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 = {29646168, 197483640, 56733348, 247896336, 117248076}
o1 : List
|
i2 : (g,z) = gcdLLL s
o2 = (372, | 9 28 0 -25 -9 |)
| 6 7 -8 34 -8 |
| -10 7 -25 -14 -4 |
| 4 -11 5 -19 6 |
| -16 1 15 -4 5 |
o2 : Sequence
|
i3 : matrix{s} * z
o3 = | 0 0 0 0 372 |
1 5
o3 : Matrix ZZ <--- ZZ
|