```rationalize``` method for integer

[ErikQQY]

Hello guys, I notice the rationalize method is only supporting floating point numbers, and support for complex floating point numbers are in process, I think maybe this method should also support rationalizing integer.

In Matlab, there are rats method to get rationalized expression of any number, floating point numbers, complex numbers and integer.

And in python, there is also integer numbers rationalizing method.

So I think the rationalize(x::Integer; tol::Real) should be included in this method.

Would be happy to hear your thoughts.

[vtjnash]

The main challenge is simply that it is defined to be an approximation from a decimal number, while integer conversion is always exact:

julia> Rational(10)
10//1

julia> Rational(.1)
3602879701896397//36028797018963968

julia> rationalize(.1)
1//10

help?> rationalize
search: rationalize Rational Irrational AbstractIrrational

  rationalize([T<:Integer=Int,] x; tol::Real=eps(x))

  Approximate floating point number x as a Rational number with components of the given integer type. The result will differ from x by no more than
  tol.

[ErikQQY]

Yes, I see the Rational(::Integer) could return the rational expression of integer, but I think when users are using rationalize to handle their data, it is a little weird that rationalize can’t rationalize integer🤨.

I don’t think this method should only limit to approximation of decimal number, a rational number should be a number that can be expressed as the quotient of two integers, so it is reasonable to make the rationalize able to handle integer.

BTW, from my point, I would use the rationalize method to get rationalized expression of an array, there is also no such method any way.🤔

julia> arr = [1.2, 2, 3.4]
julia> rationalize(arr)
Error……

[dkarrasch]

BTW, from my point, I would use the rationalize method to get rationalized expression of an array, there is also no such method any way

You would use broadcasting for this:

julia> arr = [1.2, 2, 3.4]
3-element Vector{Float64}:
 1.2
 2.0
 3.4

julia> rationalize.(arr)
3-element Vector{Rational{Int64}}:
  6//5
  2//1
 17//5

[ErikQQY]

@dkarrasch Yes, the broadcasting is working, but in your example, the integer 2 is first being converted to a floating number

Then the rationalize method works on 2.0

I think adding the rationalize method for integers would be more suitable for more data types.

[dkarrasch]

But that has nothing to do with the rationalize function. As you can see from the example, that promotion takes place before rationalize. If you want to avoid that, you'd need to write it as a tuple.

[ErikQQY]

Thanks for your immediate response!

Yes, the type promotion happened after we created the array, the problem is, for example, if I pass an integer to rationalize:

julia> rationalize(1)
ERROR:...

Or, if I pass an integer array to rationalize.():

julia> rationalize.([1, 2, 3])
ERROR:...

[dkarrasch]

Yes, but all of this has nothing to do with a missing method of rationalize for arrays as you seemed to suggest initially. There is only one issue here: rationalize for integers, which is dealt with IIUC in #43427 alongside.

[ErikQQY]

Wow thanks! Didn’t notice it at first

That PR is adding the relating method~

So I would close this issue😄