Real algebraic curves
نویسندگان
چکیده
منابع مشابه
Real Plane Algebraic Curves
We study real algebraic plane curves, at an elementary level, using as little algebra as possible. Both cases, affine and projective, are addressed. A real curve is infinite, finite or empty according to the fact that a minimal polynomial for the curve is indefinite, semi–definite nondefinite or definite. We present a discussion about isolated points. By means of the operator, these points can ...
متن کاملReal Parametrization of Algebraic Curves
There are various algorithms known for deciding the parametrizability (rationality) of a plane algebraic curve, and if the curve is rational, actually computing a parametrization. Optimality criteria such as low degrees in the parametrization or low degree field extensions are met by some parametrization algorithms. In this paper we investigate real curves. Given a parametrizable plane curve ov...
متن کاملAnalysis of Real Algebraic Plane Curves
This work describes a new method to compute geometric properties of a real algebraic plane curve of arbitrary degree. These properties contain the topology of the curve as well as the location of singular points and vertical asymptotes. The algorithm is based on the Bitstream Descartes method (Eigenwillig et al.: “A Descartes Algorithm for Polynomials with Bit-Stream Coefficients”, LNCS 3718), ...
متن کاملArf Invariants of Real Algebraic Curves
. Let CA be the complex curve in CP(2) given by the same polynomial as RA. Thus RA = CA∩RP(2). RA is a M-curve precisely when CA \ RA consists of two punctured spheres which are interchanged by complex conjugation. Arbitrarily choose one of these components, say CA. The complex structure on CA induces an orientation on CA, and thus on each immersed circle of RA. Of course if we choose the other...
متن کاملSums of Squares on Real Algebraic Curves
Given an affine algebraic variety V over R with compact set V (R) of real points, and a non-negative polynomial function f ∈ R[V ] with finitely many real zeros, we establish a local-global criterion for f to be a sum of squares in R[V ]. We then specialize to the case where V is a curve. The notion of virtual compactness is introduced, and it is shown that in the localglobal principle, compact...
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ژورنال
عنوان ژورنال: Annales scientifiques de l'École normale supérieure
سال: 1981
ISSN: 0012-9593,1873-2151
DOI: 10.24033/asens.1401