Index

Symbols

* AIntervalCategory, [1], [2], [3] QEtaAlgebra, [1] QEtaLazyAlgebra + AIntervalCategory, [1] QEtaAlgebra - AIntervalCategory, [1] QEtaAlgebra, [1] / AIntervalCategory QEtaAlgebraCachedSamba QEtaExtendedAlgebra QEtaPowerGradedAlgebra

0 AIntervalCategory QEtaAlgebra 1 AIntervalCategory QEtaAlgebra = AIntervalCategory ^ AIntervalCategory, [1] QEtaAlgebra

A

abs AIntervalCategory absList AlgebraicNumberTool addBasisElementPairs! QEtaComputation addGapPair! QEtaComputation addGapPairs! QEtaComputation addPair! QEtaComputation addWeight QEtaWeightedDomain AInterval AIntervalCategory *, [1], [2], [3] +, [1] -, [1] / 0 1 = ^, [1] abs coerce contains?, [1] error? inf interval inv negative? one? positive? qinterval sup unit? width zero? algebraBasis QEtaComputationCategory QEtaRamanujanKolbergIdentity AlgebraicNumberTool absList approximateNestedRadical approximateNthRoot combineCommonSqrt combineIntegerRoot? combinePositiveIntegerRoot? combineSameRoot? combineSqrtFactors complexValue integerRootFactor integerRootFactorK integerRootKernel? integerRootKernels isSqrt mapOverFactors recursiveRootSimplification recursiveRootSimplificationPoly rootCombine rootFactor rootFactorK rootFactorPol simpler? simplifyRadicals sqrtArgument sqrtSum sqrtSumArguments

algebraicRelations QEtaIdealCategory allGeneralizedEtaFunctionIndices QEtaSpecification allPureExponents QEtaSpecification alphaInfinity QEtaRamanujanKolbergIdentity QEtaSpecification alphaOrbitInfinity QEtaRamanujanKolbergIdentity alphaSchoenebergContribution QEtaAuxiliaryPackage applyLambdaTransformation QEtaModularLambdaTools approximateNestedRadical AlgebraicNumberTool approximateNthRoot AlgebraicNumberTool approximatesPi? QEtaOneOverPiQ asExpression? QEtaSpecification

B

balance QEtaAuxiliaryPackage basefactor SymbolicModularEtaQuotientGamma basis QEtaAlgebraBasisCategory, [1] QEtaComputation QEtaComputationModularEquation

basisElements QEtaAlgebraBasis QEtaPowerAlgebraBasisCategory

C

CachedPower power!, [1] CachedPowerScaled elt, [1] CachedQFunctions eulerFunctionPower jacobiFunctionPower kleinJInvariantPower modularLambdaPower thetaPower4 candidateLevelsCoEtaQuotient QEtaModularCategory cdExponent SymbolicEtaGamma SymbolicEtaQuotientLambdaGamma chineseRemainder QEtaAuxiliaryPackage choose QEtaLaurentSeriesCategory chudnovskyA2tau QEtaOneOverPiQ chudnovskyABFCoefficients QEtaOneOverPiQ chudnovskyB2tauCandidates QEtaOneOverPiQ chudnovskyChi QEtaOneOverPiQ chudnovskyContainsOneOverPiInterval? QEtaOneOverPiQ chudnovskyModularPolynomial QEtaOneOverPiQ chudnovskyOneOverPiFormula QEtaOneOverPiQ chudnovskyOneOverPiSummand QEtaOneOverPiQ chudnovskySelectABF QEtaOneOverPiQ classicalModularPolynomial QEtaClassicalModularPolynomial, [1], [2], [3] clearCache! QEtaAlgebraCachedSamba clearDenominator QAuxiliaryTools clearDenominators X4ti2 coefficient QEtaRamanujanKolbergIdentity coerce AIntervalCategory Cusp ModularEtaQuotientQSeriesInfinityTools, [1] ModularEtaQuotientQSeriesTools ModularFunctionQSeries ModularFunctionQSeriesConstructor ModularFunctionQSeriesInfinity, [1] PolynomialConversion, [1] QEtaAlgebraCachedSamba QEtaCheckingTruncatedLaurentSeries QEtaExtendedAlgebraBasis QEtaLazyAlgebra, [1] QEtaPolynomialAlgebra, [1] QEtaPowerPolynomialAlgebra QEtaSpecificationRing, [1] QEtaTruncatedTaylorSeries, [1] SymbolicModularEtaQuotientGamma TruncatedModularFunctionQSeriesInfinity, [1] cofactor SymbolicModularEtaQuotientGamma cofactorX QEtaRamanujanKolbergIdentity combineCommonSqrt AlgebraicNumberTool combineIntegerRoot? AlgebraicNumberTool combinePositiveIntegerRoot? AlgebraicNumberTool combineSameRoot? AlgebraicNumberTool combineSqrtFactors AlgebraicNumberTool complexValue AlgebraicNumberTool component QEtaPowerAlgebraBasisCategory computePairs! QEtaComputation computeReducedCusps QEtaModularLambdaAuxiliaryPackage

conditionCoEtaQuotient? QEtaModularCategory conditionEvenMultiplier? QEtaCofactorConditions conditionGSigma0? QEtaCofactorConditions conditionMmN? QEtaCofactorConditions conditionNDivisor? QEtaCofactorConditions conditionOrbitLength? QEtaCofactorConditions conditionPrimeDivisors? QEtaCofactorConditions conditionRho0ProperGeneralized? QEtaCofactorConditions conditionRho0Pure? QEtaCofactorConditions conditionSumExponentsProperGeneralized? QEtaCofactorConditions conditionSumExponentsPure? QEtaCofactorConditions CongruenceSubgroup cusps cuspToMatrix dimensionOfCuspForms dimensionOfEisensteinSubspace dimensionOfModularForms doubleCosetRepresentatives equivalentCusps? even? genus index member? normalizeCusp nu2 nu3 numberOfCusps projectiveIndex rightCosetRepresentatives width, [1] CongruenceSubgroupGamma0 CongruenceSubgroupGamma1 CongruenceSubgroupGammaN constant? SymbolicModularEtaQuotient contains? AIntervalCategory, [1] QEtaAuxiliaryPackage containsOneOverPiInterval? QEtaOneOverPiQ continue? QEtaComputationCategory convergentInterval QEtaOneOverPiQ coSpecification QEtaRamanujanKolbergIdentity SymbolicModularEtaQuotient countRoots QEtaAuxiliaryPackage cqD QEtaOneOverPi criticalElements? QEtaComputationCategory Cusp coerce cusp, [1] cuspToMatrix denom infinity infinity? moebiusTransform, [1] numer rational cusp Cusp, [1] cuspDeltaMatrices QEtaModularLambdaAuxiliaryPackage, [1] cuspMatrices QEtaModularCategory cusps CongruenceSubgroup QEtaModularCategory cuspToMatrix CongruenceSubgroup Cusp QEtaModularCategory

