Name
Abstract | ||
|---|---|---|
In this paper, we describe new methods to compute the radical (resp. real radical) of an ideal, assuming its complex (resp. real) variety is finite. The aim is to combine approaches for solving a system of polynomial equations with dual methods which involve moment matrices and semi-definite programming. While the border basis algorithms of Mourrain and Trebuchet (2005) are efficient and numerically stable for computing complex roots, algorithms based on moment matrices (Lasserre et al., 2008) 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 unified treatment for the computation of border bases for the ideal, the radical ideal and the real radical ideal. |
Year | DOI | Venue |
|---|---|---|
2013 | 10.1016/j.jsc.2012.03.007 | J. Symb. Comput. |
Keywords | DocType | Volume |
real radical ideal,radical ideal,input ideal,border basis algorithm,border base,border basis,complex root,Grobner base,real radical computation,real root,moment matrix | Journal | 51, |
ISSN | Citations | PageRank |
0747-7171 | 6 | 0.45 |
References | Authors | |
7 | 5 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| jeanbernard lasserre | 1 | 443 | 34.37 |
| Monique Laurent | 2 | 19 | 2.43 |
| Bernard Mourrain | 3 | 1074 | 113.70 |
| Philipp Rostalski | 4 | 94 | 12.03 |
| Philippe Trébuchet | 5 | 40 | 4.45 |