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"

#include "perm.h"

static void
TEMPLATE(T, to_mat_col) (TEMPLATE(T, mat_t) mat, slong col,
                         TEMPLATE(T, poly_t) poly,
                         const TEMPLATE(T, ctx_t) ctx)
{
    slong i;

    for (i = 0; i < poly->length; i++)
        TEMPLATE(T, set) (TEMPLATE(T, mat_entry) (mat, i, col),
                          poly->coeffs + i, ctx);

    for (; i < mat->r; i++)
        TEMPLATE(T, zero) (TEMPLATE(T, mat_entry) (mat, i, col), ctx);

}

static void
TEMPLATE(T, mat_col_to_shifted) (TEMPLATE(T, poly_t) poly,
                                 TEMPLATE(T, mat_t) mat,
                                 slong col, slong * shift,
                                 const TEMPLATE(T, ctx_t) ctx)
{
    slong i, j, rows = mat->r;

    TEMPLATE(T, poly_fit_length) (poly, rows, ctx);

    for (i = 0, j = 0; j < rows; j++)
    {
        if (shift[j])
            TEMPLATE(T, zero) (poly->coeffs + j, ctx);
        else
        {
            TEMPLATE(T, set) (poly->coeffs + j,
                              TEMPLATE(T, mat_entry) (mat, i, col), ctx);
            i++;
        }
    }

    _TEMPLATE(T, poly_set_length) (poly, rows, ctx);
    _TEMPLATE(T, poly_normalise) (poly, ctx);
}

static void
__TEMPLATE(T, poly_factor_berlekamp) (TEMPLATE(T, poly_factor_t) factors,
                                      flint_rand_t state,
                                      const TEMPLATE(T, poly_t) f,
                                      const TEMPLATE(T, ctx_t) ctx)
{
    const slong n = TEMPLATE(T, poly_degree) (f, ctx);

    TEMPLATE(T, poly_factor_t) fac1, fac2;
    TEMPLATE(T, poly_t) x, x_q;
    TEMPLATE(T, poly_t) x_qi, x_qi2;
    TEMPLATE(T, poly_t) Q, r;

    TEMPLATE(T, mat_t) matrix;
    TEMPLATE(T, t) mul, coeff, neg_one;
    fmpz_t q, s, pow;
    slong i, nullity, col, row;
    slong *shift;

    TEMPLATE(T, poly_t) * basis;

    if (f->length <= 2)
    {
        TEMPLATE(T, poly_factor_insert) (factors, f, 1, ctx);
        return;
    }

    TEMPLATE(T, init) (coeff, ctx);
    TEMPLATE(T, init) (neg_one, ctx);
    TEMPLATE(T, init) (mul, ctx);

    fmpz_init(q);
    TEMPLATE(T, ctx_order) (q, ctx);

    TEMPLATE(T, one) (neg_one, ctx);
    TEMPLATE(T, neg) (neg_one, neg_one, ctx);


    /* s = q - 1 */
    fmpz_init_set(s, q);
    fmpz_sub_ui(s, s, 1);

    /* pow = (q-1)/2 */
    fmpz_init(pow);
#if defined(FQ_NMOD_POLY_FACTOR_H) || defined(FQ_ZECH_POLY_FACTOR_H)
    if (TEMPLATE(T, ctx_prime)(ctx) > UWORD(3))
    {
#else
    if (fmpz_cmp_ui(TEMPLATE(T, ctx_prime)(ctx), 3) > 0)
    {
#endif
        fmpz_set(pow, s);
        fmpz_divexact_ui(pow, pow, 2);
    }

    /* Step 1, compute x^q mod f in F_p[X]/<f> */
    TEMPLATE(T, poly_init) (x, ctx);
    TEMPLATE(T, poly_init) (x_q, ctx);

    TEMPLATE(T, poly_gen) (x, ctx);
    TEMPLATE(T, poly_powmod_fmpz_binexp) (x_q, x, q, f, ctx);
    TEMPLATE(T, poly_clear) (x, ctx);

