Sparse Resultant Perturbations

Carlos D’ Andrea () and Ioannis Z. Emiris ()
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Carlos D’ Andrea: Univ. of California at Berkeley, Dept. of Mathematics
Ioannis Z. Emiris: Univ. of Athens, Dept. of Informatics & Telecommunications

A chapter in Algebra, Geometry and Software Systems, 2003, pp 93-107 from Springer

Abstract: Abstract We consider linear infinitesimal perturbations on sparse resultants. This yields a family of projection operators, hence a general method for handling algebraic systems in the presence of “excess” components or other degenerate inputs. The complexity is simply exponential in the dimension and polynomial in the sparse resultant degree. Our perturbation generalizes Canny’s Generalized Characteristic Polynomial (GCP) for the homogeneous case, while it provides a new and faster algorithm for computing Rojas’ toric perturbation. We illustrate our approach through its Maple implementation applied to specific examples. This work generalizes the linear perturbation schemes proposed in computational geometry and is also applied to the problem of rational implicitization with hase points.

Keywords: Base Point; Projection Operator; Toric Variety; Computational Geometry; Linear Perturbation (search for similar items in EconPapers)
Date: 2003
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-662-05148-1_5

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DOI: 10.1007/978-3-662-05148-1_5

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