D

decomposeIntoSTProduct QEtaFundamentalDomain dedekindSum QEtaAuxiliaryPackage definingSpecification QEtaRamanujanKolbergIdentity SymbolicEtaQuotientGamma SymbolicEtaQuotientLambdaGamma SymbolicModularEtaQuotient delta SymbolicEtaGamma denom Cusp QEtaSpecification

denomB QEtaOneOverPiLambda dilate QEtaSpecification dimensionOfCuspForms CongruenceSubgroup dimensionOfEisensteinSubspace CongruenceSubgroup dimensionOfModularForms CongruenceSubgroup doubleCosetRepresentatives CongruenceSubgroup downloadClassicalModularPolynomial QEtaClassicalModularPolynomial

E

eisensteinE2 QFunctions, [1] eisensteinE4 QFunctions eisensteinE6 QFunctions elt CachedPowerScaled, [1] ModularFunctionQSeriesCategory SymbolicEtaQuotientGamma SymbolicEtaQuotientLambdaGamma SymbolicModularEtaQuotient embed QEtaAlgebraCachedSamba QEtaExtendedAlgebra equationX QEtaRamanujanKolbergIdentity, [1] equivalentCusps? CongruenceSubgroup equivalentCuspsByMatrices? QEtaModularLambdaAuxiliaryPackage error? AIntervalCategory estimatedWeightAfterReduction QEtaMultiReductionCategory estimateExpansionOrders QEtaOneOverPiLambda eta EtaQuotientQSeriesInfinity SymbolicEtaGamma etaCofactorInfinity QEtaModularPackage, [1] etaCofactorNoPoles QEtaModularPackage etaCofactorNoPolesSystem QEtaModularPackage etaCofactorSpace QEtaModularCategory QEtaModularPackage, [1] etaCofactorSpaceSystem QEtaModularCategory etaFunctionIndices QEtaSpecification etaLaurentIdealGenerators QEtaIdealCategory, [1] etaLaurentIdealLists QEtaIdealCategory etaPolynomial QEtaSpecification, [1], [2] QEtaSpecificationRing, [1] etaPower EtaQuotientQSeriesInfinity etaQuotient QEtaRamanujanKolbergIdentity QEtaSpecification SymbolicEtaQuotientGamma, [1] SymbolicEtaQuotientLambdaGamma SymbolicModularEtaQuotient, [1], [2], [3], [4], [5] SymbolicModularEtaQuotientGamma, [1], [2] etaQuotientIdealGenerators QEtaIdealCategory, [1], [2] etaQuotientInfinity EtaQuotientQSeriesInfinity etaQuotientInfinitySpecifications QEtaQuotientSpecifications4ti2 etaQuotientMonoidInfinitySpecifications QEtaQuotientSpecifications4ti2, [1] etaQuotientMonoidInfinitySystem QEtaModularCategory etaQuotientMonoidInfinityZSpecifications QEtaQuotientSpecifications4ti2 etaQuotientMonoidNoPolesSolutions QEtaQuotientSpecifications4ti2 etaQuotientMonoidNoPolesSystem QEtaModularCategory etaQuotientMonoidNoPolesZSpecifications QEtaQuotientSpecifications4ti2 etaQuotientMonoidSolutions QEtaQuotientSpecifications4ti2, [1], [2] etaQuotientMonoidSystem QEtaModularCategory, [1], [2] etaQuotientMonoidZSpecifications QEtaQuotientSpecifications4ti2, [1], [2] EtaQuotientQSeriesInfinity eta etaPower etaQuotientInfinity eulerExpansion eulerExponent eulerFunctionPower expansion generalizedEtaPower polynomialToEta prefactor seriesPart

etaQuotientRepresentation QEtaRamanujanKolbergIdentity etaQuotientSpecification QEtaSpecification, [1], [2], [3], [4], [5], [6], [7], [8], [9], [10] etaQuotientTraceExpansions SymbolicEtaQuotientQSeriesTools, [1] etaQuotientX QEtaRamanujanKolbergIdentity etaQuotientZSpecifications QEtaQuotientSpecifications4ti2 etaRationalFunction QEtaSpecification, [1], [2] QEtaSpecificationRing, [1] etaRelation QEtaRamanujanKolbergIdentity etaRelationMonomial QEtaRamanujanKolbergIdentity etaRelations QEtaIdealCategory, [1], [2] eulerExpansion EtaQuotientQSeriesInfinity eulerExponent EtaQuotientQSeriesInfinity eulerFunction QFunctions eulerFunction2 QFunctions eulerFunctionPower CachedQFunctions EtaQuotientQSeriesInfinity eulerFunctionPower3 QFunctions eulerStream QFunctions eval PolynomialEvaluation, [1] evalAtModularLambda QEtaModularLambdaTools, [1] evaluate QEtaModularEquation even? CongruenceSubgroup exact? QEtaCheckingTruncatedLaurentSeries QEtaTruncatedLaurentSeries QEtaTruncatedTaylorSeries TruncatedModularFunctionQSeriesInfinity execute RunExternalCommand exIota1 QEtaOneOverPiLambda exIotaN QEtaOneOverPiLambda exp2PiI QEtaOneOverPiQ exp2PiIInterval QEtaOneOverPiQ expand? QEtaRamanujanKolbergIdentity expandB QEtaOneOverPiLambda expandK QEtaOneOverPiLambda expandL QEtaOneOverPiLambda expandPhiTerm QEtaOneOverPiLambda expansion EtaQuotientQSeriesInfinity exponent QEtaSpecification, [1] exponentGcd QEtaLaurentSeriesCategory QEtaTaylorSeriesCategory exponents QEtaSpecification expPiI QEtaOneOverPiQ expPiIInterval QEtaOneOverPiQ expPrecisionOdd QEtaAuxiliaryPackage expTruncated QEtaOneOverPi extendedNormalForm QEtaGroebner, [1] extendedNormalForms QEtaGroebner extractNext! QEtaComputationCategory

