QEtaScalingCuspReduction(C, xiord, CX, xi, G)ΒΆ
qetascal.spad line 86 [edit on github]
- C: Field 
- xiord: PositiveInteger 
- xi: CX 
QEtaScalingCuspReduction provides functions to reduce the number of cusps for a multisamba computation.
- functionExpansionPair: ((Record(fdelta: PositiveInteger, fgamma: Matrix Integer, fred: Matrix Integer, ftriang: Matrix Integer), Fraction Integer) -> QEtaLaurentSeries CX, (Record(fdelta: PositiveInteger, fgamma: Matrix Integer, fred: Matrix Integer, ftriang: Matrix Integer), Fraction Integer) -> QEtaLaurentSeries CX, List Record(fdelta: PositiveInteger, fgamma: Matrix Integer, fred: Matrix Integer, ftriang: Matrix Integer), PositiveInteger) -> List XHashTable(Matrix Integer, QEtaLaurentSeries CX)
- functionExpansionPair(fa,fb,cmats,nterms)returns an expansion of- faand- fbat the cusps (given by- cmats, where the delta factor is supposed to be build into the- cmatsdatastructure). The result comes as a triple [- ws,hta,- htb] where hta and- htbcorrespond to the actual expansions and- wsrepresents values- wso that the expansion of hta.cusp and- htb.cusp is given as an expansion in- q^(1/w). Note that- wneed not be the width of the cusp.
- reduceCuspsByScaling: ((Record(fdelta: PositiveInteger, fgamma: Matrix Integer, fred: Matrix Integer, ftriang: Matrix Integer), Fraction Integer) -> QEtaLaurentSeries CX, (Record(fdelta: PositiveInteger, fgamma: Matrix Integer, fred: Matrix Integer, ftriang: Matrix Integer), Fraction Integer) -> QEtaLaurentSeries CX, List Record(fdelta: PositiveInteger, fgamma: Matrix Integer, fred: Matrix Integer, ftriang: Matrix Integer)) -> List Record(fdelta: PositiveInteger, fgamma: Matrix Integer, fred: Matrix Integer, ftriang: Matrix Integer)
- reduceCuspsByScaling(fa,fb,cmats)removes all the cusps from- cmatsthat lead to scaling equivalent series expansion of- faand- fb. Earlier entries survive.- cmatsshould be (a subset of) the cusps of the congruence subgroup- G. We expand at a cusp in terms of- q^(1/w) (where- wis the width of a cusp in- G).