/*
* /// <summary>
* /// Creating an additional polynom for using Lagrange's interpolating method.
* /// </summary>
* /// <param name="arg"></param>
* /// <param name="val"></param>
* public RealPolynom Interpolate(double[] arg)
* {
* if(arg.Length != val.Length)
* {
* throw new Exception("Number of arguments is not eqal to number of values");
* }
* RealPolynom r = new RealPolynom(arg.Length);
* r[0] = 1;
* RealPolynom mult = new RealPolynom(2);
* mult[1] = 1;
* for(int i = 0; i < arg.Length; i++)
* {
* for(int j = 0; j < arg.Length; j++)
* {
* if(i != j){}
* }
* }
*
* }*/
/// <summary>
/// Clones itself
/// </summary>
/// <returns>Clone</returns>
public object Clone()
{
RealPolynom p = new RealPolynom(coeffs.Length);
p.coeffs = coeffs.Clone() as double[];
return(p);
}
/// <summary>
/// Sum
/// </summary>
/// <param name="p">First term</param>
/// <param name="q">Second term</param>
/// <returns>Sum</returns>
static public RealPolynom operator +(RealPolynom p, RealPolynom q)
{
RealPolynom r = new RealPolynom(0);
if (p.coeffs.Length < q.coeffs.Length)
{
for (int i = 0; i < p.coeffs.Length; i++)
{
r.coeffs[i] = p.coeffs[i] + q.coeffs[i];
}
for (int i = p.coeffs.Length - 1; i < q.coeffs.Length; i++)
{
r.coeffs[i] = q.coeffs[i];
}
return(r);
}
for (int i = 0; i < q.coeffs.Length; i++)
{
r.coeffs[i] = p.coeffs[i] + q.coeffs[i];
}
for (int i = q.coeffs.Length - 1; i < p.coeffs.Length; i++)
{
r.coeffs[i] = p.coeffs[i];
}
r.Reduce();
return(r);
}
/// <summary>
/// Minus constant left
/// </summary>
/// <param name="d">Constant</param>
/// <param name="p">Polynom</param>
/// <returns>Result polynom</returns>
static public RealPolynom operator -(double d, RealPolynom p)
{
RealPolynom r = -p;
r.coeffs[0] += d;
return(r);
}
/// <summary>
/// Minus constant
/// </summary>
/// <param name="p">Polynom</param>
/// <param name="d">Constant</param>
/// <returns>Result polynom</returns>
static public RealPolynom operator -(RealPolynom p, double d)
{
RealPolynom r = p.Clone() as RealPolynom;
r.coeffs[0] -= d;
return(r);
}
/// <summary>
/// Plus constant left
/// </summary>
/// <param name="d">Constant</param>
/// <param name="p">Polynom</param>
/// <returns>Result polynom</returns>
static public RealPolynom operator +(double d, RealPolynom p)
{
RealPolynom r = p.Clone() as RealPolynom;
r.coeffs[0] += d;
r.Reduce();
return(r);
}
/// <summary>
/// Derivation
/// </summary>
/// <param name="p">Prototype</param>
/// <returns>Redult polynon</returns>
static public RealPolynom operator !(RealPolynom p)
{
RealPolynom r = new RealPolynom(p.coeffs.Length - 1);
for (int i = 0; i < r.coeffs.Length; i++)
{
r.coeffs[i] = p.coeffs[i + 1] * i;
}
return(r);
}
/// <summary>
/// Integration
/// </summary>
/// <param name="p">Prototype</param>
/// <returns>Redult polynon</returns>
static public RealPolynom operator ~(RealPolynom p)
{
RealPolynom r = new RealPolynom(p.coeffs.Length + 1);
for (int i = 0; i < p.coeffs.Length; i++)
{
r.coeffs[i + 1] = p.coeffs[i] / (double)(i + 1);
}
r.coeffs[0] = 0;
return(r);
}
/// <summary>
/// Multiply to constant left
/// </summary>
/// <param name="d">Constant</param>
/// <param name="p">Polynom</param>
/// <returns>Result polynom</returns>
static public RealPolynom operator *(double d, RealPolynom p)
{
RealPolynom r = p.Clone() as RealPolynom;
for (int i = 0; i < r.coeffs.Length; i++)
{
r.coeffs[i] *= d;
}
r.Reduce();
return(r);
}
/// <summary>
/// Minus
/// </summary>
/// <param name="p">Argument</param>
/// <returns>Minus</returns>
static public RealPolynom operator -(RealPolynom p)
{
RealPolynom r = new RealPolynom(p.coeffs.Length);
for (int i = 0; i < p.coeffs.Length; i++)
{
p.coeffs[i] = -p.coeffs[i];
}
return(r);
}
/// <summary>
/// Divide to constant
/// </summary>
/// <param name="p">Polynom</param>
/// <param name="d">Constant</param>
/// <returns>Result polynom</returns>
static public RealPolynom operator /(RealPolynom p, double d)
{
if (d == 0)
{
throw new Exception("Can not divide by zero");
}
RealPolynom r = p.Clone() as RealPolynom;
for (int i = 0; i < r.coeffs.Length; i++)
{
r.coeffs[i] /= d;
}
return(r);
}
/// <summary>
/// Multiplication
/// </summary>
/// <param name="p">First term</param>
/// <param name="q">Second term</param>
/// <returns>Product</returns>
static public RealPolynom operator *(RealPolynom p, RealPolynom q)
{
if ((p.isZero) | (q.isZero))
{
RealPolynom r = new RealPolynom(1);
return(r);
}
RealPolynom s = new RealPolynom(p.coeffs.Length + q.coeffs.Length - 1);
for (int i = 0; i < p.coeffs.Length; i++)
{
for (int j = 0; j < q.coeffs.Length; j++)
{
s.coeffs[i + j] += p.coeffs[i] * q.coeffs[j];
}
}
return(s);
}