So it it a TeX programming limitation.
The risk of leading to an exponential number of branches is addressed
by Knuth at the beginning of Chapter 17 of the TeXbook (p. 139):
"Mathematicians tend to \quote{overuse} \over when they first begin to
typeset their own work on a system like \TEX." ...
At one point, I went back to using \over rather than \frac as the later
was broken and gave no output. This has since been fixed, but I stayed
with \over as I find primary operators to be much more elegant syntax
than multiple argument macros. It is too bad that luatex does not
employ a better programming solution, as the use of \frac{}{} leads to
ugly mathematical source code.
I guess that I should not worry about it too much since, as Knuth points
out in Chapter 17, overuse of \over, etc. leads to ugly results
anyways, just as well as an overuse of \text in mathematical formulas
(as we physicists tend to abuse) also leads to ugly mathematics.
Alan
On Tue, 22 Dec 2015 17:30:22 -0500
Aditya Mahajan <adit...@umich.edu> wrote:
> On Tue, 22 Dec 2015, Alan BRASLAU wrote:
>
> > Wolfgang,
> >
> > Can you explain to us why it should be preferable for ConTeXt users
> > to employ \frac12 rather than the native TeX construction {1\over
> > 2}? I understand that the macro \frac does some additional trickery
> > but the two constructions should *always* yield identical results
> > (when keyed-in properly).
>
> One of the troubles with { .... \over ...} and the like is that TeX
> does not know which "style" to use. This can lead to extra processing
> when using any command defined using \mathpalatte (such as \text,
> stacked arrows, and others).
>
> Consider \text{...}. Basically, we want \text{...} to typeset it's
> argument in a \hbox with textsize equal to the normalsize in normal
> mode and equal to script size when used in a subscript and in
> scriptsciptsize when used in a sub-subscript. Now, in traditional
> tex, when parsing
>
> {\text{hello} \over 2}
>
> TeX does not kow what size to use for \text{...} until it encounters
> the \over. So, when parsing \text{hello}, TeX generates all possible
> sizes and then prunes them later on. With nested constructs like
>
> {\text{hello}_{\text{world} \over 2} \over 2}
>
> it can lead to exponential number of branches.
>
> With \frac{\text{hello}}{2}, TeX "knows" what style to use for the
> arguments. So, extra processing is not needed (at least, this is the
> idea in LuaTeX; in PDFTeX, multiple sizes need to be generated). This
> can lead to some slightly faster processing.
>
> Also see http://tex.stackexchange.com/a/1261/ answer from Taco.
> Contrast the definition of \cramped given there from one in the LaTeX
> mathtools package
> (http://ctan.bppro.ca/macros/latex/contrib/mathtools/mathtools.dtx)
> [search from MT_cramped_clap_internal:Nn]
>
> Aditya
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--
Alan Braslau
CEA DSM-IRAMIS-SPEC
CNRS UMR 3680
Orme des Merisiers
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