ReductionCog

• class ReductionCogBase
• implementations

class ReductionCogBase

ReductionCogBase is an abstract class to perform a full reduction: it contains two parts:

• IgnoredPPs summands whose PPs are to be ignored
• Active the part which will be reduced

Thanks to the limited operations allowed on a ReductionCog, all PPs in IgnoredPPs are guaranteed bigger than those in the Active part.

With a ReductionCog F you can compute:

• ActiveLPP(F) the LPP of the Active part
• IsActiveZero(F) is the Active part zero?

• F.myMoveToNextLM() move the LM of the Active part to the IgnoredPPs
• F.myReduce(f) reduce the Active part with f
• F.myAssignReset(f) the Active part gets f; f and IgnoredPPs get 0
• F.myAssignReset(f, fLen) same as above but faster for geobucket implementation
• F.myRelease(f) F gets the total value of f; f gets 0
• F.myOutput(out)

The idea is that LM will be reduced first; if the result is not 0 it will be "set aside and ignored" and the new LM of the Active part will be reduced, and so on.

The result of myReduce is defined up to an invertible (in the coefficient ring) constant factor.

Constructors are

    ReductionCog NewRedCogPolyField(const SparsePolyRing& P);
    ReductionCog NewRedCogPolyGCD(const SparsePolyRing& P);
    ReductionCog NewRedCogGeobucketField(const SparsePolyRing& P);
    ReductionCog NewRedCogGeobucketGCD(const SparsePolyRing& P);

In the "GCD" version, myRelease makes poly content free. In the "Field" version: myRelease does NOT make poly monic. ... I can't remember why I made this choice....

example

    ReductionCog F = ChooseReductionCogGeobucket(myGRingInfoValue);
    F->myAssignReset(f, fLen);
    while ( !IsActiveZero(F) )
    {
      (..) // find reducer g or break
      F->myReduce(g);
    }
    F->myRelease(f);

implementations

In general the geobucket implementation are to be preferred

RedCog::PolyFieldImpl

this implementation contains two RingElem.

RedCog::PolyGCDImpl

this implementation contains two polynomials [RingElem] two coefficients [RingElem] and a counter

RedCog::GeobucketFieldImpl

this implementation contains a RingElem for the IgnoredPPs and a geobucket for the Active part

RedCog::GeobucketGCDImpl

this implementation contains a RingElem for the IgnoredPPs and a geobucket for the Active part two coefficients [RingElem] and a counter