Computation of Difference Grobner Bases

• Main Authors: Vladimir P. Gerdt, Daniel Robertz
• Format: Article
• Language: English
• Published: Institute of Mathematics and Computer Science of the Academy of Sciences of Moldova 2012-07-01
• Series: Computer Science Journal of Moldova
• Online Access: http://www.math.md/files/csjm/v20-n2/v20-n2-(pp203-226).pdf

This paper is an updated and extended version of our note \cite{GR'06} (cf.\ also \cite{GR-ACAT}). To compute difference \Gr 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 package. Its applications are illustrated by generation of finite difference approximations to linear partial differential equations and by reduction of Feynman integrals. We also present the algorithm for an ideal generated by a finite set of nonlinear difference polynomials. If the algorithm terminates, then it constructs a \Gr basis of the ideal.