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This code is automatically generated. Never edit it manually.
For details of generating the code see `rubi_parsing_guide.md` in `parsetools`.
    )import_modulematchpy)PatternReplacementRuleCustomConstraintis_match(  IntSumSetWithModuleScanMapAndFalseQZeroQ	NegativeQNonzeroQFreeQNFreeQListLog	PositiveQPositiveIntegerQNegativeIntegerQIntegerQ	IntegersQComplexNumberQPureComplexNumberQRealNumericQPositiveOrZeroQNegativeOrZeroQFractionOrNegativeQNegQEqualUnequalIntPartFracPart	RationalQProductQSumQNonsumQSubstFirstRestSqrtNumberQSqrtNumberSumQLinearQSqrtArcCoshCoefficientDenominatorHypergeometric2F1NotSimplifyFractionalPartIntegerPartAppellF1
EllipticPi	EllipticE	EllipticFArcTanArcCotArcCothArcTanhArcSinArcSinhArcCosArcCscArcSecArcCschArcSechSinhTanhCoshSechCschCoth	LessEqualLessGreaterGreaterEqual	FractionQIntLinearcQExpandIndependentQPowerQIntegerPowerQPositiveIntegerPowerQFractionalPowerQAtomQExpQLogQHeadMemberQTrigQSinQCosQTanQCotQSecQCscQSinCosTanCotSecCscHyperbolicQSinhQCoshQTanhQCothQSechQCschQInverseTrigQSinCosQ	SinhCoshQ	LeafCount	NumeratorNumberQNumericQLengthListQImReInverseHyperbolicQInverseFunctionQTrigHyperbolicFreeQInverseFunctionFreeQRealQEqQFractionalPowerFreeQComplexFreeQPolynomialQFactorSquareFreePowerOfLinearQExponent
QuadraticQLinearPairQBinomialPartsTrinomialPartsPolyQEvenQOddQPerfectSquareQNiceSqrtAuxQ	NiceSqrtQTogetherPosAuxPosQCoefficientList
ReplaceAllExpandLinearProductGCDContentFactorNumericFactorNonnumericFactorsMakeAssocListGensymSubstKernelSubstExpandExpressionApart
SmartApartMatchQPolynomialQuotientRemainderFreeFactorsNonfreeFactorsRemoveContentAuxRemoveContent	FreeTermsNonfreeTermsExpandAlgebraicFunctionCollectReciprocalsExpandCleanupAlgebraicFunctionQCoeffLeadTermRemainingTerms
LeadFactorRemainingFactorsLeadBase
LeadDegreeNumerDenom	hypergeomExponMergeMonomialsPolynomialDivide	BinomialQ
TrinomialQGeneralizedBinomialQGeneralizedTrinomialQFactorSquareFreeListPerfectPowerTestSquareFreeFactorTestRationalFunctionQRationalFunctionFactorsNonrationalFunctionFactorsReverseRationalFunctionExponentsRationalFunctionExpandExpandIntegrandSimplerQSimplerSqrtQSumSimplerQBinomialDegreeTrinomialDegreeCancelCommonFactorsSimplerIntegrandQGeneralizedBinomialDegreeGeneralizedBinomialPartsGeneralizedTrinomialDegreeGeneralizedTrinomialParts	MonomialQMonomialSumQMinimumMonomialExponentMonomialExponentLinearMatchQPowerOfLinearMatchQQuadraticMatchQCubicMatchQBinomialMatchQTrinomialMatchQGeneralizedBinomialMatchQGeneralizedTrinomialMatchQQuotientOfLinearsMatchQPolynomialTermQPolynomialTermsNonpolynomialTermsPseudoBinomialPartsNormalizePseudoBinomialPseudoBinomialPairQPseudoBinomialQPolynomialGCDPolyGCDAlgebraicFunctionFactorsNonalgebraicFunctionFactorsQuotientOfLinearsPQuotientOfLinearsPartsQuotientOfLinearsQFlattenSortAbsurdNumberQAbsurdNumberFactorsNonabsurdNumberFactorsSumSimplerAuxQPrependDropCombineExponentsFactorIntegerFactorAbsurdNumberSubstForInverseFunctionSubstForFractionalPower*SubstForFractionalPowerOfQuotientOfLinears"FractionalPowerOfQuotientOfLinearsSubstForFractionalPowerQSubstForFractionalPowerAuxQFractionalPowerOfSquareQFractionalPowerSubexpressionQApplyFactorNumericGcdMergeableFactorQMergeFactorMergeFactorsTrigSimplifyQTrigSimplifyTrigSimplifyRecurOrderFactorOrderSmallestOrderedQMinimumDegreePositiveFactorsSignNonpositiveFactorsPolynomialInAuxQPolynomialInQExponentInAux
