# C# Polynomial Example

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using System;

using CenterSpace.NMath.Core;

namespace CenterSpace.NMath.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" );