t t d  | | | |  t d  | t d  | | t d  |  | | | | |  |  S(   NiÕ  i   i   (   R°  RÀ  Rà  R   (   R¯  R¶  R»  R­  Rº  R®  R²  R¹  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1749^  s    c            sQ     j  d  t t | | | | | | | | | t d  |  |  |  S(   NiÖ  i   (   R°  R   RÊ   Rà  (   R¯  R¶  R»  R­  Rº  R®  R²  R¹  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1750c  s    c   	      S   sb   t  | t t t t f  r t St | | | | | t d   } t t	 | |   r^ t
 St S(   Ni   (   Rý  Rþ  Rä  Rÿ  Rå  R   RÅ  Rà  R'   R§   R  (	   R¯  R¶  R»  R­  Rº  R®  R²  R¹  RŸ  (    (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   With1751g  s    &c   	         s{   t  | | | | | t d   }   j d  t t | |  |  t | | | | t t | |  |   |  |  S(   Ni   i×  (   RÅ  Rà  R°  RÀ  RŠ   R   R  R§   (	   R¯  R¶  R»  R­  Rº  R®  R²  R¹  RŸ  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1751o  s    &c   	         sÄ  t  t d  | | t d  t d  t t d   | t t d  | t d  | t d  t d  | t d  |  t d   }   j d  t t d  t d  |  | t d  |  t | | | | t d  | | t d  t d  d t d  | | t d  t t d   t t d  t d  d | t d  t d  t t d   t t d  | |  t d  | | t d  t d  d t d  | | t d  t t d   t t d  t d  d | t d  t d  t t d   t t d  | |  t d  | | t d  t d  d t d  | | t d  t d  d | t d  t d  | |  |  |  S(   Ni   i   i   i   iØ  i   i   (   R  Rà  Rá  R°  RÀ  R   Rç  (	   R¯  R¶  R»  R­  Rº  R®  R²  R¹  Rž  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   With1752u  s    c            sâ     j  d  t t d  | | | |  t d  | t d  | | t d  |  | | | | | t d  |  t t d  | | | |  t d  | t d  | | t d  |  | | | | |  |  S(   NiÙ  i   i   (   R°  RÀ  Rà  R   (   R¯  R¶  R»  R­  Rº  R®  R²  R¹  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1753|  s    c   	      S   sb   t  | t t t t f  r t St t | | | | | t d   |  } t	 |  r^ t
 St S(   Ni   (   Rý  Rþ  Rä  Rÿ  Rå  R   R§   RÅ  Rà  R'   R  (	   R¯  R¶  R»  R­  Rº  R®  R²  R¹  RŸ  (    (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   With1754  s    /c   	         s   t  t | | | | | t d   |  }   j d  t | | | | | t d  |  t | |   t | | | | t | |   |  |  S(   Ni   iÚ  (   R§   RÅ  Rà  R°  RÀ  R  R   (	   R¯  R¶  R»  R­  Rº  R®  R²  R¹  RŸ  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1754  s    /c   	         s  t  t d  | | t d  t d  t t d   | t t d  | t d  | t d  t d  | t d  |  t d   }   j d  t t d  | | t d  t d  d t d  | | t d  t t d   t t d  t d  d | t d  t d  t t d   t t d  | |  t d  | | t d  t d  d t d  | | t d  t t d   t t d  t d  d | t d  t d  t t d   t t d  | |  t d  | | t d  t d  d t d  | | t d  t d  d | t d  t d  | |  | | | | | t d  |  t | | | | t d  | | t d  t d  d t d  | | t d  t t d   t t d  t d  d | t d  t d  t t d   t t d  | |  t d  | | t d  t d  d t d  | | t d  t t d   t t d  t d  d | t d  t d  t t d   t t d  | |  t d  | | t d  t d  d t d  | | t d  t d  d | t d  t d  | |  |  |  S(   Ni   i   i   i   iÛ  i   i   (   R  Rà  Rá  R°  RÀ  Rç  R   (	   R¯  R¶  R»  R­  Rº  R®  R²  R¹  Rž  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   With1755  s    c            s     j  d  t t d  t d  |  | t d  |  t | t d  | | |  t d  | t d  | | t d  |  |  |  S(   NiÜ  i   i   (   R°  RÀ  Rà  R   (   R¯  Rº  R®  R¬  R²  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1756  s    c            sK     j  d  t t | | | t d  | | t d  |  |  |  S(   NiÝ  i   i   (   R°  R   R1  Rà  (   R¯  Rº  R®  R¬  R²  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1757  s    c         S   sl   t  | t t t t f  r t St | | | t d  | | t d   } t t	 | |   rh t
 St S(   Ni   i   (   Rý  Rþ  Rä  Rÿ  Rå  R   RÅ  Rà  R'   R§   R  (   R¯  Rº  R®  R¬  R²  RŸ  (    (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   With1758  s    0c            su   t  | | | t d  | | t d   }   j d  t t | |  |  t t t | |  |   |  |  S(   Ni   i   iÞ  (   RÅ  Rà  R°  RÀ  RŠ   R   R  R§   (   R¯  Rº  R®  R¬  R²  RŸ  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1758Š  s    0c            sè  t  t d  | | t d  t d  | t d  t d  t t d   | t t d  | t d  | t d  t d  | | t d   t d   }   j d  t t d  t d  |  | t d  |  t | t d  | | t d  t d  d t d  | t d  t d  t d  d | t d  t d  | |  | t d  | | t d  t d  d t d  | t d  t d  t t d   t t d  t d  d | t d  t d  t t d   t t d  | |  | t d  | | t d  t d  d t d  | t d  t d  t t d   t t d  t d  d | t d  t d  t t d   t t d  | |  |  |  S(   Ni   i   i   i   iß  i   (   R  Rà  Rá  R°  RÀ  R   Rç  (   R¯  Rº  R®  R¬  R²  Rž  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   With1759¬  s    ¬c            sÜ     j  d  t | t d  | | |  t d  | t d  | | t d  |  | | | t d  | | t d  |  t | t d  | | |  t d  | t d  | | t d  |  |  |  S(   Nià  i   i   (   R°  RÀ  Rà  R   (   R¯  Rº  R®  R¬  R²  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1760³  s    c         S   sl   t  | t t t t f  r t St t | | | t d  | | t d   |  } t	 |  rh t
 St S(   Ni   i   (   Rý  Rþ  Rä  Rÿ  Rå  R   R§   RÅ  Rà  R'   R  (   R¯  Rº  R®  R¬  R²  RŸ  (    (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   With1761·  s    9c            s   t  t | | | t d  | | t d   |  }   j d  t | | | t d  | | t d  |  t | |   t t | |   |  |  S(   Ni   i   iá  (   R§   RÅ  Rà  R°  RÀ  R  R   (   R¯  Rº  R®  R¬  R²  RŸ  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1761¿  s    9c            sÝ  t  t d  | | t d  t d  | t d  t d  t t d   | t t d  | t d  | t d  t d  | | t d   t d   }   j d  t | | | t d  | | t d  |  | t d  | | t d  t d  d t d  | t d  t d  t d  d | t d  t d  | |  | t d  | | t d  t d  d t d  | t d  t d  t t d   t t d  t d  d | t d  t d  t t d   t t d  | |  | t d  | | t d  t d  d t d  | t d  t d  t t d   t t d  t d  d | t d  t d  t t d   t t d  | |  t | t d  | | t d  t d  d t d  | t d  t d  t d  d | t d  t d  | |  | t d  | | t d  t d  d t d  | t d  t d  t t d   t t d  t d  d | t d  t d  t t d   t t d  | |  | t d  | | t d  t d  d t d  | t d  t d  t t d   t t d  t d  d | t d  t d  t t d   t t d  | |  |  |  S(   Ni   i   i   i   iâ  i   (   R  Rà  Rá  R°  RÀ  Rç  R   (   R¯  Rº  R®  R¬  R²  Rž  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   With1762Å  s    ¬c            s£     j  d  t t d  t d  |  | t d  |  t | t d  | | |  t d  | t d  | | t d  |  | | | | |  |  S(   Niã  i   i   (   R°  RÀ  Rà  R   (   R¯  R¶  R»  Rº  R¬  R®  R²  R¹  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1763Ì  s    c            s[     j  d  t t | | | | | | | t d  | | t d  |  |  |  S(   Niä  i   i   (   R°  R   RÊ   Rà  (   R¯  R¶  R»  Rº  R¬  R®  R²  R¹  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1764Ñ  s    c   	      S   sl   t  | t t t t f  r t St | | | t d  | | t d   } t t	 | |   rh t
 St S(   Ni   i   (   Rý  Rþ  Rä  Rÿ  Rå  R   RÅ  Rà  R'   R§   R  (	   R¯  R¶  R»  Rº  R¬  R®  R²  R¹  RŸ  (    (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   With1765Õ  s    0c   	         s   t  | | | t d  | | t d   }   j d  t t | |  |  t | | | | t t | |  |   |  |  S(   Ni   i   iå  (   RÅ  Rà  R°  RÀ  RŠ   R   R  R§   (	   R¯  R¶  R»  Rº  R¬  R®  R²  R¹  RŸ  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1765Ý  s    0c   	         sø  t  t d  | | t d  t d  | t d  t d  t t d   | t t d  | t d  | t d  t d  | | t d   t d   }   j d  t t d  t d  |  | t d  |  t | | | | | t d  | | t d  t d  d t d  | t d  t d  t d  d | t d  t d  | |  | t d  | | t d  t d  d t d  | t d  t d  t t d   t t d  t d  d | t d  t d  t t d   t t d  | |  | t d  | | t d  t d  d t d  | t d  t d  t t d   t t d  t d  d | t d  t d  t t d   t t d  | |  |  |  S(   Ni   i   i   i   iæ  i   (   R  Rà  Rá  R°  RÀ  R   Rç  (	   R¯  R¶  R»  Rº  R¬  R®  R²  R¹  Rž  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   With1766ã  s    ¬c            sì     j  d  t | t d  | | |  t d  | t d  | | t d  |  | | | t d  | | t d  |  t | t d  | | |  t d  | t d  | | t d  |  | | | | |  |  S(   Niç  i   i   (   R°  RÀ  Rà  R   (   R¯  R¶  R»  Rº  R¬  R®  R²  R¹  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1767ê  s    c   	      S   sl   t  | t t t t f  r t St t | | | t d  | | t d   |  } t	 |  rh t
 St S(   Ni   i   (   Rý  Rþ  Rä  Rÿ  Rå  R   R§   RÅ  Rà  R'   R  (	   R¯  R¶  R»  Rº  R¬  R®  R²  R¹  RŸ  (    (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   With1768î  s    9c   	         s­   t  t | | | t d  | | t d   |  }   j d  t | | | t d  | | t d  |  t | |   t | | | | t | |   |  |  S(   Ni   i   iè  (   R§   RÅ  Rà  R°  RÀ  R  R   (	   R¯  R¶  R»  Rº  R¬  R®  R²  R¹  RŸ  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1768ö  s    9c   	         sí  t  t d  | | t d  t d  | t d  t d  t t d   | t t d  | t d  | t d  t d  | | t d   t d   }   j d  t | | | t d  | | t d  |  | t d  | | t d  t d  d t d  | t d  t d  t d  d | t d  t d  | |  | t d  | | t d  t d  d t d  | t d  t d  t t d   t t d  t d  d | t d  t d  t t d   t t d  | |  | t d  | | t d  t d  d t d  | t d  t d  t t d   t t d  t d  d | t d  t d  t t d   t t d  | |  t | | | | | t d  | | t d  t d  d t d  | t d  t d  t d  d | t d  t d  | |  | t d  | | t d  t d  d t d  | t d  t d  t t d   t t d  t d  d | t d  t d  t t d   t t d  | |  | t d  | | t d  t d  d t d  | t d  t d  t t d   t t d  t d  d | t d  t d  t t d   t t d  | |  |  |  S(   Ni   i   i   i   ié  i   (   R  Rà  Rá  R°  RÀ  Rç  R   (	   R¯  R¶  R»  Rº  R¬  R®  R²  R¹  Rž  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   With1769ü  s    ¬c            sY     j  d  t t d  |  | |  | |  t | | | t d  |  |  |  S(   Niê  i   (   R°  RÀ  Rà  R   (   R¯  R­  Rº  R¬  R®  R²  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1770  s    c      	      s¡     j  d  t t d  |  | |  | |  t t t d  | | | | t d  | t d  | t d  |  |  | | t d  | |  |  S(   Nië  i   (   R°  RÀ  Rà  R*   R   (   R¯  R­  Rº  R¬  R®  R²  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1771  s    c            s  t  t d  | | | | t d  t d   }   j d  t t d  |  | |  | |  t | | | | |  | | | | t d  t t d   t t d  |  | | | | t d  t t d   t t d  |  |  |  S(   Ni   iì  i   i   (   R  Rà  R°  RÀ  R   Rá  Rç  (   R¯  R­  Rº  R¬  R®  R²  Rž  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   With1772  s    6c            sS     j  d  t t | | | | | t d  | | t d  |  |  |  S(   Nií  i   i   (   R°  R   R1  Rà  (   R¯  R­  Rº  R¬  R®  R²  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1773  s    c         S   st   t  | t t t t f  r t St | | | | | t d  | | t d   } t t	 | |   rp t
 St S(   Ni   i   (   Rý  Rþ  Rä  Rÿ  Rå  R   RÅ  Rà  R'   R§   R  (   R¯  R­  Rº  R¬  R®  R²  RŸ  (    (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   With1774  s    8c            s}   t  | | | | | t d  | | t d   }   j d  t t | |  |  t t t | |  |   |  |  S(   Ni   i   iî  (   RÅ  Rà  R°  RÀ  RŠ   R   R  R§   (   R¯  R­  Rº  R¬  R®  R²  RŸ  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1774  s    8c      
      s    j  d  t t d  t d  |  | t d  |  t t t d  | | t d  t d  | | | t d  | t d  t d  | t d  | t d  t d  | | t d  | | | t d  |  |  | | t d  | |  |  S(   Niï  i   i   i   i	   (   R°  RÀ  Rà  R*   R   (   R¯  R­  Rº  R¬  R®  R²  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1775&  s    c            s     j  d  t | | | t d  |  | | | | | t d  | | t d  |  t | | | t d  |  |  |  S(   Nið  i   i   (   R°  RÀ  Rà  R   (   R¯  R­  Rº  R¬  R®  R²  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1776+  s    c      
      s£  t  t d  | | | | t d  t d   }   j d  t | | | | |  | | | | t d  t t d   t t d  |  | | | | t d  t t d   t t d  |  | | | | | t d  | | t d  |  t | | | | |  | | | | t d  t t d   t t d  |  | | | | t d  t t d   t t d  |  |  |  S(   Ni   iñ  i   i   (   R  Rà  R°  RÀ  Rá  Rç  R   (   R¯  R­  Rº  R¬  R®  R²  Rž  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   With1777/  s    6c            s£  t  t d  | | | | t d  t d   }   j d  t | | | | |  | | | | t d  t t d   t t d  |  | | | | t d  t t d   t t d  |  | | | | | t d  | | t d  |  t | | | | |  | | | | t d  t t d   t t d  |  | | | | t d  t t d   t t d  |  |  |  S(   Ni   iò  i   i   (   R  Rà  R°  RÀ  Rá  Rç  R   (   R¯  R­  Rº  R¬  R®  R²  Rž  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   With17785  s    6c         S   st   t  | t t t t f  r t St t | | | | | t d  | | t d   |  } t	 |  rp t
 St S(   Ni   i   (   Rý  Rþ  Rä  Rÿ  Rå  R   R§   RÅ  Rà  R'   R  (   R¯  R­  Rº  R¬  R®  R²  RŸ  (    (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   With1779;  s    Ac            s­   t  t | | | | | t d  | | t d   |  }   j d  t | | | | | t d  | | t d  |  t | |   t t | |   |  |  S(   Ni   i   ió  (   R§   RÅ  Rà  R°  RÀ  R  R   (   R¯  R­  Rº  R¬  R®  R²  RŸ  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1779C  s    Ac            s  t  t d  | | t d  t d  | | | t d  | t d  t d  t t d   | t t d  | t d  | t d  t d  | | | | t d  | | t d  t d  | t d  | | t d  | t d   t d   }   j d  t | t d  | | t d  t d  d t d	  | | t d  | t d  t d  t d  d | t d  t d  | |  | t d  | | t d  t d  d t d	  | | t d  t t d   t t d  | t d  t d  t t d   t t d  t d  d t | t d  t t d   t t d  | |  | t d  | | t d  t d  d t d	  | | t d  t t d   t t d  | t d  t d  t t d   t t d  t d  d t | t d  t t d   t t d  | |  | | | | | t d  | | t d  |  t | t d  | | t d  t d  d t d	  | | t d  | t d  t d  t d  d | t d  t d  | |  | t d  | | t d  t d  d t d	  | | t d  t t d   t t d  | t d  t d  t t d   t t d  t d  d t | t d  t t d   t t d  | |  | t d  | | t d  t d  d t d	  | | t d  t t d   t t d  | t d  t d  t t d   t t d  t d  d t | t d  t t d   t t d  | |  |  |  S(
   Ni   i   i	   i   i   i   iô  i   i   (   R  Rà  Rá  R°  RÀ  Rç  R   (   R¯  R­  Rº  R¬  R®  R²  Rž  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   With1780I  s    ÿ c            s'     j  d  t t | |   | |   S(   Niõ  (   R°  R   R1  (   R²  R¯  RŸ  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1781P  s    c	   	         si     j  d  t t d  |  | |  | |  t | | | t d  |  | | | | |  |  S(   Niö  i   (   R°  RÀ  Rà  R   (	   R¯  R¶  R»  R­  Rº  R®  R¬  R²  R¹  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1782U  s    c	   
   
