Imports System Imports CenterSpace.NMath.Core Namespace CenterSpace.NMath.Examples.VisualBasic A .NET example in Visual Basic showing how to create and manipulate polynomial objects. Module PolynomialExample Sub Main() Console.WriteLine() Module Polynomial represents a polynomial by its coefficients, arranged in ascending orderâ-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. Dim Coef As New DoubleVector("3 1 -2 0 5") Dim F As 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}" & Environment.NewLine, 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): Dim X As New DoubleVector("1 2 3") Dim Y As New DoubleVector("6 11 20") Dim G As 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}" & Environment.NewLine, 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}" & Environment.NewLine, Y) Module 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: Dim H As Polynomial = (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. Dim hAntiDeriv As Polynomial = 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() End Sub End Module End Namespace← All NMath Code Examples