Index

Symbols

# PreNewtonPuiseux * QEtaAlgebra, [1] QEtaAlgebraCachedPower + QEtaAlgebra - QEtaAlgebra, [1]

/ QEtaExtendedAlgebra XEtaGradedAlgebra 0 QEtaAlgebra 1 QEtaAlgebra ^ QEtaAlgebra

A

addBasisElementPairs! QEtaComputation addGapPair! QEtaComputation addGapPairs! QEtaComputation addPair! QEtaComputation algebraBasis QEtaComputationCategory QEtaRamanujanKolbergIdentity

algebraicRelations QEtaIdealCategory allGeneralizedEtaFunctionIndices QEtaSpecification allPureExponents QEtaSpecification alphaInfinity QEtaRamanujanKolbergIdentity QEtaSpecification alphaOrbitInfinity QEtaRamanujanKolbergIdentity

B

basefactor SymbolicModularEtaQuotientGamma basis QEtaAlgebraBasisCategory, [1] QEtaComputation

basisElements QEtaAlgebraBasis XEtaAlgebraBasisCategory basisReduction QEtaQuotientMonoidExponentVectorsStar

C

CachedPower power!, [1] CachedQPochhammerPower eulerFunctionPower jacobiFunctionPower candidateLevelsCoEtaQuotient QEtaModularCategory cdExponent SymbolicEtaGamma SymbolicEtaQuotientLambdaGamma CheckSomos fromEta member? toEta choose QEtaLaurentSeriesCategory clearDenominator QAuxiliaryTools clearDenominators X4ti2 coefficient QEtaRamanujanKolbergIdentity coefficientRelation NewtonPuiseux coerce Cusp Finite0Series, [1] ModularFunctionExpansionsAtCusps NewtonPuiseux PolynomialConversion, [1] QEtaExtendedAlgebraBasis QEtaLaurentSeriesCategory, [1] QEtaTaylorSeriesCategory, [1] SymbolicModularEtaQuotientGamma cofactor SymbolicModularEtaQuotientGamma cofactorX QEtaRamanujanKolbergIdentity component XEtaAlgebraBasisCategory computePairs! QEtaComputation conditionCoEtaQuotient? QEtaModularCategory conditionEvenMultiplier? QEtaCofactorConditions conditionGSigma0? QEtaCofactorConditions conditionMmN? QEtaCofactorConditions conditionNDivisor? QEtaCofactorConditions conditionOrbitLength? QEtaCofactorConditions conditionPrimeDivisors? QEtaCofactorConditions

conditionRho0ProperGeneralized? QEtaCofactorConditions conditionRho0Pure? QEtaCofactorConditions conditionSumExponentsProperGeneralized? QEtaCofactorConditions conditionSumExponentsPure? QEtaCofactorConditions CongruenceSubgroup cuspOf cusps cuspToMatrix dimensionOfCuspForms dimensionOfEisensteinSubspace dimensionOfModularForms doubleCosetRepresentatives equivalentCusps? genus index member? normalizeCusp nu2 nu3 numberOfCusps projectiveIndex rightCosetRepresentatives width, [1] CongruenceSubgroupGamma0 CongruenceSubgroupGamma1 constant? SymbolicModularEtaQuotient coSpecification QEtaRamanujanKolbergIdentity criticalElements? QEtaComputationCategory Cusp coerce cusp cuspToMatrix denom infinity infinity? numer rational cusp Cusp cuspOf CongruenceSubgroup cusps CongruenceSubgroup QEtaModularCategory SymbolicModularEtaQuotient cuspToMatrix CongruenceSubgroup Cusp QEtaModularCategory

