flint-sys 0.9.0

/*
    Copyright (C) 2007 David Howden
    Copyright (C) 2007, 2008, 2009, 2010 William Hart
    Copyright (C) 2008 Richard Howell-Peak
    Copyright (C) 2011 Fredrik Johansson
    Copyright (C) 2012 Lina Kulakova
    Copyright (C) 2013 Mike Hansen
    Copyright (C) 2024 Albin Ahlbäck

    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/>.
*/

#ifdef T

#include "templates.h"


void
TEMPLATE(T, poly_factor_squarefree) (TEMPLATE(T, poly_factor_t) res,
                                     const TEMPLATE(T, poly_t) f,
                                     const TEMPLATE(T, ctx_t) ctx)
{
    TEMPLATE(T, poly_t) f_d, g, g_1, r;
    TEMPLATE(T, t) x;
    slong deg, i, p_ui;

    if (f->length <= 1)
    {
        res->num = 0;
        return;
    }

    if (f->length == 2)
    {
        TEMPLATE(T, poly_factor_insert) (res, f, 1, ctx);
        TEMPLATE(T, poly_make_monic) (res->poly + (res->num - 1),
                                      res->poly + (res->num - 1), ctx);
        return;
    }

    deg = TEMPLATE(T, poly_degree) (f, ctx);

    /* Step 1, look at f', if it is zero then we are done since f = h(x)^p
       for some particular h(x), clearly f(x) = sum a_k x^kp, k <= deg(f) */

    TEMPLATE(T, init) (x, ctx);
    TEMPLATE(T, poly_init) (g_1, ctx);
    TEMPLATE(T, poly_init) (f_d, ctx);
    TEMPLATE(T, poly_init) (g, ctx);
    TEMPLATE(T, poly_derivative) (f_d, f, ctx);

    /* Case 1 */
    if (TEMPLATE(T, poly_is_zero) (f_d, ctx))
    {
        TEMPLATE(T, poly_factor_t) new_res;
        TEMPLATE(T, poly_t) h;

        /* We can do this since deg is a multiple of p in this case */
#if defined(FQ_NMOD_POLY_FACTOR_H) || defined(FQ_ZECH_POLY_FACTOR_H)
        p_ui = TEMPLATE(T, ctx_prime)(ctx);
#else
        p_ui = fmpz_get_ui(TEMPLATE(T, ctx_prime)(ctx));
#endif

        TEMPLATE(T, poly_init) (h, ctx);

        for (i = 0; i <= deg / p_ui; i++)   /* this will be an integer since f'=0 */
        {
            TEMPLATE(T, poly_get_coeff) (x, f, i * p_ui, ctx);
            TEMPLATE(T, pth_root) (x, x, ctx);
            TEMPLATE(T, poly_set_coeff) (h, i, x, ctx);
        }

        /* Now run squarefree on h, and return it to the pth power */
        TEMPLATE(T, poly_factor_init) (new_res, ctx);

        TEMPLATE(T, poly_factor_squarefree) (new_res, h, ctx);
        TEMPLATE(T, poly_factor_pow) (new_res, p_ui, ctx);

        TEMPLATE(T, poly_factor_concat) (res, new_res, ctx);
        TEMPLATE(T, poly_clear) (h, ctx);
        TEMPLATE(T, poly_factor_clear) (new_res, ctx);
    }
    else
    {
        TEMPLATE(T, poly_t) h, z;

        TEMPLATE(T, poly_init) (r, ctx);

        TEMPLATE(T, poly_gcd) (g, f, f_d, ctx);
        TEMPLATE(T, poly_divrem) (g_1, r, f, g, ctx);

        i = 1;

        TEMPLATE(T, poly_init) (h, ctx);
        TEMPLATE(T, poly_init) (z, ctx);

        /* Case 2 */
        while (g_1->length > 1)
        {
            TEMPLATE(T, poly_gcd) (h, g_1, g, ctx);
            TEMPLATE(T, poly_divrem) (z, r, g_1, h, ctx);

            /* out <- out.z */
            if (z->length > 1)
            {
                TEMPLATE(T, poly_factor_insert) (res, z, 1, ctx);
                TEMPLATE(T, poly_make_monic) (res->poly + (res->num - 1),
                                              res->poly + (res->num - 1), ctx);
                if (res->num)
                    res->exp[res->num - 1] *= i;
            }

            i++;
            TEMPLATE(T, poly_set) (g_1, h, ctx);
            TEMPLATE(T, poly_divrem) (g, r, g, h, ctx);
        }

        TEMPLATE(T, poly_clear) (h, ctx);
        TEMPLATE(T, poly_clear) (z, ctx);
        TEMPLATE(T, poly_clear) (r, ctx);

        TEMPLATE(T, poly_make_monic) (g, g, ctx);

        if (g->length > 1)
        {
            /* so now we multiply res with squarefree(g^1/p) ^ p  */
            TEMPLATE(T, poly_t) g_p;    /* g^(1/p) */
            TEMPLATE(T, poly_factor_t) new_res_2;

            TEMPLATE(T, poly_init) (g_p, ctx);

#if defined(FQ_NMOD_POLY_FACTOR_H) || defined(FQ_ZECH_POLY_FACTOR_H)
            p_ui = TEMPLATE(T, ctx_prime)(ctx);
#else
            p_ui = fmpz_get_ui(TEMPLATE(T, ctx_prime)(ctx));
#endif

            for (i = 0; i <= TEMPLATE(T, poly_degree) (g, ctx) / p_ui; i++)
            {
                TEMPLATE(T, poly_get_coeff) (x, g, i * p_ui, ctx);
                TEMPLATE(T, pth_root) (x, x, ctx);
                TEMPLATE(T, poly_set_coeff) (g_p, i, x, ctx);
            }

            TEMPLATE(T, poly_factor_init) (new_res_2, ctx);

            /* squarefree(g^(1/p)) */
            TEMPLATE(T, poly_factor_squarefree) (new_res_2, g_p, ctx);
            TEMPLATE(T, poly_factor_pow) (new_res_2, p_ui, ctx);

            TEMPLATE(T, poly_factor_concat) (res, new_res_2, ctx);
            TEMPLATE(T, poly_clear) (g_p, ctx);
            TEMPLATE(T, poly_factor_clear) (new_res_2, ctx);
        }
    }

    TEMPLATE(T, clear) (x, ctx);
    TEMPLATE(T, poly_clear) (g_1, ctx);
    TEMPLATE(T, poly_clear) (f_d, ctx);
    TEMPLATE(T, poly_clear) (g, ctx);
}


#endif