468 lines
13 KiB
C
468 lines
13 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) 2011, 2012, 2013 Sebastian Pancratz
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******************************************************************************/
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#ifndef QADIC_H
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#define QADIC_H
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#undef ulong
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#define ulong ulongxx /* interferes with system includes */
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#include <stdlib.h>
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#include <stdio.h>
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#undef ulong
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#include <gmp.h>
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#include "flint.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 "ulong_extras.h"
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#include "padic.h"
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#include "padic_poly.h"
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#define ulong mp_limb_t
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#ifdef __cplusplus
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extern "C" {
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#endif
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/* Data types and context ****************************************************/
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typedef padic_poly_t qadic_t;
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typedef padic_poly_struct qadic_struct;
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static __inline__ slong qadic_val(const qadic_t op)
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{
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return padic_poly_val(op);
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}
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static __inline__ slong qadic_prec(const qadic_t op)
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{
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return padic_poly_prec(op);
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}
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typedef struct
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{
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padic_ctx_struct pctx;
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fmpz *a;
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slong *j;
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slong len;
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char *var;
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}
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qadic_ctx_struct;
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typedef qadic_ctx_struct qadic_ctx_t[1];
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void qadic_ctx_init_conway(qadic_ctx_t ctx,
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const fmpz_t p, slong d, slong min, slong max,
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const char *var, enum padic_print_mode mode);
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void qadic_ctx_clear(qadic_ctx_t ctx);
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static __inline__ slong qadic_ctx_degree(const qadic_ctx_t ctx)
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{
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return ctx->j[ctx->len - 1];
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}
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static __inline__ void qadic_ctx_print(const qadic_ctx_t ctx)
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{
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slong i, k;
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flint_printf("p = "), fmpz_print((&ctx->pctx)->p), flint_printf("\n");
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flint_printf("d = %wd\n", ctx->j[ctx->len - 1]);
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flint_printf("f(X) = ");
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fmpz_print(ctx->a + 0);
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for (k = 1; k < ctx->len; k++)
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{
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i = ctx->j[k];
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flint_printf(" + ");
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if (fmpz_is_one(ctx->a + k))
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{
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if (i == 1)
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flint_printf("X");
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else
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flint_printf("X^%wd", i);
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}
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else
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{
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fmpz_print(ctx->a + k);
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if (i == 1)
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flint_printf("*X");
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else
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flint_printf("*X^%wd", i);
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}
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}
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flint_printf("\n");
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}
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/* Memory management *********************************************************/
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static __inline__ void qadic_init(qadic_t x)
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{
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padic_poly_init(x);
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}
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static __inline__ void qadic_init2(qadic_t rop, slong prec)
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{
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padic_poly_init2(rop, 0, prec);
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}
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static __inline__ void qadic_clear(qadic_t x)
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{
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padic_poly_clear(x);
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}
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/*
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TODO: Consider renaming this function, prefix for the "qadic" module.
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*/
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static __inline__ void
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_fmpz_poly_reduce(fmpz *R, slong lenR, const fmpz *a, const slong *j, slong len)
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{
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const slong d = j[len - 1];
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slong i, k;
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FMPZ_VEC_NORM(R, lenR);
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for (i = lenR - 1; i >= d; i--)
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{
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for (k = len - 2; k >= 0; k--)
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{
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fmpz_submul(R + j[k] + i - d, R + i, a + k);
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}
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fmpz_zero(R + i);
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}
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}
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/*
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TODO: Consider renaming this function, prefix for the "qadic" module.