    /* Step 2, compute the matrix for the Berlekamp Map */
    TEMPLATE(T, mat_init) (matrix, n, n, ctx);
    TEMPLATE(T, poly_init) (x_qi, ctx);
    TEMPLATE(T, poly_init) (x_qi2, ctx);
    TEMPLATE(T, poly_one) (x_qi, ctx);

    for (i = 0; i < n; i++)
    {
        /* Q - I */
        TEMPLATE(T, poly_set) (x_qi2, x_qi, ctx);
        TEMPLATE(T, poly_get_coeff) (coeff, x_qi2, i, ctx);
        TEMPLATE(T, sub_one) (coeff, coeff, ctx);
        TEMPLATE(T, poly_set_coeff) (x_qi2, i, coeff, ctx);
        TEMPLATE(T, to_mat_col) (matrix, i, x_qi2, ctx);
        TEMPLATE(T, poly_mulmod) (x_qi, x_qi, x_q, f, ctx);
    }

    TEMPLATE(T, poly_clear) (x_q, ctx);
    TEMPLATE(T, poly_clear) (x_qi, ctx);
    TEMPLATE(T, poly_clear) (x_qi2, ctx);

    /* Row reduce Q - I */
    nullity = n - TEMPLATE(T, mat_rref) (matrix, matrix, ctx);

    /* Find a basis for the nullspace */
    basis = flint_malloc(nullity * sizeof(TEMPLATE(T, poly_t)));
    shift = (slong *) flint_calloc(n, sizeof(slong));

    col = 1;                    /* first column is always zero */
    row = 0;
    shift[0] = 1;

    for (i = 1; i < nullity; i++)
    {
        TEMPLATE(T, poly_init) (basis[i], ctx);
        while (!TEMPLATE(T, is_zero)
               (TEMPLATE(T, mat_entry) (matrix, row, col), ctx))
        {
            row++;
            col++;
        }
        TEMPLATE(T, mat_col_to_shifted) (basis[i], matrix, col, shift, ctx);
        TEMPLATE(T, poly_set_coeff) (basis[i], col, neg_one, ctx);
        shift[col] = 1;
        col++;
    }

    flint_free(shift);
    TEMPLATE(T, mat_clear) (matrix, ctx);

    /* we are done */
    if (nullity == 1)
    {
        TEMPLATE(T, poly_factor_insert) (factors, f, 1, ctx);
    }
    else
    {
        /* Generate random linear combinations */
        TEMPLATE(T, poly_t) factor, b, power, g;
        TEMPLATE(T, poly_init) (factor, ctx);
        TEMPLATE(T, poly_init) (b, ctx);
        TEMPLATE(T, poly_init) (power, ctx);
        TEMPLATE(T, poly_init) (g, ctx);

        while (1)
        {
            do
            {
                TEMPLATE(T, poly_zero) (factor, ctx);
                for (i = 1; i < nullity; i++)
                {
                    TEMPLATE(T, randtest) (mul, state, ctx);
                    TEMPLATE(T, TEMPLATE(poly_scalar_mul, T)) (b, basis[i],
                                                               mul, ctx);
                    TEMPLATE(T, poly_add) (factor, factor, b, ctx);
                }

                TEMPLATE(T, randtest) (coeff, state, ctx);
                TEMPLATE(T, poly_set_coeff) (factor, 0, coeff, ctx);
                if (!TEMPLATE(T, poly_is_zero) (factor, ctx))
                    TEMPLATE(T, poly_make_monic) (factor, factor, ctx);
            }
            while (TEMPLATE(T, poly_is_zero) (factor, ctx) ||
                   (factor->length < 2
                    && TEMPLATE(T, is_one) (factor->coeffs, ctx)));

            TEMPLATE(T, poly_gcd) (g, f, factor, ctx);

            if (TEMPLATE(T, poly_length) (g, ctx) != 1)
                break;

