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https://github.com/vale981/arb
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112 lines
3.2 KiB
C
112 lines
3.2 KiB
C
/*=============================================================================
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This file is part of ARB.
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ARB 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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ARB 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 ARB; 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) 2012 Fredrik Johansson
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******************************************************************************/
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#include "fmpz_holonomic.h"
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#include "fmpz_poly_mat.h"
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void
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fmpz_holonomic_seq_section(fmpz_holonomic_t res, const fmpz_holonomic_t op, long m)
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{
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long i, j, r, rows, cols, left_cols, right_cols, pos;
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fmpz_poly_mat_t mat;
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fmpz_poly_t t;
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r = fmpz_holonomic_order(op);
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if (m == 0)
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{
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if (r < 1)
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fmpz_holonomic_one(res);
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else
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fmpz_holonomic_seq_set_const(res);
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return;
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}
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else if (m == 1)
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{
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fmpz_holonomic_set(res, op);
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return;
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}
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else if (m < 0)
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{
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fmpz_holonomic_seq_section(res, op, -m);
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fmpz_holonomic_seq_reverse(res, res);
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return;
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}
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/*
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Algorithm: by shifting the input recurrence, we obtain a set of
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linear relations over c[m*k], c[m*k+1], c[m*k+2]..., c[m*(k+r)].
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We use Gaussian elimination to eliminate the offsets that
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are not multiples of m, obtaining a relation for c[m*k], c[m*(k+1)],
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..., c[m*(k+r)].
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*/
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rows = m * r - r + 1;
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cols = m * r + 1;
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/* we put the non-multiples of m on the left of the matrix
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and the multiples on the right */
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right_cols = r + 1;
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left_cols = cols - right_cols;
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fmpz_poly_mat_init(mat, rows, cols);
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fmpz_poly_init(t);
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for (i = 0; i < rows; i++)
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{
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fmpz_poly_zero(t);
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fmpz_poly_set_coeff_si(t, 0, i);
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fmpz_poly_set_coeff_si(t, 1, m);
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for (j = 0; j < cols; j++)
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{
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/* zero */
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if (j < i || j - i > r)
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continue;
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/* insert in the right or the left part of the matrix */
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if (j % m == 0)
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pos = left_cols + (j / m);
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else
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pos = j - (j / m) - 1;
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fmpz_poly_compose(mat->rows[i] + pos, op->coeffs + j - i, t);
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}
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}
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/* Do Gaussian elimination */
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fmpz_poly_mat_fflu(mat, t, NULL, mat, 0);
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/* The relation is the last row */
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fmpz_holonomic_fit_length(res, r + 1);
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for (i = 0; i <= r; i++)
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fmpz_poly_neg(res->coeffs + i, mat->rows[rows - 1] + left_cols + i);
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_fmpz_holonomic_set_length(res, r + 1);
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fmpz_holonomic_seq_normalise(res);
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fmpz_poly_mat_clear(mat);
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fmpz_poly_clear(t);
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}
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