Classes of unimodular integral symmetric positive definite matrices

It is shown that the number of classes of nonisometric lattices on the space of rational n-tuples is the same as the number of classes of n x n integral, symmetric, positive definite, unimodular matrices under integral congruence. A method is given to determine the number of classes of nonisometric lattices; this method is used to determine the number of classes for n↖ 16. A representative of each class of symmetric, integral, positive definite, unimodular 16x16 matrices is given.Science, Faculty ofMathematics, Department ofGraduat