public static double CalculateLagrangeRemainder(Expr function, string variableName, int n, FloatingPoint x, FloatingPoint x0)
{
var results = new List <double>();
var length = GetLength(Math.Min(x.RealValue, x0.RealValue), Math.Max(x.RealValue, x0.RealValue));
var increment = length / 10;
double currentIncrement = Math.Min(x.RealValue, x0.RealValue);
var factorial = (FloatingPoint)SpecialFunctions.Factorial(n + 1);
while (currentIncrement < Math.Max(x.RealValue, x0.RealValue))
{
var variable = new Dictionary <string, FloatingPoint>
{
{ variableName, currentIncrement }
};
var derivativeResult = function.CalculateFunctionAtDerivative(variable, Expr.Variable(variableName), n + 1);
var result = derivativeResult.RealValue / factorial.RealValue * Math.Pow(Math.Abs(x.RealValue - x0.RealValue), n + 1);
results.Add(Math.Abs(result));
currentIncrement += increment;
}
var variableMax = new Dictionary <string, FloatingPoint>
{
{ variableName, Math.Max(x.RealValue, x0.RealValue) }
};
var derivativeResultMax = function.CalculateFunctionAtDerivative(variableMax, Expr.Variable(variableName), n + 1);
var resultMax = derivativeResultMax.RealValue / factorial.RealValue * Math.Pow(Math.Abs(x.RealValue - x0.RealValue), n + 1);
results.Add(Math.Abs(resultMax));
return(results.Max(x => x));
}
