256 lines
7.4 KiB
C
256 lines
7.4 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) 2010, 2011 Sebastian Pancratz
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******************************************************************************/
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#include "fmpq_poly.h"
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#include "fmpz_poly_q.h"
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void fmpz_poly_q_add_in_place(fmpz_poly_q_t rop, const fmpz_poly_q_t op)
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{
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fmpz_poly_t d, poly, r2, s2;
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if (rop == op)
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{
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fmpz_poly_q_scalar_mul_si(rop, rop, 2);
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return;
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}
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if (fmpz_poly_q_is_zero(rop))
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{
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fmpz_poly_q_set(rop, op);
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return;
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}
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if (fmpz_poly_q_is_zero(op))
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{
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return;
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}
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/* Polynomials? */
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if (fmpz_poly_length(rop->den) == 1 && fmpz_poly_length(op->den) == 1)
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{
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const slong len1 = fmpz_poly_length(rop->num);
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const slong len2 = fmpz_poly_length(op->num);
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fmpz_poly_fit_length(rop->num, FLINT_MAX(len1, len2));
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_fmpq_poly_add(rop->num->coeffs, rop->den->coeffs,
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rop->num->coeffs, rop->den->coeffs, len1,
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op->num->coeffs, op->den->coeffs, len2);
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_fmpz_poly_set_length(rop->num, FLINT_MAX(len1, len2));
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_fmpz_poly_set_length(rop->den, 1);
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_fmpz_poly_normalise(rop->num);
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return;
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}
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/* Denominators equal to one? */
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if (fmpz_poly_is_one(rop->den))
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{
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fmpz_poly_mul(rop->num, rop->num, op->den);
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fmpz_poly_add(rop->num, rop->num, op->num);
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fmpz_poly_set(rop->den, op->den);
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return;
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}
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if (fmpz_poly_is_one(op->den))
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{
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fmpz_poly_init(poly);
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fmpz_poly_mul(poly, rop->den, op->num);
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fmpz_poly_add(rop->num, rop->num, poly);
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fmpz_poly_clear(poly);
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return;
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}
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/* Henrici's algorithm for summation in quotient fields */
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fmpz_poly_init(d);
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fmpz_poly_gcd(d, rop->den, op->den);
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if (fmpz_poly_is_one(d))
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{
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fmpz_poly_mul(rop->num, rop->num, op->den);
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fmpz_poly_mul(d, rop->den, op->num); /* Using d as temp */
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fmpz_poly_add(rop->num, rop->num, d);
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fmpz_poly_mul(rop->den, rop->den, op->den);
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}
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else
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{
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fmpz_poly_init(r2);
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fmpz_poly_init(s2);
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fmpz_poly_div(r2, rop->den, d);
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fmpz_poly_div(s2, op->den, d);
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fmpz_poly_mul(rop->num, rop->num, s2);
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fmpz_poly_mul(s2, op->num, r2); /* Using s2 as temp */
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fmpz_poly_add(rop->num, rop->num, s2);
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if (fmpz_poly_is_zero(rop->num))
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{
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fmpz_poly_zero(rop->den);
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fmpz_poly_set_coeff_si(rop->den, 0, 1);
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}
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else
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{
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fmpz_poly_mul(rop->den, r2, op->den);
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fmpz_poly_gcd(r2, rop->num, d); /* Using r2 as temp */
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if (!fmpz_poly_is_one(r2))
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{
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fmpz_poly_div(rop->num, rop->num, r2);
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fmpz_poly_div(rop->den, rop->den, r2);
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}
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}
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fmpz_poly_clear(r2);
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fmpz_poly_clear(s2);
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}
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fmpz_poly_clear(d);
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}
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void
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fmpz_poly_q_add(fmpz_poly_q_t rop,
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const fmpz_poly_q_t op1, const fmpz_poly_q_t op2)
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{
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fmpz_poly_t d, r2, s2;
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if (fmpz_poly_q_is_zero(op1))
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{
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fmpz_poly_q_set(rop, op2);
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return;
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}
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if (fmpz_poly_q_is_zero(op2))
