Polar Varieties and Efficient Real Equation Solving: The Hypersurface Case

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dc.creatorBank, B.
dc.creatorGiusti, M.
dc.creatorHeintz, J.
dc.creatorMandel, R.
dc.creatorMbakop, G. M.
dc.date1996-09-06
dc.date.accessioned2026-07-07T09:06:57Z
dc.date.available2026-07-07T09:06:57Z
dc.descriptionThe objective of this paper is to show how the recently proposed method by Giusti, Heintz, Morais, Morgenstern, Pardo \cite{gihemorpar} can be applied to a case of real polynomial equation solving. Our main result concerns the problem of finding one representative point for each connected component of a real bounded smooth hypersurface. The algorithm in \cite{gihemorpar} yields a method for symbolically solving a zero-dimensional polynomial equation system in the affine (and toric) case. Its main feature is the use of adapted data structure: Arithmetical networks and straight-line programs. The algorithm solves any affine zero-dimensional equation system in non-uniform sequential time that is polynomial in the length of the input description and an adequately defined {\em affine degree} of the equation system. Replacing the affine degree of the equation system by a suitably defined {\em real degree} of certain polar varieties associated to the input equation, which describes the hypersurface under consideration, and using straight-line program codification of the input and intermediate results, we obtain a method for the problem introduced above that is polynomial in the input length and the real degree.
dc.descriptionLatex
dc.identifierhttps://arxiv.org/abs/alg-geom/9609003
dc.identifierhttp://arxiv.org/abs/alg-geom/9609003
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/150200
dc.subjectAlgebraic Geometry
dc.titlePolar Varieties and Efficient Real Equation Solving: The Hypersurface Case
dc.typetext

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