833 lines
29 KiB
C
833 lines
29 KiB
C
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/*=============================================================================
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This file is part of FLINT.
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FLINT is free software; you can redistribute it and/or modify
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it under the terms of the GNU General Public License as published by
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the Free Software Foundation; either version 2 of the License, or
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(at your option) any later version.
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FLINT is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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GNU General Public License for more details.
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You should have received a copy of the GNU General Public License
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along with FLINT; if not, write to the Free Software
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Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
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=============================================================================*/
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/******************************************************************************
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Copyright (C) 2011 Sebastian Pancratz
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******************************************************************************/
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#ifndef FMPZ_MOD_POLY_H
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#define FMPZ_MOD_POLY_H
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#undef ulong
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#define ulong ulongxx /* interferes with system includes */
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#include <stdio.h>
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#undef ulong
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#include <gmp.h>
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#define ulong mp_limb_t
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#include "flint.h"
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#include "fmpz.h"
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#include "fmpz_poly.h"
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#include "fmpz_mat.h"
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#ifdef __cplusplus
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extern "C" {
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#endif
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/* Type definitions *********************************************************/
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typedef struct
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{
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fmpz * coeffs;
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slong alloc;
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slong length;
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fmpz p;
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} fmpz_mod_poly_struct;
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typedef fmpz_mod_poly_struct fmpz_mod_poly_t[1];
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/* Initialisation and memory management *************************************/
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void fmpz_mod_poly_init(fmpz_mod_poly_t poly, const fmpz_t p);
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void fmpz_mod_poly_init2(fmpz_mod_poly_t poly, const fmpz_t p, slong alloc);
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void fmpz_mod_poly_clear(fmpz_mod_poly_t poly);
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void fmpz_mod_poly_realloc(fmpz_mod_poly_t poly, slong alloc);
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void fmpz_mod_poly_fit_length(fmpz_mod_poly_t poly, slong len);
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/* Normalisation and truncation *********************************************/
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void _fmpz_mod_poly_normalise(fmpz_mod_poly_t poly);
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static __inline__
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void _fmpz_mod_poly_set_length(fmpz_mod_poly_t poly, slong len)
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{
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if (poly->length > len)
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{
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slong i;
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for (i = len; i < poly->length; i++)
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_fmpz_demote(poly->coeffs + i);
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}
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poly->length = len;
