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/*
Copyright (C) 2016 Pascal Molin
This file is part of FLINT.
FLINT is free software: you can redistribute it and/or modify it under
the terms of the GNU Lesser General Public License (LGPL) as published
by the Free Software Foundation; either version 3 of the License, or
(at your option) any later version. See <https://www.gnu.org/licenses/>.
*/
#include "dirichlet.h"
/* order of an element knowing the factorization of a multiple */
static ulong
nmod_order_precomp(ulong a, nmod_t mod, ulong expo, n_factor_t fac)
{
int k;
ulong pe, ap, order = 1;
for (k = 0; k < fac.num; k++)
{
pe = n_pow(fac.p[k], fac.exp[k]);
ap = nmod_pow_ui(a, expo / pe, mod);
while ( ap != 1)
{
ap = nmod_pow_ui(ap, fac.p[k], mod);
order *= fac.p[k];
}
}
return order;
}
ulong
dirichlet_order_ui(const dirichlet_group_t G, ulong a)
{
n_factor_t fac;
n_factor_init(&fac);
n_factor(&fac, G->expo, 1);
return nmod_order_precomp(a, G->mod, G->expo, fac);
}