Year: 2024
Type: preprint
Abstract: We obtain new complexity bounds for computing a triangular integral basis of a number field or a function field. We reach for function fields a softly linear cost with respect to the size of the output when the residual characteristic is zero or big enough. Analogous results are obtained for integral basis of fractional ideals, key ingredients towards fast computation of Riemann-Roch spaces. The proof is based on the recent fast OM algorithm of the authors and on the MaxMin algorithm of Stainsby, together with optimal truncation bounds and a precise complexity analysis.
Source: arXiv (Cornell University)
Authors: Poteaux, Adrien, Weimann, Martin
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4398795698