On the computation of graded components of Laurent polynomial rings
Rueda, Sonia L.
Original · EN
In this paper, we present several algorithms for dealing with graded components of Laurent polynomial rings. To be more precise, let S be the Laurent polynomial ring k[x₁,...,xᵣ,xᵣ₊₁± ¹,..., xₙ± ¹], k algebraicaly closed field of characteristic 0. We define the multigrading of S by an arbitrary finitely generated abelian group A. We construct a set of fans compatible with the multigrading and use this fans to compute the graded components of S using polytopes. We give an algorithm to check whether the graded components of S are finite dimensional. Regardless of the dimension, we determine a finite set of generators of each graded component as a module over the component of homogeneous polynomials of degree 0.
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