/*
    Copyright (C) 2006, 2007, 2008, 2009, 2010, 2013 William Hart
    Copyright (C) 2009, 2011 Andy Novocin
    Copyright (C) 2010 Sebastian Pancratz
    Copyright (C) 2011 Fredrik Johansson

    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 2.1 of the License, or
    (at your option) any later version.  See <https://www.gnu.org/licenses/>.
*/

#ifndef FMPZ_POLY_H
#define FMPZ_POLY_H

#ifdef FMPZ_POLY_INLINES_C
#define FMPZ_POLY_INLINE FLINT_DLL
#else
#define FMPZ_POLY_INLINE static __inline__
#endif

#undef ulong
#define ulong ulongxx /* interferes with system includes */
#include <stdio.h>
#undef ulong

#include <gmp.h>
#define ulong mp_limb_t

#include "flint.h"
#include "fmpz.h"
#include "fmpz_vec.h"
#include "nmod_poly.h"
#include "fmpq.h"

#ifdef __cplusplus
 extern "C" {
#endif

#define FMPZ_POLY_INV_NEWTON_CUTOFF 32
#define FMPZ_POLY_SQRT_DIVCONQUER_CUTOFF 16
#define FMPZ_POLY_SQRTREM_DIVCONQUER_CUTOFF 16

/*  Type definitions *********************************************************/

typedef struct
{
    fmpz * coeffs;
    slong alloc;
    slong length;
} fmpz_poly_struct;

typedef fmpz_poly_struct fmpz_poly_t[1];

typedef struct
{
   fmpz ** powers;
   slong len;
} fmpz_poly_powers_precomp_struct;

typedef fmpz_poly_powers_precomp_struct fmpz_poly_powers_precomp_t[1];

typedef struct {
    fmpz c;
    fmpz_poly_struct *p;
    slong *exp;
    slong num;
    slong alloc;
} fmpz_poly_factor_struct;

typedef fmpz_poly_factor_struct fmpz_poly_factor_t[1];

typedef struct
{
   mp_limb_t ** jj; /* used by fft_convolution_precache */
   slong n;
   slong len2;
   slong loglen;
   slong bits2;
   slong limbs;
   fmpz_poly_t poly2;
} fmpz_poly_mul_precache_struct;

typedef fmpz_poly_mul_precache_struct fmpz_poly_mul_precache_t[1];

/*  Memory management ********************************************************/

FLINT_DLL void fmpz_poly_init(fmpz_poly_t poly);

FLINT_DLL void fmpz_poly_init2(fmpz_poly_t poly, slong alloc);

FLINT_DLL void fmpz_poly_realloc(fmpz_poly_t poly, slong alloc);

FLINT_DLL void fmpz_poly_fit_length(fmpz_poly_t poly, slong len);

FLINT_DLL void fmpz_poly_clear(fmpz_poly_t poly);

FLINT_DLL void _fmpz_poly_normalise(fmpz_poly_t poly);

FMPZ_POLY_INLINE
void _fmpz_poly_set_length(fmpz_poly_t poly, slong newlen)
{
    if (poly->length > newlen)
    {
        slong i;
        for (i = newlen; i < poly->length; i++)
           _fmpz_demote(poly->coeffs + i); 
    }
    poly->length = newlen;
}

FMPZ_POLY_INLINE
void fmpz_poly_attach_truncate(fmpz_poly_t trunc,
                                               const fmpz_poly_t poly, slong n)
{
   trunc->coeffs = poly->coeffs;
   trunc->alloc = poly->alloc;
   trunc->length = FLINT_MIN(poly->length, n);
}
 
FMPZ_POLY_INLINE
void fmpz_poly_attach_shift(fmpz_poly_t trunc, const fmpz_poly_t poly, slong n)
{
   trunc->coeffs = poly->coeffs + n;
   trunc->alloc = poly->alloc - n;
   trunc->length = FLINT_MAX(poly->length - n, 0);
}
 
/*  Polynomial parameters  ***************************************************/

FMPZ_POLY_INLINE
slong fmpz_poly_length(const fmpz_poly_t poly)
{
    return poly->length;
}

FMPZ_POLY_INLINE
slong fmpz_poly_degree(const fmpz_poly_t poly)
{
    return poly->length - 1;
}

/*  Assignment and basic manipulation  ***************************************/

FLINT_DLL void fmpz_poly_set(fmpz_poly_t poly1, const fmpz_poly_t poly2);

FLINT_DLL void fmpz_poly_set_ui(fmpz_poly_t poly, ulong c);

FLINT_DLL void fmpz_poly_set_si(fmpz_poly_t poly, slong c);

FLINT_DLL void fmpz_poly_set_fmpz(fmpz_poly_t poly, const fmpz_t c);

FLINT_DLL void fmpz_poly_set_mpz(fmpz_poly_t poly, const mpz_t c);

FLINT_DLL int _fmpz_poly_set_str(fmpz * poly, const char * str);

FLINT_DLL int fmpz_poly_set_str(fmpz_poly_t poly, const char * str);

FLINT_DLL char * _fmpz_poly_get_str(const fmpz * poly, slong len);

FLINT_DLL char * fmpz_poly_get_str(const fmpz_poly_t poly);

FLINT_DLL char * _fmpz_poly_get_str_pretty(const fmpz * poly, slong len, const char * x);

FLINT_DLL char * fmpz_poly_get_str_pretty(const fmpz_poly_t poly, const char * x);

FMPZ_POLY_INLINE
void fmpz_poly_zero(fmpz_poly_t poly)
{
   _fmpz_poly_set_length(poly, 0);
}

FMPZ_POLY_INLINE
void fmpz_poly_one(fmpz_poly_t poly)
{
    fmpz_poly_set_ui(poly, UWORD(1));
}

FLINT_DLL void fmpz_poly_zero_coeffs(fmpz_poly_t poly, slong i, slong j);

FLINT_DLL void fmpz_poly_swap(fmpz_poly_t poly1, fmpz_poly_t poly2);

FLINT_DLL void _fmpz_poly_reverse(fmpz * res, const fmpz * poly, slong len, slong n);

FLINT_DLL void fmpz_poly_reverse(fmpz_poly_t res, const fmpz_poly_t poly, slong n);

FLINT_DLL ulong fmpz_poly_deflation(const fmpz_poly_t input);

FLINT_DLL void fmpz_poly_deflate(fmpz_poly_t result, const fmpz_poly_t input,
                                                              ulong deflation);

FLINT_DLL void fmpz_poly_inflate(fmpz_poly_t result, const fmpz_poly_t input,
                                                              ulong inflation);

FMPZ_POLY_INLINE
void fmpz_poly_truncate(fmpz_poly_t poly, slong newlen)
{
    if (poly->length > newlen)
    {
        slong i;
        for (i = newlen; i < poly->length; i++)
            _fmpz_demote(poly->coeffs + i);
        poly->length = newlen;
        _fmpz_poly_normalise(poly);
    }  
}

FLINT_DLL void fmpz_poly_set_trunc(fmpz_poly_t res, const fmpz_poly_t poly, slong n);

/*  Randomisation  ***********************************************************/

FLINT_DLL void fmpz_poly_randtest(fmpz_poly_t f, flint_rand_t state, 
                                                slong len, flint_bitcnt_t bits);

FLINT_DLL void fmpz_poly_randtest_unsigned(fmpz_poly_t f, flint_rand_t state, 
                                                slong len, flint_bitcnt_t bits);

FLINT_DLL void fmpz_poly_randtest_not_zero(fmpz_poly_t f, flint_rand_t state,
                                                slong len, flint_bitcnt_t bits);

FLINT_DLL void fmpz_poly_randtest_no_real_root(fmpz_poly_t p, flint_rand_t state,
                                                slong len, flint_bitcnt_t bits);

/*  Getting and setting coefficients  ****************************************/

FLINT_DLL slong fmpz_poly_get_coeff_si(const fmpz_poly_t poly, slong n);

FLINT_DLL void fmpz_poly_set_coeff_si(fmpz_poly_t poly, slong n, slong x);

FLINT_DLL ulong fmpz_poly_get_coeff_ui(const fmpz_poly_t poly, slong n);

FLINT_DLL void fmpz_poly_set_coeff_ui(fmpz_poly_t poly, slong n, ulong x);

FLINT_DLL void fmpz_poly_set_coeff_fmpz(fmpz_poly_t poly, slong n, const fmpz_t x);

FLINT_DLL void fmpz_poly_get_coeff_fmpz(fmpz_t x, const fmpz_poly_t poly, slong n);

#define fmpz_poly_get_coeff_ptr(poly, n) \
    ((n) < (poly)->length ? (poly)->coeffs + (n) : NULL)

#define fmpz_poly_lead(poly) \
    ((poly)->length ? (poly)->coeffs + (poly)->length - 1 : NULL)

