Gröbner Bases and Systems Theory

COMBINATORIAL-ALGEBRAIC TECHNIQUES IN GRÖBNER BASES THEORY by

§ 0. Preliminary notations and main definitions.

Solving linear systems of equations over integers with Gröbner bases

Gröbner Bases over Finitely Generated Affine Monoids and Applications. The Direct Sum Case

For multidimensional linear systems with constant coefficients, Gröbner bases are the universal tool to solve algorithmically a multitude of problems which arise in control theory. Gröbner bases are defined over the polynomial ring which means that the domain of definition of discrete systems is the positive orthant. However, often the individual variables are interpreted diversely, e.g., some ...

Gröbner-Shirshov Bases for Lie Algebras: after A. I. Shirshov

In this paper, we review Shirshov’s method for free Lie algebras invented by him in 1962 [17] which is now called the Gröbner-Shirshov bases theory.

A Step in Castelnuovo Theory via Gröbner Bases

We establish the first previously unknown case of the EisenbudHarris conjecture in Castelnuovo theory concerning algebraic curves of high genus in Pn. The problem is reduced to a question about zero-dimensional schemes Γ ⊂ P in symmetric position with certain constrains on the Hilbert function. The method of Gröbner bases is then applied to study the homogeneous ideal of Γ.