/// <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));
}
}
internal static ComplexNumber FindGoodRoot(ComplexNumber @base, IntegerNumber power)
{
var list = new List <ComplexNumber>();
foreach (var root in GetAllRoots(@base, (long)power.Value).FiniteSet())
{
MathS.Settings.FloatToRationalIterCount.Set(15);
MathS.Settings.PrecisionErrorZeroRange.Set(1e-6m);
var downcasted = Functional.Downcast((root as NumberEntity).Value) as ComplexNumber;
MathS.Settings.PrecisionErrorZeroRange.Unset();
MathS.Settings.FloatToRationalIterCount.Unset();
if (downcasted.IsRational() && Number.IsZero(Number.Pow(downcasted, power) - @base)) // To keep user's desired precision
{
return(downcasted);
}
list.Add(downcasted);
}
foreach (var el in list)
{
if (el.IsReal() && (el as RealNumber) > 0)
{
return(el);
}
}
foreach (var el in list)
{
if (el.IsReal())
{
return(el);
}
}
return(list[0]);
}