{"id":{"repo_id":"calgary","oai_identifier":"oai:ucalgary.scholaris.ca:1880/122828"},"canonical_url":"https://search.dev.ndltd.org/etd/calgary/oai:ucalgary.scholaris.ca:1880/122828","repository":{"repo_id":"calgary","name":"University of Calgary","base_url":"https://ucalgary.scholaris.ca/server/oai/request"},"display":{"title":"Comparison of and Improvements to Degree Zero Divisor Class Group Arithmetic in Algebraic Function Fields","abstract":"This 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.","abstract_html":"This 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. 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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. 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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. 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For uses that are not allowable under copyright legislation or licensing, you are required to seek permission."],"dc:subject":["global function fields","divisor class group","Jacobian"],"dc:title":["Comparison of and Improvements to Degree Zero Divisor Class Group Arithmetic in Algebraic Function Fields"],"dc:type":["master thesis"],"thesis:degree_discipline":["Mathematics & Statistics"],"thesis:degree_name":["Master of Science (MSc)"],"thesis:institution_name":["University of Calgary"]},"updated_at":"2026-07-24T01:30:13Z"}