738 lines
25 KiB
C
738 lines
25 KiB
C
/*============================================================================
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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) 2010 Sebastian Pancratz
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Copyright (C) 2010 William Hart
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Copyright (C) 2011 Fredrik Johansson
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******************************************************************************/
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#ifndef FMPQ_POLY_H
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#define FMPQ_POLY_H
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#include <gmp.h>
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#include "fmpz.h"
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#include "fmpq.h"
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#include "fmpz_vec.h"
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#include "fmpz_poly.h"
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#include "flint.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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fmpz_t den;
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slong alloc;
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slong length;
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} fmpq_poly_struct;
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typedef fmpq_poly_struct fmpq_poly_t[1];
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typedef struct
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{
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fmpq_poly_struct * powers;
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slong len;
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} fmpq_poly_powers_precomp_struct;
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typedef fmpq_poly_powers_precomp_struct fmpq_poly_powers_precomp_t[1];
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#define WEAK_CANONICALISE_CUTOFF 25600
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/* Memory management *******************************************************/
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void fmpq_poly_init(fmpq_poly_t poly);
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void fmpq_poly_init2(fmpq_poly_t poly, slong alloc);
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void fmpq_poly_realloc(fmpq_poly_t poly, slong alloc);
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void fmpq_poly_fit_length(fmpq_poly_t poly, slong len);
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void _fmpq_poly_set_length(fmpq_poly_t poly, slong len);
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void fmpq_poly_clear(fmpq_poly_t poly);
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void _fmpq_poly_normalise(fmpq_poly_t poly);
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/* Accessing numerator and denominator *************************************/
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#define fmpq_poly_numref(poly) ((poly)->coeffs)
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#define fmpq_poly_denref(poly) ((poly)->den)
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static __inline__ void
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fmpq_poly_get_numerator(fmpz_poly_t res, const fmpq_poly_t poly)
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{
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fmpz_poly_fit_length(res, poly->length);
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_fmpz_vec_set(res->coeffs, poly->coeffs, poly->length);
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_fmpz_poly_set_length(res, poly->length);
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}
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/* Canonicalisation *************************************/
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void _fmpq_poly_canonicalise(fmpz * rpoly, fmpz_t den, slong len);
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void fmpq_poly_canonicalise(fmpq_poly_t poly);
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int _fmpq_poly_is_canonical(const fmpz * poly, const fmpz_t den, slong len);
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int fmpq_poly_is_canonical(const fmpq_poly_t poly);
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/* Polynomial parameters ***************************************************/
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static __inline__
