Efficient Algorithms in Zero-Characteristic for a New Model of Representation of Algebraic Varieties

We suggest a model of representation of algebraic varieties based on representative systems of points of its irreducible components. Deterministic polynomial–time algorithms to substantiate this model are described in zero–characteristic. The main result here is a construction of the intersection of algebraic varieties. As applications we get efficient algorithms for constructing the smooth stratification and smooth cover of an algebraic variety introduced by the author earlier.