Mathematical Precision in the Paper

[AndreG-P]

@HowardCohl @physikerwelt One reviewer pointed out that

The paper is not as precise as it could be. [...] The key point is that there are several different concepts of equivalent. [...] In general, there is not enough discussion of the removable singularities issue.

He said that the translations (6), (7), and (8) based on different concepts of equivalence. I have rewritten this paragraph and cited the Corless et al. paper. The translations (7) and (8) are adapted from (23) and (25) in Corless et al.

However, how can we respond to the reviewer now? I would say, that we think the audience of this Journal are rather mathematicians but computer scientists. Thus we decided to introduce the wordings appropriate and unappropriate translations rather than handling different equivalence concepts. We hope that this decision helps the reader to focus on the problems of translations.

[HowardCohl]

@AndreG-P @physikerwelt

unappropriate sounds weird.

inappropriate might be better, but I need to understand better what is going on here.

[HowardCohl]

Oh, I see, actually in the paper it is written as "inappropriate", which is much better.

On p.4, where you introduce "appropriate" and "inappropriate" perhaps indicate "we introduce the terms appropriate and inappropriate"

@physikerwelt @AndreG-P Doesn't it make sense to give here precise definitions (or as good as we can do it) for these terms instead of giving examples?

[AndreG-P]

@HowardCohl Yeah, I would prefer this way also. But I don't know how to define such translations. Do you have an idea? Maybe something like:

A translation is appropriate when a numerical evaluation returns the same values in both concepts up to machine epsilon for all possible points in the domain of the functions.

I'm not happy with this solution but it might be a starting point. Also, what is concept here?

[physikerwelt]

I like that definition. It's similar to the dots used in dlmf

[HowardCohl]

I inserted some HSC stuff and made a new paragraph for "in/appropriate" section and pushed new version.

Please clean up.

[AndreG-P]

@HowardCohl I like the definition. Can't we just say, a translations is inappropriate if it is not appropriate?

To answer your question:

I don't understand how equivalent translations has anything at all to do with appropriate or inapppropriate translations.

We try to describe when a translated expression is equivalent to the input expression. For example, how can we proof that \cos@{x} is equivalent to cos(x) in Maple or Cos[x] in Mathematica? I think that's not possible since \cos@{x} describes the theoretical concept of the trigonometric function while cos(x) and Cos[x] are implementations which try to be as close as possible to this concept.

So instead of using the term equivalent, which seems to be not adequate for translations, we introduce the terms appropriate and inappropriate. Does this makes sense?

[AndreG-P]

I included and uploaded the changes with 3ea76d1b7ef5fef7ee015bf4440f77400a8dd547. I think we are almost done if @HowardCohl is satisfied with these changes.

[HowardCohl]

I have modified the relevant text surrounding the definitions of (in)/appropriate. Have a look and let me know what you think.

[AndreG-P]

I like it. Thanks