private Node GenerateMaclaurinSeriesPolynomial(double x, int order)
{
if (order == 0)
{
return(this);
}
if (order == 1)
{
return(new PlusSign(new MultiplicationSign(ReturnDerivative(x), new VariableNode()), this));
}
VariableNode variableNode = new VariableNode();
NaturalNumberNode orderNode = new NaturalNumberNode(order);
CaretSign caretSign = new CaretSign(variableNode, orderNode);
Node f0 = ReturnDerivative(x);
for (int i = 1; i < order; i++)
{
f0 = f0.ReturnDerivative(x);
}
MultiplicationSign multiplicationSign = new MultiplicationSign(caretSign, new RationalNumberNode(f0.Calculate(0)));
FactorialFunction factorialFunction = new FactorialFunction(orderNode);
DivisionSign divisionSign = new DivisionSign(multiplicationSign, factorialFunction);
return(new PlusSign(divisionSign, ReturnMaclaurinSeriesPolynomial(x, order - 1)));
}
public double ReturnMaclaurinSeries(double x, int order)
{
if (order == 0)
{
return(Calculate(0));
}
if (order == 1)
{
return(ReturnDerivative(x).Calculate(0) * x + Calculate(0));
}
VariableNode variableNode = new VariableNode();
NaturalNumberNode orderNode = new NaturalNumberNode(order);
CaretSign caretSign = new CaretSign(variableNode, orderNode);
Node f0 = ReturnDerivative(x);
for (int i = 1; i < order; i++)
{
f0 = f0.ReturnDerivative(x);
}
MultiplicationSign multiplicationSign = new MultiplicationSign(caretSign, new RationalNumberNode(f0.Calculate(0)));
FactorialFunction factorialFunction = new FactorialFunction(orderNode);
DivisionSign divisionSign = new DivisionSign(multiplicationSign, factorialFunction);
return(divisionSign.Calculate(x) + ReturnMaclaurinSeries(x, order - 1));
}
public override Node ReturnDerivative(double x)
{
NaturalNumberNode zero = new NaturalNumberNode(0);
SineFunction sineNode = new SineFunction(child.Copy());
MinusSign minusNode = new MinusSign(zero, sineNode);
Node childDerivative = child.ReturnDerivative(x);
MultiplicationSign multiplicationSign = new MultiplicationSign(minusNode, childDerivative);
return(multiplicationSign);
}
public override Node ReturnDerivative(double x)
{
MultiplicationSign multiplicationSignA = new MultiplicationSign(leftNode.ReturnDerivative(x), rightNode.Copy());
MultiplicationSign multiplicationSignB = new MultiplicationSign(leftNode.Copy(), rightNode.ReturnDerivative(x));
MinusSign minusSign = new MinusSign(multiplicationSignA, multiplicationSignB);
NaturalNumberNode naturalNumberNode = new NaturalNumberNode(2);
CaretSign caretSign = new CaretSign(rightNode.Copy(), naturalNumberNode);
DivisionSign division = new DivisionSign(minusSign, caretSign);
return(division);
}
private PlusSign[] ReturnNewtonIndeterminates(int order)
{
PlusSign[] funcs = new PlusSign[order + 1];
HNode hNode = new HNode();
NaturalNumberNode orderNode;
MultiplicationSign multiplicationSign;
VariableNode variableNode = new VariableNode();
for (int i = 0; i <= order; i++)
{
orderNode = new NaturalNumberNode(order - i);
multiplicationSign = new MultiplicationSign(orderNode, hNode);
funcs[i] = new PlusSign(variableNode, multiplicationSign);
}
return(funcs);
}
public double ReturnNewtonMaclaurinSeries(double x, int order)
{
if (order == 0)
{
return(Calculate(0));
}
if (order == 1)
{
return(ReturnNewtonDerivative(0) * x + Calculate(0));
}
VariableNode variableNode = new VariableNode();
NaturalNumberNode orderNode = new NaturalNumberNode(order);
CaretSign caretSign = new CaretSign(variableNode, orderNode);
