## LLLGCD examples

In our paper
*Extended gcd and Hermite normal form algorithms via lattice basis reduction*, G. Havas, B.S. Majewski, K.R. Matthews, Experimental Mathematics, Vol 7 (1998) 125-136,
we show that if 1 ≥ α ≥ 3/8, our LLLGCD algorithm delivers a multiplier vector b[3] for three numbers such that one of b[3]+e[1]b[1]+e[2]b[2] is a shortest multiplier, where e[i]=0,-1, or 1. A similar result also holds for four integers with 1 ≥ α > (5 + √33)/16 = ·671···, (proved by Sean Byrnes), but not for five integers - see below.
- gcd(4,6,9) (
*20th July 1997*) (lllgcd step by step)
- gcd(113192, 763836, 1066557, 1785102) (algorithm 2 of HMM, step by step)
- gcd(116085838, 181081878, 314252913, 10346840) (lllgcd step by step)
- gcd of five numbers (
*14th December 1998*)
- gcd of ten numbers (
*17th December 1998*)
- gcd of twenty numbers (
*17th December 1998*)
- gcd of thirty, forty, fifty, sixty integers (
*9th December 1998*)

* Last modified 28th January 2014*