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slong fmpq_poly_degree(const fmpq_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 fmpq_poly_length(const fmpq_poly_t poly)
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{
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return poly->length;
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}
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/* Randomisation ***********************************************************/
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void fmpq_poly_randtest(fmpq_poly_t f, flint_rand_t state,
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slong len, mp_bitcnt_t bits_in);
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void fmpq_poly_randtest_unsigned(fmpq_poly_t f, flint_rand_t state,
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slong len, mp_bitcnt_t bits_in);
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void fmpq_poly_randtest_not_zero(fmpq_poly_t f, flint_rand_t state,
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slong len, mp_bitcnt_t bits_in);
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/* Assignment and basic manipulation ***************************************/
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void fmpq_poly_set(fmpq_poly_t poly1, const fmpq_poly_t poly2);
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void fmpq_poly_set_si(fmpq_poly_t poly, slong x);
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void fmpq_poly_set_ui(fmpq_poly_t poly, ulong x);
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void fmpq_poly_set_fmpz(fmpq_poly_t poly, const fmpz_t x);
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void fmpq_poly_set_fmpq(fmpq_poly_t poly, const fmpq_t x);
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void fmpq_poly_set_mpz(fmpq_poly_t poly, const mpz_t x);
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void fmpq_poly_set_mpq(fmpq_poly_t poly, const mpq_t x);
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void fmpq_poly_set_fmpz_poly(fmpq_poly_t rop, const fmpz_poly_t op);
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void _fmpq_poly_set_array_mpq(fmpz * poly, fmpz_t den, const mpq_t * a, slong n);
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void fmpq_poly_set_array_mpq(fmpq_poly_t poly, const mpq_t * a, slong n);
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int _fmpq_poly_set_str(fmpz * poly, fmpz_t den, const char * str);
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int fmpq_poly_set_str(fmpq_poly_t poly, const char * str);
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char * fmpq_poly_get_str(const fmpq_poly_t poly);
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char * fmpq_poly_get_str_pretty(const fmpq_poly_t poly, const char * var);
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void fmpq_poly_zero(fmpq_poly_t poly);
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static __inline__ void fmpq_poly_one(fmpq_poly_t poly)
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{
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fmpq_poly_fit_length(poly, 1);
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_fmpq_poly_set_length(poly, 1);
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fmpz_one(poly->coeffs);
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fmpz_one(poly->den);
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}
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void fmpq_poly_neg(fmpq_poly_t poly1, const fmpq_poly_t poly2);
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void fmpq_poly_inv(fmpq_poly_t poly1, const fmpq_poly_t poly2);
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void fmpq_poly_swap(fmpq_poly_t poly1, fmpq_poly_t poly2);
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static __inline__
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void fmpq_poly_truncate(fmpq_poly_t poly, slong n)
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{
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if (poly->length > n)
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{
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slong i;
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for (i = n; i < poly->length; i++)
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_fmpz_demote(poly->coeffs + i);
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poly->length = n;
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fmpq_poly_canonicalise(poly);
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}
