Landau-Mignotte Bound

The Landau-Mignotte bound, also known as the Mignotte bound, is used in univariate polynomial factorization to determine the number of Hensel lifting steps needed. It gives an upper bound for the absolute value of coefficients of any nontrivial factor of a polynomial  in .

The bound is given by

where  is the 2-norm and

Factorization over the integers is done by factoring the polynomial modulo a "good" prime  using the Berlekamp-Zassenhaus algorithm, and the irreducible factors are then lifted to ones modulo . There are guidelines for choosing . For example,  should not evenly divide the leading coefficient of the polynomial, and  should be squarefree.

REFERENCES:

van Hoeij, M. "Factoring Polynomials and the Knapsack Problem." J. Number Th. 95, 167-189, 2002.