Geodesic
On generating points of a lattice in the region
Glasgow mathematical journal, Tome 6 (1964) no. 3, pp. 141-155

Voir la notice de l'article provenant de la source Cambridge University Press

A lattice An in n-dimensional Euclidean space En consists of the aggregate of all points with coordinates (xx,..., xn), wherefor some real ars (r, s = 1,..., n), subject to the condition ∥ αrs ∥nn ╪ 0. The determinant Δn of Λn, is denned by the relation , the sign being chosen to ensure that Δn > 0.If A1..., An are the n points of Λn having coordinates (a11, a21..., anl),..., (a1n, a2n,..., ann), respectively, then every point of Λn may be expressed in the formand Ai,..., An, together with the origin O, are said to generate Λn. This particular set of generating points is not unique; it may be proved that a necessary and sufficient condition that n points of Λn should generate the lattice is that the n × n determinant formed by their x coordinates should be ±Δn, or, equivalently, that the n×n determinant formed by their corresponding u-coordinates should be ±1. 
Foster, D. M. E. On generating points of a lattice in the region. Glasgow mathematical journal, Tome 6 (1964) no. 3, pp. 141-155. doi: 10.1017/S2040618500034912
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