A polynomial-time algorithm for the topological type of a real algebraic curve
نویسندگان
چکیده
منابع مشابه
A Polynominal Time Algorithm for the Topological Type of a Real Algebraic Curve
Let I (:z: ,y ,z) be a homogeneous polynomial With. rational coefficients. Let C, be the real projective curve defined by ! = 0" and suppos~ that C/ is nonsingular. It is well known that C/ is essentially a finite collection of disjoint circles, all except possibly one of which lie in th~ projective plane Rp2 in such a way as to have both an interior (homeomorphic to a disk), and an exterior (h...
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Probabilistic Algorithm for Polynomial Optimization over a Real Algebraic Set
Let f, f1, . . . , fs be n-variate polynomials with rational coefficients of maximum degree D and let V be the set of common complex solutions of F = (f1, . . . , fs). We give an algorithm which, up to some regularity assumptions on F, computes an exact representation of the global infimum f? of the restriction of the map x → f (x) to V ∩ Rn, i.e. a univariate polynomial vanishing at f? and an ...
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ژورنال
عنوان ژورنال: Rocky Mountain Journal of Mathematics
سال: 1984
ISSN: 0035-7596
DOI: 10.1216/rmj-1984-14-4-847