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}
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void fmpq_poly_get_slice(fmpq_poly_t rop,
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const fmpq_poly_t op, slong i, slong j);
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void fmpq_poly_reverse(fmpq_poly_t res, const fmpq_poly_t poly, slong n);
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/* Getting and setting coefficients ****************************************/
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void fmpq_poly_get_coeff_fmpq(fmpq_t x, const fmpq_poly_t poly, slong n);
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void fmpq_poly_get_coeff_mpq(mpq_t x, const fmpq_poly_t poly, slong n);
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void fmpq_poly_set_coeff_si(fmpq_poly_t poly, slong n, slong x);
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void fmpq_poly_set_coeff_ui(fmpq_poly_t poly, slong n, ulong x);
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void fmpq_poly_set_coeff_fmpz(fmpq_poly_t poly, slong n, const fmpz_t x);
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void fmpq_poly_set_coeff_fmpq(fmpq_poly_t poly, slong n, const fmpq_t x);
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void fmpq_poly_set_coeff_mpz(fmpq_poly_t poly, slong n, const mpz_t x);
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void fmpq_poly_set_coeff_mpq(fmpq_poly_t poly, slong n, const mpq_t x);
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/* Comparison **************************************************************/
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int fmpq_poly_equal(const fmpq_poly_t poly1, const fmpq_poly_t poly2);
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int fmpq_poly_cmp(const fmpq_poly_t left, const fmpq_poly_t right);
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static __inline__
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int fmpq_poly_is_zero(const fmpq_poly_t poly)
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{
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return poly->length == WORD(0);
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}
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static __inline__
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int fmpq_poly_is_one(const fmpq_poly_t poly)
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{
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return (poly->length == WORD(1)) && (fmpz_equal(poly->coeffs, poly->den));
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}
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/* Addition and subtraction ************************************************/
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void _fmpq_poly_add(fmpz * rpoly, fmpz_t rden,
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const fmpz * poly1, const fmpz_t den1, slong len1,
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const fmpz * poly2, const fmpz_t den2, slong len2);
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void fmpq_poly_add(fmpq_poly_t res,
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const fmpq_poly_t poly1, const fmpq_poly_t poly2);
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void _fmpq_poly_add_can(fmpz * rpoly, fmpz_t rden,
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const fmpz * poly1, const fmpz_t den1, slong len1,
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const fmpz * poly2, const fmpz_t den2, slong len2, int can);
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void fmpq_poly_add_can(fmpq_poly_t res,
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const fmpq_poly_t poly1, const fmpq_poly_t poly2, int can);
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void _fmpq_poly_sub(fmpz * rpoly, fmpz_t rden,
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const fmpz * poly1, const fmpz_t den1, slong len1,
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const fmpz * poly2, const fmpz_t den2, slong len2);
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void fmpq_poly_sub(fmpq_poly_t res,
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const fmpq_poly_t poly1, const fmpq_poly_t poly2);
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void _fmpq_poly_sub_can(fmpz * rpoly, fmpz_t rden,
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const fmpz * poly1, const fmpz_t den1, slong len1,
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const fmpz * poly2, const fmpz_t den2, slong len2, int can);
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void fmpq_poly_sub_can(fmpq_poly_t res,
