/**
* Calculates the Sturm chain to a given polynomial
*
* @param function
* the polynomial function
* @return the Sturm chain of <code>function</code> as array
*/
public static Polynomial[] calculateSturm(Polynomial function)
{
LinkedList <Polynomial> sturm = new LinkedList <Polynomial>();
// add the original function and its derivation
sturm.AddFirst(function);
sturm.AddFirst(function.diff());
// iteratively perform polynomial divison
while (sturm.First.Value.degree() > 0)
{
sturm.AddFirst(sturm.First.Next.Value.mod(sturm.First.Value).multiply(-1));
}
// convert the list to an array for efficiency purposes
Polynomial[] result = new Polynomial4[sturm.Count];
int i = 0;
foreach (Polynomial poly in sturm)
{
result[i] = poly;
i++;
}
return(result);
}
// Actually a degree4-result is sufficient (and we want to make our users
// benefit from this fact, so we define a Polynomial4-mod-method)...
public Polynomial4 mod(Polynomial4 other)
{
return(new Polynomial4(mod(toArray(), degree(), other.toArray(), other
.degree())));
}