why does the first compile but not the second and third?
#\sqrt\frac12 vs \sqrt\sqrt1 and \frac\frac123
timber pebbleBOT
fadaaszhi
inner veldt
$\sqrt\sqrt1$
fad
$\sqrt\sqrt1$
```Compilation error:```! Missing { inserted.
<to be read again>
\let
l.49 $\sqrt\sqrt
1$
A left brace was mandatory here, so I've put one in.
You might want to delete and/or insert some corrections
so that I will find a matching right brace soon.
(If you're confused by all this, try typing `I}' now.)```
inner veldt
$\frac\frac123$
fad
$\frac\frac123$
```Compilation error:```! Missing } inserted.
<inserted text>
}
l.49 $\frac\frac1
23$
I've inserted something that you may have forgotten.
(See the <inserted text> above.)
With luck, this will get me unwedged. But if you
really didn't forget anything, try typing `2' now; then
my insertion and my current dilemma will both disappear.```
inner veldt
(i know all of these should in practice use grouping like \frac{\frac{1}{2}}{3} in order to work correctly but i'm curious about the apparent discrepancy between the above cases)
stray island
```latex
$\sqrt\frac12$
```
The fact that this works is merely a coincidence with the particular implementation of \sqrt
inner veldt
You are invoking undefined behaviour here
thanks for responding, do you have a reference to undefined behaviours in (La)TeX?
stray island
There's no reference for latex like there is for a standardised language
I was simply appropriating the concept
inner veldt
do you know what's going on behind the scenes that makes \sqrt\frac12 work but not \frac\frac123?
stray island
I can give an explanation, but it will not make sense if you haven't read the TeXbook
inner veldt
i've skimmed through the TeXbook before
stray island
Sure. First look at the expansion of \sqrt to see that it is essentially \radical "xxxxxx
,,cmeans sqrt,sqrtsign
timber pebbleBOT
stray island
What's the syntax for \radical? Flip to the TeXbook, Chapter 26, to find
\radical〈27-bit number〉〈math field〉
What's a math field? We find
〈math field〉 → 〈filler〉〈math symbol〉 | 〈filler〉{〈math mode material〉}
OK, since \frac12 certainly isn't a math symbol, it must be { math mode material }. Let's verify this
,,\edef\temp{\frac12} \cmean temp
timber pebbleBOT
inner veldt
i'm following so far
stray island
Well the explanation is complete
the tldr is just \frac12 happens to expand to something that \radical can accept
ie a braced group
inner veldt
what happens when TeX sees \frac\frac123? does it become {\begingroup \frac\endgroup \over 1}23?
stray island
Yes, because \frac is a macro
\frac would take #1 <- \frac, #2 <- 1
which is obviously nonsense
inner veldt
ah, and then the second \frac ends up getting #1 <- \endgroup, #2 <- \over, giving even more nonsense
${\begingroup {\begingroup \endgroup\endgroup \over \over} 1}23$
timber pebbleBOT
fad
${\begingroup {\begingroup \endgroup\endgroup \over \over} 1}23$
```Compilation error:```! Missing } inserted.
<inserted text>
}
l.49 ${\begingroup {\begingroup \endgroup\endgroup
\over \over} 1}23$
I've inserted something that you may have forgotten.
(See the <inserted text> above.)
With luck, this will get me unwedged. But if you
really didn't forget anything, try typing `2' now; then
my insertion and my current dilemma will both disappear.```
inner veldt
same output, same error
and when parsing {\begingroup \endgroup\endgroup it expects } instead of the last \endgroup
did i get it right?
inner veldt
OK, since \frac12 certainly isn't a math symbol, it must be { math mode material...
when expanding \frac\frac123, the first \frac gets #1 <- \frac and #2 <- 1.
when expanding \sqrt\frac12, why doesn't \sqrt get #1 <- \frac?
stray island
and when parsing `{\begingroup \endgroup\endgroup` it expects `}` instead of the...
yes
stray island
when expanding `\frac\frac123`, the first `\frac` gets `#1 <- \frac` and `#2 <- ...
\sqrt expands to \radical which is a tez primitive
It has different parsing rules
In particular, it would expand ahead in search of a math symbol or a <general text> construction
inner veldt
ah, so \sqrt is a macro that takes zero parameters