Simboli per unione ascendente/intersezione discendente
Aug 19 2020
Quando scrivo su carta o sulla lavagna, di solito indico un'unione ascendente \bigcup
con una freccia verso l'alto all'estremità del polo destro. Allo stesso modo, indico un'intersezione discendente \bigcap
con una freccia rivolta verso il basso all'estremità del polo destro. Questi simboli sono inclusi in qualche pacchetto standard? Se no, come posso definirli?
MWE:
\documentclass{article}
\begin{document}
\[
(0,1)=\bigcup_n \left[\frac1n, 1-\frac1n\right]
\]
\[
\{0\}=\bigcap_n \left(-\frac1n,\frac1n\right)
\]
\end{document}
Risposte
6 StevenB.Segletes Aug 19 2020 at 19:12
\documentclass{article}
\usepackage{stackengine,amsmath}
\stackMath
\DeclareMathOperator*\dcap{{\stackinset{r}{-1.02ex}{c}{-1.9pt}{\downarrow}
{\bigcap}\mkern2mu}}
\DeclareMathOperator*\acup{{\stackinset{r}{-1.02ex}{c}{1.9pt}{\uparrow}
{\bigcup}\mkern2mu}}
\begin{document}
\[
(0,1)=\acup_n \left[\frac1n, 1-\frac1n\right]
\]
\[
\{0\}=\dcap_n \left(-\frac1n,\frac1n\right)
\]
\end{document}

Se dovessi usarlo sempre in \displaystyle
, ci si potrebbe adattare:
\documentclass{article}
\usepackage{stackengine,amsmath}
\stackMath
\DeclareMathOperator*\dcap{{\stackinset{r}{-1ex}{c}{-3.1pt}{\downarrow}
{\displaystyle\bigcap}\mkern2mu}}
\DeclareMathOperator*\acup{{\stackinset{r}{-1ex}{c}{3.1pt}{\uparrow}
{\displaystyle\bigcup}\mkern2mu}}
\begin{document}
\[
(0,1)=\acup_n \left[\frac1n, 1-\frac1n\right]
\]
\[
\{0\}=\dcap_n \left(-\frac1n,\frac1n\right)
\]
\end{document}

3 egreg Aug 19 2020 at 22:58
I simboli assomigliano molto di più alle inversioni a U su un segnale stradale, a dire il vero.
\documentclass{article}
\usepackage{amsmath}
\makeatletter
\DeclareRobustCommand{\ubigcup}{\DOTSB\mathop{\,\ubigcup@\,}\slimits@}
\DeclareRobustCommand{\dbigcap}{\DOTSB\mathop{\,\dbigcap@\,}\slimits@}
\newcommand{\ubigcup@}{\mathpalette\ubigcup@@\relax}
\newcommand{\ubigcup@@}[2]{%
\begingroup
\sbox\z@{$\m@th#1\bigcup$}%
\sbox\tw@{$\m@th#1\uparrow$}%
\copy\z@
\mkern-6.3mu\ifx#1\scriptscriptstyle\mkern0.3mu\fi
\dimen@=\dimexpr\ht\z@-\ht\tw@
\ifx#1\displaystyle\else
\ifx#1\scriptscriptstyle\advance\dimen@ 0.5pt\else
\advance\dimen@ 1pt
\fi\fi
\raisebox{\dimen@}[0pt][0pt]{\rlap{\copy\tw@}}%
\mkern6.3mu\ifx#1\scriptscriptstyle\mkern-0.3mu\fi
\endgroup
}
\newcommand{\dbigcap@}{\mathpalette\dbigcap@@\relax}
\newcommand{\dbigcap@@}[2]{%
\begingroup
\sbox\z@{$\m@th#1\bigcap$}%
\sbox\tw@{$\m@th#1\downarrow$}%
\copy\z@
\mkern-6.3mu\ifx#1\scriptscriptstyle\mkern0.3mu\fi
\dimen@=\dimexpr\dp\z@-\dp\tw@
\ifx#1\displaystyle\else
\ifx#1\scriptscriptstyle\advance\dimen@ 0.5pt\else
\advance\dimen@ 1pt
\fi\fi
\raisebox{-\dimen@}[0pt][0pt]{\rlap{\copy\tw@}}%
\mkern6.3mu\ifx#1\scriptscriptstyle\mkern-0.3mu\fi
\endgroup
}
\makeatother
\begin{document}
$\displaystyle\ubigcup_{n=1}^{\infty} A_n$
$\displaystyle\bigcup_{n=1}^{\infty} A_n$
$\displaystyle\bigcup_{n=1}^{\infty} A_n$
\bigskip
$\textstyle\ubigcup_{n=1}^{\infty} A_n$
$\scriptstyle\ubigcup_{n=1}^{\infty} A_n$
$\scriptscriptstyle\ubigcup_{n=1}^{\infty} A_n$
\bigskip
$\displaystyle\dbigcap_{n=1}^{\infty} B_n$
$\displaystyle\bigcap_{n=1}^{\infty} B_n$
$\displaystyle\bigcap_{n=1}^{\infty} B_n$
\bigskip
$\textstyle\dbigcap_{n=1}^{\infty} B_n$
$\scriptstyle\dbigcap_{n=1}^{\infty} B_n$
$\scriptscriptstyle\dbigcap_{n=1}^{\infty} B_n$
\end{document}