D

dedekindSum QEtaAuxiliaryPackage definingSpecification QEtaRamanujanKolbergIdentity SymbolicEtaQuotientGamma SymbolicEtaQuotientLambdaGamma delta SymbolicEtaGamma denom Cusp QEtaSpecification dilate QEtaSpecification dimensionOfCuspForms CongruenceSubgroup dimensionOfEisensteinSubspace CongruenceSubgroup

dimensionOfModularForms CongruenceSubgroup doubleCosetRepresentatives CongruenceSubgroup DynamicAlgebraicClosureFiniteField extendBy! getGenerator minimalPolynomial rank show DynamicAlgebraicNumber extendBy! extensionPolynomial getRoot primitiveNthRootOfUnity rank show

E

eisensteinE2 QFunctions eisensteinE4 QFunctions eisensteinE6 QFunctions elt NewtonPuiseux PreNewtonPuiseux SymbolicEtaQuotientGamma SymbolicEtaQuotientLambdaGamma SymbolicModularEtaQuotient embed QEtaExtendedAlgebra empty XEtaAlgebraBasis equationX QEtaRamanujanKolbergIdentity, [1] equivalentCusps? CongruenceSubgroup eta EtaQuotientInfinity SymbolicEtaGamma etaCofactorInfinity QEtaModularPackage etaCofactorInfinitySpaceSystem QEtaModularPackage etaCofactorSpace QEtaModularCategory etaCofactorSpaceSystem QEtaModularCategory etaFunctionIndices QEtaSpecification etaLaurentIdealGenerators QEtaIdealCategory, [1] etaLaurentIdealLists QEtaIdealCategory etaPower EtaQuotientInfinity etaQuotient QEtaRamanujanKolbergIdentity SymbolicEtaQuotientGamma, [1] SymbolicEtaQuotientLambdaGamma SymbolicModularEtaQuotient, [1], [2], [3] SymbolicModularEtaQuotientGamma, [1], [2] etaQuotientIdealGenerators QEtaIdealCategory EtaQuotientInfinity eta etaPower etaQuotientInfinity eulerExpansion eulerExponent eulerFunctionPower expansion generalizedEtaPower polynomialToEta prefactor seriesPart etaQuotientInfinity EtaQuotientInfinity

etaQuotientMonoidExponentVectors QEtaQuotientMonoidExponentVectorsStar etaQuotientMonoidExponentVectorsX QEtaQuotientMonoidExponentVectorsStar etaQuotientMonoidInfinitySpecifications QEtaQuotientSpecifications4ti2 etaQuotientMonoidSolutions QEtaQuotientSpecifications4ti2 etaQuotientMonoidSpecifications QEtaQuotientSpecifications4ti2 etaQuotientMonoidSystem QEtaModularCategory etaQuotientMonomial QEtaIdealCategory, [1] etaQuotientSpecification QEtaRepresentation, [1], [2] QEtaSpecification, [1], [2], [3], [4], [5] etaQuotientSpecifications QEtaQuotientSpecifications4ti2 etaQuotientX QEtaRamanujanKolbergIdentity etaRelation QEtaRamanujanKolbergIdentity etaRelationMonomial QEtaRamanujanKolbergIdentity etaRelations QEtaIdealCategory, [1] eulerExpansion EtaQuotientInfinity eulerExponent EtaQuotientInfinity eulerFunction QFunctions eulerFunction2 QFunctions eulerFunctionPower CachedQPochhammerPower EtaQuotientInfinity eulerFunctionPower3 QFunctions eulerStream QFunctions eval PolynomialEvaluation, [1] expansion EtaQuotientInfinity extend! PreNewtonPuiseux extendBy! DynamicAlgebraicClosureFiniteField DynamicAlgebraicNumber InnerFiniteFieldExtensionByTriangularSet extendedBasisReduction QEtaQuotientMonoidExponentVectorsStar extendedNormalForm QEtaGroebner, [1] extendedNormalForms QEtaGroebner extensionPolynomial DynamicAlgebraicNumber extractNext! QEtaComputationCategory