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}
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static __inline__
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void fmpz_mod_poly_truncate(fmpz_mod_poly_t poly, slong len)
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{
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if (poly->length > len)
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{
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slong i;
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for (i = len; i < poly->length; i++)
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_fmpz_demote(poly->coeffs + i);
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poly->length = len;
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_fmpz_mod_poly_normalise(poly);
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}
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}
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/* Randomisation ************************************************************/
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void
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fmpz_mod_poly_randtest(fmpz_mod_poly_t f, flint_rand_t state, slong len);
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void
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fmpz_mod_poly_randtest_irreducible(fmpz_mod_poly_t f,
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flint_rand_t state, slong len);
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void
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fmpz_mod_poly_randtest_not_zero(fmpz_mod_poly_t f,
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flint_rand_t state, slong len);
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void
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fmpz_mod_poly_randtest_monic(fmpz_mod_poly_t f, flint_rand_t state, slong len);
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void
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fmpz_mod_poly_randtest_monic_irreducible(fmpz_mod_poly_t f,
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flint_rand_t state, slong len);
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void
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fmpz_mod_poly_randtest_trinomial(fmpz_mod_poly_t f, flint_rand_t state, slong len);
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int
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fmpz_mod_poly_randtest_trinomial_irreducible(fmpz_mod_poly_t f,
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flint_rand_t state, slong len,
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slong max_attempts);
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void
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fmpz_mod_poly_randtest_pentomial(fmpz_mod_poly_t f, flint_rand_t state, slong len);
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int
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fmpz_mod_poly_randtest_pentomial_irreducible(fmpz_mod_poly_t f,
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flint_rand_t state, slong len,
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slong max_attempts);
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void
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fmpz_mod_poly_randtest_sparse_irreducible(fmpz_mod_poly_t poly,
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flint_rand_t state, slong len);
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/* Attributes ***************************************************************/
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#define fmpz_mod_poly_modulus(poly) (&((poly)->p))
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static __inline__
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slong fmpz_mod_poly_degree(const fmpz_mod_poly_t poly)
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{
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return poly->length - 1;
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}
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static __inline__
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slong fmpz_mod_poly_length(const fmpz_mod_poly_t poly)
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{
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return poly->length;
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}
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static __inline__
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fmpz * fmpz_mod_poly_lead(const fmpz_mod_poly_t poly)
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{
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if (poly->length)
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return poly->coeffs + (poly->length - 1);
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else
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return NULL;
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}
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/* Assignment and basic manipulation ****************************************/
