public override Function Derivatives()
{
Function DerivativeNode = new Divide();
Function TopDerivative = new Substract();
DerivativeNode.Left = TopDerivative;
Function TopLeftDerivative = new Multiply();
Function TopRightDerivative = new Multiply();
TopDerivative.Left = TopLeftDerivative;
TopDerivative.Right = TopRightDerivative;
TopLeftDerivative.Left = Left.Derivatives();
TopLeftDerivative.Right = Right;
TopRightDerivative.Left = Left;
TopRightDerivative.Right = Right.Derivatives();
Function BottomDerivative = new Multiply();
DerivativeNode.Right = BottomDerivative;
BottomDerivative.Left = Right;
BottomDerivative.Right = Right;
return(DerivativeNode);
}
public override Function Derivatives()
{
Function DerivativeNode = new Substract();
DerivativeNode.Left = Left.Derivatives();
DerivativeNode.Right = Right.Derivatives();
return(DerivativeNode);
}
public override Function GetDerivativeAnalytically()
{
Substract derivative = new Substract();
if (this.LeftFunc != null)
{
derivative.LeftFunc = this.LeftFunc.GetDerivativeAnalytically();
}
derivative.RightFunc = this.RightFunc.GetDerivativeAnalytically();
return(derivative);
}
public override Function SimplifyFunction()
{
Left = Left.SimplifyFunction();
Right = Right.SimplifyFunction();
if (Left.IsConstant() && Right.IsConstant())
{
return(new RealNumber(CalculateValue(0)));
}
if (Right.ToString() == "0")
{
return(Left);
}
if (Left is Substract && Right.IsConstant())
{
if (Left.Left.IsConstant())
{
Function function = new Substract();
function.Left = new RealNumber(Left.Left.CalculateValue(0) - Right.CalculateValue(0));
function.Right = Left.Right;
return(function.SimplifyFunction());
}
if (Left.Right.IsConstant())
{
Function function = new Substract();
function.Left = Left.Left;
function.Right = new RealNumber(Left.Right.CalculateValue(0) + Right.CalculateValue(0));
return(function.SimplifyFunction());
}
}
if (Right is Substract && Left.IsConstant())
{
if (Right.Left.IsConstant())
{
Function function = new Plus();
function.Left = new RealNumber(Left.CalculateValue(0) - Right.Left.CalculateValue(0));
function.Right = Right.Right;
return(function.SimplifyFunction());
}
if (Right.Right.IsConstant())
{
Function function = new Substract();
function.Left = new RealNumber(Left.CalculateValue(0) + Right.Right.CalculateValue(0));
function.Right = Right.Left;
return(function.SimplifyFunction());
}
}
if (Left is Plus && Right.IsConstant())
{
if (Left.Left.IsConstant())
{
Function function = new Plus();
function.Left = new RealNumber(Left.Left.CalculateValue(0) - Right.CalculateValue(0));
function.Right = Left.Right;
return(function.SimplifyFunction());
}
if (Left.Right.IsConstant())
{
Function function = new Plus();
function.Left = Left.Left;
function.Right = new RealNumber(Left.Right.CalculateValue(0) - Right.CalculateValue(0));
return(function.SimplifyFunction());
}
}
if (Right is Plus && Left.IsConstant())
{
if (Right.Left.IsConstant())
{
Function function = new Substract();
function.Left = new RealNumber(Left.CalculateValue(0) - Right.Left.CalculateValue(0));
function.Right = Right.Right;
return(function.SimplifyFunction());
}
if (Right.Right.IsConstant())
{
Function function = new Substract();
function.Left = new RealNumber(Left.CalculateValue(0) - Right.Right.CalculateValue(0));
function.Right = Right.Left;
return(function.SimplifyFunction());
}
}
if (Left is NaturalLogarithm && Right is NaturalLogarithm)
{
if (Left.Left.IsConstant() && Right.Left.IsConstant())
{
Function function = new NaturalLogarithm();
function.Left = new RealNumber(Left.Left.CalculateValue(0) / Right.Left.CalculateValue(0));
return(function.SimplifyFunction());
}
}
return(this);
}
private Function CreateTree()
{
Function currentNode = null;
string token = listNotations.First();
switch (token)
{
case "c":
currentNode = new Cosine();
listNotations.Remove(token);
currentNode.Left = CreateTree();
break;
case "/":
currentNode = new Divide();
listNotations.Remove(token);
currentNode.Left = CreateTree();
currentNode.Right = CreateTree();
break;
case "e":
currentNode = new Exp();
listNotations.Remove(token);
currentNode.Left = CreateTree();
