_aprcl_is_prime_jacobi_check_pk, _aprcl_is_prime_jacobi_check_21, _aprcl_is_prime_jacobi_check_22, _aprcl_is_prime_jacobi_check_2k
Synopsis
#include <flint/aprcl.h>slong _aprcl_is_prime_jacobi_check_2k(const unity_zp j, const unity_zp j2_1, const unity_zp j2_2, const fmpz_t u, ulong v)sourceThe check for odd p (with j = J(p, q)), for p^k = 2 (which reduces to (-q)^{(n-1)/2} \equiv \pm 1 \pmod n, returning 0 for +1, 1 for -1 and -1 otherwise), for p^k = 4 (with j = J(2, q); h gives \zeta_4^h \in \{1, i, -1, -i\}), and for p = 2, k \ge 3 (with j = J(2, q), j_{2,1} = J_3(q) and j_{2,2} = J_2(q)).
Cite this page
The FLINT team, “_aprcl_is_prime_jacobi_check_pk, _aprcl_is_prime_jacobi_check_21, _aprcl_is_prime_jacobi_check_22, _aprcl_is_prime_jacobi_check_2k (aprcl.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/aprcl/_aprcl_is_prime_jacobi_check_pk.html (generated 2026-10-20).
@misc{flint-doc-aprcl-aprcl-is-prime-jacobi-check-pk,
author = {{The FLINT team}},
title = {{\_aprcl\_is\_prime\_jacobi\_check\_pk, \_aprcl\_is\_prime\_jacobi\_check\_21, \_aprcl\_is\_prime\_jacobi\_check\_22, \_aprcl\_is\_prime\_jacobi\_check\_2k (aprcl.h)}},
howpublished = {FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev},
year = {2026},
url = {https://flintlib.org/doc/aprcl/_aprcl_is_prime_jacobi_check_pk.html},
note = {Generated 2026-10-20}
}