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void fmpz_mod_poly_set(fmpz_mod_poly_t poly1, const fmpz_mod_poly_t poly2);
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void fmpz_mod_poly_swap(fmpz_mod_poly_t poly1, fmpz_mod_poly_t poly2);
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void _fmpz_mod_poly_reverse(fmpz * res, const fmpz * poly, slong len, slong n);
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void fmpz_mod_poly_reverse(fmpz_mod_poly_t res, const fmpz_mod_poly_t poly, slong n);
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static __inline__
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void fmpz_mod_poly_zero(fmpz_mod_poly_t poly)
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{
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_fmpz_mod_poly_set_length(poly, 0);
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}
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void fmpz_mod_poly_zero_coeffs(fmpz_mod_poly_t poly, slong i, slong j);
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/* Conversion ***************************************************************/
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static __inline__
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void fmpz_mod_poly_set_ui(fmpz_mod_poly_t f, ulong x)
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{
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if (x == 0)
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{
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fmpz_mod_poly_zero(f);
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}
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else
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{
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fmpz_mod_poly_fit_length(f, 1);
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_fmpz_mod_poly_set_length(f, 1);
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fmpz_set_ui(f->coeffs, x);
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fmpz_mod(f->coeffs, f->coeffs, &(f->p));
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_fmpz_mod_poly_normalise(f);
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}
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}
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void fmpz_mod_poly_set_fmpz(fmpz_mod_poly_t poly, const fmpz_t c);
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void fmpz_mod_poly_set_fmpz_poly(fmpz_mod_poly_t f, const fmpz_poly_t g);
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void fmpz_mod_poly_get_fmpz_poly(fmpz_poly_t f, const fmpz_mod_poly_t g);
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/* Comparison ***************************************************************/
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static __inline__
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int fmpz_mod_poly_equal(const fmpz_mod_poly_t poly1,
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const fmpz_mod_poly_t poly2)
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{
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return fmpz_poly_equal((fmpz_poly_struct *) poly1,
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(fmpz_poly_struct *) poly2);
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}
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static __inline__
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int fmpz_mod_poly_is_zero(const fmpz_mod_poly_t poly)
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{
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return (poly->length == 0);
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}
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/* Getting and setting coefficients *****************************************/
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void fmpz_mod_poly_set_coeff_fmpz(fmpz_mod_poly_t poly, slong n, const fmpz_t x);
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void fmpz_mod_poly_set_coeff_ui(fmpz_mod_poly_t poly, slong n, ulong x);
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static __inline__
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void fmpz_mod_poly_get_coeff_fmpz(fmpz_t x, const fmpz_mod_poly_t poly, slong n)
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{
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if (n < poly->length)
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fmpz_set(x, poly->coeffs + n);
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else
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fmpz_zero(x);
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}
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static __inline__ void fmpz_mod_poly_set_coeff_mpz(fmpz_mod_poly_t poly, slong n,
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const mpz_t x)
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{
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fmpz_t t;
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fmpz_init_set_readonly(t, x);
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fmpz_mod_poly_set_coeff_fmpz(poly, n, t);
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fmpz_clear_readonly(t);
