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Reports (Research Report) Year : 2006

Elimination theory in codimension one and applications

Laurent Busé


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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Dates and versions

inria-00077120 , version 1 (29-05-2006)
inria-00077120 , version 2 (02-06-2006)
inria-00077120 , version 3 (04-03-2013)


  • HAL Id : inria-00077120 , version 3


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