fmpq_mat_charpoly, _fmpq_mat_charpoly
Synopsis
#include <flint/fmpq_mat.h>void fmpq_mat_charpoly(fmpq_poly_t pol, const fmpq_mat_t mat)sourcevoid _fmpq_mat_charpoly(fmpz * coeffs, fmpz_t den, const fmpq_mat_t mat)sourceSets pol to the characteristic polynomial of the square matrix mat; the underscore version writes the n + 1 coefficients of the numerator to coeffs and the denominator to den, not necessarily in canonical form. Throws if mat is not square.
With q the least common denominator of the entries, the characteristic polynomial \sum_k c_k x^k of the integer matrix qA is computed with _fmpz_mat_charpoly, and \chi_A(x) = q^{-n} \chi_{qA}(qx), so the coefficient of x^k is c_k / q^{n - k}.
Cite this page
The FLINT team, “fmpq_mat_charpoly, _fmpq_mat_charpoly (fmpq_mat.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/fmpq_mat/fmpq_mat_charpoly.html (generated 2026-10-20).
@misc{flint-doc-fmpq-mat-fmpq-mat-charpoly,
author = {{The FLINT team}},
title = {{fmpq\_mat\_charpoly, \_fmpq\_mat\_charpoly (fmpq\_mat.h)}},
howpublished = {FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev},
year = {2026},
url = {https://flintlib.org/doc/fmpq_mat/fmpq_mat_charpoly.html},
note = {Generated 2026-10-20}
}