/// <summary>
/// Factorizes polynomial to its linear factors.
/// </summary>
/// <returns></returns>
public FactorizedPolynomial Factorize()
{
// this is to be returned
FactorizedPolynomial p = new FactorizedPolynomial();
// cannot factorize polynomial of degree 0 or 1
if (this.Degree <= 1)
{
p.Factor = new Polynomial[] { this };
p.Power = new int[] { 1 };
return(p);
}
double[] roots = Roots(this);
Polynomial[] factor = new Polynomial[roots.Length];
int[] power = new int[roots.Length];
power[0] = 1;
factor[0] = new Polynomial(new double[] { -Coefficients[Degree] * (double)roots[0], Coefficients[Degree] });
for (int i = 1; i < roots.Length; i++)
{
power[i] = 1;
factor[i] = new Polynomial(new double[] { -(double)roots[i], 1 });
}
p.Factor = factor;
p.Power = power;
return(p);
}
/// <summary>
/// Evaluates factorized polynomial p at point x.
/// </summary>
/// <param name="p"></param>
/// <returns></returns>
public static double Evaluate(FactorizedPolynomial p, double x)
{
double z = 1;
for (int i = 0; i < p.Factor.Length; i++)
{
z *= Math.Pow(p.Factor[i].Evaluate(x), p.Power[i]);
}
return(z);
}
/// <summary>
/// Evaluates factorized polynomial p at point x.
/// </summary>
/// <param name="p"></param>
/// <returns></returns>
public static Complex Evaluate(FactorizedPolynomial p, Complex x)
{
Complex z = Complex.One;
for (int i = 0; i < p.Factor.Length; i++)
{
z *= Complex.Pow(p.Factor[i].Evaluate(x), p.Power[i]);
}
return(z);
}
/// <summary>
/// Expands factorized polynomial p_1(x)^(k_1)*...*p_r(x)^(k_r) to its normal form a_0 + a_1 x + ... + a_n x^n.
/// </summary>
/// <param name="p"></param>
/// <returns></returns>
public static Polynomial Expand(FactorizedPolynomial p)
{
Polynomial q = new Polynomial(1);
for (int i = 0; i < p.Factor.Length; i++)
{
for (int j = 0; j < p.Power[i]; j++)
{
q *= p.Factor[i];
}
q.Clean();
}
return(q);
}
/// <summary>
/// Expands factorized polynomial p_1(x)^(k_1)*...*p_r(x)^(k_r) to its normal form a_0 + a_1 x + ... + a_n x^n.
/// </summary>
/// <param name="p"></param>
/// <returns></returns>
public static Polynomial Expand(FactorizedPolynomial p)
{
Polynomial q = new Polynomial(new Complex[] { Complex.One });
for (int i = 0; i < p.Factor.Length; i++)
{
for (int j = 0; j < p.Power[i]; j++)
{
q *= p.Factor[i];
}
q.Clean();
}
// clean...
for (int k = 0; k <= q.Degree; k++)
{
q.Coefficients[k].Re = Math.Round(q.Coefficients[k].Re, 12);
q.Coefficients[k].Im = Math.Round(q.Coefficients[k].Im, 12);
}
return(q);
}
/// <summary>
/// Factorizes polynomial to its linear factors.
/// </summary>
/// <returns></returns>
public FactorizedPolynomial Factorize()
{
// this is to be returned
FactorizedPolynomial p = new FactorizedPolynomial();
// cannot factorize polynomial of degree 0 or 1
if (this.Degree <= 1)
{
p.Factor = new Polynomial[] { this };
p.Power = new int[] { 1 };
return p;
}
Complex[] roots = Roots(this);
//ArrayList rootlist = new ArrayList();
//foreach (Complex z in roots) rootlist.Add(z);
//roots = null; // don't need you anymore
//rootlist.Sort();
//// number of different roots
//int num = 1; // ... at least one
//// ...or more?
//for (int i = 1; i < rootlist.Count; i++)
// if (rootlist[i] != rootlist[i - 1]) num++;
Polynomial[] factor = new Polynomial[roots.Length];
int[] power = new int[roots.Length];
//factor[0] = new Polynomial( new Complex[]{ -(Complex)rootlist[0] * Coefficients[Degree],
// Coefficients[Degree] } );
//power[0] = 1;
//num = 1;
//len = 0;
//for (int i = 1; i < rootlist.Count; i++)
//{
// len++;
// if (rootlist[i] != rootlist[i - 1])
// {
// factor[num] = new Polynomial(new Complex[] { -(Complex)rootlist[i], Complex.One });
// power[num] = len;
// num++;
// len = 0;
// }
//}
power[0] = 1;
factor[0] = new Polynomial(new Complex[] { -Coefficients[Degree] * (Complex)roots[0], Coefficients[Degree] });
for (int i = 1; i < roots.Length; i++)
{
power[i] = 1;
factor[i] = new Polynomial(new Complex[] { -(Complex)roots[i], Complex.One });
}
p.Factor = factor;
p.Power = power;
return p;
}
/// <summary>
/// Factorizes polynomial to its linear factors.
