Rheinische Friedrich-Wilhelms-Universität Bonn Institut für Informatik
 
Abteilung V

 
Universität Bonn -> Institut für Informatik -> Abteilung V
CS-Reports 1995 Copyright 1995 Universität Bonn, Institut für Informatik, Abt. V
85141

Polynomial--Time Computation of the Degree of Algebraic Varieties in Zero--Characteristic and its Applications
Alexander L. Chistov
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Let an algebraic variety over a zero--characteristic ground field be given as a set of common zeros of a family of polynomials of the degree less than $d$ in $n$ variables. In this paper the following algorithms with the working time polynomial in the size of input and $d^n$ are constructed: an algorithm for the computation of the degrees of algebraic varieties, an algorithm for the computation of the dimension of the given algebraic variety in the neighborhood of a given point, an algorithm for the computation of the multiplicity of a given point of the algebraic variety, an algorithm for the computation smooth points with their tangent spaces on each component of a given algebraic variety.

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Universität Bonn -> Institut für Informatik -> Abteilung V

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