Partial tensor product sign

Question

There is an asymmetric tensor-like binary product operation on rings, and the notation for it is informed by both the notation for semi-direct product \rtimes and that for tensor product \otimes. It looks like a tensor product, with the arc of the surrounding "O" missing between the lower-left leg and upper-left legs of the central "X". Here is a photo of the symbol in context, hand-drawn using an iPad:

As far as I know it is so far exclusively handwritten. How can I create a glyph for this operation in LaTeX? I'd like to call it \rtensor. I have the sense that the easiest way to do this is to somehow modify the glyph for \otimes by removing an arc from one side, since I want it to be the same size and have the same spacing properties. But I don't know how to proceed.

Can someone help me typeset this symbol?

Answer 1

Here is an easy "design-your-own" TikZ solution.

Advantages: Easy. Nicer corners compared to clipping.

Disadvantage: Not truly the exact spacing of \otimes. But close.

Code:

\documentclass{article}
\usepackage{tikz,scalerel}

\newcommand{\rtensor}{\mathbin{\mkern1mu\scalerel*{\tikz[line width=.25]{
    \clip(0,0) circle[radius=1mm+.125pt];
    \draw(-45:.1)--(135:.1) arc (135:-135:.1) -- (45:.1);
    }}{\otimes}\mkern1mu}}

\begin{document}

$H\rtensor C_{H\rtensor C_{H\rtensor C}}$

\end{document}

Update: If it's important to get the spacing for \rtensor to be exactly the same as \otimes, you can redefine \otimes. Use \let to retain the original \otimes definition if you wish.

\documentclass{article}
\usepackage{tikz,scalerel}

\let\oldtimes\otimes

\renewcommand{\otimes}{\mathbin{\mkern1mu\scalerel*{\tikz[line width=.25]{
    \clip(0,0) circle[radius=1mm+.125pt];
    \draw(0,0) circle[radius=.1]; \draw (-135:.1) -- (45:.1); \draw (135:.1) -- (-45:.1);
    }}{\oldtimes}\mkern1mu}}

\newcommand{\rtensor}{\mathbin{\mkern1mu\scalerel*{\tikz[line width=.25]{
    \clip(0,0) circle[radius=1mm+.125pt];
    \draw(-45:.1)--(135:.1) arc (135:-135:.1) -- (45:.1);
    }}{\oldtimes}\mkern1mu}}

\begin{document}

$H\rtensor C_{H\rtensor C_{H\rtensor C}}$

$H\otimes C_{H\otimes C_{H\otimes C}}$

\end{document}

Answer 2

Set up to work in all math styles.

As nicely upvoted as the original answer, below, was, I took to heart Barbara's comment on how the clipping should be such to provide square corners. So here is a revision that seems to work well over the span of 10-12 pt documents, without any changes needed.

To see how this is done, you can change the white to red to see how a patch is overlaid over \otimes. Therefore, this version only works out of the box for documents with white background.

\documentclass{article}
\usepackage{amsmath,trimclip,scalerel,xcolor,stackengine}
\newcommand\rtensor{\mathbin{\ThisStyle{\sbox0{$\SavedStyle\otimes$}%
  \ensurestackMath{\stackinset{r}{.5\wd0+.1pt+.1\LMpt}{c}{}%
  {\textcolor{white}{\clipbox{1.1pt 0pt 0pt 0pt}{\rotatebox%
  [origin=c]{45}{\rule{.425\wd0}{.42\wd0}}}}}{\SavedStyle\otimes}}}}}
\begin{document}
$ A \rtensor B$

$\scriptstyle A \rtensor B$

$\scriptscriptstyle A \rtensor B$
\end{document}

ORIGINAL ANSWER

\documentclass{article}
\usepackage{amsmath,trimclip,scalerel}
\newcommand\rtensor{\mathbin{\ThisStyle{\kern1pt
  \clipbox{{\dimexpr.25ex+.12\LMex\relax} 0pt 0pt 0pt}%
  {$\SavedStyle\otimes$}}}}
\begin{document}
$ A \rtensor B$

$\scriptstyle A \rtensor B$

$\scriptscriptstyle A \rtensor B$
\end{document}

For a [12pt] document, with different sidebearings and relative scales, this adjustment seems to work

\documentclass[12pt]{article}
\usepackage{trimclip,scalerel}
\newcommand\rtensor{\mathbin{\ThisStyle{\kern1pt
  \clipbox{{\dimexpr.06ex+.31\LMex\relax} 0pt 0pt 0pt}%
  {$\SavedStyle\otimes$}}}}
\def\scriptscriptstyleScaleFactor{0.63}
\begin{document}
$ A \rtensor B$

$\scriptstyle A \rtensor B$

$\scriptscriptstyle A \rtensor B$
\end{document}

Answer 3

An alternative to Steven's answer, with the possibility of fine tuning the clipping in the various styles.

Beware that different math fonts will probably need different factors.

\documentclass{article}
\usepackage{trimclip}

\makeatletter
\DeclareRobustCommand{\rotimes}{\mathbin{\mkern1mu\mathpalette\rotimes@\relax}}
\newcommand{\rotimes@}[2]{%
  \clipbox{{\rotimes@clip{#1}} 0pt 0pt 0pt}{$\m@th#1\otimes$}%
}
\newcommand{\rotimes@clip}[1]{%
  \ifx#1\displaystyle 0.206\else
  \ifx#1\textstyle 0.206\else
  0.22\fi\fi\width
}
\makeatother

\begin{document}

$\hat{H}_l \rotimes C[\Gamma(c)]$

$\scriptstyle\hat{H}_l \rotimes C[\Gamma(c)]$

$\scriptstyle\hat{H}_l \rotimes C[\Gamma(c)]$

\Huge$H\rotimes C$

\end{document}