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 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 کاملPlane Algebraic Curves
We go over some of the basics of plane algebraic curves, which are planar curves described as the set of solutions of a polynomial in two variables. We study many basic notions, such as projective space, parametrization, and the intersection of two curves. We end with the group law on the cubic and search for torsion points.
متن کاملOn the Topology of Real Algebraic Plane Curves
We revisit the problem of computing the topology and geometry of a real algebraic plane curve. The topology is of prime interest but geometric information, such as the position of singular and critical points, is also relevant. A challenge is to compute efficiently this information for the given coordinate system even if the curve is not in generic position. Previous methods based on the cylind...
متن کاملA Compactness Criterion for Real Plane Algebraic Curves
Two sets of conditions are presented for the compactness of a real plane algebraic curve, one sufficient and one necessary, in terms of the Newton polygon of the defining polynomial.
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ژورنال
عنوان ژورنال: Expositiones Mathematicae
سال: 2002
ISSN: 0723-0869
DOI: 10.1016/s0723-0869(02)80009-3