F4-invariant algorithm for computing SAGBI-Gröbner bases

SAGBI and SAGBI-Gröbner Bases over Principal Ideal Domains

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.

Computing inhomogeneous Gröbner bases

In this paper we describe how an idea centered on the concept of self-saturation allows several improvements in the computation of Gröbner bases via Buchberger’s Algorithm. In a nutshell, the idea is to extend the advantages of computing with homogeneous polynomials or vectors to the general case. When the input data are not homogeneous, we use a technique described in Section 2: the main tool ...

Signature-Based Gröbner Basis Algorithms - Extended MMM Algorithm for computing Gröbner bases

Signature-based algorithms is a popular kind of algorithms for computing Gröbner bases, and many related papers have been published recently. In this paper, no new signature-based algorithms and no new proofs are presented. Instead, a view of signature-based algorithms is given, that is, signature-based algorithms can be regarded as an extended version of the famous MMM algorithm. By this view,...

Sagbi Bases for Rings of Invariant Laurent Polynomials

Let k be a field, Ln = k[x ±1 1 , . . . , x ±1 n ] be the Laurent polynomial ring in n variables and G be a group of k-algebra automorphisms of Ln. We give a necessary and sufficient condition for the ring of invariants Ln to have a SAGBI basis. We show that if this condition is satisfied then Ln has a SAGBI basis relative to any choice of coordinates in Ln and any term order.