void
fmpz_poly_mat_mullow(fmpz_poly_mat_t C, const fmpz_poly_mat_t A,
const fmpz_poly_mat_t B, long len)
{
long ar, bc, br;
long i, j, k;
fmpz_poly_t t;
ar = A->r;
br = B->r;
bc = B->c;
if (br == 0 || len < 1)
{
fmpz_poly_mat_zero(C);
return;
}
if (C == A || C == B)
{
fmpz_poly_mat_t T;
fmpz_poly_mat_init(T, ar, bc);
fmpz_poly_mat_mullow(T, A, B, len);
fmpz_poly_mat_swap(C, T);
fmpz_poly_mat_clear(T);
return;
}
fmpz_poly_init(t);
for (i = 0; i < ar; i++)
{
for (j = 0; j < bc; j++)
{
fmpz_poly_mullow(fmpz_poly_mat_entry(C, i, j),
fmpz_poly_mat_entry(A, i, 0),
fmpz_poly_mat_entry(B, 0, j), len);
for (k = 1; k < br; k++)
{
fmpz_poly_mullow(t, fmpz_poly_mat_entry(A, i, k),
fmpz_poly_mat_entry(B, k, j), len);
fmpz_poly_add(fmpz_poly_mat_entry(C, i, j),
fmpz_poly_mat_entry(C, i, j), t);
}
}
}
fmpz_poly_clear(t);
}
void
fmpz_poly_mat_sqrlow(fmpz_poly_mat_t B, const fmpz_poly_mat_t A, slong len)
{
slong n = A->r;
if (n == 0)
return;
if (len < 1)
{
fmpz_poly_mat_zero(B);
return;
}
if (n == 1)
{
fmpz_poly_sqrlow(E(B, 0, 0), E(A, 0, 0), len);
return;
}
if (n == 2)
{
fmpz_poly_t t, u;
fmpz_poly_init(t);
fmpz_poly_init(u);
fmpz_poly_addlow(t, E(A, 0, 0), E(A, 1, 1), len);
fmpz_poly_mullow(u, E(A, 0, 1), E(A, 1, 0), len);
fmpz_poly_sqrlow(E(B, 0, 0), E(A, 0, 0), len);
fmpz_poly_addlow(E(B, 0, 0), E(B, 0, 0), u, len);
fmpz_poly_sqrlow(E(B, 1, 1), E(A, 1, 1), len);
fmpz_poly_addlow(E(B, 1, 1), E(B, 1, 1), u, len);
fmpz_poly_mullow(E(B, 0, 1), E(A, 0, 1), t, len);
fmpz_poly_mullow(E(B, 1, 0), E(A, 1, 0), t, len);
fmpz_poly_clear(t);
fmpz_poly_clear(u);
return;
}
fmpz_poly_mat_mullow(B, A, A, len);
}
void fmpz_poly_ramanujan_tau(fmpz_poly_t res, long n)
{
long j, k, jv, kv;
fmpz_t tmp;
fmpz_poly_fit_length(res, n);
_fmpz_vec_zero(res->coeffs, n);
_fmpz_poly_set_length(res, n);
fmpz_init(tmp);
for (j = jv = 0; jv < n; jv += ++j)
{
fmpz_set_ui(tmp, 2*j+1);
for (k = kv = 0; jv + kv < n; kv += ++k)
{
if ((j+k) & 1)
fmpz_submul_ui(res->coeffs + jv+kv, tmp, 2*k+1);
else
fmpz_addmul_ui(res->coeffs + jv+kv, tmp, 2*k+1);
}
}
fmpz_poly_mullow(res, res, res, n-1);
fmpz_poly_mullow(res, res, res, n-1);
fmpz_poly_shift_left(res, res, 1);
fmpz_clear(tmp);
}
int
main(void)
{
int i, result;
FLINT_TEST_INIT(state);
flint_printf("inv_series_newton....");
fflush(stdout);
/* Check Q^{-1} * Q is congruent 1 mod t^n */
for (i = 0; i < 100 * flint_test_multiplier(); i++)
{
fmpz_poly_t a, b, c, one;
slong n = n_randint(state, 80) + 1;
fmpz_poly_init(a);
fmpz_poly_init(b);
fmpz_poly_init(c);
fmpz_poly_init(one);
fmpz_poly_randtest_not_zero(a, state, n_randint(state, 80) + 1, 100);
fmpz_poly_set_coeff_si(a, 0, n_randint(state, 2) ? 1 : -1);
fmpz_poly_set_ui(one, 1);
fmpz_poly_inv_series_newton(b, a, n);
fmpz_poly_mullow(c, a, b, n);
result = (fmpz_poly_equal(c, one));
if (!result)
{
flint_printf("FAIL:\n");
flint_printf("a = "), fmpz_poly_print(a), flint_printf("\n\n");
flint_printf("b = "), fmpz_poly_print(b), flint_printf("\n\n");
flint_printf("c = "), fmpz_poly_print(c), flint_printf("\n\n");
abort();
}
fmpz_poly_clear(a);
fmpz_poly_clear(b);
fmpz_poly_clear(c);
fmpz_poly_clear(one);
}
/* Verify bug fix for the case Q = -1 mod (x) */
{
fmpz_poly_t a, b, c, one;
slong n = 1;
fmpz_poly_init(a);
fmpz_poly_init(b);
fmpz_poly_init(c);
fmpz_poly_init(one);
fmpz_poly_set_si(a, -1);
fmpz_poly_set_ui(one, 1);
fmpz_poly_inv_series_newton(b, a, n);
fmpz_poly_mullow(c, a, b, n);
result = (fmpz_poly_equal(c, one));
if (!result)
{
flint_printf("FAIL:\n");
flint_printf("a = "), fmpz_poly_print(a), flint_printf("\n\n");
flint_printf("b = "), fmpz_poly_print(b), flint_printf("\n\n");
flint_printf("c = "), fmpz_poly_print(c), flint_printf("\n\n");
abort();
}
fmpz_poly_clear(a);
fmpz_poly_clear(b);
fmpz_poly_clear(c);
fmpz_poly_clear(one);
}
FLINT_TEST_CLEANUP(state);
flint_printf("PASS\n");
return 0;
}