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{
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fmpz_poly_q_set(rop, op1);
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return;
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}
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if (op1 == op2)
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{
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fmpz_poly_q_scalar_mul_si(rop, op1, 2);
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return;
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}
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if (rop == op1)
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{
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fmpz_poly_q_add_in_place(rop, op2);
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return;
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}
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if (rop == op2)
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{
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fmpz_poly_q_add_in_place(rop, op1);
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return;
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}
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/*
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From here on, we may assume that rop, op1 and op2 all refer to
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distinct objects in memory, although they may still be equal
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*/
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/* Polynomials? */
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if (fmpz_poly_length(op1->den) == 1 && fmpz_poly_length(op2->den) == 1)
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{
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const slong len1 = fmpz_poly_length(op1->num);
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const slong len2 = fmpz_poly_length(op2->num);
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fmpz_poly_fit_length(rop->num, FLINT_MAX(len1, len2));
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_fmpq_poly_add(rop->num->coeffs, rop->den->coeffs,
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op1->num->coeffs, op1->den->coeffs, len1,
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op2->num->coeffs, op2->den->coeffs, len2);
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_fmpz_poly_set_length(rop->num, FLINT_MAX(len1, len2));
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_fmpz_poly_set_length(rop->den, 1);
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_fmpz_poly_normalise(rop->num);
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return;
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}
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/* Denominators equal to one? */
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if (fmpz_poly_is_one(op1->den))
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{
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fmpz_poly_mul(rop->num, op1->num, op2->den);
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fmpz_poly_add(rop->num, rop->num, op2->num);
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fmpz_poly_set(rop->den, op2->den);
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return;
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}
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if (fmpz_poly_is_one(op2->den))
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{
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fmpz_poly_mul(rop->num, op2->num, op1->den);
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fmpz_poly_add(rop->num, op1->num, rop->num);
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fmpz_poly_set(rop->den, op1->den);
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return;
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}
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/* Henrici's algorithm for summation in quotient fields */
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/*
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We begin by using rop->num as a temporary variable for
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the gcd of the two denominators' greatest common divisor
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*/
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fmpz_poly_gcd(rop->num, op1->den, op2->den);
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if (fmpz_poly_is_one(rop->num))
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{
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fmpz_poly_mul(rop->num, op1->num, op2->den);
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fmpz_poly_mul(rop->den, op1->den, op2->num); /* Using rop->den as temp */
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fmpz_poly_add(rop->num, rop->num, rop->den);
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fmpz_poly_mul(rop->den, op1->den, op2->den);
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}
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else
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{
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/*
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We now copy rop->num into a new variable d, so we
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no longer need rop->num as a temporary variable
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*/
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fmpz_poly_init(d);
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fmpz_poly_swap(d, rop->num);
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fmpz_poly_init(r2);
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fmpz_poly_init(s2);
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fmpz_poly_div(r2, op1->den, d); /* +ve leading coeff */
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fmpz_poly_div(s2, op2->den, d); /* +ve leading coeff */
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fmpz_poly_mul(rop->num, op1->num, s2);
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fmpz_poly_mul(rop->den, op2->num, r2); /* Using rop->den as temp */
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fmpz_poly_add(rop->num, rop->num, rop->den);
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if (fmpz_poly_is_zero(rop->num))
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{
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fmpz_poly_zero(rop->den);
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fmpz_poly_set_coeff_si(rop->den, 0, 1);
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}
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else
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{
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fmpz_poly_mul(rop->den, op1->den, s2);
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fmpz_poly_gcd(r2, rop->num, d);
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if (!fmpz_poly_is_one(r2))
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{
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fmpz_poly_div(rop->num, rop->num, r2);
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fmpz_poly_div(rop->den, rop->den, r2);
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}
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}
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fmpz_poly_clear(d);
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fmpz_poly_clear(r2);
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fmpz_poly_clear(s2);
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}
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}
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