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 inhlx
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)
forj=2
,3,4 computes $frac{4}{pii
}frac{d
}{d
tau}(log(theta_j(tau)))$ expanded in $q=
exp(pii
tau)$, 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