Consequences of setting \mathcode of letters and symbols to "8000?

Question

I know this is not something that you’re supposed to do. But for fun, I played around with the idea of changing the \mathcode of all letters to "8000 and defining them as commands. Each such command would then correspond to the variable with that symbol. Below, I tried doing this with the letter j, though it partly failed. Similarly, I would like to redefine +, -, and all the other common math symbols.

So far, everything seems to work more or less as before. Command names, environment names, and key names containing j seem to work just fine. I have four questions:

Which LaTeX functionality would you break if you did this for all letters? What if you did it for common symbols like + and -?
How can I fix the below MWE so that j simply prints j (using \oldletter caused a loop)?
Am I doing it the “right way”, or should I rather use a different construction, e.g. using \everymath, \everydisplay, and \AtBeginDocument?
What would be the best way to wrap all of this functionality into a single command, called something like \RedefineMathLetter{<letter>} or \RedefineMathSymbol{<symbol>}?

\documentclass{article}
\let\oldletter=j
\mathcode`\j="8000
\catcode`\j=\active
\NewDocumentCommand{j}{ o }{%
    J% using \oldletter caused a loop
    \IfValueT{#1}{_{#1}}%
}
\catcode`\j=11
\begin{document}
( j = j[1] )
\end{document}

See egreg's answer at https://tex.stackexchange.com/questions/538642/epigrafica-font-and-mathastext-incompatible-for-minus-sign: If a character is assigned \mathcode 32768 (that is, "8000 in TeX hexadecimal notation), the following happens when the character is found: nothing at all when TeX is not typesetting (for instance when looking for arguments of every kind, even of primitives); the character is printed when TeX is in horizontal mode; the current definition of the character as active when TeX is in math mode and examines the character for adding it to the math list under construction. — Steven B. Segletes, Aug 24 '21 at 11:38
Also relevant: https://tex.stackexchange.com/questions/109436/what-is-the-differences-between-mathcode-and-catcode-and-how-can-i-use-mathcode — Steven B. Segletes, Aug 24 '21 at 13:10

score 4 · Accepted Answer · edited Aug 26 '21 at 09:47

4

\documentclass{article}
\mathchardef\oldletter=\mathcode`j
\mathcode`\j="8000
\catcode`\j=\active
\NewDocumentCommand{j}{ o }{%
    \oldletter
    \IfValueT{#1}{_{#1}}%
}
\catcode`\j=11
\begin{document}
( j = j[1] )
\end{document}

or wrapped as a command form:

\documentclass{article}
\def\mathdef#1{%
  \expandafter\mathchardef\csname old#1\endcsname\mathcode#1 % \mathcode#1="8000 %
  \begingroup
  \lccode\~=#1 %
  \lowercase{\endgroup\NewDocumentCommand~}}
\mathdef{j}{o}{\oldj\IfValueT{#1}{_{#1}}}
\begin{document}
( j = j[1] )
\end{document}

edited Aug 26 '21 at 09:47

Gaussler

12,801

answered Aug 24 '21 at 11:31

David Carlisle

757,742

Thanks. And what about the other things? To start with, what would be the unintended consequences of doing this in your document? – Gaussler Aug 24 '21 at 11:32
@Gaussler oh it's probably safe enough other than https://chat.stackexchange.com/transcript/41?m=18216810#18216810 – David Carlisle Aug 24 '21 at 11:35
2

@Gaussler I added a command definition wrapper – David Carlisle Aug 24 '21 at 11:42
1

I never understood: Why the need to use the \lowercase trick? – Gaussler Aug 24 '21 at 11:52
2

@Gaussler there must be an answer on site about that, but lowercase ~ gives you an active j (it's about the only thing \lowercase is good for, it can't be used for lowercasing text other than English) – David Carlisle Aug 24 '21 at 12:00
That is a cool trick!! Especially because #1 (j in this case) is absorbed before it is active, so any efforts to use #1 directly will fail. – Steven B. Segletes Aug 24 '21 at 12:01
1

