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Lattices in the sense of discrete subgroups of Euclidean spaces, as used in number theory, discrete geometry, Lie groups, etc. (Not to be confused with lattice theory or lattices as used in physics! For lattices (ordered sets), use the tag: [lattice-theory])

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Lattice reduction on an orthonormal lattice?

The only known algorithms are unfortunately those for general lattices, mainly LLL and its extension BKZ. … A similar situation occurs with other families of lattices, especially so-called ideal lattices, which are lattices obtained through the canonical embedding of ideals in number fields (see, e.g., "Lattices
Oded Regev's user avatar