85 lines
2.5 KiB
C
85 lines
2.5 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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void
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arith_dedekind_sum(fmpq_t s, const fmpz_t h, const fmpz_t k)
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{
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if (fmpz_cmp_ui(k, UWORD(2)) <= 0 || fmpz_is_zero(h) || fmpz_equal(h, k))
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{
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fmpq_zero(s);
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}
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else if (fmpz_sgn(h) < 0)
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{
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fmpz_t t;
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fmpz_init(t);
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fmpz_neg(t, h);
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arith_dedekind_sum(s, t, k);
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fmpq_neg(s, s);
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fmpz_clear(t);
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}
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else
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{
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fmpz_t t, u, q;
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fmpz_init(t);
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fmpz_init(u);
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fmpz_init(q);
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fmpz_gcd(q, h, k);
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fmpz_divexact(t, h, q);
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fmpz_divexact(u, k, q);
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if (fmpz_cmp(t, u) > 0)
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{
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fmpq_t r;
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fmpq_init(r);
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/* r = (1 + h(h-3k) + k^2) / (12hk) */
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fmpz_mul_ui(fmpq_numref(r), u, UWORD(3));
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fmpz_sub(fmpq_numref(r), t, fmpq_numref(r));
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fmpz_mul(fmpq_numref(r), fmpq_numref(r), t);
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fmpz_addmul(fmpq_numref(r), u, u);
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fmpz_add_ui(fmpq_numref(r), fmpq_numref(r), UWORD(1));
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fmpz_mul(fmpq_denref(r), t, u);
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fmpz_mul_ui(fmpq_denref(r), fmpq_denref(r), UWORD(12));
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fmpq_canonicalise(r);
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arith_dedekind_sum_coprime(s, u, t);
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fmpq_sub(s, r, s);
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fmpq_clear(r);
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}
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else
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{
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arith_dedekind_sum_coprime(s, t, u);
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}
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fmpz_clear(t);
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fmpz_clear(u);
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fmpz_clear(q);
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}
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}
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