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/*
Copyright (C) 2010, 2011 Sebastian Pancratz
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 "fmpq_poly.h"
#include "fmpz_poly_q.h"
void fmpz_poly_q_sub_in_place(fmpz_poly_q_t rop, const fmpz_poly_q_t op)
{
if (rop == op)
{
fmpz_poly_q_zero(rop);
return;
}
fmpz_poly_q_neg(rop, rop);
fmpz_poly_q_add_in_place(rop, op);
fmpz_poly_q_neg(rop, rop);
}
void
fmpz_poly_q_sub(fmpz_poly_q_t rop,
const fmpz_poly_q_t op1, const fmpz_poly_q_t op2)
{
fmpz_poly_t d, r2, s2;
if (fmpz_poly_is_zero(op1->num))
{
fmpz_poly_q_neg(rop, op2);
return;
}
if (fmpz_poly_is_zero(op2->num))
{
fmpz_poly_q_set(rop, op1);
return;
}
if (op1 == op2)
{
fmpz_poly_q_zero(rop);
return;
}
if (rop == op1)
{
fmpz_poly_q_sub_in_place(rop, op2);
return;
}
if (rop == op2)
{
fmpz_poly_q_sub_in_place(rop, op1);
fmpz_poly_q_neg(rop, rop);
return;
}
/*
From here on, we know that rop, op1 and op2 refer to distinct objects
in memory, although as rational functions they may still be equal
XXX: Do not maintain the remaining part of the function separately!!!
Instead, note that this is very similar to the corresponding part
of the summation code.
*/
/* Polynomials? */
if (fmpz_poly_length(op1->den) == 1 && fmpz_poly_length(op2->den) == 1)
{
const slong len1 = fmpz_poly_length(op1->num);
const slong len2 = fmpz_poly_length(op2->num);
fmpz_poly_fit_length(rop->num, FLINT_MAX(len1, len2));
_fmpq_poly_sub(rop->num->coeffs, rop->den->coeffs,
op1->num->coeffs, op1->den->coeffs, len1,
op2->num->coeffs, op2->den->coeffs, len2);
_fmpz_poly_set_length(rop->num, FLINT_MAX(len1, len2));
_fmpz_poly_set_length(rop->den, 1);
_fmpz_poly_normalise(rop->num);
return;
}
/* Denominators equal to one? */
if (fmpz_poly_is_one(op1->den))
{
fmpz_poly_mul(rop->num, op1->num, op2->den);
fmpz_poly_sub(rop->num, rop->num, op2->num);
fmpz_poly_set(rop->den, op2->den);
return;
}
if (fmpz_poly_is_one(op2->den))
{
fmpz_poly_mul(rop->num, op2->num, op1->den);
fmpz_poly_sub(rop->num, op1->num, rop->num);
fmpz_poly_set(rop->den, op1->den);
return;
}
/* Henrici's algorithm for summation in quotient fields */
/*
We begin by using rop->num as a temporary variable for the gcd of the
two denominators' greatest common divisor
*/
fmpz_poly_gcd(rop->num, op1->den, op2->den);
if (fmpz_poly_is_one(rop->num))
{
fmpz_poly_mul(rop->num, op1->num, op2->den);
fmpz_poly_mul(rop->den, op1->den, op2->num); /* Using rop->den as temp */
fmpz_poly_sub(rop->num, rop->num, rop->den);
fmpz_poly_mul(rop->den, op1->den, op2->den);
}
else
{
/*
We now copy rop->num into a new variable d, so we no longer need
rop->num as a temporary variable
*/
fmpz_poly_init(d);
fmpz_poly_swap(d, rop->num);
fmpz_poly_init(r2);
fmpz_poly_init(s2);
fmpz_poly_divexact(r2, op1->den, d); /* +ve leading coeff */
fmpz_poly_divexact(s2, op2->den, d); /* +ve leading coeff */
fmpz_poly_mul(rop->num, op1->num, s2);
fmpz_poly_mul(rop->den, op2->num, r2); /* Using rop->den as temp */
fmpz_poly_sub(rop->num, rop->num, rop->den);
if (fmpz_poly_degree(rop->num) < 0)
{
fmpz_poly_zero(rop->den);
fmpz_poly_set_coeff_si(rop->den, 0, 1);
}
else
{
fmpz_poly_mul(rop->den, op1->den, s2);
fmpz_poly_gcd(r2, rop->num, d);
if (!fmpz_poly_is_one(r2))
{
fmpz_poly_divexact(rop->num, rop->num, r2);
fmpz_poly_divexact(rop->den, rop->den, r2);
}
}
fmpz_poly_clear(d);
fmpz_poly_clear(r2);
fmpz_poly_clear(s2);
}
}