The Gröbner fan of an ideal I ⊂ k[x1, . . . , xn], defined by Mora and Robbiano, is a complex of polyhedral cones in Rn. The maximal cones of the fan are in bijection with the distinct monomial initial ideals of I as the term order varies. If I is homogeneous the Gröbner fan is complete and is the normal fan of the state polytope of I. In general the Gröbner fan is not complete and therefore no...

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 concept of comprehensive Grobner bases was introduced by Weispfenning. Montes has proposed an efficient algorithm for computing these bases. But he has not explicitly used Buchberger's criteria in his algorithm. In this paper we prove that we can apply these criteria on Montes algorithm. We propose a modified version of Montes algorithm and evaluate its performance via some examples.

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...

Many problems in kinematic synthesis of mechanisms and robots lead naturally to systems of bilinear equations in design parameters. Such systems are typically solved using well-known methods for solutions of systems of polynomial equations, e.g., Dialytic Elimination, Grobner bases, and Polynomial Continuation. This paper presents a new nullspace analysis method for solving a system of bilinear...

In this paper, we first present a new class of code based public key cryptosystem(PKC) based on ReedSolomon code over extension field of less than m=9, referred to as K(XVI)SE(1)PKC. We then present a new class of quadratic multivariate PKC, K(XVI)SE(2)PKC, based on binary cyclic code. We show that both K(XVI)SE(1)PKC and K(XVI)SE(2)PKC can be secure against the various linear transformation at...

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...