flint-sys 0.9.0

/*
    Copyright (C) 2011, 2012, 2013 Sebastian Pancratz

    This file is part of FLINT.

    FLINT is free software: you can redistribute it and/or modify it under
    the terms of the GNU Lesser General Public License (LGPL) as published
    by the Free Software Foundation; either version 3 of the License, or
    (at your option) any later version.  See <https://www.gnu.org/licenses/>.
*/

#ifndef QADIC_H
#define QADIC_H

#ifdef QADIC_INLINES_C
#define QADIC_INLINE
#else
#define QADIC_INLINE static inline
#endif

#include "fmpz_vec.h"
#include "fmpz_mod_types.h"
#include "nmod_types.h"
#include "padic.h"
#include "padic_poly.h"

#ifdef __cplusplus
 extern "C" {
#endif

/* Data types and context ****************************************************/

typedef padic_poly_t qadic_t;

typedef padic_poly_struct qadic_struct;

QADIC_INLINE slong qadic_val(const qadic_t op)
{
    return padic_poly_val(op);
}

QADIC_INLINE slong qadic_prec(const qadic_t op)
{
    return padic_poly_prec(op);
}

typedef struct
{
    padic_ctx_struct pctx;

    fmpz *a;
    slong *j;
    slong len;

    char *var;
}
qadic_ctx_struct;

typedef qadic_ctx_struct qadic_ctx_t[1];

int _qadic_ctx_init_conway_ui(qadic_ctx_t ctx, ulong p, slong d,
        slong min, slong max, const char * var, enum padic_print_mode mode);

void qadic_ctx_init_conway(qadic_ctx_t ctx,
                           const fmpz_t p, slong d, slong min, slong max,
                           const char *var, enum padic_print_mode mode);

void qadic_ctx_init_modulus(qadic_ctx_t ctx, const fmpz_t p, const fmpz_mod_poly_t modulus,
                           slong min, slong max,
                           const char *var, enum padic_print_mode mode);

void qadic_ctx_init_modulus_nmod(qadic_ctx_t ctx, ulong p, const nmod_poly_t modulus,
                           slong min, slong max,
                           const char *var, enum padic_print_mode mode);

void qadic_ctx_init(qadic_ctx_t ctx,
                           const fmpz_t p, slong d, slong min, slong max,
                           const char *var, enum padic_print_mode mode);

void qadic_ctx_clear(qadic_ctx_t ctx);

QADIC_INLINE slong qadic_ctx_degree(const qadic_ctx_t ctx)
{
    return ctx->j[ctx->len - 1];
}

QADIC_INLINE void qadic_ctx_print(const qadic_ctx_t ctx)
{
    slong i, k;

    flint_printf("p    = "), fmpz_print((&ctx->pctx)->p), flint_printf("\n");
    flint_printf("d    = %wd\n", ctx->j[ctx->len - 1]);
    flint_printf("f(X) = ");
    fmpz_print(ctx->a + 0);
    for (k = 1; k < ctx->len; k++)
    {
        i = ctx->j[k];
        flint_printf(" + ");
        if (fmpz_is_one(ctx->a + k))
        {
            if (i == 1)
                flint_printf("X");
            else
                flint_printf("X^%wd", i);
        }
        else
        {
            fmpz_print(ctx->a + k);
            if (i == 1)
                flint_printf("*X");
            else
                flint_printf("*X^%wd", i);
        }
    }
    flint_printf("\n");
}

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

QADIC_INLINE void qadic_init(qadic_t x)
{
    padic_poly_init(x);
}

QADIC_INLINE void qadic_init2(qadic_t rop, slong prec)
{
    padic_poly_init2(rop, 0, prec);
}

QADIC_INLINE void qadic_clear(qadic_t x)
{
    padic_poly_clear(x);
}

/*
    TODO:  Consider renaming this function, prefix for the "qadic" module.
 */

