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 = {189110292, 73375512, 173602356, 44913048, 98758188}
o1 : List
|
i2 : (g,z) = gcdLLL s
o2 = (372, | -5 8 4 58 -3 |)
| -8 -3 -15 -39 3 |
| 2 -3 13 -68 2 |
| 11 7 -14 -32 0 |
| 7 -11 -13 52 0 |
o2 : Sequence
|
i3 : matrix{s} * z
o3 = | 0 0 0 0 372 |
1 5
o3 : Matrix ZZ <--- ZZ
|