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