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<a name="Roots-of-Polynomials-Examples"></a>
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Next: <a href="Roots-of-Polynomials-References-and-Further-Reading.html#Roots-of-Polynomials-References-and-Further-Reading" accesskey="n" rel="next">Roots of Polynomials References and Further Reading</a>, Previous: <a href="General-Polynomial-Equations.html#General-Polynomial-Equations" accesskey="p" rel="previous">General Polynomial Equations</a>, Up: <a href="Polynomials.html#Polynomials" accesskey="u" rel="up">Polynomials</a> [<a href="Function-Index.html#Function-Index" title="Index" rel="index">Index</a>]</p>
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<a name="Examples-1"></a>
<h3 class="section">6.6 Examples</h3>
<p>To demonstrate the use of the general polynomial solver we will take the
polynomial <em>P(x) = x^5 - 1</em> which has the following roots,
</p>
<div class="example">
<pre class="example">1, e^{2\pi i /5}, e^{4\pi i /5}, e^{6\pi i /5}, e^{8\pi i /5}
</pre></div>
<p>The following program will find these roots.
</p>
<div class="example">
<pre class="verbatim">#include <stdio.h>
#include <gsl/gsl_poly.h>
int
main (void)
{
int i;
/* coefficients 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;
}
</pre></div>
<p>The output of the program is,
</p>
<div class="example">
<pre class="example">$ ./a.out
</pre><pre class="verbatim">z0 = -0.809016994374947673 +0.587785252292473359
z1 = -0.809016994374947673 -0.587785252292473359
z2 = +0.309016994374947507 +0.951056516295152976
z3 = +0.309016994374947507 -0.951056516295152976
z4 = +0.999999999999999889 +0.000000000000000000
</pre></div>
<p>which agrees with the analytic result, <em>z_n = \exp(2 \pi n i/5)</em>.
</p>
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