logicmath-modemath-operatorssymbolsturnstile
I'm new to the turnstile package, and I'm trying to figure out how to get a negated double turnstile sign, like the one with the regular \nvDash, but that allows me to have arguments above and below the line, as with \sdtstile{\mathrm{a}}{b}.
Any ideas?
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.
The table you show is relative to the symbols provided by mathabx. One can say
\usepackage{mathabx}
but this will change many symbols and not always in a desirable way.
For negated relations one can first try preceding the command by \not:
\not\approx
The placement of the diagonal bar is not always ideal, which is why the negation of \in has its own command \notin. In the case of \not\approx there is no problem.
Here's a visual comparison: above the normal rendition of the symbol, using Computer Modern Math Symbols, below the mathabx rendition. A difference in shape is evident.
Best Answer
Your best bet here, due to the size of the turnstiles, is to use the
cancelpackage. Here is a minimal example:\canceloverprints a SW-NE line, while\bcancel(backwards/backslash) overprints a NW-SE line. As you can see, it prints the lines to match the content width. So, if you want the line to be a bit more diagonal, you could add some space around the turnstiles. However, I'm not sure what the exact contents is, and whether there are other objects around it, which would be affected by the spacing.