F

f QEtaRamanujanKolbergIdentity findIdentity QEtaRamanujanKolberg, [1], [2], [3], [4], [5], [6], [7] Finite0Series coerce, [1] first QEtaExtendedAlgebra fractionalBernoulli1 QEtaAuxiliaryPackage fractionalBernoulli2 QEtaAuxiliaryPackage

fractionalPart QEtaAuxiliaryPackage freeSpecifications QEtaQuotientSpecifications4ti2 fromEta CheckSomos functionalInverse FunctionalLaurentInverse FunctionalLaurentInverse functionalInverse

G

gamma1 SymbolicEtaGamma GaussRoot squareRoot generalizedDedekindSum QEtaAuxiliaryPackage generalizedEtaFunctionIndices QEtaSpecification generalizedEtaPower EtaQuotientInfinity generalizedEulerProduct QFunctions genus CongruenceSubgroup QEtaModularCategory

getGenerator DynamicAlgebraicClosureFiniteField InnerFiniteFieldExtensionByTriangularSet getRelation InnerFiniteFieldExtensionByTriangularSet getRelations InnerFiniteFieldExtensionByTriangularSet getRoot DynamicAlgebraicNumber greaterGrade? QEtaReductionCategory XEtaReductionCategory groebner QEtaGroebner groebnerExtend QEtaGroebner

H

homogeneousSpecifications QEtaQuotientSpecifications4ti2

I

identity QEtaRamanujanKolbergIdentity identityPolynomial QEtaRamanujanKolbergIdentity index CongruenceSubgroup IndexedVariable indexedSymbol QAuxiliaryTools indexedSymbols QAuxiliaryTools, [1], [2] IndexedVariable index lookup new rank indexPermutation XEtaAlgebraBasisCategory

infinity Cusp infinity? Cusp initialize QEtaAlgebraBasis QEtaComputationCategory InnerFiniteFieldExtensionByTriangularSet extendBy! getGenerator getRelation getRelations minimalPolynomial rank show size

J

jacobiFunction QFunctions, [1] jacobiFunctionPower CachedQPochhammerPower

jacobiLowerStar QEtaAuxiliaryPackage jacobiUpperStar QEtaAuxiliaryPackage

K

kappaSchoeneberg QEtaAuxiliaryPackage, [1] kappaYang QEtaAuxiliaryPackage, [1]

kleinJInvariant QFunctions

L

lambda SymbolicEtaGamma SymbolicEtaQuotientLambdaGamma laurent QEtaLaurentSeriesCategory QEtaSeriesExpansion laurentExpansion QEtaSeriesExpansion laurentExpansionInfinity QEtaModularInfinityExpansion, [1] QEtaSeriesExpansion

laurentExpansions QEtaSeriesExpansion, [1] laurentRelations QEtaIdealCategory leadingPuiseuxMonomials NewtonPuiseux, [1], [2], [3] level QEtaSpecification lookup IndexedVariable

M

map QEtaLaurentSeriesFunctions2 matrixAtkinLehner QEtaAuxiliaryPackage matrixEtaOrder QEtaModularCategory matrixEtaOrderElement QEtaModularCategory matrixEtaOrderFull QEtaModularCategory matrixEtaOrderRow QEtaModularCategory matrixLigozat QEtaModularGamma0 matrixLigozatElement QEtaModularGamma0 matrixModular QEtaModularCategory maxIndex PreNewtonPuiseux XEtaGradedAlgebra member? CheckSomos CongruenceSubgroup minimalLevelCoEtaQuotient QEtaModularCategory minimalPolynomial DynamicAlgebraicClosureFiniteField InnerFiniteFieldExtensionByTriangularSet minimalRootOfUnity SymbolicEtaQuotientGamma SymbolicModularEtaQuotient SymbolicModularEtaQuotientGamma minimalSquareRootOfUnity QEtaAuxiliaryPackage minimizeVector QEtaAuxiliaryPackage modular? QEtaModularCategory, [1]

