QEtaQuotientSortPackage QMOD¶
qetaqmspecs.spad line 114 [edit on github]
- QMOD: QEtaModularCategory 
QEtaQuotientSortPackage provides sorting functions for (modular) eta-quotients.
- lessLex?: (List List Integer, List List Integer) -> Boolean
- lessLex?(w1,w2)returns- falseif- w1=w2. It returns- trueif first(- w1)<first(- w2) or (first(- w1)=first(- w2) and lessLex?(rest(- w1),rest(- w2))).
- sortByComponentGrade: (List QEtaSpecification, List Cusp) -> List QEtaSpecification
- sortByComponentGrade(specs,spitzen)computes the level- nn, the common indices idxs and the respective exponent vectors gens and then sorts the- specslike sortByComponentGrade(- nn,idxs,gens,- spitzen).
- sortByComponentGrade: (PositiveInteger, List List Integer, List Vector Integer, List Cusp) -> List Vector Integer
- sortByComponentGrade(nn,idxs,gens,spitzen)returns- genssorted in the following way. Note that spec=etaQuotientSpecification(- nn,- idxs,- s) is for each- sfrom- genssupposed to be a (modular) eta-quotient specification. Let- grd(- s)- =g=(- g1,…,- gk) be the grades (=poleorders) at the cusps (given by- spitzen) of a (modular) eta-specification- s,- sw(- g)=sort(>,[[- g1,1],…[- gk,- k]]),- len2(- g)=reduce(+,[- l(1)- z^2for- lin- sw(- g)],0), and- w(- g)=cons([- len2(- g),0],- sw(- g)), then- s1<s2is- trueif lessLex?(- w(- grd(- s1)),- w(- grd(- s2))),- s1<s2is- falseif lessLex?(- w(- grd(- s2)),- w(- grd(- s1))). If- w(- grd(- s1))- =w(- grd(- s2), then ties are broken by a similar comparison at setDifference(cusps(- nn),- spitzen) where the cusps remain in the order given by cusps$QMOD.