/*  Comparison  **************************************************************/

FLINT_DLL int fmpz_poly_equal(const fmpz_poly_t poly1, const fmpz_poly_t poly2);

FLINT_DLL int fmpz_poly_equal_trunc(const fmpz_poly_t poly1, 
                                             const fmpz_poly_t poly2, slong n);

#define fmpz_poly_is_zero(poly) \
    ((poly)->length == 0)

FMPZ_POLY_INLINE
int _fmpz_poly_is_one(const fmpz *poly, slong len)
{
    return (len > 0 && fmpz_is_one(poly) 
                    && _fmpz_vec_is_zero(poly + 1, len - 1));
}

FMPZ_POLY_INLINE
int fmpz_poly_is_one(const fmpz_poly_t op)
{
    return (op->length) == 1 && (*(op->coeffs) == WORD(1));
}

FMPZ_POLY_INLINE
int fmpz_poly_is_unit(const fmpz_poly_t op)
{
    return (op->length == 1) && (*(op->coeffs) == WORD(1) || *(op->coeffs) == WORD(-1));
}

FMPZ_POLY_INLINE
int fmpz_poly_is_gen(const fmpz_poly_t op)
{
    return (op->length) == 2 && (*(op->coeffs + 1) == WORD(1)) && (*(op->coeffs + 0) == WORD(0));
}

/* Deprecated */
#define fmpz_poly_is_x fmpz_poly_is_gen

FMPZ_POLY_INLINE
int fmpz_poly_equal_fmpz(const fmpz_poly_t poly, const fmpz_t c)
{
	return ((poly->length == 0) && fmpz_is_zero(c)) ||
        ((poly->length == 1) && fmpz_equal(poly->coeffs, c));
}

/*  Addition and subtraction  ************************************************/

FLINT_DLL void _fmpz_poly_add(fmpz * res, const fmpz * poly1, slong len1, 
                                               const fmpz * poly2, slong len2);

FLINT_DLL void fmpz_poly_add(fmpz_poly_t res, const fmpz_poly_t poly1, 
                                                      const fmpz_poly_t poly2);

FLINT_DLL void fmpz_poly_add_series(fmpz_poly_t res, const fmpz_poly_t poly1,
                                             const fmpz_poly_t poly2, slong n);

FLINT_DLL void _fmpz_poly_sub(fmpz * res, const fmpz * poly1, slong len1, 
                                               const fmpz * poly2, slong len2);

FLINT_DLL void fmpz_poly_sub(fmpz_poly_t res, const fmpz_poly_t poly1, 
                                                      const fmpz_poly_t poly2);

FLINT_DLL void fmpz_poly_sub_series(fmpz_poly_t res, const fmpz_poly_t poly1,
                                             const fmpz_poly_t poly2, slong n);

FLINT_DLL void fmpz_poly_neg(fmpz_poly_t res, const fmpz_poly_t poly);

FLINT_DLL void fmpz_poly_add_si(fmpz_poly_t res, const fmpz_poly_t poly, slong c);
FLINT_DLL void fmpz_poly_sub_si(fmpz_poly_t res, const fmpz_poly_t poly, slong c);
FLINT_DLL void fmpz_poly_si_sub(fmpz_poly_t res, slong c, const fmpz_poly_t poly);
FLINT_DLL void fmpz_poly_add_fmpz(fmpz_poly_t res, const fmpz_poly_t poly, fmpz_t c);
FLINT_DLL void fmpz_poly_sub_fmpz(fmpz_poly_t res, const fmpz_poly_t poly, fmpz_t c);
FLINT_DLL void fmpz_poly_fmpz_sub(fmpz_poly_t res, fmpz_t c, const fmpz_poly_t poly);

/*  Scalar absolute value multiplication and division  ***********************/

FLINT_DLL void fmpz_poly_scalar_abs(fmpz_poly_t res, const fmpz_poly_t poly);

FLINT_DLL void fmpz_poly_scalar_mul_ui(fmpz_poly_t poly1, 
                             const fmpz_poly_t poly2, ulong x);

FLINT_DLL void fmpz_poly_scalar_mul_si(fmpz_poly_t poly1, 
                             const fmpz_poly_t poly2, slong x);

FLINT_DLL void fmpz_poly_scalar_mul_fmpz(fmpz_poly_t poly1, 
                               const fmpz_poly_t poly2, const fmpz_t x);

FLINT_DLL void fmpz_poly_scalar_addmul_fmpz(fmpz_poly_t poly1, 
                                   const fmpz_poly_t poly2, const fmpz_t x);

FLINT_DLL void fmpz_poly_scalar_submul_fmpz(fmpz_poly_t poly1, 
                                   const fmpz_poly_t poly2, const fmpz_t x);

FLINT_DLL void fmpz_poly_scalar_fdiv_ui(fmpz_poly_t poly1, 
                              const fmpz_poly_t poly2, ulong x);

FLINT_DLL void fmpz_poly_scalar_fdiv_si(fmpz_poly_t poly1, 
                              const fmpz_poly_t poly2, slong x);

FLINT_DLL void fmpz_poly_scalar_fdiv_fmpz(fmpz_poly_t poly1, 
                                const fmpz_poly_t poly2, const fmpz_t x);

FLINT_DLL void fmpz_poly_scalar_tdiv_ui(fmpz_poly_t poly1, 
                              const fmpz_poly_t poly2, ulong x);

FLINT_DLL void fmpz_poly_scalar_tdiv_si(fmpz_poly_t poly1, 
                              const fmpz_poly_t poly2, slong x);

FLINT_DLL void fmpz_poly_scalar_tdiv_fmpz(fmpz_poly_t poly1, 
                                const fmpz_poly_t poly2, const fmpz_t x);

FLINT_DLL void fmpz_poly_scalar_divexact_ui(fmpz_poly_t poly1, 
                                  const fmpz_poly_t poly2, ulong x);

FLINT_DLL void fmpz_poly_scalar_divexact_si(fmpz_poly_t poly1, 
                                  const fmpz_poly_t poly2, slong x);

FLINT_DLL void fmpz_poly_scalar_divexact_fmpz(fmpz_poly_t poly1, 
                                    const fmpz_poly_t poly2, const fmpz_t x);

FLINT_DLL void fmpz_poly_scalar_fdiv_2exp(fmpz_poly_t poly1, const fmpz_poly_t poly2,
                           ulong exp);

FLINT_DLL void fmpz_poly_scalar_tdiv_2exp(fmpz_poly_t poly1, const fmpz_poly_t poly2,
                           ulong exp);

FLINT_DLL void fmpz_poly_scalar_mul_2exp(fmpz_poly_t poly1, const fmpz_poly_t poly2,
                           ulong exp);

FMPZ_POLY_INLINE
void fmpz_poly_scalar_mod_fmpz(fmpz_poly_t poly1, 
                               const fmpz_poly_t poly2, const fmpz_t x)
{
    if (poly2->length == 0)
    {
        fmpz_poly_zero(poly1);
    }
    else
    {
        fmpz_poly_fit_length(poly1, poly2->length);
        _fmpz_vec_scalar_mod_fmpz(poly1->coeffs, poly2->coeffs, poly2->length, x);
        _fmpz_poly_set_length(poly1, poly2->length);
        _fmpz_poly_normalise(poly1);
    }
}

FMPZ_POLY_INLINE
void fmpz_poly_scalar_smod_fmpz(fmpz_poly_t poly1, 
                                const fmpz_poly_t poly2, const fmpz_t x)
{
    if (poly2->length == 0)
    {
        fmpz_poly_zero(poly1);
    }
    else
    {
        fmpz_poly_fit_length(poly1, poly2->length);
        _fmpz_vec_scalar_smod_fmpz(poly1->coeffs, poly2->coeffs, poly2->length, x);
        _fmpz_poly_set_length(poly1, poly2->length);
        _fmpz_poly_normalise(poly1);

    }
}

FLINT_DLL slong _fmpz_poly_remove_content_2exp(fmpz * pol, slong len);

FLINT_DLL void _fmpz_poly_scale_2exp(fmpz * pol, slong len, slong k);

/*  Bit packing  *************************************************************/

FLINT_DLL void _fmpz_poly_bit_pack(mp_ptr arr, const fmpz * poly,
                                slong len, flint_bitcnt_t bit_size, int negate);

FLINT_DLL int _fmpz_poly_bit_unpack(fmpz * poly, slong len, 
                           mp_srcptr arr, flint_bitcnt_t bit_size, int negate);

FLINT_DLL void _fmpz_poly_bit_unpack_unsigned(fmpz * poly, slong len, 
                                       mp_srcptr arr, flint_bitcnt_t bit_size);

FLINT_DLL void fmpz_poly_bit_pack(fmpz_t f, const fmpz_poly_t poly,
        flint_bitcnt_t bit_size);

