void
fmpz_mat_mul_classical(fmpz_mat_t C, const fmpz_mat_t A, const fmpz_mat_t B)
{
long ar, bc, br;
long i, j, k;
ar = A->r;
br = B->r;
bc = B->c;
if (br == 0)
{
fmpz_mat_zero(C);
return;
}
for (i = 0; i < ar; i++)
{
for (j = 0; j < bc; j++)
{
fmpz_mul(fmpz_mat_entry(C, i, j),
fmpz_mat_entry(A, i, 0),
fmpz_mat_entry(B, 0, j));
for (k = 1; k < br; k++)
{
fmpz_addmul(fmpz_mat_entry(C, i, j),
fmpz_mat_entry(A, i, k),
fmpz_mat_entry(B, k, j));
}
}
}
}
int
fmpz_mat_randpermdiag(fmpz_mat_t mat, flint_rand_t state,
const fmpz * diag, long n)
{
int parity;
long i;
long * rows;
long * cols;
rows = malloc(sizeof(long) * mat->r);
cols = malloc(sizeof(long) * mat->c);
for (i = 0; i < mat->r; i++) rows[i] = i;
for (i = 0; i < mat->c; i++) cols[i] = i;
parity = shuffle(rows, state, mat->r);
parity ^= shuffle(cols, state, mat->c);
fmpz_mat_zero(mat);
for (i = 0; i < n; i++)
fmpz_set(&mat->rows[rows[i]][cols[i]], &diag[i]);
free(rows);
free(cols);
return parity;
}
void
fmpz_mat_unit(fmpz_mat_t mat)
{
long i;
fmpz_mat_zero(mat);
for (i = 0; i < FLINT_MIN(mat->r, mat->c); i++)
fmpz_set_ui(mat->rows[i] + i, 1UL);
}
void
_brute_force_all_pairs_longest_walk(fmpz_mat_t B, const bool_mat_t A)
{
slong i, j, n;
n = bool_mat_nrows(A);
/* set entries of B according to the longest observed walk */
{
slong k;
bool_mat_t T;
bool_mat_init(T, n, n);
bool_mat_one(T);
fmpz_mat_zero(B);
for (k = 0; k < 2*n+1; k++)
{
for (i = 0; i < n; i++)
{
for (j = 0; j < n; j++)
{
if (bool_mat_get_entry(T, i, j))
{
fmpz_set_si(fmpz_mat_entry(B, i, j), k);
}
}
}
bool_mat_mul(T, T, A);
}
bool_mat_clear(T);
}
/* set special values 0, -1, -2 */
{
for (i = 0; i < n; i++)
{
for (j = 0; j < n; j++)
{
slong x;
fmpz *p;
p = fmpz_mat_entry(B, i, j);
x = fmpz_get_si(p);
if (x < 1)
{
x = (i == j) ? 0 : -1;
}
else if (x > n-1)
{
x = -2;
}
fmpz_set_si(p, x);
}
}
}
}
int
main(void)
{
long m, n, i, j, rep;
flint_rand_t state;
printf("zero....");
fflush(stdout);
flint_randinit(state);
for (rep = 0; rep < 1000; rep++)
{
fmpz_mat_t A;
m = n_randint(state, 20);
n = n_randint(state, 20);
fmpz_mat_init(A, m, n);
fmpz_mat_randtest(A, state, 100);
fmpz_mat_zero(A);
for (i = 0; i < m; i++)
{
for (j = 0; j < n; j++)
{
if (!fmpz_is_zero(fmpz_mat_entry(A,i,j)))
{
printf("FAIL: nonzero entry\n");
abort();
}
}
}
fmpz_mat_clear(A);
}
flint_randclear(state);
_fmpz_cleanup();
printf("PASS\n");
return 0;
}
slong
bool_mat_nilpotency_degree(const bool_mat_t A)
{
slong n;
if (!bool_mat_is_square(A))
{
flint_printf("bool_mat_nilpotency_degree: a square matrix is required!\n");
abort();
}
if (bool_mat_is_empty(A))
return 0;
n = bool_mat_nrows(A);
if (n == 1)
{
return bool_mat_get_entry(A, 0, 0) ? -1 : 1;
}
else
{
_toposort_s s;
slong i;
int has_cycle;
int result;
_toposort_init(&s, n);
for (has_cycle = 0, i = 0; !has_cycle && i < n; i++)
if (!s.v[i])
has_cycle = _toposort_visit(&s, A, i);
if (has_cycle)
{
result = -1;
}
else
{
/* Find the length of the longest path within the DAG */
/* http://stackoverflow.com/a/10737524/4072759 */
slong x, y, z;
slong max_overall;
fmpz_mat_t E;
fmpz_mat_init(E, n, n);