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const fmpq_poly_t poly1, const fmpq_poly_t poly2, int can);
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/* Scalar multiplication and division **************************************/
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void _fmpq_poly_scalar_mul_si(fmpz * rpoly, fmpz_t rden,
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const fmpz * poly, const fmpz_t den, slong len, slong c);
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void _fmpq_poly_scalar_mul_ui(fmpz * rpoly, fmpz_t rden,
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const fmpz * poly, const fmpz_t den, slong len, ulong c);
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void _fmpq_poly_scalar_mul_fmpz(fmpz * rpoly, fmpz_t rden,
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const fmpz * poly, const fmpz_t den, slong len, const fmpz_t c);
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void _fmpq_poly_scalar_mul_fmpq(fmpz * rpoly, fmpz_t rden, const fmpz * poly,
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const fmpz_t den, slong len, const fmpz_t r, const fmpz_t s);
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void fmpq_poly_scalar_mul_si(fmpq_poly_t rop, const fmpq_poly_t op, slong c);
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void fmpq_poly_scalar_mul_ui(fmpq_poly_t rop, const fmpq_poly_t op, ulong c);
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void fmpq_poly_scalar_mul_fmpz(fmpq_poly_t rop,
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const fmpq_poly_t op, const fmpz_t c);
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void fmpq_poly_scalar_mul_fmpq(fmpq_poly_t rop,
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const fmpq_poly_t op, const fmpq_t c);
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void fmpq_poly_scalar_mul_mpz(fmpq_poly_t rop,
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const fmpq_poly_t op, const mpz_t c);
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void fmpq_poly_scalar_mul_mpq(fmpq_poly_t rop,
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const fmpq_poly_t op, const mpq_t c);
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void _fmpq_poly_scalar_div_si(fmpz * rpoly, fmpz_t rden,
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const fmpz * poly, const fmpz_t den, slong len, slong c);
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void _fmpq_poly_scalar_div_ui(fmpz * rpoly, fmpz_t rden,
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const fmpz * poly, const fmpz_t den, slong len, ulong c);
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void _fmpq_poly_scalar_div_fmpz(fmpz * rpoly, fmpz_t rden,
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const fmpz * poly, const fmpz_t den, slong len, const fmpz_t c);
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void _fmpq_poly_scalar_div_fmpq(fmpz * rpoly, fmpz_t rden, const fmpz * poly,
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const fmpz_t den, slong len, const fmpz_t r, const fmpz_t s);
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void fmpq_poly_scalar_div_si(fmpq_poly_t rop, const fmpq_poly_t op, slong c);
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void fmpq_poly_scalar_div_ui(fmpq_poly_t rop, const fmpq_poly_t op, ulong c);
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void fmpq_poly_scalar_div_fmpz(fmpq_poly_t rop,
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const fmpq_poly_t op, const fmpz_t c);
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void fmpq_poly_scalar_div_fmpq(fmpq_poly_t rop,
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const fmpq_poly_t op, const fmpq_t c);
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void fmpq_poly_scalar_div_mpz(fmpq_poly_t rop,
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const fmpq_poly_t op, const mpz_t c);
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void fmpq_poly_scalar_div_mpq(fmpq_poly_t rop,
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const fmpq_poly_t op, const mpq_t c);
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/* Multiplication **********************************************************/
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void _fmpq_poly_mul(fmpz * rpoly, fmpz_t rden,
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const fmpz * poly1, const fmpz_t den1, slong len1,
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const fmpz * poly2, const fmpz_t den2, slong len2);
