# [NTG-context] Suggestions for more math classes?

Hans Hagen j.hagen at xs4all.nl
Thu Jan 27 19:43:25 CET 2022

On 1/27/2022 9:36 AM, Mikael Sundqvist via ntg-context wrote:
> Dear all,
>
> While discussing spacing in math with Hans, we have come to the
> conclusion that to have better control and cleaner code there might be
> a good idea to have more math classes than the usual ones in TeX (ord,
> op, bin, rel, open, close, punct, inner (and some that we need not to
> think about)).
>
> So far, Hans has implemented frac and rad for fractions and radicals.
> The fractions has been a funny construction, being put inside empty
> delimiters, and so surrounded by the \nulldelimiterspace (which has
> been set to 1.2pt, independent of font size). Now we have better
> control of the spacing around fractions.
>
> Hans has opened up (even in the code) for the addition of more
> classes. The overall aim is to have a more coherent and logical way of
> typing math, without manual adding of (arbitrary) spaces every now and
> then. For example, we have always written \int f(x)\, dx to have a
> thin space between the closing parenthesis and the d in integrals.
> There will (most likely) be a differential class. Since the d might
> occur in other places in a formula with integrals, one cannot just
> simply give the letter d the differential class, and we are currently
> discussing the correct way for the user to type it. If you have
> suggestions, please let us hear!
>
> Some further suggestions by Hans are (see below for two more)
>
> 13 imaginary
> 14 differential
> 15 exponential
> 16 function
>
> Q1: Do you have any further suggestions on new classes (or comments on
> these)? It might be good to think about situations where you have felt
> that you need to insert manual spaces such as \, or \! to obtain a
> better result.
>
> I give one contribution: I asked a colleague to look in his TeX files
> for manual spaces, and he came up with several \, (usually before the
> d in integrals) but also with \!. This \! occurred mostly in fencing
> situations to have the exponent come a bit closer to the closing
> parenthesis.
>
> \left( \frac{x}{2} \right)^{\! k+2n}
>
> I have seen this in many places before, so no originality is claimed.
>
> Two more classes that we thought of are under and over. Say that we
> have a\overbar{bc}d. Should the spacing between a and the \overbar{bc}
> and the spacing between \overbar{bc} and d always be tight? If so,
> these might just be ord, and no new class needed (although one could
> argue for adding the classes now, set them up as ord, and thus being
> able to configure them according to taste/need).
>
> Q2: Do you have any real examples of constructions with \overbar,
> \underbar, \overbrace, ... or if you have any strong opinion, please
> raise your voice!
Here is a teaser:

\starttext

% in context we put digits in their own class, the next is the default:

\letmathspacing \mathdigitcode \mathordinarycode \mathordinarycode
\mathordinarycode \mathordinarycode

% but we can adapt the inter digit spacing (\mathdigitcode == 20 in
context, \mathordinarycode is one fo the traditional class codes):

\setmathspacing \mathdigitcode \mathdigitcode \allmathstyles = 2mu

% and also change it when needed

\startTEXpage[offset=10pt]
$x = 1234 = z$\par
\begingroup
\setmathspacing \mathdigitcode \mathdigitcode \allmathstyles = 4mu
$x = 1234 = z$\par
\endgroup
$x = 1234 = z$\par
\stopTEXpage

\stoptext

The result is attached. So maybe Mikaels explanation above and this
example will trigger demand.

One of the possibilities is that users define their own classes and put
characters in it. (this can be domain specific and domains is something
that has been on the todo for quite a while.)

For that reason we might bump the current number of classes (we have 32
classes compared to the 8 that regular tex has) to 64 (which is possible
when we bring down the number of families to 64 (currently 128 compared
to 256 in luatex and 16 in regular tex) which is still plenty and way
more than we ever need (so if needed we can borrow bits for the math
unicode range which is now limited to 0xFFFFF; it was already limited
anyway).

This move also makes it possible to remove some other hacks (with the
usual 'a pity to throw nice code away syndrome' side effect) and can
have some 'initialization of old school ascii' side effects (neglectable
because we can set it up via the emacro package).

For the record: the \Umath<class><class>spacing primitives have been
dropped but can be emulated easily (in the end it saves hundreds of
primitives).

Hans

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Hans Hagen | PRAGMA ADE
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