A Systematic Study of Gröbner Basis Methods

Residual Generator Design for Non-linear, Polynomial Systems – a Gröbner Basis Approach

Design and analysis of residual generators for polynomial systems is considered. This paper presents a systematic procedure, given an input-output description of system dynamics, to design residual generators for fault diagnosis. The design procedure is based on standard elimination theory. The design procedure is applied in a simulation study on a non-linear system, where it is showed how mult...

Efficient encoding via Gröbner bases and discrete Fourier transforms for several kinds of algebraic codes

Abstract—Novel encoding scheme for algebraic codes, such as codes on algebraic curves, multidimensional cyclic codes, and hyperbolic cascaded Reed–Solomon codes, is proposed with numerical examples. We make use of the 2-dimensional inverse discrete Fourier transform, which generalizes the Mattson–Solomon polynomial for Reed–Solomon codes. We also generalize the workings of the generator polynom...

Parametrised Gröbner-Shirshov Bases

We consider the problem of describing Gröbner-Shirshov bases for free associative algebras in finite terms. To this end we consider parametrised elements of an algebra and give methods for working with them which under favourable conditions lead to a basis given by finitely many patterns. On the negative side we show that in general there can be no algorithm. We relate our study to the problem ...

Gröbner Basis Techniques in Algebraic Combinatorics

Gröbner basis techniques in the algebraic study of triangulations of convex polytopes as well as of the number of faces of simplicial complexes will be discussed. Of these two traditional topics in combinatorics, the first will be studied by using initial ideals of toric ideals and the second will be studied by using generic initial ideals of monomial ideals.

Automatic Geometric Theorem Proving using Gröbner Bases