F

f QEtaRamanujanKolbergIdentity findIdentity QEtaRamanujanKolberg, [1], [2], [3], [4], [5], [6], [7] first QEtaExtendedAlgebra forgetWeight QEtaWeightedDomain formatAsExpression QEtaSpecification formatAsNonModular QEtaRamanujanKolbergIdentity formatExpanded QEtaRamanujanKolbergIdentity formatWithQFactor QEtaSpecification

formatWithSubscript QEtaSpecification fractionalBernoulli1 QEtaAuxiliaryPackage fractionalBernoulli2 QEtaAuxiliaryPackage fractionalPart QEtaAuxiliaryPackage fromEtaToQPochhammer QAuxiliaryTools, [1] fromQPochhammerToEta QAuxiliaryTools, [1] functionExpansionPair QEtaScalingCuspReduction

G

gamma1 SymbolicEtaGamma gammaCandidate SatoEigenValueProblem gammaCandidateWurm SatoEigenValueProblem gammaTauQCandidateAux SatoEigenValueProblem gammaTauQCandidates SatoEigenValueProblem gammaTauQCandidatesAux SatoEigenValueProblem gammaTauQCandidatesWurm SatoEigenValueProblem GaussRoot squareRoot squareRootOfRadicalInteger generalizedDedekindSum QEtaAuxiliaryPackage generalizedEtaFunctionIndices QEtaSpecification generalizedEtaPower EtaQuotientQSeriesInfinity generalizedEulerProduct QFunctions genus CongruenceSubgroup QEtaModularCategory getCache QEtaAlgebraCachedSamba gosperABFCoefficients QEtaOneOverPiQ gosperAtau QEtaOneOverPiQ

gosperBtauCandidates QEtaOneOverPiQ gosperCheckModularPolynomial QEtaOneOverPiQ gosperContainsOneOverPiInterval? QEtaOneOverPiQ gosperIotaAt QEtaOneOverPiQ gosperIotaInterval QEtaOneOverPiQ gosperModularPolynomial QEtaOneOverPiQ, [1] gosperModularPolynomial1N QEtaOneOverPiQ gosperOneOverPiFormula QEtaOneOverPiQ gosperOneOverPiSummand QEtaOneOverPiQ gosperSelectABF QEtaOneOverPiQ greater? QEtaMultiWeightSorting greaterGrade? QEtaLinearReduction QEtaPowerReductionCategory groebner QEtaGroebner groebnerBasis QEtaGroebnerBasisTools groebnerEliminate QEtaGroebnerBasisTools groebnerExtend QEtaGroebner guessEtaQuotientSpecification QEtaRepresentation, [1], [2]

H

hasEquivalentCuspByMatrices? QEtaModularLambdaAuxiliaryPackage

I

identifier QEtaAlgebraCachedSamba identity QEtaRamanujanKolbergIdentity identityPolynomial QEtaRamanujanKolbergIdentity index CongruenceSubgroup QAuxiliaryTools indexedSymbol QAuxiliaryTools indexedSymbols QAuxiliaryTools, [1], [2] indexPermutation QEtaPowerAlgebraBasisCategory indices QEtaSpecification inf AIntervalCategory infinity Cusp infinity? Cusp

initialize QEtaAlgebraBasisCategory QEtaComputationCategory, [1] QEtaPowerAlgebraBasisCategory integerPrimitivePart QAuxiliaryTools integerRootFactor AlgebraicNumberTool integerRootFactorK AlgebraicNumberTool integerRootKernel? AlgebraicNumberTool integerRootKernels AlgebraicNumberTool interMinimizeVectors QEtaAuxiliaryPackage interval AIntervalCategory inv AIntervalCategory isSqrt AlgebraicNumberTool

J

jacobiFunction QFunctions, [1] jacobiFunctionPower CachedQFunctions jacobiLowerStar QEtaAuxiliaryPackage jacobiThetaPermutation QEtaAuxiliaryPackage, [1]

jacobiThetaPermutation2 QEtaAuxiliaryPackage jacobiThetaUpsilonExponent QEtaAuxiliaryPackage jacobiUpperStar QEtaAuxiliaryPackage join SageMathTools

K

kappaSchoeneberg QEtaAuxiliaryPackage, [1] kappaYang QEtaAuxiliaryPackage, [1] kleinJAt QEtaOneOverPiQ kleinJInterval QEtaOneOverPiQ

kleinJInvariant QFunctions kleinJInvariantPower CachedQFunctions knownCommands RunExternalCommand

L

lambda SymbolicEtaGamma SymbolicEtaQuotientLambdaGamma laurent QEtaLaurentSeriesCategory QEtaQSeriesTools, [1] QEtaTruncatedLaurentSeries, [1] laurentExpansion SymbolicEtaQuotientQSeriesTools laurentExpansionInfinity ModularEtaQuotientQSeriesInfinityTools, [1] SymbolicEtaQuotientQSeriesTools laurentExpansions SymbolicEtaQuotientQSeriesTools, [1], [2] laurentRelations QEtaIdealCategory less? QEtaMultiWeightSorting

lessLex? QEtaMultiWeightSorting QEtaQuotientSortPackage lessWeight? QEtaWeightedDomain level QAuxiliaryTools, [1] QEtaSpecification QEtaSpecificationRing SymbolicModularEtaQuotient linearTransform QEtaLinearReduction, [1] listTranspose QEtaAuxiliaryPackage logDtheta4 QEtaOneOverPiLambda

