Create a resizable symbol?

Question

Some symbols can be resized automatically with \middle when placed between a \left. and a \right. They can usually also be resized using \big or \bigg. Examples of such symbols are |and / and pretty much all the brackets; (, [, \{, \langle, and so on. I have never seen a complete list of symbols which can be resized this way. Are they special in some way or is it possible to create new resizable symbols? If it is possible: What is the "correct" way to create a new resizable symbol? By that, I mean a symbol \mysymbol such that, e.g.

\left( \somethinghuge \middle\mysymbol b \right)

will have the "correct" size. Of course, bear in mind that one would usually want to apply this to already existing symbols which do not resize. Like the \# symbol, for instance.

Answer 1

Using \scalerel, one can make one argument match the vertical extent of another argument. The optional argument is a max-width constraint (in this case, I chose 2ex). Here's an example of the same code working on two different \somethinghuge arguments. In this case, I chose \mysymbol as a / sign.

\documentclass{article}
\usepackage{scalerel}
\def\mysymbol{/}
\begin{document}
\def\somethinghuge{\rule[-2.2ex]{2ex}{6ex}}
$\left( \somethinghuge \scalerel*[2ex]{\mysymbol}{\somethinghuge} b \right)$
\def\somethinghuge{\rule[-3.2ex]{2ex}{8ex}}
$\left( \somethinghuge \scalerel*[2ex]{\mysymbol}{\somethinghuge} b \right)$
\end{document}

Here's an equivalent syntax that would allow you to avoid typing \somethinghuge twice.

$\left( \scaleleftright[2ex]{.}{\somethinghuge}{\mysymbol} b \right)$

Answer 2

The characters which can be resized with \left, \middle and \right are those with a non zero \delcode. Commands are also allowed, provided their expansion starts with \delimiter; they are defined by \DeclareMathDelimiter in fontmath.ltx:

%%% characters
\DeclareMathDelimiter{(}{\mathopen} {operators}{"28}{largesymbols}{"00}
\DeclareMathDelimiter{)}{\mathclose}{operators}{"29}{largesymbols}{"01}
\DeclareMathDelimiter{[}{\mathopen} {operators}{"5B}{largesymbols}{"02}
\DeclareMathDelimiter{]}{\mathclose}{operators}{"5D}{largesymbols}{"03}
\DeclareMathDelimiter{<}{\mathopen}{symbols}{"68}{largesymbols}{"0A}
\DeclareMathDelimiter{>}{\mathclose}{symbols}{"69}{largesymbols}{"0B}
\DeclareMathDelimiter{/}{\mathord}{operators}{"2F}{largesymbols}{"0E}
\DeclareMathSymbol{/}{\mathord}{letters}{"3D}
\DeclareMathDelimiter{|}{\mathord}{symbols}{"6A}{largesymbols}{"0C}
%%% commands
\DeclareMathDelimiter{\lmoustache}   % top from (, bottom from )
   {\mathopen}{largesymbols}{"7A}{largesymbols}{"40}
\DeclareMathDelimiter{\rmoustache}   % top from ), bottom from (
   {\mathclose}{largesymbols}{"7B}{largesymbols}{"41}
\DeclareMathDelimiter{\arrowvert}    % arrow without arrowheads
   {\mathord}{symbols}{"6A}{largesymbols}{"3C}
\DeclareMathDelimiter{\Arrowvert}    % double arrow without arrowheads
   {\mathord}{symbols}{"6B}{largesymbols}{"3D}
\DeclareMathDelimiter{\Vert}
   {\mathord}{symbols}{"6B}{largesymbols}{"0D}
\let\|=\Vert
\DeclareMathDelimiter{\vert}
   {\mathord}{symbols}{"6A}{largesymbols}{"0C}
\DeclareMathDelimiter{\uparrow}
   {\mathrel}{symbols}{"22}{largesymbols}{"78}
\DeclareMathDelimiter{\downarrow}
   {\mathrel}{symbols}{"23}{largesymbols}{"79}
\DeclareMathDelimiter{\updownarrow}
   {\mathrel}{symbols}{"6C}{largesymbols}{"3F}
\DeclareMathDelimiter{\Uparrow}
   {\mathrel}{symbols}{"2A}{largesymbols}{"7E}
\DeclareMathDelimiter{\Downarrow}
   {\mathrel}{symbols}{"2B}{largesymbols}{"7F}
\DeclareMathDelimiter{\Updownarrow}
   {\mathrel}{symbols}{"6D}{largesymbols}{"77}
\DeclareMathDelimiter{\backslash}    % for double coset G\backslash H
   {\mathord}{symbols}{"6E}{largesymbols}{"0F}
\DeclareMathDelimiter{\rangle}
   {\mathclose}{symbols}{"69}{largesymbols}{"0B}
\DeclareMathDelimiter{\langle}
   {\mathopen}{symbols}{"68}{largesymbols}{"0A}
\DeclareMathDelimiter{\rbrace}
   {\mathclose}{symbols}{"67}{largesymbols}{"09}
\DeclareMathDelimiter{\lbrace}
   {\mathopen}{symbols}{"66}{largesymbols}{"08}
\DeclareMathDelimiter{\rceil}
   {\mathclose}{symbols}{"65}{largesymbols}{"07}
\DeclareMathDelimiter{\lceil}
   {\mathopen}{symbols}{"64}{largesymbols}{"06}
\DeclareMathDelimiter{\rfloor}
   {\mathclose}{symbols}{"63}{largesymbols}{"05}
\DeclareMathDelimiter{\lfloor}
   {\mathopen}{symbols}{"62}{largesymbols}{"04}
\DeclareMathDelimiter{\lgroup} % extensible ( with sharper tips
     {\mathopen}{largesymbols}{"3A}{largesymbols}{"3A}
\DeclareMathDelimiter{\rgroup} % extensible ) with sharper tips
     {\mathclose}{largesymbols}{"3B}{largesymbols}{"3B}
\DeclareMathDelimiter{\bracevert} % the vertical bar that extends braces
     {\mathord}{largesymbols}{"3E}{largesymbols}{"3E}

Other may be defined by other packages.

In order to know whether a character corresponds to a resizable delimiter, inspect its \delcode:

\showthe\delcode`(

would output 164608. For a command, use \show; for instance, \show\bracevert would output

\bracevert:
macro:->\delimiter "033E33E 

Some delimiters are arbitrarily resizable like braces, which in large sizes are made up by repeatable parts. Others, like / have a maximum size.