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void fmpq_poly_mul(fmpq_poly_t res,
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const fmpq_poly_t poly1, const fmpq_poly_t poly2);
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void _fmpq_poly_mullow(fmpz * rpoly, fmpz_t rden,
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const fmpz * poly1, const fmpz_t den1, slong len1,
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const fmpz * poly2, const fmpz_t den2, slong len2, slong n);
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void fmpq_poly_mullow(fmpq_poly_t res,
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const fmpq_poly_t poly1, const fmpq_poly_t poly2, slong n);
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static __inline__
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void fmpq_poly_addmul(fmpq_poly_t rop, const fmpq_poly_t op1, const fmpq_poly_t op2)
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{
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fmpq_poly_t t;
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fmpq_poly_init(t);
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fmpq_poly_mul(t, op1, op2);
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fmpq_poly_add(rop, rop, t);
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fmpq_poly_clear(t);
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}
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static __inline__
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void fmpq_poly_submul(fmpq_poly_t rop, const fmpq_poly_t op1, const fmpq_poly_t op2)
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{
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fmpq_poly_t t;
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fmpq_poly_init(t);
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fmpq_poly_mul(t, op1, op2);
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fmpq_poly_sub(rop, rop, t);
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fmpq_poly_clear(t);
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}
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/* Powering ****************************************************************/
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void _fmpq_poly_pow(fmpz * rpoly, fmpz_t rden, const fmpz * poly,
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const fmpz_t den, slong len, ulong e);
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void fmpq_poly_pow(fmpq_poly_t rpoly, const fmpq_poly_t poly, ulong e);
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/* Shifting ****************************************************************/
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void fmpq_poly_shift_left(fmpq_poly_t res, const fmpq_poly_t poly, slong n);
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void fmpq_poly_shift_right(fmpq_poly_t res, const fmpq_poly_t poly, slong n);
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/* Euclidean division ******************************************************/
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void _fmpq_poly_divrem(fmpz * Q, fmpz_t q, fmpz * R, fmpz_t r,
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const fmpz * A, const fmpz_t a, slong lenA,
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const fmpz * B, const fmpz_t b, slong lenB, const fmpz_preinvn_t inv);
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void fmpq_poly_divrem(fmpq_poly_t Q, fmpq_poly_t R,
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const fmpq_poly_t poly1, const fmpq_poly_t poly2);
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void _fmpq_poly_div(fmpz * Q, fmpz_t q,
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const fmpz * A, const fmpz_t a, slong lenA,
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const fmpz * B, const fmpz_t b, slong lenB, const fmpz_preinvn_t inv);
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void fmpq_poly_div(fmpq_poly_t Q,
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const fmpq_poly_t poly1, const fmpq_poly_t poly2);
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void _fmpq_poly_rem(fmpz * R, fmpz_t r,
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const fmpz * A, const fmpz_t a, slong lenA,
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const fmpz * B, const fmpz_t b, slong lenB, const fmpz_preinvn_t inv);
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void fmpq_poly_rem(fmpq_poly_t R,
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const fmpq_poly_t poly1, const fmpq_poly_t poly2);
