{
  "abstract": "We explore a fairly generic method to compute roots of polynomials over number fields through complex embeddings. Our main contribution is to show how to use a structure of a relative extension to decode in a subfield. Additionally we describe several heuristic options to improve practical efficiency. We provide experimental data from our implementation and compare our methods to the state of the art algorithm implemented in Pari/Gp .",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 3,
  "authors": [
    {
      "name": "Andrea Lesavourey"
    },
    {
      "name": "Thomas Plantard"
    },
    {
      "name": "Willy Susilo"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1xwyt4mnrw1fs.bib",
  "cited_by": 1,
  "doi": "10.1016/j.jaca.2024.100026",
  "fulltext_url": null,
  "id": "1xwyt4mnrw1fs",
  "issns": [
    "2772-8277",
    "2772-8277"
  ],
  "landing_url": "https://hal.science/hal-05779143v1",
  "language": "en",
  "licence": "CC-BY-NC",
  "licence_label": "CC BY-NC",
  "licence_source": "journal",
  "licence_url": "https://creativecommons.org/licenses/by-nc/4.0/",
  "metadata_licence": null,
  "native_subjects": [
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    [
      "openalex",
      "1703|Polynomial and algebraic computation"
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  "openalex": "W4403600214",
  "pdf_url": null,
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1xwyt4mnrw1fs.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:48Z",
      "native_id": "hal-05779143",
      "source": "hal",
      "url": "https://hal.science/hal-05779143v1"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "hal:1.math.math-nt",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Improved computation of polynomial roots over number fields when using complex embeddings",
  "title_text": "Improved computation of polynomial roots over number fields when using complex embeddings",
  "type": "peer-reviewed",
  "updated_at": "2026-10-30T12:17:48Z",
  "url": "https://research.draconitic.com/paper/1xwyt4mnrw1fs",
  "venue": "Journal of Computational Algebra",
  "versions": []
}