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Effective equidimensional decomposition of affine varieties

✍ Scribed by Gabriela Jeronimo; Juan Sabia

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
169 KB
Volume
169
Category
Article
ISSN
0022-4049

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✦ Synopsis

In this paper we present a probabilistic algorithm which computes, from a ΓΏnite set of polynomials deΓΏning an algebraic variety V , the decomposition of V into equidimensional components. If V is deΓΏned by s polynomials in n variables of degrees bounded by an integer d ΒΏ n and V = r '=0 V ' is the equidimensional decomposition of V , the algorithm obtains in sequential time bounded by s O(1) d O(n) , for each 0 6 ' 6 r, a set of n + 1 polynomials of degrees bounded by deg (V ' ) which deΓΏne V ' .

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