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In this paper we describe an algorithm for classifying orbits of vectors inLorentzian lattices. The main point of this is that isomorphism classes ofpositive definite lattices in some genus often correspond to orbits of vectorsin some Lorentzian lattice, so we can classify some positive definite lattices.As an application we give the classification of the 665 25-dimensionalunimodular positive definite lattices and the 121 even 25 dimensional positivedefinite lattices of determinant 2. We also use this algorithm to show thatthere is a unique 26 dimensional unimodular positive definite lattice with noroots.

Classification of positive definite lattices