//Returns a string representing the division of the mathematical values the operands represent.
public static string DivideStrings(string operand1, string operand2)
{
if (operand1 == "0")
{
return("0");
}
if (operand2 == "1")
{
return(operand1);
}
if (DifferentiationTokenizer.IsNumber(operand1) && DifferentiationTokenizer.IsNumber(operand2))
{
return((int.Parse(operand1) / int.Parse(operand2)).ToString());
}
return(ToPrefixFormat(operand1, operand2, '/'));
}
//Returns a string representing the addition of the mathematical values the operands represent.
//Also support operatorSymbol = '-'. Then it acts as subtraction on the values.
public static string AddStrings(string operand1, string operand2, char operatorSymbol = '+')
{
if (operand1 == "0")
{
return((operatorSymbol == '-') ? InvertString(operand2) : operand2);
}
if (operand2 == "0")
{
return(operand1);
}
if (DifferentiationTokenizer.IsNumber(operand1) && DifferentiationTokenizer.IsNumber(operand2))
{
return((int.Parse(operand1) + (operatorSymbol == '+' ? 1 : -1) * int.Parse(operand2)).ToString());
}
return(ToPrefixFormat(operand1, operand2, operatorSymbol));
}
//Returns a string representing the power function applied to the mathematical values the operands represent.
public static string PowerStrings(string operand1, string operand2)
{
if (operand2 == "0")
{
return("1");
}
if (operand2 == "1")
{
return(operand1);
}
if (operand1 == "0")
{
return("0");
}
if (DifferentiationTokenizer.IsNumber(operand1) && DifferentiationTokenizer.IsNumber(operand2))
{
return(((int)Math.Round(Math.Pow(int.Parse(operand1), int.Parse(operand2)))).ToString());
}
return(ToPrefixFormat(operand1, operand2, '^'));
}
/*
* Differentiates an operator expression. Uses rules for operands being general diffentiable functions.
* +/-: Differentiation linear over +/-
* *: Chain rule
*./: https://www.wolframalpha.com/input/?i=differentiate+f%28x%29%2Fg%28x%29
* ^: https://www.wolframalpha.com/input/?i=differentiate+f%28x%29%5Eg%28x%29 (using expanded form)
*/
public static string DifferentiateOperator(string operatorSymbol, string arguments)
{
string[] operands = DifferentiationTokenizer.SplitArguments(arguments);
string firstDerivative = Differentiate(operands[0]);
string secondDerivative = Differentiate(operands[1]);
switch (operatorSymbol[0])
{
case '+':
case '-':
return(StringMath.AddStrings(firstDerivative, secondDerivative, operatorSymbol[0]));
case '*':
return(StringMath.AddStrings(StringMath.MultiplyStrings(firstDerivative, operands[1]), StringMath.MultiplyStrings(secondDerivative, operands[0])));
case '/':
return(StringMath.DivideStrings(
StringMath.AddStrings(
StringMath.MultiplyStrings(firstDerivative, operands[1]),
StringMath.MultiplyStrings(secondDerivative, operands[0]), '-'),
StringMath.PowerStrings(operands[1], "2")));
case '^':
return(StringMath.AddStrings(
StringMath.MultiplyStrings(
StringMath.MultiplyStrings(firstDerivative, operands[1]),
StringMath.PowerStrings(operands[0], StringMath.AddStrings(operands[1], "1", '-'))),
StringMath.MultiplyStrings(
StringMath.MultiplyStrings(secondDerivative, StringMath.LogarithmString(operands[0])),
StringMath.PowerStrings(operands[0], operands[1])
)
));
default:
throw new FormatException();
}
}