pn(xi,...,xn) = 0 for x = (x\,... ,xn). This problem is very common in many fields of science and engineering, such as formula construction, geometric intersection problems, inverse kinematics, power flow problems with PQ-specified bases, computation of equilibrium states, etc. Elimination theory-based methods, most notably the Buchberger algorithm (Buchberger 1985) for constructing Grobner bas...

The principal result described in this report is the design and implementation of a parallel version of Buchberger's algorithm. Its correctness is stated and some experimental results are given. The first parts are devoted to a partial review of Grobner bases, of Buchberger's algorithm which computes them, and of some of their applications.

This paper discusses a result by Fliess about input-output equations [or polynomial systems with time delays, and strengthens the result somewhat. The proof given is more detailed and opens the way [or constructive methods [or determining the input-output behavior. Some such methods based on Grobner bases are described in detail. Furthermore, some connections with observability are exploited.

In this research communication on commutative algebra it was proposed to deal with Grobner Bases and its applications in signals and systems domain.This is one of the pioneering communications in dealing with Cryo-EM Image Processing application using multi-disciplinary concepts involving thermodynamics and electromagnetics based on first principles approach. keywords: Commutative Algebra/HOL/S...

In this paper, we develop the Gr6bner-Shirshov basis theory for the representations of associative algebras by introducing the notion of Gr6bner-Shirshov pairs. Our result can be applied to solve the reduction problem in representation theory and to construct monomial bases of representations of associative algebras. As an illustration, we give an explicit construction of Gr6bner-Shirshov pairs...

To integer programming, a ideals have been problems, which Hiroki Nakayama The University of Tokyo (Received October 27, 2003) Hiroshi Imai jases and standard pairs via toric ilgebraic approaches using Grobner k studied in recent years. In this paper, we consider a unimodular case, e.g., network flow enables us to analyze primal and dual problems in an equal setting. By combining existing resul...