modularEtaQuotientInfinity QEtaModularInfinityExpansion, [1] ModularFunctionExpansionsAtCusps coerce series modularGamma0 QEtaAuxiliaryPackage QEtaSpecification modularGamma0? QEtaAuxiliaryPackage QEtaSpecification modularGamma1 QEtaSpecification modularGamma1? QEtaSpecification modularOrbit QEtaModularCategory moduleCoefficients QEtaRamanujanKolbergIdentity monoidSpecifications QEtaRamanujanKolbergIdentity monomial QEtaRamanujanKolbergIdentity monomialQuotient QEtaRamanujanKolbergIdentity monomialQuotientX QEtaRamanujanKolbergIdentity Monomials monomialX QEtaRamanujanKolbergIdentity multiplier QEtaAlgebraBasisCategory QEtaRamanujanKolbergIdentity SymbolicEtaGamma SymbolicEtaQuotientGamma SymbolicEtaQuotientLambdaGamma multipliers XEtaAlgebraBasisCategory multisect QEtaTaylorSeriesCategory

N

new IndexedVariable PreNewtonPuiseux NewtonPolygon pointsOfNewtonPolygon slopePointsOfNewtonPolygon NewtonPuiseux coefficientRelation coerce elt leadingPuiseuxMonomials, [1], [2], [3] nextPuiseuxMonomials nextY poly2KPXY polynomial2Points, [1], [2] puiseuxSolutions nextPuiseuxMonomials NewtonPuiseux nextY NewtonPuiseux nonConstantEtaQuotientMonoidInfinitySpecifications QEtaQuotientSpecifications4ti2 nonConstantEtaQuotientMonoidSpecifications QEtaQuotientSpecifications4ti2

nonConstantMonoidSpecifications QEtaRamanujanKolbergIdentity, [1] normalForms QEtaGroebner normalizeCusp CongruenceSubgroup noTrace QEtaComputationCategory QEtaReductionCategory XEtaReductionCategory noTraceEnter QEtaReductionCategory XEtaReductionCategory nu2 CongruenceSubgroup nu3 CongruenceSubgroup numberOfCusps CongruenceSubgroup numberOfGaps QEtaAlgebraBasisCategory QEtaAuxiliaryPackage numer Cusp QEtaSpecification

O

offset SymbolicEtaQuotientGamma one? SymbolicEtaQuotientGamma SymbolicModularEtaQuotient SymbolicModularEtaQuotientGamma oneStep! QEtaComputationCategory oneStepComputation! QEtaComputationCategory oneTracedStep! QEtaComputationCategory oneTracedStepComputation! QEtaComputationCategory

oneVerboseStep! QEtaComputation QEtaComputationDelayedPairs XEtaComputation orbit QEtaRamanujanKolbergIdentity orbitProduct QEtaRamanujanKolbergIdentity orbitProductX QEtaRamanujanKolbergIdentity, [1] orderMin SymbolicModularEtaQuotientGamma ordersMin SymbolicModularEtaQuotient

P

partitionSeries QFunctions parts QEtaSpecification pointsOfNewtonPolygon NewtonPolygon poly2KPXY NewtonPuiseux polynomial2Points NewtonPuiseux, [1], [2] PolynomialConversion coerce, [1] PolynomialEvaluation eval, [1] polynomialToEta EtaQuotientInfinity PolynomialTool xPolynomials postProcess! QEtaComputationCategory power! CachedPower, [1] prefactor EtaQuotientInfinity PreNewtonPuiseux # elt extend! maxIndex new setelt!

pretty QEtaRamanujanKolbergIdentity, [1], [2] primePower QEtaAuxiliaryPackage primitiveNthRootOfUnity DynamicAlgebraicNumber projectiveIndex CongruenceSubgroup properGeneralizedEtaFunctionIndices QEtaSpecification properGeneralizedParts QEtaSpecification puiseux QEtaPuiseuxSeries puiseuxExpansion QEtaSeriesExpansion, [1], [2] puiseuxSolutions NewtonPuiseux pure? QEtaSpecification SymbolicEtaGamma pureExponents QEtaSpecification pureParts QEtaSpecification purify QEtaSpecification

