public void ExecuteTest5()
{
var complex = new Complex(-3, 2);
var exp = new Pow(new ComplexNumber(complex), new Number(10));
Assert.Equal(Complex.Pow(complex, 10), exp.Execute());
}
public void PartialDerivativeTest2()
{
// (yx) ^ 3
IExpression exp = new Pow(new Mul(new Variable("y"), new Variable("x")), new Number(3));
IExpression deriv = exp.Differentiate(new Variable("y"));
Assert.AreEqual("(1 * x) * (3 * ((y * x) ^ (3 - 1)))", deriv.ToString());
}
public void DerivativeTest3()
{
// x ^ 3
Variable x = new Variable("x");
Number num1 = new Number(3);
IExpression exp = new Pow(x, num1);
IExpression deriv = exp.Differentiate();
Assert.AreEqual("1 * (3 * (x ^ (3 - 1)))", deriv.ToString());
num1.Value = 4;
Assert.AreEqual("x ^ 4", exp.ToString());
Assert.AreEqual("1 * (3 * (x ^ (3 - 1)))", deriv.ToString());
// 2 ^ (3x)
Number num2 = new Number(2);
num1 = new Number(3);
Mul mul = new Mul(num1, x.Clone());
exp = new Pow(num2, mul);
deriv = exp.Differentiate();
Assert.AreEqual("(ln(2) * (2 ^ (3 * x))) * (3 * 1)", deriv.ToString());
num1.Value = 4;
Assert.AreEqual("2 ^ (4 * x)", exp.ToString());
Assert.AreEqual("(ln(2) * (2 ^ (3 * x))) * (3 * 1)", deriv.ToString());
}
public void DerivativeTest1()
{
IExpression exp = new Pow(new Variable("x"), new Number(3));
IExpression deriv = exp.Differentiate();
Assert.AreEqual("1 * (3 * (x ^ (3 - 1)))", deriv.ToString());
}
public void DerivativeTest2()
{
// 2 ^ (3x)
IExpression exp = new Pow(new Number(2), new Mul(new Number(3), new Variable("x")));
IExpression deriv = exp.Differentiate();
Assert.AreEqual("(ln(2) * (2 ^ (3 * x))) * (3 * 1)", deriv.ToString());
}
public void ExecuteTest4()
{
var complex1 = new Complex(-3, 2);
var complex2 = new Complex(-4, 5);
var exp = new Pow(new ComplexNumber(complex1), new ComplexNumber(complex2));
Assert.Equal(Complex.Pow(complex1, complex2), exp.Execute());
}
public void MulSameVar10()
{
// 2x * -2x
var var = new Variable("x");
var mul = new Mul(new Mul(new Number(2), var), new Mul(new Number(0.5), var));
var expected = new Pow(var, new Number(2));
SimpleTest(mul, expected);
}
public void PowPartialDerivativeTest3()
{
var exp = new Pow(new Variable("x"), new Number(3));
var deriv = Differentiate(exp, new Variable("y"));
Assert.Equal("0", deriv.ToString());
}
public void PowDerivativeTest3()
{
// x ^ 3
var x = new Variable("x");
var num1 = new Number(3);
var exp = new Pow(x, num1);
var deriv = Differentiate(exp);
Assert.Equal("1 * 3 * (x ^ (3 - 1))", deriv.ToString());
num1.Value = 4;
Assert.Equal("x ^ 4", exp.ToString());
Assert.Equal("1 * 3 * (x ^ (3 - 1))", deriv.ToString());
// 2 ^ (3x)
var num2 = new Number(2);
num1 = new Number(3);
var mul = new Mul(num1, x.Clone());
exp = new Pow(num2, mul);
deriv = Differentiate(exp);
Assert.Equal("ln(2) * (2 ^ (3 * x)) * 3 * 1", deriv.ToString());
num1.Value = 4;
Assert.Equal("2 ^ (4 * x)", exp.ToString());
Assert.Equal("ln(2) * (2 ^ (3 * x)) * 3 * 1", deriv.ToString());
}
public void PowDerivativeTest1()
{
var exp = new Pow(new Variable("x"), new Number(3));
var deriv = Differentiate(exp);
Assert.Equal("1 * 3 * (x ^ (3 - 1))", deriv.ToString());
}
/// <summary>
/// Differentiates the specified expression.
/// </summary>
/// <param name="expression">The expression.</param>
/// <param name="variable">The variable.</param>
/// <returns>Returns the derivative.</returns>
protected virtual IExpression Root(Root expression, Variable variable)
{
var div = new Div(new Number(1), expression.Right.Clone());
var pow = new Pow(expression.Left.Clone(), div);
return Pow(pow, variable);
}
/// <summary>
/// Differentiates the specified expression.
