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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 "fmpq_poly.h"
void _fmpq_poly_laguerre_l(fmpz * coeffs, fmpz_t den, ulong n)
{
fmpz_t c;
ulong k;
if (n == 0)
{
fmpz_one(coeffs);
fmpz_one(den);
return;
}
if (n == 1)
{
fmpz_one(coeffs);
fmpz_one(coeffs + 1);
fmpz_neg(coeffs + 1, coeffs + 1);
fmpz_one(den);
return;
}
fmpz_init(c);
fmpz_one(c);
if (n%2 == 1)
fmpz_neg(c, c);
fmpz_set(coeffs + n, c);
for (k = 0; k < n; k++)
{
fmpz_mul2_uiui(c, c, n-k, n-k);
fmpz_divexact_ui(c, c, k+1);
fmpz_neg(c, c);
fmpz_set(coeffs + n - k - 1, c);
}
fmpz_set(den, coeffs);
fmpz_clear(c);
}
void
fmpq_poly_laguerre_l(fmpq_poly_t poly, ulong n)
{
fmpq_poly_fit_length(poly, n + 1);
_fmpq_poly_laguerre_l(poly->coeffs, poly->den, n);
_fmpq_poly_set_length(poly, n + 1);
}