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/*
Copyright (C) 2011 Ralf Stephan
Copyright (C) 2021 Mathieu Gouttenoire
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 "fmpz_poly.h"
void
_fmpz_poly_hermite_h(fmpz * coeffs, ulong n)
{
if (n == 0)
{
fmpz_one(coeffs);
return;
}
if (n == 1)
{
fmpz_zero(coeffs);
fmpz_set_ui(coeffs + 1, 2);
return;
}
for (ulong k = n & 1; k < n; k += 2)
{
fmpz_zero(coeffs + k);
}
fmpz_one(coeffs + n);
fmpz_mul_2exp(coeffs + n, coeffs + n, n);
for (slong k = n - 2; k >= 0; k -= 2)
{
fmpz_mul2_uiui(coeffs + k, coeffs + k+2, k+1, k+2);
fmpz_divexact_ui(coeffs + k, coeffs + k, (n - k) << 1);
fmpz_neg(coeffs + k, coeffs + k);
}
}
void
fmpz_poly_hermite_h(fmpz_poly_t poly, ulong n)
{
fmpz_poly_fit_length(poly, n + 1);
_fmpz_poly_hermite_h(poly->coeffs, n);
_fmpz_poly_set_length(poly, n + 1);
}