Ytukyg

EDIT: As clarified in the answers below, this appears to be a bug with amsmath and colon and thus doesn't really have anything to do with mathrm versus operatorname.

This question contains an enlightening discussion between using mathrm and operatorname. The tl;dr version is: whenever you have an operator, use operatorname.

However it seems bad to use operatorname if what you are defining is a set, since in general operatorname adds a little space before it. This means that an expression like:

f colon operatorname{End}(V) to mathbb{R}

renders badly, as there is too much white space between the colon and the operatorname{End}. Using mathrm (the RHS) is more visually appealing:

Thus if one views operatorname{End}(V) as a set, then it makes more sense to write mathrm{End}(V).

Now one can view operatorname{End} also a functor on the category of vector spaces, for instance, then you would want the operatorname:

My question is this: What is the best practice when dealing with a quantity that is used both as a set and an operator? Should one really switch between mathrm and operatorname as appropriate? Or is there a better option.

That's a very interesting observation.

The definition of colon in amsmath is

renewcommand{colon}{

  nobreak

  mskip 2mu

  mathpunct{}

  nonscript

  mkern-thinmuskip

  {:}

  mskip 6mu plus 1murelax

}

(edited to show the various parts). The space you see is a consequence of the fact that colon ends with an ordinary atom, namely {:}.

It would have been better to use mathopen, as the following test shows. I first get an alias of colon and patch it to change {:} into mathopen:.

documentclass{article}

usepackage{amsmath}

usepackage{etoolbox}



letpcoloncolon

patchcmd{pcolon}{{:}}{mathopen:}{}{}



begin{document}



$f colon operatorname{End}(V) to R$



$f pcolon operatorname{End}(V) to R$



bigskip



begin{tabular}{@{}*{8}{l}@{}}

&0&1&2&3&4&5&6 \

verb|colon| &

  $colon A$ &

  $colon max$ &

  $colon +$ &

  $colon sim$ &

  $colon ($ &

  $colon )$ &

  $colon ,$

\

verb|pcolon| &

  $pcolon A$ &

  $pcolon max$ &

  $pcolon +$ &

  $pcolon sim$ &

  $pcolon ($ &

  $pcolon )$ &

  $pcolon ,$

end{tabular}



end{document}

In the tests, colon is followed by a symbol in each class.

The only noticeable differences are in the cases when colon is followed by atoms of class 1 (operators) and 3 (relations), performing perhaps better in both.

If you want to follow this suggestion, your document can load etoolbox and do

patchcmd{colon}{{:}}{mathopen:}{}{}

I don't think that it's possible to fix amsmath as many existing documents depend on it and such a change would affect the output and line breaks. It might be possible to add an option for using a fixed definition.