      s  t  t d  | | | | t d  t d   }	   j d  t t d  |  | |  | |  t | | | | | | | |	 |  | | | |	 t d  t t d   t t d  |  | | | |	 t d  t t d   t t d  |  |  |  S(   Ni   i÷  i   i   (   R  Rà  R°  RÀ  R   Rá  Rç  (
   R¯  R¶  R»  R­  Rº  R®  R¬  R²  R¹  Rž  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   With1783Y  s    6c	   
         s  t  t d  | | | | t d  t d   }	   j d  t t d  |  | |  | |  t | | | |	 |  | | | |	 t d  t t d   t t d  |  | | | |	 t d  t t d   t t d  |  | | | | |  |  S(   Ni   iø  i   i   (   R  Rà  R°  RÀ  R   Rá  Rç  (
   R¯  R¶  R»  R­  Rº  R®  R¬  R²  R¹  Rž  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   With1784_  s    6c	   	         sc     j  d  t t | | | | | | | | | t d  | | t d  |  |  |  S(   Niù  i   i   (   R°  R   RÊ   Rà  (	   R¯  R¶  R»  R­  Rº  R®  R¬  R²  R¹  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1785f  s    c	   
      S   st   t  | t t t t f  r t St | | | | | t d  | | t d   }	 t t	 |	 |   rp t
 St S(   Ni   i   (   Rý  Rþ  Rä  Rÿ  Rå  R   RÅ  Rà  R'   R§   R  (
   R¯  R¶  R»  R­  Rº  R®  R¬  R²  R¹  RŸ  (    (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   With1786j  s    8c	   
         s   t  | | | | | t d  | | t d   }	   j d  t t |	 |  |  t | | | | t t |	 |  |   |  |  S(   Ni   i   iú  (   RÅ  Rà  R°  RÀ  RŠ   R   R  R§   (
   R¯  R¶  R»  R­  Rº  R®  R¬  R²  R¹  RŸ  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1786r  s    8c	   	   
      s    j  d  t t d  t d  |  | t d  |  t t t d  | | t d  t d  | | | t d  | t d  t d  | t d  | t d  t d  | | t d  | | | t d  |  |  | | t d  | |  |  S(   Niû  i   i   i   i	   (   R°  RÀ  Rà  R*   R   (	   R¯  R¶  R»  R­  Rº  R®  R¬  R²  R¹  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1787y  s    c	   	         s     j  d  t | | | t d  |  | | | | | t d  | | t d  |  t | | | t d  |  | | | | |  |  S(   Niü  i   i   (   R°  RÀ  Rà  R   (	   R¯  R¶  R»  R­  Rº  R®  R¬  R²  R¹  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1788~  s    c	   
   
