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/*
Copyright (C) 2011 Fredrik Johansson
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 "fmpz.h"
#include "fmpq_poly.h"
#include "arith.h"
void arith_euler_polynomial(fmpq_poly_t poly, ulong n)
{
fmpz_t t;
slong k;
if (n == 0)
{
fmpq_poly_set_ui(poly, UWORD(1));
return;
}
arith_bernoulli_polynomial(poly, n + 1);
fmpz_init(t);
fmpz_set_si(t, WORD(-2));
for (k = n; k >= 0; k--)
{
fmpz_mul(poly->coeffs + k, poly->coeffs + k, t);
fmpz_mul_ui(t, t, UWORD(2));
fmpz_sub_ui(t, t, UWORD(2));
}
fmpz_zero(poly->coeffs + n + 1);
fmpz_mul_ui(poly->den, poly->den, n + 1);
fmpq_poly_canonicalise(poly);
fmpz_clear(t);
}