Why does \tag require braces while \frac doesn't?

Question

I'm used to using \tag without braces like \tag3 instead of \tag{3} in Markdown+MathJax, where it works as fine as does \frac12 in normal LaTeX. But when I tried to do this in a real .tex source processed with pdflatex, I got some errors.

Here's the code:

\documentclass[]{article}
\usepackage{amsmath}
\begin{document}

\[f(x)=\frac32\tag1\]

\end{document}

And this is what pdflatex says

This is pdfTeX, Version 3.14159265-2.6-1.40.18 (TeX Live 2017/Debian) (preloaded format=pdflatex)
 restricted \write18 enabled.
entering extended mode
(./test.tex
LaTeX2e <2017-04-15>
Babel <3.18> and hyphenation patterns for 3 language(s) loaded.
(/usr/share/texlive/texmf-dist/tex/latex/base/article.cls
Document Class: article 2014/09/29 v1.4h Standard LaTeX document class
(/usr/share/texlive/texmf-dist/tex/latex/base/size10.clo))
(/usr/share/texlive/texmf-dist/tex/latex/amsmath/amsmath.sty
For additional information on amsmath, use the `?' option.
(/usr/share/texlive/texmf-dist/tex/latex/amsmath/amstext.sty
(/usr/share/texlive/texmf-dist/tex/latex/amsmath/amsgen.sty))
(/usr/share/texlive/texmf-dist/tex/latex/amsmath/amsbsy.sty)
(/usr/share/texlive/texmf-dist/tex/latex/amsmath/amsopn.sty))
No file test.aux.
Runaway argument?
1\] 
! Paragraph ended before \tag was complete.
<to be read again> 
                   \par 
l.6

When I surround the 1 with braces, it compiles fine, and I get the expected PDF output. So I wonder, why does \tag require braces while \frac doesn't? Is there some difference in "type" of the object, like e.g. \tag being a package-supplied facility while \frac is from the language core (doesn't need \usepackage at least) or something like that?

yes they are differently defined. Better don't be lazy and avoid argument braces -- as you can see it can break. — Ulrike Fischer, Aug 13 '19 at 12:07

campa · Accepted Answer · 2019-08-14T07:17:32.947

The macro \frac is defined (robustly) as

\frac#1#2 -> \begingroup #1 \endgroup \@@over #2

where \@@over is (a copy of) the TeX primitive. So in this case you can indeed write \frac12 and it will be the same as \frac{1}{2}. A lot of people, included myself, will tell you not to do this. (Although for such short fractions I don't always follow my own advice...)

On the other hand, at the beginning of displaymath \tag is \let to \tag@in@display, whose definition reads

\def\tag@in@display#1#{\relax\tag@in@display@a{#1}}

The tricky bit is the # before the opening brace of the replacement text. TeX looks for the first argument up to an opening brace (later it will check if this first argument is a star *). For details on how this mechanism works I refer to the questions Grab to #{ macro arguments (in particular Martin Scharrer's answer) and Macros with # as the last parameter. But the short answer is: TeX is scanning for an opening brace to collect the argument #1 and at some point finds the empty line (which is converted to a new paragraph), which isn't allowed, and hence the Paragraph ended error.

I think the last sentence is not correct. TeX finds \par (namely the empty line after \]) before expanding \tag, while it is scanning for its argument. It isn't looking for a closing brace but scanning for the opening brace delimiting that argument. — schtandard, Aug 13 '19 at 21:54

Why does \tag require braces while \frac doesn't?

1 Answers1