Moment matrices, trace matrices and the radical of ideals
| dc.creator | Janovitz-Freireich, Itnuit | |
| dc.creator | Szanto, Agnes | |
| dc.creator | Mourrain, Bernard | |
| dc.creator | Ronyai, Lajos | |
| dc.date | 2008-11-29 | |
| dc.date.accessioned | 2026-07-07T12:32:46Z | |
| dc.date.available | 2026-07-07T12:32:46Z | |
| dc.description | Let $f_1,...,f_s \in \mathbb{K}[x_1,...,x_m]$ be a system of polynomials generating a zero-dimensional ideal $\I$, where $\mathbb{K}$ is an arbitrary algebraically closed field. Assume that the factor algebra $\A=\mathbb{K}[x_1,...,x_m]/\I$ is Gorenstein and that we have a bound $δ>0$ such that a basis for $\A$ can be computed from multiples of $f_1,...,f_s$ of degrees at most $δ$. We propose a method using Sylvester or Macaulay type resultant matrices of $f_1,...,f_s$ and $J$, where $J$ is a polynomial of degree $δ$ generalizing the Jacobian, to compute moment matrices, and in particular matrices of traces for $\A$. These matrices of traces in turn allow us to compute a system of multiplication matrices $\{M_{x_i}|i=1,...,m\}$ of the radical $\sqrt{\I}$, following the approach in the previous work by Janovitz-Freireich, Rónyai and Szántó. Additionally, we give bounds for $δ$ for the case when $\I$ has finitely many projective roots in $\mathbb{P}^m_\CC$. | |
| dc.identifier | https://arxiv.org/abs/0812.0088 | |
| dc.identifier | http://arxiv.org/abs/0812.0088 | |
| dc.identifier | nternational Conference on Symbolic and Algebraic Computation (2008) 125-132 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/216897 | |
| dc.subject | Symbolic Computation | |
| dc.title | Moment matrices, trace matrices and the radical of ideals | |
| dc.type | text |