Lattice Isometries and Short Vector Enumeration
| atmire.migration.oldid | 2678 | |
| dc.contributor.advisor | Bauer, Mark | |
| dc.contributor.author | Meissen, Rebecca | |
| dc.date.accessioned | 2014-10-08T21:44:11Z | |
| dc.date.available | 2014-11-17T08:00:53Z | |
| dc.date.issued | 2014-10-08 | |
| dc.date.submitted | 2014 | en |
| dc.description.abstract | We present an implementation in Sage and overview of several algorithms for integer lattices. The first builds an isometry between lattices by considering partial maps. It also determines whether two lattices are nonisometric by exhaustively searching all possible maps. Using this algorithm, we give a method for computing the automorphism group of a lattice using strong generating sets. These both make use of the set of small vectors of a lattice, which can be enumerated using the last algorithm we present. We discuss the use of determining isometry classes as part of computing the Smith-Minkowski-Siegel mass formula. | en_US |
| dc.identifier.citation | Meissen, R. (2014). Lattice Isometries and Short Vector Enumeration (Master's thesis, University of Calgary, Calgary, Canada). Retrieved from https://prism.ucalgary.ca. doi:10.11575/PRISM/26732 | en_US |
| dc.identifier.doi | http://dx.doi.org/10.11575/PRISM/26732 | |
| dc.identifier.uri | http://hdl.handle.net/11023/1924 | |
| dc.language.iso | eng | |
| dc.publisher.faculty | Graduate Studies | |
| dc.publisher.institution | University of Calgary | en |
| dc.publisher.place | Calgary | en |
| dc.rights | University of Calgary graduate students retain copyright ownership and moral rights for their thesis. 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. | |
| dc.subject | Mathematics | |
| dc.subject.classification | Lattice | en_US |
| dc.subject.classification | isometry | en_US |
| dc.subject.classification | enumeration | en_US |
| dc.title | Lattice Isometries and Short Vector Enumeration | |
| dc.type | master thesis | |
| thesis.degree.discipline | Mathematics and Statistics | |
| thesis.degree.grantor | University of Calgary | |
| thesis.degree.name | Master of Science (MSc) | |
| ucalgary.item.requestcopy | true |