fmpz_mat_zero(E);
max_overall = 0;
for (i = n - 1; i >= 0; i--)
{
slong max_in = 0;
y = s.post[i];
for (x = 0; x < n; x++)
{
max_in = FLINT_MAX(max_in,
fmpz_get_si(fmpz_mat_entry(E, x, y)));
}
for (z = 0; z < n; z++)
{
if (bool_mat_get_entry(A, y, z))
{
fmpz_set_si(fmpz_mat_entry(E, y, z), max_in + 1);
max_overall = FLINT_MAX(max_overall, max_in + 1);
}
}
}
fmpz_mat_clear(E);
result = max_overall + 1;
}
_toposort_clear(&s);
return result;
}
}
long
fmpz_mat_nullspace(fmpz_mat_t res, const fmpz_mat_t mat)
{
long i, j, k, m, n, rank, nullity;
long * pivots;
long * nonpivots;
fmpz_mat_t tmp;
fmpz_t den;
m = mat->r;
n = mat->c;
fmpz_mat_init_set(tmp, mat);
fmpz_init(den);
rank = fmpz_mat_rref(tmp, den, NULL, mat);
nullity = n - rank;
fmpz_mat_zero(res);
if (rank == 0)
{
for (i = 0; i < nullity; i++)
fmpz_one(res->rows[i] + i);
}
else if (nullity)
{
pivots = flint_malloc(rank * sizeof(long));
nonpivots = flint_malloc(nullity * sizeof(long));
for (i = j = k = 0; i < rank; i++)
{
while (fmpz_is_zero(tmp->rows[i] + j))
{
nonpivots[k] = j;
k++;
j++;
}
pivots[i] = j;
j++;
}
while (k < nullity)
{
nonpivots[k] = j;
k++;
j++;
}
fmpz_set(den, tmp->rows[0] + pivots[0]);
for (i = 0; i < nullity; i++)
{
for (j = 0; j < rank; j++)
fmpz_set(res->rows[pivots[j]] + i, tmp->rows[j] + nonpivots[i]);
fmpz_neg(res->rows[nonpivots[i]] + i, den);
}
flint_free(pivots);
flint_free(nonpivots);
}
fmpz_clear(den);
fmpz_mat_clear(tmp);
return nullity;
}
void nf_elem_rep_mat_fmpz_mat_den(fmpz_mat_t res, fmpz_t den, const nf_elem_t a, const nf_t nf)
{
if (nf->flag & NF_LINEAR)
{
fmpz_set(fmpz_mat_entry(res, 0, 0), LNF_ELEM_NUMREF(a));
fmpz_set(den, LNF_ELEM_DENREF(a));
}
else if (nf->flag & NF_QUADRATIC)
{
nf_elem_t t;
const fmpz * const anum = QNF_ELEM_NUMREF(a);
const fmpz * const aden = QNF_ELEM_DENREF(a);
fmpz * const tnum = QNF_ELEM_NUMREF(t);
fmpz * const tden = QNF_ELEM_DENREF(t);
nf_elem_init(t, nf);
nf_elem_mul_gen(t, a, nf);
if (fmpz_equal(tden, aden))
{
fmpz_set(fmpz_mat_entry(res, 0, 0), anum);
fmpz_set(fmpz_mat_entry(res, 0, 1), anum + 1);
fmpz_set(fmpz_mat_entry(res, 1, 0), tnum);
fmpz_set(fmpz_mat_entry(res, 1, 1), tnum + 1);
fmpz_set(den, tden);
}
else
{
fmpz_lcm(den, tden, aden);
fmpz_divexact(fmpz_mat_entry(res, 0, 0), den, aden);
fmpz_mul(fmpz_mat_entry(res, 0, 1), anum + 1, fmpz_mat_entry(res, 0, 0));
fmpz_mul(fmpz_mat_entry(res, 0, 0), anum, fmpz_mat_entry(res, 0, 0));
fmpz_divexact(fmpz_mat_entry(res, 1, 0), den, tden);
fmpz_mul(fmpz_mat_entry(res, 1, 1), tnum + 1, fmpz_mat_entry(res, 1, 0));
fmpz_mul(fmpz_mat_entry(res, 1, 0), tnum, fmpz_mat_entry(res, 1, 0));
}
nf_elem_clear(t, nf);
}
else
{
slong i, j;
nf_elem_t t;
slong d = fmpq_poly_degree(nf->pol);
nf_elem_init(t, nf);
nf_elem_set(t, a, nf);
if (NF_ELEM(a)->length == 0)
{
fmpz_mat_zero(res);
fmpz_one(den);
}
else if (NF_ELEM(a)->length == 1)
{
fmpz_mat_zero(res);
for (i = 0; i <= d - 1; i++)
{
fmpz_set(fmpz_mat_entry(res, i, i), fmpq_poly_numref(NF_ELEM(a)));
}
fmpz_set(den, fmpq_poly_denref(NF_ELEM(a)));
}
else
{
/* Special case if defining polynomial is monic and integral and the element also has trivial denominator */
