Shapes such as triangles or rectangles can be defined in terms of geometric properties invariant under a group of transformations. Complex shapes can be described by logic formulae w i th simpler shapes as the atoms. A standard technique for computing invariant properties of simple shapes is the method of moment invariants, known since the early sixties. We generalize this technique to shapes d...

Generalized quasi-cyclic (GQC) codes form a wide and useful class of linear codes that includes thoroughly quasi-cyclic codes, finite geometry (FG) low density parity check (LDPC) codes, and Hermitian codes. Although it is known that the systematic encoding of GQC codes is equivalent to the division algorithm in the theory of Gröbner basis of modules, there has been no algorithm that computes G...

The definition and main results connected with Gröbner basis, Hilbert series and Anick's resolution are formulated. The method of the infinity behavior prediction of Gröbner basis in noncommu-tative case is presented. The extensions of BERGMAN package for IBM PC compatible computers are described. Let A =< X|R > be a finitely presented associative algebra over field K. Here are the main example...

A number of problems in control can be reduced to finding suitable real solutions of algebraic equations. In particular, such a problem arises in the context of switching surfaces in optimal control. Recently, a powerful new methodology for doing symbolic manipulations with polynomial data has been developed and tested, namely the use of Gröbner bases. In this paper, we apply the Gröbner basis ...

Mixed-integer polynomial programming (MIPP) problems are one class of mixed-integer nonlinear programming (MINLP) problems where objective function and constraints are restricted to the polynomial functions. Although the MINLP problem is NP-hard, in special cases such as MIPP problems, an efficient algorithm can be extended to solve it. In this research, we propose an algorit...

This paper uniies most of the current literature on 3D geometric invariants from point correspondences across multiple 2D views by using the tool of Elimination from algebraic geometry. The technique allows one to predict results by counting parameters and reduces many complicated results obtained in the past (reconstruction from two and three views, epipolar geometry from seven points, triline...

This article investigates the forward kinematics problem formulation and resolution specifically applied to spatial parallel manipulators which allow only for translationnal displacements of the end-effector. The translation manipulator is usually constituted of three to six kinematics chains with three actuators usually located on the base. These mechanisms are designed to prevent any rotation...

In this paper, a modied version of LLL algorithm, which is a an algorithm with output-sensitivecomplexity, is presented to convert a given Grobner basis with respect to a specic order of a polynomialideal I in arbitrary dimensions to a Grobner basis of I with respect to another term order.Also a comparison with the FGLM conversion and Buchberger method is considered.