public static RPN.Node increaseExponentTwo(RPN.Node node)
{
RPN.Node temp = node.Children[0].Children[0];
temp.Replace(temp.GetNumber() + 1);
node.Children[1].Children[0].Remove(new RPN.Node(1));
return(node);
}
public static RPN.Node Power(RPN.Node node)
{
RPN.Node power = node[3, 0].Clone();
RPN.Node end = node[0].Clone();
RPN.Token _fac = new RPN.Token("!", 1, RPN.Type.Operator);
RPN.Token _total = new RPN.Token("total", (int)power.GetNumber(), RPN.Type.Function);
RPN.Node total = new RPN.Node(_total);
double max = power.GetNumber();
RPN.Node numeratorAddition = new RPN.Node(power.GetNumber() + 1); //(p + 1)
for (int i = 0; i <= max; i++)
{
RPN.Node j = new RPN.Node(i);
RPN.Node subtraction = new RPN.Node(power.GetNumber() - j.GetNumber()); //(p - j)
RPN.Node addition = new RPN.Node(subtraction.GetNumber() + 1); //(p - j + 1)
RPN.Node exponent = new Pow(end.Clone(), addition.Clone()); //n^(p - j + 1)
RPN.Node bernoulli = Sum.getBernoulliNumber(i); //B(j)
RPN.Node numerator = new RPN.Node(new RPN.Node[] { numeratorAddition.Clone() }, _fac); //(p + 1)!
RPN.Node denominatorFactorial = new RPN.Node(new RPN.Node[] { addition.Clone() }, _fac); //(p - j + 1)!
RPN.Node jFactorial = new RPN.Node(new RPN.Node[] { j.Clone() }, _fac); //j!
RPN.Node denominator = new Mul(jFactorial, denominatorFactorial); // j! * (p - j + 1)!
RPN.Node fraction = new Div(numerator, denominator);
RPN.Node negativeOneExponent = new Pow(new RPN.Node(-1), j.Clone()); //(-1)^j
RPN.Node multiplication = new Mul(new Mul(negativeOneExponent, fraction), new Mul(bernoulli, exponent));
total.AddChild(multiplication);
}
return(new Div(total, numeratorAddition.Clone()));
}