Equations for the projective closure and effective Nullstellensatz (Q1180147)

The paper presents two algorithms, which compute equations of a projective closure of an affine algebraic set defined by given polynomials. The problem is that simple homogenization of initial polynomials often gives extra components in the infinitely far hyperplane. The first presented algorithm is a modification of the usual Gröbner basis algorithm. --- The second one is more complicated, it is based on linear algebra subroutines and works in parallel time \(O(n^ 4\ln^ 2(md))\), where \(n\) is the number of variables, \(m\) is the number of initial polynomials, \(d\) is the maximal degree.