Q

QAuxiliaryTools clearDenominator indexedSymbol indexedSymbols, [1], [2] qcofactorX QEtaRamanujanKolbergIdentity qequationX QEtaRamanujanKolbergIdentity, [1] QEtaAlgebra *, [1] + -, [1] 0 1 ^ traceout zero? QEtaAlgebraBasis basisElements initialize QEtaAlgebraBasisCategory basis, [1] multiplier numberOfGaps QEtaAlgebraCachedPower * QEtaAuxiliaryPackage dedekindSum fractionalBernoulli1 fractionalBernoulli2 fractionalPart generalizedDedekindSum jacobiLowerStar jacobiUpperStar kappaSchoeneberg, [1] kappaYang, [1] matrixAtkinLehner minimalSquareRootOfUnity minimizeVector modularGamma0 modularGamma0? numberOfGaps primePower rationalSquareRoot sawTooth splitMatrix, [1], [2] upsilonExponent, [1] verticalConcat qetaCoefficient QEtaGradedAlgebra QEtaCofactorConditions conditionEvenMultiplier? conditionGSigma0? conditionMmN? conditionNDivisor? conditionOrbitLength? conditionPrimeDivisors? conditionRho0ProperGeneralized? conditionRho0Pure? conditionSumExponentsProperGeneralized? conditionSumExponentsPure? QEtaComputation addBasisElementPairs! addGapPair! addGapPairs! addPair! basis computePairs! oneVerboseStep! update! QEtaComputationCategory algebraBasis criticalElements? extractNext! initialize noTrace oneStep! oneStepComputation! oneTracedStep! oneTracedStepComputation! postProcess! trace QEtaComputationDelayedPairs oneVerboseStep! QEtaExtendedAlgebra / embed first second QEtaExtendedAlgebraBasis coerce QEtaExtendedReduction QEtaExtendedTopReduction qetaGrade QEtaGradedAlgebra XEtaGradedAlgebra, [1] QEtaGradedAlgebra qetaCoefficient qetaGrade qetaLeadingCoefficient qetaGrades QEtaModularPackage, [1], [2] XEtaGradedAlgebra QEtaGroebner extendedNormalForm, [1] extendedNormalForms groebner groebnerExtend normalForms QEtaIdealCategory algebraicRelations etaLaurentIdealGenerators, [1] etaLaurentIdealLists etaQuotientIdealGenerators etaQuotientMonomial, [1] etaRelations, [1] laurentRelations relationsIdealGenerators QEtaIdealHemmecke QEtaIdealHemmeckeCached qetaIndex XEtaGradedAlgebra qetaLaurentRep QEtaPuiseuxSeries QEtaLaurentSeries QEtaLaurentSeriesCategory choose coerce, [1] laurent qetaTaylorRep removeZeroes, [1] QEtaLaurentSeriesFunctions2 map qetaLeadingCoefficient QEtaGradedAlgebra XEtaGradedAlgebra QEtaModularCategory candidateLevelsCoEtaQuotient conditionCoEtaQuotient? cusps cuspToMatrix etaCofactorSpace etaCofactorSpaceSystem etaQuotientMonoidSystem genus matrixEtaOrder matrixEtaOrderElement matrixEtaOrderFull matrixEtaOrderRow matrixModular minimalLevelCoEtaQuotient modular?, [1] modularOrbit width, [1] QEtaModularGamma0 matrixLigozat matrixLigozatElement QEtaModularGamma1 QEtaModularInfinityExpansion laurentExpansionInfinity, [1] modularEtaQuotientInfinity, [1]

