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In mathematics, the Hermite constant, named after Charles Hermite, determines how short an element of a lattice in Euclidean space can be.
The constant γn for integers n > 0 is defined as follows. For a lattice L in Euclidean space R with unit covolume, i.e. vol = 1, let λ1 denote the least length of a nonzero element of L. Then √γn is the maximum of λ1 over all such lattices L.
The square root in the definition of the Hermite constant is a matter of historical convention.
Alternatively, the Hermite constant γn can be defined as the square of the maximal systole of a flat n-dimensional torus of unit volume.
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