A macro that draws a half-disk for use in mathmode

Question

I'd like to define macros to be able to use each of the following six shapes as subscripts in math mode.

I'd try to draw them using tikz, but I don't know if I could use those as subscripts.

Answer 1

Picture mode!

\documentclass{article}
\usepackage{amsmath}
\usepackage{pict2e}

\DeclareRobustCommand{\fullcircle}{%
  \mspace{2mu}\mathord{
    \sbox{0}{$\scriptstyle O$}%
    \setlength{\unitlength}{\ht0}%
    \begin{picture}(1,1)
    \put(0.5,0.5){\arc{0.5}}
    \end{picture}
  }\mspace{2mu}
}
\DeclareRobustCommand{\upsemicircle}{%
  \mspace{2mu}\mathord{
    \sbox{0}{$\scriptstyle O$}%
    \setlength{\unitlength}{\ht0}%
    \begin{picture}(1,1)
    \put(0.5,0.5){\arc[0,180]{0.5}}
    \end{picture}
  }\mspace{2mu}
}
\DeclareRobustCommand{\downsemicircle}{%
  \mspace{2mu}\mathord{
    \sbox{0}{$\scriptstyle O$}%
    \setlength{\unitlength}{\ht0}%
    \begin{picture}(1,1)
    \put(0.5,0.5){\arc[180,360]{0.5}}
    \end{picture}
  }\mspace{2mu}
}
\DeclareRobustCommand{\upsemicirclediam}{%
  \mspace{2mu}\mathord{
    \sbox{0}{$\scriptstyle O$}%
    \setlength{\unitlength}{\ht0}%
    \begin{picture}(1,1)
    \moveto(0.5,0.5)
    \circlearc{0.5}{0.5}{0.5}{0}{180}
    \lineto(0.5,0.5)
    \strokepath
    \end{picture}
  }\mspace{2mu}
}
\DeclareRobustCommand{\downsemicirclediam}{%
  \mspace{2mu}\mathord{
    \sbox{0}{$\scriptstyle O$}%
    \setlength{\unitlength}{\ht0}%
    \begin{picture}(1,1)
    \moveto(0.5,0.5)
    \circlearc{0.5}{0.5}{0.5}{180}{360}
    \lineto(0.5,0.5)
    \strokepath
    \end{picture}
  }\mspace{2mu}
}
\DeclareRobustCommand{\diam}{%
  \mspace{2mu}\mathord{
    \sbox{0}{$\scriptstyle O$}%
    \setlength{\unitlength}{\ht0}%
    \begin{picture}(1,1)
    \Line(0,0.5)(1,0.5)
    \end{picture}
  }\mspace{2mu}
}

\begin{document}

$X_{\fullcircle\upsemicircle\downsemicircle\upsemicirclediam\downsemicirclediam\diam}$

\end{document}

An enhanced version that can cope with the symbols at every level.

\documentclass{article}
\usepackage{amsmath}
\usepackage{pict2e}

\makeatletter
\DeclareRobustCommand{\fullcircle}{\peter@symbol\peter@fullcircle}
\DeclareRobustCommand{\upsemicircle}{\peter@symbol\peter@upsemicircle}
\DeclareRobustCommand{\downsemicircle}{\peter@symbol\peter@downsemicircle}
\DeclareRobustCommand{\upsemicirclediam}{\peter@symbol\peter@upsemicirclediam}
\DeclareRobustCommand{\downsemicirclediam}{\peter@symbol\peter@downsemicirclediam}
\DeclareRobustCommand{\diam}{\peter@symbol\peter@diam}

\newcommand{\peter@symbol}[1]{\mathord{\mspace{2mu}\mathpalette#1\relax\mspace{2mu}}}
\newcommand{\peter@unitlength}[1]{%
  \settoheight{\unitlength}{$\m@th#1O$}%
  \linethickness{\fontdimen 8
    \ifx#1\displaystyle\textfont\else
    \ifx#1\textstyle\textfont\else
    \ifx#1\scriptstyle\scriptfont\else
    \scriptscriptfont\fi\fi\fi 3
  }%
}

