On Computing Janet Bases for Degree Compatible Orderings
نویسندگان
چکیده
We consider three modifications of our involutive algorithm for computing Janet bases. These modifications are related to degree compatible monomial orders and specify selection strategies for non-multiplicative prolongations. By using the standard data base of polynomial benchmarks for Gröbner bases software we compare the modifications and confront them with Magma that implements Faugère’s F4 algorithm.
منابع مشابه
A new algorithm for computing SAGBI bases up to an arbitrary degree
We present a new algorithm for computing a SAGBI basis up to an arbitrary degree for a subalgebra generated by a set of homogeneous polynomials. Our idea is based on linear algebra methods which cause a low level of complexity and computational cost. We then use it to solve the membership problem in subalgebras.
متن کاملMonomial Orderings, Rewriting Systems, and Gröbner Bases for the Commutator Ideal of a Free Algebra
In this paper we consider a free associative algebra on three generators over an arbitrary field K. Given a term ordering on the commutative polynomial ring on three variables over K, we construct uncountably many liftings of this term ordering to a monomial ordering on the free associative algebra. These monomial orderings are total well orderings on the set of monomials, resulting in a set of...
متن کاملCombination of Compatible Reduction
Reduction orderings that are compatible with an equational theory E and total on (the E-equivalence classes of) ground terms play an important r^ ole in automated deduction. We present a general approach for combining such orderings. To be more precise, we show how E 1-compatible reduction orderings total on 1-ground terms and E 2-compatible reduction orderings total on 2-ground terms can be us...
متن کاملComputing Grr Obner Bases by Fglm Techniques in a Noncommutative Setting
A generalization of the FGLM technique is given to compute Grr obner bases for two-sided ideals of free nitely generated algebras. Specializations of this algorithm are presented for the cases in which the ideal is determined by either functionals or monoid (group) presentations. Generalizations are discussed in order to compute G-bases on (twisted) semigroup rings. It is well known that the co...
متن کاملJanet Bases and Resolutions in CoCoALib
Recently, the authors presented a novel approach to computing resolutions and Betti numbers using Pommaret bases. For Betti numbers, this algorithm is for most examples much faster than the classical methods (typically by orders of magnitude). As the problem of δ-regularity often makes the determination of a Pommaret basis rather expensive, we extend here our algorithm to Janet bases. Although ...
متن کامل