/usr/include/flint/fmpz_mat.h is in libflint-dev 2.4.4-2.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
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This file is part of FLINT.
FLINT is free software; you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation; either version 2 of the License, or
(at your option) any later version.
FLINT is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with FLINT; if not, write to the Free Software
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
=============================================================================*/
/******************************************************************************
Copyright (C) 2010 William Hart
Copyright (C) 2010 Fredrik Johansson
******************************************************************************/
#ifndef FMPZ_MAT_H
#define FMPZ_MAT_H
#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 "nmod_mat.h"
#include "fmpz_poly.h"
#ifdef __cplusplus
extern "C" {
#endif
typedef struct
{
fmpz * entries;
slong r;
slong c;
fmpz ** rows;
} fmpz_mat_struct;
typedef fmpz_mat_struct fmpz_mat_t[1];
/* Memory management ********************************************************/
#define fmpz_mat_entry(mat,i,j) ((mat)->rows[i] + (j))
#define fmpz_mat_nrows(mat) ((mat)->r)
#define fmpz_mat_ncols(mat) ((mat)->c)
void fmpz_mat_init(fmpz_mat_t mat, slong rows, slong cols);
void fmpz_mat_init_set(fmpz_mat_t mat, const fmpz_mat_t src);
void fmpz_mat_swap(fmpz_mat_t mat1, fmpz_mat_t mat2);
void fmpz_mat_set(fmpz_mat_t mat1, const fmpz_mat_t mat2);
void fmpz_mat_clear(fmpz_mat_t mat);
int fmpz_mat_equal(const fmpz_mat_t mat1, const fmpz_mat_t mat2);
int fmpz_mat_is_zero(const fmpz_mat_t mat);
static __inline__ int
fmpz_mat_is_empty(const fmpz_mat_t mat)
{
return (mat->r == 0) || (mat->c == 0);
}
static __inline__ int
fmpz_mat_is_square(const fmpz_mat_t mat)
{
return (mat->r == mat->c);
}
void fmpz_mat_zero(fmpz_mat_t mat);
void fmpz_mat_one(fmpz_mat_t mat);
/* Input and output *********************************************************/
int fmpz_mat_fprint(FILE * file, const fmpz_mat_t mat);
int fmpz_mat_fprint_pretty(FILE * file, const fmpz_mat_t mat);
static __inline__
int fmpz_mat_print(const fmpz_mat_t mat)
{
return fmpz_mat_fprint(stdout, mat);
}
static __inline__
int fmpz_mat_print_pretty(const fmpz_mat_t mat)
{
return fmpz_mat_fprint_pretty(stdout, mat);
}
int fmpz_mat_fread(FILE* file, fmpz_mat_t mat);
static __inline__
int fmpz_mat_read(fmpz_mat_t mat)
{
return fmpz_mat_fread(stdin, mat);
}
/* Random matrix generation *************************************************/
void fmpz_mat_randbits(fmpz_mat_t mat, flint_rand_t state, mp_bitcnt_t bits);
void fmpz_mat_randtest(fmpz_mat_t mat, flint_rand_t state, mp_bitcnt_t bits);
void fmpz_mat_randtest_unsigned(fmpz_mat_t mat, flint_rand_t state, mp_bitcnt_t bits);
void fmpz_mat_randintrel(fmpz_mat_t mat, flint_rand_t state, mp_bitcnt_t bits);
void fmpz_mat_randsimdioph(fmpz_mat_t mat, flint_rand_t state, mp_bitcnt_t bits, mp_bitcnt_t bits2);
void fmpz_mat_randntrulike(fmpz_mat_t mat, flint_rand_t state, mp_bitcnt_t bits, ulong q);
void fmpz_mat_randntrulike2(fmpz_mat_t mat, flint_rand_t state, mp_bitcnt_t bits, ulong q);
