Polynomial-Time Computation of the Dimension of Algebraic Varieties in Zero-Characteristic

Abstract In this paper an algorithm is described for the computation of the dimension of a projective algebraic variety over a zero characteristic ground field. The variety is given as a set of zeros of a family of homogeneous polynomials of the degree less than d in n +1 variables. The working time of the algorithm is polynomial in the size of input and d n .