Groebner Bases Applied to Systems of Linear Difference Equations

Computation of Difference Groebner Bases

This paper is an updated and extended version of our note [1] (cf. also [2]). To compute difference Gröbner bases of ideals generated by linear polynomials we adopt to difference polynomial rings the involutive algorithm based on Janet-like division. The algorithm has been implemented in Maple in the form of the package LDA (Linear Difference Algebra) and we describe the main features of the pa...

A Maple Package for Computing Groebner Bases for Linear Recurrence Relations

A Maple package for computing Gröbner bases of linear difference ideals is described. The underlying algorithm is based on Janet and Janet-like monomial divisions associated with finite difference operators. The package can be used, for example, for automatic generation of difference schemes for linear partial differential equations and for reduction of multiloop Feynman integrals. These two po...

A Numerical Approach for Solving of Two-Dimensional Linear Fredholm Integral Equations with Boubaker Polynomial Bases

In this paper, a new collocation method, which is based on Boubaker polynomials, is introduced for the approximate solutions of a class of two-dimensional linear Fredholm integral equationsof the second kind. The properties of two-dimensional Boubaker functions are presented. The fundamental matrices of integration with the collocation points are utilized to reduce the solution of the integral ...

Algebraic Solution of Systems of Polynomial Equations Using Groebner Bases

An Application of Groebner Bases to Planarity of Intersection of Surfaces

In this paper we use Groebner bases theory with the purpose to determine planarity of intersections of two algebraic surfaces in R. There are specially considered plane sections of a type of conoid which has a cubic egg curve as one of the directrices. The paper investigates a possibility of conic plane sections of this type of conoid. 1. THE BASIC CONCEPT OF GROEBNER BASES Many problems in mat...