QADIC_INLINE void
_fmpz_poly_reduce(fmpz *R, slong lenR, const fmpz *a, const slong *j, slong len)
{
    const slong d = j[len - 1];
    slong i, k;

    FMPZ_VEC_NORM(R, lenR);

    for (i = lenR - 1; i >= d; i--)
    {
        for (k = len - 2; k >= 0; k--)
        {
            fmpz_submul(R + j[k] + i - d, R + i, a + k);
        }
        fmpz_zero(R + i);
    }
}

/*
    TODO:  Consider renaming this function, prefix for the "qadic" module.
 */

QADIC_INLINE void
_fmpz_mod_poly_reduce(fmpz *R, slong lenR,
                      const fmpz *a, const slong *j, slong len, const fmpz_t p)
{
    const slong d = j[len - 1];

    if (lenR > d)
    {
        _fmpz_poly_reduce(R, lenR, a, j, len);
        _fmpz_vec_scalar_mod_fmpz(R, R, d, p);
    }
    else
    {
        _fmpz_vec_scalar_mod_fmpz(R, R, lenR, p);
    }
}

QADIC_INLINE void qadic_reduce(qadic_t x, const qadic_ctx_t ctx)
{
    const slong N = qadic_prec(x);
    const slong d = ctx->j[ctx->len - 1];

    if (x->length == 0 || x->val >= N)
    {
        padic_poly_zero(x);
    }
    else
    {
        fmpz_t pow;
        int alloc;

        alloc = _padic_ctx_pow_ui(pow, N - x->val, &ctx->pctx);

        _fmpz_mod_poly_reduce(x->coeffs, x->length, ctx->a, ctx->j, ctx->len, pow);
        _padic_poly_set_length(x, FLINT_MIN(x->length, d));
        _padic_poly_normalise(x);
        padic_poly_canonicalise(x, (&ctx->pctx)->p);

        if (alloc)
            fmpz_clear(pow);
    }
}

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

QADIC_INLINE void
qadic_randtest(qadic_t x, flint_rand_t state, const qadic_ctx_t ctx)
{
    padic_poly_randtest(x, state, qadic_ctx_degree(ctx), &ctx->pctx);
}

QADIC_INLINE void
qadic_randtest_not_zero(qadic_t x, flint_rand_t state, const qadic_ctx_t ctx)
{
    padic_poly_randtest_not_zero(x, state, qadic_ctx_degree(ctx),
                                 &ctx->pctx);
}

QADIC_INLINE void
qadic_randtest_val(qadic_t x, flint_rand_t state, slong val,
                   const qadic_ctx_t ctx)
{
    padic_poly_randtest_val(x, state, val, qadic_ctx_degree(ctx), &ctx->pctx);
}

QADIC_INLINE void
qadic_randtest_int(qadic_t x, flint_rand_t state, const qadic_ctx_t ctx)
{
    const slong N = qadic_prec(x);

    if (N <= 0)
    {
        padic_poly_zero(x);
    }
    else
    {
        padic_poly_randtest_val(x, state, n_randint(state, N),
                                qadic_ctx_degree(ctx), &ctx->pctx);
    }
}

/* Assignments and conversions ***********************************************/

QADIC_INLINE void qadic_zero(qadic_t op)
{
    padic_poly_zero(op);
}

QADIC_INLINE void qadic_one(qadic_t op)
{
    padic_poly_one(op);
}

QADIC_INLINE void qadic_gen(qadic_t x, const qadic_ctx_t ctx)
{
    const slong N = qadic_prec(x);
    const slong d = qadic_ctx_degree(ctx);

    if (d > 1)
    {
        if (N > 0)
        {
            padic_poly_fit_length(x, 2);
            fmpz_zero(x->coeffs + 0);
            fmpz_one(x->coeffs + 1);
            _padic_poly_set_length(x, 2);
            x->val = 0;
        }
        else
        {
            padic_poly_zero(x);
        }
    }
    else
    {
        padic_poly_fit_length(x, 1);
	fmpz_neg(x->coeffs + 0, ctx->a + 0);
	_padic_poly_set_length(x, 1);
	x->val = 0;
    }
}

