Bauer, MarkGreenberg, MatthewChisholm, Sarah2014-10-082014-11-172014-10-082014Chisholm, S. (2014). Algorithmic enumeration of quaternionic lattices (Doctoral thesis, University of Calgary, Calgary, Canada). Retrieved from https://prism.ucalgary.ca. doi:10.11575/PRISM/24766http://hdl.handle.net/11023/1920In this thesis, we develop and implement an algorithm in Magma for enumerating isometry classes of quaternionic lattices. This algorithm can be viewed as a higher rank generalization of that used for enumerating equivalence classes of left-ideals of quaternionic orders. Our key technical innovation is an adaptation of Kneser’s method of neighbours to the setting of quaternionic lattices. Central to this adaptation is the Morita equivalence between Hermitian spaces over the split quaternion algebra M2(F) and symplectic spaces over F.engUniversity 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.Education--MathematicsNumber Thoerydoctoral thesis10.11575/PRISM/24766