      s³  t  t d  | | | | t d  t d   }	   j d  t | | | |	 |  | | | |	 t d  t t d   t t d  |  | | | |	 t d  t t d   t t d  |  | | | | | t d  | | t d  |  t | | | | | | | |	 |  | | | |	 t d  t t d   t t d  |  | | | |	 t d  t t d   t t d  |  |  |  S(   Ni   iý  i   i   (   R  Rà  R°  RÀ  Rá  Rç  R   (
   R¯  R¶  R»  R­  Rº  R®  R¬  R²  R¹  Rž  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   With1789  s    6c	   
         s³  t  t d  | | | | t d  t d   }	   j d  t | | | |	 |  | | | |	 t d  t t d   t t d  |  | | | |	 t d  t t d   t t d  |  | | | | | t d  | | t d  |  t | | | |	 |  | | | |	 t d  t t d   t t d  |  | | | |	 t d  t t d   t t d  |  | | | | |  |  S(   Ni   iþ  i   i   (   R  Rà  R°  RÀ  Rá  Rç  R   (
   R¯  R¶  R»  R­  Rº  R®  R¬  R²  R¹  Rž  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   With1790  s    6c	   
      S   st   t  | t t t t f  r t St t | | | | | t d  | | t d   |  }	 t	 |	  rp t
 St S(   Ni   i   (   Rý  Rþ  Rä  Rÿ  Rå  R   R§   RÅ  Rà  R'   R  (
   R¯  R¶  R»  R­  Rº  R®  R¬  R²  R¹  RŸ  (    (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   With1791  s    Ac	   
         sœ   t  t | | | | | t d  | | t d   |  }	   j d  t | | | | | t d  | | t d  |  t |	 |   t | | | | t |	 |   |  |  S(   Ni   i   iÿ  (   R§   RÅ  Rà  R°  RÀ  R  R   (
   R¯  R¶  R»  R­  Rº  R®  R¬  R²  R¹  RŸ  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1791  s    Ac	   
         s/  t  t d  | | t d  t d  | | | t d  | t d  t d  t t d   | t t d  | t d  | t d  t d  | | | | t d  | | t d  t d  | t d  | | t d  | t d   t d   }	   j d  t | t d  | | t d  t d  d t d	  | | t d  | t d  t d  t d  d |	 t d  t d  |	 |  | t d  | | t d  t d  d t d	  | | t d  t t d   t t d  | t d  t d  t t d   t t d  t d  d t |	 t d  t t d   t t d  |	 |  | t d  | | t d  t d  d t d	  | | t d  t t d   t t d  | t d  t d  t t d   t t d  t d  d t |	 t d  t t d   t t d  |	 |  | | | | | t d  | | t d  |  t | | | | | t d  | | t d  t d  d t d	  | | t d  | t d  t d  t d  d |	 t d  t d  |	 |  | t d  | | t d  t d  d t d	  | | t d  t t d   t t d  | t d  t d  t t d   t t d  t d  d t |	 t d  t t d   t t d  |	 |  | t d  | | t d  t d  d t d	  | | t d  t t d   t t d  | t d  t d  t t d   t t d  t d  d t |	 t d  t t d   t t d  |	 |  |  |  S(
   Ni   i   i	   i   i   i   i   i   i   (   R  Rà  Rá  R°  RÀ  Rç  R   (
   R¯  R¶  R»  R­  Rº  R®  R¬  R²  R¹  Rž  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   With1792  s    ÿ c            s8     j  d  t t | |  | t |  |  | |  S(   Ni  (   R°  R   R1  (   RÏ  R¯  RŸ  R¶  R²  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1793£  s    c            s2    j  d  t | | t | | | t d  | | | t d  | t d  t d  | | | t d  t d  t | | t d  | | | t d  | | | | t d   t | t d  t d  | | t d    | t | t d  t d  | | t d   |  S(   Ni  i   i   i   (   R°  R€  R=   Rà  Rá  R  (   Rì  R­  R»  Rº  R¬  R®  R²  R¹  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1794š  s    c            s5    j  d  t | | t | | | t d  | | | t d  | t d  t d  | | | t d  t d  t | | t d  | | | t d  | | | | t d   t | t d  t d  | | t d    | t | t d  t d  | | t d   |  S(   Ni  i   i   i   (   R°  R€  Rû  Rà  Rá  R  (   Rì  R­  R»  Rº  R¬  R®  R²  R¹  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1795­  s    c      
      sË     j  d  t t t | | | t d  | | t d  t d  | t d  | | t d  | t d  | t d  | t d  t d  | |  |  |  | | t d  | |  S(   Ni  i   i   i   i   i   (   R°  R*   R   R,  Rà  (   R¯  R­  Rº  R¬  R®  R²  R¹  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1796²  s    c         S   sö   t  | t t t t f  r t St |  | t d   } t |  | t d   } t |  | t d   } t |  | t d   } t |  | t d   } t t	 t d  | | t d  t d  | | | | t d   t
 |   rò t St S(   Ni    i   i   i   i   i   (   Rý  Rþ  Rä  Rÿ  Rå  R   R2   Rà  Râ  R   R   R  (   RÏ  R²  R¯  R®  R­  R¬  Rº  R¹  (    (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   With1797¶  s    Wc      
      sC  t  |  | t d   } t  |  | t d   } t  |  | t d   } t  |  | t d   } t  |  | t d   }   j d  t t t | | | t d  | | t d  t d  | t d  | | t d  | t d  | t d  | t d  t d  | | |  |  | | t d  | |  S(	   Ni    i   i   i   i   i  i   i   (   R2   Rà  R°  R*   R   R,  (   RÏ  R²  R¯  R®  R­  R¬  Rº  R¹  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1797Â  s    c            sô     j  d  t t t | | | t d  | | t d  t d  | t d  | | t d  | t d  | t d  | t d  t d  | |  t | t | | t d  | |   |  |  | | t d  | |  S(   Ni  i   i   i   i   i   (   R°  R*   R   R,  Rà  R   RË  (   R¯  RŸ  R­  Rº  R¬  R®  R²  R¹  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1798Í  s    c   	      S   sö   t  | t t t t f  r t St |  | t d   } t |  | t d   } t |  | t d   } t |  | t d   } t |  | t d   } t t	 t d  | | t d  t d  | | | | t d   t
 |   rò t St S(   Ni    i   i   i   i   i   (   Rý  Rþ  Rä  Rÿ  Rå  R   R2   Rà  Râ  R   R   R  (	   RÏ  R²  R¯  RŸ  R®  R­  R¬  Rº  R¹  (    (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   With1799Ñ  s    Wc   	         sl  t  |  | t d   } t  |  | t d   } t  |  | t d   } t  |  | t d   } t  |  | t d   }   j d  t t t | | | t d  | | t d  t d  | t d  | | t d  | t d  | t d  | t d  t d  | | t | t | | t d  | |   |  |  | | t d  | |  S(	   Ni    i   i   i   i   i  i   i   (   R2   Rà  R°  R*   R   R,  R   RË  (	   RÏ  R²  R¯  RŸ  R®  R­  R¬  Rº  R¹  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1799Ý  s    c            s    j  d  t t d  | t d  t t | t d  | t d  | t d  t d  | t d  | t d  | t d  | | t d  | t d  | t d  t d	  | | t d  | t d  t d  | | t d  | t d  | t d  t d  | | | t d  |  t d  | | | t d  |  | t d
  | | t d  |  |  S(   Ni  i   i   i   i   i   i@   i    i   i   (   R°  RÀ  Rà  R*   R   (   R¯  R­  Rº  R¬  R®  R²  R¹  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1800è  s    c         S   sÿ   t  | t t t t f  r t St |  | t d   } t |  | t d   } t |  | t d   } t |  | t d   } t |  | t d   } t t	 |  t	 |  t
 t d  | t d  | t d  | | | | t d    rû t St S(   Ni    i   i   i   i   i   (   Rý  Rþ  Rä  Rÿ  Rå  R   R2   Rà  Râ  R   R   R  (   RÏ  R²  R¯  R®  R­  R¬  Rº  R¹  (    (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   With1801ì  s    `c            s  t  |  | t d   } t  |  | t d   } t  |  | t d   } t  |  | t d   } t  |  | t d   }   j d  t t d  | t d  t t | t d  | t d  | t d  t d  | t d  | t d	  | t d  | | t d
  | t d  | t d  t d  | | t d  | t d  t d  | | t d  | t d  | t d  t d  | | | t d  | t d  | | | t d  |  | t d  | | t d  |  |  S(   Ni    i   i   i   i   i	  i   i   i@   i    i   (   R2   Rà  R°  RÀ  R*   R   (   RÏ  R²  R¯  R®  R­  R¬  Rº  R¹  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1801ø  s    c
      	      sÐ  t  t d  | t d  t d  | | | t d   }
   j d  t t d  |
 t |	 | |	 |
 t d  |  | t d  | | | t d  |	 | t d  | | | | | |
 t d  | | t d  t d  | | | |
 |  |  t t d  |
 t |	 | |	 |
 t d  |  | t d  | | | t d  |	 | t d  | | | | | |
 t d  | | t d  t d  | | | |
 |  |  S(   Ni   i   i   i
  i   (   Rá  Rà  R°  RÀ  R   (   R  R  R¹  R­  R¿  Rº  R¬  R®  R²  R  R³  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   With1802	  s    @R¿  c	   
   	      s¬  t  t d  | t d  t d  | | | t d   }	   j d  t t d  |	 t | | | |	 t d  |  | t d  | | | t d  | | | | | |	 t d  | | t d  t d  | | | |	 |  |  t t d  |	 t | | | |	 t d  |  | t d  | | | t d  | | | | | |	 t d  | | t d  t d  | | | |	 |  |  S(   Ni   i   i   i  i   (   Rá  Rà  R°  RÀ  R   (
   R  R¹  R­  R¿  Rº  R¬  R®  R²  R  R³  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   With1803	  s    @c      
      sà  t  t d  | t d  t d  | | | t d   }   j d  t t d  | t |	 | |
 | |
 | t d  |  | t d  | | |	 t d  |
 | t d  | | | | | | t d  | |	 t d  t d  | |	 | | |	  |	  t t d  | t |	 | |
 | |
 | t d  |  | t d  | | |	 t d  |
 | t d  | | | | | | t d  | |	 t d  t d  | |	 | | |	  |	  S(   Ni   i   i   i  i   (   Rá  Rà  R°  RÀ  R   (   R  R  R¹  R¶  R­  R¿  Rº  R¬  R®  R²  R  R³  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   With1804	  s    @c
      
      sŒ  t  t d  | t d  t d  | | | t d   }
   j d  t t d  |
 t | | |	 | |	 |
 t d  |  | t d  | | | t d  |	 | | | | |
 t d  | | t d  t d  | | | |
 |  |  t t d  |
 t | | |	 | |	 |
 t d  |  | t d  | | | t d  |	 | | | | |
 t d  | | t d  t d  | | | |
 |  |  S(   Ni   i   i   i  i   (   Rá  Rà  R°  RÀ  R   (   R  R¹  R¶  R­  R¿  Rº  R¬  R®  R²  R  R³  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   With1805	  s    @c	   
   
      s  t  | | t d  | | | t d  t d  | t d  | | |  | t d   }	   j d  t t d  | t d  t |  | | | t d  | | | |	  |	 |  t t d  | t d  t | t d  | |  | t d  | | | t d  |  t d  | t d  |  | | t d  | t d  | | t d  t d  | | t d  |  | t d  | | t d  | | t d  | | |  | t d  | | |	 t d  | | |  t d   |	 |  S(   Ni   i   i  i   i   i   (   R  Rà  R°  R€  Rû  (
   R  R  R¹  R­  Rº  R¬  R®  R²  R  R³  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   With1806	  s    cc   	   
      sK  t  |  t d  | | t d  |  t d  | | | t d  t d   }   j d  t t d  |  t d  t |  | t d  | | |  | |  t t d  |  t d  t |  | | t d  |  | | t d  t d  |  | | t d  t d  | | | |  | | |  | |  S(   Ni   i   i   i  i   (   R  Rà  R°  R€  Rû  (	   R  R¹  R­  Rº  R¬  R®  R²  R  R³  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   With1807 	  s    Wc	   
   
      s  t  | | t d  | | | t d  t d  | t d  | | |  | t d   }	   j d  t t d  | t d  t |  | | | t d  | | | |	  |	 |  t t d  | t d  t | t d  | |  | t d  | | | t d  |  t d  | t d  |  | | t d  | t d  | | t d  t d  | | t d  |  | t d  | | t d  | | t d  | | |  | t d  | | |	 t d  | | |  t d   |	 |  S(   Ni   i   i  i   i   i   (   R  Rà  R°  R€  R=   (
   R  R  R¹  R­  Rº  R¬  R®  R²  R  R³  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   With1808&	  s    dc   	   
      sQ  t  |  t d  | | t d  |  t d  | | | t d  t d   }   j d  t t d  |  t d  t |  | t d  |  | | |  | |  t t d  |  t d  t |  | | t d  |  | | t d  t d  |  | | t d  t d  | | | |  | | |  | |  S(   Ni   i   i   i  i   (   R  Rà  R°  R€  R=   (	   R  R¹  R­  Rº  R¬  R®  R²  R  R³  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   With1809,	  s    Xc
   
