QEtaGeneralizedRamanujan CΒΆ

qetark.spad line 808 [edit on github]

QEtaGeneralizedRamanujan provides functions to compute Ramanujan identities by an algorithm that was developed by Radu in cite{Radu:RamanujanKolberg:2015} (`DOI=10.1016/j.jsc.2014.09.018 <https://doi.org/10.1016/j.jsc.2014.09.018>`_), see RISC Report 16-06 <https://www.risc.jku.``at/publications/download/risc_5069/zzz3`.pdf>`_. See also at the top of the qetark.spad file where this package is implemented. This package builds on the work of cite{Chen+Du+Zhao:FindingModularFunctionsRamanujan:2019} and finds identities with generalized eta-quotients.

findIdentity: (PositiveInteger, List List Integer, QEtaSpecification, PositiveInteger, NonNegativeInteger, List List Integer) -> QEtaRamanujanKolbergIdentity C

findIdentity(nn, sidxs, rspec, m, k, bidxs) returns all data for a generalized Ramanujan identity where the indices for the cofactor and the generalized eta-quotients on the right-hand side are given by sidxs and bidxs, respectively.

findIdentity: (PositiveInteger, List List Integer, QEtaSpecification, PositiveInteger, NonNegativeInteger, List QEtaSpecification) -> QEtaRamanujanKolbergIdentity C

findIdentity(nn, idxs, rspec, m, k, bgens) returns all data for a generalized Ramanujan identity where the cofactor may only involve generalized eta-functions given through the indices idxs.

findIdentity: (PositiveInteger, List List Integer, QEtaSpecification, PositiveInteger, NonNegativeInteger, QEtaRamanujanKolbergIdentity C) -> QEtaRamanujanKolbergIdentity C

findIdentity(nn, sidxs, rspec, m, k, id) returns all data for a generalized Ramanujan identity. The basis elements are taken from a previously computed identity, if possible.

findIdentity: (QEtaSpecification, QEtaSpecification, PositiveInteger, NonNegativeInteger, List List Integer) -> QEtaRamanujanKolbergIdentity C

findIdentity(sspec, rspec, m, k, idxs) returns all data for a generalized Ramanujan identity where the right-hand side may only involve generalized eta-quotients that are given through the indices idxs.

findIdentity: (QEtaSpecification, QEtaSpecification, PositiveInteger, NonNegativeInteger, List QEtaSpecification) -> QEtaRamanujanKolbergIdentity C

findIdentity(sspec, rspec, m, k, bspecs) returns all data for a generalized Ramanujan identity.

findIdentity: (QEtaSpecification, QEtaSpecification, PositiveInteger, NonNegativeInteger, List QEtaSpecification, QEtaAlgebraBasis(C, QEtaExtendedAlgebra(C, QEtaAlgebraCachedPower(C, Finite0Series C), QEtaAlgebraCachedPower(C, Polynomial C)))) -> QEtaRamanujanKolbergIdentity C

findIdentity(sspec, rspec, m, k, bspecs, xab) returns all data for a generalized Ramanujan identity.

findIdentity: (QEtaSpecification, QEtaSpecification, PositiveInteger, NonNegativeInteger, QEtaRamanujanKolbergIdentity C) -> QEtaRamanujanKolbergIdentity C

findIdentity(sspec, rspec, m, k, id) returns all data for a generalized Ramanujan identity. The basis elements are taken from a previously computed identity, if possible.