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/*
Copyright (C) 2016 Ralf Stephan
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_legendre_pt(fmpz * coeffs, ulong n)
{
fmpz_t c;
ulong k, facnp, facnm;
if (n == 0)
{
fmpz_one(coeffs);
return;
}
if (n == 1)
{
fmpz_set_si(coeffs, -1);
fmpz_set_ui(coeffs + 1, 2);
return;
}
fmpz_init(c);
fmpz_one(c);
if (n%2 == 1)
fmpz_neg(c, c);
facnp = n;
facnm = n+1;
fmpz_set(coeffs, c);
for (k = 1; k<=n; k++)
{
++facnp;
--facnm;
fmpz_mul2_uiui(c, c, facnp, facnm);
fmpz_divexact2_uiui(c, c, k, k);
fmpz_neg(c, c);
fmpz_set(coeffs + k, c);
}
fmpz_clear(c);
}
void
fmpz_poly_legendre_pt(fmpz_poly_t poly, ulong n)
{
fmpz_poly_fit_length(poly, n + 1);
_fmpz_poly_legendre_pt(poly->coeffs, n);
_fmpz_poly_set_length(poly, n + 1);
}