Implicitization of rational hypersurfaces via linear syzygies: a practical overview

N. BOTBOL, A. DICKENSTEIN

JOURNAL OF SYMBOLIC COMPUTATION

ACADEMIC PRESS LTD-ELSEVIER SCIENCE LTD

Lugar: Amsterdam; Año: 2016 vol. 74 p. 493 - 512

0747-7171

We unveil in concrete terms the general machinery of the syzygy-based algorithms for the implicitization of rational surfaces in terms of the monomials in the polynomials defining the parametrization, following and expanding our joint article with M. Dohm. These algebraic techniques, based on the theory of approximation complexes due to J. Herzog, A. Simis and W. Vasconcelos, were introduced for the implicitization problem by J.-P. Jouanolou, L.Busé, and M. Chardin. Their work was inspired by the practical method of moving curves, proposed by T. Sederberg and F. Chen, translated into the language of syzygies by D. Cox. Our aim is to express the theoretical results and resulting algorithms into very concrete terms, avoiding the use of the advanced homological commutative algebraic tools which are needed for their proofs.