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}
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static __inline__ void fmpz_mod_poly_get_coeff_mpz(mpz_t x, const fmpz_mod_poly_t poly, slong n)
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{
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fmpz_t t;
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fmpz_init(t);
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fmpz_mod_poly_get_coeff_fmpz(t, poly, n);
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fmpz_get_mpz(x, t);
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fmpz_clear(t);
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}
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/* Shifting *****************************************************************/
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void _fmpz_mod_poly_shift_left(fmpz * res, const fmpz * poly, slong len, slong n);
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void fmpz_mod_poly_shift_left(fmpz_mod_poly_t f,
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const fmpz_mod_poly_t g, slong n);
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void _fmpz_mod_poly_shift_right(fmpz * res, const fmpz * poly, slong len, slong n);
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void fmpz_mod_poly_shift_right(fmpz_mod_poly_t f,
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const fmpz_mod_poly_t g, slong n);
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/* Addition and subtraction *************************************************/
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void _fmpz_mod_poly_add(fmpz *res, const fmpz *poly1, slong len1,
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const fmpz *poly2, slong len2, const fmpz_t p);
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void fmpz_mod_poly_add(fmpz_mod_poly_t res,
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const fmpz_mod_poly_t poly1, const fmpz_mod_poly_t poly2);
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void _fmpz_mod_poly_sub(fmpz *res, const fmpz *poly1, slong len1,
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const fmpz *poly2, slong len2, const fmpz_t p);
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void fmpz_mod_poly_sub(fmpz_mod_poly_t res,
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const fmpz_mod_poly_t poly1, const fmpz_mod_poly_t poly2);
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void _fmpz_mod_poly_neg(fmpz *res, const fmpz *poly, slong len, const fmpz_t p);
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void fmpz_mod_poly_neg(fmpz_mod_poly_t res, const fmpz_mod_poly_t poly);
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/* Scalar multiplication ****************************************************/
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void _fmpz_mod_poly_scalar_mul_fmpz(fmpz *res, const fmpz *poly, slong len,
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const fmpz_t x, const fmpz_t p);
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void fmpz_mod_poly_scalar_mul_fmpz(fmpz_mod_poly_t res,
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const fmpz_mod_poly_t poly, const fmpz_t x);
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/* Multiplication ***********************************************************/
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void _fmpz_mod_poly_mul(fmpz *res, const fmpz *poly1, slong len1,
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const fmpz *poly2, slong len2, const fmpz_t p);
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void fmpz_mod_poly_mul(fmpz_mod_poly_t res,
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const fmpz_mod_poly_t poly1, const fmpz_mod_poly_t poly2);
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void _fmpz_mod_poly_mullow(fmpz *res, const fmpz *poly1, slong len1,
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const fmpz *poly2, slong len2,
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const fmpz_t p, slong n);
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void fmpz_mod_poly_mullow(fmpz_mod_poly_t res,
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const fmpz_mod_poly_t poly1, const fmpz_mod_poly_t poly2, slong n);
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void _fmpz_mod_poly_sqr(fmpz *res, const fmpz *poly, slong len, const fmpz_t p);
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void fmpz_mod_poly_sqr(fmpz_mod_poly_t res, const fmpz_mod_poly_t poly);
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void _fmpz_mod_poly_mulmod(fmpz * res, const fmpz * poly1, slong len1,
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const fmpz * poly2, slong len2, const fmpz * f,
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slong lenf, const fmpz_t p);
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void fmpz_mod_poly_mulmod(fmpz_mod_poly_t res, const fmpz_mod_poly_t poly1,
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const fmpz_mod_poly_t poly2, const fmpz_mod_poly_t f);
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void _fmpz_mod_poly_mulmod_preinv(fmpz * res, const fmpz * poly1, slong len1,