void fmpz_mat_randajtai(fmpz_mat_t mat, flint_rand_t state, double alpha);
void fmpz_mat_randrank(fmpz_mat_t mat, flint_rand_t state, slong rank, mp_bitcnt_t bits);
void fmpz_mat_randdet(fmpz_mat_t mat, flint_rand_t state, const fmpz_t det);
void fmpz_mat_randops(fmpz_mat_t mat, flint_rand_t state, slong count);
int fmpz_mat_randpermdiag(fmpz_mat_t mat, flint_rand_t state, const fmpz * diag, slong n);
/* Norms */
slong fmpz_mat_max_bits(const fmpz_mat_t mat);
/* Transpose */
void fmpz_mat_transpose(fmpz_mat_t B, const fmpz_mat_t A);
/* Addition and subtraction */
void fmpz_mat_add(fmpz_mat_t C, const fmpz_mat_t A, const fmpz_mat_t B);
void fmpz_mat_sub(fmpz_mat_t C, const fmpz_mat_t A, const fmpz_mat_t B);
void fmpz_mat_neg(fmpz_mat_t B, const fmpz_mat_t A);
/* Scalar operations */
void fmpz_mat_scalar_mul_fmpz(fmpz_mat_t B, const fmpz_mat_t A, const fmpz_t c);
void fmpz_mat_scalar_mul_si(fmpz_mat_t B, const fmpz_mat_t A, slong c);
void fmpz_mat_scalar_mul_ui(fmpz_mat_t B, const fmpz_mat_t A, ulong c);
void fmpz_mat_scalar_addmul_fmpz(fmpz_mat_t B, const fmpz_mat_t A, const fmpz_t c);
void fmpz_mat_scalar_addmul_si(fmpz_mat_t B, const fmpz_mat_t A, slong c);
void fmpz_mat_scalar_addmul_ui(fmpz_mat_t B, const fmpz_mat_t A, ulong c);
void fmpz_mat_scalar_submul_fmpz(fmpz_mat_t B, const fmpz_mat_t A, const fmpz_t c);
void fmpz_mat_scalar_submul_si(fmpz_mat_t B, const fmpz_mat_t A, slong c);
void fmpz_mat_scalar_submul_ui(fmpz_mat_t B, const fmpz_mat_t A, ulong c);
void fmpz_mat_scalar_addmul_nmod_mat_fmpz(fmpz_mat_t B, const nmod_mat_t A, const fmpz_t c);
void fmpz_mat_scalar_addmul_nmod_mat_ui(fmpz_mat_t B, const nmod_mat_t A, ulong c);
void fmpz_mat_scalar_divexact_fmpz(fmpz_mat_t B, const fmpz_mat_t A, const fmpz_t c);
void fmpz_mat_scalar_divexact_si(fmpz_mat_t B, const fmpz_mat_t A, slong c);
void fmpz_mat_scalar_divexact_ui(fmpz_mat_t B, const fmpz_mat_t A, ulong c);
void fmpz_mat_scalar_mod_fmpz(fmpz_mat_t B, const fmpz_mat_t A, const fmpz_t m);
/* Multiplication */
void fmpz_mat_mul(fmpz_mat_t C, const fmpz_mat_t A, const fmpz_mat_t B);
void fmpz_mat_mul_classical(fmpz_mat_t C, const fmpz_mat_t A,
const fmpz_mat_t B);
void fmpz_mat_mul_classical_inline(fmpz_mat_t C, const fmpz_mat_t A,
const fmpz_mat_t B);
void _fmpz_mat_mul_multi_mod(fmpz_mat_t C, const fmpz_mat_t A,
const fmpz_mat_t B, mp_bitcnt_t bits);
void fmpz_mat_mul_multi_mod(fmpz_mat_t C, const fmpz_mat_t A,
const fmpz_mat_t B);
void fmpz_mat_sqr(fmpz_mat_t B, const fmpz_mat_t A);
void fmpz_mat_pow(fmpz_mat_t B, const fmpz_mat_t A, ulong exp);
/* Permutations */
static __inline__ void
fmpz_mat_swap_rows(fmpz_mat_t mat, slong * perm, slong r, slong s)
{
if (r != s)
{
fmpz * u;
slong t;
if (perm)
{
t = perm[s];
perm[s] = perm[r];
perm[r] = t;
}
u = mat->rows[s];
mat->rows[s] = mat->rows[r];
mat->rows[r] = u;
}
}
/* Gaussian elimination *****************************************************/
slong fmpz_mat_find_pivot_any(const fmpz_mat_t mat,
slong start_row, slong end_row, slong c);
slong fmpz_mat_fflu(fmpz_mat_t B, fmpz_t den, slong * perm,
const fmpz_mat_t A, int rank_check);
slong fmpz_mat_rref(fmpz_mat_t B, fmpz_t den, const fmpz_mat_t A);
/* Modular gaussian elimination *********************************************/
