Abstract
Using work of Colmez, we give a quick algorithm for obtaining a clean fundamental domain for the action on R + 3 of the totally positive units of a totally real cubic field. The fundamental domain consists of two infinite solid cones in R 3 , one generated by 1 , ε 1 and ε 1 ε 2 , the other by 1 , ε 2 and ε 1 ε 2 . Here ε 1 , ε 2 are certain fundamental totally positive units, included in R + 3 by the usual geometric embedding, which we show to be easily computable from any set of fundamental units of k . Similar cones were found by Thomas and Vasquez in 1980, and by Halbritter and Pohst in 2000, but their methods did not result in practical algorithms.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