M

makedir QEtaAuxiliaryPackage map QEtaLaurentSeriesFunctions2 mapn QEtaLaurentSeriesCategory QEtaTaylorSeriesCategory mapOverFactors AlgebraicNumberTool matrixAtkinLehner QEtaAuxiliaryPackage matrixEtaOrder QEtaModularCategory matrixEtaOrderElement QEtaModularCategory matrixEtaOrderFull QEtaModularCategory matrixEtaOrderRow QEtaModularCategory matrixLigozat QEtaModularGamma0 matrixLigozatElement QEtaModularGamma0 matrixModular QEtaModularCategory maxIndex QEtaPowerGradedAlgebra member? CongruenceSubgroup QEtaGroebner minimalLevelCoEtaQuotient QEtaModularCategory minimalRootOfUnity SymbolicEtaGamma SymbolicEtaQuotientGamma SymbolicEtaQuotientLambdaGamma SymbolicModularEtaQuotient SymbolicModularEtaQuotientGamma minimalRootOfUnityForSquareRootOf MinimalSquareRoot minimalRootOfUnityForSquareRootOfRadicalInteger MinimalSquareRoot minimalRootOfUnityWithoutPrefactors SymbolicEtaGamma minimalRootOfUnityWithoutUnityExponent SymbolicEtaQuotientLambdaGamma MinimalSquareRoot minimalRootOfUnityForSquareRootOf minimalRootOfUnityForSquareRootOfRadicalInteger rationalSquareRoot minimizeOrderVectors QEtaModularPackage minimizeVector QEtaAuxiliaryPackage, [1] modular? QEtaModularCategory, [1] modularEtaQuotient ModularEtaQuotientQSeriesTools, [1] modularEtaQuotientInfinity ModularEtaQuotientQSeriesInfinityTools, [1] ModularEtaQuotientQSeriesInfinityTools coerce, [1] laurentExpansionInfinity, [1] modularEtaQuotientInfinity, [1] ModularEtaQuotientQSeriesTools coerce modularEtaQuotient, [1] modularFormGenerators QEtaModularFormGenerators4ti2, [1] modularFormSolutions QEtaModularFormGenerators4ti2, [1] modularFormSystem QEtaModularFormGeneratorsSystem, [1] QEtaModularFormSystem, [1] modularFunctionIdentity? QEtaRamanujanKolbergIdentity

ModularFunctionQSeries coerce ModularFunctionQSeriesCategory elt removeZeroes, [1] series ModularFunctionQSeriesConstructor coerce ModularFunctionQSeriesInfinity coerce, [1] qetaTaylorRep modularGamma0 QEtaAuxiliaryPackage QEtaSpecification modularGamma0? QEtaAuxiliaryPackage QEtaSpecification QEtaSpecificationRing modularGamma1 QEtaSpecification modularGamma1? QEtaSpecification QEtaSpecificationRing modularLambdaInterval QEtaOneOverPiQ modularLambdaPower CachedQFunctions modularOrbit QEtaModularCategory modularPolynomial QEtaModularEquation, [1], [2], [3], [4] QEtaModularEquationPrimeField, [1], [2], [3] QEtaModularEquationQ, [1], [2] QEtaModularEquationT, [1], [2], [3], [4] modularPolynomialCached QEtaModularEquation, [1], [2], [3], [4], [5] moduleCoefficients QEtaRamanujanKolbergIdentity moduleRepresentation QEtaRamanujanKolbergIdentity moebiusTransform Cusp, [1] QEtaOneOverPi, [1] monoidGenerators QEtaQuotientMonoidTools monoidSpecifications QEtaRamanujanKolbergIdentity monomial QEtaRamanujanKolbergIdentity QEtaSpecification, [1], [2] monomialQuotient QEtaRamanujanKolbergIdentity QEtaSpecification monomialQuotientX QEtaRamanujanKolbergIdentity Monomials monomialX QEtaRamanujanKolbergIdentity multiplier QEtaAlgebraBasisCategory QEtaRamanujanKolbergIdentity SymbolicEtaGamma SymbolicEtaQuotientGamma SymbolicEtaQuotientLambdaGamma SymbolicModularEtaQuotient multiplierPower! QEtaAlgebraBasisCategory multipliers QEtaPowerAlgebraBasisCategory multiplyExponents QEtaLaurentSeries QEtaTaylorSeries multisect QEtaTaylorSeriesCategory

N

negative? AIntervalCategory nextIdentifier QEtaAlgebraCachedSamba nonConstantMonoidSpecifications QEtaRamanujanKolbergIdentity, [1] nonPositive? QEtaMultiComputationCategory normalForms QEtaGroebner normalizeCusp CongruenceSubgroup noTrace QEtaComputationCategory QEtaComputationReductionCategory QEtaPowerReductionCategory

noTraceEnter QEtaComputationReductionCategory QEtaPowerReductionCategory nu2 CongruenceSubgroup nu3 CongruenceSubgroup numberOfCusps CongruenceSubgroup numberOfGaps QEtaAlgebraBasisCategory QEtaAuxiliaryPackage numberOfGapsForSamba QEtaModularCategory numer Cusp QEtaSpecification

O

offset SymbolicEtaQuotientGamma SymbolicModularEtaQuotient one? AIntervalCategory SymbolicEtaQuotientGamma SymbolicModularEtaQuotient SymbolicModularEtaQuotientGamma oneOverPiFormulaInterval QEtaOneOverPiQ oneOverPiTerm QEtaOneOverPiQ oneStep! QEtaComputationCategory oneStepComputation! QEtaComputationCategory oneTracedStep! QEtaComputationCategory oneTracedStepComputation! QEtaComputationCategory

oneVerboseStep! QEtaComputation QEtaComputationDelayedPairs QEtaComputationModularEquation QEtaComputationNoPairs QEtaMultiComputationCategory QEtaPowerComputation orbit QEtaRamanujanKolbergIdentity orbitProduct QEtaRamanujanKolbergIdentity, [1] orbitProductX QEtaRamanujanKolbergIdentity, [1] order SymbolicModularEtaQuotientGamma orderMin SymbolicModularEtaQuotientGamma orders SymbolicModularEtaQuotient ordersMin SymbolicModularEtaQuotient

