Computing the Dimension of a Projective Variety: the Projective Noether Maple Package

Abstract : Recent theoretical advances in elimination theory use non-classical data structures to represent multivariate polynomials. We present the {\em Projective Noether Package\/} which is a Maple implementation of a series of these new algorithms for the computation of the dimension of a projective variety. The package contains hybrid code mixing the old and new approaches, thus allowing to investigate the potential of the new techniques. We present a comparison of the more traditional algorithms already available within Maple with the new ones, trying several possible strategies. Comparative results on benchmarks for time and space of three different families of multivariate polynomial equation systems are given and we point out both weaknesses and advantages of the different approaches.
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Submitted on : Wednesday, May 24, 2006 - 12:55:47 PM
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Marc Giusti, Klemens Hägele, Grégoire Lecerf, Joël Marchand, Bruno Salvy. Computing the Dimension of a Projective Variety: the Projective Noether Maple Package. [Research Report] RR-3224, INRIA. 1997. ⟨inria-00073465⟩

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