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The Lenstra–Lenstra–Lovász (LLL) lattice basis reduction algorithm efficiently finds a short, nearly orthogonal lattice basis form an arbitrary one

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Gram-Schmidt coefficients in LLL algorithm

To my understanding the LLL lattice reduction algorithm starts with a set of integer vectors $\{b_1, \dots, b_2\}$, which span a lattice, and tries to generate a new basis of shorter vectors of the sa …
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