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Mini Shell
Mini Shell
"""
This code is automatically generated. Never edit it manually.
For details of generating the code see `rubi_parsing_guide.md` in `parsetools`.
"""
from sympy.external import import_module
matchpy = import_module("matchpy")
if matchpy:
from matchpy import Pattern, ReplacementRule, CustomConstraint, is_match
from sympy.integrals.rubi.utility_function import (
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, SubstFor, SubstForAux, 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, Factor, PolyLog, CosIntegral, SinIntegral, LogIntegral, SinhIntegral,
CoshIntegral, Rule, Erf, PolyGamma, ExpIntegralEi, ExpIntegralE, LogGamma , UtilityOperator, Factorial,
Zeta, ProductLog, DerivativeDivides, HypergeometricPFQ, IntHide, OneQ, Null, rubi_exp as exp, rubi_log as log, Discriminant,
Negative, Quotient
)
from sympy import (Integral, S, sqrt, And, Or, Integer, Float, Mod, I, Abs, simplify, Mul,
Add, Pow, sign, EulerGamma)
from sympy.integrals.rubi.symbol import WC
from sympy.core.symbol import symbols, Symbol
from sympy.functions import (sin, cos, tan, cot, csc, sec, sqrt, erf)
from sympy.functions.elementary.hyperbolic import (acosh, asinh, atanh, acoth, acsch, asech, cosh, sinh, tanh, coth, sech, csch)
from sympy.functions.elementary.trigonometric import (atan, acsc, asin, acot, acos, asec, atan2)
from sympy import pi as Pi
A_, B_, C_, F_, G_, H_, a_, b_, c_, d_, e_, f_, g_, h_, i_, j_, k_, l_, m_, n_, p_, q_, r_, t_, u_, v_, s_, w_, x_, y_, z_ = [WC(i) for i in 'ABCFGHabcdefghijklmnpqrtuvswxyz']
a1_, a2_, b1_, b2_, c1_, c2_, d1_, d2_, n1_, n2_, e1_, e2_, f1_, f2_, g1_, g2_, n1_, n2_, n3_, Pq_, Pm_, Px_, Qm_, Qr_, Qx_, jn_, mn_, non2_, RFx_, RGx_ = [WC(i) for i in ['a1', 'a2', 'b1', 'b2', 'c1', 'c2', 'd1', 'd2', 'n1', 'n2', 'e1', 'e2', 'f1', 'f2', 'g1', 'g2', 'n1', 'n2', 'n3', 'Pq', 'Pm', 'Px', 'Qm', 'Qr', 'Qx', 'jn', 'mn', 'non2', 'RFx', 'RGx']]
i, ii, Pqq, Q, R, r, C, k, u = symbols('i ii Pqq Q R r C k u')
_UseGamma = False
ShowSteps = False
StepCounter = None
def {}():
Zerion Mini Shell 1.0