Computation of Difference Grobner Bases
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GERDT, Vladimir; ROBERTZ, Daniel. Computation of Difference Grobner Bases. In: Computer Science Journal of Moldova. 2012, nr. 2(59), pp. 203-226. ISSN 1561-4042.
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Computer Science Journal of Moldova
Numărul 2(59) / 2012 / ISSN 1561-4042

Computation of Difference Grobner Bases

CZU: 004.421:[512.6+519.6]
Pag. 203-226

Gerdt Vladimir, Robertz Daniel
Disponibil în IBN: 30 noiembrie 2013


This paper is an updated and extended version of our note [1] (cf. also [2]). To compute difference Grobner 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 GrÄobner basis of the ideal.