QEtaSambaPackage(F, AB, Y)¶
qetasamba.spad line 688 [edit on github]
- F: Type 
- AB: Type 
- Y: QEtaComputationCategory(F, AB) 
QEtaSambaPackage implements the algorithm Samba from an article of Ralf Hemmecke: “Dancing Samba with Ramanujan Partition Congruences” (Journal of Symbolic Computation). doi:10.1016/j.jsc.2017.02.001 http://www.risc.jku.at/publications/download/risc_5338/DancingSambaRamanujan.pdf
- samba: (List F, Integer, Y -> Y) -> AB
- samba(m, g, oneStep!)returns algebraBasis(sambaComputation(- m,- g,oneStep!)).
- samba: (List F, Y -> Y) -> AB
- samba(m, oneStep!)returns samba(- m,- -1,oneStep!).
- samba: List F -> AB
- samba(m)returns samba(- m,- -1).
- sambaComputation: (List F, Integer) -> Y
- sambaComputation(m,g)returns sambaComputation(- m,- g,oneStep!).
- sambaComputation: (List F, Integer, Y -> Y) -> Y
- sambaComputation(m,g,oneStep!)repeats- oneStep!as long as continue?(- y) returns- trueand eventually returns the computation data object. If- gis negative all critical elements will be checked, otherwise the computation is stopped if the number of gaps of the intermediate basis reaches this threshold. For computations with eta-quotients over $Gamma_0(- N)$,- gshould be equalt to genus of the modular curve over this group, which can be computed by genus$- CongruenceSubgroupGamma0(- N).
- sambaComputation: (List F, Y -> Y) -> Y
- sambaComputation(m,oneStep!)returns sambaComputation(- m,- -1,- oneStep!).
- sambaComputation: List F -> Y
- sambaComputation(m)returns sambaComputation(- m,- -1).