   	      sS    j  d  t t d  t d  | t t d  |	 | | | | t d  t d  | | t d  | | t d  | t d  |  | | | | | | | | t d  | | t d  | | t d  |  |  t | t | | | | | t d  | | t d  | | t d   t d  | |  S(   Ni  i   i   i   i   (   R°  RÀ  Rà  R   R€  R   (
   R  R  R¹  R­  R¿  Rº  R¬  R®  R²  R  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement18103	  s    c	   	   	      s@    j  d  t t d  t d  | t t d  | | | | t d  | | | t d  t d  | t d  |  | | | | | | | | t d  | | t d  | | t d  |  |  t | t | | | | | t d  | | t d  | | t d   t d  | |  S(   Ni  i   i   i   i   (   R°  RÀ  Rà  R   R€  R   (	   R  R¹  R­  R¿  Rº  R¬  R®  R²  R  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement18118	  s    c      	      s     j  d  t | | | | | | t |  t | | |  | |  |  t | | | | | | t |  t | | |  | |  |  S(   Ni  (   R°  RÀ  R   Rá  (   RŸ  R»  R­  Rº  R¬  R®  R²  R¹  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1812=	  s    c      	      s     j  d  t | | | | | | t |  t | | |  |  |  t | | | | | | t |  t | | |  |  |  S(   Ni  (   R°  RÀ  R   Rá  (   RŸ  R»  R­  Rº  R¬  R®  R²  R¹  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1813B	  s    c            sû     j  d  t | t |  t | | |  | | t d  | | t d  | | | t d  | | t d  |  |  t | t |  t | | |  | | t d  | | t d  | | | t d  | | t d  |  |  S(   Ni  i   (   R°  RÀ  R   Rá  Rà  (   RŸ  R»  R­  Rº  R¬  R®  R²  R¹  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1814G	  s    c      
      s}     j  d  t t d  | | t | t | | | t d  |  |  |  t | | | t | | | |  |  S(   Ni  i   i   (   R°  RÀ  Rà  R   Rá  (   R¯  RŸ  R­  Rº  R¬  R±  R®  R²  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1815L	  s    c            só     j  d  t | t | | t | | | t d  |  | | t d  | t d  | | | t d  | t d  |  |  t | t | | | | | t d  | t d  | | | t d  | t d  |  |  S(   Ni  i   (   R°  RÀ  R   Rá  Rà  (   R¯  R¶  R­  Rº  R¬  R±  R®  R²  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1816Q	  s    c            s;  t  t | | t d    } t t | | t d    }   j d  t | t d  | t t d  | | | t | | | |  | t d   |  |  t | t d  | t t d  | | | t | | | |  | t d   | t d  | | | | t d  | t d  |  |  S(   Ni   i  i   i   (   Rw   R  Rà  R3   R°  RÀ  R   Rá  (   R»  R­  Rº  R®  R²  R¹  Rž  RŒ  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   With1817U	  s    c            s+  t  t | | t d    } t t | | t d    }   j d  t | t d  | t t d  t | |  | t d   | | | |  |  t | t d  | t t d  | | | t | |  | t d   | t d  | | | | t d  | t d  |  |  S(   Ni   i  i   i   (   Rw   R  Rà  R3   R°  RÀ  R   Rá  (   R»  R­  Rº  R®  R²  Rž  RŒ  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   With1818\	  s    c            s=  t  t | | t d    } t t | | t d    }   j d  t | t d  | t t d  | | | t | | | |  | t d   |  |  t | t d  | t t d  | | | t | | | |  | t d   | t d  | | | | t d  | t d  |  |  S(   Ni   i  i   i   (   Rw   R  Rà  R3   R°  RÀ  R   Rá  (   R»  R­  Rº  R®  R²  R¹  Rž  RŒ  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   With1819c	  s      c            s-  t  t | | t d    } t t | | t d    }   j d  t | t d  | t t d  t | |  | t d   | | | |  |  t | t d  | t t d  | | | t | |  | t d   | t d  | | | | t d  | t d  |  |  S(   Ni   i  i   i   (   Rw   R  Rà  R3   R°  RÀ  R   Rá  (   R»  R­  Rº  R®  R²  Rž  RŒ  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   With1820j	  s      c            sõ     j  d  t | t t d  | t d  | t d  | t d  t | |  | t d  | | t d   |  |  t | t | | t d  | t d  | t d  t | |  | t d  | | t d   |  |  S(   Ni  i   i   i   (   R°  RÀ  R   Rà  Rá  (   R­  Rº  R¬  R®  R²  R¹  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1821r	  s    c            sÑ     j  d  t |  t t d  t | | | t d   |  t d  | t d  | t d  |  |  t | t | t | | | t d   |  t d  | t d  | t d  |  |  S(   Ni  i   i   i   (   R°  RÀ  R   Rà  Rá  (   Rº  R¬  R®  R²  R¹  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1822w	  s    c      
      sT    j  d  t | | | t d  |  | t d  | t d  | | t d  t | t d  | t d  | t d  t | |  | t d  | | t d   |  |  t | t d  t | |  | t d  | | t d   | | | | | t d  |  | t d  | t d  | | t d  |  S(   Ni  i   i   i   (   R°  RÀ  Rà  R   Rá  R€  (   R­  Rº  R¬  R®  R²  R¹  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1823|	  s    c            s    j  d  t | | | t d  |  | t d  | t d  | | t d  t | t d  | t d  | t d  t | |  | t d  | | t d   |  |  t |  | | t d  t d  | | t d  | | t d  |  | t d  | t d  | | t d  t t d  | | | t | |  | t d  | | t d   |  |  t | t d  t | |  | t d  | | t d   | | | | | t d  |  | t d  | t d  | | t d  |  S(   Ni   i   i   i   i   (   R°  RÀ  Rà  R   Rá  R€  (   R­  Rº  R¬  R®  R²  R¹  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1824	  s    c            ss    j  d  t | | | t d  | |  t d  t |  t d  | t d  | t d  t | | | t d   |  |  t t d  | |  t d  | | t d  | |  t d  t t d  t | | | t d   |  | | |  |  t | t d  t | | | t d   |  | | | | t d  | |  t d  |  S(   Ni!  i   i   i   i   (   R°  RÀ  Rà  R   Rá  R€  (   Rº  R¬  R®  R²  R¹  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1825	  s    c            s     j  d  t | t t t d  | | t d  t d  | | | | |  | | t | | | t d  | | t d    |  S(   Ni"  i   i   i   (   R°  RÀ  R*   R   Rà  Rá  (   R  R¹  R­  Rº  R¬  R®  R²  R  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1826	  s    c            sx     j  d  t | t t t d  t d  | | | t d  | |  | | t | | | t d    |  S(   Ni#  i   i   i   (   R°  RÀ  R*   R   Rà  Rá  (   R  R¹  Rº  R¬  R®  R²  R  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1827	  s    c	   	         s     j  d  t | t t t d  | | t d  | | | | |  | | t | | | t d  | | t d    |  S(   Ni$  i   i   i   (   R°  RÀ  R*   R   Rà  Rá  (	   R  R»  R­  Rº  R¬  R®  R  R²  R¹  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1828	  s    c            sn     j  d  t | t t t d  | | | t d  | |  | | t | | | t d    |  S(   Ni%  i   i   i   (   R°  RÀ  R*   R   Rà  Rá  (   R  R¹  R»  Rº  R¬  R®  R²  R  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1829	  s    c            s     j  d  t | t t t d  | | | t d  | |  | | t | | | t d  | | t d    |  S(   Ni&  i   i   i   (   R°  RÀ  R*   R   Rà  Rá  (   R  R»  R­  Rº  R¬  R®  R²  R  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1830	  s    c            sÀ     j  d  t | | t t t d  t d  |  | t d  | t d  t d  | | |  t d  t d  |  | | t | |  | t d  | | t d    |  S(   Ni'  i   i   i   (   R°  RÀ  R*   R   Rà  Rá  (   R­  Rº  R¬  R®  R²  R¹  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1831€	  s    c            s  t  t d  | | |  t d   }   j d  t t  t d   | t  |  |  t t  t d   | t  |  |  |  t d  | | t d  | t d  t  | |  | t d  | | t d   t | | t d    t d  | t | | t d   |  t t  t d   | t  |  |  t t  t d   | t  |  |  |  t d  | | t d  | t d  t  | |  | t d  | | t d   t | | t d    t d  | t | | t d   |  S(   Ni   i   i(  (   Rá  Rà  R°  R€  Rû  R  R=   (   R­  Rº  R¬  R®  R²  R¹  R³  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   With1832š	  s    )c            s	    j  d  t | t t d  | t d  | t d  | t d  t | | | t d   t | |  | t d   |  |  t | t | | t d  | t d  | t d  t | | | t d   t | |  | t d   |  |  S(   Ni)  i   i   (   R°  RÀ  R   Rà  Rá  (   R»  R­  Rº  R®  R¬  R²  R¹  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1833¯	  s    c	   	         s    j  d  t t d  t | | | | t | | | | | t d    t d  | t d  | |  | | t d  t d  | t d  | | t d  | t d  | | | | | t d  | |  | t d  | |  t d  | t d  | | | t d  t d  | | |  | t d  | t d  |  | t d  | | |  t d  | | | |  t | | | | | t d   t d  | | t d  | |  | | | t d  | t d  | |  | | |  S(   Ni*  i   i	   i   i
   i   i   (   R°  R€  Rà  Rá  (	   Rì  R»  R­  Rº  R®  R¬  R²  Rë  R¹  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1834Ž	  s    c
   
         sZ     j  d  t | |	 | | | | t t |  |   t | | | |  | |  S(   Ni+  (   R°  R   Rá  R1  (
   RÏ  RŸ  RU  RV  R¶  Rì  R»  R±  R²  Rë  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1835¹	  s    c            s$    j  d  t t d  t t | |	 | | |  | t d  |
 |
 | t d  | t d  | |
 | | | | | t d  t d  | |
 | | t d  t d  | |
 t d  |
 | t d  |  | | |
 | | t | | | | | t d    |  S(   Ni,  i   (   R°  RÀ  Rà  R*   R   Rá  (   R¯  Rì  R»  R­  Rº  R®  R¬  R±  R²  Rë  R¹  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1836Ÿ	  s    c
   
         sÐ     j  d  t t d  t d  |	 t t | | | | |  | | t d  | t d  t d  | | | t d  | | t d  |  | | |	 | | t | | | t d    |  S(   Ni-  i   i   (   R°  RÀ  Rà  R*   R   Rá  (
   R¯  Rì  R»  Rº  R¬  R®  R±  R²  Rë  R¹  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1837Ã	  s    c            sJ     j  d  t | | | t t |  |   t | |  | | |  S(   Ni.  (   R°  R   Rá  R1  (   RÏ  R¯  RŸ  Rì  R»  R±  R²  Rë  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1838È	  s    c	   	         sô     j  d  t t d  |  t d  | |  t d  t t | |  | t d  | | t d  | t d  | | t d  | t d  | | | | | t d  |  |  | | | | t | | | t d    |  S(   Ni/  i   iÿÿÿÿiþÿÿÿ(   R°  RÀ  Rà  R*   R   Rá  (	   R¶  Rì  R»  R®  R¬  R±  R²  Rë  R¹  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1839Í	  s    Rú  c
   
         s)    j  d  t t d  t d  | |  t d  |	 |  t d  | t d  | | | | t t | t d  | | |  t d  | | t d  | t d  |  | | t d  | t d  t d  | t d  |  | |	 | | t | | | t d    |  S(   Ni0  i   iÿÿÿÿiþÿÿÿi   (   R°  RÀ  Rà  R*   R   Rá  (
   R¯  R¶  R»  Rì  Rú  R¬  R±  R®  R²  R¹  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1840Ò	  s    c            s^    j  d  t t d  | t d  |  | | |  t t |	 | | | t d  t d  | | t d  | |	 t d  |  t d  | t d  | | |	 t d  | t d  | | | | |	 | | t d  t d  | | t d  |  t d  |	  |	 | | |	 | t | | |	 | |	 t d    |	  S(   Ni1  i   iþÿÿÿi   (   R°  RÀ  Rà  R*   R   Rá  (   R¶  Rì  R»  R­  Rú  Rº  R®  R¬  R±  R²  Rë  R¹  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1841×	  s    c
   
