inria-00077120, version 2
Elimination theory in codimension one and applications
N° RR-5918 (2006)
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.
- a – INRIA
- 1: GALAAD (INRIA Sophia Antipolis)
- INRIA – CNRS : UMR6621 – Université de Nice Sophia Antipolis (UNS)
- Domain : Mathematics/Commutative Algebra
Computer Science/Symbolic Computation - Keywords : Elimination theory – homogeneous polynomial systems – resultants – determinants of complexes – computational algebra – implicitization of rational hypersurfaces
- Internal note : RR-5918
- Comment : Notes of lectures given at the CIMPA-UNESCO-IRAN school in Zanjan – Iran – July 9-22 2005
- Available versions : v1 (2006-05-30) v2 (2006-06-02)
- inria-00077120, version 2
- http://hal.inria.fr/inria-00077120
- oai:hal.inria.fr:inria-00077120
- From: Rapport De Recherche Inria
- Submitted on: Friday, 2 June 2006 17:05:49
- Updated on: Tuesday, 30 September 2008 13:36:05
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