o *ήcYJ@s ddlZddlmZedZesdZejdddkrdZddlmZmZm Z m Z m Z m Z m Z mZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZm Z m!Z!m"Z"m#Z#m$Z$m%Z%m&Z&m'Z'm(Z(m)Z)m*Z*m+Z+m,Z,m-Z-m.Z.m/Z/m0Z0m1Z1m2Z2m3Z3m4Z4m5Z5m6Z6m7Z7m8Z8m9Z9m:Z:m;Z;mZ>m?Z?m@Z@mAZAmBZBmCZCmDZDmEZEmFZFmGZGmHZHmIZImJZJmKZKmLZLmMZMmNZNmOZOmPZPmQZQmRZRmSZSmTZTmUZUmVZVmWZWmXZXmYZYmZZZm[Z[m\Z\m]Z]m^Z^m_Z_m`Z`maZambZbmcZcmdZdmeZemfZfmgZgmhZhmiZimjZjmkZkmlZlmmZmmnZnmoZompZpmqZqmrZrmsZsmtZtmuZumvZvmwZwmxZxmyZymzZzm{Z{m|Z|m}Z}m~Z~mZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZm Z m Z m Z m Z m Z mZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZm Z m!Z!m"Z"m#Z#m$Z$m%Z%m&Z&m'Z'm(Z(m)Z)m*Z*m+Z+m,Z,m-Z-m.Z.m/Z/m0Z0m1Z1m2Z2m3Z3m4Z4m5Z5m6Z6m7Z7m8Z8m9Z9m:Z:m;Z;m<Z<m=Z=m>Z>m?Z?m@Z@mAZAmBZBmCZCmDZDmEZEmFZFmGZGmHZHmIZImJZJmKZKmLZLmMZMmNZNmOZOmPZPmQZQmRZRmSZSmTZTmUZUmVZVmWZWmXZXmYZYmZZZm[Z[m\Z\m]Z]m^Z^m_Z_m`Z`maZambZbmcZcmdZdmeZemfZfmgZgmhZhmiZimjZjmkZkmlZlmmZmmnZnmoZompZpmqZqmrZrmsZsmtZtmuZumvZvmwZwmxZxmyZymzZzm{Z{m|Z|m}Z}m~Z~mZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmGZGmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmÐZÐmĐZĐmŐZŐmƐZƐmZmǐZǐmȐZȐmɐZɐmʐZʐmːZːm̐Z̐m͐Z͐mΐZΐmϐZϐmАZАmѐZѐmҐZҐmӐZӐmԐZԐmՐZՐm֐Z֐mאZאmؐZؐmِZddlڐmېZdd lܐmݐZdd lސmߐZdd lmZmZmZdd lmZdd lmZddlmZddlmZddlmZddlmZmZddlmZddlmZddlmZmZddlmZmZmZmZmZmZmZmZmZmZddlmZmZmZmZmZm Z m Z m Z m Z m Z mZmZddlmZmZmZmZmZmZddlmZddlmZed\ZZZZZZ Z!Z"Z#Z$Z%Z&Z'Z(Z)Z*Z+ed\Z,Z-Z.ZZZZZZZ Z/Z0Z1Z2Z!Z"Z&Z3Z$Z4Z5Z6ddZ7dS)N) import_modulematchpyT)(sympy_op_factoryIntSumSetWithModuleScanMapAndFalseQZeroQ NegativeQNonzeroQFreeQNFreeQListLog PositiveQPositiveIntegerQNegativeIntegerQIntegerQ IntegersQComplexNumberQPureComplexNumberQ RealNumericQPositiveOrZeroQNegativeOrZeroQFractionOrNegativeQNegQEqualUnequalIntPartFracPart RationalQProductQSumQNonsumQSubstFirstRest SqrtNumberQSqrtNumberSumQLinearQSqrtArcCosh Coefficient DenominatorHypergeometric2F1NotSimplifyFractionalPart IntegerPartAppellF1 EllipticPi EllipticE EllipticFArcTanArcCotArcCothArcTanhArcSinArcSinhArcCosArcCscArcSecArcCschArcSechSinhTanhCoshSechCschCoth LessEqualLessGreater GreaterEqual FractionQ IntLinearcQExpand IndependentQPowerQ IntegerPowerQPositiveIntegerPowerQFractionalPowerQAtomQExpQLogQHeadMemberQTrigQSinQCosQTanQCotQSecQCscQSinCosTanCotSecCsc HyperbolicQSinhQCoshQTanhQCothQSechQCschQ InverseTrigQSinCosQ SinhCoshQ LeafCount NumeratorNumberQNumericQLengthListQImReInverseHyperbolicQInverseFunctionQTrigHyperbolicFreeQInverseFunctionFreeQRealQEqQFractionalPowerFreeQ ComplexFreeQ PolynomialQFactorSquareFreePowerOfLinearQExponent QuadraticQ LinearPairQ BinomialPartsTrinomialPartsPolyQEvenQOddQPerfectSquareQ NiceSqrtAuxQ NiceSqrtQTogetherPosAuxPosQCoefficientList ReplaceAllExpandLinearProductGCD ContentFactor NumericFactorNonnumericFactors MakeAssocList GensymSubst KernelSubstExpandExpressionApart SmartApartMatchQPolynomialQuotientRemainder FreeFactorsNonfreeFactorsRemoveContentAux RemoveContent FreeTerms NonfreeTermsExpandAlgebraicFunctionCollectReciprocals ExpandCleanupAlgebraicFunctionQCoeffLeadTermRemainingTerms LeadFactorRemainingFactorsLeadBase LeadDegreeNumerDenom hypergeomExponMergeMonomialsPolynomialDivide BinomialQ TrinomialQGeneralizedBinomialQGeneralizedTrinomialQFactorSquareFreeListPerfectPowerTestSquareFreeFactorTestRationalFunctionQRationalFunctionFactorsNonrationalFunctionFactorsReverseRationalFunctionExponentsRationalFunctionExpandExpandIntegrandSimplerQ SimplerSqrtQ SumSimplerQBinomialDegreeTrinomialDegreeCancelCommonFactorsSimplerIntegrandQGeneralizedBinomialDegreeGeneralizedBinomialPartsGeneralizedTrinomialDegreeGeneralizedTrinomialParts