FLINT3.7.0-dev
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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)source
void _fmpq_mat_charpoly(fmpz * coeffs, fmpz_t den, const fmpq_mat_t mat)source

Sets pol to the characteristic polynomial of the square matrix mat; the underscore version writes the n+1n + 1 coefficients of the numerator to coeffs and the denominator to den, not necessarily in canonical form. Throws if mat is not square.

With qq the least common denominator of the entries, the characteristic polynomial ∑kckxk\sum_k c_k x^k of the integer matrix qAqA is computed with _fmpz_mat_charpoly, and χA(x)=q−nχqA(qx)\chi_A(x) = q^{-n} \chi_{qA}(qx), so the coefficient of xkx^k is ck/qn−kc_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 2026-11-02).