FLINT_DLL void fmpz_poly_bit_unpack(fmpz_poly_t poly, const fmpz_t f,
        flint_bitcnt_t bit_size);

FLINT_DLL void fmpz_poly_bit_unpack_unsigned(fmpz_poly_t poly, const fmpz_t f,
        flint_bitcnt_t bit_size);


/*  Multiplication  **********************************************************/

FLINT_DLL void _fmpz_poly_mul_classical(fmpz * res, const fmpz * poly1, slong len1, 
                                             const fmpz * poly2, slong len2);

FLINT_DLL void fmpz_poly_mul_classical(fmpz_poly_t res, 
                          const fmpz_poly_t poly1, const fmpz_poly_t poly2);

FLINT_DLL void _fmpz_poly_mullow_classical(fmpz * res, const fmpz * poly1, slong len1, 
                                     const fmpz * poly2, slong len2, slong n);

FLINT_DLL void fmpz_poly_mullow_classical(fmpz_poly_t res, const fmpz_poly_t poly1, 
                                           const fmpz_poly_t poly2, slong n);

FLINT_DLL void _fmpz_poly_mulhigh_classical(fmpz * res, const fmpz * poly1, 
                      slong len1, const fmpz * poly2, slong len2, slong start);

FLINT_DLL void fmpz_poly_mulhigh_classical(fmpz_poly_t res, 
              const fmpz_poly_t poly1, const fmpz_poly_t poly2, slong start);

FLINT_DLL void _fmpz_poly_mulmid_classical(fmpz * res, const fmpz * poly1, 
                                  slong len1, const fmpz * poly2, slong len2);

FLINT_DLL void fmpz_poly_mulmid_classical(fmpz_poly_t res, 
                          const fmpz_poly_t poly1, const fmpz_poly_t poly2);

FLINT_DLL void fmpz_poly_mul_karatsuba(fmpz_poly_t res, 
                          const fmpz_poly_t poly1, const fmpz_poly_t poly2);

FLINT_DLL void _fmpz_poly_mul_karatsuba(fmpz * res, const fmpz * poly1, 
                                  slong len1, const fmpz * poly2, slong len2);

FLINT_DLL void _fmpz_poly_mullow_karatsuba_n(fmpz * res, const fmpz * poly1, 
                                                const fmpz * poly2, slong n);

FLINT_DLL void fmpz_poly_mullow_karatsuba_n(fmpz_poly_t res, 
                  const fmpz_poly_t poly1, const fmpz_poly_t poly2, slong n);

FLINT_DLL void _fmpz_poly_mulhigh_karatsuba_n(fmpz * res, const fmpz * poly1, 
                                              const fmpz * poly2, slong len);

FLINT_DLL void fmpz_poly_mulhigh_karatsuba_n(fmpz_poly_t res, 
             const fmpz_poly_t poly1, const fmpz_poly_t poly2, slong length);

FLINT_DLL void _fmpz_poly_mul_KS(fmpz * res, const fmpz * poly1, slong len1, 
                                             const fmpz * poly2, slong len2);

FLINT_DLL void fmpz_poly_mul_KS(fmpz_poly_t res, 
                          const fmpz_poly_t poly1, const fmpz_poly_t poly2);

FLINT_DLL void _fmpz_poly_mullow_KS(fmpz * res, const fmpz * poly1, slong len1, 
                                     const fmpz * poly2, slong len2, slong n);

FLINT_DLL void fmpz_poly_mullow_KS(fmpz_poly_t res, const fmpz_poly_t poly1, 
                                           const fmpz_poly_t poly2, slong n);

FLINT_DLL void _fmpz_poly_mul_SS(fmpz * output, const fmpz * input1, slong length1, 
                                         const fmpz * input2, slong length2);

FLINT_DLL void fmpz_poly_mul_SS(fmpz_poly_t res,
                          const fmpz_poly_t poly1, const fmpz_poly_t poly2);

FLINT_DLL void _fmpz_poly_mullow_SS(fmpz * output, const fmpz * input1, slong length1, 
                                 const fmpz * input2, slong length2, slong n);

FLINT_DLL void fmpz_poly_mullow_SS(fmpz_poly_t res,
                  const fmpz_poly_t poly1, const fmpz_poly_t poly2, slong n);

FLINT_DLL void _fmpz_poly_mul(fmpz * res, const fmpz * poly1, 
                                  slong len1, const fmpz * poly2, slong len2);

FLINT_DLL void fmpz_poly_mul(fmpz_poly_t res, 
                          const fmpz_poly_t poly1, const fmpz_poly_t poly2);

FLINT_DLL void _fmpz_poly_mullow(fmpz * res, const fmpz * poly1, slong len1, 
                                     const fmpz * poly2, slong len2, slong n);

FLINT_DLL void fmpz_poly_mullow(fmpz_poly_t res, 
                  const fmpz_poly_t poly1, const fmpz_poly_t poly2, slong n);

FLINT_DLL void fmpz_poly_mulhigh_n(fmpz_poly_t res, 
                  const fmpz_poly_t poly1, const fmpz_poly_t poly2, slong n);

/* FFT precached multiplication **********************************************/

FLINT_DLL void fmpz_poly_mul_SS_precache_init(fmpz_poly_mul_precache_t pre,
                             slong len1, slong bits1, const fmpz_poly_t poly2);

FLINT_DLL void fmpz_poly_mul_precache_clear(fmpz_poly_mul_precache_t pre);

FLINT_DLL void _fmpz_poly_mullow_SS_precache(fmpz * output,
   const fmpz * input1, slong len1, fmpz_poly_mul_precache_t pre, slong trunc);

FLINT_DLL void fmpz_poly_mullow_SS_precache(fmpz_poly_t res,
               const fmpz_poly_t poly1, fmpz_poly_mul_precache_t pre, slong n);

FMPZ_POLY_INLINE void fmpz_poly_mul_SS_precache(fmpz_poly_t res,
                         const fmpz_poly_t poly1, fmpz_poly_mul_precache_t pre)
{
    fmpz_poly_mullow_SS_precache(res, poly1, pre,
		                  FLINT_MAX(poly1->length + pre->len2 - 1, 0));
}

/* Squaring ******************************************************************/

FLINT_DLL void _fmpz_poly_sqr_KS(fmpz * rop, const fmpz * op, slong len);

FLINT_DLL void fmpz_poly_sqr_KS(fmpz_poly_t rop, const fmpz_poly_t op);

FLINT_DLL void fmpz_poly_sqr_karatsuba(fmpz_poly_t rop, const fmpz_poly_t op);

FLINT_DLL void _fmpz_poly_sqr_karatsuba(fmpz * rop, const fmpz * op, slong len);

FLINT_DLL void _fmpz_poly_sqr_classical(fmpz * rop, const fmpz * op, slong len);

FLINT_DLL void fmpz_poly_sqr_classical(fmpz_poly_t rop, const fmpz_poly_t op);

FLINT_DLL void _fmpz_poly_sqr(fmpz * rop, const fmpz * op, slong len);

FLINT_DLL void fmpz_poly_sqr(fmpz_poly_t rop, const fmpz_poly_t op);

FLINT_DLL void _fmpz_poly_sqrlow_KS(fmpz * res, const fmpz * poly, slong len, slong n);

FLINT_DLL void fmpz_poly_sqrlow_KS(fmpz_poly_t res, const fmpz_poly_t poly, slong n);

FLINT_DLL void _fmpz_poly_sqrlow_karatsuba_n(fmpz * res, const fmpz * poly, slong n);

FLINT_DLL void fmpz_poly_sqrlow_karatsuba_n(fmpz_poly_t res, const fmpz_poly_t poly, slong n);

FLINT_DLL void _fmpz_poly_sqrlow_classical(fmpz * res, const fmpz * poly, slong len, slong n);

FLINT_DLL void fmpz_poly_sqrlow_classical(fmpz_poly_t res, const fmpz_poly_t poly, slong n);

FLINT_DLL void _fmpz_poly_sqrlow(fmpz * res, const fmpz * poly, slong len, slong n);

FLINT_DLL void fmpz_poly_sqrlow(fmpz_poly_t res, const fmpz_poly_t poly, slong n);

/*  Powering  ****************************************************************/

FLINT_DLL void _fmpz_poly_pow_multinomial(fmpz * res, const fmpz * poly, slong len, ulong e);

FLINT_DLL void fmpz_poly_pow_multinomial(fmpz_poly_t res, const fmpz_poly_t poly, ulong e);

FLINT_DLL void _fmpz_poly_pow_binomial(fmpz * res, const fmpz * poly, ulong e);

FLINT_DLL void fmpz_poly_pow_binomial(fmpz_poly_t res, const fmpz_poly_t poly, ulong e);

FLINT_DLL void _fmpz_poly_pow_binexp(fmpz * res, const fmpz * poly, slong len, ulong e);

