`fmpq_simplest_between, _fmpq_simplest_between`

Synopsis#include <flint/fmpq.h>

void fmpq_simplest_between(fmpq_t x, const fmpq_t l, const fmpq_t r)source

void _fmpq_simplest_between(fmpz_t x_num, fmpz_t x_den, const fmpz_t l_num, const fmpz_t l_den, const fmpz_t r_num, const fmpz_t r_den)

source

Set $x$ to the simplest fraction in the closed interval between $l$ and $r$ , where $a_1/b_1$ is simpler than $a_2/b_2$ if $b_1 < b_2$ , or $b_1 = b_2$ and $a_1 < a_2$ . The endpoints need not be canonical, but their denominators must be positive; the result is canonical.

fmpq_simplest_between accepts the endpoints in either order; the underscore version requires $l \le r$ . The simplest fraction is read off the common prefix of the continued fraction expansions of the endpoints, computed by _fmpq_ball_get_cfrac; see Continued fractions of rational numbers.

Cite this page

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

@misc{flint-doc-fmpq-fmpq-simplest-between,
  author       = {{The FLINT team}},
  title        = {{fmpq\_simplest\_between, \_fmpq\_simplest\_between (fmpq.h)}},
  howpublished = {FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev},
  year         = {2026},
  url          = {https://flintlib.org/doc/fmpq/fmpq_simplest_between.html},
  note         = {Generated 2026-11-02}
}

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