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!)
repeatsoneStep!
as long as continue?(y
) returnstrue
and eventually returns the computation data object. Ifg
is 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 $Gamma_0(N
)$,g
should 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
).