Re: strange output in math display mode

[Hans Hagen <pragma@wxs.nl>]

On 12/22/2015 11:30 PM, Aditya Mahajan 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.

normally this is not what tex spends most time on although indeed it get 
slow as soon as you do 8 (massive) font switches plus other 
initializations (more a macro package issue then)

> 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]

the \over and \above primitives are kind of special in the sense that 
they force the tex parser to backtrack (in practice it goes into another 
state and reconsiders the previous mathlist (of char) to become part of 
the fraction specification)

in the end there is a math list that gets processed and at that point 
tex will figure out the size (it only calculates once not four times as 
it knows what size it's in then)

as adity mantiones, as soon as one wants control over the size one runs 
into the problem that one has to use some construct that calculates all 
sizes (as then we pass an already typeset stream) so that tex when doing 
the fraction can choose the one it needs; this is referred to as 
"choices": if you want a smaller 1 and 2 in  {1\over2} then you need 
something {\allfour{1}\over\allfour{2}} which then quickly let you make 
a helper which then tends to be called \frac and 1\frac2 is not 
something you can do in macros

you can just use {{foo}\over{bar}} if you prefer (use all those braces 
to make things predictable) but then you cannot easily influence styling

luatex introduces a mechanism to predict the upcoming style so that one 
can act upon it and avoid the four choices but that is normally not a 
user level operation (too much code)

the whole idea of \frac is to provide a way to control styling (smaller 
that normal for instance)

in context the fraction mechanism is quite complex as all permutations 
you can imagine are wanted by (different) users and usage (and you don't 
want to know what people put in fractions)

basically you have

   style-a {style-b {{style-c}\over{style-d}}}

kind of cases and every style influences a nested one (in font size, 
spacing etc) and of course mixed use complicates matters (consistent 
spacing, coloring, etc)


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