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const fmpz * poly2, slong len2, const fmpz * f, slong lenf,
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const fmpz* finv, slong lenfinv, const fmpz_t p);
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void
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fmpz_mod_poly_mulmod_preinv(fmpz_mod_poly_t res, const fmpz_mod_poly_t poly1,
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const fmpz_mod_poly_t poly2, const fmpz_mod_poly_t f,
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const fmpz_mod_poly_t finv);
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/* Powering *****************************************************************/
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void _fmpz_mod_poly_pow(fmpz *rop, const fmpz *op, slong len, ulong e,
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const fmpz_t p);
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void fmpz_mod_poly_pow(fmpz_mod_poly_t rop, const fmpz_mod_poly_t op, ulong e);
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void _fmpz_mod_poly_pow_trunc(fmpz * res, const fmpz * poly,
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ulong e, slong trunc, const fmpz_t p);
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void fmpz_mod_poly_pow_trunc(fmpz_mod_poly_t res,
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const fmpz_mod_poly_t poly, ulong e, slong trunc);
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|
|
||
|
|
void _fmpz_mod_poly_pow_trunc_binexp(fmpz * res, const fmpz * poly,
|
||
|
|
ulong e, slong trunc, const fmpz_t p);
|
||
|
|
|
||
|
|
void fmpz_mod_poly_pow_trunc_binexp(fmpz_mod_poly_t res,
|
||
|
|
const fmpz_mod_poly_t poly, ulong e, slong trunc);
|
||
|
|
|
||
|
|
void
|
||
|
|
_fmpz_mod_poly_powmod_ui_binexp(fmpz * res, const fmpz * poly,
|
||
|
|
ulong e, const fmpz * f, slong lenf, const fmpz_t p);
|
||
|
|
|
||
|
|
void
|
||
|
|
fmpz_mod_poly_powmod_ui_binexp(fmpz_mod_poly_t res,
|
||
|
|
const fmpz_mod_poly_t poly, ulong e,
|
||
|
|
const fmpz_mod_poly_t f);
|
||
|
|
|
||
|
|
|
||
|
|
void
|
||
|
|
_fmpz_mod_poly_powmod_ui_binexp_preinv(fmpz * res, const fmpz * poly,
|
||
|
|
ulong e, const fmpz * f, slong lenf,
|
||
|
|
const fmpz * finv, slong lenfinv, const fmpz_t p);
|
||
|
|
|
||
|
|
void
|
||
|
|
fmpz_mod_poly_powmod_ui_binexp_preinv(fmpz_mod_poly_t res,
|
||
|
|
const fmpz_mod_poly_t poly, ulong e,
|
||
|
|
const fmpz_mod_poly_t f, const fmpz_mod_poly_t finv);
|
||
|
|
|
||
|
|
void
|
||
|
|
_fmpz_mod_poly_powmod_fmpz_binexp(fmpz * res, const fmpz * poly,
|
||
|
|
const fmpz_t e, const fmpz * f,
|
||
|
|
slong lenf, const fmpz_t p);
|
||
|
|
|
||
|
|
void
|
||
|
|
fmpz_mod_poly_powmod_fmpz_binexp(fmpz_mod_poly_t res,
|
||
|
|
const fmpz_mod_poly_t poly, const fmpz_t e,
|
||
|
|
const fmpz_mod_poly_t f);
|
||
|
|
|
||
|
|
void
|
||
|
|
_fmpz_mod_poly_powmod_fmpz_binexp_preinv(fmpz * res, const fmpz * poly,
|
||
|
|
const fmpz_t e, const fmpz * f, slong lenf,
|
||
|
|
const fmpz* finv, slong lenfinv,
|
||
|
|
const fmpz_t p);
|
||
|
|
|
||
|
|
void
|
||
|
|
fmpz_mod_poly_powmod_fmpz_binexp_preinv(fmpz_mod_poly_t res,
|
||
|
|
const fmpz_mod_poly_t poly, const fmpz_t e,
|
||
|
|
const fmpz_mod_poly_t f, const fmpz_mod_poly_t finv);
|
||
|
|
|
||
|
|
void
|
||
|
|
_fmpz_mod_poly_powmod_x_fmpz_preinv(fmpz * res, const fmpz_t e, const fmpz * f,
|
||
|
|
slong lenf, const fmpz* finv, slong lenfinv,
|
||
|
|
const fmpz_t p);
|
||
|
|
|
||
|
|
void
|
||
|
|
fmpz_mod_poly_powmod_x_fmpz_preinv(fmpz_mod_poly_t res, const fmpz_t e,
|
||
|
|
const fmpz_mod_poly_t f, const fmpz_mod_poly_t finv);
|
||
|
|
|
||
|
|
/* Division *****************************************************************/
|
||
|
|
|
||
|
|
void _fmpz_mod_poly_divrem_basecase(fmpz * Q, fmpz * R,
|
||
|
|
const fmpz * A, slong lenA, const fmpz * B, slong lenB,
|
||
|
|
const fmpz_t invB, const fmpz_t p);
|
||
|
|
|
||
|
|
void fmpz_mod_poly_divrem_basecase(fmpz_mod_poly_t Q, fmpz_mod_poly_t R,
|
||
|
|
const fmpz_mod_poly_t A, const fmpz_mod_poly_t B);
|
||
|
|
|
||
|
|
void _fmpz_mod_poly_div_basecase(fmpz * Q, fmpz * R,
|
||
|
|
const fmpz * A, slong lenA, const fmpz * B, slong lenB,
|
||
|
|
const fmpz_t invB, const fmpz_t p);
|
||
|
|
|
||
|
|
void fmpz_mod_poly_div_basecase(fmpz_mod_poly_t Q,
|
||
|
|
const fmpz_mod_poly_t A, const fmpz_mod_poly_t B);
|
||
|
|
|
||
|
|
void
|
||
|
|
_fmpz_mod_poly_div_newton_n_preinv (fmpz* Q, const fmpz* A, slong lenA,
|
||
|
|
const fmpz* B, slong lenB, const fmpz* Binv,
|
||
|
|
slong lenBinv, const fmpz_t mod);
|
||
|
|
|
||
|
|
void
|
||
|
|
fmpz_mod_poly_div_newton_n_preinv(fmpz_mod_poly_t Q, const fmpz_mod_poly_t A,
|
||
|
|
const fmpz_mod_poly_t B, const fmpz_mod_poly_t Binv);
|
||
|
|
|
||
|
|
void
|
||
|
|
_fmpz_mod_poly_divrem_newton_n_preinv (fmpz* Q, fmpz* R, const fmpz* A,
|
||
|
|
slong lenA, const fmpz* B, slong lenB,
|
||
|
|
const fmpz* Binv, slong lenBinv, const fmpz_t mod);
|
||
|
|
|
||
|
|
void
|
||
|
|
fmpz_mod_poly_divrem_newton_n_preinv(fmpz_mod_poly_t Q, fmpz_mod_poly_t R,
|
||
|
|
const fmpz_mod_poly_t A, const fmpz_mod_poly_t B,
|
||
|
|
const fmpz_mod_poly_t Binv);
