This function is provided by the package
LLLBases.
The first n-1 columns of the matrix z form a basis of the kernel of the n integers of the list s, and the dot product of the last column of z and s is the gcd g.
The method used is described in the paper:
Havas, Majewski, Matthews,
Extended GCD and Hermite Normal Form Algorithms via Lattice Basis Reduction, Experimental Mathematics 7:2 p. 125 (1998).
For an example,
i1 : s = apply(5,i->372*(random 1000000))
o1 = {155167152, 236385540, 249429720, 357378168, 91896276}
o1 : List
|
i2 : (g,z) = gcdLLL s
o2 = (372, | 1 29 8 17 -1 |)
| 30 2 0 -23 6 |
| -4 -7 -6 33 -11 |
| -18 -8 -7 -17 8 |
| 2 -4 30 7 -15 |
o2 : Sequence
|
i3 : matrix{s} * z
o3 = | 0 0 0 0 372 |
1 5
o3 : Matrix ZZ <--- ZZ
|