P

partitionSeries QFunctions parts QEtaSpecification PolynomialConversion coerce, [1] PolynomialEvaluation eval, [1] polynomialToEta EtaQuotientQSeriesInfinity positive? AIntervalCategory QEtaMultiComputationCategory postProcess! QEtaComputationCategory power QEtaAlgebraCachedSamba power! CachedPower, [1] precision QEtaCheckingTruncatedLaurentSeries QEtaTruncatedLaurentSeries QEtaTruncatedTaylorSeries TruncatedModularFunctionQSeriesInfinity prefactor EtaQuotientQSeriesInfinity pretty QEtaRamanujanKolbergIdentity, [1], [2], [3], [4] QEtaSpecificationRing, [1], [2]

prettyVariable QEtaSpecification primePower QEtaAuxiliaryPackage project QEtaModularEquationPrimeField, [1], [2], [3] projectiveIndex CongruenceSubgroup properGeneralizedEtaFunctionIndices QEtaSpecification properGeneralizedParts QEtaSpecification puiseux QEtaPuiseuxSeries puiseuxExpansion SymbolicEtaQuotientQSeriesTools, [1], [2] pure? QEtaSpecification SymbolicEtaGamma pureExponents QEtaSpecification pureParts QEtaSpecification purify QEtaSpecification QEtaSpecificationRing

Q

QAuxiliaryTools clearDenominator fromEtaToQPochhammer, [1] fromQPochhammerToEta, [1] index indexedSymbol indexedSymbols, [1], [2] integerPrimitivePart level, [1] qcofactor QEtaRamanujanKolbergIdentity qcofactorX QEtaRamanujanKolbergIdentity qequationX QEtaRamanujanKolbergIdentity, [1] QEtaAlgebra *, [1] + -, [1] 0 1 ^ traceout zero? QEtaAlgebraBasis basisElements QEtaAlgebraBasisCategory basis, [1] initialize multiplier multiplierPower! numberOfGaps QEtaAlgebraCachedSamba / clearCache! coerce embed getCache identifier nextIdentifier power setCache! QEtaAuxiliaryPackage alphaSchoenebergContribution balance chineseRemainder contains? countRoots dedekindSum expPrecisionOdd fractionalBernoulli1 fractionalBernoulli2 fractionalPart generalizedDedekindSum interMinimizeVectors jacobiLowerStar jacobiThetaPermutation, [1] jacobiThetaPermutation2 jacobiThetaUpsilonExponent jacobiUpperStar kappaSchoeneberg, [1] kappaYang, [1] listTranspose makedir matrixAtkinLehner minimizeVector, [1] modularGamma0 modularGamma0? numberOfGaps primePower quadraticIrrational readInputFromFile readPolynomialFromFile readPolynomialListFromFile realExpPiIForm sawTooth signVariations splitMatrix, [1], [2] sturmSequence upsilonExponent, [1] verticalConcat writeValueToFile QEtaCheckingTruncatedLaurentSeries coerce exact? precision truncateAt zero? QEtaClassicalModularPolynomial classicalModularPolynomial, [1], [2], [3] downloadClassicalModularPolynomial qetaCoefficient QEtaGradedAlgebra QEtaCofactorConditions conditionEvenMultiplier? conditionGSigma0? conditionMmN? conditionNDivisor? conditionOrbitLength? conditionPrimeDivisors? conditionRho0ProperGeneralized? conditionRho0Pure? conditionSumExponentsProperGeneralized? conditionSumExponentsPure? QEtaComputation addBasisElementPairs! addGapPair! addGapPairs! addPair! basis computePairs! oneVerboseStep! update! QEtaComputationCategory algebraBasis continue? criticalElements? extractNext! initialize, [1] noTrace oneStep! oneStepComputation! oneTracedStep! oneTracedStepComputation! postProcess! trace QEtaComputationDelayedPairs oneVerboseStep! QEtaComputationModularEquation basis oneVerboseStep! update! QEtaComputationNoPairs oneVerboseStep! QEtaComputationReductionCategory noTrace noTraceEnter reduce topReducible? tracedReduce traceEnter traceLoop traceReturn QEtaExtendedAlgebra / embed first second QEtaExtendedAlgebraBasis coerce QEtaExtendedReduction QEtaFundamentalDomain decomposeIntoSTProduct toFundamentalDomain qetaGrade QEtaGradedAlgebra QEtaPowerGradedAlgebra, [1] QEtaGradedAlgebra qetaCoefficient qetaGrade qetaLeadingCoefficient qetaGrades QEtaModularPackage, [1], [2] QEtaPowerGradedAlgebra QEtaGroebner extendedNormalForm, [1] extendedNormalForms groebner groebnerExtend member? normalForms QEtaGroebnerBasisTools groebnerBasis groebnerEliminate QEtaIdealCategory algebraicRelations etaLaurentIdealGenerators, [1] etaLaurentIdealLists etaQuotientIdealGenerators, [1], [2] etaRelations, [1], [2] laurentRelations relationsIdealGenerators QEtaIdealHemmecke qetaIndex QEtaPowerGradedAlgebra qetaLaurentRep QEtaPuiseuxSeries QEtaLaurentSeries multiplyExponents qetaTaylorRep traceout zeroCheckingChoose QEtaLaurentSeriesCategory choose exponentGcd laurent mapn removeZeroes, [1] revert QEtaLaurentSeriesFunctions2 map QEtaLazyAlgebra * coerce, [1] show size qetaLeadingCoefficient QEtaGradedAlgebra QEtaPowerGradedAlgebra QEtaLinearReduction greaterGrade? linearTransform, [1] reduce reducible? rowEchelon tailReduce topReduce triangularize QEtaModularCategory candidateLevelsCoEtaQuotient conditionCoEtaQuotient? cuspMatrices cusps cuspToMatrix etaCofactorSpace etaCofactorSpaceSystem etaQuotientMonoidInfinitySystem etaQuotientMonoidNoPolesSystem etaQuotientMonoidSystem, [1], [2] genus matrixEtaOrder matrixEtaOrderElement matrixEtaOrderFull matrixEtaOrderRow matrixModular minimalLevelCoEtaQuotient modular?, [1] modularOrbit numberOfGapsForSamba rightCosetRepresentatives weaklyModular? width, [1] QEtaModularEquation evaluate modularPolynomial, [1], [2], [3], [4] modularPolynomialCached, [1], [2], [3], [4], [5] QEtaModularEquationPrimeField modularPolynomial, [1], [2], [3] project, [1], [2], [3] QEtaModularEquationQ modularPolynomial, [1], [2] QEtaModularEquationT modularPolynomial, [1], [2], [3], [4] QEtaModularFormGenerators4ti2 modularFormGenerators, [1] modularFormSolutions, [1] QEtaModularFormGeneratorsSystem modularFormSystem, [1] QEtaModularFormSystem modularFormSystem, [1] QEtaModularGamma0 matrixLigozat matrixLigozatElement QEtaModularGamma1 QEtaModularLambdaAuxiliaryPackage computeReducedCusps cuspDeltaMatrices, [1] equivalentCuspsByMatrices? hasEquivalentCuspByMatrices? QEtaModularLambdaTools applyLambdaTransformation evalAtModularLambda, [1] transformAtModularLambda QEtaModularPackage etaCofactorInfinity, [1] etaCofactorNoPoles etaCofactorNoPolesSystem etaCofactorSpace, [1] minimizeOrderVectors qetaGrades, [1], [2] reduceSystem QEtaMultiComputation QEtaMultiComputationCategory nonPositive? oneVerboseStep! positive? QEtaMultiComputationModularEquation QEtaMultiComputationNoPairs QEtaMultiReduction QEtaMultiReductionCategory estimatedWeightAfterReduction reducer reducers3 QEtaMultiWeightSorting greater? less? lessLex? weight QEtaOneOverPi cqD expTruncated moebiusTransform, [1] theta2ConstantQIncompleteH theta2ConstantQIncompleteL theta3ConstantH theta3ConstantL toQHTTL transformTau uIPiCoefficient uNCoefficient

