/// <summary>
/// Method's sole purpose is to create the i-th MacLaurin polynomial term.
/// </summary>
/// <param name="expression">
/// Requires an Operand, representing expression or a derrivative
/// </param>
/// <param name="i">An integer the i-th degree</param>
/// <returns></returns>
private Operand CreateMaclaurinTerm(Operand expression, int i)
{
// The zero-th order MacLaurin Polynomial is (P0(x)) =
// f(0) * (x^0)/0! which simplifies to a constant?
if (i == 0)
{
// We can return calculate and return the function value
// evaluated in x = 0.
double functionValue = expression.Calculate(0);
return(new RealNumber(functionValue));
}
else
{
// The expression is differentiated if i != 0.
// Calculate the coefficient in a = 0.
double slope = expression.Calculate(0);
// If the slope is NaN we pretty much evaluated all possible
// derivatives (there is no more derivative possible)
// Thus return 0 such that we can simplify later on.
if (double.IsNaN(slope))
{
slope = 0;
}
Operand resultSlope = new RealNumber(slope);
Multiplication MacLaurinTerm = new Multiplication();
MacLaurinTerm.LeftSuccessor = resultSlope;
Division div = new Division();
MacLaurinTerm.RightSuccessor = div;
// Now create the right part of the multiplication (f'i(0) * (x - 0)^i / i!)
// Create the numerator (x - 0)^i
Power numerator = new Power();
numerator.LeftSuccessor = new DependentVariableX();
numerator.RightSuccessor = new Integer(i);
// Create the denominator (i)!.
Factorial denominator = new Factorial();
denominator.LeftSuccessor = new Integer(i);
// Add the numerator and denominator into the division Operator.
div.LeftSuccessor = numerator;
div.RightSuccessor = denominator;
return(MacLaurinTerm);
}
}
private double CalculateMacLaurinPolynomial(double a, double x, int i)
{
// If some counter = 0, return the constant.
if (i == 0)
{
// return f(0) * x^0 / 0!
Factorial iFactorial = new Factorial();
iFactorial.LeftSuccessor = new Integer(i);
//Console.WriteLine(expressionRoot);
return(expressionRoot.Calculate(0) * Math.Pow(x, i) / iFactorial.Calculate(x));
}
else
{
// calc the i-th term of the maclaurin polynomial + any lower polynomial.
Factorial iFactorial = new Factorial();
iFactorial.LeftSuccessor = new Integer(i);
return((HigherOrderDerivativeByDifferenceQuotient(a, i) * Math.Pow(x, i) / iFactorial.Calculate(x)) + CalculateMacLaurinPolynomial(a, x, i - 1)); // ith term + (i - 1) term if the order/degree is > 0.
}
}
// Method that will create an appropriate operator class
// from the obtained character.
private void CreateNode(char operat0r)
{
Operand result = null;
switch (operat0r)
{
case '+':
result = new Addition();
break;
case '-':
result = new Subtraction();
break;
case '*':
result = new Multiplication();
break;
case '/':
result = new Division();
break;
case '^':
result = new Power();
break;
// Now for operators that take one argument.
case '!':
result = new Factorial();
break;
case 'l':
result = new NaturalLog();
break;
case 'e':
result = new Exp();
break;
case 'c':
result = new Cosine();
break;
case 's':
result = new Sine();
break;
}
if (result is BinaryOperator)
{
// Add the operands to the binary operator.
((BinaryOperator)result).LeftSuccessor = operands[operands.Count - 2];
((BinaryOperator)result).RightSuccessor = operands[operands.Count - 1];
// Remove the operands from the stack.
operands.RemoveAt(operands.Count - 1);
operands.RemoveAt(operands.Count - 1);
}
else
{
// Same story, add operand to unary operator.
((UnaryOperator)result).LeftSuccessor = operands[operands.Count - 1];
// Remove operand from stack.
operands.RemoveAt(operands.Count - 1);
}
// Add the sub tree on top of the operands stack.
operands.Add(result);
}