`fmpq_poly_xgcd`

Synopsis#include <flint/fmpq_poly.h>

void fmpq_poly_xgcd(fmpq_poly_t G, fmpq_poly_t S, fmpq_poly_t T, const fmpq_poly_t A, const fmpq_poly_t B)source

Computes polynomials $G$ , $S$ , and $T$ such that $G = \gcd(A, B) = S A + T B$ , where $G$ is the monic greatest common divisor of $A$ and $B$ .

The outputs $G$ , $S$ , $T$ must be distinct objects (an exception is raised otherwise). Corner cases are handled as follows. If $A = B = 0$ , returns $G = S = T = 0$ . If $A \neq 0$ , $B = 0$ , returns the suitable scalar multiple of $G = A$ , $S = 1$ , and $T = 0$ . The case when $A = 0$ , $B \neq 0$ is handled similarly.

Cite this page

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

@misc{flint-doc-fmpq-poly-fmpq-poly-xgcd,
  author       = {{The FLINT team}},
  title        = {{fmpq\_poly\_xgcd (fmpq\_poly.h)}},
  howpublished = {FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev},
  year         = {2026},
  url          = {https://flintlib.org/doc/fmpq_poly/fmpq_poly_xgcd.html},
  note         = {Generated 2026-11-02}
}

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