Abstract
We develop a basic theory of Grobner bases for ideals in the algebra of Laurent polynomials (and, more generally, in its monomial subalgebras). For this we have to generalize the notion of term order. The theory is applied to systems of linear partial difference equations (with constant coefficients) on ℤn. Furthermore, we present a method to compute the intersection of an ideal in the algebra of Laurent polynomials with the subalgebra of all polynomials.
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