MonomialQ MonomialSumQMinimumMonomialExponentMonomialExponent LinearMatchQPowerOfLinearMatchQQuadraticMatchQ CubicMatchQBinomialMatchQTrinomialMatchQGeneralizedBinomialMatchQGeneralizedTrinomialMatchQQuotientOfLinearsMatchQPolynomialTermQPolynomialTermsNonpolynomialTermsPseudoBinomialPartsNormalizePseudoBinomialPseudoBinomialPairQPseudoBinomialQ PolynomialGCDPolyGCDAlgebraicFunctionFactorsNonalgebraicFunctionFactorsQuotientOfLinearsPQuotientOfLinearsPartsQuotientOfLinearsQFlattenSort AbsurdNumberQAbsurdNumberFactorsNonabsurdNumberFactorsSumSimplerAuxQPrependDropCombineExponents FactorIntegerFactorAbsurdNumberSubstForInverseFunctionSubstForFractionalPower*SubstForFractionalPowerOfQuotientOfLinears"FractionalPowerOfQuotientOfLinearsSubstForFractionalPowerQSubstForFractionalPowerAuxQFractionalPowerOfSquareQFractionalPowerSubexpressionQApplyFactorNumericGcdMergeableFactorQ MergeFactor MergeFactors TrigSimplifyQ TrigSimplifyTrigSimplifyRecurOrder FactorOrderSmallestOrderedQ MinimumDegreePositiveFactorsSignNonpositiveFactorsPolynomialInAuxQ PolynomialInQ ExponentInAux ExponentInPolynomialInSubstAuxPolynomialInSubstDistribDistributeDegreeFunctionOfPowerDivideDegreesOfFactorsMonomialFactor FullSimplifyFunctionOfLinearSubstFunctionOfLinearNormalizeIntegrandNormalizeIntegrandAuxNormalizeIntegrandFactorNormalizeIntegrandFactorBaseNormalizeTogetherNormalizeLeadTermSignsAbsorbMinusSignNormalizeSumFactors SignOfFactorNormalizePowerOfLinearSimplifyIntegrand SimplifyTermTogetherSimplify SmartSimplify SubstForExpn ExpandToSumUnifySum UnifyTerms UnifyTerm CalculusQFunctionOfInverseLinearPureFunctionOfSinhQPureFunctionOfTanhQPureFunctionOfCoshQIntegerQuotientQ OddQuotientQ EvenQuotientQFindTrigFactorFunctionOfSinhQFunctionOfCoshQOddHyperbolicPowerQFunctionOfTanhQFunctionOfTanhWeightFunctionOfHyperbolicQSmartNumeratorSmartDenominator SubstForAux ActivateTrig ExpandTrig TrigExpand SubstForTrigSubstForHyperbolicInertTrigFreeQLCMSubstForFractionalPowerOfLinearFractionalPowerOfLinearInverseFunctionOfLinear InertTrigQInertReciprocalQDeactivateTrigFixInertTrigFunctionDeactivateTrigAuxPowerOfInertTrigSumQPiecewiseLinearQKnownTrigIntegrandQKnownSineIntegrandQKnownTangentIntegrandQKnownCotangentIntegrandQKnownSecantIntegrandQTryPureTanSubst TryTanhSubstTryPureTanhSubstAbsurdNumberGCDAbsurdNumberGCDListExpandTrigExpandExpandTrigReduceExpandTrigReduceAux NormalizeTrig TrigToExpExpandTrigToExp TrigReduceFunctionOfTrigAlgebraicTrigFunctionQFunctionOfHyperbolic FunctionOfQFunctionOfExpnQPureFunctionOfSinQPureFunctionOfCosQPureFunctionOfTanQPureFunctionOfCotQFunctionOfCosQFunctionOfSinQ OddTrigPowerQFunctionOfTanQFunctionOfTanWeightFunctionOfTrigQFunctionOfDensePolynomialsQ FunctionOfLogPowerVariableExpnPowerVariableDegreePowerVariableSubstEulerIntegrandQFunctionOfSquareRootOfQuadraticSquareRootOfQuadraticSubstDividesEasyDQProductOfLinearPowersQRtNthRoot AtomBaseQSumBaseQ NegSumBaseQ AllNegTermQ SomeNegTermQ TrigSquareQRtAux TrigSquareIntSumIntTermMap2ConstantFactorSameQ ReplacePart CommonFactorsMostMainFactorPositionFunctionOfExponentialQFunctionOfExponentialFunctionOfExponentialFunction FunctionOfExponentialFunctionAuxFunctionOfExponentialTestFunctionOfExponentialTestAuxstdev rubi_testIf IntQuadraticQ IntBinomialQRectifyTangentRectifyCotangent Inequality ConditionSimpSimpHelp SplitProductSplitSumSubstForrGFresnelSFresnelCErfcErfiGammaFunctionOfTrigOfLinearQElementaryFunctionQComplexUnsameQ_SimpFixFactor SimpFixFactor _FixSimplify