Spacing around a custom operator with stacked elements using centernot

Question

I am using an operator with the definition

\newcommand{\tom}[2]{{\displaystyle\mathrel{\mathop{\to}^{#1}_{#2}}}}

with negation

\newcommand{\ntom}[2]{\centernot{\displaystyle\mathrel{\mathop{\to}^{#1}_{#2}}}}

The operator looks like this, with markup u\tom km w:

and the negation looks like this, u\ntom km w:

Notice in \tom the u and w are smashed up against the arrow, whereas in the negation there is spacing around it. I'm not sure which one looks better, but is there a way to keep it consistent?

I'm also not too comfortable with using \displaystyle, but it was the only way I could see to ensure the k and m stay above and below the arrow in \mathrel/\mathop.

Answer 1

You can keep it consistent:

\documentclass{article}
\usepackage{amsmath,centernot}

\makeatletter
\newcommand{\tom}{\n@tom{\n@tom@to}}
\newcommand{\ntom}{\n@tom{\n@tom@nto}}

\newcommand{\n@tom}[3]{\overunderset{#2}{#3}{#1}}

\newcommand{\n@tom@to}{\rightarrow\mathrel{\vphantom{\not}}}
\newcommand{\n@tom@nto}{\centernot\rightarrow}
\makeatother

\begin{document}

$u\tom{k}{m}w$ $u\ntom{k}{m}w$

\end{document}

The seemingly mysterious programming style is aimed of splitting the job in layers. One main macro \n@tom takes as first argument the type of arrow and then the top and bottom limits. The two types of arrow are defined separately, so as to make it easier to modify just them.

For instance, if we load amssymb instead of centernot and change the two final definitions into

\newcommand{\n@tom@to}{\rightarrow}
\newcommand{\n@tom@nto}{\nrightarrow}

we'd get

which I think is better.