Moment matrices, border bases and radical computation
Journal of Symbolic Computation , Volume 51 p. 63- 85
In this paper, we describe new methods to compute the radical (resp. real radical) of an ideal, assuming it complex (resp. real) variety is nte. The aim is to combine approaches for solving a system of polynomial equations with dual methods which involve moment matrices and semi-denite programming. While the border basis algorithms of  are ecient and numerically stable for computing complex roots, algorithms based on moment matrices  allow the incorporation of additional polynomials, e.g., to restrict the computation to real roots or to eliminate multiple solutions. The proposed algorithm can be used to compute a border basis of the input ideal and, as opposed to other approaches, it can also compute the quotient structure of the (real) radical ideal directly, i.e., without prior algebraic techniques such as Grobner bases. It thus combines the strength of existing algorithms and provides a unied treatment for the computation of border bases for the ideal, the radical ideal and the real radical ideal.
|Keywords||polynomial equation, real root, border base, semidefinite programming|
|THEME||Other (theme 6)|
|Journal||Journal of Symbolic Computation|
|Project||Semidefinite programming and combinatorial optimization|
Mourrain, B, Lasserre, J.B, Laurent, M, Rostalski, P, & Trebuchet, P. (2013). Moment matrices, border bases and radical computation. Journal of Symbolic Computation, 51, 63–85.