|Title||Computation of difference Gr\"obner bases.|
|Author(s)|| Vladimir P. Gerdt, Daniel Robertz|
|Type||Article in Journal|
|Abstract||This paper is an updated and extended version of our note [“Computation of Gröbner bases for systems of linear difference equations”, in: Computeralgebra-Rundbrief Nr. 37, GI DMV GAMM, 8-13 (2005)] (cf. also [the authors, “A Maple package for computing Gröbner bases for linear recurrence|
relations”, Nucl. Instrum. Methods 559, No. 1, 215–219 (2006), arXiv:cs.SC/0509070]). 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 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 Gröbner basis of the ideal.
|Journal||Comput. Sci. J. Mold.|
|Publisher||Academy of Sciences of Moldova, Institute of Mathematics and Computer Science, Chicsinuau|