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 = {159041160, 76300920, 23173368, 67844244, 106954464}
o1 : List
|
i2 : (g,z) = gcdLLL s
o2 = (372, | 11 5 7 18 4 |)
| -6 -16 14 1 6 |
| -8 7 26 23 12 |
| -10 -4 -30 4 5 |
| -4 5 -7 -35 -16 |
o2 : Sequence
|
i3 : matrix{s} * z
o3 = | 0 0 0 0 372 |
1 5
o3 : Matrix ZZ <--- ZZ
|