FLINT_DLL void fmpz_poly_pow_binexp(fmpz_poly_t res, const fmpz_poly_t poly, ulong e);

FLINT_DLL void _fmpz_poly_pow_addchains(fmpz * res, const fmpz * poly, slong len, const int * a, int n);

FLINT_DLL void fmpz_poly_pow_addchains(fmpz_poly_t res, const fmpz_poly_t poly, ulong e);

FLINT_DLL void _fmpz_poly_pow_small(fmpz * res, const fmpz * poly, slong len, ulong e);

FLINT_DLL void _fmpz_poly_pow(fmpz * res, const fmpz * poly, slong len, ulong e);

FLINT_DLL void fmpz_poly_pow(fmpz_poly_t res, const fmpz_poly_t poly, ulong e);

FLINT_DLL void _fmpz_poly_pow_trunc(fmpz * res, const fmpz * poly, ulong e, slong n);

void 
FLINT_DLL fmpz_poly_pow_trunc(fmpz_poly_t res, const fmpz_poly_t poly, ulong e, slong n);

/*  Shifting  ****************************************************************/

FLINT_DLL void _fmpz_poly_shift_left(fmpz * res, const fmpz * poly, slong len, slong n);

FLINT_DLL void _fmpz_poly_shift_right(fmpz * res, const fmpz * poly, slong len, slong n);

FLINT_DLL void fmpz_poly_shift_left(fmpz_poly_t res, const fmpz_poly_t poly, slong n);

FLINT_DLL void fmpz_poly_shift_right(fmpz_poly_t res, const fmpz_poly_t poly, slong n);

/*  Norms  *******************************************************************/

FLINT_DLL void _fmpz_poly_2norm(fmpz_t res, const fmpz * poly, slong len);

FLINT_DLL void fmpz_poly_2norm(fmpz_t res, const fmpz_poly_t poly);

FLINT_DLL flint_bitcnt_t _fmpz_poly_2norm_normalised_bits(const fmpz * poly, slong len);

FMPZ_POLY_INLINE
ulong fmpz_poly_max_limbs(const fmpz_poly_t poly)
{
    return _fmpz_vec_max_limbs(poly->coeffs, poly->length);
}

FMPZ_POLY_INLINE
slong fmpz_poly_max_bits(const fmpz_poly_t poly)
{
    return _fmpz_vec_max_bits(poly->coeffs, poly->length);
}

FMPZ_POLY_INLINE
void fmpz_poly_height(fmpz_t res, const fmpz_poly_t poly)
{
    _fmpz_vec_height(res, poly->coeffs, poly->length);
}

/*  Greatest common divisor  *************************************************/

FLINT_DLL void _fmpz_poly_gcd_subresultant(fmpz * res, const fmpz * poly1, slong len1, 
                                              const fmpz * poly2, slong len2);

FLINT_DLL void fmpz_poly_gcd_subresultant(fmpz_poly_t res, const fmpz_poly_t poly1, 
                                                    const fmpz_poly_t poly2);

FLINT_DLL int _fmpz_poly_gcd_heuristic(fmpz * res, const fmpz * poly1, slong len1, 
                                              const fmpz * poly2, slong len2);

FLINT_DLL int fmpz_poly_gcd_heuristic(fmpz_poly_t res,
                           const fmpz_poly_t poly1, const fmpz_poly_t poly2);

FLINT_DLL void _fmpz_poly_gcd_modular(fmpz * res, const fmpz * poly1, slong len1, 
                                              const fmpz * poly2, slong len2);

FLINT_DLL void fmpz_poly_gcd_modular(fmpz_poly_t res,
                           const fmpz_poly_t poly1, const fmpz_poly_t poly2);

FLINT_DLL void _fmpz_poly_gcd(fmpz * res, const fmpz * poly1, slong len1, 
                                               const fmpz * poly2, slong len2);

FLINT_DLL void fmpz_poly_gcd(fmpz_poly_t res, const fmpz_poly_t poly1, 
                                                      const fmpz_poly_t poly2);

FLINT_DLL void _fmpz_poly_lcm(fmpz * res, const fmpz * poly1, slong len1, 
                                               const fmpz * poly2, slong len2);

FLINT_DLL void fmpz_poly_lcm(fmpz_poly_t res, const fmpz_poly_t poly1, 
                                                      const fmpz_poly_t poly2);

FLINT_DLL void _fmpz_poly_resultant_euclidean(fmpz_t res, const fmpz * poly1, slong len1, 
                                               const fmpz * poly2, slong len2);

FLINT_DLL void fmpz_poly_resultant_euclidean(fmpz_t res, const fmpz_poly_t poly1, 
                                                      const fmpz_poly_t poly2);

FLINT_DLL void _fmpz_poly_resultant_modular(fmpz_t res, const fmpz * poly1, slong len1, 
                                               const fmpz * poly2, slong len2);

FLINT_DLL void fmpz_poly_resultant_modular(fmpz_t res, const fmpz_poly_t poly1,
                                                      const fmpz_poly_t poly2);

FLINT_DLL void _fmpz_poly_resultant(fmpz_t res, const fmpz * poly1, slong len1, 
                                               const fmpz * poly2, slong len2);

FLINT_DLL void fmpz_poly_resultant(fmpz_t res, const fmpz_poly_t poly1,
                                                      const fmpz_poly_t poly2);

FLINT_DLL void _fmpz_poly_resultant_modular_div(fmpz_t res,
       const fmpz * poly1, slong len1, 
       const fmpz * poly2, slong len2, const fmpz_t divisor, slong nbits);

FLINT_DLL void fmpz_poly_resultant_modular_div(fmpz_t res, 
               const fmpz_poly_t poly1, const fmpz_poly_t poly2,
               const fmpz_t divisor, slong nbits);

FLINT_DLL void _fmpz_poly_xgcd_modular(fmpz_t r, fmpz * s, fmpz * t, 
               const fmpz * poly1, slong len1, const fmpz * poly2, slong len2);

FLINT_DLL void fmpz_poly_xgcd_modular(fmpz_t r, fmpz_poly_t s, fmpz_poly_t t,
                             const fmpz_poly_t poly1, const fmpz_poly_t poly2);

FMPZ_POLY_INLINE
void _fmpz_poly_xgcd(fmpz_t r, fmpz * s, fmpz * t, 
                const fmpz * poly1, slong len1, const fmpz * poly2, slong len2)
{
    _fmpz_poly_xgcd_modular(r, s, t, poly1, len1, poly2, len2);
}

FMPZ_POLY_INLINE
void fmpz_poly_xgcd(fmpz_t r, fmpz_poly_t s, fmpz_poly_t t,
                            const fmpz_poly_t poly1, const fmpz_poly_t poly2)
{
    fmpz_poly_xgcd_modular(r, s, t, poly1, poly2);
}

/*  Discriminant  ********************************************************/

FLINT_DLL void _fmpz_poly_discriminant(fmpz_t res, const fmpz * poly, slong len);

FLINT_DLL void fmpz_poly_discriminant(fmpz_t res, const fmpz_poly_t poly);

/*  Gaussian content  ********************************************************/

FLINT_DLL void _fmpz_poly_content(fmpz_t res, const fmpz * poly, slong len);

FLINT_DLL void fmpz_poly_content(fmpz_t res, const fmpz_poly_t poly);

FLINT_DLL void _fmpz_poly_primitive_part(fmpz * res, const fmpz * poly, slong len);

FLINT_DLL void fmpz_poly_primitive_part(fmpz_poly_t res, const fmpz_poly_t poly);

/*  Square-free  *************************************************************/

FLINT_DLL int _fmpz_poly_is_squarefree(const fmpz * poly, slong len);

FLINT_DLL int fmpz_poly_is_squarefree(const fmpz_poly_t poly);

/*  Euclidean division  ******************************************************/

FLINT_DLL int _fmpz_poly_divrem_basecase(fmpz * Q, fmpz * R, const fmpz * A, 
                            slong lenA, const fmpz * B, slong lenB, int exact);

FLINT_DLL void fmpz_poly_divrem_basecase(fmpz_poly_t Q, fmpz_poly_t R, 
                                   const fmpz_poly_t A, const fmpz_poly_t B);

FLINT_DLL int _fmpz_poly_divrem_divconquer_recursive(fmpz * Q, fmpz * BQ,
              fmpz * W, const fmpz * A, const fmpz * B, slong lenB, int exact);

FLINT_DLL int _fmpz_poly_divrem_divconquer(fmpz * Q, fmpz * R, 
            const fmpz * A, slong lenA, const fmpz * B, slong lenB, int exact);

FLINT_DLL void fmpz_poly_divrem_divconquer(fmpz_poly_t Q, fmpz_poly_t R, 
                                     const fmpz_poly_t A, const fmpz_poly_t B);

FLINT_DLL int _fmpz_poly_divrem(fmpz * Q, fmpz * R, const fmpz * A, slong lenA, 
                                        const fmpz * B, slong lenB, int exact);

