Custom division symbol

Question

I would like to define a new division symbol similar to the bar "/" but which is a minus sign (-) rotated 45 degrees, in the same way \times is a + rotated. I want it to have the same properties as the other arithmetic symbols (+,- and \times), I mean, the same spacing etc.

What I have tried to do is the following.

% Inversa da multiplicação em anéis e grupos
\makeatletter
    \providecommand{\newdiv}{%
    \mathbin{
    \hspace{-1.5pt}\mathpalette\@rotatinganeighth{-}\hspace{-1.5pt}
    }
}
\newcommand*{\@rotatinganeighth}[2]{%
    \rotatebox[origin=c]{45}{$\m@th#1#2$}%
    }
\makeatother

The results seem fine, but I would like to have something "cleaner", I don't like the fact that I input the specific space \hspace{-1.5pt}, I just wanted it to behave as a binary operation and, if possible, as an unary operation when there is no symbol before it (the same way the minus sign behaves).

Answer 1

I suggest \mathpalette in order that the symbol properly scales in subscripts and superscripts.

The minus sign has height equal to the plus sign, so we need to smash it and to set it in a box as wide as the plus sign. A vertical phantom will ensure the correct height and depth.

\documentclass{article}
\usepackage{graphicx}

\makeatletter
\newcommand{\newdiv}{\mathbin{\mathpalette\@newdiv\relax}}
\newcommand{\@newdiv}[2]{%
  \begingroup
  \sbox\z@{$\m@th#1+$}%
  \makebox[\wd\z@]{\smash{\rotatebox[origin=c]{45}{$\m@th#1-$}}}%
  \vphantom{\usebox{\z@}}%
  \endgroup
}
\makeatother

\setlength{\fboxsep}{0pt}\setlength{\fboxrule}{0.1pt}% just for the example

\begin{document}

$a+b$ \fbox{$a+b$}

$a\newdiv b$ \fbox{$a\newdiv b$}

$\scriptstyle a+b\newdiv c$

\end{document}

Answer 2

Like this one, from \usepackage{fdsymbol}:

$a\medslash b$ $f_{a\medslash b}$