The scope of \newcommand is the entire page

Question

LaTeX on this site supports \newcommand and \renewcommand. This is very nice, but I noticed that the scope of these definitions is the entire rest of the page. That's consistent with how LaTeX behaves, but it could be undesirable on this site where the page contains posts by different people: one person's \newcommand affects everyone who posts below them.

To illustrate the problem, in this question I am including

\renewcommand{\sin}{\cos}

$\renewcommand{\sin}{\cos}$Now anyone who uses \sin in an answer or a comment will get $\cos$ instead.

(I considered exploiting this when asking some simple trig question on main and then watching the confusion, but decided not to be evil.)

It would be good if the scope of \newcommand and friends could be limited to the current question/answer/comment, but I don't know whether this is possible.

Answer 1

It pains me to break this thread by fixing the issue, but here we are. :)

We are now inserting \begingroup and \endgroup directives into post and comment bodies, so all command definitions should be scoped to individual posts.

For now, I'm only enabling this on Math (and here on meta), but barring any issues this change will go live on all MathJax-enabled sites next week.

Answer 2

As Mariano points out, this has been reported before. Because of that conversation, MathJax v2.0 includes an extension (the begingroup extension) that would allow you to isolate the effects of \def, \newcommand, etc. to a single question, answer, or comment, but it would require changes to the SE code to force that to be used.

The changes would be to include begingroup.js in the TeX extensions array for the site's configuration, and outputing a $\begingroup$ at the beginning of each questions/answer/comment and an $\endgroup$ at the end. (These might want to be enclosed in a hidden <div> or some other tag so that they don't introduce any unwanted space.) The preview code would also have to be modified to include these, but that would need to be a bit more sophisticated, since the typesetting can be canceled in the middle (by new characters being typed) so the final \endgroup would need to be handled separately in that case. I would be happy to work that out if the powers-that-be wanted to coordinate efforts on that.

Edit: Asaf asks whether you can do anything like this "by hand". I had considered telling you about the \require{} command that will load extensions that haven't been included in the configuration, but I didn't. That's because the current preview code will not work well with the begingroup extension. If you include a $\begingroup$ in your post, but haven't yet typed the $\endgroup$, then each character you type will cause the post to be reprocessed, and each reprocessing will cause a new \begingroup to be performed without a corresponding \endgroup. This will use up memory that will not be freed (until you go to another page), and can slow MathJax down.

Similarly, if you have a long post, then even if you do have matching \begingroup and \endgroup tags, if you type fast, each letter will cancel MathJax in the middle of what it is doing, and so MathJax may be canceled after processing the \begingroup but before the \endgroup. Again, you can use up memory.

This is what I meant when I said that the preview code would need to be modified to take that into account.

While it is technically possible to use the begingroup extension by hand, you would have to be careful about how you do it. On the plus side, it only affects you when you are editing (or someone else who is editing your work), so perhaps you would be willing to put up with the difficulties.

In any case, your example doesn't really show how it would work, since \begingroup and \endgroup don't protect you from definitions from outside your answer; they protect others from definitions in your answer. So to see it really work, you would need to use something like

$$
  \require{begingroup}
  \begingroup
\renewcommand{\tan}{\operatorname{grey}}
\tan\theta
  \endgroup
  \ne
  \tan\phi
$$

to get

$$ \require{begingroup} \begingroup \renewcommand{\tan}{\operatorname{grey}} \tan\theta \endgroup \ne \tan\phi $$

This works, but if you don't get the balancing of begin and end groups properly during the editing process, you can be left with a lot of open begin groups, that contain local definitions that don't go away (until you reload the page).

Answer 3

This answer will serve as a demonstration:

$$\sin \pi = 0$$

What I typed was true (edit or view source), but what you see is false.

Answer 4

$\require{begingroup} \begingroup$As discussed in the comments to Davide Cervone's answer, I have added a client-side fix to this bug to version 1.2. of the Stack Overflow Unofficial Patch.

The fix works by injecting a special hidden TeX command (currently named \resetstack) at the beggining of each post, comment, snippet (as shown e.g. on the front page) or question/answer link (as in the sidebar), which resets the TeX InputJax macro definitions to their default values.

The implementation is currently a bit complicated, but hopefully it can be simplified later, if some of the needed code is incorporated directly into MathJax as Davide suggests in the comments.

Some important notes about the fix:

Since SOUP is a client-side user script, installing it will fix the bug for you, but not for others. In particular, any definitions made in your posts will still leak to other posts when viewed by users who don't have SOUP installed (which, alas, means most of them).

I therefore strongly recommend that, if you use \def, \(re)newcommand or other such features in your posts, you should always prefix them with:

$\require{begingroup} \begingroup$

and end them with:

$\endgroup$

to keep your definitions from leaking into other posts. (Note that using SOUP should eliminate any memory leak issues due to unclosed \begingroup tags while composing a post, since SOUP will reset the definition stack whenever the preview pane is re-typeset.)

You should also avoid redefining symbols in question titles, or anywhere near the top of your posts where the definitions would be likely to show up on the front page or in search results. (Alas, there's currently no 100% reliable way to prevent that from happening, except by not redefining TeX commands at all.)

Because of these issues, \def and friends are still best used sparingly, and only for things that would be unlikely to conflict with notation in other posts. For example, \newcommand{\foo}{\operatorname{foo}} is probably fine, but \newcommand{\sin}{\cos} is not.

Also note that, even with SOUP, definitions imported from extensions via \require will still leak into other posts. This is pretty much impossible to avoid without breaking some extensions badly, and should basically be considered as being by design.$\endgroup$

---

Edit: Turns out that my original implementation of this fix suffered from a race condition that made it work on Firefox only occasionally. This should be fixed in v1.2.1 that I just released; anyone using it is strongly advised to upgrade.

(Also, the upcoming v1.4 release of SOUP will have more MathJax scoping fixes, including one for \labels, again based on a suggestion by Davide Cervone. Those still need some more testing before release, though.)

Answer 5

Fun fact:

in addition to

\newcommand{\sin}{\cos}

you can also include

\newcommand{\cos}{\sin}

and flat-out break all the code that uses those commands. Or, if you felt inclined to be evil, you could e.g. do a cyclic redefinition of the entire Greek alphabet, or something. Not that you should, of course.