Guides for implementing generic math interfaces

[WhiteBlackGoose]

Hello. I want to ask for a guide or maybe article on implementing generic math interfaces.

The question is not about how to implement them. What I don't fully understand is what interfaces and when I want to implement.

For example, there's INumber<>, which inherits a ton of interfaces. I have type Complex, which can implement most of INumber's methods, but not, for instance, the Max method. Should I implement INumber and then throw unsupported wherever a method doesn't make sense? Or should I implement all and only interfaces which make 100% sense for Complex, but not implement INumber itself?

[FaustVX]

I think you should implement only working interfaces.
I don't think throw NotSupportedException in Release version is a good practice.
And when creating API, only support the minimal interface needed :

public T SumAll<T>(params T[] values)
where T : IAdditionOperators<T, T, T>, IAdditionIdentity<T> // don't use INumber<T>
{
    var sum = T.Zero;
    foreach (var value in values)
        sum += value;
    return sum;
}

[tannergooding]

This is probably a better issue for dotnet/runtime or dotnet/docs than csharplang.

That being said, INumber<T> is really meant for representing "scalar" numbers (a), that is numbers that are representable by a single value. A Complex number is really more like a 2-dimensional number (and so is a type of "vector"), as they represent two parts: a Real part and an Imaginary part (a + bi, where a is the real part and bi represents the imaginary part, which more concretely is a real part b and the imaginary unit i).

"Vector" like values come with additional complexities and considerations which can come in terms of representation, access, creation, general use, and more. Its something that has already had some thought in place and which should hopefully have a more concrete representation in .NET 7 (and which types like System.Numerics.Complex should implement).