QEtaModularPackage QMOD¶

undocumented

etaCofactorInfinity: (PositiveInteger, QEtaSpecification, PositiveInteger, NonNegativeInteger, List List Integer) -> QEtaSpecification: etaCofactorInfinity(nn,rspec,m,t,idxs) returns a specification sspec such that sspec has only indices from idxs, modular?(sspec,rspec,m,t)$QMOD and etaQuotient(sspec,rspec,m,t)$SymbolicModularEtaQuotient(QMOD) corresponds to a modular function with poles only at infinity and with smallest pole order.

etaCofactorInfinitySpaceSystem: (List QEtaSpecification, List Integer, List Cusp) -> Record(zmat: Matrix Integer, zrels: Vector Integer, zrhs: Vector Integer): etaCofactorInfinitySpaceSystem(bspecs,grds,spitzen) returns a matrix A and a right-hand side v for a system A*x>=v where the right-hand side is grds (which is the expansion poleorders ath the cusps spitzen and A is the expansion poleorders of the basis elements given by bspecs. The rows are indexed by the cusps.

qetaGrades: (QEtaSpecification, QEtaSpecification, PositiveInteger, NonNegativeInteger) -> List Integer: qetaGrades(sspec,rspec,m,t) returns qetaGrades(y) where y=etaQuotient(sspec,rspec,m,t)$SymbolicModularEtaQuotient(QMOD).

qetaGrades: (QEtaSpecification, QEtaSpecification, PositiveInteger, NonNegativeInteger, List Cusp) -> List Integer: qetaGrades(sspec,rspec,m,t,spitzen) returns qetaGrades(y) where y=etaQuotient(sspec,rspec,m,t,spitzen) from SymbolicModularEtaQuotient(QMOD).

qetaGrades: SymbolicModularEtaQuotient QMOD -> List Integer: qetaGrads(y) returns the poleorders of the modular function corresponding to y. In the special case when e is the expansion and qetaGrade(e.c) is less than 0 for every cusp c in cusps(y), the function returns a value of -1 for each cusp although this might not be the true poleorder of the expansion, it rather is the value for the case that y represents zero. This special treatment avoids running into an infinite loop if y represents the zero function.

reduceSystem: Record(zmat: Matrix Integer, zrels: Vector Integer, zrhs: Vector Integer) -> Record(zmat: Matrix Integer, zrels: Vector Integer, zrhs: Vector Integer): reduceSystem([A,v]) returns a matrix B and a right-hand side w such that A*x >= v and B*x >= w have the same solutions, but B has duplicate rows removed. The order of distinct rows is kept.