public override void CopyDerivedFunctionToStack(ExpressionTree cur, ExpressionTree inner, StaticStack<MathOperation> DeriveStack, MathState State)
{
//ln(x)' = 1/x
// 1 x /
DeriveStack.Push((Number)1);
inner.CopyToStack(DeriveStack);
DeriveStack.Push(State.GetOperator("/"));
}
public virtual void CopyDerivedFunctionToStack(ExpressionTree cur,ExpressionTree inner, StaticStack<MathOperation> DeriveStack,MathState State)
{
throw new MathEvaluator.Exceptions.UndefinedResultException(ToString() + " is not derivable");
}
public override void CopyDerivedFunctionToStack(ExpressionTree cur, ExpressionTree inner, StaticStack<MathOperation> DeriveStack, MathState State)
{
//sqrt(x)' = 1/(2*sqrt(x))
// 1 2 x sqrt * /
DeriveStack.Push((Number)1,(Number)2);
inner.CopyToStack(DeriveStack);
DeriveStack.Push(State.GetFunction("sqrt"), State.GetOperator("*"), State.GetOperator("/"));
}
public override void CopyDerivedFunctionToStack(ExpressionTree cur, ExpressionTree inner, StaticStack<MathOperation> DeriveStack, MathState State)
{
//sqrt(x)' = 1/(x * ln 10)
// 1 x 10 ln * /
DeriveStack.Push((Number)1);
inner.CopyToStack(DeriveStack);
DeriveStack.Push((Number)10,State.GetFunction("ln"),State.GetOperator("*"), State.GetOperator("/"));
}
public override void CopyDerivedFunctionToStack(ExpressionTree cur,ExpressionTree inner, StaticStack<MathOperation> DeriveStack,MathState State)
{
inner.CopyToStack(DeriveStack);
DeriveStack.Push(State.GetFunction("cos"));
}
public override void CopyDerivedFunctionToStack(ExpressionTree cur, ExpressionTree inner, StaticStack<MathOperation> DeriveStack,MathState State)
{
inner.CopyToStack(DeriveStack);
DeriveStack.Push(State.GetFunction("sin"), (Number)(-1), State.GetOperator("*"));
}
public override void DeriveToStack(ExpressionTree cur, MathState State, StaticStack<MathOperation> DeriveStack)
{
DeriveStack.Push((Number)0);
}
public override void DeriveToStack(ExpressionTree cur, MathState State, StaticStack<MathOperation> DeriveStack)
{
//f(x) = u(v(x))
//f'(x) = u'(v(x))*v'(x)
// v u' v' *
if(ArgumentCount != 1)
throw new MathEvaluator.Exceptions.UndefinedResultException(ToString() + " is not derivable");
ExpressionTree inner = cur.FunctionParameters[0];
CopyDerivedFunctionToStack(cur,inner, DeriveStack,State);
inner.DeriveToStack(DeriveStack,State);
DeriveStack.Push(new Multiplication());
}
public override void DeriveToStack(ExpressionTree cur, MathState State, StaticStack<MathOperation> DeriveStack)
{
throw new UndefinedResultException(ToString() + " is not derivable");
}
public override void DeriveToStack(ExpressionTree cur, MathState State, StaticStack<MathOperation> DeriveStack)
{
DeriveStack.Push((Number)(_name.ToLower() == "x" ? 1 : 0));
}
public override void DeriveToStack(ExpressionTree cur, MathState State, StaticStack<MathOperation> DeriveStack)
{
// (f(x)^g(x))'
// f(x)^(g(x)-1) (g(x) f'(x)+f(x) ln(f(x)) g'(x))
// f(x) g(x) 1 - ^ g(x) f'(x) * f(x) f(x) ln * + * g'(x) *
// f g 1 - ^ g v * f f ln * b * + *
ExpressionTree f = cur.Left;
ExpressionTree g = cur.Right;
f.CopyToStack(DeriveStack);
g.CopyToStack(DeriveStack);
DeriveStack.Push((Number)1, State.GetOperator("-"), State.GetOperator("^"));
g.CopyToStack(DeriveStack);
f.DeriveToStack(DeriveStack,State);
DeriveStack.Push(State.GetOperator("*"));
f.CopyToStack(DeriveStack);
f.CopyToStack(DeriveStack);
DeriveStack.Push(State.GetFunction("ln"), State.GetOperator("*"));
g.DeriveToStack(DeriveStack,State);
DeriveStack.Push(State.GetOperator("*"), State.GetOperator("+"), State.GetOperator("*"));
/*
if (cur.Left.ContainsVariable("x"))
{
//(x^n)' = n * x^(n-1)
ExpressionTree left = cur.Left;
ExpressionTree right = cur.Right;
right.CopyToStack(DeriveStack);
left.CopyToStack(DeriveStack);
right.CopyToStack(DeriveStack);
DeriveStack.Push((Number)1,State.GetOperator("-"),State.GetOperator("^"),State.GetOperator("*"));
}
else if (cur.Right.ContainsVariable("x"))
{
// (a^x)' = a^x * ln a
// a x ^ a ln *
ExpressionTree left = cur.Left;
ExpressionTree right = cur.Right;
left.CopyToStack(DeriveStack);
right.CopyToStack(DeriveStack);
DeriveStack.Push(State.GetOperator("^"));
left.CopyToStack(DeriveStack);
DeriveStack.Push(State.GetFunction("ln"), State.GetOperator("*"));
//chain rule
right.DeriveToStack(DeriveStack, State);
DeriveStack.Push(State.GetOperator("*"));
}
else if (cur.Left.ToString() == "e" && cur.Right.ToString() == "x")
{
cur.Left.CopyToStack(DeriveStack);
cur.Right.CopyToStack(DeriveStack);
DeriveStack.Push(this);
}
else
{
DeriveStack.Push((Number)0);
}*/
}
public override void DeriveToStack(ExpressionTree cur, MathState State, StaticStack<MathOperation> DeriveStack)
{
//(u * v)' = u' * v + u * v'
//PF: = u' v * u v' * +
ExpressionTree left = cur.Left;
ExpressionTree right = cur.Right;
left.DeriveToStack(DeriveStack,State);
right.CopyToStack(DeriveStack);
DeriveStack.Push(State.GetOperator("*"));
left.CopyToStack(DeriveStack);
right.DeriveToStack(DeriveStack,State);
DeriveStack.Push(State.GetOperator("*"), State.GetOperator("+"));
}
public abstract void DeriveToStack(ExpressionTree cur,MathState State,StaticStack<MathOperation> DeriveStack);
public override void DeriveToStack(ExpressionTree cur, MathState State, StaticStack<MathOperation> DeriveStack)
{
//(u * v)' = (u'v - uv')/v²
//PF: = u' v * u v' * - v 2 ^ /
ExpressionTree left = cur.Left;
ExpressionTree right = cur.Right;
left.DeriveToStack(DeriveStack,State);
right.CopyToStack(DeriveStack);
DeriveStack.Push(State.GetOperator("*"));
left.CopyToStack(DeriveStack);
right.DeriveToStack(DeriveStack,State);
DeriveStack.Push(State.GetOperator("*"), State.GetOperator("-"));
right.CopyToStack(DeriveStack);
DeriveStack.Push((Number)2, State.GetOperator("^"), State.GetOperator("/"));
}
public override void DeriveToStack(ExpressionTree cur, MathState State, StaticStack<MathOperation> DeriveStack)
{
cur.Left.DeriveToStack(DeriveStack, State);
cur.Right.DeriveToStack(DeriveStack, State);
DeriveStack.Push(this);
}