public static RPN.Node LogExponentExpansion(RPN.Node node)
{
RPN.Node exponent = node.Children[0];
RPN.Node baseNode = exponent.Children[1];
RPN.Node power = exponent.Children[0];
RPN.Node log = new RPN.Node(new[] { baseNode.Clone(), node.Children[1] }, new RPN.Token("log", 2, RPN.Type.Function));
return(new Mul(power, log));
}
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()));
}
public static RPN.Node expressionTimesDivision(RPN.Node node)
{
RPN.Node division;
RPN.Node expression;
if (node.Children[0].IsDivision())
{
division = node.Children[0];
expression = node.Children[1];
}
else
{
division = node.Children[1];
expression = node.Children[0];
}
RPN.Node numerator = division.Children[1];
RPN.Node multiply = new Mul(expression.Clone(), numerator.Clone());
numerator.Remove(multiply);
expression.Remove(new RPN.Node(1));
return(node);
}
public static RPN.Node Propagation(RPN.Node node)
{
RPN.Node sum = new RPN.Node(new RPN.Node[] { node[0].Clone(), node[1].Clone(), node[2].Clone(), node[3, 1].Clone() }, _sum);
node.Replace(node[3], node[3, 0]); //This saves a simplification step later
return(new Add(node.Clone(), sum));
}