FLINT_DLL void fmpz_poly_divrem(fmpz_poly_t Q, fmpz_poly_t R,
                                     const fmpz_poly_t A, const fmpz_poly_t B);

FLINT_DLL int _fmpz_poly_div_basecase(fmpz * Q, fmpz * R, const fmpz * A,
                            slong lenA, const fmpz * B, slong lenB, int exact);

FLINT_DLL void fmpz_poly_div_basecase(fmpz_poly_t Q, 
                                     const fmpz_poly_t A, const fmpz_poly_t B);

FLINT_DLL int _fmpz_poly_divremlow_divconquer_recursive(fmpz * Q, fmpz * QB, 
                        const fmpz * A, const fmpz * B, slong lenB, int exact);

FLINT_DLL int _fmpz_poly_div_divconquer_recursive(fmpz * Q, fmpz * temp, 
                        const fmpz * A, const fmpz * B, slong lenB, int exact);

FLINT_DLL int _fmpz_poly_div_divconquer(fmpz * Q, const fmpz * A, slong lenA, 
                                        const fmpz * B, slong lenB, int exact);

FLINT_DLL void fmpz_poly_div_divconquer(fmpz_poly_t Q, 
                                     const fmpz_poly_t A, const fmpz_poly_t B);

FLINT_DLL int _fmpz_poly_div(fmpz * Q, const fmpz * A, slong lenA, 
                                        const fmpz * B, slong lenB, int exact);

FLINT_DLL void fmpz_poly_div(fmpz_poly_t Q, const fmpz_poly_t A,
                                                          const fmpz_poly_t B);

FLINT_DLL void _fmpz_poly_preinvert(fmpz * B_inv, const fmpz * B, slong n);

FLINT_DLL void fmpz_poly_preinvert(fmpz_poly_t B_inv, const fmpz_poly_t B);

FLINT_DLL void _fmpz_poly_div_preinv(fmpz * Q, const fmpz * A, slong len1, 
                               const fmpz * B, const fmpz * B_inv, slong len2);

FLINT_DLL void fmpz_poly_div_preinv(fmpz_poly_t Q, const fmpz_poly_t A, 
                                 const fmpz_poly_t B, const fmpz_poly_t B_inv);

FLINT_DLL void _fmpz_poly_divrem_preinv(fmpz * Q, fmpz * A, slong len1, 
                               const fmpz * B, const fmpz * B_inv, slong len2);

FLINT_DLL void fmpz_poly_divrem_preinv(fmpz_poly_t Q, fmpz_poly_t R, 
            const fmpz_poly_t A, const fmpz_poly_t B, const fmpz_poly_t B_inv);

FLINT_DLL fmpz ** _fmpz_poly_powers_precompute(const fmpz * B, slong len);

FLINT_DLL void fmpz_poly_powers_precompute(fmpz_poly_powers_precomp_t pinv, 
                                                             fmpz_poly_t poly);

FLINT_DLL void _fmpz_poly_powers_clear(fmpz ** powers, slong len);

FLINT_DLL void fmpz_poly_powers_clear(fmpz_poly_powers_precomp_t pinv);

FLINT_DLL void _fmpz_poly_rem_powers_precomp(fmpz * A, slong m, 
                                const fmpz * B, slong n, fmpz ** const powers);

FLINT_DLL void fmpz_poly_rem_powers_precomp(fmpz_poly_t R, 
                             const fmpz_poly_t A, const fmpz_poly_t B, 
                                       const fmpz_poly_powers_precomp_t B_inv);

FLINT_DLL void _fmpz_poly_rem_basecase(fmpz * Q, const fmpz * A, slong lenA,
                                                   const fmpz * B, slong lenB);

FLINT_DLL void fmpz_poly_rem_basecase(fmpz_poly_t R, 
                                     const fmpz_poly_t A, const fmpz_poly_t B);

FLINT_DLL void _fmpz_poly_rem(fmpz * R, const fmpz * A, slong lenA, 
                              const fmpz * B, slong lenB);

FLINT_DLL void fmpz_poly_rem(fmpz_poly_t R, const fmpz_poly_t A, const fmpz_poly_t B);

FLINT_DLL void fmpz_poly_div_root(fmpz_poly_t Q, const fmpz_poly_t A, const fmpz_t c);

FLINT_DLL void _fmpz_poly_div_root(fmpz * Q, const fmpz * A, slong len, const fmpz_t c);

/*  Power series division  ***************************************************/

FLINT_DLL void _fmpz_poly_inv_series_basecase(fmpz * Qinv, const fmpz * Q, slong Qlen, slong n);

FLINT_DLL void fmpz_poly_inv_series_basecase(fmpz_poly_t Qinv, const fmpz_poly_t Q, slong n);

FLINT_DLL void _fmpz_poly_inv_series_newton(fmpz * Qinv, const fmpz * Q, slong Qlen, slong n);

FLINT_DLL void fmpz_poly_inv_series_newton(fmpz_poly_t Qinv, const fmpz_poly_t Q, slong n);

FLINT_DLL void _fmpz_poly_inv_series(fmpz * Qinv, const fmpz * Q, slong Qlen, slong n);

FLINT_DLL void fmpz_poly_inv_series(fmpz_poly_t Qinv, const fmpz_poly_t Q, slong n);

FLINT_DLL void _fmpz_poly_div_series_basecase(fmpz * Q, const fmpz * A, slong Alen,
    const fmpz * B, slong Blen, slong n);

FLINT_DLL void _fmpz_poly_div_series_divconquer(fmpz * Q, const fmpz * A, slong Alen,
    const fmpz * B, slong Blen, slong n);

FLINT_DLL void _fmpz_poly_div_series(fmpz * Q, const fmpz * A, slong Alen,
    const fmpz * B, slong Blen, slong n);

FLINT_DLL void fmpz_poly_div_series_basecase(fmpz_poly_t Q,
		    const fmpz_poly_t A, const fmpz_poly_t B, slong n);

FLINT_DLL void fmpz_poly_div_series_divconquer(fmpz_poly_t Q,
		    const fmpz_poly_t A, const fmpz_poly_t B, slong n);

FLINT_DLL void fmpz_poly_div_series(fmpz_poly_t Q, const fmpz_poly_t A, 
                                         const fmpz_poly_t B, slong n);

/*  Divisibility testing  ***************************************************/

FLINT_DLL int _fmpz_poly_divides(fmpz * q, const fmpz * a, 
                                       slong len1, const fmpz * b, slong len2);

FLINT_DLL int fmpz_poly_divides(fmpz_poly_t q,
		                     const fmpz_poly_t a, const fmpz_poly_t b);

FLINT_DLL slong fmpz_poly_remove(fmpz_poly_t res, const fmpz_poly_t poly1,
		                                      const fmpz_poly_t poly2);

/*  Pseudo division  *********************************************************/

FLINT_DLL void _fmpz_poly_pseudo_divrem_basecase(fmpz * Q, fmpz * R, 
                   ulong * d, const fmpz * A, slong A_len, 
                        const fmpz * B, slong B_len, const fmpz_preinvn_t inv);

FLINT_DLL void fmpz_poly_pseudo_divrem_basecase(fmpz_poly_t Q, fmpz_poly_t R, 
                          ulong * d, const fmpz_poly_t A, const fmpz_poly_t B);

FLINT_DLL void _fmpz_poly_pseudo_divrem_divconquer(fmpz * Q, fmpz * R, 
                    ulong * d, const fmpz * A, slong lenA, 
                         const fmpz * B, slong lenB, const fmpz_preinvn_t inv);

FLINT_DLL void fmpz_poly_pseudo_divrem_divconquer(fmpz_poly_t Q, fmpz_poly_t R, 
                          ulong * d, const fmpz_poly_t A, const fmpz_poly_t B);

FLINT_DLL void _fmpz_poly_pseudo_divrem_cohen(fmpz * Q, fmpz * R, const fmpz * A, 
                                       slong lenA, const fmpz * B, slong lenB);

FLINT_DLL void fmpz_poly_pseudo_divrem_cohen(fmpz_poly_t Q, fmpz_poly_t R, 
                                     const fmpz_poly_t A, const fmpz_poly_t B);

FLINT_DLL void _fmpz_poly_pseudo_rem_cohen(fmpz * R, const fmpz * A, slong lenA, 
                                                   const fmpz * B, slong lenB);

FLINT_DLL void fmpz_poly_pseudo_rem_cohen(fmpz_poly_t R, const fmpz_poly_t A, 
                                                          const fmpz_poly_t B);

FMPZ_POLY_INLINE
void _fmpz_poly_pseudo_divrem(fmpz * Q, fmpz * R, 
                    ulong * d, const fmpz * A, slong A_len, 
                         const fmpz * B, slong B_len, const fmpz_preinvn_t inv)
{
    _fmpz_poly_pseudo_divrem_divconquer(Q, R, d, A, A_len, B, B_len, inv);
}

