fmpz_poly_CLD_bound
#include <flint/fmpz_poly.h>void fmpz_poly_CLD_bound(fmpz_t res, const fmpz_poly_t f, slong n)sourceSets res to a bound for the absolute value of the coefficient of x^n in f g'/g for every factor g of f in \mathbb{Z}[x] (the coefficients of the logarithmic derivative used by van Hoeij's algorithm, Logarithmic derivatives). Requires 0 \le n < \deg f.
With f = \sum_{i=0}^N a_i x^i, B_1(r) = r^{-(n+1)} \sum_{i \le n} |a_i| r^i and B_2(r) = r^{-(n+1)} \sum_{i > n} |a_i| r^i, the bound is N \max(B_1(r), B_2(r)) for an r > 0 that approximately minimises the maximum, found by a search on \log_2 r in double precision with an extra safety margin [HvHN2011].
References#
- [HvHN2011] W. Hart, M. van Hoeij and A. Novocin. Practical polynomial factoring in polynomial time. ISSAC 2011, 163–170. https://doi.org/10.1145/1993886.1993915
The FLINT team, “fmpz_poly_CLD_bound (fmpz_poly.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/fmpz_poly/fmpz_poly_CLD_bound.html (generated 2026-10-20).
@misc{flint-doc-fmpz-poly-fmpz-poly-CLD-bound,
author = {{The FLINT team}},
title = {{fmpz\_poly\_CLD\_bound (fmpz\_poly.h)}},
howpublished = {FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev},
year = {2026},
url = {https://flintlib.org/doc/fmpz_poly/fmpz_poly_CLD_bound.html},
note = {Generated 2026-10-20}
}