QEtaOneOverPiLambda CΒΆ

oneoverpi.spad line 254 [edit on github]

QEtaOneOverPi provides functions to find formulas for the computation of 1/pi.

denomB: Matrix Integer -> QEtaLaurentSeries C if C has Field

estimateExpansionOrders: (XHashTable(Matrix Integer, List Integer), XHashTable(Matrix Integer, List Integer)) -> XHashTable(Matrix Integer, Integer)

estimateExpansionOrders(hlx, hly) tries to come up with an estimate of how many coefficients are needed in the course of a modular polynomial computation of the modular functions encoded in hlx and hly.

exIota1: (Record(fdelta: PositiveInteger, fgamma: Matrix Integer, fred: Matrix Integer, ftriang: Matrix Integer), Fraction Integer) -> QEtaLaurentSeries C if C has Field

exIotaN: (Record(fdelta: PositiveInteger, fgamma: Matrix Integer, fred: Matrix Integer, ftriang: Matrix Integer), Fraction Integer) -> QEtaLaurentSeries C if C has Field

expandB: Record(fdelta: PositiveInteger, fgamma: Matrix Integer, fred: Matrix Integer, ftriang: Matrix Integer) -> QEtaLaurentSeries C if C has Field

expandK: (Record(fdelta: PositiveInteger, fgamma: Matrix Integer, fred: Matrix Integer, ftriang: Matrix Integer), Fraction Integer) -> QEtaLaurentSeries C if C has Field

expandL: (Record(fdelta: PositiveInteger, fgamma: Matrix Integer, fred: Matrix Integer, ftriang: Matrix Integer), Fraction Integer) -> QEtaLaurentSeries C if C has Field

expandPhiTerm: Matrix Integer -> QEtaLaurentSeries C

logDtheta4: PositiveInteger -> QEtaLaurentSeries C if C has Field

logDtheta4(j) for j=2,3,4 computes $frac{4}{pi i}frac{d}{dtau}(log(theta_j(tau)))$ expanded in $q=exp(pi itau)$, i.e. 4*q*D(thetajConstant())/thetajConstant(), and caches the result.

sortForMultiSamba: (List Matrix Integer, XHashTable(Matrix Integer, List Integer), XHashTable(Matrix Integer, List Integer)) -> List Matrix Integer

sortForMultiSamba: (List Matrix Integer, XHashTable(Matrix Integer, QEtaLaurentSeries C), XHashTable(Matrix Integer, QEtaLaurentSeries C)) -> List Matrix Integer