Effective equidimensional decomposition of affine varieties

GABRIELA JERONIMO; JUAN SABIA

JOURNAL OF PURE AND APPLIED ALGEBRA

Elsevier

Lugar: Amsterdam; Año: 2002 vol. 169 p. 229 - 248

0022-4049

In this paper we present a probabilistic algorithm which computes, from a finite set of polynomials defining an algebraic variety V, the decomposition of V into equidimensional components. If V is defined by s polynomials in n variables of degrees bounded by an integer d>=n and V=⋃ℓ=0rVℓ is the equidimensional decomposition of V, the algorithm obtains in sequential time bounded by sO(1)dO(n), for each ℓ=0,...,r, a set of n+1 polynomials of degrees bounded by which define Vℓ.