Stability Computation via Gröbner Basis

On Gröbner Bases Computation on a Supercomputer Using REDUCE

Exact Computat ion Using Approximate Gröbner Bases

We discuss computation of approximate Gröbner bases at high but finite precision. We show how this can be used to deduce exact results for various applications. Examples include implicitizing surfaces, finding multivariate polynomial greatest common divisors and factorizations over the rational and complex number fields. This is an extended version of a paper for SYNASC 2010, titled úPolynomial...

Towards Computing a Gröbner Basis of a Polynomial Ideal over a Field by Using Matrix Triangularization

We give first results of our investigation of the connection between Gröbner bases computation and Gaussian elimination. We show that for every input set F of polynomials a matrix of shifts of those polynomials exists such that by triangularizing this matrix we obtain a Gröbner basis of F .

Computing SAGB-Gröbner Basis of Ideals of Invariant Rings by Using Gaussian Elimination

The link between Gröbner basis and linear algebra was described by Lazard [4,5] where he realized the Gröbner basis computation could be archived by applying Gaussian elimination over Macaulay’s matrix . In this paper, we indicate how same technique may be used to SAGBIGröbner basis computations in invariant rings. . Keywords— Gröbner basis, SAGBIGröbner basis, reduction, Invariant ring, permut...

Efficient decoding of (binary) cyclic codes above the correction capacity of the code using Gröbner bases

This paper revisits the topic of decoding cyclic codes with Gröbner bases. We introduce new algebraic systems, for which the Gröbner basis computation is easier. We show that formal decoding formulas are too huge to be useful, and that the most efficient technique seems to be to recompute a Gröbner basis for each word (online decoding). We use new Gröbner basis algorithms and “trace preprocessi...