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;
}
}
int main(int argc, char *argv[])
{
fmpz_poly_t f, g;
fmpz_poly_factor_t fac;
fmpz_t t;
slong compd, printd, i, j;
if (argc < 2)
{
flint_printf("poly_roots [-refine d] [-print d] <poly>\n\n");
flint_printf("Isolates all the complex roots of a polynomial with integer coefficients.\n\n");
flint_printf("If -refine d is passed, the roots are refined to an absolute tolerance\n");
flint_printf("better than 10^(-d). By default, the roots are only computed to sufficient\n");
flint_printf("accuracy to isolate them. The refinement is not currently done efficiently.\n\n");
flint_printf("If -print d is passed, the computed roots are printed to d decimals.\n");
flint_printf("By default, the roots are not printed.\n\n");
flint_printf("The polynomial can be specified by passing the following as <poly>:\n\n");
flint_printf("a <n> Easy polynomial 1 + 2x + ... + (n+1)x^n\n");
flint_printf("t <n> Chebyshev polynomial T_n\n");
flint_printf("u <n> Chebyshev polynomial U_n\n");
flint_printf("p <n> Legendre polynomial P_n\n");
flint_printf("c <n> Cyclotomic polynomial Phi_n\n");
flint_printf("s <n> Swinnerton-Dyer polynomial S_n\n");
flint_printf("b <n> Bernoulli polynomial B_n\n");
flint_printf("w <n> Wilkinson polynomial W_n\n");
flint_printf("e <n> Taylor series of exp(x) truncated to degree n\n");
flint_printf("m <n> <m> The Mignotte-like polynomial x^n + (100x+1)^m, n > m\n");
flint_printf("coeffs <c0 c1 ... cn> c0 + c1 x + ... + cn x^n\n\n");
flint_printf("Concatenate to multiply polynomials, e.g.: p 5 t 6 coeffs 1 2 3\n");
flint_printf("for P_5(x)*T_6(x)*(1+2x+3x^2)\n\n");
return 1;
}
compd = 0;
printd = 0;
fmpz_poly_init(f);
fmpz_poly_init(g);
fmpz_init(t);
fmpz_poly_one(f);
for (i = 1; i < argc; i++)
{
if (!strcmp(argv[i], "-refine"))
{
compd = atol(argv[i+1]);
i++;
}
else if (!strcmp(argv[i], "-print"))
{
printd = atol(argv[i+1]);
i++;
}
else if (!strcmp(argv[i], "a"))
{
slong n = atol(argv[i+1]);
fmpz_poly_zero(g);
for (j = 0; j <= n; j++)
fmpz_poly_set_coeff_ui(g, j, j+1);
fmpz_poly_mul(f, f, g);
i++;
}
else if (!strcmp(argv[i], "t"))
{
arith_chebyshev_t_polynomial(g, atol(argv[i+1]));
fmpz_poly_mul(f, f, g);
i++;
}
else if (!strcmp(argv[i], "u"))
{
arith_chebyshev_u_polynomial(g, atol(argv[i+1]));
fmpz_poly_mul(f, f, g);
i++;
}
else if (!strcmp(argv[i], "p"))
{
fmpq_poly_t h;
fmpq_poly_init(h);
arith_legendre_polynomial(h, atol(argv[i+1]));
fmpq_poly_get_numerator(g, h);
fmpz_poly_mul(f, f, g);
fmpq_poly_clear(h);
i++;
}
else if (!strcmp(argv[i], "c"))
{
arith_cyclotomic_polynomial(g, atol(argv[i+1]));
fmpz_poly_mul(f, f, g);
i++;
}
else if (!strcmp(argv[i], "s"))
{
arith_swinnerton_dyer_polynomial(g, atol(argv[i+1]));
fmpz_poly_mul(f, f, g);
i++;
}
else if (!strcmp(argv[i], "b"))
{
fmpq_poly_t h;
fmpq_poly_init(h);
arith_bernoulli_polynomial(h, atol(argv[i+1]));
fmpq_poly_get_numerator(g, h);
fmpz_poly_mul(f, f, g);
fmpq_poly_clear(h);
i++;
}
else if (!strcmp(argv[i], "w"))
{
slong n = atol(argv[i+1]);
fmpz_poly_zero(g);
fmpz_poly_fit_length(g, n+2);
arith_stirling_number_1_vec(g->coeffs, n+1, n+2);
_fmpz_poly_set_length(g, n+2);
fmpz_poly_shift_right(g, g, 1);
fmpz_poly_mul(f, f, g);
i++;
}
else if (!strcmp(argv[i], "e"))
{
fmpq_poly_t h;
fmpq_poly_init(h);
fmpq_poly_set_coeff_si(h, 0, 0);
fmpq_poly_set_coeff_si(h, 1, 1);
fmpq_poly_exp_series(h, h, atol(argv[i+1]) + 1);
fmpq_poly_get_numerator(g, h);
fmpz_poly_mul(f, f, g);
fmpq_poly_clear(h);
i++;
}
else if (!strcmp(argv[i], "m"))
{
fmpz_poly_zero(g);
fmpz_poly_set_coeff_ui(g, 0, 1);
fmpz_poly_set_coeff_ui(g, 1, 100);
fmpz_poly_pow(g, g, atol(argv[i+2]));
fmpz_poly_set_coeff_ui(g, atol(argv[i+1]), 1);
fmpz_poly_mul(f, f, g);
i += 2;
}
else if (!strcmp(argv[i], "coeffs"))
{
fmpz_poly_zero(g);
i++;
j = 0;
while (i < argc)
{
if (fmpz_set_str(t, argv[i], 10) != 0)
{
i--;
break;
}
fmpz_poly_set_coeff_fmpz(g, j, t);
i++;
j++;
}
fmpz_poly_mul(f, f, g);
}
}
fmpz_poly_factor_init(fac);
flint_printf("computing squarefree factorization...\n");
TIMEIT_ONCE_START
fmpz_poly_factor_squarefree(fac, f);
TIMEIT_ONCE_STOP
TIMEIT_ONCE_START
for (i = 0; i < fac->num; i++)
{
flint_printf("roots with multiplicity %wd\n", fac->exp[i]);
fmpz_poly_complex_roots_squarefree(fac->p + i,
32, compd * 3.32193 + 2, printd);
}
TIMEIT_ONCE_STOP
fmpz_poly_factor_clear(fac);
fmpz_poly_clear(f);
fmpz_poly_clear(g);
fmpz_clear(t);
flint_cleanup();
return EXIT_SUCCESS;
}
