Topology of real algebraic curves and integrability of geodesic flows on algebraic surfaces
نویسندگان
چکیده
منابع مشابه
Topology of real algebraic space curves
In this paper we give a new projection-based algorithm for computing the topology of a real algebraic space curve given implicitly by a set of equations. Under some genericity conditions, which may be reached through a linear change of coordinates, we show that a plane projection of the given curve, together with a special polynomial in the ideal of the curve contains all the information needed...
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In this talk, an algorithm is proposed to determine the topology of an implicit real algebraic surface in R. The algorithm consists of four steps: surface projection, projection curve topology determination, surface patch composition, and combination of surface patches. The algorithm gives an intrinsic representation for the topology of the surface. Some examples are used to show that the algor...
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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...
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In this paper, we consider the problem of analysing the shape of an object defined by polynomial equations in a domain. We describe regularity criteria which allow us to determine the topology of the implicit object in a box from information on the boundary of this box. Such criteria are given for planar and space algebraic curves and for algebraic surfaces. These tests are used in subdivision ...
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ژورنال
عنوان ژورنال: Functional Analysis and Its Applications
سال: 2008
ISSN: 0016-2663,1573-8485
DOI: 10.1007/s10688-008-0038-y