QEtaOneOverPiLambda denomB estimateExpansionOrders exIota1 exIotaN expandB expandK expandL expandPhiTerm logDtheta4 sortForMultiSamba, [1] QEtaOneOverPiQ approximatesPi? chudnovskyA2tau chudnovskyABFCoefficients chudnovskyB2tauCandidates chudnovskyChi chudnovskyContainsOneOverPiInterval? chudnovskyModularPolynomial chudnovskyOneOverPiFormula chudnovskyOneOverPiSummand chudnovskySelectABF containsOneOverPiInterval? convergentInterval exp2PiI exp2PiIInterval expPiI expPiIInterval gosperABFCoefficients gosperAtau gosperBtauCandidates gosperCheckModularPolynomial gosperContainsOneOverPiInterval? gosperIotaAt gosperIotaInterval gosperModularPolynomial, [1] gosperModularPolynomial1N gosperOneOverPiFormula gosperOneOverPiSummand gosperSelectABF kleinJAt kleinJInterval modularLambdaInterval oneOverPiFormulaInterval oneOverPiTerm tauDInterval tauInterval QEtaPolynomialAlgebra coerce, [1] QEtaPolynomialTools xPolynomials QEtaPowerAlgebraBasis QEtaPowerAlgebraBasisCategory basisElements component indexPermutation initialize multipliers QEtaPowerComputation oneVerboseStep! QEtaPowerGradedAlgebra / maxIndex qetaGrade, [1] qetaGrades qetaIndex qetaLeadingCoefficient QEtaPowerPolynomialAlgebra coerce QEtaPowerReduction QEtaPowerReductionCategory greaterGrade? noTrace noTraceEnter reduce reducer topReducible? tracedReduce traceEnter traceLoop traceReturn QEtaPuiseuxSeries puiseux qetaLaurentRep rationalPower removeZeroes QEtaQSeriesTools laurent, [1] substitute, [1] xiPower, [1] qEtaQuotient QEtaSpecification QEtaQuotientMonoidTools monoidGenerators QEtaQuotientSortPackage lessLex? sortByComponentGrade, [1] QEtaQuotientSpecifications4ti2 etaQuotientInfinitySpecifications etaQuotientMonoidInfinitySpecifications, [1] etaQuotientMonoidInfinityZSpecifications etaQuotientMonoidNoPolesSolutions etaQuotientMonoidNoPolesZSpecifications etaQuotientMonoidSolutions, [1], [2] etaQuotientMonoidZSpecifications, [1], [2] etaQuotientZSpecifications withProperPoles QEtaRamanujanKolberg findIdentity, [1], [2], [3], [4], [5], [6], [7] QEtaRamanujanKolbergIdentity algebraBasis alphaInfinity alphaOrbitInfinity coefficient cofactorX coSpecification definingSpecification equationX, [1] etaQuotient etaQuotientRepresentation etaQuotientX etaRelation etaRelationMonomial expand? f formatAsNonModular formatExpanded identity identityPolynomial modularFunctionIdentity? moduleCoefficients moduleRepresentation monoidSpecifications monomial monomialQuotient monomialQuotientX monomialX multiplier nonConstantMonoidSpecifications, [1] orbit orbitProduct, [1] orbitProductX, [1] pretty, [1], [2], [3], [4] qcofactor qcofactorX qequationX, [1] sumX QEtaReduction QEtaReductionCategory reducer tailReduce tailReducible? topReduce tracedTailReduce tracedTopReduce QEtaRepresentation guessEtaQuotientSpecification, [1], [2] QEtaSambaPackage samba, [1], [2], [3] sambaComputation, [1], [2], [3] QEtaScalingCuspReduction functionExpansionPair reduceCuspsByScaling QEtaSpecification allGeneralizedEtaFunctionIndices allPureExponents alphaInfinity asExpression? denom dilate etaFunctionIndices etaPolynomial, [1], [2] etaQuotient etaQuotientSpecification, [1], [2], [3], [4], [5], [6], [7], [8], [9], [10] etaRationalFunction, [1], [2] exponent, [1] exponents formatAsExpression formatWithQFactor formatWithSubscript generalizedEtaFunctionIndices indices level modularGamma0 modularGamma0? modularGamma1 modularGamma1? monomial, [1], [2] monomialQuotient numer parts prettyVariable properGeneralizedEtaFunctionIndices properGeneralizedParts pure? pureExponents pureParts purify qEtaQuotient qQuotient quotient, [1] rho0 rho0ProperGeneralized rho0Pure rhoInfinity specDelta specExponent specIndex specSubindex var varEta varPochhammer varPower varsub weaklyModularGamma0 weaklyModularGamma0? weaklyModularGamma1 weaklyModularGamma1? weight withQFactor? withSubscript? QEtaSpecificationRing coerce, [1] etaPolynomial, [1] etaRationalFunction, [1] level modularGamma0? modularGamma1? pretty, [1], [2] purify specificationPolynomial, [1], [2], [3], [4] qetaTaylorRep ModularFunctionQSeriesInfinity QEtaLaurentSeries QEtaTruncatedLaurentSeries QEtaTaylorSeries multiplyExponents zeroCheckingChoose, [1] QEtaTaylorSeriesCategory exponentGcd mapn multisect revert QEtaTopReduction QEtaTruncatedLaurentSeries exact? laurent, [1] precision qetaTaylorRep traceout truncateAt, [1] zero? QEtaTruncatedTaylorSeries coerce, [1] exact? precision reduce, [1] removeInitial taylor truncateAt, [1] zero? QEtaWeightedDomain addWeight forgetWeight lessWeight? weight qExponent SymbolicEtaGamma SymbolicEtaQuotientLambdaGamma SymbolicModularEtaQuotientGamma qExponentMin SymbolicEtaQuotientGamma SymbolicModularEtaQuotientGamma QFunctions eisensteinE2, [1] eisensteinE4 eisensteinE6 eulerFunction eulerFunction2 eulerFunctionPower3 eulerStream generalizedEulerProduct jacobiFunction, [1] kleinJInvariant partitionSeries qPochhammer, [1], [2], [3], [4] theta2ConstantIncomplete theta2ConstantQIncomplete theta3Constant theta4Constant qinterval AIntervalCategory qPochhammer QFunctions, [1], [2], [3], [4] qPochhammerPart SymbolicEtaQuotientQSeriesTools qQuotient QEtaSpecification quadraticIrrational QEtaAuxiliaryPackage quotient QEtaSpecification, [1]