FixSimplify_SimplifyAntiderivativeSumSimplifyAntiderivativeSum_SimplifyAntiderivativeSimplifyAntiderivative_TrigSimplifyAuxTrigSimplifyAuxCancelPartPolyLogDDistSum_doitPolynomialQuotientFloorPolynomialRemainderFactorr CosIntegral SinIntegral LogIntegral SinhIntegral CoshIntegralRuleErf PolyGamma ExpIntegralEi ExpIntegralELogGammaUtilityOperator FactorialZeta ProductLogDerivativeDividesHypergeometricPFQIntHideOneQ)Add)Mod)Mul)FloatIInteger)Pow)S)Abs)sqrt)Integral)AndOr)simplify)WC)symbolsSymbol) sincostancotcscsecrerfexplog) acoshasinhatanhacothacschasechcoshsinhtanhcothsechcsch)atanacscasinacotacosasec)rubi_integrate)piz!a b c d e f m n x u k p r s t i jz+A B C D a b c d e f g h y z m n p q u v w Fc Csttttdtttttttdttttdttd ttdtdtddtdttdtdttd ttdtdtddtdttdtttd ttdtdtdttddddd sJttttdtttttttdttttdttdtttd ttdtdtd ttdttttd ttdtdtd ttdtdttttd ttddddd sJttttdtttttttdttttdttd ttdtdtddtd ttdtttd ttdtdtdttddddd snJttttttttttdttttdttttd ttdtdtdtttttdttddddd sJttttttttttttttd ttdtdtdddd sJttttttttt ttdt tdtttttdt t tdtttt tdttttttttdtddddd sEJtttttttdttt t tttd ttdtdttttdddd s}Jtttttttdttt tttd ttdtdtdtttttdttddddd sJtttttttdttttd t tttd ttdtdtd ttttd ttdtdtd ttdttttdttddddd s(Jtttttttdttttd tttd ttdtdtd tttttd ttdtdtdttdttttdttddddd sJtttttttd tttd ttdt tttd ttdtdtdtdttdtttd ttdtdtdttdttttd ttdtdtdttdttttdttddddd s!Jttttdttttdttttdttttdtdtdttdtdtdttdtttd ttdtdttttdttdttdtdttdtdttdtttd ttdtdttttdttdtd ttdttdtd tttd ttdtdttttdttddddd sJttttdttttdttttdttttdtdttdtd ttdtttd ttdtdttttdttdttdtd ttdtdttttd ttdtdttttd ttdtdttttdtd ttddddd sJttttdttttdttttdttttdtdtdttdtdtdttdtttd ttdtdttttd ttdttd ttdtdtttd ttdtdttttd ttddddd sRJtttttttdttttdttttdtdttdtdttttd ttdtdttttdtttttdtdttddddd sJttttttdtttttttdtdttdtttd ttdtdttttdddd sJttttttdtttt ttdt tdtttttttttdt tdtttttdt t tdtttt tdttttdtttttdtddddd s~Jttttttdttdtttdttttdt tttt tdttttdt tttttdttttt t ttttttttdtdddd sJttttttdttdttttdt tttttd ttdtdttttttttdtdttddddd sDJttttttdttdttttdt ttdttdtttd ttdtdttttdtttdtdttdttttd ttdtdttttd ttdttttdtdttddddd sJttttdttttdttttdttttdtdtd ttdttttdtdttdtttd ttdtdttttdtdttdttdttttdttdtdttdtttd ttdtdttttdtdttdtd tttttdttdtd ttd ttdtdtddtdttdtdttd ttdtdtddtdttdtdtttd ttdtdttttdtdttdtdtttd ttdtdtdttddddd  sDJttttdttttdttttdttttdtdtdttdttttd tdttdtttd ttdtdttttdtd ttdttdtttd ttdtdtdttd ttdttttd ttdtd ttttd ttdtdttttdtd ttdtdttttd ttdtdtdttdtdttttdtd ttdtdttttdttddddd  snJttttdttttdttttdttttdtdtdttdttttd ttdtttd ttdtdttttdtdttdtttttdttdtdttd ttdtdtddtdttdtdtttd ttdtdttttdtdttdtdtttd ttdtdtd ttddddd  sbJtttttttdttttdttttdtdtdttdttttdtdttttd ttdtdttttdtdttdttttd ttdtdtdtttttdtdttdtdttttdttddddd  sJttttttdtttttttdtd tttttdtttd ttdtdttttdttd tttd ttdtdtdddd  s|Jttttttdttttd tttdt tdttttttttdtdtdttdt tdttttttttdtdtttdt tdtttttdt t tdtttt tdttttdtttttdtddddd s)Jttttttdttdtttd ttttdt tttt ttttd ttttdt ttttttttd tttdt tttt td tttdt tttttd tttttdt t ttttttttdtdddd sJttttttdttdtttd tttdttdt tdtttttdtdttdt t tdtttt tdttttdtttdttttdtdtdttttd ttdtdttttdtdtttttdtdttddddd sJttttttdttdttt ttdttdt tdtttttdttdt t tdtttt tdttttttdttttdtdttdtttd ttdtdttttdtdtttdtttd ttdtdtdtttdttttdttdttttd ttdtdttttdtdttdttttdtdttddddd sJttttdttttdttttd ttttdtd ttd ttttdtdttd td ttdtttd ttdtdttttdtd tttdtttd ttdtdttttd!ttdttdttttdtd"ttdtd#ttdtd$ttdtdttdtttd ttdtdttttdtd%ttdtd#ttdtttd ttdtdttttd&ttdtdttdttttdtd ttdtd'ttdtd(ttdtdttttd ttdtdttttdtd)ttdtd'ttttd ttdtdttttd*ttdtdttttdtd+ttd td'ttttdtd(ttd dddd sJttttdttttdttttdttttdtdtdttdttttdtdtd)ttdtd,tdttdtttd ttdtdttttdtdttd)ttdtttd ttdtdttttdttd ttdttttdtdttdtd-ttdtd.ttdtd ttdtttd ttdtdttttdtdttdtd-ttdtttd