Algebraic decomposition of regular curves
type: Item
instance of: scholarly article
title: Algebraic decomposition of regular curves
zbMATH Open document ID: 0666.14012
DOI: 10.1016/S0747-7171(88)80009-9
author: Stefan Arnborg
author: Huichun Feng
published in: Journal of Symbolic Computation
publication date: 1988-01-01T00:00:00Z
review text: An algorithm is presented in the paper for computing the topological type of a nonsingular real-algebraic curve on a projective plane. The topological type is a structure including \((1)\quad the\) parity of the degree of the curve; \((2)\quad the\) number of ovals to which the curve splits; \((3)\quad partial\) ordering of ovals by inclusion. The algorithm works for curves defined by integral homogeneous polynomials. It is based on cylindrical algebraic decomposition and has polynomial complexity assessed as a nice \(O(n^{27}L(d)^ 3)\) where n is the degree of the defining polynomial and L(d) is the total coefficients length.
Mathematics Subject Classification ID: 14H10
Mathematics Subject Classification ID: 68W30
zbMATH DE Number: 4089706
zbMATH Keywords: cylindrical decomposition
zbMATH Keywords: CAD
zbMATH Keywords: computing the topological type of a nonsingular real-algebraic curve
zbMATH Keywords: ovals
MaRDI profile type: Publication
cites work: Q3716289
cites work: Cylindrical Algebraic Decomposition I: The Basic Algorithm
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description: scientific article; zbMATH DE number 4089706