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Figure 1
Example of the LLL algorithm with a 20×20 matrix representing a list of 20 vectors whose coordinates are written in rows. (a) Input list. (b) Output list determined with the function LatticeReduce of Mathe­matica. (a) Basis before reduction; the values of the rhombicity [R=\sum_N\|{\bf b}_i\|^2 +2\sum_{i\lt j\le N}\|{\bf b}_i^{\rm t}{\bf b}_j\|] and of the sum of the squares of the norms [S = \sum _{N}\| {\bf b}_{i}\|^{2}] are R = 453988268, S = 61580172. (b) Basis after reduction; the parameters decreased to R = 531, S = 99.

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ISSN: 2053-2733
Volume 78| Part 1| January 2022| Pages 1-9
https://doi.org/10.1107/S2053273321011037
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