public static RealNumber operator /(RealNumber a, RealNumber b)
{
if (!a.IsDefinite() || !b.IsDefinite())
{
return(UndefinedStateSuperSwitch.Switch(
() => new RealNumber(UndefinedState.NAN),
() => new RealNumber(UndefinedState.NAN),
() => new RealNumber(UndefinedState.NAN),
() => new RealNumber(UndefinedState.NAN),
() => b.Value >= 0 ? new RealNumber(UndefinedState.POSITIVE_INFINITY) : new RealNumber(UndefinedState.NEGATIVE_INFINITY),
() => b.Value >= 0 ? new RealNumber(UndefinedState.NEGATIVE_INFINITY) : new RealNumber(UndefinedState.POSITIVE_INFINITY),
() => RealNumber.NaN(),
() => RealNumber.NaN(),
a, b));
}
if (!Functional.BothAreEqual(a, b, HierarchyLevel.REAL))
{
return(Number.OpDiv(a, b) as RealNumber);
}
if (b.Value != 0)
{
return(Number.Functional.Downcast(new RealNumber(a.Value / b.Value)) as RealNumber);
}
else
{
return a.Value switch
{
var x when x > 0 => new RealNumber(UndefinedState.POSITIVE_INFINITY),
var x when x < 0 => new RealNumber(UndefinedState.NEGATIVE_INFINITY),
_ => new RealNumber(UndefinedState.NAN)
}
};
}
/// <summary>
/// e. g. Pow(2, 5) = 32
/// </summary>
/// <param name="base">
/// The base of the exponential, base^power
/// </param>
/// <param name="power">
/// The power of the exponential, base^power
/// </param>
/// <returns></returns>
public static ComplexNumber Pow(ComplexNumber @base, ComplexNumber power)
{
// TODO: make it more detailed (e. g. +oo ^ +oo = +oo)
if (power.IsInteger())
{
return(Functional.Downcast(Functional.BinaryIntPow(@base as ComplexNumber, power.AsInt())) as ComplexNumber);
}
if (power.IsRational() && ((power as RationalNumber).Denominator.Value).Abs() < 10) // there should be a minimal threshold to avoid long searches
{
return(Number.Pow(FindGoodRoot(@base, (power as RationalNumber).Denominator), (power as RationalNumber).Numerator));
}
var baseCom = @base.AsComplexNumber();
var powerCom = power.AsComplexNumber();
if (baseCom.IsDefinite() && powerCom.IsDefinite())
{
try
{
return(Functional.Downcast(
Complex.Pow(baseCom.AsComplex(), powerCom.AsComplex())
) as ComplexNumber);
}
catch (OverflowException)
{
return(RealNumber.NaN());
}
}
else
{
return(ComplexNumber.Indefinite(RealNumber.UndefinedState.NAN));
}
}
/// <summary>
/// e. g. Pow(2, 5) = 32
/// </summary>
/// <param name="base">
/// The base of the exponential, base^power
/// </param>
/// <param name="power">
/// The power of the exponential, base^power
/// </param>
/// <returns></returns>
public static ComplexNumber Pow(Number @base, Number power)
{
// TODO: make it more detailed (e. g. +oo ^ +oo = +oo)
if (power.IsInteger())
{
return(Functional.Downcast(Functional.BinaryIntPow(@base as ComplexNumber, power.AsInt())) as ComplexNumber);
}
var baseCom = @base.AsComplexNumber();
var powerCom = power.AsComplexNumber();
if (baseCom.IsDefinite() && powerCom.IsDefinite())
{
try
{
return(Functional.Downcast(
Complex.Pow(baseCom.AsComplex(), powerCom.AsComplex())
) as ComplexNumber);
}
catch (OverflowException)
{
return(RealNumber.NaN());
}
}
else
{
return(ComplexNumber.Indefinite(RealNumber.UndefinedState.NAN));
}
}
public static RealNumber operator /(RealNumber a, RealNumber b)
{
if (!a.IsDefinite() || !b.IsDefinite())
{
return(UndefinedStateSuperSwitch.Switch(
() => RealNumber.NaN(),
() => RealNumber.NaN(),
() => RealNumber.NaN(),
() => RealNumber.NaN(),
() => b.Value switch {
var x when EDecimalWrapper.IsGreater(x, 0) => new RealNumber(UndefinedState.POSITIVE_INFINITY),
var x when EDecimalWrapper.IsLess(x, 0) => new RealNumber(UndefinedState.NEGATIVE_INFINITY),
var x when EDecimalWrapper.IsEqual(x, 0) => RealNumber.NaN()
},
public static RealNumber operator /(IntegerNumber a, IntegerNumber b)
{
if (!Functional.BothAreEqual(a, b, HierarchyLevel.INTEGER))
{
return(Number.OpDiv(a, b) as IntegerNumber);
}
if (b == 0 && a == 0)
{
return(RealNumber.NaN());
}
if (b == 0)
{
return(a > 0
? RealNumber.PositiveInfinity()
: RealNumber.NegativeInfinity());
}
return(Number.Functional.Downcast(new RationalNumber(a, b)) as RationalNumber);
}
public static RealNumber operator /(RationalNumber a, RationalNumber b)
{
if (!Functional.BothAreEqual(a, b, HierarchyLevel.RATIONAL))
{
return(Number.OpDiv(a, b) as RationalNumber);
}
var num = CtxMultiply(a.Numerator, b.Denominator);
var den = CtxMultiply(a.Denominator, b.Numerator);
if (EDecimalWrapper.IsEqual(den, 0))
{
return(RealNumber.NaN());
}
else
{
return(Number.Functional.Downcast(new RationalNumber(num, den)) as RationalNumber);
}
}
/// <summary>
/// Calculates the exact value of arccotangent of num
/// </summary>
/// <param name="num"></param>
/// <returns></returns>
public static ComplexNumber Arccotan(Number num)
=> (num as ComplexNumber).IsDefinite()
? Functional.Downcast(Complex.Atan(1 / num.AsComplex())) as ComplexNumber
: RealNumber.NaN();
/// <summary>
/// Calculates the exact value of cosine of num
/// </summary>
/// <param name="num"></param>
/// <returns></returns>
public static ComplexNumber Cos(Number num)
=> (num as ComplexNumber).IsDefinite()
? Functional.Downcast(Complex.Cos(num.AsComplex())) as ComplexNumber
: RealNumber.NaN();