QEtaReductionCategory(C, F, AB)¶

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

reducer: (F, AB) -> Union(F, failed): reducer(u, ab) returns an element b from basis(ab) or b=1 such that grade u - grade b is divisible by grade(multiplier ab) or returns “failed” if no such b exists. 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 true iff there exists f in F such that for v = u - f*b, c = qetaCoefficient(u, n), and d = qetaCoefficient(v, n) zero? d holds 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 behaves performs 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 behaves like 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)