FMPZ_POLY_INLINE
void fmpz_poly_pseudo_divrem(fmpz_poly_t Q, fmpz_poly_t R, 
                           ulong * d, const fmpz_poly_t A, const fmpz_poly_t B)
{
    fmpz_poly_pseudo_divrem_divconquer(Q, R, d, A, B);
}

FLINT_DLL void _fmpz_poly_pseudo_div(fmpz * Q, ulong * d, const fmpz * A,
             slong lenA, const fmpz * B, slong lenB, const fmpz_preinvn_t inv);

FLINT_DLL void fmpz_poly_pseudo_div(fmpz_poly_t Q, ulong * d,
                                     const fmpz_poly_t A, const fmpz_poly_t B);

FLINT_DLL void _fmpz_poly_pseudo_rem(fmpz * R, ulong * d, const fmpz * A,
             slong lenA, const fmpz * B, slong lenB, const fmpz_preinvn_t inv);

FLINT_DLL void fmpz_poly_pseudo_rem(fmpz_poly_t R, ulong * d, 
                                     const fmpz_poly_t A, const fmpz_poly_t B);

FLINT_DLL void fmpz_poly_divlow_smodp(fmpz * res,
            const fmpz_poly_t f, const fmpz_poly_t g, const fmpz_t p, slong n);

FLINT_DLL void fmpz_poly_divhigh_smodp(fmpz * res,
            const fmpz_poly_t f, const fmpz_poly_t g, const fmpz_t p, slong n);

/*  Derivative  **************************************************************/

FLINT_DLL void _fmpz_poly_derivative(fmpz * rpoly, const fmpz * poly, slong len);
 
FLINT_DLL void fmpz_poly_derivative(fmpz_poly_t res, const fmpz_poly_t poly);

/*  Evaluation  **************************************************************/

void 
FLINT_DLL _fmpz_poly_evaluate_divconquer_fmpz(fmpz_t res, const fmpz * poly, slong len, 
                                                const fmpz_t a);

FLINT_DLL void fmpz_poly_evaluate_divconquer_fmpz(fmpz_t res, const fmpz_poly_t poly, 
                                        const fmpz_t a);

FLINT_DLL void _fmpz_poly_evaluate_horner_fmpz(fmpz_t res, const fmpz * f, slong len, 
                                                               const fmpz_t a);

FLINT_DLL void fmpz_poly_evaluate_horner_fmpz(fmpz_t res, const fmpz_poly_t f, 
                                                               const fmpz_t a);

FLINT_DLL void _fmpz_poly_evaluate_fmpz(fmpz_t res, const fmpz * f, slong len, const fmpz_t a);

FLINT_DLL void fmpz_poly_evaluate_fmpz(fmpz_t res, const fmpz_poly_t f, const fmpz_t a);

FLINT_DLL void _fmpz_poly_evaluate_horner_fmpq(fmpz_t rnum, fmpz_t rden, 
                                    const fmpz * f, slong len, 
                                    const fmpz_t anum, const fmpz_t aden);

FLINT_DLL void fmpz_poly_evaluate_horner_fmpq(fmpq_t res, const fmpz_poly_t f, 
                                                               const fmpq_t a);

FLINT_DLL void _fmpz_poly_evaluate_divconquer_fmpq(fmpz_t rnum, fmpz_t rden, 
                                    const fmpz * f, slong len, 
                                    const fmpz_t anum, const fmpz_t aden);

FLINT_DLL void fmpz_poly_evaluate_divconquer_fmpq(fmpq_t res,
                                          const fmpz_poly_t f, const fmpq_t a);

FLINT_DLL void _fmpz_poly_evaluate_fmpq(fmpz_t rnum, fmpz_t rden, 
                                    const fmpz * f, slong len, 
                                    const fmpz_t anum, const fmpz_t aden);

FLINT_DLL void fmpz_poly_evaluate_fmpq(fmpq_t res,
                                          const fmpz_poly_t f, const fmpq_t a);


FLINT_DLL void fmpz_poly_evaluate_mpq(mpq_t res,
                                           const fmpz_poly_t f, const mpq_t a);

FLINT_DLL mp_limb_t _fmpz_poly_evaluate_mod(const fmpz * poly, slong len,
                                     mp_limb_t a, mp_limb_t n, mp_limb_t ninv);

FLINT_DLL mp_limb_t fmpz_poly_evaluate_mod(const fmpz_poly_t poly, mp_limb_t a, 
                                 mp_limb_t n);

FLINT_DLL double _fmpz_poly_evaluate_horner_d(const fmpz * poly, slong n,
                                                                     double d);

FLINT_DLL double fmpz_poly_evaluate_horner_d(const fmpz_poly_t poly, double d);

FLINT_DLL double _fmpz_poly_evaluate_horner_d_2exp(slong * exp, 
                                         const fmpz * poly, slong n, double d);

FLINT_DLL double fmpz_poly_evaluate_horner_d_2exp(slong * exp, 
                                             const fmpz_poly_t poly, double d);

FLINT_DLL double _fmpz_poly_evaluate_horner_d_2exp2(slong * exp, const fmpz * poly,
                                      slong n, double d, slong dexp);

FLINT_DLL double fmpz_poly_evaluate_horner_d_2exp2(slong * exp,
		     const fmpz_poly_t poly, double d, slong dexp);

/*  Composition  *************************************************************/

FLINT_DLL void _fmpz_poly_compose_horner(fmpz * res, const fmpz * poly1, slong len1, 
                                                const fmpz * poly2, slong len2);

FLINT_DLL void fmpz_poly_compose_horner(fmpz_poly_t res, const fmpz_poly_t poly1, 
                                                      const fmpz_poly_t poly2);

FLINT_DLL void _fmpz_poly_compose_divconquer(fmpz * res, const fmpz * poly1, slong len1, 
                                                const fmpz * poly2, slong len2);

FLINT_DLL void fmpz_poly_compose_divconquer(fmpz_poly_t res, const fmpz_poly_t poly1, 
                                                      const fmpz_poly_t poly2);

FLINT_DLL void _fmpz_poly_compose(fmpz * res, const fmpz * poly1, slong len1, 
                                                const fmpz * poly2, slong len2);

FLINT_DLL void fmpz_poly_compose(fmpz_poly_t res, const fmpz_poly_t poly1, 
                                                      const fmpz_poly_t poly2);

/*  Taylor shift  ************************************************************/

FLINT_DLL void _fmpz_poly_taylor_shift_horner(fmpz * poly, const fmpz_t c, slong n);

FLINT_DLL void fmpz_poly_taylor_shift_horner(fmpz_poly_t g, const fmpz_poly_t f,
    const fmpz_t c);

FLINT_DLL void _fmpz_poly_taylor_shift_divconquer(fmpz * poly, const fmpz_t c, slong n);

FLINT_DLL void fmpz_poly_taylor_shift_divconquer(fmpz_poly_t g, const fmpz_poly_t f,
    const fmpz_t c);

FLINT_DLL void _fmpz_poly_taylor_shift_multi_mod(fmpz * poly, const fmpz_t c, slong n);

FMPZ_POLY_INLINE
void fmpz_poly_taylor_shift_multi_mod(fmpz_poly_t g, const fmpz_poly_t f, const fmpz_t c)
{
    if (f != g)
        fmpz_poly_set(g, f);
    _fmpz_poly_taylor_shift_multi_mod(g->coeffs, c, g->length);
}

FLINT_DLL void _fmpz_poly_taylor_shift(fmpz * poly, const fmpz_t c, slong n);

FLINT_DLL void fmpz_poly_taylor_shift(fmpz_poly_t g, const fmpz_poly_t f, const fmpz_t c);

/*  Power series composition and compositional inverse  **********************/

FLINT_DLL void _fmpz_poly_compose_series_brent_kung(fmpz * res, const fmpz * poly1, slong len1, 
                                      const fmpz * poly2, slong len2, slong n);

FLINT_DLL void fmpz_poly_compose_series_brent_kung(fmpz_poly_t res, 
                    const fmpz_poly_t poly1, const fmpz_poly_t poly2, slong n);

FLINT_DLL void _fmpz_poly_compose_series_horner(fmpz * res, const fmpz * poly1, slong len1, 
                                      const fmpz * poly2, slong len2, slong n);

FLINT_DLL void fmpz_poly_compose_series_horner(fmpz_poly_t res, 
                    const fmpz_poly_t poly1, const fmpz_poly_t poly2, slong n);

FLINT_DLL void _fmpz_poly_compose_series(fmpz * res, const fmpz * poly1, slong len1, 
                                      const fmpz * poly2, slong len2, slong n);

FLINT_DLL void fmpz_poly_compose_series(fmpz_poly_t res, 
                    const fmpz_poly_t poly1, const fmpz_poly_t poly2, slong n);

