Effective equidimensional decomposition of affine varieties

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 dgreater-or-equal, slantedn and V=union operatorℓ=0rVℓ is the equidimensional decomposition of V, the algorithm obtains in sequential time bounded by sO(1)dO(n), for each 0less-than-or-equals, slantℓless-than-or-equals, slantr, a set of n+1 polynomials of degrees bounded by deg (Vℓ) which define Vℓ.