Modify braket package to control the space between text and brackets

Question

Significant EDIT: Stimulated by the comments of the users egreg and schtandard, I found a solution to my original problem. Now, the problem has slightly changed, but it is still about the control between text and brackets with the braket page.

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As in the title of the question, I would like to modify the package braket (in the link the whole .sty file, which is quite small) to control the space between the brackets and the text.

This question is a follow up of this previous question of mine: Modify braket package for different brackets forms.

Thus, the idea is that I would like to adapt this sty file to make it work with other brackets (as in the previous question) and to have different spacings for all those new brackets. If you are wondering why I want to modify braket instead of writing my own macro, the reason is that doing this would be way above my level (which should not be surprising considering the level of this question).

Here there is an example of what I would like to get in the sty file.

\documentclass{article}
\usepackage{braket}

\begin{document}
$\Set { a | b }$
$A \Foo { \hspace{-0.1cm} a \hspace{-0.1cm}| \hspace{-0.1cm}b \hspace{-0.1cm} }$

\end{document}

We can call \Foo the command that should correspond to the second line, which should look something like A(a|b).

To get what I want, the line from braket should be modified as follows:

{\catcode`\|=\active
  \xdef\Foo{\protect\expandafter\noexpand\csname Foo \endcsname}
  \expandafter\gdef\csname Foo \endcsname#1{\mathinner
        {\lbrace\,{\mathcode`\|32768\let|\midvert #1}\,\rbrace}}
  \xdef\Foo{\protect\expandafter\noexpand\csname Foo \endcsname}
  \expandafter\gdef\csname Foo \endcsname#1{\left(
    %
        \ifx\SavedDoubleVert\relax \let\SavedDoubleVert\|\fi
        %\:
        {\let\|\FooDoubleVert
        \mathcode`\|32768\let|\FooVert
        #1}
        %\:
        \right)}
}

\def\midvert{\egroup\mid\bgroup}
\def\FooVert{\@ifnextchar|{\|\@gobble}% turn || into \|
        {\egroup
        %\;
        \mid@vertical
        %\;
        \bgroup}}
\def\FooDoubleVert{\egroup
    %\;
    \mid@dblvertical
    %\;
    \bgroup}

The code above is nothing more than the code from braket regrouped for readability reasons, with:

1. Foo instead of Set,
2. \left( and \right) instead of \left\{ and \right\},
3. and with the horizontal spacing commands \: and \; commented.

This is enough to get one part of the result.

The bit that is missing is the following:

How do we control in braket the space in the line of code A \Foo { a | b } between the letter "A" and the bracket "("?

Here there are two examples of commands that should be created in braket to achieve the following output.

% Command Fou
$A \hspace{3cm} \Set { \hspace{3cm} a \hspace{-0.1cm} | \hspace{-0.05cm} b \hspace{5cm} }$

%Command Fouo
$A \hspace{-0.05cm} \Set { \hspace{-0.05cm} a \hspace{-0.1cm} | \hspace{-0.1cm} b \hspace{-0.05cm} }$

Any help is going to be greatly appreciated!

Answer 1

Your questions are still not entirely clear to me, but here is an attempt to answer:

• While the decision to want to remove all those spaces is rather questionable, if you want to do it, I think it is best to just write a new command than to modify the braket definitions. (After all, you don't really want to use any of it.) This is easily done using xparse with mleftright for the space around the braces.

  \documentclass{article}
  
  \usepackage{xparse}
  \usepackage{mleftright}
  
  \NewDocumentCommand\kolmin{ O{0mu} O{#1} m }{%
    \mleft\{ \mkern #1\relax #3 \mkern #2\relax \mright\}
  }
  
  \begin{document}
  
  \(X \kolmin{a|b} X\)
  
  \(X \kolmin[10mu]{a|b} X\)
  
  \(X \kolmin[10mu][5mu]{a|b} X\)
  
  \end{document}
  

• The \spacefactor error you got is due to the fact that you forgot to use \makeatletter before your definitions. See this question for an explanation.
• Since you noted that macro definition is "way over your head", if you are interested in a technical, but not too in-depth description of how macro expansion in TeX works this blog series might be a good starting point. (If anyone knows of a good answer on-site, feel free to comment.)

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Regarding your updated request, you can of course define a macro like

\NewDocumentCommand\Fou{ m m }{%
  \hspace{3cm} \Set { \hspace{3cm} #1 \hspace{-0.1cm} | \hspace{-0.05cm} #2 \hspace{5cm} }
}

to get the output you specified, but that seems like a backwards approach to me. It is easier and cleaner to just not use braket, as shown above, and adjust the spacing to your liking, e.g.

\NewDocumentCommand\Fou{ m m }{%
  \mskip 150mu\relax\mleft\{ \mkern 150mu\relax #1 \middle| \mkern 5mu\relax #2 \mkern 200mu\relax \mright\}%
}

though this is obviously terrible typography.