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/*
Copyright (C) 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 "fmpz.h"
#include "fmpz_vec.h"
#include "fmpz_poly.h"
#include "fmpq_poly.h"
void _fmpq_poly_gcd(fmpz *G, fmpz_t denG,
const fmpz *A, slong lenA, const fmpz *B, slong lenB)
{
if (lenA == 1) /* lenA == lenB == 1 */
{
fmpz_one(G);
fmpz_one(denG);
}
else
{
fmpz *primA, *primB;
fmpz_t s, t;
slong lenG;
fmpz_init(s);
fmpz_init(t);
_fmpz_vec_content(s, A, lenA);
_fmpz_vec_content(t, B, lenB);
/* Set primA, primB to the primitive multiples of A, B */
if (fmpz_is_one(s))
{
if (fmpz_is_one(t))
{
primA = (fmpz *) A;
primB = (fmpz *) B;
}
else
{
primA = (fmpz *) A;
primB = _fmpz_vec_init(lenB);
_fmpz_vec_scalar_divexact_fmpz(primB, B, lenB, t);
}
}
else
{
if (fmpz_is_one(t))
{
primA = _fmpz_vec_init(lenA);
primB = (fmpz *) B;
_fmpz_vec_scalar_divexact_fmpz(primA, A, lenA, s);
}
else
{
primA = _fmpz_vec_init(lenA + lenB);
primB = primA + lenA;
_fmpz_vec_scalar_divexact_fmpz(primA, A, lenA, s);
_fmpz_vec_scalar_divexact_fmpz(primB, B, lenB, t);
}
}
_fmpz_poly_gcd(G, primA, lenA, primB, lenB);
for (lenG = lenB - 1; !G[lenG]; lenG--) ;
lenG++;
fmpz_set(denG, G + (lenG - 1));
if (A != primA)
_fmpz_vec_clear(primA, lenA + (B != primB) * lenB);
else if (B != primB)
_fmpz_vec_clear(primB, lenB);
fmpz_clear(s);
fmpz_clear(t);
}
}
void fmpq_poly_gcd(fmpq_poly_t G, const fmpq_poly_t A, const fmpq_poly_t B)
{
if (A->length < B->length)
{
fmpq_poly_gcd(G, B, A);
}
else
{
slong lenA = A->length, lenB = B->length;
if (lenA == 0) /* lenA = lenB = 0 */
{
fmpq_poly_zero(G);
}
else if (lenB == 0) /* lenA > lenB = 0 */
{
fmpq_poly_make_monic(G, A);
}
else /* lenA >= lenB >= 1 */
{
if (G == A || G == B)
{
fmpq_poly_t t;
fmpq_poly_init2(t, lenB);
_fmpq_poly_gcd(t->coeffs, t->den, A->coeffs, A->length,
B->coeffs, B->length);
fmpq_poly_swap(t, G);
fmpq_poly_clear(t);
}
else
{
fmpq_poly_fit_length(G, lenB);
_fmpq_poly_gcd(G->coeffs, G->den, A->coeffs, A->length,
B->coeffs, B->length);
}
_fmpq_poly_set_length(G, lenB);
_fmpq_poly_normalise(G);
}
}
}