Abstract
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 a smooth stratification and a smooth cover of an algebraic variety, which were introduced by the author earlier. Bibliography: 16 titles.
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