|
||
|
|
|
||
|
|
ulong fmpz_mod_poly_remove(fmpz_mod_poly_t f, const fmpz_mod_poly_t p);
|
||
|
|
|
||
|
|
void _fmpz_mod_poly_rem_basecase(fmpz * R,
|
||
|
|
const fmpz * A, slong lenA, const fmpz * B, slong lenB,
|
||
|
|
const fmpz_t invB, const fmpz_t p);
|
||
|
|
|
||
|
|
void fmpz_mod_poly_rem_basecase(fmpz_mod_poly_t R,
|
||
|
|
const fmpz_mod_poly_t A, const fmpz_mod_poly_t B);
|
||
|
|
|
||
|
|
void _fmpz_mod_poly_divrem_divconquer_recursive(fmpz * Q, fmpz * BQ, fmpz * W,
|
||
|
|
const fmpz * A, const fmpz * B, slong lenB,
|
||
|
|
const fmpz_t invB, const fmpz_t p);
|
||
|
|
|
||
|
|
void _fmpz_mod_poly_divrem_divconquer(fmpz * Q, fmpz * R,
|
||
|
|
const fmpz * A, slong lenA, const fmpz * B, slong lenB,
|
||
|
|
const fmpz_t invB, const fmpz_t p);
|
||
|
|
|
||
|
|
void fmpz_mod_poly_divrem_divconquer(fmpz_mod_poly_t Q, fmpz_mod_poly_t R,
|
||
|
|
const fmpz_mod_poly_t A, const fmpz_mod_poly_t B);
|
||
|
|
|
||
|
|
static __inline__
|
||
|
|
void _fmpz_mod_poly_divrem(fmpz *Q, fmpz *R,
|
||
|
|
const fmpz *A, slong lenA, const fmpz *B, slong lenB,
|
||
|
|
const fmpz_t invB, const fmpz_t p)
|
||
|
|
{
|
||
|
|
_fmpz_mod_poly_divrem_divconquer(Q, R, A, lenA, B, lenB, invB, p);
|
||
|
|
}
|
||
|
|
|
||
|
|
static __inline__
|
||
|
|
void fmpz_mod_poly_divrem(fmpz_mod_poly_t Q, fmpz_mod_poly_t R,
|
||
|
|
const fmpz_mod_poly_t A, const fmpz_mod_poly_t B)
|
||
|
|
{
|
||
|
|
fmpz_mod_poly_divrem_divconquer(Q, R, A, B);
|
||
|
|
}
|
||
|
|
|
||
|
|
void _fmpz_mod_poly_divrem_f(fmpz_t f, fmpz *Q, fmpz *R,
|
||
|
|
const fmpz *A, slong lenA,
|
||
|
|
const fmpz *B, slong lenB, const fmpz_t p);
|
||
|
|
|
||
|
|
void fmpz_mod_poly_divrem_f(fmpz_t f, fmpz_mod_poly_t Q, fmpz_mod_poly_t R,
|
||
|
|
const fmpz_mod_poly_t A, const fmpz_mod_poly_t B);
|
||
|
|
|
||
|
|
static __inline__
|
||
|
|
void _fmpz_mod_poly_rem(fmpz *R,
|
||
|
|
const fmpz *A, slong lenA, const fmpz *B, slong lenB,
|
||
|
|
const fmpz_t invB, const fmpz_t p)
|
||
|
|
{
|
||
|
|
fmpz *Q = _fmpz_vec_init(lenA - lenB + 1);
|
||
|
|
fmpz *T = _fmpz_vec_init(lenA);
|
||
|
|
|
||
|
|
if (lenA < lenB)
|
||
|
|
{
|
||
|
|
_fmpz_vec_set(R, A, lenA);
|
||
|
|
_fmpz_vec_zero(R + lenA, lenB - 1 - lenA);
|
||
|
|
} else
|
||
|
|
{
|
||
|
|
_fmpz_mod_poly_divrem_divconquer(Q, T, A, lenA, B, lenB, invB, p);
|
||
|
|
_fmpz_vec_set(R, T, lenB - 1);
|
||
|
|
}
|
||
|
|
|
||
|
|
_fmpz_vec_clear(T, lenA);
|
||
|
|
_fmpz_vec_clear(Q, lenA - lenB + 1);
|
||
|
|
}
|
||
|
|
|
||
|
|
static __inline__
|
||
|
|
void fmpz_mod_poly_rem(fmpz_mod_poly_t R,
|
||
|
|
const fmpz_mod_poly_t A, const fmpz_mod_poly_t B)
|
||
|
|
{
|
||
|
|
fmpz_mod_poly_t Q;
|
||
|
|
|
||
|
|
fmpz_mod_poly_init(Q, &(A->p));
|
||
|
|
fmpz_mod_poly_divrem(Q, R, A, B);
|
||
|
|
fmpz_mod_poly_clear(Q);
|
||
|
|
}
|
||
|
|
|
||
|
|
void _fmpz_mod_poly_div_newton_n_preinv (fmpz *Q, const fmpz* A, slong lenA,
|
||
|
|
const fmpz* B, slong lenB, const fmpz* Binv,
|
||
|
|
slong lenBinv, const fmpz_t p);
|
||
|
|
|
||
|
|
void fmpz_mod_poly_div_newton_n_preinv (fmpz_mod_poly_t Q, const fmpz_mod_poly_t A,
|
||
|
|
const fmpz_mod_poly_t B, const fmpz_mod_poly_t Binv);
|
||
|
|
|
||
|
|
|
||
|
|
void _fmpz_mod_poly_divrem_newton_n_preinv (fmpz* Q, fmpz* R, const fmpz* A,
|
||
|
|
slong lenA, const fmpz* B, slong lenB,
|
||
|
|
const fmpz* Binv, slong lenBinv, const fmpz_t p);
|
||
|
|
|
||
|
|
void fmpz_mod_poly_divrem_newton_n_preinv(fmpz_mod_poly_t Q, fmpz_mod_poly_t R,
|
||
|
|
const fmpz_mod_poly_t A, const fmpz_mod_poly_t B,
|
||
|
|
const fmpz_mod_poly_t Binv);
|
||
|
|
|
||
|
|
/* Power series inversion ***************************************************/
|
||
|
|
|
||
|
|
void
|
||
|
|
_fmpz_mod_poly_inv_series_newton(fmpz * Qinv, const fmpz * Q, slong n,
|
||
|
|
const fmpz_t cinv, const fmpz_t p);
|
||
|
|
|
||
|
|
void fmpz_mod_poly_inv_series_newton(fmpz_mod_poly_t Qinv,
|
||
|
|
const fmpz_mod_poly_t Q, slong n);
|
||
|
|
|
||
|
|
/* Greatest common divisor **************************************************/
|
||
|
|
|
||
|
|
void fmpz_mod_poly_make_monic(fmpz_mod_poly_t res, const fmpz_mod_poly_t poly);
|
||
|
|
|
||
|
|
slong _fmpz_mod_poly_gcd_euclidean(fmpz *G, const fmpz *A, slong lenA,
|
||
|
|
const fmpz *B, slong lenB,
|
||
|
|
const fmpz_t invB, const fmpz_t p);
|
||
|
|
|
||
|
|
void fmpz_mod_poly_gcd_euclidean(fmpz_mod_poly_t G,
|
||
|
|
const fmpz_mod_poly_t A,
|
||
|
|
const fmpz_mod_poly_t B);
|
||
|
|
|
||
|
|
static __inline__
|
||
|
|
slong _fmpz_mod_poly_gcd(fmpz *G, const fmpz *A, slong lenA,
|
||
|
|
const fmpz *B, slong lenB,
|
||
|
|
const fmpz_t invB, const fmpz_t p)
|
||
|
|
{
|
||
|
|
return _fmpz_mod_poly_gcd_euclidean(G, A, lenA, B, lenB, invB, p);
|
||
|
|
}
|
||
|
|
|
||
|
|
static __inline__
|
||
|
|
void fmpz_mod_poly_gcd(fmpz_mod_poly_t G,
|
||
|
|
const fmpz_mod_poly_t A, const fmpz_mod_poly_t B)
|
||
|
|
{
|
||
|
|
fmpz_mod_poly_gcd_euclidean(G, A, B);
|
||
|
|
}
|
||
|
|
|
||
|
|
slong _fmpz_mod_poly_gcd_euclidean_f(fmpz_t f, fmpz *G,
|
||
|
|
const fmpz *A, slong lenA,
|
||
|
|
const fmpz *B, slong lenB, const fmpz_t p);
|
||
|
|
|
||
|
|
void fmpz_mod_poly_gcd_euclidean_f(fmpz_t f, fmpz_mod_poly_t G,
|
||
|
|
const fmpz_mod_poly_t A,
|
||
|
|
const fmpz_mod_poly_t B);