ttdtdttttd/ttdtd tttttdtdttdtd0ttd/ttdtd tttd ttdtdttttdtdttdtd0tttd ttdtdttttd/ttddddd s9Jttttdttttdttttdttttdtdtdttdttttdtd tdttdtdttdtttd ttdtdttttdtdttdttdtttd ttdtdttttd ttd ttdttttdtd ttdtdttdtdttdtdttttd ttdtdttttdtdttdtdttttd ttdtdttttd1ttdtdttttdtd ttdtdttttdtdttddddd sJttttdttttdttttdttttdtdtdttdttttdtd tdttdtd2tdttdtttd ttdtdttttdtd ttdttdtttd ttdtdttttdttdtttttdtdttdtd3ttdttdtdtttd ttdtdttttdtd ttdtd3tttd ttdtdttttdttddddd sJtttttttdttttdttttdtdtdttdttttdtdtdttdtdttttd ttdtdttttdttdttttd ttdtdttttdtttttdtdttdtdttttdtdttddddd sJttttttdtttttttdtdtttttdtd)ttdtttd ttdtdttttdttd)tttd ttdtdttttdddd sJttttttdttttd tttdt tdttttttttdtdttdt tdttttttttdtdtttdt tdttttttttdttdt tdtttttdt t tdtttt tdttttdtttttdtddddd sJttttttdttdtttdttttdt tttt ttttdtdttttdt ttttttttdtd)tttdt tttt ttttd)tttdt ttttttttd)ttttdt tttt td)ttttdt tttttdtttttdt t ttttttttdtdddd sJttttttdttdtttd  tttdttdt tdttttttttdttdttdt tdtttttd ttdt t tdtttt tdttttdtdtttdttttdtdttttd ttdtdttttdtttttdtdttddddd sJttttttdttdtttdtttdttdt tttt ttttdtdtttdttdt tttt tdtttdttdt ttttttttdtdtttdttdt tttttdttdttdt tttt ttttdttdttdt ttttttttdtttdttdt tttt tdtttdttdt tttttdttdttttdt t tttttdtdttdtttt t tttttdttdttttdttdttttd ttdtdttttdtdttdttttdtdttddddd s4Jttttd ttttttdt ttttd1ttd4td t tdttttd1ttd4tdt tdttttd1ttd4t td4ttttd1ttd4dddd sJttttdttttttdt tdttttd ttd t tdttttdttd t td ttttd ttd dddd s Jttttdtttttt ttttdttdtdt tdttttd ttdt tdttttd ttddddd sdJttttdtttttt tdttttdttdt tdttttdttddddd sJttttdtttttt ttttdttdt tdttttdttddddd sJttttttttt tdttttdttddddd sJtttdtttttt ttttdddd s2Jtttdttttttttdtttttdddd sYJtttdttdtttttttdttdttttdddd sJttttd ttttdttttd  tttd ttdtdtttttdt ttttd1ttd4tdt tdttttd1ttd4tdt tdttttd1ttd4td4t td4ttttd1ttd4dddd s*Jttttdttttdttttd tttd ttdtdtttttdt tdttttd ttd t tdttttdttd tdt td ttttd ttd dddd sJttttdttttdttttd tttd ttdtdttttt ttttdttdtd t tdttttd ttdtdt tdttttd ttddddd  s6Jttttdttttdttttd tttd ttdtdttttt tdttttdttdt tdttttdttddddd  sJttttdttttdttttd tttd ttdtdttttt ttttdttdtdt tdttttdttddddd !s Jtttttttdttt tttd ttdtdttttt tdtttttddddd !sRJttttttd5tttttd ttdtd ttttt ttttdddd !sJtttdtttttdttttdtttttdtdddd !sJtttdttdttttdttttdttdttttdtdddd !sJttttdttttdtttdttdtdtttttdtttd ttdtdtdtttttdtdttdttdtttt ttttd ttdtdt tdttttd ttdtdt tdttttd ttddddd "sJttttdttttdtttdttdtttttdtttd ttdtdtdtttttdtdttdtdttdtttt tdttttdttdt tdtttttddddd #s@Jttttdttttdtttdttdtdtttttdtttd ttdtdtdtttttdtttdtttt ttttdttdtd t tdttttdttddddd #sJtttttttdttttdtttttttd ttdtdtdtttttdt tdtttttdtdtdttdtttdddd $sBJttttttd6ttttdttttttd ttdtdtdtttttdt ttttdtdddd $sJtttdtttttdttttdtttttdtdddd $sJtttdttdttttdttttdttdttttdtdddd $sJttttdttttdtttdttdtd ttttdtdttdtttd ttdtdtd ttttttdtttd ttdtdtdtttttdtdttdtdttdttttdtdttdtttd ttdtdttdtttt ttttd"ttdtdt tdttttd ttdtdt tdttttd+ttddddd &sJttttdttttdtttdttdtdttttdtdttdtttd ttdtdtdttttttdtttd ttdtdtdtttttdttdtdttdttttdttttd ttdtdttdtttt tdttttdttdtdt tdttttdttddddd &sJttttdttttdttttdtdttttdtdttdtttd ttdtdtdttttttdtttd ttdtdtdtttttdttdttdttttdtttd ttdtdtdttdtttt ttttd)ttdtd t tdttttdttddddd 'sJtttttttdttttdtdttttdtdttttd ttdtdtdttttttttd ttdtdtdtttttdtdt tdttttdttdtdtd ttdttttddddd (sJttttttd7ttttd ttttdtttd ttdtdtd tttttttd ttdtdtdtttttdt ttttd tdddd )sJtttdtttttdttttdtttttdtdddd )s3Jtttdttdttttdttttdttdttttdtdddd )sjJttttdttttttttd8 tttttd8ttdttttttd9ttdttdtttttdttdttttttd ttdttd tttttd ttdttttttd+ttdttdtttttddddd *sJttttdttttttttttdtttttttd ttdttdttttdttdttdttttttdttdttdtttttdtdtttttd ttddddd *sJttttdttttttttd tttttdttdttttttdttdttd tttttd ttdttttttd:ttdttdtttttddddd +s2Jtttttttttttttdtttttttdttdttdtttttdtttttdttddddd +sJttttttttttd tttttdttdttttttdttttttdddd +sJttttttttttttttttdddd +sJttttdttttddtttd ttd8tttttd8ttdttttttd;ttdtdttdtttttdttdttttttd ttdttd tttttd ttdttttttd<ttdttdttttddtdtdttdtttd ttdtdtttttd=ttdttdtttd ttdtdtttttdttdtdtttd ttdtdtttttdttddddd .s|ttttdttttddtttd ttd8tttttd8ttdttttttd;ttdtdttdtttttdttdttttttd ttdttd tttttd ttdttttttd<ttdttdttttddtdtdttdtttd ttdtdtttttd=ttdttdtttd ttdtdtttttdttdtdtttd ttdtdtttttdttddddd .s|Jttttdttttddtttd ttttdtttttttd1ttdtdttdttttdttdttdttttttd>ttdttdttttddtdtdttdtttd ttdtdtttttd ttd ttttd ttdtdtttttd1ttdtdttttddtd ttddddd /syJttttdttttddtttd ttdtttttdttdttttttd ttdttd tttttd ttdttttttd?ttdttdttttddtdttdtttd ttdtdtttttd ttttd ttdtdtttttdttddddd 0sVJtttttttddtttd ttttdtttttttd ttdttdttttddtdtdttttd ttdtdtttttdtttttddtdttddddd 0sJttttttddtttd ttdtttttdttdttttttdttttttddtdtttd ttdtdtttttdtdddd 1s`Jttttttddttttttttddttdddd 1sJttttdttttddtttdttd8tttttd8ttdttttttd@ttdtdttdtttttdttdttttttd1ttdtdttd tttttd ttdttttttd(ttdttdttttddtdtdttdtttttdAttdtttd ttdtdttttddtd8tttdtttttdttdtdttdtttd ttdtdttttddtdttdtdttttttdttdtdtttd ttdtdttttddtdttddddd 4sttttdttttddtttdttd8tttttd8ttdttttttd@ttdtdttdtttttdttdttttttd1ttdtdttd tttttd ttdttttttd(ttdttdttttddtdtdttdtttttdAttdtttd ttdtdttttddtd8tttdtttttdttdtdttdtttd ttdtdttttddtdttdtdttttttdttdtdtttd ttdtdttttddtdttddddd 4sJttttdttttddtttd ttttdtttttttdttdtdttdttttdttdttdttttttdBttdttdttttddtdtdttdtttttdtdttdtttd ttdtdttttddtd ttdttdtttttdttdtdttttd ttdtdttttddtd1ttdtdttttddtd ttdtdtttttdCttddddd 6sJttttdttttddtttdttdtttttdttdttttttd ttdtdttd tttttd ttdttttttd&ttdttdttttddtdtdttdtttttd%tdttdtttd ttdtdttttddtdttdttttttd ttdtdtttd ttdtdttttddtd ttddddd 7sJtttttttddtttd ttttdtttttttdttdttdttttddtdtdttdtttttd tdttttd ttdtdttttddtdtttttddtdttdtdtttttd1ttddddd 7sJttttttddtttdttdtttttdttdttttttdttttttddtdttttttdtdtttd ttdtdttttddtdtdddd 8smJttttttddttttttttddttdddd 8sJttttdttttttttd8tttttd8ttdttttttdDttdttdtttttdttdttttttdttdttd tttttd ttdttttttd ttddddd 9s6Jttttdttttttttttdtttttttdttdttdttttdttdttdttttttd ttddddd 9sJttttdttttttttdtttttdttdttttttdttdttd tttttd ttdttttttdttddddd :sJtttttttttttttdtttttttdttddddd :sHJtttdttttttttdtttttdttdttttttdddd :sJtttdtttttttttdttttttdddd :sJtttdttdttttttttdttdtttttdddd :sJttttd ttttddtttd ttd8tttttd8ttdttttttd ttd4ttdtttttdttdttttttd ttd4tdttdtttttdttdttttttd ttd4td ttd tttttd ttdttttttd ttd4tdttd tttd ttdtdtttttdddd ;sJttttdttttddtttdttttdtttttttdttd ttdttttdttdttdttttttdttd ttdttttdttdttdttttttdttd tdttdtttd ttdtdtttttdddd s Jttttdttttddttttd tttttdttdttttttdttdttd tttttd ttdttttttdttdtdttdtttd ttdtdtttttdddd >sJtttttttddtttdttttdttttttttdtdttttd ttdtdtttttdddd ?sJttttttd6dtttd ttdtttttdttdtttttttdtttd ttdtdtttttdddd ?siJtttdtttttddttttdtttttddtdddd ?sJttttdttttddtttd ttd8tttttd8ttdttttttdttdttdtttttdttdttttttd ttdtdttd tttttd ttdttttttdttdtdttdtdtttttdttdtttd ttdtdtdtttttddtd ttdtdttdttttdddd Asttttdttttddtttd ttd8tttttd8ttdttttttdttdttdtttttdttdttttttd ttdtdttd tttttd ttdttttttdttdtdttdtdtttttdttdtttd ttdtdtdtttttddtd ttdtdttdttttdddd AsJttttdttttddtttd ttttdtttttttdttdtdttdttttdttdttdttttttdttdtd ttdtdtttttdttdtttd ttdtdtdtttttddtdttdttdttttdddd BsJttttdttttddttttd tttttdttdttttttdttdttd tttttd ttdtttttttdtdttdtttttdttdtttd ttdtdtdtttttddtdttdttdttttdddd CsRJtttttttddtttd ttttdtttttttdttdtdttdtdtttttdttttd ttdtdtdtttttddtdtdttdttttdddd CsJttttttdEdtttd ttdtttttdttdttttttdttdttdtttttdtttd ttdtdtdtttttdddddd DshJtttdtttttddttttdtttttddtdddd DsJttttdttttd4dtttdttd8tttttd8ttdttttttd ttdttdtttttdttdttttttdttdtd ttd tttttd ttdttttttd8ttdtdttdtdttttddtdttdtttd ttdtdtdttttttdttdtttd