int
main(void)
{
flint_rand_t state;
long i;
printf("inv....");
fflush(stdout);
flint_randinit(state);
/* Test aliasing */
for (i = 0; i < 400; i++)
{
fmpz_poly_mat_t A, Ainv;
fmpz_poly_t den1, den2;
long n, bits, deg;
float density;
int ns1, ns2;
int result;
n = n_randint(state, 8);
deg = 1 + n_randint(state, 5);
bits = 1 + n_randint(state, 100);
density = n_randint(state, 100) * 0.01;
fmpz_poly_mat_init(A, n, n);
fmpz_poly_mat_init(Ainv, n, n);
fmpz_poly_init(den1);
fmpz_poly_init(den2);
fmpz_poly_mat_randtest_sparse(A, state, deg, bits, density);
ns1 = fmpz_poly_mat_inv(Ainv, den1, A);
ns2 = fmpz_poly_mat_inv(A, den2, A);
result = ns1 == ns2;
if (result && ns1 != 0)
{
result = fmpz_poly_equal(den1, den2) &&
fmpz_poly_mat_equal(A, Ainv);
}
if (!result)
{
printf("FAIL (aliasing)!\n");
fmpz_poly_mat_print(A, "x"); printf("\n");
fmpz_poly_mat_print(Ainv, "x"); printf("\n");
abort();
}
fmpz_poly_mat_clear(A);
fmpz_poly_mat_clear(Ainv);
fmpz_poly_clear(den1);
fmpz_poly_clear(den2);
}
/* Check A^(-1) = A = 1 */
for (i = 0; i < 1000; i++)
{
fmpz_poly_mat_t A, Ainv, B, Iden;
fmpz_poly_t den, det;
long n, bits, deg;
float density;
int nonsingular;
n = n_randint(state, 10);
deg = 1 + n_randint(state, 5);
bits = 1 + n_randint(state, 100);
density = n_randint(state, 100) * 0.01;
fmpz_poly_mat_init(A, n, n);
fmpz_poly_mat_init(Ainv, n, n);
fmpz_poly_mat_init(B, n, n);
fmpz_poly_mat_init(Iden, n, n);
fmpz_poly_init(den);
fmpz_poly_init(det);
fmpz_poly_mat_randtest_sparse(A, state, deg, bits, density);
nonsingular = fmpz_poly_mat_inv(Ainv, den, A);
fmpz_poly_mat_det_interpolate(det, A);
if (n == 0)
{
if (nonsingular == 0 || !fmpz_poly_is_one(den))
{
printf("FAIL: expected empty matrix to pass\n");
abort();
}
}
else
{
if (!fmpz_poly_equal(den, det))
{
fmpz_poly_neg(det, det);
printf("FAIL: den != det(A)\n");
abort();
}
fmpz_poly_mat_mul(B, Ainv, A);
fmpz_poly_mat_one(Iden);
fmpz_poly_mat_scalar_mul_fmpz_poly(Iden, Iden, den);
if (!fmpz_poly_mat_equal(B, Iden))
{
printf("FAIL:\n");
printf("A:\n");
fmpz_poly_mat_print(A, "x");
printf("Ainv:\n");
fmpz_poly_mat_print(Ainv, "x");
printf("B:\n");
fmpz_poly_mat_print(B, "x");
printf("den:\n");
fmpz_poly_print_pretty(den, "x");
abort();
}
}
fmpz_poly_clear(den);
fmpz_poly_clear(det);
fmpz_poly_mat_clear(A);
fmpz_poly_mat_clear(Ainv);
fmpz_poly_mat_clear(B);
fmpz_poly_mat_clear(Iden);
}
flint_randclear(state);
_fmpz_cleanup();
printf("PASS\n");
return 0;
}
int
main(void)
{
slong i;
FLINT_TEST_INIT(state);
flint_printf("nullspace....");
fflush(stdout);
for (i = 0; i < 200 * flint_test_multiplier(); i++)
{
fmpz_poly_mat_t A, N, AN;
slong n, m, bits, deg, rank, nullity;
float density;
m = n_randint(state, 13);
n = n_randint(state, 13);
deg = 1 + n_randint(state, 5);
bits = 1 + n_randint(state, 100);
density = n_randint(state, 100) * 0.01;
fmpz_poly_mat_init(A, m, n);
fmpz_poly_mat_init(N, n, n);
fmpz_poly_mat_init(AN, m, n);
fmpz_poly_mat_randtest_sparse(A, state, deg, bits, density);
rank = fmpz_poly_mat_rank(A);
nullity = fmpz_poly_mat_nullspace(N, A);
if (nullity + rank != n)
{
flint_printf("FAIL: wrong nullity!\n");
flint_printf("rank = %wd\n", rank);
flint_printf("nullity = %wd\n", nullity);
fmpz_poly_mat_print(A, "x");
flint_printf("\n");
fmpz_poly_mat_print(N, "x");
flint_printf("\n");
abort();
}
if (fmpz_poly_mat_rank(N) != nullity)
{
flint_printf("FAIL: wrong rank(N) != nullity!\n");
abort();
}
fmpz_poly_mat_mul(AN, A, N);
if (!fmpz_poly_mat_is_zero(AN))
{
flint_printf("FAIL: A * N != 0\n");
abort();
}
fmpz_poly_mat_clear(A);
fmpz_poly_mat_clear(N);
fmpz_poly_mat_clear(AN);
}
FLINT_TEST_CLEANUP(state);
flint_printf("PASS\n");
return 0;
}
