math-operatorssymbols
To insert the abstract algebra operators, I tried:
\documentclass{article}
\usepackage{stackengine}
\usepackage{scalerel}
\newlength\triwidth
\newcommand\tridelt[1]{%
\setlength\triwidth{\widthof{#1\ }}%
\stackengine{-.1\triwidth}{#1\ }%
{\scaleto{\Delta}{1\triwidth}}{O}{c}{F}{F}{L}%
}
\begin{document}
\begin{equation}
C = A \tridelt{+} B, C = A \tridelt{x} B
\end{equation}
\end{document}
as in
but the result looks ugly, how to fix it?
I once proposed the following definitions
\newcommand\varpm{\mathbin{\vcenter{\hbox{%
\oalign{\hfil$\scriptstyle+$\hfil\cr
\noalign{\kern-.3ex}
$\scriptscriptstyle({-})$\cr}%
}}}}
\newcommand\varmp{\mathbin{\vcenter{\hbox{%
\oalign{$\scriptstyle({+})$\cr
\noalign{\kern-.3ex}
\hfil$\scriptscriptstyle-$\hfil\cr}%
}}}}
Example
\documentclass{article}
\newcommand\varpm{\mathbin{\vcenter{\hbox{%
\oalign{\hfil$\scriptstyle+$\hfil\cr
\noalign{\kern-.3ex}
$\scriptscriptstyle({-})$\cr}%
}}}}
\newcommand\varmp{\mathbin{\vcenter{\hbox{%
\oalign{$\scriptstyle({+})$\cr
\noalign{\kern-.3ex}
\hfil$\scriptscriptstyle-$\hfil\cr}%
}}}}
\begin{document}
$a\varpm b\varmp c$
\end{document}
The overlapping of the symbols \leftrightarrow and \updownarrow can be done with
\ooalign:
\ooalign{$\leftrightarrow$\cr\hfil$\updownarrow$\hfil}
Some additional work is needed:
\textstyle.\mathsurround is set, then the additional space would be added above to the
left and right. This can be cured by \m@th that sets \mathsurround to zero.\mathbin notifies TeX to
put additinal space for binary operators.File:
\documentclass{article}
% \usepackage{txfonts} % similar \usepacakge{pxfonts}
% \usepackage{mathabx}
% \usepackage{MnSymbol}
\makeatletter
\newcommand*{\extendadd}{%
\mathbin{%
\mathpalette\extend@add{}%
}%
}
\newcommand*{\extend@add}[2]{%
\ooalign{%
$\m@th#1\leftrightarrow$%
\vphantom{$\m@th#1\updownarrow$}% fix the height
\cr
\hfil$\m@th#1\updownarrow$\hfil
}%
}
\makeatother
% for testing the bounding box of the symbol
\setlength{\fboxsep}{0pt}
\setlength{\fboxrule}{.2pt}
\begin{document}
\[
\mathcal{F}_\mathbf{i} =
\mathcal{F}_\mathbf{i}^0
\extendadd
\mathcal{U}_{\mathbf{c}_1}
\extendadd
\mathcal{U}_{\mathbf{c}_2}
\qquad
\fbox{$\extendadd$}^{\extendadd^{\extendadd}}
\]
\end{document}
Result for CM fonts:
Result for package txfonts:
Result for package mathabx:
Result for package MnSymbol:
Observations:
\updownarrow might have a smaller total height
than the width of \leftrightarrow.The idea is to resize \longleftrightarrow to the width of \leftrightarrow to get
smaller arrow heads. However, this will also make the lines thinner.
The tricky part is that scaling also changes the vertical position of the symbol.
Because of the arrows the height of the character bounding box \leftrightarrow is not too helpful. But we can assume the symbol is vertically centered respective to the mathematical axis. Therefore the code below puts \leftrightarrow to the base line, resizes it and moves it back to the mathematical axis.
to the mathematical axis.
The vertical double arrow cannot generated the same way. First the symbol \longupdownarrow is missing. Also we have seen above, that the symbol might be
too small in comparison with the \leftrightarrow. Therefore the symbol is generated by rotating the horizontal double arrow.
\documentclass{article}
% \usepackage{txfonts}
% \usepackage{pxfonts}
% \usepackage{mathabx}
% \usepackage{MnSymbol}
\usepackage{graphicx}% (only graphics is needed)
\makeatletter
\newdimen\extend@width
\newdimen\extend@mathaxis
\newcommand*{\extendadd}{%
\mathbin{%
\mathpalette\extend@add{}%
}%
}
\newcommand{\extend@add}[2]{%
\m@th
\sbox0{$#1\vcenter{}\smash{\leftrightarrow}$}%
\extend@width=\wd0 %
\extend@mathaxis=\ht0 %
\sbox0{%
\resizebox{\extend@width}{!}{%
\raisebox{-\extend@mathaxis}{$#1\longleftrightarrow$}%
}%
}%
\rlap{%
\raisebox{\extend@mathaxis}{%
\copy0 %
}%
}%
\dp0=0pt %
\ht0=0pt %
\hbox to\extend@width{%
\hfil
$#1%
\vcenter{%
\hbox{%
\rotatebox{90}{\copy0}%
}%
}%
$%
\hfil
}%
}
\makeatother
% for testing the bounding box of the symbol
\setlength{\fboxsep}{0pt}
\setlength{\fboxrule}{.2pt}
\begin{document}
\[
\mathcal{F}_\mathbf{i} =
\mathcal{F}_\mathbf{i}^0
\extendadd
\mathcal{U}_{\mathbf{c}_1}
\extendadd
\mathcal{U}_{\mathbf{c}_2}
\qquad
\fbox{$\extendadd$}^{\extendadd^{\extendadd}}
\]
\end{document}
Result for CM fonts:
Result for package txfonts:
Result for package mathabx:
Result for package MnSymbol:
It is also possible to have something in between, less scaling, by composing
a smaller \longleftrightarrow from \leftarrow and \rightarrow as base for the resized double arrow.
Best Answer
The symbols can be found in the in the Comprehensive LaTeX symbols list.
As shown above, this package provides lots of symbols that can be used in abstract algebra (
\boxplus \boxminus \boxtimes).