symbols
I am reading a textbook which uses the LaTeX \smile symbol (a sort of sideways parenthesis) for concatenation of lists. I have never seen this symbol anywhere before except in the document which lists all LaTeX symbols. It may be that this use of \smile for concatenation is standard, and has passed me by. I myself either simply use + for concatenation, or if in pseudo code write it out in words.
Anyway, I'm just curious as to this use of the smile symbol.
The turnstile package provides
\turnstile[<size>]{<lvert>}{<horz>}{<below>}{<above>}{<rvert>}
where <horz> calls the macro
\makehor{<line type>}{<thickness>}{<length>}{<sep>}
to draw the horizontal line(s) of the turnstile. In the following code, I've redefined \makehor (and consequently also \turnstile) to take a first argument w (for wavy) which typesets the symbol $\sim$ as the "horizontal line". The adjustbox package provides some clipping and resizing.
\documentclass{article}
\usepackage{turnstile}% http://ctan.org/pkg/turnstile
\usepackage{adjustbox}% http://ctan.org/pkg/adjustbox
\renewcommand{\makehor}[4]
{\ifthenelse{\equal{#1}{n}}{\hspace{#3}}{}
\ifthenelse{\equal{#1}{s}}{\rule[-0.5#2]{#3}{#2}}{}
\ifthenelse{\equal{#1}{d}}{\setlength{\lengthvar}{#2}
\addtolength{\lengthvar}{0.5#4}
\rule[-\lengthvar]{#3}{#2}
\hspace{-#3}
\rule[0.5#4]{#3}{#2}}{}
\ifthenelse{\equal{#1}{t}}{\setlength{\lengthvar}{1.5#2}
\addtolength{\lengthvar}{#4}
\rule[-\lengthvar]{#3}{#2}
\hspace{-#3}
\rule[-0.5#2]{#3}{#2}
\hspace{-#3}
\setlength{\lengthvar}{0.5#2}
\addtolength{\lengthvar}{#4}
\rule[\lengthvar]{#3}{#2}}{}
\ifthenelse{\equal{#1}{w}}{% New wavy $\sim$ definition
\setbox0=\hbox{$\sim$}%
\raisebox{-.6ex}{\hspace*{-.05ex}\adjustbox{width=#3,height=\height}{\clipbox{0.75 0 0 0}{\usebox0}}}}{}
}
\begin{document}
\[
\renewcommand{\arraystretch}{2}%
\begin{array}{ll}
\textrm{Regular}\ \verb!s! & \textrm{Wavy}\ \verb!w! \\ \hline
A\turnstile{s}{s}{}{}{n}B & A\turnstile{s}{w}{}{}{n}B \\
A\turnstile{s}{s}{L}{}{n}B & A\turnstile{s}{w}{L}{}{n}B \\
A\turnstile{s}{s}{}{D}{n}B & A\turnstile{s}{w}{}{D}{n}B \\
A\turnstile{s}{s}{L}{D}{n}B & A\turnstile{s}{w}{L}{D}{n}B
\end{array}
\]
\end{document}
The main advantage of tapping into the existing command (or extending it) rather than writing one's own is that it is easier to use. Additionally, since \turnstile takes the upper/lower letters as arguments, it's easier to grab hold of them than (say) defining a new command that requires some interpretation of limit use, like \wavyturn_{L}^{D} (say). As such, the other features of \turnstile is adopted (like the \rule for the vertical line and the other spacing.
The above code currently only works for a single wavy line. However, if needed, it could be extended to work for more than one (like the original \turnstile..{d}... and \turnstile..{t}.. commands). For now, it works based on the MWE, but not work as expected with other variations (longer phrases and/or right vertical line). That may require more work, since I haven't tested it.