FLINT_DLL void _fmpz_poly_revert_series_lagrange(fmpz * Qinv, const fmpz * Q, slong Qlen, slong n);

FLINT_DLL void fmpz_poly_revert_series_lagrange(fmpz_poly_t Qinv, const fmpz_poly_t Q, slong n);

FLINT_DLL void _fmpz_poly_revert_series_lagrange_fast(fmpz * Qinv, const fmpz * Q, slong Qlen, slong n);

FLINT_DLL void fmpz_poly_revert_series_lagrange_fast(fmpz_poly_t Qinv,
    const fmpz_poly_t Q, slong n);

FLINT_DLL void _fmpz_poly_revert_series_newton(fmpz * Qinv, const fmpz * Q, slong Qlen, slong n);

FLINT_DLL void fmpz_poly_revert_series_newton(fmpz_poly_t Qinv, const fmpz_poly_t Q, slong n);

FLINT_DLL void _fmpz_poly_revert_series(fmpz * Qinv, const fmpz * Q, slong Qlen, slong n);

FLINT_DLL void fmpz_poly_revert_series(fmpz_poly_t Qinv, const fmpz_poly_t Q, slong n);

/*  Square root  *************************************************************/

FLINT_DLL int _fmpz_poly_sqrtrem_classical(fmpz * res, fmpz * r, 
                                                 const fmpz * poly, slong len);

FLINT_DLL int fmpz_poly_sqrtrem_classical(fmpz_poly_t b, 
                                           fmpz_poly_t r, const fmpz_poly_t a);

FLINT_DLL int _fmpz_poly_sqrtrem_divconquer(fmpz * res, fmpz * r, 
                                    const fmpz * poly, slong len, fmpz * temp);

FLINT_DLL int fmpz_poly_sqrtrem_divconquer(fmpz_poly_t b, 
                                           fmpz_poly_t r, const fmpz_poly_t a);

FLINT_DLL int _fmpz_poly_sqrt_classical(fmpz * res, const fmpz * poly,
                                                         slong len, int exact);

FLINT_DLL int fmpz_poly_sqrt_classical(fmpz_poly_t b, const fmpz_poly_t a);

FLINT_DLL int _fmpz_poly_sqrt_divconquer(fmpz * res, const fmpz * poly,
                                                         slong len, int exact);

FLINT_DLL int fmpz_poly_sqrt_divconquer(fmpz_poly_t b, const fmpz_poly_t a);

FLINT_DLL int _fmpz_poly_sqrt_KS(fmpz *rop, const fmpz *op, slong len);

FLINT_DLL int fmpz_poly_sqrt_KS(fmpz_poly_t b, const fmpz_poly_t a);

FLINT_DLL int _fmpz_poly_sqrt(fmpz * res, const fmpz * poly, slong len);

FLINT_DLL int fmpz_poly_sqrt(fmpz_poly_t b, const fmpz_poly_t a);

FLINT_DLL int _fmpz_poly_sqrt_series(fmpz * res, 
                                        const fmpz * poly, slong len, slong n);

FLINT_DLL int fmpz_poly_sqrt_series(fmpz_poly_t b,
                                                 const fmpz_poly_t a, slong n);

/* Power sums ****************************************************************/

FLINT_DLL void _fmpz_poly_power_sums_naive(fmpz * res, const fmpz * poly, slong len, slong n);

FLINT_DLL void fmpz_poly_power_sums_naive(fmpz_poly_t res, const fmpz_poly_t poly, slong n);

FLINT_DLL void fmpz_poly_power_sums(fmpz_poly_t res, const fmpz_poly_t poly, slong n);

FLINT_DLL void _fmpz_poly_power_sums_to_poly(fmpz * res, const fmpz * poly, slong len);

FLINT_DLL void fmpz_poly_power_sums_to_poly(fmpz_poly_t res, const fmpz_poly_t Q);

/*  Signature  ***************************************************************/

FLINT_DLL void _fmpz_poly_signature(slong * r1, slong * r2, const fmpz * poly, slong len);

FLINT_DLL void fmpz_poly_signature(slong * r1, slong * r2, const fmpz_poly_t poly);

/*  Input and output  ********************************************************/
FLINT_DLL int _fmpz_poly_fprint(FILE * file, const fmpz * poly, slong len);

FLINT_DLL int fmpz_poly_fprint(FILE * file, const fmpz_poly_t poly);

FLINT_DLL int _fmpz_poly_fprint_pretty(FILE * file, 
                             const fmpz * poly, slong len, const char * x);

FLINT_DLL int fmpz_poly_fprint_pretty(FILE * file, 
                                       const fmpz_poly_t poly, const char * x);

FMPZ_POLY_INLINE
int _fmpz_poly_print_pretty(const fmpz * poly, slong len, const char * x)
{
  return _fmpz_poly_fprint_pretty(stdout, poly, len, x);
}

FMPZ_POLY_INLINE
int _fmpz_poly_print(const fmpz * poly, slong n)
{
  return _fmpz_poly_fprint(stdout, poly, n);
}

FMPZ_POLY_INLINE
int fmpz_poly_print(const fmpz_poly_t poly)
{
    return fmpz_poly_fprint(stdout, poly);
}

FMPZ_POLY_INLINE
int fmpz_poly_print_pretty(const fmpz_poly_t poly, const char * x)
{
    return fmpz_poly_fprint_pretty(stdout, poly, x);
}

FLINT_DLL int fmpz_poly_fread(FILE * file, fmpz_poly_t poly);

FLINT_DLL int fmpz_poly_fread_pretty(FILE *file, fmpz_poly_t poly, char **x);

FMPZ_POLY_INLINE
int fmpz_poly_read(fmpz_poly_t poly)
{
    return fmpz_poly_fread(stdin, poly);
}

FMPZ_POLY_INLINE
int fmpz_poly_read_pretty(fmpz_poly_t poly, char **x)
{
    return fmpz_poly_fread_pretty(stdin, poly, x);
}

FMPZ_POLY_INLINE
void fmpz_poly_debug(const fmpz_poly_t poly)
{
    flint_printf("(alloc = %wd, length = %wd, vec = ", poly->alloc, poly->length);
    if (poly->coeffs)
    {
        flint_printf("{");
        _fmpz_vec_print(poly->coeffs, poly->alloc);
        flint_printf("}");
    }
    else
    {
        flint_printf("NULL");
    }
    flint_printf(")");
    fflush(stdout);
}

/*  CRT  ********************************************************************/

FLINT_DLL void fmpz_poly_get_nmod_poly(nmod_poly_t res, const fmpz_poly_t poly);

FLINT_DLL void fmpz_poly_set_nmod_poly(fmpz_poly_t res, const nmod_poly_t poly);

FLINT_DLL void fmpz_poly_set_nmod_poly_unsigned(fmpz_poly_t res, const nmod_poly_t poly);

void
FLINT_DLL _fmpz_poly_CRT_ui_precomp(fmpz * res, const fmpz * poly1, slong len1,
               const fmpz_t m1, mp_srcptr poly2, slong len2, mp_limb_t m2,
                mp_limb_t m2inv, fmpz_t m1m2, mp_limb_t c, int sign);

FLINT_DLL void _fmpz_poly_CRT_ui(fmpz * res, const fmpz * poly1, slong len1,
               const fmpz_t m1, mp_srcptr poly2, slong len2, mp_limb_t m2,
                                                    mp_limb_t m2inv, int sign);

FLINT_DLL void fmpz_poly_CRT_ui(fmpz_poly_t res, const fmpz_poly_t poly1,
                                     const fmpz_t m1, const nmod_poly_t poly2,
                                        int sign);


/* Products *****************************************************************/

FLINT_DLL void _fmpz_poly_product_roots_fmpz_vec(fmpz * poly,
                                        const fmpz * xs, slong n);

FLINT_DLL void fmpz_poly_product_roots_fmpz_vec(fmpz_poly_t poly,
                                        const fmpz * xs, slong n);

FLINT_DLL void _fmpz_poly_product_roots_fmpq_vec(fmpz * poly,
                                        const fmpq * xs, slong n);

FLINT_DLL void fmpz_poly_product_roots_fmpq_vec(fmpz_poly_t poly,
                                        const fmpq * xs, slong n);


/* Newton basis *************************************************************/

FLINT_DLL void _fmpz_poly_monomial_to_newton(fmpz * poly, const fmpz * roots, slong n);

FLINT_DLL void _fmpz_poly_newton_to_monomial(fmpz * poly, const fmpz * roots, slong n);


/* Multipoint evaluation and interpolation *********************************/

FLINT_DLL void fmpz_poly_evaluate_fmpz_vec(fmpz * res, const fmpz_poly_t f,
                                const fmpz * a, slong n);