|
||
|
|
|
||
|
|
static __inline__
|
||
|
|
slong _fmpz_mod_poly_gcd_f(fmpz_t f, fmpz *G,
|
||
|
|
const fmpz *A, slong lenA,
|
||
|
|
const fmpz *B, slong lenB, const fmpz_t p)
|
||
|
|
{
|
||
|
|
return _fmpz_mod_poly_gcd_euclidean_f(f, G, A, lenA, B, lenB, p);
|
||
|
|
}
|
||
|
|
|
||
|
|
static __inline__
|
||
|
|
void fmpz_mod_poly_gcd_f(fmpz_t f, fmpz_mod_poly_t G,
|
||
|
|
const fmpz_mod_poly_t A, const fmpz_mod_poly_t B)
|
||
|
|
{
|
||
|
|
fmpz_mod_poly_gcd_euclidean_f(f, G, A, B);
|
||
|
|
}
|
||
|
|
|
||
|
|
slong _fmpz_mod_poly_xgcd_euclidean(fmpz *G, fmpz *S, fmpz *T,
|
||
|
|
const fmpz *A, slong lenA,
|
||
|
|
const fmpz *B, slong lenB,
|
||
|
|
const fmpz_t invB, const fmpz_t p);
|
||
|
|
|
||
|
|
void fmpz_mod_poly_xgcd_euclidean(fmpz_mod_poly_t G,
|
||
|
|
fmpz_mod_poly_t S, fmpz_mod_poly_t T,
|
||
|
|
const fmpz_mod_poly_t A, const fmpz_mod_poly_t B);
|
||
|
|
|
||
|
|
static __inline__ slong
|
||
|
|
_fmpz_mod_poly_xgcd(fmpz *G, fmpz *S, fmpz *T,
|
||
|
|
const fmpz *A, slong lenA, const fmpz *B, slong lenB,
|
||
|
|
const fmpz_t invB, const fmpz_t p)
|
||
|
|
{
|
||
|
|
return _fmpz_mod_poly_xgcd_euclidean(G, S, T, A, lenA, B, lenB, invB, p);
|
||
|
|
}
|
||
|
|
|
||
|
|
static __inline__ void
|
||
|
|
fmpz_mod_poly_xgcd(fmpz_mod_poly_t G, fmpz_mod_poly_t S, fmpz_mod_poly_t T,
|
||
|
|
const fmpz_mod_poly_t A, const fmpz_mod_poly_t B)
|
||
|
|
{
|
||
|
|
fmpz_mod_poly_xgcd_euclidean(G, S, T, A, B);
|
||
|
|
}
|
||
|
|
|
||
|
|
slong _fmpz_mod_poly_gcdinv(fmpz *G, fmpz *S,
|
||
|
|
const fmpz *A, slong lenA, const fmpz *B, slong lenB,
|
||
|
|
const fmpz_t p);
|
||
|
|
|
||
|
|
void fmpz_mod_poly_gcdinv(fmpz_mod_poly_t G, fmpz_mod_poly_t S,
|
||
|
|
const fmpz_mod_poly_t A, const fmpz_mod_poly_t B);
|
||
|
|
|
||
|
|
int _fmpz_mod_poly_invmod(fmpz *A,
|
||
|
|
const fmpz *B, slong lenB,
|
||
|
|
const fmpz *P, slong lenP, const fmpz_t p);
|
||
|
|
|
||
|
|
int fmpz_mod_poly_invmod(fmpz_mod_poly_t A,
|
||
|
|
const fmpz_mod_poly_t B, const fmpz_mod_poly_t P);
|
||
|
|
|
||
|
|
/* Derivative **************************************************************/
|
||
|
|
|
||
|
|
void _fmpz_mod_poly_derivative(fmpz *res, const fmpz *poly, slong len,
|
||
|
|
const fmpz_t p);
|
||
|
|
|
||
|
|
void fmpz_mod_poly_derivative(fmpz_mod_poly_t res, const fmpz_mod_poly_t poly);
|
||
|
|
|
||
|
|
/* Evaluation **************************************************************/
|
||
|
|
|
||
|
|
void _fmpz_mod_poly_evaluate_fmpz(fmpz_t res, const fmpz *poly, slong len,
|
||
|
|
const fmpz_t a, const fmpz_t p);
|
||
|
|
|
||
|
|
void fmpz_mod_poly_evaluate_fmpz(fmpz_t res,
|
||
|
|
const fmpz_mod_poly_t poly, const fmpz_t a);
|
||
|
|
|
||
|
|
fmpz_poly_struct ** _fmpz_mod_poly_tree_alloc(slong len);
|
||
|
|
|
||
|
|
void _fmpz_mod_poly_tree_free(fmpz_poly_struct ** tree, slong len);
|
||
|
|
|
||
|
|
void _fmpz_mod_poly_tree_build(fmpz_poly_struct ** tree,
|
||
|
|
const fmpz * roots, slong len, const fmpz_t mod);
|
||
|
|
|
||
|
|
void _fmpz_mod_poly_evaluate_fmpz_vec_iter(fmpz * ys, const fmpz * coeffs,
|
||
|
|
slong len, const fmpz * xs, slong n, const fmpz_t mod);
|
||
|
|
|
||
|
|
void fmpz_mod_poly_evaluate_fmpz_vec_iter(fmpz * ys,
|
||
|
|
const fmpz_mod_poly_t poly, const fmpz * xs, slong n);
|
||
|
|
|
||
|
|
void _fmpz_mod_poly_evaluate_fmpz_vec_fast_precomp(fmpz * vs,
|
||
|
|
const fmpz * poly, slong plen, fmpz_poly_struct * const * tree,
|
||
|
|
slong len, const fmpz_t mod);
|
||
|
|
|
||
|
|
void _fmpz_mod_poly_evaluate_fmpz_vec_fast(fmpz * ys,
|
||
|
|
const fmpz * poly, slong plen, const fmpz * xs, slong n, const fmpz_t mod);
|
||
|
|
|
||
|
|
void fmpz_mod_poly_evaluate_fmpz_vec_fast(fmpz * ys,
|
||
|
|
const fmpz_mod_poly_t poly, const fmpz * xs, slong n);
|
||
|
|
|
||
|
|
void _fmpz_mod_poly_evaluate_fmpz_vec(fmpz * ys, const fmpz * coeffs,
|
||
|
|
slong len, const fmpz * xs, slong n, const fmpz_t mod);
|
||
|
|
|
||
|
|
void fmpz_mod_poly_evaluate_fmpz_vec(fmpz * ys,
|
||
|
|
const fmpz_mod_poly_t poly, const fmpz * xs, slong n);
|
||
|
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|
||
|
|
|
||
|
|
|
||
|
|
/* Composition *************************************************************/
|
||
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|
|
||
|
|
void _fmpz_mod_poly_compose_horner(fmpz *res, const fmpz *poly1, slong len1,
|
||
|
|
const fmpz *poly2, slong len2,
|
||
|
|
const fmpz_t p);
|
||
|
|
|
||
|
|
void fmpz_mod_poly_compose_horner(fmpz_mod_poly_t res,
|
||
|
|
const fmpz_mod_poly_t poly1,
|
||
|
|
const fmpz_mod_poly_t poly2);
|
||
|
|
|
||
|
|
void _fmpz_mod_poly_compose_divconquer(fmpz *res,
|
||
|
|
const fmpz *poly1, slong len1,
|
||
|
|
const fmpz *poly2, slong len2,
|
||
|
|
const fmpz_t p);
|
||
|
|
|
||
|
|
void fmpz_mod_poly_compose_divconquer(fmpz_mod_poly_t res,
|
||
|
|
const fmpz_mod_poly_t poly1,
|
||
|
|
const fmpz_mod_poly_t poly2);
|
||
|
|
|
||
|
|
static __inline__
|
||
|
|
void _fmpz_mod_poly_compose(fmpz *res, const fmpz *poly1, slong len1,
|
||
|
|
const fmpz *poly2, slong len2,
|
||
|
|
const fmpz_t p)
|
||
|
|
{
|
||
|
|
_fmpz_mod_poly_compose_divconquer(res, poly1, len1, poly2, len2, p);
|
||
|
|
}
|
||
|
|
|
||
|
|
static __inline__
|
||
|
|
