flint-sys 0.9.0

Bindings to the FLINT C library
Documentation 
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/*
    Copyright (C) 2011 William Hart
    Copyright (C) 2012 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_mod.h"
#include "fmpz_mod_poly.h"

slong _fmpz_mod_poly_gcdinv_f(fmpz_t f, fmpz *G, fmpz *S,
                           const fmpz *A, slong lenA, const fmpz *B, slong lenB,
                           const fmpz_mod_ctx_t ctx)
{
    fmpz *T;
    fmpz_t inv;
    slong ans = 0;

    fmpz_init(inv);
    fmpz_gcdinv(f, inv, A + (lenA - 1), fmpz_mod_ctx_modulus(ctx));

    if (fmpz_is_one(f))
    {
        if (lenB < 16)
        {
            ans = _fmpz_mod_poly_gcdinv_euclidean_f(f, G, S,
			                               A, lenA, B, lenB, inv, ctx);
        } else
        {
            T = _fmpz_vec_init(lenA - 1);

            ans = _fmpz_mod_poly_xgcd_f(f, G, T, S, B, lenB, A, lenA, inv, ctx);

            _fmpz_vec_clear(T, lenA - 1);
        }
    }

    fmpz_clear(inv);

    return ans;
}

void fmpz_mod_poly_gcdinv_f(fmpz_t f, fmpz_mod_poly_t G, fmpz_mod_poly_t S,
                            const fmpz_mod_poly_t A, const fmpz_mod_poly_t B,
                                                      const fmpz_mod_ctx_t ctx)
{
    const slong lenA = A->length, lenB = B->length;

    if (lenB < 2)
    {
        flint_throw(FLINT_ERROR, "Exception (fmpz_mod_poly_gcdinv). lenB < 2.\n");
    }
    if (lenA >= lenB)
    {
        fmpz_mod_poly_t T;

        fmpz_mod_poly_init(T, ctx);
        fmpz_mod_poly_rem_f(f, T, A, B, ctx);

        if (fmpz_is_one(f))
           fmpz_mod_poly_gcdinv_f(f, G, S, T, B, ctx);

        fmpz_mod_poly_clear(T, ctx);

        return;
    }

    if (lenA == 0)
    {
        fmpz_mod_poly_zero(G, ctx);
        fmpz_mod_poly_zero(S, ctx);
        fmpz_one(f);
    }
    else
    {
        fmpz *g, *s;
        slong lenG;

        if (G == A || G == B)
        {
            g = _fmpz_vec_init(lenA);
        }
        else
        {
            fmpz_mod_poly_fit_length(G, lenA, ctx);
            g = G->coeffs;
        }
        if (S == A || S == B)
        {
            s = _fmpz_vec_init(lenB - 1);
        }
        else
        {
            fmpz_mod_poly_fit_length(S, lenB - 1, ctx);
            s = S->coeffs;
        }

        lenG = _fmpz_mod_poly_gcdinv_f(f, g, s,
                  A->coeffs, lenA, B->coeffs, lenB, ctx);

        if (G == A || G == B)
        {
            _fmpz_vec_clear(G->coeffs, G->alloc);
            G->coeffs = g;
            G->alloc  = lenA;
        }
        if (S == A || S == B)
        {
            _fmpz_vec_clear(S->coeffs, S->alloc);
            S->coeffs = s;
            S->alloc  = lenB - 1;
        }

        if (fmpz_is_one(f))
        {
            _fmpz_mod_poly_set_length(G, lenG);
            _fmpz_mod_poly_set_length(S, lenB - lenG);
            _fmpz_mod_poly_normalise(S);

            if (!fmpz_is_one(fmpz_mod_poly_lead(G, ctx)))
            {
               fmpz_t inv;

               fmpz_init(inv);
               fmpz_gcdinv(f, inv, fmpz_mod_poly_lead(G, ctx),
                                                    fmpz_mod_ctx_modulus(ctx));
               fmpz_mod_poly_scalar_mul_fmpz(G, G, inv, ctx);
               fmpz_mod_poly_scalar_mul_fmpz(S, S, inv, ctx);
               fmpz_clear(inv);
            }
        }
    }
}