Description
LLLBases is a package implementing several variants of LLL bases. Some of these are implemented in the Macaulay2 engine, some by Victor Shoup's NTL package, and some are implemented at top level.
A matrix over ZZ determines a lattice: this is the ZZ-module generated by the columns. It also determines a generating set. See the book: [H. Cohen, ...] for the definition and the basic algorithms for computing LLL bases.
LLL bases have nice theoretical properties, but the main benefit of LLL bases is that the entries of the resulting matrix often have dramatically small size, even smaller than theory would imply.
This package implements the following functions.