void fmpz_mod_poly_compose(fmpz_mod_poly_t res, const fmpz_mod_poly_t poly1,
|
||
|
|
const fmpz_mod_poly_t poly2)
|
||
|
|
{
|
||
|
|
fmpz_mod_poly_compose_divconquer(res, poly1, poly2);
|
||
|
|
}
|
||
|
|
|
||
|
|
/* Modular composition ******************************************************/
|
||
|
|
|
||
|
|
void
|
||
|
|
_fmpz_mod_poly_compose_mod(fmpz * res, const fmpz * f, slong lenf, const fmpz * g,
|
||
|
|
const fmpz * h, slong lenh, const fmpz_t p);
|
||
|
|
|
||
|
|
void
|
||
|
|
fmpz_mod_poly_compose_mod(fmpz_mod_poly_t res, const fmpz_mod_poly_t poly1,
|
||
|
|
const fmpz_mod_poly_t poly2, const fmpz_mod_poly_t poly3);
|
||
|
|
|
||
|
|
void
|
||
|
|
_fmpz_mod_poly_compose_mod_brent_kung(fmpz * res, const fmpz * poly1, slong len1,
|
||
|
|
const fmpz * poly2, const fmpz * poly3, slong len3, const fmpz_t p);
|
||
|
|
|
||
|
|
void
|
||
|
|
fmpz_mod_poly_compose_mod_brent_kung(fmpz_mod_poly_t res, const fmpz_mod_poly_t poly1,
|
||
|
|
const fmpz_mod_poly_t poly2, const fmpz_mod_poly_t poly3);
|
||
|
|
|
||
|
|
void
|
||
|
|
_fmpz_mod_poly_reduce_matrix_mod_poly (fmpz_mat_t A, const fmpz_mat_t B,
|
||
|
|
const fmpz_mod_poly_t f);
|
||
|
|
|
||
|
|
void
|
||
|
|
_fmpz_mod_poly_precompute_matrix (fmpz_mat_t A, const fmpz * poly1,
|
||
|
|
const fmpz * poly2, slong len2, const fmpz * poly2inv,
|
||
|
|
slong len2inv, const fmpz_t p);
|
||
|
|
|
||
|
|
void
|
||
|
|
fmpz_mod_poly_precompute_matrix(fmpz_mat_t A, const fmpz_mod_poly_t poly1,
|
||
|
|
const fmpz_mod_poly_t poly2, const fmpz_mod_poly_t poly2inv);
|
||
|
|
|
||
|
|
void
|
||
|
|
_fmpz_mod_poly_compose_mod_brent_kung_precomp_preinv(fmpz * res,
|
||
|
|
const fmpz * poly1, slong len1, const fmpz_mat_t A, const fmpz * poly3,
|
||
|
|
slong len3, const fmpz * poly3inv, slong len3inv, const fmpz_t p);
|
||
|
|
|
||
|
|
void
|
||
|
|
fmpz_mod_poly_compose_mod_brent_kung_precomp_preinv(fmpz_mod_poly_t res,
|
||
|
|
const fmpz_mod_poly_t poly1, const fmpz_mat_t A,
|
||
|
|
const fmpz_mod_poly_t poly3, const fmpz_mod_poly_t poly3inv);
|
||
|
|
|
||
|
|
void
|
||
|
|
_fmpz_mod_poly_compose_mod_brent_kung_preinv(fmpz * res, const fmpz * poly1,
|
||
|
|
slong len1, const fmpz * poly2, const fmpz * poly3, slong len3,
|
||
|
|
const fmpz * poly3inv, slong len3inv, const fmpz_t p);
|
||
|
|
|
||
|
|
void
|
||
|
|
fmpz_mod_poly_compose_mod_brent_kung_preinv(fmpz_mod_poly_t res,
|
||
|
|
const fmpz_mod_poly_t poly1, const fmpz_mod_poly_t poly2,
|
||
|
|
const fmpz_mod_poly_t poly3, const fmpz_mod_poly_t poly3inv);
|
||
|
|
|
||
|
|
void
|
||
|
|
_fmpz_mod_poly_compose_mod_horner(fmpz * res, const fmpz * f, slong lenf, const fmpz * g,
|
||
|
|
const fmpz * h, slong lenh, const fmpz_t p);
|
||
|
|
|
||
|
|
void
|
||
|
|
fmpz_mod_poly_compose_mod_horner(fmpz_mod_poly_t res, const fmpz_mod_poly_t poly1,
|
||
|
|
const fmpz_mod_poly_t poly2, const fmpz_mod_poly_t poly3);
|
||
|
|
|
||
|
|
/* Radix conversion *********************************************************/
|
||
|
|
|
||
|
|
typedef struct {
|
||
|
|
fmpz *V;
|
||
|
|
fmpz *W;
|
||
|
|
fmpz **Rpow;
|
||
|
|
fmpz **Rinv;
|
||
|
|
slong degR;
|
||
|
|
slong k;
|
||
|
|
fmpz invL;
|
||
|
|
} fmpz_mod_poly_radix_struct;
|
||
|
|
|
||
|
|
typedef fmpz_mod_poly_radix_struct fmpz_mod_poly_radix_t[1];
|
||
|
|
|
||
|
|
void _fmpz_mod_poly_radix_init(fmpz **Rpow, fmpz **Rinv,
|
||
|
|
const fmpz *R, slong lenR, slong k,
|
||
|
|
const fmpz_t invL, const fmpz_t p);
|
||
|
|
|
||
|
|
void fmpz_mod_poly_radix_init(fmpz_mod_poly_radix_t D,
|
||
|
|
const fmpz_mod_poly_t R, slong degF);
|
||
|
|
|
||
|
|
void fmpz_mod_poly_radix_clear(fmpz_mod_poly_radix_t D);
|
||
|
|
|
||
|
|
void _fmpz_mod_poly_radix(fmpz **B, const fmpz *F, fmpz **Rpow, fmpz **Rinv,
|
||
|
|
slong degR, slong k, slong i, fmpz *W, const fmpz_t p);
|
||
|
|
|
||
|
|
void fmpz_mod_poly_radix(fmpz_mod_poly_struct **B, const fmpz_mod_poly_t F,
|
||
|
|
const fmpz_mod_poly_radix_t D);
|
||
|
|
|
||
|
|
/* Input and output *********************************************************/
|
||
|
|
|
||
|
|
int _fmpz_mod_poly_fprint(FILE * file, const fmpz *poly, slong len,
|
||
|
|
const fmpz_t p);
|
||
|
|
|
||
|
|
int fmpz_mod_poly_fprint(FILE * file, const fmpz_mod_poly_t poly);
|
||
|
|
|
||
|
|
int fmpz_mod_poly_fread(FILE * file, fmpz_mod_poly_t poly);
|
||
|
|
|
||
|
|
static __inline__
|
||
|
|
int fmpz_mod_poly_fprint_pretty(FILE * file,
|
||
|
|
const fmpz_mod_poly_t poly, const char * x)
|
||
|
|
{
|
||
|
|
return _fmpz_poly_fprint_pretty(file, poly->coeffs, poly->length, x);
|
||
|
|
}
|
||
|
|
|
||
|
|
static __inline__
|
||
|
|
int _fmpz_mod_poly_print(const fmpz *poly, slong len, const fmpz_t p)
|
||
|
|
{
|
||
|
|
return _fmpz_mod_poly_fprint(stdout, poly, len, p);
|
||
|
|
}
|
||
|
|
|
||
|
|
static __inline__
|
||
|
|
int fmpz_mod_poly_print(const fmpz_mod_poly_t poly)
|
||
|
|
{
|
||
|
|
return fmpz_mod_poly_fprint(stdout, poly);
|
||
|
|
}
|
||
|
|
|
||
|
|
static __inline__
|
||
|
|
int fmpz_mod_poly_print_pretty(const fmpz_mod_poly_t poly, const char * x)
|
||
|
|
{
|
||
|
|
return fmpz_mod_poly_fprint_pretty(stdout, poly, x);
|
||
|
|
}
|
||
|
|
|
||
|
|
#ifdef __cplusplus
|
||
|
|
}
|
||
|
|
#endif
|
||
|
|
|
||
|
|
#include "fmpz_mod_poly_factor.h"
|
||
|
|
|
||
|
|
#endif
|
||
|
|
|