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

摘要

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.