## Examples

To demonstrate the use of the general polynomial solver we will take the polynomial @math{P(x) = x^5 - 1} which has the following roots,

The following program will find these roots.

#include <stdio.h>
#include <gsl/gsl_poly.h>

int
main (void)
{
int i;
/* coefficient of P(x) =  -1 + x^5  */
double a[6] = { -1, 0, 0, 0, 0, 1 };
double z[10];

gsl_poly_complex_workspace * w
= gsl_poly_complex_workspace_alloc (6);

gsl_poly_complex_solve (a, 6, w, z);

gsl_poly_complex_workspace_free (w);

for (i = 0; i < 5; i++)
{
printf("z%d = %+.18f %+.18f\n",
i, z[2*i], z[2*i+1]);
}

return 0;
}


The output of the program is,

bash\$ ./a.out
z0 = -0.809016994374947451 +0.587785252292473137
z1 = -0.809016994374947451 -0.587785252292473137
z2 = +0.309016994374947451 +0.951056516295153642
z3 = +0.309016994374947451 -0.951056516295153642
z4 = +1.000000000000000000 +0.000000000000000000


which agrees with the analytic result, @math{z_n = \exp(2 \pi n i/5)}.