 TOPICS  # 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.

Hensel Lifting

This entry contributed by Bhuvanesh Bhatt

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## References

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

## Referenced on Wolfram|Alpha

Landau-Mignotte Bound

## Cite this as:

Bhatt, Bhuvanesh. "Landau-Mignotte Bound." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/Landau-MignotteBound.html