slong
fmpz_mat_rref_mod(slong * perm, fmpz_mat_t A, const fmpz_t p);
/* Trace ********************************************************************/
void fmpz_mat_trace(fmpz_t trace, const fmpz_mat_t mat);
/* Determinant **************************************************************/
void fmpz_mat_det(fmpz_t det, const fmpz_mat_t A);
void fmpz_mat_det_cofactor(fmpz_t det, const fmpz_mat_t A);
void _fmpz_mat_det_cofactor_2x2(fmpz_t det, fmpz ** const x);
void _fmpz_mat_det_cofactor_3x3(fmpz_t det, fmpz ** const x);
void _fmpz_mat_det_cofactor_4x4(fmpz_t det, fmpz ** const x);
void fmpz_mat_det_bareiss(fmpz_t det, const fmpz_mat_t A);
void fmpz_mat_det_modular(fmpz_t det, const fmpz_mat_t A, int proved);
void fmpz_mat_det_modular_accelerated(fmpz_t det,
const fmpz_mat_t A, int proved);
void fmpz_mat_det_modular_given_divisor(fmpz_t det, const fmpz_mat_t A,
const fmpz_t d, int proved);
void fmpz_mat_det_bound(fmpz_t bound, const fmpz_mat_t A);
void fmpz_mat_det_divisor(fmpz_t d, const fmpz_mat_t A);
/* Characteristic polynomial ************************************************/
void _fmpz_mat_charpoly(fmpz *cp, const fmpz_mat_t mat);
void fmpz_mat_charpoly(fmpz_poly_t cp, const fmpz_mat_t mat);
/* Rank *********************************************************************/
slong fmpz_mat_rank(const fmpz_mat_t A);
/* Nonsingular solving ******************************************************/
void fmpz_mat_solve_bound(fmpz_t N, fmpz_t D,
const fmpz_mat_t A, const fmpz_mat_t B);
int fmpz_mat_solve(fmpz_mat_t X, fmpz_t den,
const fmpz_mat_t A, const fmpz_mat_t B);
int fmpz_mat_solve_cramer(fmpz_mat_t X, fmpz_t den,
const fmpz_mat_t A, const fmpz_mat_t B);
int fmpz_mat_solve_fflu(fmpz_mat_t X, fmpz_t den,
const fmpz_mat_t A, const fmpz_mat_t B);
void fmpz_mat_solve_fflu_precomp(fmpz_mat_t X, const slong * perm,
const fmpz_mat_t FFLU, const fmpz_mat_t B);
int fmpz_mat_solve_dixon(fmpz_mat_t X, fmpz_t mod,
const fmpz_mat_t A, const fmpz_mat_t B);
/* Nullspace ****************************************************************/
slong fmpz_mat_nullspace(fmpz_mat_t res, const fmpz_mat_t mat);
/* Inverse ******************************************************************/
int fmpz_mat_inv(fmpz_mat_t B, fmpz_t den, const fmpz_mat_t A);
/* Modular reduction and reconstruction *************************************/
void fmpz_mat_set_nmod_mat(fmpz_mat_t A, const nmod_mat_t Amod);
void fmpz_mat_set_nmod_mat_unsigned(fmpz_mat_t A, const nmod_mat_t Amod);
void fmpz_mat_get_nmod_mat(nmod_mat_t Amod, const fmpz_mat_t A);
void fmpz_mat_CRT_ui(fmpz_mat_t res, const fmpz_mat_t mat1,
const fmpz_t m1, const nmod_mat_t mat2, int sign);
void
fmpz_mat_multi_mod_ui_precomp(nmod_mat_t * residues, slong nres,
const fmpz_mat_t mat, const fmpz_comb_t comb, fmpz_comb_temp_t temp);
void
fmpz_mat_multi_mod_ui(nmod_mat_t * residues, slong nres, const fmpz_mat_t mat);
void
fmpz_mat_multi_CRT_ui_precomp(fmpz_mat_t mat,
nmod_mat_t * const residues, slong nres,
const fmpz_comb_t comb, fmpz_comb_temp_t temp, int sign);
void fmpz_mat_multi_CRT_ui(fmpz_mat_t mat, nmod_mat_t * const residues,
slong nres, int sign);
#ifdef __cplusplus
}
#endif
#endif
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