ttdtdtdtttttddtd ttdtdttdttttddtd ttdtttd ttdtdtdttdttttdddd FsJttttdttttd4dtttd  ttttdtttttttdttdtd ttdttttdttdttdttttttdttdtd ttdtdttttddtdttdtttd ttdtdtdttttttdttdtttd ttdtdtdtttttddtdttdtdttdttttddtd ttttd ttdtdtdttdttttdddd Gs>Jttttdttttd4dtttdttdtttttdttdttttttdttdtd ttd tttttd ttdttttttdttdtdttdtdttttddtd)ttdtttd ttdtdtdttttttdttdtttd ttdtdtdtttttddtdttdttdttttddtd tttd ttdtdtdttdttttdddd HsuJtttttttd4dtttd  ttttdtttttttdttdtdttdtdttttddtd ttttd ttdtdtdttttttdttttd ttdtdtdtttttddtdtdttdttttdddddd Is:JttttttdFdtttdttdtttttdttdttttttdttdttdttttddtdtttd ttdtdtdttttttdtttd ttdtdtdtttttdddddd IsJtttdtttttd4dttttdtttttd4dtdddd JsJtttttttttdtttd ttttttdttttdtttd ttdtdttttdttttdttttdtttddddd JsJtttttttttdtttd ttttttdttttdtttd ttdtdttttdttttdttttdtttddddd JsJtttttttttdtttdttdttttdtttdttdtddttdtddtttdtdttdtddttdttdttdttdttdttdtdtttttdttddttdtdttdtdttdttdtttttdttdttdttttdttttdtttddddd KsJttttttttttt ttttdttddttdtdttdtdttdttdttdttdttdttttdttttttddddd Ls[Jttttttttttttttttttdddd LsJtttttttttdttttttttttdtdddd LsJtttttttttddttttttttttddtdddd LsJttttttttttttttttttttdddd MsJttttttttttttttttttttdddd Ms:Jtttttttttddttttttttttddtdddd MsmJttttttttttttttttttttdddd MsJttttdtttttttdt tdGtt tttt tttdtd tttttttttdttdtdt tdGtttttt tttdtdtttttttttdttdtt tttt tttdt ttttttttdttdtttttt tttdtttttttttdttddddd NsJttttttttttdt td6 t tttt tttdtd ttttttttttdtdt td6ttttt tttdtdttttttttttddddd OsJttttttttt t tttt tttdt ttttttttdttttttt tttdtttttttttdtdddd Os~Jttttttttttttttttdddd OsJttttttttdtttttttttdtdddd OsJtttttddttttttttttddtttttdddd OsJttttttttttttttttttttdddd Ps*Jttttttttttttttttttttdddd PsUJtttttttttddttttttttttddtdddd PsJttttdttttttttttdtttd ttdtdtd ttdtttttd ttdtdtd ttdtdtttttd ttdttdttttttddddd QsJttttdtttttttt ttd ttdtdtddtd ttdttttd ttdtdtdttdttdttttttddddd QsJtttttttttttttttd ttdtdtdttttttdttdttdttttttddddd QsJttttttttttttttttttttd ttdtdtdddd RsJttttttttttt tttdt tdtttttdtttttt t tdtttt tdtttttttdtdtdddd RsJtttttttttdttt tt tttd ttdtdttttttdddd RsJtttttttttdttt ttttd ttdtdtdtttttttdttddddd SsJtttttttttdttt ttdt tttd ttdtdtd tttttd ttdtdtd ttdttttttdttddddd SsJttttdttttttdtttd ttdttdtdtdttdttd ttdtdtttdttttttttd ttdtdtd ttdtttttttttd ttdtdtd ttdttdttttttdtddddd TsHJtttttttttdttttd ttdtdttttttttttd ttdtdtdtttdttttttdtdttttttdtdttddddd TsJttttttttdtttd ttdttdtttttttttd ttdtdttttttttddddd Us(Jttttttttdtttttdttdt tdtttttdtttttttttdt tdttttttttttdt t tdtttt tdtttttttdtdtdddd UsJttttttttdttdtttdtttdtttdt tttt tdtttdtttdt tttttdtttttttt t ttttttttttdtdddd VsDJttttdttttttdtttd tttdttdttdtdttdtttttdttdtdttdttd ttdtdtddtdttdtdttdtttd ttdtdtd ttdtdttdttdttttttd tttdttttttdtttd ttdtdtdttdtttttttdtttd ttdtdtdttdttdttttttdtddddd WsJtttttttttdtttd ttdttttd ttdtdtdttdttdttttdttdtdttdttdttttttdtdttttttttdtttd ttdtdtdtttdttttttdtdttttttdtdttddddd XsZJttttttttdtttd  tttdttd ttdtttttd ttdtttd ttdtdttdtttttttdtttd ttdtdttttttttddddd XsJttttttttdttttdtttdttdt tdtttttdtdttdtttttttdt tdtttttdtdttttttttdttdt tdtttttdttttttdt t tdtttt tdtttttttdtdtdddd YsJttttttttdttdtttd  ttdtttdt tttt td ttdtttdt tttttd tttdttttttttdt tttt td tttdttttttttdt tttttd ttttttttdt t ttttttttttdtdddd ZsJttttdtttttttt tttttttttdtttdt tdtttdtttttdtttdtttdt tttttttttdtttdt tdtttdtttttdtttdtttddddd [sBJttttttttttt tdtttdttt ttdtttdtttdt tdtttdtttttdtttdtttddddd [sJtttdtttttttt tttttttttttt tttttttttttdddd [sJtttdttttttttttdtttttttdddd \s(Jtttdttdtttttttttdttdttttttdddd \s_Jttttdttttttdttttd tttd ttdtdtttttttt tttttttttdttdttdtdt tdtttdtttttdtttdttdttdt tttttttttdttdttdtdt tdtttdtttttdtttdttdttddddd ]sOJtttttttttdttt tttd ttdtdtttttttt