/// </summary>
/// <param name="expression">The expression.</param>
/// <param name="variable">The variable.</param>
/// <returns>Returns the derivative.</returns>
protected virtual IExpression Div(Div expression, Variable variable)
{
var first = Parser.HasVar(expression.Left, variable);
var second = Parser.HasVar(expression.Right, variable);
if (first && second)
{
var mul1 = new Mul(_Differentiate(expression.Left.Clone(), variable), expression.Right.Clone());
var mul2 = new Mul(expression.Left.Clone(), _Differentiate(expression.Right.Clone(), variable));
var sub = new Sub(mul1, mul2);
var inv = new Pow(expression.Right.Clone(), new Number(2));
var division = new Div(sub, inv);
return division;
}
if (first)
{
return new Div(_Differentiate(expression.Left.Clone(), variable), expression.Right.Clone());
}
if (second)
{
var mul2 = new Mul(expression.Left.Clone(), _Differentiate(expression.Right.Clone(), variable));
var unMinus = new UnaryMinus(mul2);
var inv = new Pow(expression.Right.Clone(), new Number(2));
var division = new Div(unMinus, inv);
return division;
}
return new Number(0);
}
/// <summary>
/// Differentiates the specified expression.
/// </summary>
/// <param name="expression">The expression.</param>
/// <param name="variable">The variable.</param>
/// <returns>Returns the derivative.</returns>
protected virtual IExpression Arccot(Arccot expression, Variable variable)
{
var involution = new Pow(expression.Argument.Clone(), new Number(2));
var add = new Add(new Number(1), involution);
var div = new Div(_Differentiate(expression.Argument.Clone(), variable), add);
var unMinus = new UnaryMinus(div);
return unMinus;
}
/// <summary>
/// Differentiates the specified expression.
/// </summary>
/// <param name="expression">The expression.</param>
/// <param name="variable">The variable.</param>
/// <returns>Returns the derivative.</returns>
protected virtual IExpression Arccos(Arccos expression, Variable variable)
{
var pow = new Pow(expression.Argument.Clone(), new Number(2));
var sub = new Sub(new Number(1), pow);
var sqrt = new Sqrt(sub);
var division = new Div(_Differentiate(expression.Argument.Clone(), variable), sqrt);
var unMinus = new UnaryMinus(division);
return unMinus;
}
public void PowPartialDerivativeTest3()
{
IExpression exp = new Pow(new Variable("x"), new Number(3));
IExpression deriv = Differentiate(exp, new Variable("y"));
Assert.AreEqual("0", deriv.ToString());
}
/// <summary>
/// Differentiates the specified expression.
/// </summary>
/// <param name="expression">The expression.</param>
/// <param name="variable">The variable.</param>
/// <returns>Returns the derivative.</returns>
protected virtual IExpression Cot(Cot expression, Variable variable)
{
var sine = new Sin(expression.Argument.Clone());
var involution = new Pow(sine, new Number(2));
var division = new Div(_Differentiate(expression.Argument.Clone(), variable), involution);
var unMinus = new UnaryMinus(division);
return unMinus;
}
/// <summary>
/// Differentiates the specified expression.
/// </summary>
/// <param name="expression">The expression.</param>
/// <param name="variable">The variable.</param>
/// <returns>Returns the derivative.</returns>
protected virtual IExpression Coth(Coth expression, Variable variable)
{
var sinh = new Sinh(expression.Argument.Clone());
var inv = new Pow(sinh, new Number(2));
var div = new Div(_Differentiate(expression.Argument.Clone(), variable), inv);
var unMinus = new UnaryMinus(div);
return unMinus;
}
/// <summary>
/// Differentiates the specified expression.
/// </summary>
/// <param name="expression">The expression.</param>
/// <param name="variable">The variable.</param>
/// <returns>Returns the derivative.</returns>
protected virtual IExpression Arcsch(Arcsch expression, Variable variable)
{
var inv = new Pow(expression.Argument.Clone(), new Number(2));
var add = new Add(new Number(1), inv);
var sqrt = new Sqrt(add);
var abs = new Abs(expression.Argument.Clone());
var mul = new Mul(abs, sqrt);
var div = new Div(_Differentiate(expression.Argument.Clone(), variable), mul);
var unMinus = new UnaryMinus(div);
return unMinus;
}
/// <summary>
/// Differentiates the specified expression.
/// </summary>
/// <param name="expression">The expression.</param>
/// <param name="variable">The variable.</param>
/// <returns>Returns the derivative.</returns>
protected virtual IExpression Pow(Pow expression, Variable variable)
{
if (Parser.HasVar(expression.Left, variable))
{
var sub = new Sub(expression.Right.Clone(), new Number(1));
var inv = new Pow(expression.Left.Clone(), sub);
var mul1 = new Mul(expression.Right.Clone(), inv);
var mul2 = new Mul(_Differentiate(expression.Left.Clone(), variable), mul1);
return mul2;
}
// if (Parser.HasVar(expression.Right, variable))
var ln = new Ln(expression.Left.Clone());
var mul3 = new Mul(ln, expression.Clone());
var mul4 = new Mul(mul3, _Differentiate(expression.Right.Clone(), variable));
return mul4;
}
/// <summary>
/// Differentiates the specified expression.
