QEtaReductionCategory(C, F, AB)¶
qetasamba.spad line 396 [edit on github]
- F: QEtaGradedAlgebra C 
- AB: Type 
QEtaReductionCategory lists the functions used in the restricted reduction as described in “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
- noTrace: F -> Void
- from QEtaComputationReductionCategory(F, AB) 
- noTraceEnter: (F, AB) -> Void
- from QEtaComputationReductionCategory(F, AB) 
- reduce: (F, AB) -> F
- from QEtaComputationReductionCategory(F, AB) 
- reducer: (F, AB) -> Union(F, failed)
- reducer(u, ab)returns an element- bfrom basis(ab) or- b=1such that grade- u- grade- bis divisible by grade(multiplier ab) or returns “failed” if no such- bexists. This functions corresponds to the function “select_{- t,basis}(- u)” as in Definition 2.6 of cite{- Hemmecke_DancingSambaRamanujan_2018}. That reducer yields the element with biggest possible grade is ensured by the requirement that “basis” is appropriately sorted by greaterGrade?.
- tailReduce: (F, AB) -> F
- tailReduce - ==tracedTailReduce(- noTraceEnter,- noTrace,- noTrace)
- tailReducible?: (F, Integer, F) -> Boolean
- tailReducible?(u, n, b)returns- trueiff there exists- fin- Fsuch that for- v=- u-- f*b,- c= qetaCoefficient(- u,- n), and- d= qetaCoefficient(- v,- n) zero?- dholds or euclideanSize- c> euclideanSize- d. Initially it is assumed that not zero?(- c).
- topReduce: (F, AB) -> F
- topReduce - ==tracedTopReduce(- noTraceEnter,- noTrace,- noTrace)
- topReducible?: (F, F, F) -> Boolean
- from QEtaComputationReductionCategory(F, AB) 
- tracedReduce: ((F, AB) -> Void, F -> Void, F -> Void) -> (F, AB) -> F
- from QEtaComputationReductionCategory(F, AB) 
- tracedTailReduce: ((F, AB) -> Void, F -> Void, F -> Void) -> (F, AB) -> F
- tracedTailReduce behavesperforms only tail-reductions, i.e. the qetaGrade of the result will be the same as the qetaGrade of the input element. Tail-reductions are reductions that are performed on the non-leading terms of the input up to (and including) the constant term of the series.
- tracedTopReduce: ((F, AB) -> Void, F -> Void, F -> Void) -> (F, AB) -> F
- tracedTopReduce behaveslike tracedReduce, but performing only top-reductions.
- traceEnter: NonNegativeInteger -> (F, AB) -> Void
- from QEtaComputationReductionCategory(F, AB) 
- traceLoop: NonNegativeInteger -> F -> Void
- from QEtaComputationReductionCategory(F, AB) 
- traceReturn: NonNegativeInteger -> F -> Void
- from QEtaComputationReductionCategory(F, AB)