int main(void)
{
int i;
FLINT_TEST_INIT(state);
flint_printf("parity....");
fflush(stdout);
/* check inv(inv(a)) == a */
for (i = 0; i < 10000; i++)
{
slong n, *a, *b, *c;
int ap, bp, cp, ap2, bp2, cp2;
n = n_randint(state, 100);
a = _perm_init(n);
b = _perm_init(n);
c = _perm_init(n);
ap = _perm_randtest(a, n, state);
bp = _perm_randtest(b, n, state);
_perm_compose(c, a, b, n);
cp = ap ^ bp;
ap2 = _perm_parity(a, n);
bp2 = _perm_parity(b, n);
cp2 = _perm_parity(c, n);
if (ap != ap2 || bp != bp2 || cp != cp2)
{
flint_printf("FAIL:\n");
flint_printf("a: "); _perm_print(a, n); flint_printf("\n\n");
flint_printf("b: "); _perm_print(b, n); flint_printf("\n\n");
flint_printf("c: "); _perm_print(c, n); flint_printf("\n\n");
flint_printf("ap = %d\n", ap);
flint_printf("bp = %d\n", bp);
flint_printf("cp = %d\n", cp);
flint_printf("ap2 = %d\n", ap2);
flint_printf("bp2 = %d\n", bp2);
flint_printf("cp2 = %d\n", cp2);
abort();
}
_perm_clear(a);
_perm_clear(b);
_perm_clear(c);
}
FLINT_TEST_CLEANUP(state);
flint_printf("PASS\n");
return 0;
}
mp_limb_t
_nmod_mat_det(nmod_mat_t A)
{
mp_limb_t det;
long * P;
long m = A->r;
long rank;
long i;
P = flint_malloc(sizeof(long) * m);
rank = nmod_mat_lu(P, A, 1);
det = 0UL;
if (rank == m)
{
det = 1UL;
for (i = 0; i < m; i++)
det = n_mulmod2_preinv(det, nmod_mat_entry(A, i, i),
A->mod.n, A->mod.ninv);
}
if (_perm_parity(P, m) == 1)
det = nmod_neg(det, A->mod);
flint_free(P);
return det;
}
void
_fmpz_mat_det_bareiss(fmpz_t det, fmpz_mat_t tmp)
{
long *perm, n = fmpz_mat_nrows(tmp);
perm = _perm_init(n);
fmpz_mat_fflu(tmp, det, perm, tmp, 1);
if (_perm_parity(perm, n) == 1)
fmpz_neg(det, det);
_perm_clear(perm);
}
int
fmpz_poly_mat_inv(fmpz_poly_mat_t Ainv, fmpz_poly_t den,
const fmpz_poly_mat_t A)
{
long n = fmpz_poly_mat_nrows(A);
if (n == 0)
{
fmpz_poly_one(den);
return 1;
}
else if (n == 1)
{
fmpz_poly_set(den, E(A, 0, 0));
fmpz_poly_one(E(Ainv, 0, 0));
return !fmpz_poly_is_zero(den);
}
else if (n == 2)
{
fmpz_poly_mat_det(den, A);
if (fmpz_poly_is_zero(den))
{
return 0;
}
else if (Ainv == A)
{
fmpz_poly_swap(E(A, 0, 0), E(A, 1, 1));
fmpz_poly_neg(E(A, 0, 1), E(A, 0, 1));
fmpz_poly_neg(E(A, 1, 0), E(A, 1, 0));
return 1;
}
else
{
fmpz_poly_set(E(Ainv, 0, 0), E(A, 1, 1));
fmpz_poly_set(E(Ainv, 1, 1), E(A, 0, 0));
fmpz_poly_neg(E(Ainv, 0, 1), E(A, 0, 1));
fmpz_poly_neg(E(Ainv, 1, 0), E(A, 1, 0));
return 1;
}
}
else
{
fmpz_poly_mat_t LU, I;
long * perm;
int result;
perm = _perm_init(n);
fmpz_poly_mat_init_set(LU, A);
result = (fmpz_poly_mat_fflu(LU, den, perm, LU, 1) == n);
if (result)
{
fmpz_poly_mat_init(I, n, n);
fmpz_poly_mat_one(I);
fmpz_poly_mat_solve_fflu_precomp(Ainv, perm, LU, I);
fmpz_poly_mat_clear(I);
}
else
fmpz_poly_zero(den);
if (_perm_parity(perm, n))
{
fmpz_poly_mat_neg(Ainv, Ainv);
fmpz_poly_neg(den, den);
}
_perm_clear(perm);
fmpz_poly_mat_clear(LU);
return result;
}
}
