In this paper we present an algorithm for computing a matrix representationfor a surface in P^3 parametrized over a 2-dimensional toric variety T. Thisalgorithm follows the ideas of [Botbol-Dickenstein-Dohm-09] and it wasimplemented in Macaulay2. We showed in [BDD09] that such a surface can berepresented by a matrix of linear syzygies if the base points are finite innumber and form locally a complete intersection, and in [Botbol-09] wegeneralized this to the case where the base locus is not necessarily a localcomplete intersection. The key point consists in exploiting the sparsestructure of the parametrization, which allows us to obtain significantlysmaller matrices than in the homogeneous case.
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