Edit: Admittedly my tikz-prowess requires a heavy boost of steroids. The following addition to the turnstile horizontal rule is provided by the symbol z. It draws a thin wavy line using a sine curve. I'm pretty sure the horizontal (\hspace) and vertical (\raisebox) adjustments can be done inside \tikz, so suggestions are welcome and encouraged. The same goes for the adjustbox modifications, and whether that can be incorporated in \tikz as well:
\documentclass{article}
\usepackage{turnstile}% http://ctan.org/pkg/turnstile
\usepackage{tikz}% http://ctan.org/pkg/pgf
\usepackage{adjustbox}% http://ctan.org/pkg/adjustbox
\renewcommand{\makehor}[4]
{\ifthenelse{\equal{#1}{n}}{\hspace{#3}}{}
\ifthenelse{\equal{#1}{s}}{\rule[-0.5#2]{#3}{#2}}{}
\ifthenelse{\equal{#1}{d}}{\setlength{\lengthvar}{#2}
\addtolength{\lengthvar}{0.5#4}
\rule[-\lengthvar]{#3}{#2}
\hspace{-#3}
\rule[0.5#4]{#3}{#2}}{}
\ifthenelse{\equal{#1}{t}}{\setlength{\lengthvar}{1.5#2}
\addtolength{\lengthvar}{#4}
\rule[-\lengthvar]{#3}{#2}
\hspace{-#3}
\rule[-0.5#2]{#3}{#2}
\hspace{-#3}
\setlength{\lengthvar}{0.5#2}
\addtolength{\lengthvar}{#4}
\rule[\lengthvar]{#3}{#2}}{}
\ifthenelse{\equal{#1}{w}}{% New wavy $\sim$ definition
\setbox0=\hbox{$\sim$}%
\raisebox{-.6ex}{\hspace*{-.05ex}\adjustbox{width=#3,height=\height}{\clipbox{0.75 0 0 0}{\usebox0}}}}{}
\ifthenelse{\equal{#1}{z}}{% New tikz wavy definition
\raisebox{-.4ex}{\hspace*{-.08ex}\tikz \draw [thin,x=0.5ex,y=.25ex] (0,0) sin (1,1) cos (2,0) sin (3,-1) cos (4,0);\hspace*{.2ex}}}{}
}
\begin{document}
\[
\renewcommand{\arraystretch}{2}%
\begin{array}{lll}
\textrm{Regular}\ \verb!s! & \textrm{Wavy}\ \verb!w! & \textrm{TikZ}\ \verb!z! \\ \hline
A\turnstile{s}{s}{}{}{n}B & A\turnstile{s}{w}{}{}{n}B & A\turnstile{s}{z}{}{}{n}B \\
A\turnstile{s}{s}{L}{}{n}B & A\turnstile{s}{w}{L}{}{n}B & A\turnstile{s}{z}{L}{}{n}B \\
A\turnstile{s}{s}{}{D}{n}B & A\turnstile{s}{w}{}{D}{n}B & A\turnstile{s}{z}{}{D}{n}B \\
A\turnstile{s}{s}{L}{D}{n}B & A\turnstile{s}{w}{L}{D}{n}B & A\turnstile{s}{z}{L}{D}{n}B
\end{array}
\]
\end{document}
It needs improvement for a number of reasons:
There is a very minute difference in the typesetting of a "denominator-only" and "numerator+denominator" \turnstile. For example, look at the close-up between
Unexpected results may occur from adding the ending vertical line(s).
The spacing of the right operand (B in this case) is too far off. This can be accommodated by means of an intermediate macro, but it is best suited inside the \turnstile macro.
I think all of the above items would be addressed by someone with a better handle on tikz-related commands. But then again, perhaps this is not a problem.
For Linux, there are two nice character selectors, KCharSelect for KDE,
and Gucharmap for GNOME,
You can browse the various characters by script or Unicode block, or search by character description. Both programs are very nice, but personally, I prefer KCharSelect, as it has an incremental search bar which makes it faster to find the characters you need, and it displays all the information about a character, without you having to switch between the glyph ťab and the character information tab.
For Windows, you can use the built-in Character Map program, which supports Unicode in later versions of Windows:
Best Answer
It is very common in Mathematics, more specific in Algebraic Topology. It is used to denote the cup product.