R

rational Cusp rationalPower QEtaPuiseuxSeries rationalPrefactor SymbolicEtaGamma SymbolicEtaQuotientLambdaGamma rationalSquareRoot MinimalSquareRoot readInputFromFile QEtaAuxiliaryPackage readPolynomialFromFile QEtaAuxiliaryPackage readPolynomialListFromFile QEtaAuxiliaryPackage realExpPiIForm QEtaAuxiliaryPackage recursiveRootSimplification AlgebraicNumberTool recursiveRootSimplificationPoly AlgebraicNumberTool reduce QEtaComputationReductionCategory QEtaLinearReduction QEtaPowerReductionCategory QEtaTruncatedTaylorSeries, [1] reduceCuspsByScaling QEtaScalingCuspReduction reducer QEtaMultiReductionCategory QEtaPowerReductionCategory QEtaReductionCategory reducers3 QEtaMultiReductionCategory reduceSystem QEtaModularPackage reducible? QEtaLinearReduction

relationsIdealGenerators QEtaIdealCategory removeInitial QEtaTruncatedTaylorSeries removeZeroes ModularFunctionQSeriesCategory, [1] QEtaLaurentSeriesCategory, [1] QEtaPuiseuxSeries revert QEtaLaurentSeriesCategory QEtaTaylorSeriesCategory rho0 QEtaSpecification rho0ProperGeneralized QEtaSpecification rho0Pure QEtaSpecification rhoInfinity QEtaSpecification rightCosetRepresentatives CongruenceSubgroup QEtaModularCategory rootCombine AlgebraicNumberTool rootFactor AlgebraicNumberTool rootFactorK AlgebraicNumberTool rootFactorPol AlgebraicNumberTool rowEchelon QEtaLinearReduction run RunExternalCommand, [1] RunExternalCommand execute knownCommands run, [1] setExecutable!

S

sage SageMathTools sageGroebnerBasis SageMathTools sageGroebnerEliminate SageMathTools sageInteger SageMathTools SageMathTools join sage sageGroebnerBasis sageGroebnerEliminate sageInteger sageModularFormBasisGamma0 sageVersion sageModularFormBasisGamma0 SageMathTools sageVersion SageMathTools samba QEtaSambaPackage, [1], [2], [3] sambaComputation QEtaSambaPackage, [1], [2], [3] SatoEigenValueProblem gammaCandidate gammaCandidateWurm gammaTauQCandidateAux gammaTauQCandidates gammaTauQCandidatesAux gammaTauQCandidatesWurm satoTriples satoTriples SatoEigenValueProblem sawTooth QEtaAuxiliaryPackage second QEtaExtendedAlgebra series ModularFunctionQSeriesCategory seriesPart EtaQuotientQSeriesInfinity setCache! QEtaAlgebraCachedSamba setExecutable X4ti2 setExecutable! RunExternalCommand setOptions X4ti2 show QEtaLazyAlgebra signVariations QEtaAuxiliaryPackage simpler? AlgebraicNumberTool simplifyRadicals AlgebraicNumberTool size QEtaLazyAlgebra sortByComponentGrade QEtaQuotientSortPackage, [1] sortForMultiSamba QEtaOneOverPiLambda, [1] specDelta QEtaSpecification specExponent QEtaSpecification specificationPolynomial QEtaSpecificationRing, [1], [2], [3], [4] specIndex QEtaSpecification specSubindex QEtaSpecification splitMatrix QEtaAuxiliaryPackage, [1], [2] sqrtArgument AlgebraicNumberTool sqrtSum AlgebraicNumberTool sqrtSumArguments AlgebraicNumberTool squareRoot GaussRoot squareRootOfRadicalInteger GaussRoot