QEtaModularPackage etaCofactorInfinity etaCofactorInfinitySpaceSystem qetaGrades, [1], [2] reduceSystem QEtaPuiseuxSeries puiseux qetaLaurentRep rationalPower qEtaQuotient QEtaRamanujanKolbergIdentity QEtaQuotientExponentVectorsAux smallerGrade? sortByComponentGrade QEtaQuotientMonoidExponentVectorsStar basisReduction etaQuotientMonoidExponentVectors etaQuotientMonoidExponentVectorsX extendedBasisReduction QEtaQuotientSpecifications4ti2 etaQuotientMonoidInfinitySpecifications etaQuotientMonoidSolutions etaQuotientMonoidSpecifications etaQuotientSpecifications freeSpecifications homogeneousSpecifications nonConstantEtaQuotientMonoidInfinitySpecifications nonConstantEtaQuotientMonoidSpecifications QEtaRamanujanKolberg findIdentity, [1], [2], [3], [4], [5], [6], [7] QEtaRamanujanKolbergIdentity algebraBasis alphaInfinity alphaOrbitInfinity coefficient cofactorX coSpecification definingSpecification equationX, [1] etaQuotient etaQuotientX etaRelation etaRelationMonomial f identity identityPolynomial moduleCoefficients monoidSpecifications monomial monomialQuotient monomialQuotientX monomialX multiplier nonConstantMonoidSpecifications, [1] orbit orbitProduct orbitProductX, [1] pretty, [1], [2] qcofactorX qequationX, [1] qEtaQuotient qQuotient sumX var varEta varPochhammer varPower varsub QEtaReduction QEtaReductionCategory greaterGrade? noTrace noTraceEnter reduce reducer tailReduce tailReducible? topReduce topReducible? tracedReduce tracedTailReduce tracedTopReduce traceEnter traceLoop traceReturn QEtaRepresentation etaQuotientSpecification, [1], [2] QEtaSambaPackage samba, [1], [2] QEtaSeriesExpansion laurent laurentExpansion laurentExpansionInfinity laurentExpansions, [1] puiseuxExpansion, [1], [2] substitute QEtaSpecification allGeneralizedEtaFunctionIndices allPureExponents alphaInfinity denom dilate etaFunctionIndices etaQuotientSpecification, [1], [2], [3], [4], [5] generalizedEtaFunctionIndices level modularGamma0 modularGamma0? modularGamma1 modularGamma1? numer parts properGeneralizedEtaFunctionIndices properGeneralizedParts pure? pureExponents pureParts purify rho0 rho0ProperGeneralized rho0Pure rhoInfinity specDelta specExponent specIndex specSubindex qetaTaylorRep QEtaLaurentSeriesCategory QEtaTaylorSeries QEtaTaylorSeriesCategory coerce, [1] multisect revert QEtaTopReduction qExponent SymbolicEtaGamma SymbolicEtaQuotientLambdaGamma qExponentMin SymbolicEtaQuotientGamma SymbolicModularEtaQuotientGamma QFunctions eisensteinE2 eisensteinE4 eisensteinE6 eulerFunction eulerFunction2 eulerFunctionPower3 eulerStream generalizedEulerProduct jacobiFunction, [1] kleinJInvariant partitionSeries qPochhammer, [1], [2], [3], [4] qPochhammer QFunctions, [1], [2], [3], [4] QPower qQuotient QEtaRamanujanKolbergIdentity

R

rank DynamicAlgebraicClosureFiniteField DynamicAlgebraicNumber IndexedVariable InnerFiniteFieldExtensionByTriangularSet rational Cusp rationalPower QEtaPuiseuxSeries rationalPrefactor SymbolicEtaGamma SymbolicEtaQuotientLambdaGamma rationalSquareRoot QEtaAuxiliaryPackage reduce QEtaReductionCategory XEtaReductionCategory reducer QEtaReductionCategory XEtaReductionCategory

reduceSystem QEtaModularPackage relationsIdealGenerators QEtaIdealCategory removeZeroes QEtaLaurentSeriesCategory, [1] revert QEtaTaylorSeriesCategory rho0 QEtaSpecification rho0ProperGeneralized QEtaSpecification rho0Pure QEtaSpecification rhoInfinity QEtaSpecification rightCosetRepresentatives CongruenceSubgroup

