QEtaQuotientSpecifications4ti2 QMOD¶

QEtaQuotientSpecificationss4ti2 computes a monoid basis of (specifications for) (generalized) eta-quotients with a pole at most at infinity.

etaQuotientMonoidInfinitySpecifications: (PositiveInteger, List List Integer) -> List QEtaSpecification: etaQuotientMonoidInfinitySpecifications(nn,idxs) returns etaQuotientMonoidSpecifications(nn,[infinity()],idxs).

etaQuotientMonoidSolutions: (PositiveInteger, List Cusp, List List Integer) -> Record(zinhom: List Vector Integer, zhom: List Vector Integer, zfree: List Vector Integer): etaQuotientMonoidSolutions(nn,polesat,idxs) returns zsolve(etaQuotientMonoidSystem(nn,polesat,idxs)).

etaQuotientMonoidSpecifications: (PositiveInteger, List Cusp, List List Integer) -> List QEtaSpecification: etaQuotientMonoidSpecifications(nn,polesat,idxs) returns specifications of (generalized) eta-quotients that (together with 1) generate the (multiplicative) monoid of all (generalized) eta-quotients (corresponding to the indices given by idxs) that are modular functions wrt. QMOD and have at most poles at the cuspe given by polesat. Specifications s that are known to represent constant modular function, are included in the result as s and inv(s).

etaQuotientSpecifications: (PositiveInteger, List List Integer, Integer) -> List QEtaSpecification: etaQuotientSpecifications(nn,idxs,grd) returns specifications for generatilzed eta-quotients with a pole of pole-order grd>0 at infinity and no pole at any other cusp.

freeSpecifications: (PositiveInteger, List List Integer, Record(zinhom: List Vector Integer, zhom: List Vector Integer, zfree: List Vector Integer)) -> List QEtaSpecification: freeSpecifications(nn,idxs,zres) extracts from zres the zfree part sorted with smallest poleorder(s) first.

homogeneousSpecifications: (PositiveInteger, List List Integer, Record(zinhom: List Vector Integer, zhom: List Vector Integer, zfree: List Vector Integer)) -> List QEtaSpecification: homogeneousSpecifications(nn,idxs,zres) extracts from zres the zhom part sorted with smallest poleorder(s) first.

nonConstantEtaQuotientMonoidInfinitySpecifications: (PositiveInteger, List List Integer) -> List QEtaSpecification: nonConstantEtaQuotientMonoidInfinitySpecifications(nn,idxs) returns nonConstantEtaQuotientMonoidSpecifications(nn,[infinity()],idxs).

nonConstantEtaQuotientMonoidSpecifications: (PositiveInteger, List Cusp, List List Integer) -> List QEtaSpecification: nonConstantEtaQuotientMonoidSpecifications(nn,polesat,idxs) returns those elements from etaQuotientMonoidSpecifications(nn,polesat,idxs) that do not represent a constant modular functions.