FLINT_DLL void fmpz_poly_interpolate_fmpz_vec(fmpz_poly_t poly,
                                    const fmpz * xs, const fmpz * ys, slong n);

/* Hensel lifting ************************************************************/

FLINT_DLL void fmpz_poly_hensel_build_tree(slong * link, fmpz_poly_t *v, fmpz_poly_t *w, 
                                 const nmod_poly_factor_t fac);

FLINT_DLL void fmpz_poly_hensel_lift(fmpz_poly_t Gout, fmpz_poly_t Hout, 
    fmpz_poly_t Aout, fmpz_poly_t Bout, 
    const fmpz_poly_t f, 
    const fmpz_poly_t g, const fmpz_poly_t h, 
    const fmpz_poly_t a, const fmpz_poly_t b, 
    const fmpz_t p, const fmpz_t p1);

FLINT_DLL void _fmpz_poly_hensel_lift_without_inverse(fmpz *G, fmpz *H, 
    const fmpz *f, slong lenF, 
    const fmpz *g, slong lenG, const fmpz *h, slong lenH, 
    const fmpz *a, slong lenA, const fmpz *b, slong lenB, 
    const fmpz_t p, const fmpz_t p1);

FLINT_DLL void fmpz_poly_hensel_lift_without_inverse(fmpz_poly_t Gout, fmpz_poly_t Hout, 
    const fmpz_poly_t f, const fmpz_poly_t g, const fmpz_poly_t h, 
    const fmpz_poly_t a, const fmpz_poly_t b, 
    const fmpz_t p, const fmpz_t p1);

FLINT_DLL void _fmpz_poly_hensel_lift_only_inverse(fmpz *A, fmpz *B, 
    const fmpz *G, slong lenG, const fmpz *H, slong lenH, 
    const fmpz *a, slong lenA, const fmpz *b, slong lenB, 
    const fmpz_t p, const fmpz_t p1);

FLINT_DLL void fmpz_poly_hensel_lift_only_inverse(fmpz_poly_t Aout, fmpz_poly_t Bout, 
    const fmpz_poly_t G, const fmpz_poly_t H, 
    const fmpz_poly_t a, const fmpz_poly_t b, 
    const fmpz_t p, const fmpz_t p1);

FLINT_DLL void fmpz_poly_hensel_lift_tree_recursive(slong *link, 
    fmpz_poly_t *v, fmpz_poly_t *w, fmpz_poly_t f, slong j, slong inv, 
    const fmpz_t p0, const fmpz_t p1);

FLINT_DLL void fmpz_poly_hensel_lift_tree(slong *link, fmpz_poly_t *v, fmpz_poly_t *w, 
    fmpz_poly_t f, slong r, const fmpz_t p, slong e0, slong e1, slong inv);

FLINT_DLL slong _fmpz_poly_hensel_start_lift(fmpz_poly_factor_t lifted_fac, slong *link, 
    fmpz_poly_t *v, fmpz_poly_t *w, const fmpz_poly_t f, 
    const nmod_poly_factor_t local_fac, slong target_exp);

FLINT_DLL slong _fmpz_poly_hensel_continue_lift(fmpz_poly_factor_t lifted_fac, 
    slong *link, fmpz_poly_t *v, fmpz_poly_t *w, const fmpz_poly_t f, 
    slong prev, slong curr, slong N, const fmpz_t p);

FLINT_DLL void fmpz_poly_hensel_lift_once(fmpz_poly_factor_t lifted_fac, 
                                const fmpz_poly_t f, 
                                const nmod_poly_factor_t local_fac, slong N);

/* Some functions for backwards compatibility */

FMPZ_POLY_INLINE
void fmpz_poly_scalar_mul_mpz(fmpz_poly_t poly1,
                               const fmpz_poly_t poly2, const mpz_t x)
{
    fmpz_t t;
    fmpz_init_set_readonly(t, x);
    fmpz_poly_scalar_mul_fmpz(poly1, poly2, t);
    fmpz_clear_readonly(t);
}

FMPZ_POLY_INLINE
void fmpz_poly_scalar_divexact_mpz(fmpz_poly_t poly1,
                               const fmpz_poly_t poly2, const mpz_t x)
{
    fmpz_t t;
    fmpz_init_set_readonly(t, x);
    fmpz_poly_scalar_divexact_fmpz(poly1, poly2, t);
    fmpz_clear_readonly(t);
}

FMPZ_POLY_INLINE
void fmpz_poly_scalar_fdiv_mpz(fmpz_poly_t poly1,
                               const fmpz_poly_t poly2, const mpz_t x)
{
    fmpz_t t;
    fmpz_init_set_readonly(t, x);
    fmpz_poly_scalar_fdiv_fmpz(poly1, poly2, t);
    fmpz_clear_readonly(t);
}

FMPZ_POLY_INLINE
void fmpz_poly_set_coeff_mpz(fmpz_poly_t poly, slong n,
    const mpz_t x)
{
    fmpz_t t;
    fmpz_init_set_readonly(t, x);
    fmpz_poly_set_coeff_fmpz(poly, n, t);
    fmpz_clear_readonly(t);
}

FMPZ_POLY_INLINE
void fmpz_poly_get_coeff_mpz(mpz_t x, const fmpz_poly_t poly, slong n)
{
    fmpz_t t;
    fmpz_init(t);
    fmpz_poly_get_coeff_fmpz(t, poly, n);
    fmpz_get_mpz(x, t);
    fmpz_clear(t);
}

/* Roots */

FLINT_DLL void _fmpz_poly_bound_roots(fmpz_t bound, const fmpz * poly, slong len);

FLINT_DLL void fmpz_poly_bound_roots(fmpz_t bound, const fmpz_poly_t poly);

FLINT_DLL void _fmpz_poly_num_real_roots_sturm(slong * n_neg, slong * n_pos, const fmpz * pol, slong len);

FLINT_DLL slong fmpz_poly_num_real_roots_sturm(const fmpz_poly_t poly);

FLINT_DLL slong _fmpz_poly_num_real_roots(const fmpz * pol, slong len);

FLINT_DLL slong fmpz_poly_num_real_roots(const fmpz_poly_t poly);

/* CLD bounds */

FLINT_DLL void fmpz_poly_CLD_bound(fmpz_t res, const fmpz_poly_t f, slong n);

/* Special polynomials */

FLINT_DLL void _fmpz_poly_cyclotomic(fmpz * a, ulong n, mp_ptr factors,
                                        slong num_factors, ulong phi);
FLINT_DLL void fmpz_poly_cyclotomic(fmpz_poly_t poly, ulong n);

FLINT_DLL ulong _fmpz_poly_is_cyclotomic(const fmpz * poly, slong len);

FLINT_DLL ulong fmpz_poly_is_cyclotomic(const fmpz_poly_t poly);

FLINT_DLL void _fmpz_poly_cos_minpoly(fmpz * f, ulong n);

FLINT_DLL void fmpz_poly_cos_minpoly(fmpz_poly_t f, ulong n);

FLINT_DLL void _fmpz_poly_swinnerton_dyer(fmpz * T, ulong n);

FLINT_DLL void fmpz_poly_swinnerton_dyer(fmpz_poly_t poly, ulong n);

FLINT_DLL void _fmpz_poly_chebyshev_t(fmpz * coeffs, ulong n);

FLINT_DLL void fmpz_poly_chebyshev_t(fmpz_poly_t poly, ulong n);

FLINT_DLL void _fmpz_poly_chebyshev_u(fmpz * coeffs, ulong n);

FLINT_DLL void fmpz_poly_chebyshev_u(fmpz_poly_t poly, ulong n);

FLINT_DLL void _fmpz_poly_legendre_pt(fmpz * coeffs, ulong n);

FLINT_DLL void fmpz_poly_legendre_pt(fmpz_poly_t poly, ulong n);

FLINT_DLL void _fmpz_poly_hermite_h(fmpz * coeffs, ulong n);

FLINT_DLL void fmpz_poly_hermite_h(fmpz_poly_t poly, ulong n);

FLINT_DLL void _fmpz_poly_hermite_he(fmpz * coeffs, ulong n);

FLINT_DLL void fmpz_poly_hermite_he(fmpz_poly_t poly, ulong n);

FLINT_DLL void _fmpz_poly_fibonacci(fmpz * coeffs, ulong n);

FLINT_DLL void fmpz_poly_fibonacci(fmpz_poly_t poly, ulong n);

FLINT_DLL void _fmpz_poly_eta_qexp(fmpz * f, slong e, slong n);

FLINT_DLL void fmpz_poly_eta_qexp(fmpz_poly_t f, slong e, slong n);

FLINT_DLL void _fmpz_poly_theta_qexp(fmpz * f, slong e, slong n);

FLINT_DLL void fmpz_poly_theta_qexp(fmpz_poly_t f, slong e, slong n);

#ifdef __cplusplus
}
#endif

#include "fmpz_poly_factor.h"

#endif