Constructors

• geobucket(const SparsePolyRing&);

Queries

• IsZero(g) -- true iff g is the zero polynomial (potentially costly because it compares the buckets)

Operations

Let gbk be a geobucket, f a RingElem& (see RingElem)

• CoeffRing(gbk) -- the ring of coefficients of the ring of gbk
• PPM(gbk) -- the PPMonoid of the ring of gbk
• LC(gbk) -- the leading coeff of gbk; it is an element of CoeffRing(gbk) (potentially costly because it compares the buckets)
• content(gbk) -- the gcd of all coefficients in gbk; it is an element of CoeffRing(gbk) (it is the gcd of all bucket contents)
• RemoveBigContent(gbk) -- if gbk has a big content, gbk is divided by it
• AddClear(f, gbk) -- assign the polynomial value of gbk to f, and set 0 to gbk
• MoveLMToFront(f, gbk); -- moves the LM of gbk to f (using PushFront)
• MoveLMToBack(f, gbk); -- moves the LM of gbk to f (using PushBack)
• ReductionStep(gbk, f, RedLen); -- reduces gbk with f
• ReductionStepGCD(gbk, f, FScale, RedLen); -- same as above, but multiplies by a scalar if needed
• operator<<(std::ostream&, gbk) -- prints the buckets (mainly for debugging)
• PrintLengths(std::ostream&, gbk) -- just for debugging

bucket

This class is to be used only by geobuckets.

A bucket represents a polynomial as a product of a polynomial and a coefficient, two RingElem respectivey in a SparsePolyRing P and CoeffRing(P).

The coeffient factor is used for fast multiplication of a geobucket by a coefficient and it comes useful in the reduction process over a field of fraction of a GCD ring.

We normalize the bucket (i.e. multiply the polynomial by the coefficient) only when it is necessary: e.g. to compute a reference to the LC of the bucket.

All methods are private (to be used only by geobuckets, friend)

Methods on buckets (weak exception guarantee)

• myNormalize(void) -- myPoly *=myCoeff; myCoeff 1
• myAddClear(RingElem& f, int FLen) -- *this += f; f = 0; *this normalized
• myAddClear(bucket& b) -- *this += b; b = 0; *this normalized
• myMul(ConstRefRingElem coeff) -- *this *= coeff
• myDiv(ConstRefRingElem coeff) -- *this /= coeff; assumes *this divisible by coeff