{"paper":{"title":"On the Computation of Matrices of Traces and Radicals of Ideals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"cs.SC","authors_text":"Agnes Szanto, Bernard Mourrain (INRIA Sophia Antipolis), Itnuit Janovitz-Freireich, Lajos Ronayi","submitted_at":"2009-01-19T07:57:18Z","abstract_excerpt":"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. We study the computation of \"matrices of traces\" for the factor algebra $\\A := \\CC[x_1, ..., x_m]/ \\I$, 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 $\\sqrt{\\I}$. We first propose a method using Macaulay type resultant matrices of $f_1,...,f_s$ and a polynomial $J$ "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0901.2778","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}