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Title: Lattice Isometries and Short Vector Enumeration
Author: Meissen, Rebecca
Advisor: Bauer, Mark
Keywords: Mathematics
Issue Date: 8-Oct-2014
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.
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