`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)source

Given $T$ 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 2026-11-02).

@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 2026-11-02}
}

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