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LLLBases > gcdLLL

gcdLLL -- compute the gcd of integers, and small multipliers

Synopsis

Description

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 = {208711344, 194936928, 3312660, 190020948, 46494420}

o1 : List
i2 : (g,z) = gcdLLL s

o2 = (372, | -7  -11 11  -28 4   |)
           | 20  -1  3   21  5   |
           | -3  19  0   -41 17  |
           | -14 14  -11 18  -13 |
           | 5   -5  -17 -33 13  |

o2 : Sequence
i3 : matrix{s} * z

o3 = | 0 0 0 0 372 |

              1        5
o3 : Matrix ZZ  <--- ZZ

See also

Ways to use gcdLLL :