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/* Precomputed inverse *****************************************************/
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fmpq_poly_struct * _fmpq_poly_powers_precompute(const fmpz * B,
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const fmpz_t denB, slong len);
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void fmpq_poly_powers_precompute(fmpq_poly_powers_precomp_t pinv,
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fmpq_poly_t poly);
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void _fmpq_poly_powers_clear(fmpq_poly_struct * powers, slong len);
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void fmpq_poly_powers_clear(fmpq_poly_powers_precomp_t pinv);
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void _fmpq_poly_rem_powers_precomp(fmpz * A, fmpz_t denA, slong m,
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const fmpz * B, const fmpz_t denB, slong n,
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fmpq_poly_struct * const powers);
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void fmpq_poly_rem_powers_precomp(fmpq_poly_t R, const fmpq_poly_t A,
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const fmpq_poly_t B, const fmpq_poly_powers_precomp_t B_inv);
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/* Power series division ***************************************************/
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void _fmpq_poly_inv_series_newton(fmpz * Qinv, fmpz_t Qinvden,
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const fmpz * Q, const fmpz_t Qden, slong n);
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void fmpq_poly_inv_series_newton(fmpq_poly_t Qinv, const fmpq_poly_t Q, slong n);
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static __inline__ void
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_fmpq_poly_inv_series(fmpz * Qinv, fmpz_t Qinvden,
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const fmpz * Q, const fmpz_t Qden, slong n)
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{
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_fmpq_poly_inv_series_newton(Qinv, Qinvden, Q, Qden, n);
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|
}
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|
|
|
static __inline__ void
|
|
fmpq_poly_inv_series(fmpq_poly_t Qinv, const fmpq_poly_t Q, slong n)
|
|
{
|
|
fmpq_poly_inv_series_newton(Qinv, Q, n);
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|
}
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|
|
|
void _fmpq_poly_div_series(fmpz * Q, fmpz_t denQ,
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|
const fmpz * A, const fmpz_t denA,
|
|
const fmpz * B, const fmpz_t denB, slong n);
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|
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|
void fmpq_poly_div_series(fmpq_poly_t Q, const fmpq_poly_t A,
|
|
const fmpq_poly_t B, slong n);
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|
|
|
/* Greatest common divisor **************************************************/
|
|
|
|
void _fmpq_poly_gcd(fmpz *G, fmpz_t denG,
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|
const fmpz *A, slong lenA, const fmpz *B, slong lenB);
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|
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|
void fmpq_poly_gcd(fmpq_poly_t G, const fmpq_poly_t A, const fmpq_poly_t B);
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|
|
|
void _fmpq_poly_xgcd(fmpz *G, fmpz_t denG,
|
|
fmpz *S, fmpz_t denS, fmpz *T, fmpz_t denT,
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|
const fmpz *A, const fmpz_t denA, slong lenA,
|
|
const fmpz *B, const fmpz_t denB, slong lenB);
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|
|
|
void fmpq_poly_xgcd(fmpq_poly_t G, fmpq_poly_t S, fmpq_poly_t T,
|
|
const fmpq_poly_t A, const fmpq_poly_t B);
|
|
|
|
void _fmpq_poly_lcm(fmpz *G, fmpz_t denG,
|
|
const fmpz *A, slong lenA, const fmpz *B, slong lenB);
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|
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|
void fmpq_poly_lcm(fmpq_poly_t L, const fmpq_poly_t A, const fmpq_poly_t B);
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|
|
|
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);
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|
|
|
void fmpq_poly_resultant(fmpq_t r, const fmpq_poly_t f, const fmpq_poly_t g);
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|
|
|
/* Derivative and integral *************************************************/
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|
|
|