/// </summary>
/// <param name="expression">The expression.</param>
/// <param name="variable">The variable.</param>
/// <returns>Returns the derivative.</returns>
protected virtual IExpression Arcsec(Arcsec expression, Variable variable)
{
var abs = new Abs(expression.Argument.Clone());
var sqr = new Pow(expression.Argument.Clone(), new Number(2));
var sub = new Sub(sqr, new Number(1));
var sqrt = new Sqrt(sub);
var mul = new Mul(abs, sqrt);
var div = new Div(_Differentiate(expression.Argument.Clone(), variable), mul);
return div;
}
/// <summary>
/// Differentiates the specified expression.
/// </summary>
/// <param name="expression">The expression.</param>
/// <param name="variable">The variable.</param>
/// <returns>Returns the derivative.</returns>
protected virtual IExpression Tanh(Tanh expression, Variable variable)
{
var cosh = new Cosh(expression.Argument.Clone());
var inv = new Pow(cosh, new Number(2));
var div = new Div(_Differentiate(expression.Argument.Clone(), variable), inv);
return div;
}
/// <summary>
/// Differentiates the specified expression.
/// </summary>
/// <param name="expression">The expression.</param>
/// <param name="variable">The variable.</param>
/// <returns>Returns the derivative.</returns>
protected virtual IExpression Arcsin(Arcsin expression, Variable variable)
{
var involution = new Pow(expression.Argument.Clone(), new Number(2));
var sub = new Sub(new Number(1), involution);
var sqrt = new Sqrt(sub);
var division = new Div(_Differentiate(expression.Argument.Clone(), variable), sqrt);
return division;
}
public void PowDerivativeTest2()
{
// 2 ^ (3x)
var exp = new Pow(new Number(2), new Mul(new Number(3), new Variable("x")));
var deriv = Differentiate(exp);
Assert.Equal("ln(2) * (2 ^ (3 * x)) * 3 * 1", deriv.ToString());
}
/// <summary>
/// Differentiates the specified expression.
/// </summary>
/// <param name="expression">The expression.</param>
/// <param name="variable">The variable.</param>
/// <returns>Returns the derivative.</returns>
protected virtual IExpression Arctan(Arctan expression, Variable variable)
{
var involution = new Pow(expression.Argument.Clone(), new Number(2));
var add = new Add(new Number(1), involution);
var div = new Div(_Differentiate(expression.Argument.Clone(), variable), add);
return div;
}
public void PowPartialDerivativeTest2()
{
// (yx) ^ 3
var exp = new Pow(new Mul(new Variable("y"), new Variable("x")), new Number(3));
var deriv = Differentiate(exp, new Variable("y"));
Assert.Equal("1 * x * 3 * ((y * x) ^ (3 - 1))", deriv.ToString());
}
/// <summary>
/// Differentiates the specified expression.
/// </summary>
/// <param name="expression">The expression.</param>
/// <param name="variable">The variable.</param>
/// <returns>Returns the derivative.</returns>
protected virtual IExpression Arsech(Arsech expression, Variable variable)
{
var inv = new Pow(expression.Argument.Clone(), new Number(2));
var sub = new Sub(new Number(1), inv);
var sqrt = new Sqrt(sub);
var mul = new Mul(expression.Argument.Clone(), sqrt);
var div = new Div(_Differentiate(expression.Argument.Clone(), variable), mul);
var unMinus = new UnaryMinus(div);
return unMinus;
}
public void MulSameVar1()
{
// x * x
var var = new Variable("x");
var mul = new Mul(var, var);
var expected = new Pow(var, new Number(2));
SimpleTest(mul, expected);
}
/// <summary>
/// Differentiates the specified expression.
/// </summary>
/// <param name="expression">The expression.</param>
/// <param name="variable">The variable.</param>
/// <returns>Returns the derivative.</returns>
protected virtual IExpression Arsinh(Arsinh expression, Variable variable)
{
var sqr = new Pow(expression.Argument.Clone(), new Number(2));
var add = new Add(sqr, new Number(1));
var sqrt = new Sqrt(add);
var div = new Div(_Differentiate(expression.Argument.Clone(), variable), sqrt);
return div;
}
public void PowerZero()
{
var pow = new Pow(new Variable("x"), new Number(0));
var expected = new Number(1);
SimpleTest(pow, expected);
}
/// <summary>
/// Differentiates the specified expression.
/// </summary>
/// <param name="expression">The expression.</param>
/// <param name="variable">The variable.</param>
/// <returns>Returns the derivative.</returns>
protected virtual IExpression Artanh(Artanh expression, Variable variable)
{
var sqr = new Pow(expression.Argument.Clone(), new Number(2));
var sub = new Sub(new Number(1), sqr);
var div = new Div(_Differentiate(expression.Argument.Clone(), variable), sub);
return div;
}
