Polynomial-time algorithms for a new model of representation of algebraic varieties (in characteristic zero)

We suggest a model of representation of algebraic varieties based on representative systems of points of their irreducible components. Deterministic polynomial-time algorithms that substantiate this model are described in characteristic zero. The main result here is a construction of the intersection of algebraic varieties. As applications, we obtain efficient algorithms for constructing the smooth stratification and smooth cover of an algebraic variety suggested by the author earlier. Bibl. 16 titles.