Here's a short discussion of the lowercase-tilde-active-char trick: https://tex.stackexchange.com/questions/246347/modify-catcode-in-the-preamble-or-in-the-atbegindocument/246454#246454 – Steven B. Segletes Aug 24 '21 at 12:21
I was also wondering: Is there a way to undo the change of \mathcode of j? I tried \mathcode`\j=\mathcode\oldj and obviously failed. – Gaussler Aug 24 '21 at 13:04
1

\mathcode\j=\oldj` @Gaussler – David Carlisle Aug 24 '21 at 13:14
@campa and David: I sometimes wonder, why can’t you use \uppercase? – Gaussler Aug 24 '21 at 15:17
3

@Gaussler tradition – David Carlisle Aug 24 '21 at 15:22
1

David: TRADITION. – Gaussler Aug 24 '21 at 15:24
1

@Gaussler rules of course are meant to be broken https://tex.stackexchange.com/questions/215249/why-in-the-discussion-of-the-definition-of-newif-are-the-following-things-true/215252#215252 showing the plain (not latex) version of \newif uses \uppercase – David Carlisle Aug 24 '21 at 15:30
David, can this method be extended to use in the classic _ way to shift a subscript? For example, can I get $j_{\;1}$ with this method? – mert Sep 04 '22 at 11:09

score 2 · Answer 2 · answered Aug 24 '21 at 16:58

2

There's still no expl3 interface for \mathchardef.

\documentclass{article}
\ExplSyntaxOn
\cs_new_protected:Nn \gaussler_mathchardef:Nn
 {
  \tex_mathchardef:D #1 = #2 \scan_stop:
 }
\cs_generate_variant:Nn \gaussler_mathchardef:Nn { c }
\NewDocumentCommand{\RedefineMathLetter}{mmm}
 {% #1 = letter to redefine, #2 = args spec, #3 = replacement text
  % save the original math code
  \gaussler_mathchardef:cn { __gaussler_letter_#1: } { \char_value_mathcode:n { #1 } } % define a new command to replace the letter \exp_args:Nc \NewDocumentCommand { __gaussler_letter_new_#1 } { #2 } { #3 } % define the active equivalent \char_set_active_eq:nc {#1 } { __gaussler_letter_new_#1 }
  % at begin document set math code "8000
  \AtBeginDocument
   {
    \char_set_mathcode:nn { `#1 } { "8000 }
   }
 }
% in the replacement text, instead of the letter x, use \STD{x}
\NewDocumentCommand{\STD}{m}{ \use:c { __gaussler_letter_#1: } }
\ExplSyntaxOff
\RedefineMathLetter{J}{o}{\STD{J}\IfValueT{#1}{_{#1}}}
\begin{document}
$J+J[1]$
\end{document}

The \STD{J} trick avoids infinite loops.

answered Aug 24 '21 at 16:58

egreg

1,121,712

Regarding my other question, would there be any unintended consequences of doing this to all letters (and maybe also to symbols like + and -)? – Gaussler Aug 25 '21 at 13:00
@Gaussler I see no consequence apart from obscuring your input – egreg Aug 25 '21 at 13:27
Well, I used to type “a squared” as \va[pow=2]. Now I can do a[pow=2]. Slightly less obscure, in fact. ;-) – Gaussler Aug 26 '21 at 11:16
@Gaussler Less obscure than a^2? – egreg Aug 26 '21 at 12:58
Indeed, a^2 is simple and short, but it would not be semantic. Superscripts can mean a lot of different things in mathematics. Plus, it’s not as easy to centrally adjust the spacing around the 2. When you use a command with keyval syntax, you can. And for more complicated constructions from advanced mathematics, it’s nice to be able to control the notation centrally. – Gaussler Aug 26 '21 at 13:12
Okay, seriously, please tell me this: Define \sheafreg to be \mathcal{O}, i.e. the structure sheaf of regular functions on some scheme. Take \sheafreg of X, restrict it to U and take the stalk at p. How would you type this? Would you just type \sheafreg_{X}|_{U,p}? Or would you try to be more semantic and use commands? Please tell me your approach to doing this without running into double subscript errors. (You already know my approach, which is to make everything keyval-based, as in semantex, i.e. something like \sheafreg[\vX,res=\vU,stalk=\vp].) – Gaussler Aug 26 '21 at 13:36

Consequences of setting \mathcode of letters and symbols to "8000?

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