/// <summary>Gets the (complex) roots of a specified polynomial of degree up to 2.
/// </summary>
/// <param name="absoluteCoefficient">The absolute coefficient.</param>
/// <param name="firstOrderCoefficient">The first order coefficient.</param>
/// <param name="secondOrderCoefficient">The second order coefficient.</param>
/// <param name="thirdOrderCoefficient">The third order coefficient.</param>
/// <param name="firstRoot">The first root (output).</param>
/// <param name="secondRoot">The second root (output).</param>
/// <param name="thirdRoot">The third root (output).</param>
/// <returns>The order of the polynomial represented by the coefficients, i.e. the number of roots.</returns>
public static int GetRoots(System.Numerics.Complex absoluteCoefficient, System.Numerics.Complex firstOrderCoefficient, System.Numerics.Complex secondOrderCoefficient, System.Numerics.Complex thirdOrderCoefficient, out System.Numerics.Complex firstRoot, out System.Numerics.Complex secondRoot, out System.Numerics.Complex thirdRoot)
{
if (thirdOrderCoefficient.Equals(System.Numerics.Complex.Zero) == false) // degree 3
{
ComplexDegreeThreePolynomial.GetRoots(absoluteCoefficient, firstOrderCoefficient, secondOrderCoefficient, thirdOrderCoefficient, out firstRoot, out secondRoot, out thirdRoot);
return(3);
}
if (secondOrderCoefficient.Equals(System.Numerics.Complex.Zero) == false) // degree 2
{
ComplexDegreeTwoPolynomial.GetRoots(absoluteCoefficient, firstOrderCoefficient, secondOrderCoefficient, out firstRoot, out secondRoot);
thirdRoot = new System.Numerics.Complex(Double.NaN, Double.NaN);
return(2);
}
else if (firstOrderCoefficient.Equals(System.Numerics.Complex.Zero) == false) // degree 1
{
firstRoot = unchecked (-absoluteCoefficient / firstOrderCoefficient); // the highest coefficient is always != 0.0, but maybe near 0.0
secondRoot = thirdRoot = new System.Numerics.Complex(Double.NaN, Double.NaN);
return(1);
}
else // degree 0
{
firstRoot = secondRoot = thirdRoot = new System.Numerics.Complex(Double.NaN, Double.NaN);
return(0);
}
}
public static bool IsZero(this Complex self)
{
return(self.Equals(Complex.Zero));
}