S

samba QEtaSambaPackage, [1], [2] XEtaSambaPackage, [1] sambaComputation XEtaSambaPackage, [1] sawTooth QEtaAuxiliaryPackage second QEtaExtendedAlgebra series ModularFunctionExpansionsAtCusps seriesPart EtaQuotientInfinity setelt! PreNewtonPuiseux setExecutable X4ti2 setOptions X4ti2 show DynamicAlgebraicClosureFiniteField DynamicAlgebraicNumber InnerFiniteFieldExtensionByTriangularSet size InnerFiniteFieldExtensionByTriangularSet slopePointsOfNewtonPolygon NewtonPolygon smallerGrade? QEtaQuotientExponentVectorsAux sortByComponentGrade QEtaQuotientExponentVectorsAux specDelta QEtaSpecification specExponent QEtaSpecification specIndex QEtaSpecification specSubindex QEtaSpecification splitMatrix QEtaAuxiliaryPackage, [1], [2] squareRoot GaussRoot subindex SymbolicEtaGamma substitute QEtaSeriesExpansion sumX QEtaRamanujanKolbergIdentity SymbolicEtaGamma cdExponent delta eta gamma1 lambda 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 multiplier qExponent rationalPrefactor transformationMatrix unityExponent SymbolicModularEtaQuotient constant? cusps elt etaQuotient, [1], [2], [3] minimalRootOfUnity one? ordersMin SymbolicModularEtaQuotientGamma basefactor coerce cofactor etaQuotient, [1], [2] minimalRootOfUnity one? orderMin qExponentMin

T

tailReduce QEtaReductionCategory tailReducible? QEtaReductionCategory toEta CheckSomos topReduce QEtaReductionCategory topReducible? QEtaReductionCategory XEtaReductionCategory trace QEtaComputationCategory tracedReduce QEtaReductionCategory XEtaReductionCategory tracedTailReduce QEtaReductionCategory

tracedTopReduce QEtaReductionCategory traceEnter QEtaReductionCategory XEtaReductionCategory traceLoop QEtaReductionCategory XEtaReductionCategory traceout QEtaAlgebra traceReturn QEtaReductionCategory XEtaReductionCategory transformationMatrix SymbolicEtaGamma SymbolicEtaQuotientGamma SymbolicEtaQuotientLambdaGamma

U

udelta SymbolicEtaGamma unityExponent SymbolicEtaGamma SymbolicEtaQuotientGamma SymbolicEtaQuotientLambdaGamma

update! QEtaComputation upsilonExponent QEtaAuxiliaryPackage, [1]

V

var QEtaRamanujanKolbergIdentity varEta QEtaRamanujanKolbergIdentity varPochhammer QEtaRamanujanKolbergIdentity varPower QEtaRamanujanKolbergIdentity

varsub QEtaRamanujanKolbergIdentity vdelta SymbolicEtaGamma verticalConcat QEtaAuxiliaryPackage

W

width CongruenceSubgroup, [1] QEtaModularCategory, [1]

X

X4ti2 clearDenominators setExecutable setOptions zsolve, [1], [2] XEtaAlgebraBasis empty XEtaAlgebraBasisCategory basisElements component indexPermutation multipliers XEtaComputation oneVerboseStep! XEtaGradedAlgebra / maxIndex qetaGrade, [1] qetaGrades qetaIndex qetaLeadingCoefficient

XEtaReduction XEtaReductionCategory greaterGrade? noTrace noTraceEnter reduce reducer topReducible? tracedReduce traceEnter traceLoop traceReturn XEtaSambaPackage samba, [1] sambaComputation, [1] xPolynomials PolynomialTool

Z

zero? QEtaAlgebra

zsolve X4ti2, [1], [2]