128 lines
3.7 KiB
C
128 lines
3.7 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) 2010 Sebastian Pancratz
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******************************************************************************/
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#include <stdlib.h>
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#include <gmp.h>
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#include "flint.h"
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#include "fmpz.h"
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#include "fmpz_vec.h"
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#include "fmpq_poly.h"
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void _fmpq_poly_div(fmpz * Q, fmpz_t q,
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const fmpz * A, const fmpz_t a, slong lenA,
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const fmpz * B, const fmpz_t b, slong lenB, const fmpz_preinvn_t inv)
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{
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slong lenQ = lenA - lenB + 1;
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ulong d;
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const fmpz * lead = B + (lenB - 1);
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if (lenB == 1)
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{
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_fmpq_poly_scalar_div_fmpq(Q, q, A, a, lenA, B, b);
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return;
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}
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/*
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From pseudo division over Z we have
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lead^d * A = Q * B + R
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and thus
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{A, a} = {b * Q, a * lead^d} * {B, b} + {R, a * lead^d}.
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*/
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_fmpz_poly_pseudo_div(Q, &d, A, lenA, B, lenB, inv);
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/* 1. lead^d == +-1. {Q, q} = {b Q, a} up to sign */
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if (d == UWORD(0) || *lead == WORD(1) || *lead == WORD(-1))
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{
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fmpz_one(q);
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_fmpq_poly_scalar_mul_fmpz(Q, q, Q, q, lenQ, b);
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_fmpq_poly_scalar_div_fmpz(Q, q, Q, q, lenQ, a);
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if (*lead == WORD(-1) && d % UWORD(2))
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_fmpz_vec_neg(Q, Q, lenQ);
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}
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/* 2. lead^d != +-1. {Q, q} = {b Q, a lead^d} */
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else
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{
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/*
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TODO: Improve this. Clearly we do not need to compute
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den = a lead^d in many cases, but can determine the GCD from
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lead alone already.
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*/
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fmpz_t den;
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fmpz_init(den);
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fmpz_pow_ui(den, lead, d);
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fmpz_mul(den, a, den);
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fmpz_one(q);
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_fmpq_poly_scalar_mul_fmpz(Q, q, Q, q, lenQ, b);
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_fmpq_poly_scalar_div_fmpz(Q, q, Q, q, lenQ, den);
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fmpz_clear(den);
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}
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}
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void fmpq_poly_div(fmpq_poly_t Q,
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const fmpq_poly_t poly1, const fmpq_poly_t poly2)
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{
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slong lenA, lenB, lenQ;
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if (fmpq_poly_is_zero(poly2))
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{
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flint_printf("Exception (fmpq_poly_div). Division by zero.\n");
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abort();
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}
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if (poly1->length < poly2->length)
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{
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fmpq_poly_zero(Q);
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return;
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}
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/* Deal with aliasing */
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if (Q == poly1 || Q == poly2)
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{
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fmpq_poly_t tempQ;
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fmpq_poly_init(tempQ);
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fmpq_poly_div(tempQ, poly1, poly2);
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fmpq_poly_swap(Q, tempQ);
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fmpq_poly_clear(tempQ);
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return;
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}
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lenA = poly1->length;
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lenB = poly2->length;
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lenQ = lenA - lenB + 1;
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fmpq_poly_fit_length(Q, lenQ);
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_fmpq_poly_div(Q->coeffs, Q->den,
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poly1->coeffs, poly1->den, poly1->length,
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poly2->coeffs, poly2->den, poly2->length, NULL);
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_fmpq_poly_set_length(Q, lenQ);
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}
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