StreamRecurrenceTool twoTermRecurrentStream sturmSequence QEtaAuxiliaryPackage subindex SymbolicEtaGamma substitute QEtaQSeriesTools, [1] sumX QEtaRamanujanKolbergIdentity sup AIntervalCategory SymbolicEtaGamma cdExponent delta eta gamma1 lambda minimalRootOfUnity minimalRootOfUnityWithoutPrefactors multiplier pure? qExponent rationalPrefactor subindex transformationMatrix udelta unityExponent vdelta SymbolicEtaQuotientGamma definingSpecification elt etaQuotient, [1] minimalRootOfUnity multiplier offset one? qExponentMin transformationMatrix unityExponent SymbolicEtaQuotientLambdaGamma cdExponent definingSpecification elt etaQuotient lambda minimalRootOfUnity minimalRootOfUnityWithoutUnityExponent multiplier qExponent rationalPrefactor transformationMatrix unityExponent SymbolicEtaQuotientQSeriesTools etaQuotientTraceExpansions, [1] laurentExpansion laurentExpansionInfinity laurentExpansions, [1], [2] puiseuxExpansion, [1], [2] qPochhammerPart SymbolicModularEtaQuotient constant? coSpecification definingSpecification elt etaQuotient, [1], [2], [3], [4], [5] level minimalRootOfUnity multiplier offset one? orders ordersMin transformationMatrices SymbolicModularEtaQuotientGamma basefactor coerce cofactor etaQuotient, [1], [2] minimalRootOfUnity one? order orderMin qExponent qExponentMin

T

tailReduce QEtaLinearReduction QEtaReductionCategory tailReducible? QEtaReductionCategory tauDInterval QEtaOneOverPiQ tauInterval QEtaOneOverPiQ taylor QEtaTruncatedTaylorSeries theta2ConstantIncomplete QFunctions theta2ConstantQIncomplete QFunctions theta2ConstantQIncompleteH QEtaOneOverPi theta2ConstantQIncompleteL QEtaOneOverPi theta3Constant QFunctions theta3ConstantH QEtaOneOverPi theta3ConstantL QEtaOneOverPi theta4Constant QFunctions thetaPower4 CachedQFunctions toFundamentalDomain QEtaFundamentalDomain topReduce QEtaLinearReduction QEtaReductionCategory topReducible? QEtaComputationReductionCategory QEtaPowerReductionCategory toQHTTL QEtaOneOverPi trace QEtaComputationCategory

tracedReduce QEtaComputationReductionCategory QEtaPowerReductionCategory tracedTailReduce QEtaReductionCategory tracedTopReduce QEtaReductionCategory traceEnter QEtaComputationReductionCategory QEtaPowerReductionCategory traceLoop QEtaComputationReductionCategory QEtaPowerReductionCategory traceout QEtaAlgebra QEtaLaurentSeries QEtaTruncatedLaurentSeries traceReturn QEtaComputationReductionCategory QEtaPowerReductionCategory transformationMatrices SymbolicModularEtaQuotient transformationMatrix SymbolicEtaGamma SymbolicEtaQuotientGamma SymbolicEtaQuotientLambdaGamma transformAtModularLambda QEtaModularLambdaTools transformTau QEtaOneOverPi triangularize QEtaLinearReduction truncateAt QEtaCheckingTruncatedLaurentSeries QEtaTruncatedLaurentSeries, [1] QEtaTruncatedTaylorSeries, [1] TruncatedModularFunctionQSeriesInfinity coerce, [1] exact? precision twoTermRecurrentStream StreamRecurrenceTool

U

udelta SymbolicEtaGamma uIPiCoefficient QEtaOneOverPi uNCoefficient QEtaOneOverPi unit? AIntervalCategory

unityExponent SymbolicEtaGamma SymbolicEtaQuotientGamma SymbolicEtaQuotientLambdaGamma update! QEtaComputation QEtaComputationModularEquation upsilonExponent QEtaAuxiliaryPackage, [1]

V

var QEtaSpecification varEta QEtaSpecification varPochhammer QEtaSpecification varPower QEtaSpecification

varsub QEtaSpecification vdelta SymbolicEtaGamma verticalConcat QEtaAuxiliaryPackage

W

weaklyModular? QEtaModularCategory weaklyModularGamma0 QEtaSpecification weaklyModularGamma0? QEtaSpecification weaklyModularGamma1 QEtaSpecification weaklyModularGamma1? QEtaSpecification weight QEtaMultiWeightSorting QEtaSpecification QEtaWeightedDomain

width AIntervalCategory CongruenceSubgroup, [1] QEtaModularCategory, [1] withProperPoles QEtaQuotientSpecifications4ti2 withQFactor? QEtaSpecification withSubscript? QEtaSpecification writeValueToFile QEtaAuxiliaryPackage

X

X4ti2 clearDenominators setExecutable setOptions zsolve, [1], [2], [3], [4]

xiPower QEtaQSeriesTools, [1] xPolynomials QEtaPolynomialTools

Z

zero? AIntervalCategory QEtaAlgebra QEtaCheckingTruncatedLaurentSeries QEtaTruncatedLaurentSeries QEtaTruncatedTaylorSeries

zeroCheckingChoose QEtaLaurentSeries QEtaTaylorSeries, [1] zsolve X4ti2, [1], [2], [3], [4]