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 = {229545948, 143166432, 355214244, 33928260, 99512604}
o1 : List
|
i2 : (g,z) = gcdLLL s
o2 = (372, | 0 -21 -30 34 6 |)
| 3 -19 18 -18 -17 |
| 2 19 7 -23 3 |
| -16 -6 -2 -13 -12 |
| -6 10 19 34 4 |
o2 : Sequence
|
i3 : matrix{s} * z
o3 = | 0 0 0 0 372 |
1 5
o3 : Matrix ZZ <--- ZZ
|