98 lines
2.4 KiB
C
98 lines
2.4 KiB
C
/*=============================================================================
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This file is part of FLINT.
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FLINT is free software; you can redistribute it and/or modify
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it under the terms of the GNU General Public License as published by
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the Free Software Foundation; either version 2 of the License, or
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(at your option) any later version.
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FLINT is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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GNU General Public License for more details.
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You should have received a copy of the GNU General Public License
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along with FLINT; if not, write to the Free Software
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Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
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=============================================================================*/
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/******************************************************************************
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Copyright (C) 2011 Fredrik Johansson
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******************************************************************************/
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#include "arith.h"
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static __inline__ void __legendre_denom(fmpz_t den, ulong n)
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{
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ulong d, k;
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d = k = n >> 1;
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while (k)
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{
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k >>= 1;
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d += k;
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}
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fmpz_one(den);
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fmpz_mul_2exp(den, den, d);
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}
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void _arith_legendre_polynomial(fmpz * coeffs, fmpz_t den, ulong n)
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{
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fmpz * r;
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int odd;
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slong k;
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ulong L;
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L = n / 2;
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odd = n % 2;
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r = coeffs + odd;
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__legendre_denom(den, n);
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fmpz_bin_uiui(r, n, L);
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fmpz_mul(r, r, den);
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if (odd)
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fmpz_mul_ui(r, r, L + 1);
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fmpz_fdiv_q_2exp(r, r, 2*L);
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if (L % 2)
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fmpz_neg(r, r);
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for (k = 1; k <= L; k++)
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{
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fmpz_mul2_uiui(r + 2, r, L + 1 - k, 2*k + 2*L - 1 + 2*odd);
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fmpz_divexact2_uiui(r + 2, r + 2, k, 2*k - 1 + 2*odd);
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fmpz_neg(r + 2, r + 2);
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r += 2;
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}
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for (k = 1 - odd; k < n; k += 2)
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fmpz_zero(coeffs + k);
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}
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void arith_legendre_polynomial(fmpq_poly_t poly, ulong n)
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{
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if (n == 0)
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{
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fmpq_poly_set_ui(poly, UWORD(1));
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return;
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}
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fmpq_poly_fit_length(poly, n + 1);
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if (n == 1)
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{
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fmpz_zero(poly->coeffs);
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fmpz_one(poly->coeffs + 1);
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fmpz_one(poly->den);
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}
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else
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_arith_legendre_polynomial(poly->coeffs, poly->den, n);
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_fmpq_poly_set_length(poly, n + 1);
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}
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