/// </summary>
/// <returns></returns>
public FactorizedPolynomial Factorize()
{
// this is to be returned
FactorizedPolynomial p = new FactorizedPolynomial();
// cannot factorize polynomial of degree 0 or 1
if (this.Degree <= 1)
{
p.Factor = new Polynomial[] { this };
p.Power = new int[] { 1 };
return(p);
}
Complex[] roots = Roots(this);
//ArrayList rootlist = new ArrayList();
//foreach (Complex z in roots) rootlist.Add(z);
//roots = null; // don't need you anymore
//rootlist.Sort();
//// number of different roots
//int num = 1; // ... at least one
//// ...or more?
//for (int i = 1; i < rootlist.Count; i++)
// if (rootlist[i] != rootlist[i - 1]) num++;
Polynomial[] factor = new Polynomial[roots.Length];
int[] power = new int[roots.Length];
//factor[0] = new Polynomial( new Complex[]{ -(Complex)rootlist[0] * Coefficients[Degree],
// Coefficients[Degree] } );
//power[0] = 1;
//num = 1;
//len = 0;
//for (int i = 1; i < rootlist.Count; i++)
//{
// len++;
// if (rootlist[i] != rootlist[i - 1])
// {
// factor[num] = new Polynomial(new Complex[] { -(Complex)rootlist[i], Complex.One });
// power[num] = len;
// num++;
// len = 0;
// }
//}
power[0] = 1;
factor[0] = new Polynomial(new Complex[] { -Coefficients[Degree] * (Complex)roots[0], Coefficients[Degree] });
for (int i = 1; i < roots.Length; i++)
{
power[i] = 1;
factor[i] = new Polynomial(new Complex[] { -(Complex)roots[i], Complex.One });
}
p.Factor = factor;
p.Power = power;
return(p);
}
/// <summary>
/// Expands factorized polynomial p_1(x)^(k_1)*...*p_r(x)^(k_r) to its normal form a_0 + a_1 x + ... + a_n x^n.
/// </summary>
/// <param name="p"></param>
/// <returns></returns>
public static Polynomial Expand(FactorizedPolynomial p)
{
Polynomial q = new Polynomial(new Complex[] { Complex.One });
for (int i = 0; i < p.Factor.Length; i++)
{
for (int j = 0; j < p.Power[i]; j++)
q *= p.Factor[i];
q.Clean();
}
// clean...
for (int k = 0; k <= q.Degree; k++)
{
q.Coefficients[k].Re = Math.Round(q.Coefficients[k].Re, 12);
q.Coefficients[k].Im = Math.Round(q.Coefficients[k].Im, 12);
}
return q;
}
/// <summary>
/// Evaluates factorized polynomial p at point x.
/// </summary>
/// <param name="p"></param>
/// <returns></returns>
public static Complex Evaluate(FactorizedPolynomial p, Complex x)
{
Complex z = Complex.One;
for (int i = 0; i < p.Factor.Length; i++)
{
z *= Complex.Pow(p.Factor[i].Evaluate(x), p.Power[i]);
}
return z;
}
/// <summary>
/// Factorizes polynomial to its linear factors.
/// </summary>
/// <returns></returns>
public FactorizedPolynomial Factorize()
{
// this is to be returned
FactorizedPolynomial p = new FactorizedPolynomial();
// cannot factorize polynomial of degree 0 or 1
if (this.Degree <= 1)
{
p.Factor = new Polynomial[] { this };
p.Power = new int[] { 1 };
return p;
}
double[] roots = Roots(this);
Polynomial[] factor = new Polynomial[roots.Length];
int[] power = new int[roots.Length];
power[0] = 1;
factor[0] = new Polynomial(new double[] { -Coefficients[Degree] * (double)roots[0], Coefficients[Degree] });
for (int i = 1; i < roots.Length; i++)
{
power[i] = 1;
factor[i] = new Polynomial(new double[] { -(double)roots[i], 1 });
}
p.Factor = factor;
p.Power = power;
return p;
}
/// <summary>
/// Expands factorized polynomial p_1(x)^(k_1)*...*p_r(x)^(k_r) to its normal form a_0 + a_1 x + ... + a_n x^n.
/// </summary>
/// <param name="p"></param>
/// <returns></returns>
public static Polynomial Expand(FactorizedPolynomial p)
{
Polynomial q = new Polynomial(1);
for (int i = 0; i < p.Factor.Length; i++)
{
for (int j = 0; j < p.Power[i]; j++)
q *= p.Factor[i];
q.Clean();
}
return q;
}
/// <summary>
/// Evaluates factorized polynomial p at point x.
/// </summary>
/// <param name="p"></param>
/// <returns></returns>
public static double Evaluate(FactorizedPolynomial p, double x)
{
double z = 1;
for (int i = 0; i < p.Factor.Length; i++)
{
z *= Math.Pow(p.Factor[i].Evaluate(x), p.Power[i]);
}
return z;
}
