//This is what we want our end result to look like
/**
* AST Simplified Infix : {a-f,b-f,c-f,d-f}
* list [13 | 4 | Function | True | 7c563ab9893e876c49fcc316a78e6b6d]
* ├─- [12 | 2 | Operator | False | 281861c9d3dfdecb3ddffdc8930cb63e]
* │ ├─f [11 | 0 | Variable | False | 8fa14cdd754f91cc6554c9e71929cce7]
* │ └─d [10 | 0 | Variable | False | 8277e0910d750195b448797616e091ad]
* ├─- [9 | 2 | Operator | False | 4ad3c11a7d979f70332d8dbc8ab33f43]
* │ ├─f [8 | 0 | Variable | False | 8fa14cdd754f91cc6554c9e71929cce7]
* │ └─c [7 | 0 | Variable | False | 4a8a08f09d37b73795649038408b5f33]
* ├─- [6 | 2 | Operator | False | df41b29ce151a927ae80c6df545518c1]
* │ ├─f [5 | 0 | Variable | False | 8fa14cdd754f91cc6554c9e71929cce7]
* │ └─b [4 | 0 | Variable | False | 92eb5ffee6ae2fec3ad71c777531578f]
* └─- [3 | 2 | Operator | False | d5c11d5ccf6dc77d16eaf012db8813fa]
* ├─f [2 | 0 | Variable | False | 8fa14cdd754f91cc6554c9e71929cce7]
* └─a [1 | 0 | Variable | False | 0cc175b9c0f1b6a831c399e269772661]
*/
public static RPN.Node VectorFrontScalarBack(RPN.Node node)
{
RPN.Token operatorToken = node.Token;
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()));
}