RationalNumberNode f0 = new RationalNumberNode(CalculatePolynomialDerivative(0, order));
MultiplicationSign multiplicationSign = new MultiplicationSign(caretSign, f0);
FactorialFunction factorialFunction = new FactorialFunction(orderNode);
DivisionSign divisionSign = new DivisionSign(multiplicationSign, factorialFunction);
return(divisionSign.Calculate(x) + ReturnNewtonMaclaurinSeries(x, order - 1));
}
private Node ReturnNewtonPolynomial(double x, int order)
{
Operator sign = null;
int[] coefficients = ReturnIndeterminateCoefficients(order);
PlusSign[] indeterminates = ReturnNewtonIndeterminates(order);
if (order == 0)
{
return(new RationalNumberNode(Calculate(indeterminates[0].Calculate(x))));
}
if (order == 1)
{
return(new MinusSign(new RationalNumberNode(Calculate(indeterminates[0].Calculate(x))), new RationalNumberNode(Calculate(indeterminates[1].Calculate(x)))));
}
NaturalNumberNode naturalNumberNode = new NaturalNumberNode(coefficients[0]);
MultiplicationSign multiplicationSign = new MultiplicationSign(naturalNumberNode, new RationalNumberNode(Calculate(indeterminates[0].Calculate(x))));
sign = multiplicationSign;
for (int i = 1; i <= order; i++)
{
naturalNumberNode = new NaturalNumberNode(Math.Abs(coefficients[i]));
multiplicationSign = new MultiplicationSign(naturalNumberNode, new RationalNumberNode(Calculate(indeterminates[i].Calculate(x))));
if (i % 2 == 0)
{
sign = new PlusSign(sign, multiplicationSign);
}
else
{
sign = new MinusSign(sign, multiplicationSign);
}
}
return(sign);
}
private Node Parse(ref string s)
{
Node a;
Node b;
char op = ' ';
if (s[0] == '+' || s[0] == '-' || s[0] == '*' || s[0] == '/' || s[0] == '^')
{
op = s[0];
s = s.Substring(1);
SkipCharacter(ref s, '(');
a = Parse(ref s);
SkipCharacter(ref s, ',');
b = Parse(ref s);
SkipCharacter(ref s, ')');
if (op == '+')
{
return(new PlusSign(a, b));
}
else if (op == '-')
{
return(new MinusSign(a, b));
}
else if (op == '*')
{
return(new MultiplicationSign(a, b));
}
else if (op == '/')
{
return(new DivisionSign(a, b));
}
else
{
return(new CaretSign(a, b));
}
}
else if (s[0] == 's' || s[0] == 'c' || s[0] == 'e' || s[0] == 'l' || s[0] == '!')
{
op = s[0];
s = s.Substring(1);
SkipCharacter(ref s, '(');
a = Parse(ref s);
SkipCharacter(ref s, ')');
if (op == 's')
{
return(new SineFunction(a));
}
else if (op == 'c')
{
return(new CosineFunction(a));
}
else if (op == 'e')
{
return(new ExponentialFunction(a));
}
else if (op == 'l')
{
return(new LogarithmFunction(a));
}
else
{
return(new FactorialFunction(a));
}
}
else if (s[0] == 'n' || s[0] == 'r')
{
op = s[0];
s = s.Substring(1);
SkipCharacter(ref s, '(');
string tempS = s.Split(')')[0];
tempS = tempS.Replace(',', '.');
if (op == 'n')
{
if (tempS.Contains('.') || tempS.Contains('-'))
{
throw new IsNotValidNaturalNumberException();
}
}
s = s.Substring(s.IndexOf(')') + 1);
if (op == 'n')
{
return(new NaturalNumberNode(int.Parse(tempS)));
}
else
{
return(new RationalNumberNode(float.Parse(tempS)));
}
}
else if (s[0] == 'p')
{
s = s.Substring(1);
return(new PiNode());
}
else if (s[0] == 'x')
{
s = s.Substring(1);
return(new VariableNode());
}
else if (char.IsDigit(s[0]))
{
string number = s[0].ToString();
s = s.Substring(1);
while (s.Length > 0)
{
if (!char.IsDigit(s[0]))
{
break;
}
number += s[0];
s = s.Substring(1);
}
a = new NaturalNumberNode(int.Parse(number));
return(a);
}
throw new InvalidExpressionException();
}