         s    j  d  t t d  t d  |  t d  | t d  |  | | |  |	 t t | | | | t d  |  t d  | | t d  | t d  t d  | | | t d  t d  |  t d  |  | | |	 | | t | | | t d    |  S(   Ni2  i   iÿÿÿÿiþÿÿÿi   (   R°  RÀ  Rà  R*   R   Rá  (
   R¶  R»  Rì  Rú  Rº  R¬  R±  R®  R²  R¹  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1842Ü	  s    c            sÚ     j  d  t | | |  t d  d t | |
 |	 | |	 t d   t | | |	 | |	 t d   t | | |	 | |	 t d  |  | | |	 | t | | |	 | |	 t d   | |	  |	  S(   Ni3  iÿÿÿÿi   (   R°  RÀ  Rà  Rá  R   (   R¶  Rì  R»  R­  Rú  Rº  R®  R¬  R±  R²  Rë  R¹  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1843á	  s    c
   
         sº     j  d  t | | |  t d  d t | | | t d   t | | | t d   t | | | t d  |  | |	 | | t | | | t d   | |  |  S(   Ni4  iÿÿÿÿi   (   R°  RÀ  Rà  Rá  R   (
   R¶  R»  Rì  Rú  Rº  R¬  R±  R®  R²  R¹  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1844æ	  s    c            sÚ     j  d  t | | |  t d  d t | | |	 | |	 t d   t | |
 |	 | |	 t d   t | | |	 | |	 t d  |  | | |	 | t | | |	 | |	 t d   | |	  |	  S(   Ni5  i   i   (   R°  RÀ  Rà  Rá  R   (   R¶  Rì  R»  R­  Rú  Rº  R®  R¬  R±  R²  Rë  R¹  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1845ë	  s    c
   
         sº     j  d  t | | |  t d  d t | | | t d   t | | | t d   t | | | t d  |  | |	 | | t | | | t d   | |  |  S(   Ni6  i   i   (   R°  RÀ  Rà  Rá  R   (
   R¶  R»  Rì  Rú  Rº  R¬  R±  R®  R²  R¹  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1846ð	  s    c	   	         s[     j  d  t | | t t |  |   t | | | |  | t | |  | |  S(   Ni7  (   R°  R   Rá  R1  (	   RÏ  RÑ  RŸ  RU  RV  R¶  R»  R±  R²  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1847õ	  s    c            s     j  d  t t d  | t t t d  | | t d  t d  |  | | t | | t d  | | | | | t d  |   |  S(   Ni8  i   i   (   R°  RÀ  Rà  R*   R   Rá  (   R¯  R­  Rº  R¬  R±  R®  R²  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1848ú	  s    c            sÁ     j  d  t t d  | | t | |  t | | | t d    |  t t d  |  t d  | | t d  t d  | |  t | | | t d   t d  d |  S(   Ni9  i   i   (   R°  R€  Rà  Rá  (   R­  Rº  R¬  R®  R²  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1849ÿ	  s    c            s     j  d  t t t d   |  | t t t d  t t d  | t d  |  |  | | | |  t | | | t d    |  S(   Ni:  i   i   (   R°  RÀ  Rá  Rà  R*   R   (   R­  Rº  R¬  R®  R²  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1850
  s    c      
      sz     j  d  t t | | | t d  |  | | t | | | t d    | t | | | t d   |  S(   Ni;  i   (   R°  R   Rá  Rà  (   R­  Rº  R®  R¬  R²  R¹  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1851	
  s    c            s     j  d  t | t t t d  t d  | | t d  t d  |  | | t | | t d  | t | |  | t d     |  S(   Ni<  i   i   i   (   R°  RÀ  R*   R   Rà  Rá  (   R­  Rº  R¬  R®  R²  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1852
  s    c            sÓ     j  d  t t d  d t t d  t | | | |  t t |  t | | t d   |  |  t t d  d t t d  t | | | |  t t |  t | | t d   |  |  S(   Ni=  i   i   (   R°  RÀ  Rà  Rç  R   Rá  (   R¶  R­  Rº  R¬  R®  R²  R¹  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1853
  s    c            s  t  |  | t d   }   j d  t | | | | t d  t t d   t | | t d  t t d   t | |  | t d   | | | |  |  t | | | | t d  t t d   t t d  t | |  | t d   |  |  S(   Ni   i>  i   (   R  Rà  R°  RÀ  Rá  R   (   R­  Rº  R¬  R®  R²  R³  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   With1854
  s    c            s  t  |  | t d   }   j d  t | | | | t d  t t d   t | | t d  t t d   t | |  | t d   | | | |  |  t | | | | t d  t t d   t t d  t | |  | t d   |  |  S(   Ni   i?  i   (   R  Rà  R°  RÀ  Rá  R   (   R­  Rº  R¬  R®  R²  R³  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   With1855
  s    c            s  t  |  | t d   }   j d  t | | | | t t d   t d  t | | t t d   t d  t | |  | t d   | | | |  |  t | | | | t t d   t d  t t d  t | |  | t d   |  |  S(   Ni   i@  i   (   R  Rà  R°  RÀ  Rá  R   (   R­  Rº  R¬  R®  R²  R³  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   With1856#
  s    c            s  t  |  | t d   }   j d  t | | | | t t d   t d  t | | t t d   t d  t | |  | t d   | | | |  |  t | | | | t t d   t d  t t d  t | |  | t d   |  |  S(   Ni   iA  i   (   R  Rà  R°  RÀ  Rá  R   (   R­  Rº  R¬  R®  R²  R³  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   With1857)
  s    c         S   so   t  | t t t t f  r t St | | t d   } t | | |  t d  t	 t d    rk t
 St S(   Ni   i   (   Rý  Rþ  Rä  Rÿ  Rå  R   R  Rà  R   Rá  R  (   R»  R­  Rº  R¬  R®  R²  R¹  R³  (    (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   With1858/
  s    /c            sU  t  | | t d   }   j d  t t d  t d  t d  d |  t | t d  | t d  | | t d  | | t d  t t d   t d   t t t d   t d   | | t d  | t | | t d  | | t d  t t d   t d   t | | | t d   t t t d  t | t d  t d   t | t d  t d  t t d   t d   | | | t t d   t d  | | | | t d  t t d   |  | | | t d  t t d   | | t d  t t d    |  S(   Ni   iB  i   i   i   i   iÿÿÿÿ(   R  Rà  R°  RÀ  Rá  R*   R   (   R»  R­  Rº  R¬  R®  R²  R¹  R³  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement18587
  s    c         S   so   t  | t t t t f  r t St | | t d   } t | | |  t d  t	 t d    rk t
 St S(   Ni   i   (   Rý  Rþ  Rä  Rÿ  Rå  R   R  Rà  R   Rá  R  (   R»  R­  Rº  R¬  R®  R²  R¹  R³  (    (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   With1859=
  s    /c            s>  t  | | t d   }   j d  t | |  | | | | | t d  t t d   t | | t d  t t d   t | | | t d   | | | |  |  t | | |  t d  t t d   | | | t d  t t d   t t d  t | | | t d   |  |  S(   Ni   iC  i   (   R  Rà  R°  RÀ  Rá  R   (   R»  R­  Rº  R¬  R®  R²  R¹  R³  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1859E
  s    c         S   so   t  | t t t t f  r t St | | t d   } t | | |  t d  t	 t d    rk t
 St S(   Ni   i   (   Rý  Rþ  Rä  Rÿ  Rå  R   R  Rà  R   Rá  R  (   R»  R­  Rº  R¬  R®  R²  R¹  R³  (    (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   With1860K
  s    .c            sY  t  | | t d   }   j d  t t d  t d  t d  d |  t | t d  | t d  | | t d  | | t d  t t d   t d   t t t d   t d   | | t d  | t | | t d  | | t d  t t d   t d   t | | | t d   t t t d  t | t d  t d   t | t d  t d  t t d   t d   | | | t t d   t d  | | | | t d  t t d   |  | | | t d  t t d   | | t d  t t d    |  S(   Ni   iD  i   i   i   i   iÿÿÿÿ(   R  Rà  R°  RÀ  Rá  R*   R   (   R»  R­  Rº  R¬  R®  R²  R¹  R³  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1860S
  s    c         S   so   t  | t t t t f  r t St | | t d   } t | | |  t d  t	 t d    rk t
 St S(   Ni   i   (   Rý  Rþ  Rä  Rÿ  Rå  R   R  Rà  R   Rá  R  (   R»  R­  Rº  R¬  R®  R²  R¹  R³  (    (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   With1861Y
  s    .c            s=  t  | | t d   }   j d  t | |  | | | | | t d  t t d   t | | t d  t t d   t | | | t d   | | | |  |  t | | |  t d  t t d   | | | t d  t t d   t t d  t | | | t d   |  |  S(   Ni   iE  i   (   R  Rà  R°  RÀ  Rá  R   (   R»  R­  Rº  R¬  R®  R²  R¹  R³  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1861a
  s    c         S   sp   t  | t t t t f  r t St | | t d   } t | | |  t	 t d   t d   rl t
 St S(   Ni   i   (   Rý  Rþ  Rä  Rÿ  Rå  R   R  Rà  R   Rá  R  (   R»  R­  Rº  R¬  R®  R²  R¹  R³  (    (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   With1862g
  s    /c            sX  t  | | t d   }   j d  t t d  t d  t d  d |  t | t d  | t d  | | t d  | | t t d   t d  t d   t t t d   t d   | | t d  | t | | t d  | | t t d   t d  t d   t | | | t d   t t t d  t | t d  t d   t | t d  t d  t t d   t d   | | | t d  t t d   | | | | t t d   t d  |  | | | t d  t t d   | | t d  t t d    |  S(   Ni   iF  i   i   i   i   iÿÿÿÿ(   R  Rà  R°  RÀ  Rá  R*   R   (   R»  R­  Rº  R¬  R®  R²  R¹  R³  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1862o
  s    c         S   sp   t  | t t t t f  r t St | | t d   } t | | |  t	 t d   t d   rl t
 St S(   Ni   i   (   Rý  Rþ  Rä  Rÿ  Rå  R   R  Rà  R   Rá  R  (   R»  R­  Rº  R¬  R®  R²  R¹  R³  (    (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   With1863u
  s    /c            s@  t  | | t d   }   j d  t | |  | | | | | t t d   t d  t | | t t d   t d  t | | | t d   | | | |  |  t | | |  t t d   t d  | | | t t d   t d  t t d  t | | | t d   |  |  S(   Ni   iG  i   (   R  Rà  R°  RÀ  Rá  R   (   R»  R­  Rº  R¬  R®  R²  R¹  R³  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1863}
  s    c         S   sp   t  | t t t t f  r t St | | t d   } t | | |  t	 t d   t d   rl t
 St S(   Ni   i   (   Rý  Rþ  Rä  Rÿ  Rå  R   R  Rà  R   Rá  R  (   R»  R­  Rº  R¬  R®  R²  R¹  R³  (    (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   With1864
  s    0c            sV  t  | | t d   }   j d  t t d  t d  t d  d |  t | t d  | t d  | | t d  | | t t d   t d  t d   t t t d   t d   | | t d  | t | | t d  | | t t d   t d  t d   t | | | t d   t t t d  t | t d  t d   t | t d  t d  t t d   t d   | | | t d  t t d   | | | | t t d   t d  |  | | | t d  t t d   | | t d  t t d    |  S(   Ni   iH  i   i   i   i   iÿÿÿÿ(   R  Rà  R°  RÀ  Rá  R*   R   (   R»  R­  Rº  R¬  R®  R²  R¹  R³  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1864
  s    c         S   sp   t  | t t t t f  r t St | | t d   } t | | |  t	 t d   t d   rl t
 St S(   Ni   i   (   Rý  Rþ  Rä  Rÿ  Rå  R   R  Rà  R   Rá  R  (   R»  R­  Rº  R¬  R®  R²  R¹  R³  (    (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   With1865
  s    0c            sA  t  | | t d   }   j d  t | |  | | | | | t t d   t d  t | | t t d   t d  t | | | t d   | | | |  |  t | | |  t t d   t d  | | | t t d   t d  t t d  t | | | t d   |  |  S(   Ni   iI  i   (   R  Rà  R°  RÀ  Rá  R   (   R»  R­  Rº  R¬  R®  R²  R¹  R³  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1865
  s    c            s~     j  d  t t d  | t t | t d  |  t d  | | | | | t | | |  |  | | |  |  S(   NiJ  i   iÿÿÿÿ(   R°  RÀ  Rà  R*   R   Rá  (   R¶  R­  Rº  R¬  R±  R®  R²  R¹  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1866 
  s    c      
      s»     j  d  t | t |  | | t d  | t d  | | | | |  |  t | | t |  t | | | |  | | t d  | t d  | | | | |  |  S(   NiK  i   (   R°  RÀ  R   Rà  Rá  (   RŸ  R­  Rº  R¬  R±  R®  R²  R¹  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1867¥
  s    c	   	   
      sª     j  d  t | t d  | t d  t t t d  | t d  | | t d  | t d  t d  | |  | | | | t d  |  | |  |  S(   NiL  i   iÿÿÿÿi   (   R°  RÀ  Rà  R*   R   (	   R  R­  R  Rº  R¬  R±  R®  R²  R  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1868ª
  s    c            sà     j  d  t |
 t d  | | t d  | t d  t t t d  |
 t d  | |	 t d  | | t d  t d  | |	  |	 |	 | t d  |
 | | t d  |  |	 | | t d   |	  S(   NiM  i   i   (   R°  RÀ  Rà  R*   R   (   R  RV  R¶  R­  R  Rº  R¬  R±  R®  R²  R  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1869¯
  s    c            s#    j  d  t t d  | | |	 |  t d  t d  | | | t d  t | | |
 |	 | |
 t d  |	 |  t d  t | | | | | | t d  | | | | | | t d  |	 |  t d  t d  | t d  | | |	 |  |	 t d  |
 |	 | | t d  | |	 |  t d  t d  t d  | | | | |	 t d  | | |	 t d  |  t d  t d  | | | | | | |	 t d  |  t d  t d  |
  |
  |
  t |
 | | |
 |	 | |
 t d  |	 |  t d  | | | | | | t d  | | | | | | | t d  | | |
 |	 | | t d  | t d  | | | | | | | | | | | | | | |	 |  t d  t d  | | | t d  |
  S(   NiN  i   i   i   i   (   R°  RÀ  Rà  R   R€  (   R¯  R»  R­  R  Rì  Rº  R  R¬  R®  R±  R²  R¹  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1870Ž
  s    c
   
