Science
Comparison of and Improvements to Degree Zero Divisor Class Group Arithmetic in Algebraic Function Fields
Abstract
dc:description.abstractThis thesis develops improved algorithms for Jacobian arithmetic in global function fields and compares the improvements to previous works. We present two independent improvements to Jacobian arithmetic based on the unique representation described in [13]. The first improvement requires the function field to have a degree one place, and the second improvement requires a degree one infinite place. We performed a theoretical complexity analysis of our algorithms and measured the empirical performance of our implementations. To improve upon [13] we optimized for typical inputs rather than worst case performance, a strategy our empirical analysis demonstrated was worthwhile. To the best of our knowledge our implementations are the first publicly-available software implementations of Jacobian arithmetic with unique representatives. Our empirical testing demonstrates that our algorithmic improvements result in software that is faster in practice than previously published algorithms.
Degree
thesis:*- Name thesis:degree_name
- Master of Science (MSc)
- Discipline thesis:degree_discipline
- Mathematics & Statistics
- Grantor
- Science
- Year dc:date.issued
- 2025
Author and committee
dc:creator, dc:contributor.*- Author dc:creator
-
- Macri, Vincent
- Advisors dc:contributor.advisor
-
- Scheidler, Renate
- Jacobson, Michael
- Committee members dc:contributor.committeemember
-
- Bauer, Mark
- Nguyen, Dang Khoa
Subjects
dc:subject × 3Rights
dc:rights- Statement dc:rights
-
- Unless otherwise indicated, this material is protected by copyright and has been made available with authorization from the copyright owner. You may use this material in any way that is permitted by the Copyright Act or through licensing that has been assigned to the document. For uses that are not allowable under copyright legislation or licensing, you are required to seek permission.
- Language dc:language.iso
- en
Identifiers
dc:identifier.*- OAI identifier oai:identifier
- oai:ucalgary.scholaris.ca:1880/122828