How to fix the thickness of $\complement$ changes after rotatebox and scalebox

Question

I use \mathcal S^\complement as the notation of complements. However, I need to flip the \complement symbol to make the anticomplement symbol. If I only use \rotatebox, the size of the anticomplement will be bigger than the complement symbol, but if I add \scalebox{0.75}{...}, the thickness of the anticomplement symbol will change. Are there any ways to fix this problem?

\newcommand{\anticomplement}{\scalebox{0.75}{\rotatebox[origin=c]{180}{$\complement$}}}
...
$\mathcal S^\complement$, $\mathcal S^{\anticomplement}$

If you want to mimic the \complement with reflected \anticomplement, use \reflectbox{} with prepended \scriptstyle, e.g. \newcommand{\anticomplement}{\reflectbox{$\scriptstyle\complement$}} — Celdor, Sep 30 '22 at 16:20

score 4 · Accepted Answer · answered Sep 30 '22 at 03:14

4

The problem is that the content of \rotatebox doesn't realize it is supposed to be in \scriptstyle. So your unscaled version is making a \textstyle symbol. The solution is to place $\scriptstyle\complement$ inside the \rotatebox.

\documentclass{article}
\usepackage{amssymb, graphicx}
\newcommand{\anticomplement}{\rotatebox[origin=c]{180}{$\scriptstyle\complement$}}
\begin{document}
$\mathcal S^\complement$, $\mathcal S^{\anticomplement}$
\end{document}

Note that you could also use

\newcommand{\anticomplement}{\reflectbox{$\scriptstyle\complement$}}

answered Sep 30 '22 at 03:14

Sandy G

42,558

1

Probably one should define it using mathchoice? While I don't see the command used in display (and probably not text) styles, it will potentially be used in scriptscript style. – Willie Wong Sep 30 '22 at 03:21
@WillieWong: Might be better just to define \newcommand{\smallanticomplement}{\reflectbox{$\scriptscriptstyle\complement$}} for that usage, e.g., F_{\mathcal S^{\smallanticomplement}}. – Sandy G Sep 30 '22 at 03:56

egreg · Answer 2 · 2022-09-30T10:33:03.463

A simple application of \mathpalette.

\documentclass{article}
\usepackage{amsmath,amssymb,graphicx}
\makeatletter
\newcommand{\anticomplement}{{\mathpalette\anticomplement@\relax}}
\newcommand{\anticomplement@}[2]{%
  \reflectbox{$\m@th#1\complement$}%
}
\makeatother
\begin{document}
[
\mathcal{S}^{\complement}\mathcal{S}^{\anticomplement}
x^{y^{\anticomplement}}\anticomplement
]
\end{document}

I added a pair of braces in case ^\anticomplement slips in.

Note that \mathcal{S} is the correct syntax. For the particular case \reflectbox is much simpler than \rotatebox.

How to fix the thickness of $\complement$ changes after rotatebox and scalebox

2 Answers2