Details:
Title  On the computation of matrices of traces and radicals of ideals  Author(s)  Itnuit JanovitzFreireich, Bernard Mourrain, Lajos Rónyai, Ágnes Szántó  Type  Article in Journal  Abstract  Let f 1 , … , f s ∈ K [ x_1 , … , x_m ] be a system of polynomials generating a zerodimensional ideal I , where K is an arbitrary algebraically closed field. We study the computation of “matrices of traces” for the factor algebra A ≔ K [ x_1 , … , x_m ] / I , i.e. matrices with entries which are trace functions of the roots of I . Such matrices of traces in turn allow us to compute a system of multiplication matrices M x i ∣ i = 1 , … , m of the radical I . We first propose a method using Macaulay type resultant matrices of f 1 , … , f s and a polynomial J to compute moment matrices, and in particular matrices of traces for A . Here J is a polynomial generalizing the Jacobian. We prove bounds on the degrees needed for the Macaulay matrix in the case when I has finitely many projective roots in P K m . We also extend previous results which work only for the case where A is Gorenstein to the nonGorenstein case. The second proposed method uses Bezoutian matrices to compute matrices of traces of A . Here we need the assumption that s = m and f 1 , … , f m define an affine complete intersection. This second method also works if we have higherdimensional components at infinity. A new explicit description of the generators of I are given in terms of Bezoutians.  Keywords  Matrix of traces, Radical of an ideal  ISSN  07477171 
URL 
http://www.sciencedirect.com/science/article/pii/S0747717111001325 
Language  English  Journal  Journal of Symbolic Computation  Volume  47  Number  1  Pages  102  122  Year  2012  Edition  0  Translation 
No  Refereed 
No 
