 Parametrization of semialgebraic setsM.J. González-López, T. Recio and F. Santos Mathematics and Computers in Simulation (MATCOM), 1996, vol. 42, issue 4, 353-362 Abstract: In this paper we consider the problem of the algorithmic parametrization of a d-dimensional semialgebraic subset S of Rn (n > d) by a semialgebraic and continuous mapping from a subset of Rd. Using the Cylindrical Algebraic Decomposition algorithm we easily obtain semialgebraic, bijective parametrizations of any given semialgebraic set; but in this way some topological properties of S (such as being connected) do not necessarily hold on the domain of the so-constructed parametrization. If the set S is connected and of dimension one, then the Euler condition on the associated graph characterizes the existence of an almost everywhere injective, finite-to-one parametrization of S with connected domain. On the other hand, for any locally closed semialgebraic set S of dimension d > 1 and connected in dimension l (i.e. such that there exists an l-dimensional path among any two points in S) we can always algorithmically obtain a bijective parametrization of S with connected in dimension l domain. Our techniques are mainly combinatorial, relying on the algorithmic triangulation of semialgebraic sets. Keywords: Algorithmic real algebraic geometry; Semialgebraic sets; Triangulation (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:42:y:1996:i:4:p:353-362 DOI: 10.1016/S0378-4754(96)00009-2 Access Statistics for this article Mathematics and Computers in Simulation (MATCOM) is currently edited by Robert Beauwens More articles in Mathematics and Computers in Simulation (MATCOM) from Elsevier |
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