C# Polynomial Example

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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.
      var coef = new DoubleVector( "3 1 -2 0 5" );
      var 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):
      var x = new DoubleVector( "1 2 3" );
      var y = new DoubleVector( "6 11 20" );
      var 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 evaluates 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 anti-derivative (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 anti-derivative 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

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