tdtttdtttttdttttdttdt tdtttdtttttdttttdttddddd ]sJttttttttd5tttttd ttdtd tttttttt ttttttttttdtt ttttttttttdtdddd ^sSJtttdtttttttdttttdtttttttdtdddd ^sJtttdttdttttttdttttdttdttttttdtdddd ^sJttttdttttttdttttd tttd ttdtdtdttttttttdtdttdtdttdttttttttdttdtttttt tttttttttttdttdtd t tttttttttdttdttdtd t tdtttdtttttdtttdttdttdt tttttttttttdttdtd t tttttttttdttdttdtd t tdtttdtttttdtttdttdttddddd `s?Jtttttttttdttt tttd ttdtdtdttttttttdttdttdttttttdtdttdttdtttttt tdtttdtttttdttttdttdt tdtttdtttttdttttdttddddd asJttttttttd6tttttd ttdtd tdttttttttdttdttdtttttt ttttttttttdttdtt ttttttttttdttdtdddd asJtttdtttttttdttttdtttttttdtdddd asJtttdttdttttttdttttdttdttttttdtdddd bsJttttdttttttttttdtttttttdttttttttdtttttttdttdttd tttttttd ttttttttdtttttdtttd:ttdttdtttttttdttttttttdtttttttdttdttd tttttttd ttttttttdtttttdtttd:ttdttdtttttttddddd csSJtttttttttttttttttdttttttttttttdtttdttdttttttdttttttttttttdtttdttdttdtttttttdtttttttdttddddd dsJttttttttttttdtttttttdttttttttdtttttttdtttdtttttttdttttttttdtttttttdttttttttdddd dsJttttttttttttttttttttdddd dsJttttttttttdtttttttttttdtdddd dsJttttdttttttddtttd ttdttttddtttdttttttttdtttttttd ttdttd ttttddtttd ttttttttdtttttdtttd?ttdtdttdttttddtttdttttttttdtttttttd ttdttd ttttddtttd ttttttttdtttttdtttd?ttdtttdtttttttttd ttdtdtd tttttttttttd ttdtdtdttdttdttttttddtddddd fsJtttttttttddtttdttttddttdttttttttttttdtttd ttdtdttttddttdttttttttttttdtttd ttdtdtttttttttttd ttdtdtdtttdttttttddtdttttttddtdttddddd gsJttttttttddtttd ttdttttddtttdttttttttdtttttttdttdttdttttddtttdttttttttdtttttttdttdttttttttttd ttdtdtdttttttttdddddd hsJttttttttddttttttttttddttdddd hsJttttttttddttdtttttttttddttdtdddd hsJttttdttttttddtttd ttdttttddtttdttttttttdtttttttd ttdtdttd ttttddtttd ttttttttdtttttdtttd&ttdtdttdttttddtttdttttttttdtttttttd ttdtdttd ttttddtttd ttttttttdtttttdtttd&ttdtdttdttdtttttttd%tdttdttttttttd ttdtdtttdttttttddtttd ttdtdtdttdtttttttddtttd ttdtdtd ttdttdttttttddtddddd jsJtttttttttddtttd ttttddttdttttttttttttdtttdttdtdttttddttdttttttttttttdtttdttdtdttdttdtttttttd tdttdtttttttd1ttdtdttttttttddtttd ttdtdtdtttdttttttddtdttttttddtdttddddd ls8Jttttttttddtttd ttdttttddtttdttttttttdtttttttdttdttdttttddtttdttttttttdtttttttdttdttdttttttttdtdtttttttddtttd ttdtdtdttttttttdddddd ms6Jttttttttddttttttttttddttdddd msiJttttttttddttdtttttttttddttdtdddd msJttttdttttttttttdtttttdttttttttdtttttttdttttdttd tttttd ttttttttdtttttdtttdttttdttdtttttdttttttttdtttttttdttttdttd tttttd ttttttttdtttttdtttdttttddddd nsJttttttttttttt ttdttttttttttttdtttdttttdttttdttttttttttttdtttdttttddddd osIJtttdttttttttttdtttttdttttttttdtttttttttttdtttttdttttttttdtttttttttdddd osJtttdtttttttttttdttttttttdddd psJtttdttdttttttttttdttdtttttttdddd ps?Jttttdttttttddttttdtttttdttttttttdtttttttdttddttdttd tttttd ttttttttdtttttdtttdttddttdttdtttttdttttttttdtttttttdttddttdttd tttttd ttttttttdtttttdtttdttddttdtdttdtttd ttdtdttttttttdddd qsJtttttttttddtttdttttdttttttttttttdttttddttdtdttttdttttttttttttdttttddttdtdttttd ttdtdttttttttdddd rsYJttttttttd6dtttdttdtttttdttttttttdttttttttddttdttdtttttdttttttttdttttttttddttdtttd ttdtdttttttttdddd ssJtttdtttttttddttttdtttttttddtdddd ssSJtttdttdttttttddttttdttdttttttddtdddd ssJttttdttttttddttttd tttttdttttttttdtttttttdttddttdttd tttttd ttttttttdtttttdttttddttdttdtttttdttttttttdtttttttdttddttdttd tttttd ttttttttdtttttdttttddttdtdttdtttd ttdtdtdttttttttddtdttdttdtttttttdttdttdttdttttttdddd us4Jtttttttttddtttdttttdttttttttttttdtttdttddttdtdttttdttttttttttttdtttdttddttdtdttttd ttdtdtdttttttttddtdttdtdttdtttttttdtdttdttdttttttdddd vs?JttttttttdEdtttd ttdtttttdttttttttdtttttttdttddttdttdtttttdttttttttdtttttttdttddttdtttd