ExponentInPolynomialInSubstAuxPolynomialInSubstDistribDistributeDegreeFunctionOfPowerDivideDegreesOfFactorsMonomialFactorFullSimplifyFunctionOfLinearSubstFunctionOfLinearNormalizeIntegrandNormalizeIntegrandAuxNormalizeIntegrandFactorNormalizeIntegrandFactorBaseNormalizeTogetherNormalizeLeadTermSignsAbsorbMinusSignNormalizeSumFactorsSignOfFactorNormalizePowerOfLinearSimplifyIntegrandSimplifyTermTogetherSimplifySmartSimplifySubstForExpnExpandToSumUnifySum
UnifyTerms	UnifyTerm	CalculusQFunctionOfInverseLinearPureFunctionOfSinhQPureFunctionOfTanhQPureFunctionOfCoshQIntegerQuotientQOddQuotientQEvenQuotientQFindTrigFactorFunctionOfSinhQFunctionOfCoshQOddHyperbolicPowerQFunctionOfTanhQFunctionOfTanhWeightFunctionOfHyperbolicQSmartNumeratorSmartDenominatorSubstForAuxActivateTrig
ExpandTrig
TrigExpandSubstForTrigSubstForHyperbolicInertTrigFreeQLCMSubstForFractionalPowerOfLinearFractionalPowerOfLinearInverseFunctionOfLinear
InertTrigQInertReciprocalQDeactivateTrigFixInertTrigFunctionDeactivateTrigAuxPowerOfInertTrigSumQPiecewiseLinearQKnownTrigIntegrandQKnownSineIntegrandQKnownTangentIntegrandQKnownCotangentIntegrandQKnownSecantIntegrandQTryPureTanSubstTryTanhSubstTryPureTanhSubstAbsurdNumberGCDAbsurdNumberGCDListExpandTrigExpandExpandTrigReduceExpandTrigReduceAuxNormalizeTrig	TrigToExpExpandTrigToExp
TrigReduceFunctionOfTrigAlgebraicTrigFunctionQFunctionOfHyperbolicFunctionOfQFunctionOfExpnQPureFunctionOfSinQPureFunctionOfCosQPureFunctionOfTanQPureFunctionOfCotQFunctionOfCosQFunctionOfSinQOddTrigPowerQFunctionOfTanQFunctionOfTanWeightFunctionOfTrigQFunctionOfDensePolynomialsQFunctionOfLogPowerVariableExpnPowerVariableDegreePowerVariableSubstEulerIntegrandQFunctionOfSquareRootOfQuadraticSquareRootOfQuadraticSubstDividesEasyDQProductOfLinearPowersQRtNthRoot	AtomBaseQSumBaseQNegSumBaseQAllNegTermQSomeNegTermQTrigSquareQRtAux
TrigSquareIntSumIntTermMap2ConstantFactorSameQReplacePartCommonFactorsMostMainFactorPositionFunctionOfExponentialQFunctionOfExponentialFunctionOfExponentialFunction FunctionOfExponentialFunctionAuxFunctionOfExponentialTestFunctionOfExponentialTestAuxstdev	rubi_testIfIntQuadraticQIntBinomialQRectifyTangentRectifyCotangent
Inequality	ConditionSimpSimpHelpSplitProductSplitSumSubstForrG  FresnelSFresnelCErfcErfiGammaFunctionOfTrigOfLinearQElementaryFunctionQComplexUnsameQ_SimpFixFactorSimpFixFactor_FixSimplifyFixSimplify_SimplifyAntiderivativeSumSimplifyAntiderivativeSum_SimplifyAntiderivativeSimplifyAntiderivative_TrigSimplifyAuxTrigSimplifyAuxCancelPartPolyLogDDistSum_doitPolynomialQuotientFloorPolynomialRemainderFactorr  CosIntegralSinIntegralLogIntegralSinhIntegralCoshIntegralRuleErf	PolyGammaExpIntegralEiExpIntegralELogGammaUtilityOperator	FactorialZeta
ProductLogDerivativeDividesHypergeometricPFQIntHideOneQNullrubi_exprubi_logDiscriminantNegativeQuotient)IntegralSsqrtAndOrIntegerFloatModIAbssimplifyMulAddPowsign
EulerGammaWC)symbolsSymbol)sincostancotcscsecr  erf)acoshasinhatanhacothacschasechcoshsinhtanhcothsechcsch)atanacscasinacotacosasecatan2)pic                 C      g | ]}t |qS  r  .0ir  r  M/usr/lib/python3/dist-packages/sympy/integrals/rubi/rules/piecewise_linear.py
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@r?  c                 C   H   t |ttttfrdS t||}t||}t| | ||  r"dS dS ri  rj  r7  re  ro  rf  r9  r8  r  r  r  rA     rp  rA  c                 C   s`   t ||}t ||}t| | ||  | t|| td  | || t||  ||   | S Nrq  rs  r  r  r  rB     s   