void _fmpq_poly_derivative(fmpz * rpoly, fmpz_t rden,
|
|
const fmpz * poly, const fmpz_t den, slong len);
|
|
|
|
void fmpq_poly_derivative(fmpq_poly_t res, const fmpq_poly_t poly);
|
|
|
|
void _fmpq_poly_integral(fmpz * rpoly, fmpz_t rden,
|
|
const fmpz * poly, const fmpz_t den, slong len);
|
|
|
|
void fmpq_poly_integral(fmpq_poly_t res, const fmpq_poly_t poly);
|
|
|
|
/* Square roots ************************************************************/
|
|
|
|
void _fmpq_poly_invsqrt_series(fmpz * rpoly, fmpz_t rden,
|
|
const fmpz * poly, const fmpz_t den, slong n);
|
|
|
|
void fmpq_poly_invsqrt_series(fmpq_poly_t res, const fmpq_poly_t poly, slong n);
|
|
|
|
void _fmpq_poly_sqrt_series(fmpz * rpoly, fmpz_t rden,
|
|
const fmpz * poly, const fmpz_t den, slong n);
|
|
|
|
void fmpq_poly_sqrt_series(fmpq_poly_t res, const fmpq_poly_t poly, slong n);
|
|
|
|
|
|
/* Transcendental functions ************************************************/
|
|
|
|
void _fmpq_poly_log_series(fmpz * g, fmpz_t gden,
|
|
const fmpz * f, const fmpz_t fden, slong n);
|
|
|
|
void fmpq_poly_log_series(fmpq_poly_t res, const fmpq_poly_t f, slong n);
|
|
|
|
void _fmpq_poly_exp_series(fmpz * g, fmpz_t gden,
|
|
const fmpz * h, const fmpz_t hden, slong n);
|
|
|
|
void fmpq_poly_exp_series(fmpq_poly_t res, const fmpq_poly_t poly, slong n);
|
|
|
|
void _fmpq_poly_atan_series(fmpz * g, fmpz_t gden,
|
|
const fmpz * h, const fmpz_t hden, slong n);
|
|
|
|
void fmpq_poly_atan_series(fmpq_poly_t res, const fmpq_poly_t poly, slong n);
|
|
|
|
void _fmpq_poly_atanh_series(fmpz * g, fmpz_t gden,
|
|
const fmpz * h, const fmpz_t hden, slong n);
|
|
|
|
void fmpq_poly_atanh_series(fmpq_poly_t res, const fmpq_poly_t poly, slong n);
|
|
|
|
void _fmpq_poly_asin_series(fmpz * g, fmpz_t gden,
|
|
const fmpz * h, const fmpz_t hden, slong n);
|
|
|
|
void fmpq_poly_asin_series(fmpq_poly_t res, const fmpq_poly_t poly, slong n);
|
|
|
|
void _fmpq_poly_asinh_series(fmpz * g, fmpz_t gden,
|
|
const fmpz * h, const fmpz_t hden, slong n);
|
|
|
|
void fmpq_poly_asinh_series(fmpq_poly_t res, const fmpq_poly_t poly, slong n);
|
|
|
|
void _fmpq_poly_tan_series(fmpz * g, fmpz_t gden,
|
|
const fmpz * h, const fmpz_t hden, slong n);
|
|
|
|
void fmpq_poly_tan_series(fmpq_poly_t res, const fmpq_poly_t poly, slong n);
|
|
|
|
void _fmpq_poly_sin_series(fmpz * g, fmpz_t gden,
|
|
const fmpz * h, const fmpz_t hden, slong n);
|
|
|
|
void fmpq_poly_sin_series(fmpq_poly_t res, const fmpq_poly_t poly, slong n);
|
|
|
|
void _fmpq_poly_cos_series(fmpz * g, fmpz_t gden,
|
|
const fmpz * h, const fmpz_t hden, slong n);
|
|
|
|
void fmpq_poly_cos_series(fmpq_poly_t res, const fmpq_poly_t poly, slong n);
|
|
|
|
void _fmpq_poly_sinh_series(fmpz * g, fmpz_t gden,
|
|
const fmpz * h, const fmpz_t hden, slong n);
|
|
|
|
void fmpq_poly_sinh_series(fmpq_poly_t res, const fmpq_poly_t poly, slong n);
|
|
|
|
void _fmpq_poly_cosh_series(fmpz * g, fmpz_t gden,
|
|
const fmpz * h, const fmpz_t hden, slong n);
|
|
|
|
void fmpq_poly_cosh_series(fmpq_poly_t res, const fmpq_poly_t poly, slong n);
|
|
|
|
void _fmpq_poly_tanh_series(fmpz * g, fmpz_t gden,
|
|
const fmpz * h, const fmpz_t hden, slong n);
|
|
|
|
void fmpq_poly_tanh_series(fmpq_poly_t res, const fmpq_poly_t poly, slong n);
|
|
|
|
/* Evaluation **************************************************************/
|
|
|
|
void _fmpq_poly_evaluate_fmpz(fmpz_t rnum, fmpz_t rden, const fmpz * poly,
|
|
const fmpz_t den, slong len, const fmpz_t a);
|
|
|
|
void fmpq_poly_evaluate_fmpz(fmpq_t res, const fmpq_poly_t poly,
|
|
const fmpz_t a);
|
|
|
|
void
|
|
_fmpq_poly_evaluate_fmpq(fmpz_t rnum, fmpz_t rden,
|
|
const fmpz * poly, const fmpz_t den, slong len,
|
|
const fmpz_t anum, const fmpz_t aden);
|
|
|
|
void
|
|
fmpq_poly_evaluate_fmpq(fmpq_t res, const fmpq_poly_t poly, const fmpq_t a);
|
|
|
|
void fmpq_poly_evaluate_mpz(mpq_t res, const fmpq_poly_t poly, const mpz_t a);
|
|
|
|
void fmpq_poly_evaluate_mpq(mpq_t res, const fmpq_poly_t poly, const mpq_t a);
|
|
|
|
/* Interpolation ************************************************************/
|
|
|
|
void
|
|
_fmpq_poly_interpolate_fmpz_vec(fmpz * poly, fmpz_t den,
|
|
const fmpz * xs, const fmpz * ys, slong n);
|
|
|
|
void
|
|
fmpq_poly_interpolate_fmpz_vec(fmpq_poly_t poly,
|
|
const fmpz * xs, const fmpz * ys, slong n);
|
|
|
|
/* Composition *************************************************************/
|
|
|
|
void _fmpq_poly_compose(fmpz * res, fmpz_t den,
|
|
const fmpz * poly1, const fmpz_t den1, slong len1,
|
|
const fmpz * poly2, const fmpz_t den2, slong len2);
|
|
|
|
void fmpq_poly_compose(fmpq_poly_t res,
|
|
const fmpq_poly_t poly1, const fmpq_poly_t poly2);
