Elimination theory in codimension one and applications

1 GALAAD - Geometry, algebra, algorithms
CRISAM - Inria Sophia Antipolis - Méditerranée , UNS - Université Nice Sophia Antipolis, CNRS - Centre National de la Recherche Scientifique : UMR6621
Abstract : In these notes, we present a general framework to compute the codimension one part of the elimination ideal of a system of homogeneous polynomials. It is based on the computation of the so-called MacRae's invariants that we will obtain by means of determinants of complexes. Our approach mostly uses tools from commutative algebra. We begin with some basics on elimination theory and then introduce the MacRae's invariant and the so-called determinants of complexes. The rest of these notes illustrates our approach through two important examples: the Macaulay's resultant of $n$ homogeneous polynomials in $n$ variables and the computation of an implicit equation of a parameterized hypersurface using syzygies.
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Rapport
[Research Report] RR-5918, INRIA. 2006, pp.47
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https://hal.inria.fr/inria-00077120
Contributeur : Laurent Busé <>
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Dernière modification le : jeudi 11 janvier 2018 - 16:00:57
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• HAL Id : inria-00077120, version 3

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Laurent Busé. Elimination theory in codimension one and applications. [Research Report] RR-5918, INRIA. 2006, pp.47. 〈inria-00077120v3〉

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