Provide `div`, `rem` for complex integers

[eschnett]

It would be nice if div and rem were supported for complex integer types, at least when the divisor is integer (and not complex). (This would be the method div(::Complex{<:Integer}, ::Integer).) In this case, the result is uniquely defined.

In the same way, div and rem could be defined for arrays, similarly to how arrays can be multiplied and divided by scalars via * and /: [1,2,3] % 2.

[Seelengrab]

In this case, the result is uniquely defined.

Since this will probably come up later on, related to the rounding mode: #42060
So I'm not sure that this is uniquely defined without defining rounding as part of that operation.

In particular, I see at least a conflict between defining div in terms of the angle of the complex number vs. defining it in terms of diving the real & complex parts individually.

[mcabbott]

Xref also #37376, where the question is whether mod(x+im*y, n) for real n should impose one period on the complex plane, or two.

[11happy]

As of latest version of julia , I checked the div has been implemented for scalar arrays however rem is not implemented still. So the tasks remain are :

1. rem for scalar arrays.
2. div,rem for complex numbers.

Update on task : I am currently working on above tasks and will make a PR .

[11happy]

Now as for Task1, I propose the following solution :

function rem(a::Vector{Int}, y::Int)
    return rem.(a, y)
end

Should I proceed forward?
Thank you.

[Seelengrab]

rem on Vector is unrelated to rem of a Complex; they are not the same. Also, there is no div method taking in a Vector{Int} as far as I can tell.

[11happy]

Hello @Seelengrab the solution I proposed is for rem on vector . As I am taking this issue in steps , Like rem for scalar vectors as step1 . Also as I recently tried the division of an array by a scalar and it worked for me. I am also attaching the Image.
If I misunderstood anything please correct me.

Thank you

[11happy]

div for complex numbers is defined and here is a working example for division of type div(::Complex{<:Integer}, ::Integer).

and now as for rem is concerned for complex numbers I am not quite clear about how rem is defined for complex numbers can someone please guide me regrading that.
Thank you.

[KristofferC]

div for complex numbers is defined

You seem to mix up div and /.

julia> a = 1+2im
1 + 2im

julia> b = 2
2

julia> c = a/b
0.5 + 1.0im

julia> c = div(a, b)
ERROR: MethodError: no method matching div(::Complex{Int64}, ::Int64, ::RoundingMode{:ToZero})

[11happy]

Sorry I got it mixed up I will look into it and correct it.

[11happy]

Before moving forward I want to explain what i have understood from the issue and please correct me if I am wrong.Sorry for my previous mixup.
div on array/vector : div of each individual ie. element wise div.
div on complex numbers : div of real and complex parts. or div in terms of angle (I am not clear about it)
rem on array/vector : rem of each individual ie. element wise rem.
rem on complex numbers : rem of real and complex parts or if there is something different expected from it.

Please provide feedback and suggestions .
Thank you.

[KristofferC]

I personally don't think

In the same way, div and rem could be defined for arrays, similarly to how arrays can be multiplied and divided by scalars via * and /: [1,2,3] % 2.

should be done and should instead use broadcasting. Scaling a vector is in my opinion a linear algebra concept while elementwise % is noit.

[11happy]

okay , I agree with you broadcasting would be better and I believe I should close my previous PR, now for complex numbers how should I proceed ?
Thank you