         s}    j  d  t t d  | | |  t d  t d  | | | t d  t | | | | | | t d  | |  t d  t | | |	 t d  | | | | | t d  | |  t d  t d  | t d  | | |  | t d  | | t d  | | |	 | t d  |  t d  t d  | | | | | | t d  |  t d  t d  |  |  |  t | | | | | | | t d  | |  t d  | | |	 t d  | | | | | | t d  | | | t d  | | |	 | | | | | | | |  t d  t d  | | | t d  |  S(   NiO  i   i   i   i   (   R°  RÀ  Rà  R   R€  (
   R¯  R»  R­  R  Rº  R¬  R®  R±  R²  R¹  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1871¹
  s    c            s    j  d  t t d  | | | |  t d  t d  | | | t d  t | | |	 | | |	 t d  | |  t d  t | | | | | |
 t d  | | t d  | t d  | |  t d  t d  | t d  | | | |  | t d  |	 | | | t d  | | |  t d  t d  t d  | | | | | t d  | |
 | t d  |  t d  t d  | | t d  | | t d  |  t d  t d  |	  |	  |	  t |	 | | |	 | | |	 t d  | |  t d  | | | | | |
 t d  | | t d  | | t d  | | |	 | | | t d  | t d  | | | | | |
 | | t d  | | | | |  t d  t d  | | | t d  |	  S(   NiP  i   i   i   i   (   R°  RÀ  Rà  R   R€  (   R¯  Rì  R­  R  Rº  R  R¬  R®  R±  R²  R¹  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1872Ÿ
  s    c            sô    j  d  t t d  | | |	 |  t d  t d  | | | t d  t | | |
 |	 | |
 t d  |	 |  t d  t | t d  | | t d  | | | | | | t d  |	 |  t d  t d  | t d  | | |	 |  |	 t d  |
 |	 t d  | t d  | | |	 t d  | | t d  | |	 |  t d  t d  | | | | | | |	 t d  |  t d  t d  |
  |
  |
  t |
 | | |
 |	 | |
 t d  |	 |  t d  | t d  | | t d  | | | | | | | t d  | | |
 |	 t d  | t d  | | | | t d  | | | | | | | | | |	 |  t d  t d  | | | t d  |
  S(   NiQ  i   i   i   i   (   R°  RÀ  Rà  R   R€  (   R¯  R»  R­  R  Rì  Rº  R  R¬  R®  R±  R²  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1873Ã
  s    c	   	         s    j  d  t t d  | | |  t d  t d  | | | t d  t | | | | | | t d  | |  t d  t t d  | | | | | t d  | |  t d  t d  | t d  | | |  | t d  | | | | | | | | t d  |  t d  t d  |  |  |  t | | | | | | | t d  | |  t d  t d  | | | | | | t d  | | | | | | | | | | |  t d  t d  | | | t d  |  S(   NiR  i   i   i   i   (   R°  RÀ  Rà  R   R€  (	   R¯  R»  R­  R  Rº  R¬  R®  R±  R²  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1874È
  s    c
   
         së    j  d  t t d  | | | |  t d  t d  | | | t d  t | | |	 | | |	 t d  | |  t d  t | t d  | | t d  | | t d  | t d  | |  t d  t d  | t d  | | | |  | t d  |	 | t d  | t d  | | | t d  | | t d  | | |  t d  t d  | | t d  | | t d  |  t d  t d  |	  |	  |	  t |	 | | |	 | | |	 t d  | |  t d  | t d  | | t d  | | t d  | | t d  | | |	 | t d  | t d  | | | | t d  | | | t d  | | | | |  t d  t d  | | | t d  |	  S(   NiS  i   i   i   i   (   R°  RÀ  Rà  R   R€  (
   R¯  Rì  R­  R  Rº  R  R¬  R±  R®  R²  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1875Í
  s    c            s÷    j  d  t t d  t d  | t d  | t d  | |  t d  t | | |	 t d  | |  t d  t t d  | | |	 | | | | t d  | |
 | t d  |  t d  t d  t d  | | | | | | t d  | |  t d  t d  |	  |	  |	  t |	 | | |	 t d  | |  t d  t d  | | |	 | | | | |
 t d  | | | | | | t d  | t d  | t d  | |  t d  |	  S(   NiT  i   i   i   i   (   R°  RÀ  Rà  R   R€  (   R¯  R»  Rì  R  Rº  R  R¬  R®  R±  R²  R¹  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1876Ò
  s    c	   	         s³    j  d  t t d  t d  | t d  | | |  t d  t | | | t d  | |  t d  t t d  | | | | | | t d  |  t d  t d  t d  | | | | | t d  | |  t d  t d  |  |  |  t | | | | t d  | |  t d  t d  | | | | | t d  | | | | | t d  | t d  | | |  t d  |  S(   NiU  i   i   i   i   (   R°  RÀ  Rà  R   R€  (	   R¯  R»  R  Rº  R¬  R®  R±  R²  R¹  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1877×
  s    c
   