LrB  c                 C   rh  ri  rj  rn  r  r  r  rC     rp  rC  c                 C   sn   t | |}t ||}t|| | ||    ttd|  || t|| | ||    ttd| || S rd  )r  r  r   r  rn  r  r  r  rD     s   

ZrD  c                 C   d   t |ttttfrdS t| |}t||}tt| | ||   t| | ||   | r0dS dS ri  	rk  rl  r  rm  r  r  r  r   r   rn  r  r  r  rE       

2rE  c                 C   sr   t | |}t ||}ttdtt|t| | ||   | td  |t| | ||   | td  |S N   r  r  r  r>   r  r  rn  r  r  r  rF    s   

^rF  c                 C   rv  ri  	rk  rl  r  rm  r  r  r  r   r"   rn  r  r  r  rG    rx  rG  c                 C   sx   t | |}t ||}ttd tt|t| | ||    | td  |t| | ||    | td  |S ry  r  r  r  r  r  r  rn  r  r  r  rH    s   

drH  c                 C   rr  ri  rj  rs  r  r  r  rI  &  rp  rI  c                 C   s~   t ||}t ||}t|| | ||   t|| td  | || t|| td  | td | | ||    | S rd  rq  rs  r  r  r  rJ  0  s   

jrJ  c                 C   rr  ri  rj  rs  r  r  r  rK  7  rp  rK  c              
   C   s   t ||}t ||}t|| td  ttd| td | td | | | | ||    | td | | ||    |S Nr6  rz  r  r  r  r5   rs  r  r  r  rL  A  s   

nrL  c                 C   V   t |ttttfrdS t| |}t||}tt| | ||   t|| r)dS dS ri  rw  rn  r  r  r  rM  H     

$rM  c                 C   s^   t | |}t ||}ttdtt| t|| td |t|   t|| td |S ry  r}  rn  r  r  r  rN  R  s   

JrN  c                 C   r  ri  r|  rn  r  r  r  rO  Y  r  rO  c                 C   sb   t | |}t ||}ttdtt| t| | td |t|   t| | td |S ry  r{  rn  r  r  r  rP  c  s   

NrP  c                 C   H   t |ttttfrdS t||}t||}t| | ||  r"dS dS ri  rj  r5  r7  re  ro  rf  r9  r8  r  r  r  rR  j  rp  rR  c                 C   sZ   t ||}t ||}t|| td  ||td   | td | | ||    | S rd  )r  r  r  r  r  r  r  rS  t  s   

