### Finding the shortest vectors in a lattice

A is an m × n matrix of integers with nonzero first and second rows.

ℒ is the lattice spanned by the rows of A in ℤ^{n}.

The MLLL algorithm is performed on A to give a lattice basis B.
Algorithm (2.8) on page 465 of the Fincke-Pohst algorithm: *Improved methods for calculating vectors of short length in a lattice, including a complexity analysis*, Math. Comp., vol. 44, no. 170, pp. 463-471, 1985, is performed on this basis to find all vectors X in ℒ with ||X||^{2} ≤ C, where C is the minimum length squared of the rows of B.

The matrix can be entered either (i) as a string of mn integers separated by spaces, or

(ii) cut and pasted from a text file, with entries separated by spaces and each row ended by a newline:

*Last modified 18th October 2011*

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