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Computation of Difference Groebner Bases
To compute difference Groebner 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 Groebner basis of the ideal.Comment: 17 page