         sñ    j  d  t t d  t d  | t d  | t d  | |  t d  t | | | t d  | |  t d  t t d  | | t d  | t d  | |  t d  t d  t d  | | | | | | | t d  | |	 | t d  |  t d  t d  |  |  |  t | | | | t d  | |  t d  t d  | | t d  | t d  | | | | | | | |	 t d  | t d  | t d  | |  t d  |  S(   NiV  i   i   i   i   (   R°  RÀ  Rà  R   R€  (
   R¯  Rì  R  Rº  R  R¬  R®  R±  R²  R¹  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1878Ü
  s    c   
         s  t  t d  | t d  | t d  | | |  t d  |  t d  | | | t d  | t d  | | | | |  t d  | | t d   } t  | | |  t d  |  t d  | | | t d  | t d  | t d  | | t d  | | | | | | | |  t d  | | t d   }	   j d  t | t |	 t d  | |  | | |  t | t |	 t d  | |  | | |  t | t | | |  t d  | | t d  | t d  | | t d  t d  | t d  | |  | | | t d  |  | | | t d  | |  | t d  | | t d  | |  t d  | | | | t d  t d  | t d  | t d  | | |  t d  | | | | t d  | t d  | |  | | t d  | t d  | | | | t d  | t d  | | | |  | | |  | | |  S(   Ni   i   i   i   iW  i   (   R  Rà  R°  R€  R=   (
   R»  R­  Rì  Rº  R¬  R®  R²  R¹  R³  Rž  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   With1879à
  s    §¬c   	         s³  t  t d  | t d  | t d  | | |  t d  t d  | t d  | |  | | | |  t d  | | t d   } t  t d  | t d  | t d  | | |  t d  t d  | t d  | |  | | | |  t d  | | t d   }   j d  t | t | t d  | |  | | |  t | t | t d  | |  | | |  t | t | | | |  t d  | | t d  | t d  |  | | | | t d  | |  t d  | | | t d  t d  | t d  | t d  | | |  t d  t d  | t d  | |  t d  | t d  | t d  |  | | |  S(   Ni   i   i   i   iX  i   (   R  Rà  R°  R€  R=   (	   R»  Rì  Rº  R®  R¬  R²  R¹  R³  Rž  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   With1880ç
  s    c   	   	   S   s  t  | t t t t f  r t SyDt | |  } t |  |  } t | | |  | | | t d  t |  | |  } t | | |  | | | t d  t |  | |  } t	 | | | | |  | | t d  | | t d  t
 |  |  | |  } t t t d  t | t | t d   t | | | t d   t t |  | |    } Wn t t f k
 r}t SX| rt St S(   Ni   iÿÿÿÿ(   Rý  Rþ  Rä  Rÿ  Rå  R   R   R2   Rà  R¢   R¿  Râ  R¢  RO   RN   R   RÕ  t	   TypeErrort   AttributeErrorR  (	   RÏ  R²  R¯  RŸ  R¶  R±  R¬  RÑ  t   res(    (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   With1881î
  s    88Uac            s\  t  | |  } t  |  |  } t | | |  | | | t d  t |  | |  } t | | |  | | | t d  t |  | |  } t | | | | |  | | t d  | | t d  t |  |  | |  }   j d  t t t |  | |  | d | | | d | |  | d | | | d t	 |  | | |   |  S(   Ni   iY  (
   R   R2   Rà  R¢   R¿  R°  R€  R  R   R   (   RÏ  R²  R¯  RŸ  R¶  R±  R¬  RÑ  (   RŽ  (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   replacement1881þ
  s    88U(£  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  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¥  RŠ  R§  Rš  R©  Rª  R«  R¬  R­  R®  R¯  R°  R±  R²  R³  RŽ  Rµ  R¶  R·  Rž  R¹  Rº  R»  RŒ  Rœ  RŸ  R¿  RÀ  RÁ  RÂ  RÃ  RÄ  RÅ  RÆ  RÇ  RÈ  RÉ  RÊ  RË  RÌ  RÍ  RÎ  RÏ  RÐ  RÑ  RÒ  RÓ  RÔ  RÕ  RÖ  R×  RØ  RÙ  RÚ  RÛ  RÜ  RÝ  RÞ  Rß  Rà  Rá  Râ  Rã  Rä  Rå  Ræ  Rç  Rè  Ré  Rê  Rë  Rì  Rí  Rî  Rï  Rð  Rñ  Rò  Ró  Rô  Rõ  Rö  R÷  Rø  Rù  Rú  Rû  Rü  Rý  Rþ  Rÿ  R   R  R  R  R  R  R  R  R  R	  R
  R  R  R  R  R  R  R  R  R  R  R  R  R  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¥  RŠ  R§  Rš  R©  Rª  R«  R   Rß  t   x_t   n_Rï  Rà  t   q_R   t   a_t   p_t   c_t   s_t   u_t   m_t   v_t   w_t   z_t   e_t   d_t   Pq_R   t   A_t   B_Rá  t   a1_t   a2_t   Px_t   n2_t   j_t   f_t   g_t   n3_(  RŽ  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¥  RŠ  R§  Rš  R©  Rª  R«  R¬  R­  R®  R¯  R°  R±  R²  R³  RŽ  Rµ  R¶  R·  Rž  R¹  Rº  R»  RŒ  Rœ  RŸ  R¿  RÀ  RÁ  RÂ  RÃ  RÄ  RÅ  RÆ  RÇ  RÈ  RÉ  RÊ  RË  RÌ  RÍ  RÎ  RÏ  RÐ  RÑ  RÒ  RÓ  RÔ  RÕ  RÖ  R×  RØ  RÙ  RÚ  RÛ  RÜ  RÝ  RÞ  Rß  Rà  Rá  Râ  Rã  Rä  Rå  Ræ  Rç  Rè  Ré  Rê  Rë  Rì  Rí  Rî  Rï  Rð  Rñ  Rò  Ró  Rô  Rõ  Rö  R÷  Rø  Rù  Rú  Rû  Rü  Rý  Rþ  Rÿ  R   R  R  R  R  R  R  R  R  R	  R
  R  R  R  R  R  R  R  R  R  R  R  R  R  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¥  RŠ  R§  Rš  R©  Rª  R«  t   pattern1473Rµ  t   rule1473t   pattern1474R·  t   rule1474t   pattern1475Rœ  t   rule1475t   pattern1476R¿  t   rule1476t   pattern1477RÀ  t   rule1477RÁ  t   pattern1478t   rule1478RÂ  t   pattern1479t   rule1479RÃ  t   pattern1480t   rule1480RÄ  t   pattern1481t   rule1481t   pattern1482RÅ  t   rule1482t   pattern1483RÆ  t   rule1483t   pattern1484RÇ  t   rule1484t   pattern1485RÈ  t   rule1485t   pattern1486RÉ  t   rule1486t   pattern1487RÊ  t   rule1487t   pattern1488RË  t   rule1488t   pattern1489RÌ  t   rule1489t   pattern1490RÍ  t   rule1490t   pattern1491RÎ  t   rule1491t   pattern1492RÐ  t   rule1492t   pattern1493RÒ  t   rule1493t   pattern1494RÔ  t   rule1494t   pattern1495RÕ  t   rule1495t   pattern1496RÖ  t   rule1496t   pattern1497R×  t   rule1497t   pattern1498RØ  t   rule1498t   pattern1499RÙ  t   rule1499t   pattern1500RÚ  t   rule1500t   pattern1501RÛ  t   rule1501t   pattern1502RÜ  t   rule1502t   pattern1503RÝ  t   rule1503t   pattern1504RÞ  t   rule1504t   pattern1505Rß  t   rule1505t   pattern1506Rà  t   rule1506t   pattern1507Rá  t   rule1507t   pattern1508Râ  t   rule1508t   pattern1509Rã  t   rule1509t   pattern1510Rä  t   rule1510t   pattern1511Rå  t   rule1511t   pattern1512Ræ  t   rule1512t   pattern1513Rç  t   rule1513t   pattern1514Rè  t   rule1514t   pattern1515Ré  t   rule1515t   pattern1516Rê  t   rule1516t   pattern1517Rí  t   rule1517t   pattern1518Rî  t   rule1518Rï  t   pattern1519t   rule1519t   pattern1520Rð  t   rule1520t   pattern1521Rñ  t   rule1521t   pattern1522Rò  t   rule1522t   pattern1523Ró  t   rule1523t   pattern1524Rô  t   rule1524t   pattern1525Rõ  t   rule1525t   pattern1526Rö  t   rule1526t   pattern1527R÷  t   rule1527t   pattern1528Rø  t   rule1528Rù  t   pattern1529t   rule1529Rû  t   pattern1530t   rule1530Rü  t   pattern1531t   rule1531R  t   pattern1532R  t   rule1532t   pattern1533R  t   rule1533t   pattern1534R  t   rule1534t   pattern1535R  t   rule1535t   pattern1536R  t   rule1536t   pattern1537R  t   rule1537t   pattern1538R	  t   rule1538t   pattern1539R
  t   rule1539t   pattern1540R  t   rule1540R  t   pattern1541R  t   rule1541R  t   pattern1542t   rule1542R  t   pattern1543R  t   rule1543t   pattern1544R  t   rule1544R  t   pattern1545t   rule1545R  t   pattern1546t   rule1546t   pattern1547R  t   rule1547R  t   pattern1548t   rule1548R  t   pattern1549t   rule1549R  t   pattern1550t   rule1550R  t   pattern1551t   rule1551R  t   pattern1552t   rule1552R  t   pattern1553t   rule1553R   t   pattern1554t   rule1554R!  t   pattern1555t   rule1555R"  t   pattern1556t   rule1556R#  t   pattern1557t   rule1557R$  t   pattern1558t   rule1558R%  t   pattern1559t   rule1559R&  t   pattern1560t   rule1560R'  t   pattern1561t   rule1561R(  t   pattern1562t   rule1562R)  t   pattern1563t   rule1563R*  t   pattern1564t   rule1564R+  t   pattern1565t   rule1565R,  t   pattern1566t   rule1566R-  t   pattern1567t   rule1567R.  t   pattern1568t   rule1568R/  t   pattern1569t   rule1569R0  t   pattern1570t   rule1570R1  t   pattern1571t   rule1571t   pattern1572R2  t   rule1572t   pattern1573R3  t   rule1573t   pattern1574R4  t   rule1574R5  t   pattern1575t   rule1575R6  t   pattern1576t   rule1576R7  t   pattern1577t   rule1577R8  t   pattern1578t   rule1578R9  t   pattern1579t   rule1579R:  t   pattern1580t   rule1580R;  t   pattern1581R<  t   rule1581R=  t   pattern1582R>  t   rule1582R?  t   pattern1583R@  t   rule1583RA  t   pattern1584RB  t   rule1584RC  t   pattern1585RD  t   rule1585RE  t   pattern1586RF  t   rule1586RH  t   pattern1587RI  t   rule1587RJ  t   pattern1588RK  t   rule1588RL  t   pattern1589t   rule1589RM  t   pattern1590t   rule1590RN  t   pattern1591t   rule1591RO  t   pattern1592t   rule1592RP  t   pattern1593t   rule1593RQ  t   pattern1594t   rule1594t   pattern1595RR  t   rule1595t   pattern1596RS  t   rule1596t   pattern1597RT  t   rule1597RW  t   pattern1598t   rule1598RX  t   pattern1599t   rule1599t   pattern1600RY  t   rule1600t   pattern1601RZ  t   rule1601t   pattern1602R[  t   rule1602R]  t   pattern1603R^  t   rule1603R`  t   pattern1604Ra  t   rule1604Rb  t   pattern1605Rc  t   rule1605Rd  t   pattern1606t   rule1606Re  t   pattern1607t   rule1607Rf  t   pattern1608t   rule1608Rg  t   pattern1609t   rule1609Rh  t   pattern1610t   rule1610t   pattern1611Ri  t   rule1611t   pattern1612Rj  t   rule1612t   pattern1613Rk  t   rule1613t   pattern1614Rl  t   rule1614t   pattern1615Rm  t   rule1615t   pattern1616Rn  t   rule1616t   pattern1617Ro  t   rule1617t   pattern1618Rp  t   rule1618t   pattern1619Rq  t   rule1619t   pattern1620Rr  t   rule1620t   pattern1621Rs  t   rule1621t   pattern1622Rt  t   rule1622t   pattern1623Ru  t   rule1623t   pattern1624Rv  t   rule1624t   pattern1625Rw  t   rule1625t   pattern1626Rx  t   rule1626t   pattern1627Ry  t   rule1627Rz  t   pattern1628t   rule1628t   pattern1629R{  t   rule1629t   pattern1630R|  t   rule1630t   pattern1631R}  t   rule1631t   pattern1632R~  t   rule1632t   pattern1633R  t   rule1633t   pattern1634R  t   rule1634t   pattern1635R  t   rule1635t   pattern1636R  t   rule1636t   pattern1637R  t   rule1637t   pattern1638R  t   rule1638t   pattern1639R  t   rule1639t   pattern1640R  t   rule1640t   pattern1641R  t   rule1641t   pattern1642R  t   rule1642t   pattern1643R  t   rule1643t   pattern1644R  t   rule1644t   pattern1645R  t   rule1645t   pattern1646R  t   rule1646t   pattern1647R  t   rule1647R  t   pattern1648R  t   rule1648t   pattern1649R  t   rule1649t   pattern1650R  t   rule1650t   pattern1651R  t   rule1651t   pattern1652R  t   