ExtendedPolynomialReduction(C, E, R)

extred.spad line 1 [edit on github]

• C : GcdDomain
• E : OrderedAbelianMonoidSup
• R : Join(FiniteAbelianMonoidRing(C, E), VariablesCommuteWithCoefficients)

ExtendedPolynomialReduction(C, E, R) is a package that allows denominatorFree reductions of a polynomial r from R wrt a list of polynomials from R (usually such a list is a Groebner basis wrt the order given via E). Additionally, the reduction steps are recorded and provided in the output.

reduce : (R, List(R)) -> Record(poly : R, repr : Vector(R), mult : C)

reduce(r, bas) returns a triple (p, v, m) such that m*r = sum(bas.i * v.i, i=1..#bas) + p