FLINT3.7.0-dev
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fmpz_poly_CLD_bound

Synopsis#include <flint/fmpz_poly.h>
void fmpz_poly_CLD_bound(fmpz_t res, const fmpz_poly_t f, slong n)source

Sets res to a bound for the absolute value of the coefficient of xnx^n in fg′/gf g'/g for every factor gg of ff in Z[x]\mathbb{Z}[x] (the coefficients of the logarithmic derivative used by van Hoeij's algorithm, Logarithmic derivatives). Requires 0≤n<deg⁡f0 \le n < \deg f.

With f=∑i=0Naixif = \sum_{i=0}^N a_i x^i, B1(r)=r−(n+1)∑i≤n∣ai∣riB_1(r) = r^{-(n+1)} \sum_{i \le n} |a_i| r^i and B2(r)=r−(n+1)∑i>n∣ai∣riB_2(r) = r^{-(n+1)} \sum_{i > n} |a_i| r^i, the bound is Nmax⁡(B1(r),B2(r))N \max(B_1(r), B_2(r)) for an r>0r > 0 that approximately minimises the maximum, found by a search on log⁡2r\log_2 r in double precision with an extra safety margin [HvHN2011].

References#

Cite this page

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 2026-11-02).