|
|
|
|
void _fmpq_poly_rescale(fmpz * res, fmpz_t denr, const fmpz * poly,
|
|
const fmpz_t den, slong len, const fmpz_t xnum, const fmpz_t xden);
|
|
|
|
void fmpq_poly_rescale(fmpq_poly_t res,
|
|
const fmpq_poly_t poly, const fmpq_t x);
|
|
|
|
/* Power series composition ************************************************/
|
|
|
|
void
|
|
_fmpq_poly_compose_series_horner(fmpz * res, fmpz_t den, const fmpz * poly1,
|
|
const fmpz_t den1, slong len1, const fmpz * poly2,
|
|
const fmpz_t den2, slong len2, slong n);
|
|
|
|
void
|
|
fmpq_poly_compose_series_horner(fmpq_poly_t res,
|
|
const fmpq_poly_t poly1, const fmpq_poly_t poly2, slong n);
|
|
|
|
void
|
|
_fmpq_poly_compose_series_brent_kung(fmpz * res, fmpz_t den,
|
|
const fmpz * poly1, const fmpz_t den1, slong len1,
|
|
const fmpz * poly2, const fmpz_t den2, slong len2, slong n);
|
|
|
|
void
|
|
fmpq_poly_compose_series_brent_kung(fmpq_poly_t res,
|
|
const fmpq_poly_t poly1, const fmpq_poly_t poly2, slong n);
|
|
|
|
void
|
|
_fmpq_poly_compose_series(fmpz * res, fmpz_t den,
|
|
const fmpz * poly1, const fmpz_t den1, slong len1,
|
|
const fmpz * poly2, const fmpz_t den2, slong len2, slong n);
|
|
|
|
void
|
|
fmpq_poly_compose_series(fmpq_poly_t res,
|
|
const fmpq_poly_t poly1, const fmpq_poly_t poly2, slong n);
|
|
|
|
/* Power series reversion ************************************************/
|
|
|
|
void
|
|
_fmpq_poly_revert_series_lagrange(fmpz * res, fmpz_t den,
|
|
const fmpz * poly1, const fmpz_t den1, slong n);
|
|
|
|
void
|
|
fmpq_poly_revert_series_lagrange(fmpq_poly_t res,
|
|
const fmpq_poly_t poly, slong n);
|
|
|
|
void
|
|
_fmpq_poly_revert_series_lagrange_fast(fmpz * res, fmpz_t den,
|
|
const fmpz * poly1, const fmpz_t den1, slong n);
|
|
|
|
void
|
|
fmpq_poly_revert_series_lagrange_fast(fmpq_poly_t res,
|
|
const fmpq_poly_t poly, slong n);
|
|
|
|
void
|
|
_fmpq_poly_revert_series_newton(fmpz * res, fmpz_t den,
|
|
const fmpz * poly1, const fmpz_t den1, slong n);
|
|
|
|
void
|
|
fmpq_poly_revert_series_newton(fmpq_poly_t res,
|
|
const fmpq_poly_t poly, slong n);
|
|
|
|
void
|
|
_fmpq_poly_revert_series(fmpz * res, fmpz_t den,
|
|
const fmpz * poly1, const fmpz_t den1, slong n);
|
|
|
|
void
|
|
fmpq_poly_revert_series(fmpq_poly_t res,
|
|
const fmpq_poly_t poly, slong n);
|
|
|
|
/* Gaussian content ********************************************************/
|
|
|
|
void _fmpq_poly_content(fmpq_t res,
|
|
const fmpz * poly, const fmpz_t den, slong len);
|
|
|
|
void fmpq_poly_content(fmpq_t res, const fmpq_poly_t poly);
|
|
|
|
void _fmpq_poly_primitive_part(fmpz * rpoly, fmpz_t rden,
|
|
const fmpz * poly, const fmpz_t den, slong len);
|
|
|
|
void fmpq_poly_primitive_part(fmpq_poly_t res, const fmpq_poly_t poly);
|
|
|
|
int _fmpq_poly_is_monic(const fmpz * poly, const fmpz_t den, slong len);
|
|
|
|
int fmpq_poly_is_monic(const fmpq_poly_t poly);
|
|
|
|
void _fmpq_poly_make_monic(fmpz * rpoly, fmpz_t rden,
|
|
const fmpz * poly, const fmpz_t den, slong len);
|
|
|
|
void fmpq_poly_make_monic(fmpq_poly_t res, const fmpq_poly_t poly);
|
|
|
|
/* Square-free *************************************************************/
|
|
|
|
int fmpq_poly_is_squarefree(const fmpq_poly_t poly);
|
|
|
|
/* Input and output *********************************************************/
|
|
|
|
int fmpq_poly_debug(const fmpq_poly_t poly);
|
|
|
|
int _fmpq_poly_fprint(FILE * file,
|
|
const fmpz * poly, const fmpz_t den, slong len);
|
|
|
|
int fmpq_poly_fprint(FILE * file, const fmpq_poly_t poly);
|
|
|
|
int _fmpq_poly_fprint_pretty(FILE * file,
|
|
const fmpz *poly, const fmpz_t den, slong len,
|
|
const char * x);
|
|
|
|
int fmpq_poly_fprint_pretty(FILE * file,
|
|
const fmpq_poly_t poly, const char * var);
|
|
|
|
static __inline__
|
|
int _fmpq_poly_print(const fmpz * poly, const fmpz_t den, slong len)
|
|
{
|
|
return _fmpq_poly_fprint(stdout, poly, den, len);
|
|
}
|
|
|
|
static __inline__
|
|
int fmpq_poly_print(const fmpq_poly_t poly)
|
|
{
|
|
return fmpq_poly_fprint(stdout, poly);
|
|
}
|
|
|
|
static __inline__
|
|
int _fmpq_poly_print_pretty(const fmpz *poly, const fmpz_t den, slong len,
|
|
const char * x)
|
|
{
|
|
return _fmpq_poly_fprint_pretty(stdout, poly, den, len, x);
|
|
}
|
|
|
|
static __inline__
|
|
int fmpq_poly_print_pretty(const fmpq_poly_t poly, const char * var)
|
|
{
|
|
return fmpq_poly_fprint_pretty(stdout, poly, var);
|
|
}
|
|
|
|
int fmpq_poly_fread(FILE * file, fmpq_poly_t poly);
|
|
|
|
static __inline__
|
|
int fmpq_poly_read(fmpq_poly_t poly)
|
|
{
|
|
return fmpq_poly_fread(stdin, poly);
|
|
}
|
|
|
|
#ifdef __cplusplus
|
|
}
|
|
#endif
|
|
|
|
#endif
|
|
|