English

Factoring polynomials over function fields

Number Theory 2024-09-16 v4

Abstract

If K/k is a function field in one variable of positive characteristic, we describe a general algorithm to factor one-variable polynomials with coefficients in K. The algorithm is flexible enough to find factors subject to additional restrictions, e.g., to find all roots that belong to a given finite dimensional k-subspace of K more efficiently. It also provides a deterministic polynomial time irreducibility test in small characteristic. We also discuss some applications.

Keywords

Cite

@article{arxiv.2107.09865,
  title  = {Factoring polynomials over function fields},
  author = {Jose Felipe Voloch},
  journal= {arXiv preprint arXiv:2107.09865},
  year   = {2024}
}

Comments

Revised version. Accepted to ANTS XVI