FLINT3.7.0-dev
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gr_poly_dispersion, gr_poly_dispersion_factor, gr_poly_dispersion_resultant

Synopsis#include <flint/gr_poly.h>
int gr_poly_dispersion(fmpz_t disp, gr_vec_t disp_set, const gr_poly_t f, const gr_poly_t g, gr_ctx_t ctx)source
int gr_poly_dispersion_factor(fmpz_t disp, gr_vec_t disp_set, const gr_poly_t f, const gr_poly_t g, gr_ctx_t ctx)source
int gr_poly_dispersion_resultant(fmpz_t disp, gr_vec_t disp_set, const gr_poly_t f, const gr_poly_t g, gr_ctx_t ctx)source

Compute the dispersion set of f and g, over a unique factorisation domain of characteristic zero: the set of integers n \ge 0 such that f(x + n) and g(x) have a nonconstant common factor, and the dispersion, its largest element.

Either output may be NULL. If the set is empty, disp is unchanged. The elements of disp_set (of type fmpz) are sorted in increasing order. The factor version factors f and g and compares the factors as in [ManWright1994]; the resultant version finds the nonnegative integer roots of \operatorname{res}_x(f(x + y), g(x)) and is mainly meant for testing.

References#

  • [ManWright1994] Y.-K. Man and F. J. Wright. "Fast polynomial dispersion computation and its application to indefinite summation". Proceedings of the International Symposium on Symbolic and Algebraic Computation (1994), 175-180. https://doi.org/10.1145/190347.190413
Cite this page

The FLINT team, “gr_poly_dispersion, gr_poly_dispersion_factor, gr_poly_dispersion_resultant (gr_poly.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/gr_poly/gr_poly_dispersion.html (generated 2026-10-20).