FLINT3.7.0-dev
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fmpz_poly_q_derivative

Synopsis#include <flint/fmpz_poly_q.h>
void fmpz_poly_q_derivative(fmpz_poly_q_t rop, const fmpz_poly_q_t op)source

Sets rop to the derivative of op.

For op=a/b\mathit{op} = a/b with bb nonconstant, let d=gcd⁡(b,b′)d = \gcd(b, b'). Then

(ab)′=a′(b/d)−a(b′/d)b⋅(b/d),\left(\frac{a}{b}\right)' = \frac{a' (b/d) - a (b'/d)}{b \cdot (b/d)},

and the numerator and denominator of this expression can only have a constant common factor, which is removed by dividing by the gcd of their contents [Hor1972].

Guides#

References#

  • [Hor1972] Ellis Horowitz : "Algorithms for Rational Function Arithmetic Operations" Annual ACM Symposium on Theory of Computing: Proceedings of the Fourth Annual ACM Symposium on Theory of Computing (Denver) (1972), https://doi.org/10.1145/800152.804903
Cite this page

The FLINT team, “fmpz_poly_q_derivative (fmpz_poly_q.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/fmpz_poly_q/fmpz_poly_q_derivative.html (generated 2026-11-02).