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I would like to have commands \leftsemicirc, \rightsemicirc in math mode which produce left/right semicircles the size of \circ.

The best approximation of a solution I am aware is to use bbding and writing \text{HalfCircleLeft}, however this is solid and most importantly it's too big.

Thanks!

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    what are the symbols supposed to represent? – Thruston Oct 20 '17 at 16:27
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    open or closed? Unicode provides closed half circles: ◖◗ which you could use with an appropriate font... – Thruston Oct 20 '17 at 16:29
  • @Apparently open (or not filled) as the OP 'complains' aobut `HalfCircleLeft being solid – user31729 Oct 20 '17 at 16:46
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You can manually draw these using the graphics package and \put, \oval and \line commands. I understand you don't want filled semicircles, but I didn't know if you wanted open or closed. Both appear below. Also, I included a \newcirc so it is exactly the same size as the semicircles.

\documentclass{article}

\usepackage{graphics}

\newcommand{\leftsemicirc}{\put(3.5,2.5){\oval(4,4)[l]}\phantom{\circ}}
\newcommand{\rightsemicirc}{\put(1.5,2.5){\oval(4,4)[r]}\phantom{\circ}}
\newcommand{\cleftsemicirc}{\put(3.5,2.5){\oval(4,4)[l]}\put(3.5,.5){\line(0,1){4}}\phantom{\circ}}
\newcommand{\crightsemicirc}{\put(1.5,2.5){\oval(4,4)[r]}\put(1.5,.5){\line(0,1){4}}\phantom{\circ}}
\newcommand{\newcirc}{\put(2.5,2.5){\oval(4,4)}\phantom{\circ}}

\begin{document}
\noindent
$A\circ B$\\
$A\mathbin{\leftsemicirc} B$\\
$A\mathbin{\rightsemicirc} B$\\
$A\mathbin{\cleftsemicirc} B$\\
$A\mathbin{\crightsemicirc} B$\\
$A\mathbin{\newcirc} B$

\end{document}

enter image description here

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