if (nf->flag & NF_MONIC && fmpz_is_one(fmpq_poly_denref(nf->pol)) && fmpz_is_one(fmpq_poly_denref(NF_ELEM(a))))
{
fmpz_one(den);
for (i = 0; i <= NF_ELEM(a)->length - 1; i++)
fmpz_set(fmpz_mat_entry(res, 0, i), fmpq_poly_numref(NF_ELEM(a)) + i);
for (i = NF_ELEM(a)->length; i <= d - 1; i++)
fmpz_zero(fmpz_mat_entry(res, 0, i));
for (j = 1; j <= d - NF_ELEM(a)->length; j++)
{
nf_elem_mul_gen(t, t, nf);
for (i = 0; i < j; i++)
fmpz_zero(fmpz_mat_entry(res, j, i));
for (i = 0; i <= NF_ELEM(a)->length - 1; i++)
fmpz_set(fmpz_mat_entry(res, j, j + i), fmpq_poly_numref(NF_ELEM(a)) + i);
for (i = j + NF_ELEM(a)->length; i <= d - 1; i++)
fmpz_zero(fmpz_mat_entry(res, j, i));
}
for (j = d - NF_ELEM(a)->length + 1; j <= d - 1; j++)
{
nf_elem_mul_gen(t, t, nf);
for (i = 0; i <= d - 1; i++)
fmpz_set(fmpz_mat_entry(res, j, i), fmpq_poly_numref(NF_ELEM(t)) + i);
}
}
else
{
/* Now the general case. For 0 <= j < d - 2 we store the
* denominator for row j at res[d - 1, j]. At the end we
* divide the lcm of all of them by the corresponding
* denominator of the row to get the correct multiplier for
* row.
*/
for (i = 0; i <= NF_ELEM(a)->length - 1; i++)
fmpz_set(fmpz_mat_entry(res, 0, i), fmpq_poly_numref(NF_ELEM(a)) + i);
for (i = NF_ELEM(a)->length; i <= d - 1; i++)
fmpz_zero(fmpz_mat_entry(res, 0, i));
fmpz_set(fmpz_mat_entry(res, d - 1, 0), fmpq_poly_denref(NF_ELEM(a)));
for (j = 1; j <= d - NF_ELEM(a)->length; j++)
{
nf_elem_mul_gen(t, t, nf);
for (i = 0; i < j; i++)
fmpz_zero(fmpz_mat_entry(res, j, i));
for (i = 0; i <= NF_ELEM(a)->length - 1; i++)
fmpz_set(fmpz_mat_entry(res, j, j + i), fmpq_poly_numref(NF_ELEM(a)) + i);
for (i = j + NF_ELEM(a)->length; i <= d - 1; i++)
fmpz_zero(fmpz_mat_entry(res, j, i));
fmpz_set(fmpz_mat_entry(res, d - 1, j), fmpq_poly_denref(NF_ELEM(a)));
}
for (j = d - NF_ELEM(a)->length + 1; j <= d - 2; j++)
{
nf_elem_mul_gen(t, t, nf);
for (i = 0; i <= d - 1; i++)
fmpz_set(fmpz_mat_entry(res, j, i), fmpq_poly_numref(NF_ELEM(t)) + i);
fmpz_set(fmpz_mat_entry(res, d - 1, j), fmpq_poly_denref(NF_ELEM(t)));
}
nf_elem_mul_gen(t, t, nf);
/* Now compute the correct denominator */
fmpz_set(fmpz_mat_entry(res, d - 1, d - 1), fmpq_poly_denref(NF_ELEM(t)));
fmpz_set(den, fmpq_poly_denref(NF_ELEM(t)));
for (j = 0; j <= d - 2; j++)
fmpz_lcm(den, den, fmpz_mat_entry(res, d - 1, j));
for (j = 0; j <= d - 2; j++)
{
if (!fmpz_equal(den, fmpz_mat_entry(res, d - 1, j)))
{
fmpz_divexact(fmpz_mat_entry(res, d - 1, j), den, fmpz_mat_entry(res, d - 1, j));
for (i = 0; i <= d - 1; i++)
fmpz_mul(fmpz_mat_entry(res, j, i), fmpz_mat_entry(res, j, i), fmpz_mat_entry(res, d - 1, j));
}
}
if (fmpz_equal(den, fmpz_mat_entry(res, d - 1, d - 1)))
{
for (i = 0; i < d; i++)
fmpz_set(fmpz_mat_entry(res, d - 1, i), fmpq_poly_numref(NF_ELEM(t)) + i);
}
else
{
fmpz_divexact(fmpz_mat_entry(res, d - 1, d - 1), den, fmpq_poly_denref(NF_ELEM(t)));
for (i = 0; i < d; i++)
fmpz_mul(fmpz_mat_entry(res, d - 1, i), fmpq_poly_numref(NF_ELEM(t)) + i, fmpz_mat_entry(res, d - 1, d - 1));
}
}
}
nf_elem_clear(t, nf);
}
}
