Ein algorithmisches Kriterium für die Lösbarkeit eines algebraischen Gleichungssystems

CONSTRUCTION D'UN ÉLÉMENT REMARQUABLE DE L'IDÉAL DE BERNSTEIN-SATO ASSOCIÉ À DEUX COURBES PLANES ANALYTIQUES

“…, le butétant de montrer que le reste R est nul (il s'agit du critère de Buchberger démontréà l'origine dans les anneaux de polynômes [5]). Dans N 2 , considérons le secteurépointé…”

Dynamic modeling of biochemical reactions with application to signal transduction: principles and tools using Mathematica

“…Solve and Reduce are based on the algorithm for constructing Gröbner basis, which is one of the most important results in the last decades in theoretical computer science. This algorithm enables one to rewrite a polynomial system of equations into a triangular form, in almost the same way as it is done in the process of Gauss elimination for linear systems of equations (Buchberger, 1970). (Triangular here means that the first equation only contains a single variable, the second one only two etc.)…”

An Automated Confluence Proof for an Infinite Rewrite System Parametrized over an Integro-Differential Algebra

“…In fact, we prove the confluence of the rewrite system by equivalently proving that it corresponds to a Gröbner basis in this noncommutative algebra. Gröbner bases were introduced in [5,6] and have became a crucial tool in computer algebra, specifically for solving several algebraic problems concerning ideals [8], see for instance [13,14] for the commutative setting, and [4,12,17] for the noncommutative setting. A detailed presentation of the proof is given in [24]; see also [26] for a summary.…”