QEtaRepresentationΒΆ
qetarep.spad line 94 [edit on github]
QEtaRepresentation implements functions to represent a $q$-series as a (generalized) eta-quotient.
- guessEtaQuotientSpecification: (List List Integer, QEtaLaurentSeries Integer, PositiveInteger) -> Record(fspec: QEtaSpecification, fexp: Fraction Integer, fser: QEtaLaurentSeries Integer)
- guessEtaQuotientSpecification(idxs,s,n)assumes that s=q^a*t for some integer a and- tis a Taylor series with constant term 1 and returns [spec,- e,- r], i.e. an eta-quotient specification together with a (rational) exponent- eand a series- rsuch that if u=etaQuotientInfintiy(spec), then- tand eulerExpansion(- u) have the same coefficients up to the coefficient of- q^n, a=e+eulerExponent(- u), and t=r*eulerExpansion(- u). In other words, s=u*q^e*r where- uis the eta-quotient given by spec. The specification will contain only indices from- idxs. If order(eulerExpansion(- r)- -1,- n)- <n, then the function has not succeeded and only returns a specification it has found so far.
- guessEtaQuotientSpecification: (PositiveInteger, QEtaLaurentSeries Integer, PositiveInteger) -> Record(fspec: QEtaSpecification, fexp: Fraction Integer, fser: QEtaLaurentSeries Integer)
- guessEtaQuotientSpecification(nn,s,n)is equivalent to guessEtaQuotientSpecification(idxs,- s,- n) for idxs:=concat(eidxs,pidxs) where pidxs=[[- nn,- g] for- gin 1..floor((- nn-1)- /2)] and eidx=[- nn/2,- nn] if- nnis even and eidxs=[- nn] for odd- nn. The specification may contain generalized eta-quotients and will be of level- nn.
- guessEtaQuotientSpecification: (QEtaLaurentSeries Integer, PositiveInteger) -> Record(fspec: QEtaSpecification, fexp: Fraction Integer, fser: QEtaLaurentSeries Integer)
- guessEtaQuotientSpecification(s,n)is equivalent to guessEtaQuotientSpecification(idxs,- s,- n) for idxs=[[- d] for- din 1..- n]. Only pure eta-quotients are returned.