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*/
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static __inline__ void
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_fmpz_mod_poly_reduce(fmpz *R, slong lenR,
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const fmpz *a, const slong *j, slong len, const fmpz_t p)
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{
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const slong d = j[len - 1];
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if (lenR > d)
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{
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_fmpz_poly_reduce(R, lenR, a, j, len);
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_fmpz_vec_scalar_mod_fmpz(R, R, d, p);
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}
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else
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{
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_fmpz_vec_scalar_mod_fmpz(R, R, lenR, p);
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}
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}
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static __inline__ void qadic_reduce(qadic_t x, const qadic_ctx_t ctx)
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{
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const slong N = qadic_prec(x);
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const slong d = ctx->j[ctx->len - 1];
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if (x->length == 0 || x->val >= N)
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{
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padic_poly_zero(x);
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}
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else
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{
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fmpz_t pow;
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int alloc;
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alloc = _padic_ctx_pow_ui(pow, N - x->val, &ctx->pctx);
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_fmpz_mod_poly_reduce(x->coeffs, x->length, ctx->a, ctx->j, ctx->len, pow);
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_padic_poly_set_length(x, FLINT_MIN(x->length, d));
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_padic_poly_normalise(x);
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padic_poly_canonicalise(x, (&ctx->pctx)->p);
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if (alloc)
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fmpz_clear(pow);
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}
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}
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/* Randomisation *************************************************************/
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static __inline__ void
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qadic_randtest(qadic_t x, flint_rand_t state, const qadic_ctx_t ctx)
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{
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padic_poly_randtest(x, state, qadic_ctx_degree(ctx), &ctx->pctx);
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}
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static __inline__ void
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qadic_randtest_not_zero(qadic_t x, flint_rand_t state, const qadic_ctx_t ctx)
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{
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padic_poly_randtest_not_zero(x, state, qadic_ctx_degree(ctx),
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&ctx->pctx);
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}
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static __inline__ void
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qadic_randtest_val(qadic_t x, flint_rand_t state, slong val,
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const qadic_ctx_t ctx)
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{
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padic_poly_randtest_val(x, state, val, qadic_ctx_degree(ctx), &ctx->pctx);
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}
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static __inline__ void
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qadic_randtest_int(qadic_t x, flint_rand_t state, const qadic_ctx_t ctx)
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{
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const slong N = qadic_prec(x);
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if (N <= 0)
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{
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padic_poly_zero(x);
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}
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else
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{
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padic_poly_randtest_val(x, state, n_randint(state, N),
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qadic_ctx_degree(ctx), &ctx->pctx);
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}
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}
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/* Assignments and conversions ***********************************************/
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static __inline__ void qadic_zero(qadic_t op)
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{
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padic_poly_zero(op);
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}
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static __inline__ void qadic_one(qadic_t op)
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{
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padic_poly_one(op);
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}
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static __inline__ void qadic_gen(qadic_t x, const qadic_ctx_t ctx)
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{
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const slong N = qadic_prec(x);
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const slong d = qadic_ctx_degree(ctx);
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if (d > 1)
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{
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if (N > 0)
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{
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padic_poly_fit_length(x, 2);
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fmpz_zero(x->coeffs + 0);
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fmpz_one(x->coeffs + 1);
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_padic_poly_set_length(x, 2);
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x->val = 0;
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}
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else
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{
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padic_poly_zero(x);
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}
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}
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else
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{
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flint_printf("Exception (qadic_gen). Extension degree d = 1.\n");
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abort();
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}
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}
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static __inline__
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void qadic_set_ui(qadic_t rop, ulong op, const qadic_ctx_t ctx)
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{
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padic_poly_set_ui(rop, op, &ctx->pctx);
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}
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static __inline__ int
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qadic_get_padic(padic_t rop, const qadic_t op, const qadic_ctx_t ctx)
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{
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if (op->length > 0)
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{
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if (_fmpz_vec_is_zero(op->coeffs + 1, op->length - 1))
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{
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fmpz_set(padic_unit(rop), op->coeffs + 0);
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padic_val(rop) = op->val;
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_padic_canonicalise(rop, &ctx->pctx);
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return 1;
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}
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else
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{
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return 0;
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}
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}
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else
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{
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padic_zero(rop);
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return 1;
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}
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}
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static __inline__ void qadic_set(qadic_t rop, const qadic_t op, const qadic_ctx_t ctx)
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{
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padic_poly_set(rop, op, &(ctx->pctx));
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}
