fmpz_poly_factor_inflation_is_irreducible_capelli
Synopsis
#include <flint/fmpz_poly_factor.h>int fmpz_poly_factor_inflation_is_irreducible_capelli(const fmpz_poly_t T, ulong d)sourceGiven T irreducible over \mathbb{Q} of degree at least 1 and d \ge 1, returns 1 if T(x^d) is proved irreducible over \mathbb{Q} and 0 if the attempt was inconclusive. The prime-step certificate is chained over the prime factorisation of d, using T(x^d) = U(x^{d/p}) with U = T(x^p). The behaviour is undefined if T is reducible. fmpz_poly_factor uses this to avoid refactoring inflations of irreducible factors of deflated polynomials.
Cite this page
The FLINT team, “fmpz_poly_factor_inflation_is_irreducible_capelli (fmpz_poly_factor.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/fmpz_poly_factor/fmpz_poly_factor_inflation_is_irreducible_capelli.html (generated 2026-10-20).
@misc{flint-doc-fmpz-poly-factor-fmpz-poly-factor-inflation-is-irreducible-capelli,
author = {{The FLINT team}},
title = {{fmpz\_poly\_factor\_inflation\_is\_irreducible\_capelli (fmpz\_poly\_factor.h)}},
howpublished = {FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev},
year = {2026},
url = {https://flintlib.org/doc/fmpz_poly_factor/fmpz_poly_factor_inflation_is_irreducible_capelli.html},
note = {Generated 2026-10-20}
}