\newcommand{\peter@fullcircle}[2]{%
  \begingroup
  \peter@unitlength{#1}%
  \begin{picture}(1,1)
  \circlearc[1]{0.5}{0.5}{0.5}{0}{360}
  \strokepath
  \end{picture}%
  \endgroup
}
\newcommand{\peter@upsemicircle}[2]{%
  \begingroup
  \peter@unitlength{#1}%
  \begin{picture}(1,1)
  \circlearc[1]{0.5}{0.5}{0.5}{0}{180}
  \strokepath
  \end{picture}%
  \endgroup
}
\newcommand{\peter@downsemicircle}[2]{%
  \begingroup
  \peter@unitlength{#1}%
  \begin{picture}(1,1)
  \circlearc[1]{0.5}{0.5}{0.5}{180}{360}
  \strokepath
  \end{picture}%
  \endgroup
}
\newcommand{\peter@upsemicirclediam}[2]{%
  \begingroup
  \peter@unitlength{#1}%
  \begin{picture}(1,1)
  \moveto(0.5,0.5)
  \circlearc{0.5}{0.5}{0.5}{0}{180}
  \lineto(0.5,0.5)
  \strokepath
  \end{picture}%
  \endgroup
}
\newcommand{\peter@downsemicirclediam}[2]{%
  \begingroup
  \peter@unitlength{#1}%
  \begin{picture}(1,1)
  \moveto(0.5,0.5)
  \circlearc{0.5}{0.5}{0.5}{180}{360}
  \lineto(0.5,0.5)
  \strokepath
  \end{picture}%
  \endgroup
}
\newcommand{\peter@diam}[2]{%
  \begingroup
  \peter@unitlength{#1}%
  \begin{picture}(1,1)
  \Line(0,0.5)(1,0.5)
  \end{picture}%
  \endgroup
}

\begin{document}

$X\fullcircle\upsemicircle\downsemicircle\upsemicirclediam\downsemicirclediam\diam$

$X_{\fullcircle\upsemicircle\downsemicircle\upsemicirclediam\downsemicirclediam\diam}$

$X_{X_{\fullcircle\upsemicircle\downsemicircle\upsemicirclediam\downsemicirclediam\diam}}$

\end{document}

Answer 2

TikZ in boxes! (Far inferior to picture mode unfortunately)

\documentclass[]{article}

\usepackage{tikz}

\makeatletter
\newcommand\setup@crazysubscripts[2]
  {%
    \expandafter\newsavebox\csname crazysubscripts@#1\endcsname
    \expandafter\sbox\csname crazysubscripts@#1\endcsname
      {%
        \kern.1ex
        \begin{tikzpicture}
          \path[use as bounding box] circle[radius=.5ex];
          #2%
        \end{tikzpicture}%
        \kern.1ex
      }%
  }
\setup@crazysubscripts{fc}% fullcircle
  {%
    \draw circle[radius=.5ex];%
  }
\setup@crazysubscripts{lo}% lower open
  {%
    \draw (.5ex,0) arc[start angle=0, end angle=-180, radius=.5ex];%
  }
\setup@crazysubscripts{uo}% upper open
  {%
    \draw (.5ex,0) arc[start angle=0, end angle=180, radius=.5ex];%
  }
\setup@crazysubscripts{lc}% lower closed
  {%
    \draw (-.5ex,0) -- (.5ex,0) arc[start angle=0, end angle=-180, radius=.5ex]
      --cycle;%
  }
\setup@crazysubscripts{uc}% upper closed
  {%
    \draw (-.5ex,0) -- (.5ex,0) arc[start angle=0, end angle=180, radius=.5ex]
      --cycle;%
  }
\setup@crazysubscripts{b}% boring line
  {%
    \draw (-.5ex,0) -- (.5ex,0);%
  }
\newcommand\csubs[1]
  {%
    \@ifundefined{crazysubscripts@#1}
      {\GenericError{}{Undefined crazysubscript `#1`}{}{}}%
      {%
        \resizebox{.75ex}{!}
          {\expandafter\usebox\csname crazysubscripts@#1\endcsname}%
      }%
  }
\makeatother

\begin{document}
$A_{\csubs{fc}_{\csubs{lo}_{\csubs{lc}}}}$

\csubs{fc}\csubs{lo}\csubs{uo}\csubs{lc}\csubs{uc}\csubs{b}
\end{document}

Answer 3

Just a template.

\documentclass[preview,border=12pt,varwidth,12pt]{standalone}
\usepackage{tikz}

\def\alex{\tikz \draw (0,0) circle (2pt);}
\def\bobby{\tikz \draw (0,0) -- (3pt,0) -- (3pt,2pt) -- cycle;}
\begin{document}
This is an  equation $F_{\alex}^{\bobby}+1$.
\end{document}