lattice basis reduction | recognize

The process of finding a reduced set of basis vectors for a given lattice having certain special properties. Lattice reduction algorithms are used in a number of modern number theoretical applications, including in the discovery of a spigot algorithm for pi. Although determining the shortest basis is possibly an NP-complete problem, algorithms such as the LLL algorithm can find a short basis in polynomial time with guaranteed worst-case performance. The LLL algorithm of lattice reduction is implemented in the Wolfram Language using the function LatticeReduce. RootApproximant[x, n] also calls this routine in order to find a algebraic number of degree at most n such that x is an approximate zero of the number.

Gram-Schmidt orthonormalization | integer relation | LLL algorithm | PSLQ algorithm