FrS  c                 C   r  ri  rj  r  r  r  r  rT  {  rp  rT  c                 C   s   t ||}t ||}t|| || td   t|| td  ||td   || t|| td  ||  || td   | S Nr6  ru  r  r  r  r   r  r  r  r  r  rU    s   

rrU  c                 C   r  ri  rj  r  r  r  r  rV    rp  rV  c                 C      t ||}t ||}t|| | ||   || | td   t||  ||td   || t|| td  ||  || | td   | S r  r  r  r  r  r  rW       

rW  c                 C   r  ri  rj  r  r  r  r  rX    rp  rX  c                 C   r  r  r  r  r  r  r  rY    r  rY  c                 C   r  ri  rj  r  r  r  r  rZ    rp  rZ  c                 C      t ||}t ||}t|| | td  | td | | ||    t|| td  ||  ||t|| td  ||td   | td | | ||    | S Nrz  r6  r  r  r  r  r  r[       

r[  c                 C   r  ri  rj  r  r  r  r  r\    rp  r\  c                 C   r  r  r  r  r  r  r  r]    r  r]  c                 C   r  ri  rj  r  r  r  r  r^    rp  r^  c              
   C   s   t ||}t ||}t||  ||td   || | | ||   |    t|  |td |td | | | | ||    ||td   |S r~  r  r  r  r  r  r_    s   

r_  c                 C   s   t ||}t|| | t||td  | ||   t| ||   || t|| | t|| | ||   t| ||   | | S rt  )r  r  r   r  r`  r  )r9  r8  r7  re  rf  rg  r  r  r  ra    s   
ra  c                 C   s   t ||}t|| ||td   t||td  | ||  |td   t| ||   || ttd|td  t|| | ||  |  || t|| | ||  |td   t| ||   ||td   | S r  )r  r  r  r   r`  r  )r9  r8  r5  r7  re  rf  rg  r  r  r  rb    s   
rb  (  __doc__Zsympy.externalr   r   r   r   r   r   Z%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/   r0   r1   r2   r3   r4   r5   r6   r7   r8   r9   r:   r;   r<   r=   r>   r?   r@   rA   rB   rC   rD   rE   rF   rG   rH   rI   rJ   rK   rL   rM   rN   rO   rP   rQ   rR   rS   rT   rU   rV   rW   rX   rY   rZ   r[   r\   r]   r^   r_   r`   ra   rb   rc   rd   re   rf   rg   rh   ri   rj   rk   rl   rm   rn   ro   rp   rq   rr   rs   rt   ru   rv   rw   rx   ry   rz   r{   r|   r}   r~   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r  r  r  r  r  r  r  r  r	  r
  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r   r!  r"  r#  r$  r%  r&  r'  r(  r)  r*  r+  r,  r-  r.  r/  r0  r1  r2  r3  r4  r5  r6  r7  r8  r9  r:  r;  r<  r=  r>  r?  r@  rA  rB  rC  rD  rE  rF  rG  rH  rI  rJ  rK  rL  rM  rN  rO  rP  rQ  rR  rS  rT  rU  rV  rW  rX  rY  rZ  r[  r\  r]  r^  r_  r`  ra  rb  rc  rd  re  rf  rg  rh  ri  rj  rk  rl  rm  rn  ro  rp  rq  rr  rs  rt  ru  rv  rw  rx  ry  rz  r{  r|  r}  r~  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  Zexpr  r`  r  r  r  Zsympyr  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  Zsympy.integrals.rubi.symbolr  Zsympy.core.symbolr  r  Zsympy.functionsr  r  r  r  r  r  r  Z%sympy.functions.elementary.hyperbolicr  r  r  r  r  r   r  r  r  r  r  r  Z(sympy.functions.elementary.trigonometricr  r  r	  r
  r  r  r  r  ZPiZA_ZB_ZC_ZF_ZG_ZH_Za_Zb_Zc_Zd_Ze_Zf_Zg_Zh_Zi_Zj_Zk_Zl_rQ  r@  Zp_Zq_Zr_Zt_r:  r=  Zs_Zw_r;  Zy_Zz_Za1_Za2_Zb1_Zb2_Zc1_Zc2_Zd1_Zd2_Zn1_Zn2_Ze1_Ze2_Zf1_Zf2_Zg1_Zg2_Zn3_ZPq_ZPm_ZPx_ZQm_ZQr_ZQx_Zjn_Zmn_Znon2_ZRFx_ZRGx_r  iiZPqqQRrCkre  Z	_UseGammaZ	ShowStepsZStepCounterrc  r<  r>  r?  rA  rB  rC  rD  rE  rF  rG  rH  rI  rJ  rK  rL  rM  rN  rO  rP  rR  rS  rT  rU  rV  rW  rX  rY  rZ  r[  r\  r]  r^  r_  ra  rb  r  r  r  r  <module>   s               nJjB.
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