ttdtdtdttttttttddtdttdttdttttttdddd ws+Jtttdtttttttddttttdtttttttddtdddd wsfJtttdttdttttttddttttdttdttttttddtdddd wsJtttttddttttttttdttttddtttd ttdtdtdHttdtttdttttttd ttdtdtdIttdtdtttddttttttttttdGtdIttd4dtdtttd4dttttttd4tdddd xsnJtttttddttttttttdttttddtttd ttdtdtdttdtttddttttttttttdGtdttddtdtttddttttttttttdGtdttddtdtttddttttttdtdddd ys3Jtttttttttttttdtttttttd ttdtdtd ttdtttttttttttttdGtd ttddtdtttddttttttdtdddd ysJtttttttttttttd tttttttttttdGtttttdtttttttttttdGtttttdtttttttttdddd zs6JttttttttttddtttdtttttttttttttdGttddtdttdttttttttdddd zsJttttttttttddtttd tttddttttttttttdGtdttddtdtttddttttttttttdGtdttddtdtttttd ttdtdtdttdttttdttdtttttdttttdddddd {scJtttttddttttttdtttd ttdttdtttdJdtttdtdJdtdJdttdKdtddttdttdtdLttdtdtttttd dtttttttddtd dtdKdttdttdtdMttdtdtttd4dttttttdtd4tdddd |s9Jtttttddttttttdtttd ttdttdtttd dtttdtd dtd dttdJdtdKdttdttdtdNttdtdtttttd4dtttttttddtd4dtdJdttdttdtdOttdtdtttddttttttdtdtdddd }sJtttttttttttdtttd ttdttdtttd4dtttdtd4dtd4dttd dtdJdttdttdtdPttdtdtttttddtttttttddtddtd dttdttdtdttdtdtttddttttttdtdtdddd }sJttttttttdttttttd ttdttdtttddtttdtddtddttd4dtd dttdttdtdttdtdtttttddtttttttddtddtd4dttdttdtdttdtdtttttttttdtdddd ~sJttttttttdtttddtttd  ttdttdtttddtttddtddtdttddtd4dttdttdtdttdtdttttttttttttddtddtddttdttdttdtdttttttdttttdddd srJttttttttdtttddtttd ttdttdttttttddtddtdttddtddttdttdtdttdtdtttttttttdGdtddtddttdttdtdttdttttdttttttdtdttttdddddd s@Jtttttddttttttdtttd  ttttttddttttttdtttd ttdtdttdttdtttddttttttdtdtdddd sJtttttttttttdtttd ttttttddttttttdtttd ttdtdtttdtttddttttttdtdtdddd s>Jttttttttdttttttd  ttttttttttttdtttd ttdtdtttdtttttttttdtdddd sJttttttttdtttddtttd tttttttttdttttttd ttdtdtttdttttttdttttdddd sJttttttttdtttddtttdtttttttttdtttddtttd ttdtdtttdttttttdtdttttdddddd sJtttttddtttttttttttddttttttdddd sJttttttttttttttttttttttdddd sJtttdttttttttttttdtttttttttdddd s:Jtttdtttddtttttttttdtttddttttttdddd syJtttttddttttttdttttttddttttttdtdddd sJtttttttttttdttttttttttttdtdddd sJtttdtttttttttdttttdtttttttttdtdddd s.Jtttdtttddttttttdttttdtttddttttttdtdddd suJdS)QNrrT)expand_diff _numerical r (}KiqLiei*iw-iD60Ai $i`ii@`i5 i@iAii@@Q i Hi@2ii>di iPi1 i?i;#i)rrxrrarrrrrrrr IntegratePirrbmrrr5nrcrrdr=r<rHrH^/tmp/pip-target-vg8gfxp4/lib/python/sympy/integrals/rubi/rubi_tests/tests/test_inverse_sine.pytest_1s^p&j>2Xb\Vz vT\T@N^F x^nl0(^n*R^nd& F&V\@V>lxVf$>f4.fprRfN^fVVfVFVfVVfv (~(Z^n*n~6n~lf6Vf`fvfv@fvxvBvn^n~~n~rJ(8syssympy.externalrrdisabled version_info%sympy.integrals.rubi.utility_functionrrr r r r r rrrrrrrrrrrrrrrrrrr r!r"r#r$r%r&r'r(r)r*r+r,r-r.r/r0r1r2r3r4r5r6r7r8r9r:r;r<r=r>r?r@rArBrCrDrErFrGrHrIrJrKrLrMrNrOrPrQrRrSrTrUrVrWrXrYrZr[r\r]r^r_r`rarbrcrdrerfrgrhrirjrkrlrmrnrorprqrrrsrtrurvrwrxryrzr{r|r}r~rrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrr r r r r rrrrrrrrrrrrrrrrrrr r!r"r#r$r%r&r'r(r)r*r+r,r-r.r/r0r1r2r3r4r5r6r7r8r9r:r;r<r=r>r?r@rArBrCrDrErFrGrHrIrJrKrLrMrNrOrPrQrRrSrTrUrVrWrXrYrZr[r\r]r^r_r`rarbrcrdrerfrgrhrirjrkrlrmrnrorprqrrrsrtrurvrwrxryrzr{r|r}r~rrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrsympy.core.addrsympy.core.modrsympy.core.mulrsympy.core.numbersrrrsympy.core.powerrsympy.core.singletonr$sympy.functions.elementary.complexesr(sympy.functions.elementary.miscellaneousrsympy.integrals.integralsrrAsympy.logic.boolalgrrsympy.simplify.simplifyrsympy.integrals.rubi.symbolrsympy.core.symbolrrsympy.functionsrrrrrrrrr%sympy.functions.elementary.hyperbolicrrrrrrrrrrrr(sympy.functions.elementary.trigonometricrrrrrrsympy.integrals.rubi.rubimainrrrBr@rCrFrGefrDrEr?ukprstijABCghyzqvwFrJrHrHrHrIsN m"Zj:Nb