EuclideanGroebnerBasisPackage(Dom, Expon, VarSet, Dpol)¶
- Dom: EuclideanDomain
- Expon: OrderedAbelianMonoidSup
- VarSet: OrderedSet
- Dpol: PolynomialCategory(Dom, Expon, VarSet)
EuclideanGroebnerBasisPackage computes groebner bases for polynomial ideals over euclidean domains. The basic computation provides a distinguished set of generators for these ideals. This basis allows an easy test for membership: the operation euclideanNormalForm returns zero on ideal members. The string “info” and “redcrit” can be given as additional args to provide incremental information during the computation. If “info” is given, a computational summary is given for each
s-polynomial. If “redcrit” is given, the reduced critical pairs are printed. The term ordering is determined by the polynomial type used. Suggested types include DistributedMultivariatePolynomial, HomogeneousDistributedMultivariatePolynomial, GeneralDistributedMultivariatePolynomial.
- euclideanGroebner: (List Dpol, String) -> List Dpol
euclideanGroebner(lp, infoflag)computes a groebner basis for a polynomial ideal over a euclidean domain generated by the list of polynomials
lp. During computation, additional information is printed out if infoflag is given as either “info” (for summary information) or “redcrit” (for reduced critical pairs)
- euclideanGroebner: (List Dpol, String, String) -> List Dpol
euclideanGroebner(lp, "info", "redcrit")computes a groebner basis for a polynomial ideal generated by the list of polynomials
lp. If the second argument is
"info", a summary is given of the critical pairs. If the third argument is “redcrit”, critical pairs are printed.
- euclideanGroebner: List Dpol -> List Dpol
euclideanGroebner(lp)computes a groebner basis for a polynomial ideal over a euclidean domain generated by the list of polynomials
- euclideanNormalForm: (Dpol, List Dpol) -> Dpol
euclideanNormalForm(poly, gb)reduces the polynomial
polymodulo the precomputed groebner basis
gbgiving a canonical representative of the residue class.