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Peer-reviewedCC BY-NCJournal of Computational Algebra

Improved computation of polynomial roots over number fields when using complex embeddings

  • Andrea Lesavourey
  • Thomas Plantard
  • Willy Susilo
Open at sourceDOICite

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 .

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Cite

BibTeXRIS
BibTeX
@article{lesavourey2026improved,
  title = {{Improved computation of polynomial roots over number fields when using complex embeddings}},
  author = {Andrea Lesavourey and Thomas Plantard and Willy Susilo},
  journal = {Journal of Computational Algebra},
  year = {2026},
  month = oct,
  doi = {10.1016/j.jaca.2024.100026},
  url = {https://hal.science/hal-05779143v1},
  note = {CC BY-NC},
}
RIS
TY  - JOUR
TI  - Improved computation of polynomial roots over number fields when using complex embeddings
AU  - Andrea Lesavourey
AU  - Thomas Plantard
AU  - Willy Susilo
PY  - 2026
DA  - 2026/10/05
JO  - Journal of Computational Algebra
DO  - 10.1016/j.jaca.2024.100026
UR  - https://hal.science/hal-05779143v1
AB  - 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 .
SN  - 2772-8277
SN  - 2772-8277
ER  -