QADIC_INLINE
void qadic_set_ui(qadic_t rop, ulong op, const qadic_ctx_t ctx)
{
    padic_poly_set_ui(rop, op, &ctx->pctx);
}

QADIC_INLINE int
qadic_get_padic(padic_t rop, const qadic_t op, const qadic_ctx_t ctx)
{
    if (op->length > 0)
    {
        if (_fmpz_vec_is_zero(op->coeffs + 1, op->length - 1))
        {
            fmpz_set(padic_unit(rop), op->coeffs + 0);
            padic_val(rop) = op->val;
            _padic_canonicalise(rop, &ctx->pctx);
            return 1;
        }
        else
        {
            return 0;
        }
    }
    else
    {
        padic_zero(rop);
        return 1;
    }
}

QADIC_INLINE void qadic_set(qadic_t rop, const qadic_t op, const qadic_ctx_t ctx)
{
    padic_poly_set(rop, op, &(ctx->pctx));
}

void qadic_set_fmpz_poly(qadic_t rop, const fmpz_poly_t op,
                         const qadic_ctx_t ctx);

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

QADIC_INLINE int qadic_is_zero(const qadic_t op)
{
    return padic_poly_is_zero(op);
}

QADIC_INLINE int qadic_is_one(const qadic_t op)
{
    return padic_poly_is_one(op);
}

QADIC_INLINE int qadic_equal(const qadic_t op1, const qadic_t op2)
{
    return padic_poly_equal(op1, op2);
}

/* Basic arithmetic **********************************************************/

QADIC_INLINE void
qadic_add(qadic_t x, const qadic_t y, const qadic_t z, const qadic_ctx_t ctx)
{
    padic_poly_add(x, y, z, &ctx->pctx);
}

QADIC_INLINE void
qadic_sub(qadic_t x, const qadic_t y, const qadic_t z, const qadic_ctx_t ctx)
{
    padic_poly_sub(x, y, z, &ctx->pctx);
}

QADIC_INLINE void
qadic_neg(qadic_t x, const qadic_t y, const qadic_ctx_t ctx)
{
    padic_poly_neg(x, y, &ctx->pctx);
}

void qadic_mul(qadic_t x, const qadic_t y, const qadic_t z,
                          const qadic_ctx_t ctx);

void _qadic_inv(fmpz *rop, const fmpz *op, slong len,
                const fmpz *a, const slong *j, slong lena,
                const fmpz_t p, slong N);

void qadic_inv(qadic_t x, const qadic_t y, const qadic_ctx_t ctx);

void _qadic_pow(fmpz *rop, const fmpz *op, slong len, const fmpz_t e,
                const fmpz *a, const slong *j, slong lena,
                const fmpz_t p);

void qadic_pow(qadic_t x, const qadic_t y, const fmpz_t e, const qadic_ctx_t ctx);

/* Special functions *********************************************************/

void _qadic_exp_rectangular(fmpz *rop, const fmpz *op, slong v, slong len,
                            const fmpz *a, const slong *j, slong lena,
                            const fmpz_t p, slong N, const fmpz_t pN);

int qadic_exp_rectangular(qadic_t rop, const qadic_t op,
                          const qadic_ctx_t ctx);

void _qadic_exp_balanced(fmpz *rop, const fmpz *op, slong v, slong len,
                         const fmpz *a, const slong *j, slong lena,
                         const fmpz_t p, slong N, const fmpz_t pN);

int qadic_exp_balanced(qadic_t rop, const qadic_t op,
                       const qadic_ctx_t ctx);

void _qadic_exp(fmpz *rop, const fmpz *op, slong v, slong len,
                           const fmpz *a, const slong *j, slong lena,
                           const fmpz_t p, slong N, const fmpz_t pN);

