An Algorithm for Computing Set-Theoretic Generators of an Algebraic Variety

摘要

Based on Eisenbud's idea (see [Eisenbud, D., Evans, G., 1973. Every algebraic set in n-space is the intersection of n hypersurfaces. Invent. Math. 19, 107-112]), we present an algorithm for computing set-theoretic generators for any algebraic variety in the affine n-space, which consists of at most n polynomials. With minor modifications, this algorithm is also valid for projective algebraic variety in projec-tive n-space.