#if defined(FQ_NMOD_POLY_FACTOR_H) || defined(FQ_ZECH_POLY_FACTOR_H)
            if (TEMPLATE(T, ctx_prime)(ctx) > UWORD(3))
#else
            if (fmpz_cmp_ui(TEMPLATE(T, ctx_prime)(ctx), 3) > 0)
#endif
                TEMPLATE(T, poly_powmod_fmpz_binexp) (power, factor, pow, f,
                                                      ctx);
            else
                TEMPLATE(T, poly_set) (power, factor, ctx);

            TEMPLATE(T, sub_one) (power->coeffs, power->coeffs, ctx);

            _TEMPLATE(T, poly_normalise) (power, ctx);
            TEMPLATE(T, poly_gcd) (g, power, f, ctx);

            if (TEMPLATE(T, poly_length) (g, ctx) != 1)
                break;
        }

        TEMPLATE(T, poly_clear) (power, ctx);
        TEMPLATE(T, poly_clear) (factor, ctx);
        TEMPLATE(T, poly_clear) (b, ctx);

        if (!TEMPLATE(T, poly_is_zero) (g, ctx))
            TEMPLATE(T, poly_make_monic) (g, g, ctx);

        TEMPLATE(T, poly_factor_init) (fac1, ctx);
        TEMPLATE(T, poly_factor_init) (fac2, ctx);
        __TEMPLATE(T, poly_factor_berlekamp) (fac1, state, g, ctx);
        TEMPLATE(T, poly_init) (Q, ctx);
        TEMPLATE(T, poly_init) (r, ctx);
        TEMPLATE(T, poly_divrem) (Q, r, f, g, ctx);
        TEMPLATE(T, poly_clear) (r, ctx);

        if (!TEMPLATE(T, poly_is_zero) (Q, ctx))
            TEMPLATE(T, poly_make_monic) (Q, Q, ctx);

        __TEMPLATE(T, poly_factor_berlekamp) (fac2, state, Q, ctx);
        TEMPLATE(T, poly_factor_concat) (factors, fac1, ctx);
        TEMPLATE(T, poly_factor_concat) (factors, fac2, ctx);
        TEMPLATE(T, poly_factor_clear) (fac1, ctx);
        TEMPLATE(T, poly_factor_clear) (fac2, ctx);
        TEMPLATE(T, poly_clear) (Q, ctx);
        TEMPLATE(T, poly_clear) (g, ctx);
    }

    for (i = 1; i < nullity; i++)
        TEMPLATE(T, poly_clear) (basis[i], ctx);
    flint_free(basis);

    TEMPLATE(T, clear) (coeff, ctx);
    TEMPLATE(T, clear) (neg_one, ctx);
    TEMPLATE(T, clear) (mul, ctx);
    fmpz_clear(pow);
    fmpz_clear(q);
    fmpz_clear(s);
}

void
TEMPLATE(T, poly_factor_berlekamp) (TEMPLATE(T, poly_factor_t) factors,
                                    const TEMPLATE(T, poly_t) f,
                                    const TEMPLATE(T, ctx_t) ctx)
{
    slong i;
    flint_rand_t r;
    TEMPLATE(T, poly_t) v;
    TEMPLATE(T, poly_factor_t) sq_free;

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

    TEMPLATE(T, poly_make_monic) (v, f, ctx);

    /* compute squarefree factorisation */
    TEMPLATE(T, poly_factor_init) (sq_free, ctx);
    TEMPLATE(T, poly_factor_squarefree) (sq_free, v, ctx);

    /* run Berlekamp algorithm for all squarefree factors */
    flint_rand_init(r);
    for (i = 0; i < sq_free->num; i++)
    {
        __TEMPLATE(T, poly_factor_berlekamp) (factors, r, sq_free->poly + i,
                                              ctx);
    }
    flint_rand_clear(r);

    /* compute multiplicities of factors in f */
    for (i = 0; i < factors->num; i++)
        factors->exp[i] = TEMPLATE(T, poly_remove) (v, factors->poly + i, ctx);

    TEMPLATE(T, poly_clear) (v, ctx);
    TEMPLATE(T, poly_factor_clear) (sq_free, ctx);
}


#endif