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)
{
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 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);
}
