/// <summary>
/// The method returns product of polynominal addition
/// </summary>
/// <param name="poly">Polynominal coefficients (vector starting with free term)</param>
/// <returns>Polynominal</returns>
public Polynominal Add(Polynominal poly)
{
int M = this.Degree();
int N = poly.Degree();
int K = Math.Max(M, N);
Polynominal Poly1Ext = new Polynominal(K);
Polynominal Poly2Ext = new Polynominal(K);
Polynominal Add = new Polynominal(K);
for (int m = 0; m < M + 1; m++)
{
Poly1Ext.SetElement(m, this.Element(m));
}
for (int n = 0; n < N + 1; n++)
{
Poly2Ext.SetElement(n, poly.Element(n));
}
for (int k = 0; k < K + 1; k++)
{
Add.SetElement(k, Poly1Ext.Element(k) + Poly2Ext.Element(k));
}
return(Add);
}
/// <summary>
/// The method returns product of polynominal multiplication by scalar
/// </summary>
/// <param name="Value">Complex value</param>
/// <returns>Polynominal</returns>
public Polynominal Scale(Complex Value)
{
Polynominal scale = new Polynominal(this.Degree());
for (int i = 0; i < this.Degree() + 1; i++)
{
scale.SetElement(i, this.Element(i) * Value);
}
return(scale);
}
/// <summary>
/// The method calculates polynominal derivative
/// </summary>
/// <returns>Polynominal</returns>
public Polynominal Derivative()
{
int Degree = this.Degree();
int NumCoefs = Degree + 1;
Polynominal Derivative = new Polynominal(this.Degree() - 1);
if (Degree > 0)
{
for (int i = 1; i < NumCoefs; i++)
{
Derivative.SetElement(i - 1, i * this.Element(i));
}
}
else
{
return(new Polynominal(new Double[1] {
0
}));
}
return(Derivative);
}
/// <summary>
/// The method calculates polynominal roots
/// </summary>
/// <param name="Seed">Seed root (if unknown any complex number can be given)</param>
/// <param name="Accuracy">Result accuracy</param>
/// <returns>Polynominal roots</returns>
public Complex[] Roots(Complex Seed, Double Accuracy)
{
int N = this.Degree();
Complex[] Roots = new Complex[N];
int degree = N;
Polynominal tmpoly = this;
for (int n = 0; n < N; n++)
{
while (true)
{
Complex _tmp0 = tmpoly.Derivative().Evaluate(Seed);
Complex _tmp1 = (degree - 1) * Complex.Pow(tmpoly.Derivative().Evaluate(Seed), 2);
Complex _tmp2 = degree * tmpoly.Evaluate(Seed) * tmpoly.Derivative().Derivative().Evaluate(Seed);
Complex _tmp3 = Complex.Pow((degree - 1) * (_tmp1 - _tmp2), 0.5);
Complex _tmp4 = MaximizeResultAbsolute(_tmp0, _tmp3);
Seed = Seed - (degree * tmpoly.Evaluate(Seed)) / _tmp4;
Complex result = tmpoly.Evaluate(Seed);
if (Complex.Abs(result) < Math.Abs(Accuracy))
{
Roots[n] = Seed;
tmpoly = tmpoly.ByBinominalDivision(Seed);
degree--;
Random _Random = new Random();
Seed = -10 + (_Random.NextDouble() * 15);
break;
}
}
}
return(Roots);
}
/// <summary>
/// Subtracts two polynominals
/// </summary>
/// <param name="poly">Subtrahend polynominal</param>
/// <returns>Difference</returns>
public Polynominal Sub(Polynominal poly)
{
return(this.Add(poly.Scale(-1)));
}