How to make a variable-sized \nmid symbol for "does not divide"?

Question

For a variable-sized bar denoting "a divides b", I normally use \divides

\newcommand{\zerodel}{.\kern-\nulldelimiterspace} %removes extraneous spacing after \right etc.
\newcommand{\divides}[2]{\left\zerodel#1\ \middle|\ #2\right\zerodel}.

This yields a division bar | which scales well with arguments both for inline math and displaymode. It also has proper spacing. Here is an example (see left-hand or top picture):

left-hand (or top) picture
\divides
right-hand (or bottom) picture
\notdiv

How could one define a similary-behaving vertical line for "a does not divide b"? The command \nmid is commonly used but does not scale with arguments.

• There are many related questions on TeX.SE (e.g., 1, 2, 3, 4, 5), however the variable scaling has not been incorporated, or negated divisibility is not covered.

I tried the following non-working options

%\newcommand{\notdiv}[2]{\left\zerodel#1\ \middle\nmid\ #2\right\zerodel} %does not work
\newcommand{\notdiv}[2]{\left\zerodel#1\ \nmid\ #2\right\zerodel} % also does not work (image with this)

which gave the right-hand (or bottom) picture.

As we can see, \notdiv does not scale with the arguments.

• Question: What would be a good way to go about this?

Note: the hope is to scale only the vertical bar, not the slanted line.

---

Here is the MWE which was also used to generate the images.

\documentclass{article}

\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{amsfonts}


\newcommand{\zerodel}{.\kern-\nulldelimiterspace} %removes extraneous spacing after \right etc.
\newcommand{\divides}[2]{\left\zerodel#1\ \middle|\ #2\right\zerodel}

%modify \notdiv as you see fit
%\newcommand{\notdiv}[2]{\left\zerodel#1 \middle\nmid #2\right\zerodel} %does not work
\newcommand{\notdiv}[2]{\left\zerodel#1\nmid#2\right\zerodel} %does not work


\begin{document}


    \centering

    inline: $\divides{c}{d}$, $\divides{\dfrac{a}{b}}{c}$
    \[\divides{c}{d}\]
    \[\divides{\frac{a}{b}}{c}\]
    
    inline: $\notdiv{c}{d}$, $\notdiv{\dfrac{a}{b}}{c}$
    \[\notdiv{c}{d}\]
    \[\notdiv{\frac{a}{b}}{c}\]


\end{document}

Answer 1

A very simpleminded approach.

\documentclass{article}

\usepackage{mathtools}
\usepackage{amssymb}
\usepackage{amsfonts}
\usepackage{pict2e}
\newcommand{\PicSlash}[0]{\begin{picture}(0,0)
        %\linethickness{0.4pt}
        \put(-0.75,1){\line(1,1){4.5pt}}
\end{picture}}
%\show\delimsize
\newcommand{\zerodel}{.\kern-\nulldelimiterspace} %removes extraneous spacing after \right etc.
\newcommand{\divides}[2]{\left\zerodel#1\nonscript\;\middle|\nonscript\;#2\right\zerodel}

%modify \notdiv as you see fit
%\newcommand{\notdiv}[2]{\left\zerodel#1 \middle\nmid #2\right\zerodel} %does not work
\newcommand{\notdiv}[2]{\left\zerodel#1\nonscript\;\mathrlap{\PicSlash}\middle|\nonscript\;#2\right\zerodel}
\begin{document}


    \centering

    inline: $\divides{c}{d}$, $\divides{\dfrac{a}{b}}{c}$
    \[\divides{c}{d}\]
    \[\divides{\frac{a}{b}}{c}\]
    
    inline: $\notdiv{c}{d}$, $\notdiv{\dfrac{a}{b}}{c}$
    \[\notdiv{c}{d}\]
    \[\notdiv{\frac{a}{b}}{c}\]


\end{document}