int qadic_exp(qadic_t rop, const qadic_t op, const qadic_ctx_t ctx);

void _qadic_log_rectangular(fmpz *z, const fmpz *y, slong v, slong len,
                            const fmpz *a, const slong *j, slong lena,
                            const fmpz_t p, slong N, const fmpz_t pN);

int qadic_log_rectangular(qadic_t rop, const qadic_t op, const qadic_ctx_t ctx);

void _qadic_log_balanced(fmpz *z, const fmpz *y, slong len,
                         const fmpz *a, const slong *j, slong lena,
                         const fmpz_t p, slong N, const fmpz_t pN);

int qadic_log_balanced(qadic_t rop, const qadic_t op, const qadic_ctx_t ctx);

void _qadic_log(fmpz *z, const fmpz *y, slong v, slong len,
                const fmpz *a, const slong *j, slong lena,
                const fmpz_t p, slong N, const fmpz_t pN);

int qadic_log(qadic_t rop, const qadic_t op, const qadic_ctx_t ctx);

void _qadic_frobenius_a(fmpz *rop, slong exp,
                        const fmpz *a, const slong *j, slong lena,
                                  const fmpz_t p, slong N);


void _qadic_frobenius(fmpz *rop, const fmpz *op, slong len, slong e,
                  const fmpz *a, const slong *j, slong lena,
                  const fmpz_t p, slong N);

void qadic_frobenius(qadic_t rop, const qadic_t op, slong e, const qadic_ctx_t ctx);

void _qadic_teichmuller(fmpz *rop, const fmpz *op, slong len,
                        const fmpz *a, const slong *j, slong lena,
                        const fmpz_t p, slong N);

void qadic_teichmuller(qadic_t rop, const qadic_t op, const qadic_ctx_t ctx);

void _qadic_trace(fmpz_t rop, const fmpz *op, slong len,
                  const fmpz *a, const slong *j, slong lena, const fmpz_t pN);

void qadic_trace(padic_t rop, const qadic_t op, const qadic_ctx_t ctx);


void _qadic_norm_resultant(fmpz_t rop, const fmpz *op, slong len,
                           const fmpz *a, const slong *j, slong lena,
                           const fmpz_t p, slong N);
void _qadic_norm_analytic(fmpz_t rop, const fmpz *y, slong v, slong len,
                          const fmpz *a, const slong *j, slong lena,
                          const fmpz_t p, slong N);
void _qadic_norm(fmpz_t rop, const fmpz *op, slong len,
                 const fmpz *a, const slong *j, slong lena,
                 const fmpz_t p, slong N);

void qadic_norm(padic_t rop, const qadic_t op, const qadic_ctx_t ctx);
void qadic_norm_analytic(padic_t rop, const qadic_t op, const qadic_ctx_t ctx);
void qadic_norm_resultant(padic_t rop, const qadic_t op, const qadic_ctx_t ctx);

int qadic_sqrt(qadic_t rop, const qadic_t op, const qadic_ctx_t ctx);

struct qadic2_sqrt_precomp;

struct qadic2_sqrt_precomp *_qadic_char2_sqrt_precomp_init(const qadic_ctx_t ctx);
int _qadic_char2_sqrt_with_precomp(qadic_t rop, const qadic_t op, const qadic_ctx_t ctx,
                                   const struct qadic2_sqrt_precomp *data);
void _qadic_char2_sqrt_precomp_clear(struct qadic2_sqrt_precomp *data);

/* Output ********************************************************************/

#ifdef FLINT_HAVE_FILE
int qadic_fprint_pretty(FILE * file, const qadic_t op, const qadic_ctx_t ctx);
#endif

int qadic_print_pretty(const qadic_t op, const qadic_ctx_t ctx);
int qadic_debug(const qadic_t op);

#ifdef __cplusplus
}
#endif

#endif