C# Polynomial Example

using System;

using CenterSpace.NMath.Core;

namespace CenterSpace.NMath.Core.Examples.CSharp
{
  /// <summary>
  /// A .NET example in C# showing how to create and manipulate polynomial objects.
  /// </summary>
  class PolynomialExample
  {

    static void Main(string[] args)
    {
      Console.WriteLine();

      // Class Polynomial represents a polynomial by its coefficients, arranged in
      // ascending order—-that is, a vector of coefficients a0, a1, ... an such that
      // f(x) = a0*x^0 + a1*X^1 + ... + an*x^n.

      // A Polynomial instance can be constructed in two ways. If you know the
      // exact form of the polynomial, simply pass in a vector of coefficients.
      DoubleVector coef = new DoubleVector("3 1 -2 0 5");
      Polynomial f = new Polynomial(coef);

      // f(x) = 5x^4 - 2x^2 + x + 3
      Console.WriteLine("f(x) = {0}", f.ToString());
      Console.WriteLine("Degree = {0}", f.Degree);
      Console.WriteLine("Coefficients = {0}\n", f.Coeff);

      // You can also interpolate a polynomial through a set of points. If the
      // number of points is n, then the constructed polynomial will have degree
      // n - 1 and pass through the interpolation points. For example, this code
      // interpolates a polynomial through the points (1,6), (2,11), and (3,20):
      DoubleVector x = new DoubleVector("1 2 3");
      DoubleVector y = new DoubleVector("6 11 20");
      Polynomial g = new Polynomial(x, y);

      // g(x) = 2x^2 - x + 5
      Console.WriteLine("g(x) = {0}", g.ToString("G3"));
      Console.WriteLine("Degree = {0}", g.Degree);
      Console.WriteLine("Coefficients = {0}\n", g.Coeff);

      // The Evaluate() method evaluates a polynomial at a given x-value, or
      // vector of x-values. This code evaulates f at ten points between 0 and 1:
      x = new DoubleVector(10, 0.1, 1.0 / 10);
      y = f.Evaluate(x);
      Console.WriteLine("x = {0}", x);
      Console.WriteLine("y = {0}\n", y);

      // Class Polynomial provides overloads of the arithmetic operators (and 
      // equivalent named methods) that work with either with two polynomials, or
      // with a polynomial and a scalar. For example:
      Polynomial h = (f + g) * g / 2;
      Console.WriteLine("h(x) = {0}", h.ToString());
      Console.WriteLine("h(2) = {0}", h.Evaluate(2));
      Console.WriteLine();

      // The Integrate() method computes the integral of a polynomial over a given
      // interval. 
      Console.WriteLine("Integral of h(x) over 0 to 1 = {0}", h.Integrate(0, 1).ToString("G3"));
      Console.WriteLine();

      // The AntiDerivative() method returns a new polynomial encapsulating
      // the antiderivative (indefinite integral) of the current polynomial.
      // The constant of integration is assumed to be zero.
      Polynomial hAntiDeriv = h.AntiDerivative();
      Console.WriteLine("Antiderivative of h(x)...");
      Console.WriteLine(hAntiDeriv.ToString("G3"));
      Console.WriteLine();

      // The Differentiate() method computes the derivative of a polynomial at a
      // given x-value.
      Console.WriteLine("Derivative of h(x) at 1 = {0}", h.Differentiate(1).ToString("G3"));
      Console.WriteLine();

      // Derivative() returns a new polynomial that is the first derivative of
      // the current polynomial.
      Console.WriteLine("First derivative of h(x)...");
      Console.WriteLine(h.Derivative().ToString("G3"));
      Console.WriteLine();

      Console.WriteLine("Second derivative of h(x)...");
      Console.WriteLine(h.Derivative().Derivative().ToString("G3"));
      Console.WriteLine();

      // Check that the derivative of the antiderivative of h(x) == h(x)
      Console.WriteLine("Derivative of the antiderivative of h(x)...");
      Console.WriteLine(h.AntiDerivative().Derivative().ToString("G3"));

      Console.WriteLine();
      Console.WriteLine("Press Enter Key");
      Console.Read();

    }

  }// class

}// namespace