
Universität Bonn > Institut für Informatik > Abteilung V  
CSReports 1995  Copyright 1995 Universität Bonn, Institut für Informatik, Abt. V  
85141

PolynomialTime Computation of the Degree of Algebraic Varieties in ZeroCharacteristic and its Applications
Alexander L. Chistov [Download PostScript] [Download PDF] Let an algebraic variety over a zerocharacteristic 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 