Dtyjlui

I answered another question (LaTeX models symbol that goes both ways) creating a new symbol, a relation, without using mathrel.

In his answer to the same question, Werner used it (he also used joinrel, a command I didn't know, where I used !).

In this case, however, I see no difference in the results with or without mathrel. Is it always needed?

documentclass{article} 

newcommand{mymod}{mathrel{models!mid}} 

newcommand{mymode}{models!mid} 

newcommand{mymodel}{mathrel{modelsjoinrelmid}} 

begin{document} 

This is without verb|mathrel|, with verb|!|:

[ A mymod Bquad {scriptstyle  A mymod B }quad  {scriptscriptstyle  A mymod B }] 

This is with verb|mathrel|, with verb|!|:

[ A mymode Bquad {scriptstyle  A mymode B }quad  {scriptscriptstyle  A mymode B } ] 

This is with verb|mathrel| and verb|joinrel|:

[ A mymodel B quad {scriptstyle  A mymodel B }quad  {scriptscriptstyle  A mymodel B }] 

They seem the same to me. What is the difference?

end{document}

You can figure out what is going on using the table on page 170 of the TeXbook.

Here 0, 1, 2, and 3 stand for no space, thin space, medium space, and thick space, respectively; the table entry is parenthesized if the space is to be inserted only in display and text styles, not in script and scriptscript styles.

First we look at the definitions of models, mid, !, and joinrel. For simplicity I use the definitions from Plain TeX (the LaTeX definitions are similar but with some extra protect and stuff).

defmodels{mathrel|joinrel=}

mathchardefmid="326A

def!{mskip-thinmuskip} % thinmuskip=3mu

defjoinrel{mathrel{mkern-3mu}}

Checking in the table the spacing between a Rel and a Rel atom we find 0, i.e. no spacing at all. That means that there will be no space inserted between any of the atoms in any of the following sequences because all the atoms are Rel (except mskip which is not an atom)

models!mid

modelsjoinrelmid

Because the leftmost and rightmost atoms in these sequences are of type Rel, the whole sequence will behave like a Rel atom (with respect to spacing). So in this case the enclosing mathrel is redundant.

The ugly

newcommand{mymodel}{mathrel{modelsjoinrelmid}} 

The bad

newcommand{mymod}{mathrel{models!mid}} 

newcommand{mymode}{models!mid} 

The good

newcommand{foo}{modelsjoinrelmid}

The best™

DeclareRobustCommand{xjoinrel}{mathrel{mkern-3.5mu}}

letmodelsrelax % undefine models

DeclareRobustCommand{models}{mathrel{|}xjoinrelRelbar} %% YES!

DeclareRobustCommand{mymod}{mathrel{|}xjoinrelRelbarxjoinrelmathrel{|}}

Explanations

TeX never adds space between two consecutive relation symbols. Since models is defined as mathrel{|}joinrelRelbar and all three are relation symbols, the first method has a redundant mathrel.

The command joinrel is mathrel{mkern-3mu}. Using mid and mathrel{|} is the same, but in this context mathrel{|} is better because mid might be used for a different symbol.

Why are the other two bad? Because ! is not the right spacing.

The good is just what's needed, because it gives a relation and adds no spaces in between.

The best method avoids the little gap between the Relbar and mid. Look closely in the table below.

documentclass{article}

usepackage{amsmath}

usepackage{booktabs}



DeclareRobustCommand{xjoinrel}{mathrel{mkern-3.5mu}}



renewcommand{models}{%

  mathrel{|}

  xjoinrel

  Relbar 

}

newcommand{modeledby}{%

  Relbar 

  xjoinrel

  mathrel{|}

}

newcommand{doublemodels}{%

  mathrel{|}

  xjoinrel

  Relbar 

  xjoinrel

  mathrel{|}

}



begin{document}



begin{tabular}{cc}

toprule

New & Old \

midrule

$Amodels B$ & $AmidjoinrelRelbar B$ \

$Amodeledby B$ & $A Relbarjoinrelmid B$ \

$Adoublemodels B$ & $A midjoinrelRelbarjoinrelmid B$ \

bottomrule

end{tabular}



end{document}