flint-sys 0.9.0

/*
    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 "nmod.h"
#include "nmod_vec.h"
#include "nmod_poly.h"
#include "fmpz_vec.h"
#include "fmpz_poly.h"
#include "fmpq.h"
#include "fmpq_poly.h"

void _fmpq_poly_resultant(fmpz_t rnum, fmpz_t rden,
                          const fmpz *poly1, const fmpz_t den1, slong len1,
                          const fmpz *poly2, const fmpz_t den2, slong len2)
{
    if (len2 == 1)
    {
        if (len1 == 1)
        {
            fmpz_one(rnum);
            fmpz_one(rden);
        }
        else if (len1 == 2)
        {
            fmpz_set(rnum, poly2);
            fmpz_set(rden, den2);
        }
        else
        {
            fmpz_pow_ui(rnum, poly2, len1 - 1);
            if (fmpz_is_one(den2))
            {
                fmpz_one(rden);
            }
            else
            {
                fmpz_pow_ui(rden, den2, len1 - 1);
            }
        }
    }
    else  /* len1 >= len2 >= 2 */
    {
        fmpz_t c1, c2;
        fmpz *prim1, *prim2, *g;
        slong lenG = len2;
	ulong p;
        nmod_t mod;
	nn_ptr pp1, pp2, gp;

        fmpz_init(c1);
        fmpz_init(c2);

        _fmpz_vec_content(c1, poly1, len1);
        _fmpz_vec_content(c2, poly2, len2);

        prim1 = _fmpz_vec_init(len1);
        prim2 = _fmpz_vec_init(len2);
        g     = _fmpz_vec_init(len2);

        _fmpz_vec_scalar_divexact_fmpz(prim1, poly1, len1, c1);
        _fmpz_vec_scalar_divexact_fmpz(prim2, poly2, len2, c2);

	/* first check GCD mod a prime */
#if FLINT64
	p = UWORD(1152921504606846869);
#else
	p = UWORD(1073741789);
#endif
        /* ensure p doesn't divide the leading coeffs */
	while (fmpz_fdiv_ui(prim1 + len1 - 1, p) == 0 ||
	       fmpz_fdiv_ui(prim2 + len2 - 1, p) == 0)
	    p = n_nextprime(p, 1);

	nmod_init(&mod, p);

        pp1 = _nmod_vec_init(len1);
	pp2 = _nmod_vec_init(len2);
	gp = _nmod_vec_init(len2);

        _fmpz_vec_get_nmod_vec(pp1, prim1, len1, mod);
	_fmpz_vec_get_nmod_vec(pp2, prim2, len2, mod);

        lenG = _nmod_poly_gcd(gp, pp1, len1, pp2, len2, mod);

        if (lenG > 1) /* inconclusive, p could be a bad prime, so check over Z */
	{
	   _fmpz_poly_gcd(g, prim1, len1, prim2, len2);
           FMPZ_VEC_NORM(g, lenG);
        }

        if (lenG > 1)
        {
            fmpz_zero(rnum);
            fmpz_one(rden);
        }
        else  /* prim1, prim2 are coprime */
        {
            fmpz_t t;

            fmpz_init(t);
            _fmpz_poly_resultant(rnum, prim1, len1, prim2, len2);

            if (!fmpz_is_one(c1))
            {
                fmpz_pow_ui(t, c1, len2 - 1);
                fmpz_mul(rnum, rnum, t);
            }
            if (!fmpz_is_one(c2))
            {
                fmpz_pow_ui(t, c2, len1 - 1);
                fmpz_mul(rnum, rnum, t);
            }

            if (fmpz_is_one(den1))
            {
                if (fmpz_is_one(den2))
                    fmpz_one(rden);
                else
                    fmpz_pow_ui(rden, den2, len1 - 1);
            }
            else
            {
                if (fmpz_is_one(den2))
                    fmpz_pow_ui(rden, den1, len2 - 1);
                else
                {
                    fmpz_pow_ui(rden, den1, len2 - 1);
                    fmpz_pow_ui(t,    den2, len1 - 1);
                    fmpz_mul(rden, rden, t);
                }
            }
            _fmpq_canonicalise(rnum, rden);
            fmpz_clear(t);
        }

        _nmod_vec_clear(pp1);
	_nmod_vec_clear(pp2);
	_nmod_vec_clear(gp);
	fmpz_clear(c1);
        fmpz_clear(c2);
        _fmpz_vec_clear(prim1, len1);
        _fmpz_vec_clear(prim2, len2);
        _fmpz_vec_clear(g, len2);
    }
}

void fmpq_poly_resultant(fmpq_t r, const fmpq_poly_t f, const fmpq_poly_t g)
{
    const slong len1 = f->length;
    const slong len2 = g->length;

    if (len1 == 0 || len2 == 0)
    {
        fmpq_zero(r);
    }
    else
    {
        if (len1 >= len2)
        {
            _fmpq_poly_resultant(fmpq_numref(r), fmpq_denref(r),
                                 f->coeffs, f->den, len1,
                                 g->coeffs, g->den, len2);
        }
        else
        {
            _fmpq_poly_resultant(fmpq_numref(r), fmpq_denref(r),
                                 g->coeffs, g->den, len2,
                                 f->coeffs, f->den, len1);

            if (((len1 | len2) & WORD(1)) == WORD(0))
                fmpq_neg(r, r);
        }
    }
}