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void qadic_set_fmpz_poly(qadic_t rop, const fmpz_poly_t op,
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const qadic_ctx_t ctx);
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/* Comparison ****************************************************************/
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static __inline__ int qadic_is_zero(const qadic_t op)
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{
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return padic_poly_is_zero(op);
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}
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static __inline__ int qadic_is_one(const qadic_t op)
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{
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return padic_poly_is_one(op);
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}
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static __inline__ int qadic_equal(const qadic_t op1, const qadic_t op2)
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{
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return padic_poly_equal(op1, op2);
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}
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/* Basic arithmetic **********************************************************/
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static __inline__ void
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qadic_add(qadic_t x, const qadic_t y, const qadic_t z, const qadic_ctx_t ctx)
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{
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padic_poly_add(x, y, z, &ctx->pctx);
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}
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static __inline__ void
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qadic_sub(qadic_t x, const qadic_t y, const qadic_t z, const qadic_ctx_t ctx)
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{
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padic_poly_sub(x, y, z, &ctx->pctx);
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}
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static __inline__ void
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qadic_neg(qadic_t x, const qadic_t y, const qadic_ctx_t ctx)
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{
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padic_poly_neg(x, y, &ctx->pctx);
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}
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void qadic_mul(qadic_t x, const qadic_t y, const qadic_t z,
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const qadic_ctx_t ctx);
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void _qadic_inv(fmpz *rop, const fmpz *op, slong len,
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const fmpz *a, const slong *j, slong lena,
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const fmpz_t p, slong N);
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void qadic_inv(qadic_t x, const qadic_t y, const qadic_ctx_t ctx);
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void _qadic_pow(fmpz *rop, const fmpz *op, slong len, const fmpz_t e,
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const fmpz *a, const slong *j, slong lena,
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const fmpz_t p);
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void qadic_pow(qadic_t x, const qadic_t y, const fmpz_t e, const qadic_ctx_t ctx);
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/* Special functions *********************************************************/
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void _qadic_exp_rectangular(fmpz *rop, const fmpz *op, slong v, slong len,
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const fmpz *a, const slong *j, slong lena,
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const fmpz_t p, slong N, const fmpz_t pN);
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int qadic_exp_rectangular(qadic_t rop, const qadic_t op,
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const qadic_ctx_t ctx);
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void _qadic_exp_balanced(fmpz *rop, const fmpz *op, slong v, slong len,
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const fmpz *a, const slong *j, slong lena,
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const fmpz_t p, slong N, const fmpz_t pN);
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int qadic_exp_balanced(qadic_t rop, const qadic_t op,
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const qadic_ctx_t ctx);
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void _qadic_exp(fmpz *rop, const fmpz *op, slong v, slong len,
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const fmpz *a, const slong *j, slong lena,
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const fmpz_t p, slong N, const fmpz_t pN);
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int qadic_exp(qadic_t rop, const qadic_t op, const qadic_ctx_t ctx);
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void _qadic_log_rectangular(fmpz *z, const fmpz *y, slong v, slong len,
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const fmpz *a, const slong *j, slong lena,
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const fmpz_t p, slong N, const fmpz_t pN);
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int qadic_log_rectangular(qadic_t rop, const qadic_t op, const qadic_ctx_t ctx);
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void _qadic_log_balanced(fmpz *z, const fmpz *y, slong len,
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const fmpz *a, const slong *j, slong lena,
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const fmpz_t p, slong N, const fmpz_t pN);
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int qadic_log_balanced(qadic_t rop, const qadic_t op, const qadic_ctx_t ctx);
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void _qadic_log(fmpz *z, const fmpz *y, slong v, slong len,
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const fmpz *a, const slong *j, slong lena,
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const fmpz_t p, slong N, const fmpz_t pN);
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int qadic_log(qadic_t rop, const qadic_t op, const qadic_ctx_t ctx);
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void qadic_frobenius(qadic_t rop, const qadic_t op, slong e, const qadic_ctx_t ctx);
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void _qadic_teichmuller(fmpz *rop, const fmpz *op, slong len,
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const fmpz *a, const slong *j, slong lena,
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const fmpz_t p, slong N);
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void qadic_teichmuller(qadic_t rop, const qadic_t op, const qadic_ctx_t ctx);
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void _qadic_trace(fmpz_t rop, const fmpz *op, slong len,
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const fmpz *a, const slong *j, slong lena, const fmpz_t pN);
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void qadic_trace(padic_t rop, const qadic_t op, const qadic_ctx_t ctx);
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void _qadic_norm_resultant(fmpz_t rop, const fmpz *op, slong len,
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const fmpz *a, const slong *j, slong lena,
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const fmpz_t p, slong N);
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void _qadic_norm_analytic(fmpz_t rop, const fmpz *y, slong v, slong len,
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const fmpz *a, const slong *j, slong lena,
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const fmpz_t p, slong N);
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void _qadic_norm(fmpz_t rop, const fmpz *op, slong len,
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const fmpz *a, const slong *j, slong lena,
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const fmpz_t p, slong N);
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void qadic_norm(padic_t rop, const qadic_t op, const qadic_ctx_t ctx);
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void qadic_norm_analytic(padic_t rop, const qadic_t op, const qadic_ctx_t ctx);
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void qadic_norm_resultant(padic_t rop, const qadic_t op, const qadic_ctx_t ctx);
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int qadic_sqrt(qadic_t rop, const qadic_t op, const qadic_ctx_t ctx);
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int qadic_invsqrt(qadic_t rop, const qadic_t op, const qadic_ctx_t ctx);
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/* Output ********************************************************************/
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int qadic_fprint_pretty(FILE *file, const qadic_t op, const qadic_ctx_t ctx);
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static __inline__ int
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qadic_print_pretty(const qadic_t op, const qadic_ctx_t ctx)
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{
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return qadic_fprint_pretty(stdout, op, ctx);
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}
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static __inline__ int qadic_debug(const qadic_t op)
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{
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return padic_poly_debug(op);
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}
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#ifdef __cplusplus
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}
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#endif
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#endif
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