break;
case "!":
currentNode = new Factorial();
listNotations.Remove(token);
currentNode.Left = CreateTree();
break;
case "*":
currentNode = new Multiply();
listNotations.Remove(token);
currentNode.Left = CreateTree();
currentNode.Right = CreateTree();
break;
case "l":
currentNode = new NaturalLogarithm();
listNotations.Remove(token);
currentNode.Left = CreateTree();
break;
case "n":
listNotations.Remove(token);
string valueN = listNotations.First();
currentNode = new NaturalNumber(Convert.ToInt32(valueN));
listNotations.Remove(valueN);
break;
case "x":
currentNode = new ParameterX();
listNotations.Remove(token);
break;
case "p":
currentNode = new Pi();
listNotations.Remove(token);
break;
case "+":
currentNode = new Plus();
listNotations.Remove(token);
currentNode.Left = CreateTree();
currentNode.Right = CreateTree();
break;
case "^":
currentNode = new Power();
listNotations.Remove(token);
currentNode.Left = CreateTree();
currentNode.Right = CreateTree();
break;
case "r":
listNotations.Remove(token);
string valueR = listNotations.First();
currentNode = new RealNumber(Convert.ToDouble(valueR));
listNotations.Remove(listNotations.First());
break;
case "s":
currentNode = new Sine();
listNotations.Remove(token);
currentNode.Left = CreateTree();
break;
case "-":
currentNode = new Substract();
listNotations.Remove(token);
currentNode.Left = CreateTree();
currentNode.Right = CreateTree();
break;
default:
currentNode = new NaturalNumber(Convert.ToInt32(token));
listNotations.Remove(token);
break;
}
return(currentNode);
}
//Method
//Insert function to the binary tree
public Function Insert(ref string s)
{
Function root = null;
switch (s[0])
{
case '+':
{
root = new Plus();
s = s.Substring(2);
while (s[0] != ',')
{
root.LeftFunc = Insert(ref s);
s = s.Substring(1);
}
s = s.Substring(1);
while (s[0] != ')')
{
root.RightFunc = Insert(ref s);
s = s.Substring(1);
}
break;
}
case '-':
{
root = new Substract();
if (s[1] != '(')
{
break;
}
s = s.Substring(2);
while (s[0] != ',')
{
root.LeftFunc = Insert(ref s);
s = s.Substring(1);
}
s = s.Substring(1);
while (s[0] != ')')
{
root.RightFunc = Insert(ref s);
s = s.Substring(1);
}
break;
}
case '*':
{
root = new Multiply();
s = s.Substring(2);
while (s[0] != ',')
{
root.LeftFunc = Insert(ref s);
s = s.Substring(1);
}
s = s.Substring(1);
while (s[0] != ')')
{
root.RightFunc = Insert(ref s);
s = s.Substring(1);
}
break;
}
case '/':
{
root = new Divide();
s = s.Substring(2);
while (s[0] != ',')
{
root.LeftFunc = Insert(ref s);
s = s.Substring(1);
}
s = s.Substring(1);
while (s[0] != ')')
{
root.RightFunc = Insert(ref s);
s = s.Substring(1);
}
break;
}
case '^':
{
root = new Power();
s = s.Substring(2);
while (s[0] != ',')
{
root.LeftFunc = Insert(ref s);
s = s.Substring(1);
}
s = s.Substring(1);
while (s[0] != ')')
{
root.RightFunc = Insert(ref s);
s = s.Substring(1);
}
break;
}
case 'n':
{
root = new n();
s = s.Substring(2);
string[] parts = s.Split(')');
(root as n).Data = Convert.ToInt32(parts[0].ToString());
while (s[0] != ')')
{
s = s.Substring(1);
}
break;
}
case 'r':
{
root = new r();
s = s.Substring(2);
string[] parts = s.Split(')');
(root as r).Data = Convert.ToDouble(parts[0].ToString());
while (s[0] != ')')
{
s = s.Substring(1);
}
break;
}
case 's':
{
root = new S();
s = s.Substring(2);
while (s[0] != ')')
{
root.LeftFunc = Insert(ref s);
s = s.Substring(1);
}
break;
}
case 'c':
{
root = new c();
s = s.Substring(2);
while (s[0] != ')')
{
root.LeftFunc = Insert(ref s);
s = s.Substring(1);
}
break;
}
case 'e':
{
root = new e();
s = s.Substring(2);
while (s[0] != ')')
{
root.LeftFunc = Insert(ref s);
s = s.Substring(1);
}
break;
}
case 'l':
{
root = new l();
s = s.Substring(2);
while (s[0] != ')')
{
root.LeftFunc = Insert(ref s);
s = s.Substring(1);
}
break;
}
case '!':
{
root = new Factorial();
s = s.Substring(2);
while (s[0] != ')')
{
root.LeftFunc = Insert(ref s);
s = s.Substring(1);
}
break;
}
case 'p':
{
root = new pi();
break;
}
case 'x':
{
root = new x();
break;
}
default:
{
root = new Digit();
(root as Digit).Data = Convert.ToInt32(s[0].ToString());
break;
}
}
return(root);
}