rule1652t   pattern1653R  t   rule1653t   pattern1654R  t   rule1654t   pattern1655R  t   rule1655R  t   pattern1656R  t   rule1656R  t   pattern1657R  t   rule1657R  t   pattern1658R  t   rule1658t   pattern1659R  t   rule1659t   pattern1660R  t   rule1660R  t   pattern1661R¡  t   rule1661R¢  t   pattern1662R£  t   rule1662R€  t   pattern1663R¥  t   rule1663RŠ  t   pattern1664R§  t   rule1664Rš  t   pattern1665R©  t   rule1665Rª  t   pattern1666t   rule1666R«  t   pattern1667t   rule1667t   pattern1668R¬  t   rule1668t   pattern1669R­  t   rule1669R®  t   pattern1670t   rule1670R¯  t   pattern1671t   rule1671R°  t   pattern1672t   rule1672R±  t   pattern1673t   rule1673R²  t   pattern1674t   rule1674t   pattern1675R³  t   rule1675t   pattern1676RŽ  t   rule1676t   pattern1677Rµ  t   rule1677t   pattern1678R¶  t   rule1678t   pattern1679R·  t   rule1679Rž  t   pattern1680t   rule1680R¹  t   pattern1681t   rule1681t   pattern1682Rº  t   rule1682t   pattern1683R»  t   rule1683t   pattern1684RŒ  t   rule1684t   pattern1685Rœ  t   rule1685t   pattern1686RŸ  t   rule1686t   pattern1687R¿  t   rule1687t   pattern1688RÀ  t   rule1688t   pattern1689RÁ  t   rule1689t   pattern1690RÂ  t   rule1690t   pattern1691RÃ  t   rule1691t   pattern1692RÄ  t   rule1692t   pattern1693RÅ  t   rule1693t   pattern1694RÆ  t   rule1694t   pattern1695RÇ  t   rule1695t   pattern1696RÈ  t   rule1696t   pattern1697RÉ  t   rule1697t   pattern1698RÊ  t   rule1698t   pattern1699RË  t   rule1699t   pattern1700RÌ  t   rule1700t   pattern1701RÍ  t   rule1701t   pattern1702RÎ  t   rule1702t   pattern1703RÏ  t   rule1703t   pattern1704RÐ  t   rule1704t   pattern1705RÑ  t   rule1705t   pattern1706RÒ  t   rule1706t   pattern1707RÓ  t   rule1707t   pattern1708RÔ  t   rule1708t   pattern1709RÕ  t   rule1709t   pattern1710RÖ  t   rule1710t   pattern1711R×  t   rule1711t   pattern1712RØ  t   rule1712t   pattern1713RÙ  t   rule1713t   pattern1714RÚ  t   rule1714t   pattern1715RÛ  t   rule1715t   pattern1716RÜ  t   rule1716t   pattern1717RÝ  t   rule1717t   pattern1718RÞ  t   rule1718t   pattern1719Rß  t   rule1719t   pattern1720Rà  t   rule1720t   pattern1721Rá  t   rule1721t   pattern1722Râ  t   rule1722t   pattern1723Rã  t   rule1723t   pattern1724Rä  t   rule1724t   pattern1725Rå  t   rule1725t   pattern1726Ræ  t   rule1726t   pattern1727Rç  t   rule1727t   pattern1728Rè  t   rule1728t   pattern1729Ré  t   rule1729t   pattern1730Rê  t   rule1730Rë  t   pattern1731t   rule1731t   pattern1732Rì  t   rule1732t   pattern1733Rí  t   rule1733t   pattern1734Rî  t   rule1734Rï  t   pattern1735Rð  t   rule1735Rñ  t   pattern1736Rò  t   rule1736t   pattern1737Ró  t   rule1737t   pattern1738Rô  t   rule1738t   pattern1739Rõ  t   rule1739t   pattern1740Rö  t   rule1740t   pattern1741R÷  t   rule1741t   pattern1742Rø  t   rule1742t   pattern1743Rù  t   rule1743Rú  t   pattern1744Rû  t   rule1744Rü  t   pattern1745t   rule1745t   pattern1746Rý  t   rule1746Rþ  t   pattern1747Rÿ  t   rule1747R   t   pattern1748t   rule1748t   pattern1749R  t   rule1749t   pattern1750R  t   rule1750R  t   pattern1751R  t   rule1751R  t   pattern1752t   rule1752t   pattern1753R  t   rule1753R  t   pattern1754R  t   rule1754R	  t   pattern1755t   rule1755t   pattern1756R
  t   rule1756t   pattern1757R  t   rule1757R  t   pattern1758R  t   rule1758R  t   pattern1759t   rule1759t   pattern1760R  t   rule1760R  t   pattern1761R  t   rule1761R  t   pattern1762t   rule1762t   pattern1763R  t   rule1763t   pattern1764R  t   rule1764R  t   pattern1765R  t   rule1765R  t   pattern1766t   rule1766t   pattern1767R  t   rule1767R  t   pattern1768R  t   rule1768R  t   pattern1769t   rule1769t   pattern1770R  t   rule1770t   pattern1771R  t   rule1771R  t   pattern1772t   rule1772t   pattern1773R  t   rule1773R   t   pattern1774R!  t   rule1774t   pattern1775R"  t   rule1775t   pattern1776R#  t   rule1776R$  t   pattern1777t   rule1777R%  t   pattern1778t   rule1778R&  t   pattern1779R'  t   rule1779R(  t   pattern1780t   rule1780t   pattern1781R)  t   rule1781t   pattern1782R*  t   rule1782R+  t   pattern1783t   rule1783R,  t   pattern1784t   rule1784t   pattern1785R-  t   rule1785R.  t   pattern1786R/  t   rule1786t   pattern1787R0  t   rule1787t   pattern1788R1  t   rule1788R2  t   pattern1789t   rule1789R3  t   pattern1790t   rule1790R4  t   pattern1791R5  t   rule1791R6  t   pattern1792t   rule1792t   pattern1793R7  t   rule1793t   pattern1794R8  t   rule1794t   pattern1795R9  t   rule1795t   pattern1796R:  t   rule1796R;  t   pattern1797R<  t   rule1797t   pattern1798R=  t   rule1798R>  t   pattern1799R?  t   rule1799t   pattern1800R@  t   rule1800RA  t   pattern1801RB  t   rule1801RC  t   pattern1802t   rule1802RD  t   pattern1803t   rule1803RE  t   pattern1804t   rule1804RF  t   pattern1805t   rule1805RG  t   pattern1806t   rule1806RH  t   pattern1807t   rule1807RI  t   pattern1808t   rule1808RJ  t   pattern1809t   rule1809t   pattern1810RK  t   rule1810t   pattern1811RL  t   rule1811t   pattern1812RM  t   rule1812t   pattern1813RN  t   rule1813t   pattern1814RO  t   rule1814t   pattern1815RP  t   rule1815t   pattern1816RQ  t   rule1816RR  t   pattern1817t   rule1817RS  t   pattern1818t   rule1818RT  t   pattern1819t   rule1819RU  t   pattern1820t   rule1820t   pattern1821RV  t   rule1821t   pattern1822RW  t   rule1822t   pattern1823RX  t   rule1823t   pattern1824RY  t   rule1824t   pattern1825RZ  t   rule1825t   pattern1826R[  t   rule1826t   pattern1827R\  t   rule1827t   pattern1828R]  t   rule1828t   pattern1829R^  t   rule1829t   pattern1830R_  t   rule1830t   pattern1831R`  t   rule1831Ra  t   pattern1832t   rule1832t   pattern1833Rb  t   rule1833t   pattern1834Rc  t   rule1834t   pattern1835Rd  t   rule1835t   pattern1836Re  t   rule1836t   pattern1837Rf  t   rule1837t   pattern1838Rg  t   rule1838t   pattern1839Rh  t   rule1839t   pattern1840Ri  t   rule1840t   pattern1841Rj  t   rule1841t   pattern1842Rk  t   rule1842t   pattern1843Rl  t   rule1843t   pattern1844Rm  t   rule1844t   pattern1845Rn  t   rule1845t   pattern1846Ro  t   rule1846t   pattern1847Rp  t   rule1847t   pattern1848Rq  t   rule1848t   pattern1849Rr  t   rule1849t   pattern1850Rs  t   rule1850t   pattern1851Rt  t   rule1851t   pattern1852Ru  t   rule1852t   pattern1853Rv  t   rule1853Rw  t   pattern1854t   rule1854Rx  t   pattern1855t   rule1855Ry  t   pattern1856t   rule1856Rz  t   pattern1857t   rule1857R{  t   pattern1858R|  t   rule1858R}  t   pattern1859R~  t   rule1859R  t   pattern1860R  t   rule1860R  t   pattern1861R  t   rule1861R  t   pattern1862R  t   rule1862R  t   pattern1863R  t   rule1863R  t   pattern1864R  t   rule1864R  t   pattern1865R  t   rule1865t   pattern1866R  t   rule1866t   pattern1867R  t   rule1867t   pattern1868R  t   rule1868t   pattern1869R  t   rule1869t   pattern1870R  t   rule1870t   pattern1871R  t   rule1871t   pattern1872R  t   rule1872t   pattern1873R  t   rule1873t   pattern1874R  t   rule1874t   pattern1875R  t   rule1875t   pattern1876R  t   rule1876t   pattern1877R  t   rule1877t   pattern1878R  t   rule1878R  t   pattern1879t   rule1879R  t   pattern1880t   rule1880R  t   pattern1881R  t   rule1881(    (   RŽ  sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   miscellaneous_algebraic   s4
   ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ~ðŸÁšÅÅÜh·ÂÌ§²¹"Ke"NhK"aNhk"K"aNNhh"K;Uÿ ÿ dvVeszg\sY	S\¶¯çÃ		bd	j`ccdjdjdjdjdjdydjdydjsjdj	¢	p	v	¢	p	v	|	LiiiippppMzJJp@	w		PawkaGYg_VsYâ²ß¯ÿ âÿ Cÿ Ö£ÅõÈÿ )ûŒ¹ÿ ìÝ¿ÿ Aÿ H	wÝÃ¹ýãÿ ê		w			Šv	p	s	s	³	n²ªz²¶Å£~~~{~x~~Ž··¢±®®Ž±±±±€Óéîîñëåìþ 		¬Švoo	xor	{rµµ	Ÿµž	Ážyy	y|	|¿¿	È¿Â	ËÂ		¢"ÜÜÜÜ	åÜßßß	èßNÿ ÿ œ	1	Á	5	š	.	ÿ õÿ 4ÿ ûáûáÿ ø³³³¹À££p¡¡zÂæÂÂ¡íÉýÔàéÿ >èÿ >èÿ >èÖh»Ç°àssss		¢		¢		¢		¢¬í¹§}zôÊ	;	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¥   RŠ   R§   Rš   R©   Rª   R«   R¬   R­   R®   R¯   R°   R±   R²   R³   RŽ   Rµ   R¶   R·   Rž   R¹   Rº   R»   RŒ   Rœ   RŸ   R¿   RÀ   RÁ   RÂ   RÃ   RÄ   RÅ   RÆ   RÇ   RÈ   RÉ   RÊ   RË   RÌ   RÍ   RÎ   RÏ   RÐ   RÑ   RÒ   RÓ   RÔ   RÕ   RÖ   R×   RØ   RÙ   RÚ   RÛ   RÜ   RÝ   RÞ   Rß   Rà   Rá   Râ   Rã   Rä   Rå   Ræ   Rç   Rè   Ré   Rê   Rë   Rì   Rí   Rî   Rï   Rð   Rñ   Rò   Ró   Rô   Rõ   Rö   R÷   Rø   Rù   Rú   Rû   Rü   Rý   Rþ   Rÿ   R   R  R  R  R  R  R  R  R  R	  R
  R  R  R  R  R  R  R  R  R  R  R  R  R  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¥  RŠ  R§  Rš  R©  Rª  R«  R¬  R­  R®  R¯  R°  R±  R²  R³  RŽ  Rµ  R¶  R·  Rž  R¹  Rº  R»  RŒ  Rœ  RŸ  R¿  RÀ  RÁ  RÂ  RÃ  RÄ  RÅ  RÆ  RÇ  RÈ  RÉ  RÊ  RË  RÌ  RÍ  RÎ  RÏ  RÐ  RÑ  RÒ  RÓ  RÔ  RÕ  RÖ  R×  RØ  RÙ  RÚ  t   expRÛ  R   RÜ  RÝ  RÞ  t   sympyRß  Rà  Rá  Râ  Rã  Rä  Rå  Ræ  Rç  Rè  Ré  Rê  Rë  Rì  Rí  Rî  t   sympy.integrals.rubi.symbolRï  t   sympy.core.symbolRð  Rñ  t   sympy.functionsRò  Ró  Rô  Rõ  Rö  R÷  Rø  t%   sympy.functions.elementary.hyperbolicRù  Rú  Rû  Rü  Rý  Rþ  Rÿ  R   R  R  R  R  t(   sympy.functions.elementary.trigonometricR  R  R  R  R	  R
  R  R  t   PiRú  R¯  R°  t   C_t   F_t   G_t   H_R£  t   b_R¥  R­  R¬  R¶  R·  t   h_t   i_Rµ  t   k_t   l_Rš  R¡  R€  R¢  t   r_t   t_R§  R©  RŠ  Rª  R   t   y_R«  R±  R²  t   b1_t   b2_t   c1_t   c2_t   d1_t   d2_t   n1_RŽ  t   e1_t   e2_t   f1_t   f2_t   g1_t   g2_Rž  R®  t   Pm_R³  t   Qm_t   Qr_t   Qx_t   jn_t   mn_t   non2_t   RFx_t   RGx_RG  R_  R  R  Rž  R  RV  RŸ  R   t	   _UseGammat	   ShowStepst   Nonet   StepCounterRë  (    (    (    sQ   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_algebraic.pyt   <module>   s>   "ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ 1nj:R4|Ó'	