Moment matrices, trace matrices and the radical of ideals - Archive ouverte HAL Access content directly
Conference Papers Year : 2008

## Moment matrices, trace matrices and the radical of ideals

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Inuit Janovitz-Freireich
• Function : Author
• PersonId : 856221
Agnes Szanto
• Function : Author
• PersonId : 856222
Bernard Mourrain
Lajos Ronyai
• Function : Author
• PersonId : 856223

#### Abstract

Let $f_1,\ldots,f_s \in \mathbb{K}[x_1,\ldots,x_m]$ 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 $\A=\mathbb{K}[x_1,\ldots,x_m]/\I$ is Gorenstein and that we have a bound $\delta>0$ such that a basis for $\A$ can be computed from multiples of $f_1,\ldots,f_s$ of degrees at most $\delta$. We propose a method using Sylvester or Macaulay type resultant matrices of $f_1,\ldots,f_s$ and $J$, where $J$ is a polynomial of degree $\delta$ 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 $\{M_{x_i}|i=1,\ldots,m\}$ of the radical $\sqrt{\I}$, following the approach in the previous work by Janovitz-Freireich, R\'{o}nyai and Szántó. Additionally, we give bounds for $\delta$ for the case when $\I$ has finitely many projective roots in $\mathbb{P}^m_\CC$. \end{abstract}

#### Domains

Computer Science [cs] Symbolic Computation [cs.SC]

### Dates and versions

inria-00343126 , version 1 (29-11-2008)

### Identifiers

• HAL Id : inria-00343126 , version 1
• ARXIV :

### Cite

Inuit Janovitz-Freireich, Agnes Szanto, Bernard Mourrain, Lajos Ronyai. Moment matrices, trace matrices and the radical of ideals. ISSAC, Jul 2008, Linz, Austria. pp.125-132. ⟨inria-00343126⟩

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