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)
{
if (leftNode is NumberNode && rightNode is NumberNode)
{
return(new NaturalNumberNode(0));
}
else if (leftNode is VariableNode && (rightNode is NaturalNumberNode || rightNode is RationalNumberNode))
{
RationalNumberNode rationalNumberNodeA = new RationalNumberNode(rightNode.Calculate(x));
RationalNumberNode rationalNumberNodeB = new RationalNumberNode(rightNode.Calculate(x) - 1);
CaretSign caretSign = new CaretSign(leftNode.Copy(), rationalNumberNodeB);
MultiplicationSign multiplicationSign = new MultiplicationSign(rationalNumberNodeA, caretSign);
return(multiplicationSign);
}
else if (leftNode is NumberNode)
{
LogarithmFunction logarithmFunction = new LogarithmFunction(leftNode.Copy());
CaretSign caretSign = new CaretSign(leftNode.Copy(), rightNode.Copy());
MultiplicationSign multiplicationSignA = new MultiplicationSign(logarithmFunction, caretSign);
MultiplicationSign multiplicationSignB = new MultiplicationSign(multiplicationSignA, caretSign.rightNode.ReturnDerivative(x));
return(multiplicationSignB);
}
else
{
MinusSign minusSign = new MinusSign(rightNode.Copy(), new NaturalNumberNode(1));
CaretSign caretSign = new CaretSign(leftNode.Copy(), minusSign);
MultiplicationSign multiplicationSignA = new MultiplicationSign(rightNode.Copy(), caretSign);
MultiplicationSign multiplicationSignB = new MultiplicationSign(multiplicationSignA, leftNode.ReturnDerivative(x));
return(multiplicationSignB);
}
}
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);
}
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));
}
public override Node Simplify()
{
Node simplifiedLeftNode = leftNode.Simplify();
Node simplifiedRightNode = rightNode.Simplify();
if (simplifiedLeftNode.GetType() == simplifiedRightNode.GetType() && simplifiedLeftNode.Calculate(2) == simplifiedRightNode.Calculate(2))
{
return(new NaturalNumberNode(1)); //5 / 5 = 1, x / x = 1
}
else if (simplifiedRightNode is NaturalNumberNode && simplifiedRightNode.Calculate(0) == 1)
{
return(simplifiedLeftNode); //5 / 1 = 5, x / 1 = 1
}
else if (simplifiedLeftNode is NaturalNumberNode && simplifiedLeftNode.Calculate(0) == 0)
{
return(new NaturalNumberNode(0)); //0 / 5 = 0
}
else if (simplifiedLeftNode is SineFunction && simplifiedRightNode is CosineFunction || (simplifiedLeftNode is CosineFunction && simplifiedRightNode is SineFunction))
{
Operation functionB = (Operation)simplifiedRightNode;
if (simplifiedLeftNode is Operation && simplifiedRightNode is Operation)
{
Operation functionA = (Operation)simplifiedLeftNode;
double childValueA = functionA.ReturnChild().Calculate(5);
double childValueB = functionB.ReturnChild().Calculate(5);
if (simplifiedLeftNode is SineFunction && simplifiedRightNode is CosineFunction)
{
if (childValueA == childValueB)
{
return(new TangentFunction(functionA.ReturnChild())); //sin(x) / cos(x) = tan(x)
}
}
else if (simplifiedLeftNode is CosineFunction && simplifiedRightNode is SineFunction)
{
if (childValueA == childValueB)
{
return(new CotangentFunction(functionA.ReturnChild())); //cos(x) / sin(x) = cotg(x)
}
}
}
return(new DivisionSign(simplifiedLeftNode, simplifiedRightNode));
}
//else if (simplifiedLeftNode is NaturalNumberNode && simplifiedLeftNode.Calculate(5) == 1 && simplifiedRightNode is TangentFunction) //1 / tan(x) = cotg(x)
// return new CotangentFunction(functionB.ReturnChild());
//else if (simplifiedLeftNode is NaturalNumberNode && simplifiedLeftNode.Calculate(5) == 1 && simplifiedRightNode is CotangentFunction) // 1 / cotg(x) = tan(x)
// return new TangentFunction(functionB.ReturnChild());
else if (simplifiedLeftNode is NumberNode && simplifiedRightNode is NumberNode) // 10 / 2 = 5
{
double valueA = 0;
double valueB = 0;
if (simplifiedLeftNode is RationalNumberNode)
{
valueA = ((RationalNumberNode)simplifiedLeftNode).Value;
}
if (simplifiedLeftNode is NaturalNumberNode)
{
valueA = ((NaturalNumberNode)simplifiedLeftNode).Value;
}
if (simplifiedRightNode is RationalNumberNode)
{
valueB = ((RationalNumberNode)simplifiedRightNode).Value;
}
if (simplifiedRightNode is NaturalNumberNode)
{
valueB = ((NaturalNumberNode)simplifiedRightNode).Value;
}
return(new RationalNumberNode(valueA / valueB));
}
else if (simplifiedLeftNode is ExponentialFunction && simplifiedRightNode is ExponentialFunction) //e^5 / e^3 = e^2
{
return(new ExponentialFunction(new MinusSign(((Operation)simplifiedLeftNode).ReturnChild().Simplify(),
((Operation)simplifiedRightNode).ReturnChild().Simplify()).Simplify()));
}
else if (simplifiedLeftNode is VariableNode && simplifiedRightNode is CaretSign)
{
CaretSign caretSign = (CaretSign)simplifiedRightNode;
if (caretSign.ReturnLeftNode() is VariableNode && caretSign.ReturnRightNode() is NaturalNumberNode) //x / x^5 = 1 / x^4
{
return(new DivisionSign(new NaturalNumberNode(1), new CaretSign(new VariableNode(),
new NaturalNumberNode(Convert.ToInt32(caretSign.ReturnRightNode().Calculate(1)) - 1))));
}
else
{
return(new CaretSign(simplifiedLeftNode, simplifiedRightNode));
}
}
else if (simplifiedRightNode is VariableNode && simplifiedLeftNode is CaretSign)
{
CaretSign caretSign = (CaretSign)simplifiedLeftNode;
if (caretSign.ReturnLeftNode() is VariableNode && caretSign.ReturnRightNode() is NaturalNumberNode)
{
return(new CaretSign(new VariableNode(), new NaturalNumberNode(Convert.ToInt32(caretSign.ReturnRightNode().Calculate(1)) - 1))); //x^5 / x = x^4
}
else
{
return(new CaretSign(simplifiedLeftNode, simplifiedRightNode));
}
}
else
{
return(new DivisionSign(simplifiedLeftNode, simplifiedRightNode));
}
}