15

I am reading H. Sati and U. Schreiber's article "Proper Orbifold Cohomology" -- see https://arxiv.org/pdf/2008.01101. On page 2, there is a formula almost at the bottom of the page, with a leaning U after the integral (Borel space). Does anyone know what font this leaning symbol is written with? Or how to produce one in LaTeX?

enter image description here

Cheers from Mikael in Sweden!

4
  • 4
    if you are reading from PDF you can (probably) see what font is being used from pffonts utility, otherwise you should at least give an image of the formula, most people will have no access to it just from the article title. Sep 5 '20 at 9:46
  • 1
    I've taken the liberty of adding a URL link to the paper on arxiv as well as a screenshot of the equation in question. Feel free to revert.
    – Mico
    Sep 5 '20 at 10:01
  • 4
    It can be a rotatebox \cup.
    – Sebastiano
    Sep 5 '20 at 10:15
  • Note that it is often (not always) possible to copy such character and paste it into some search software or websearch. In this case, I could copy the character, enter it into Google and find out it's a subset symbol, although rotated.
    – phresnel
    Sep 7 '20 at 12:17
26

The source is actually available: Select Other formats in the box on the right and download the source as a zip file.

Inspecting the code, it turns out that the author typeset the symbol using this macro:

\def\smooth{\rotatebox[origin=c]{70}{$\subset$}}
10

Some comments and observations:

  • What you refer to as an integral symbol is actually called an "esh" by the authors -- see footnote 2 on page 2 of the paper. The symbol may be produced by loading the tipa package and typing \text{\textesh}. Importantly, the \esh symbol is smaller than a text-style \int symbol.

  • What you call a "leaning U" may be generated via \rotatebox[origin=b]{-20}{$\cup$} (requires the graphicx package).

    Remark: Shortly after I posted this answer, @HaraldHancheOlsen posted an answer in which he showed that the "leaning U" symbol is actually produced by \rotatebox[origin=c]{70}{$\subset$}.

enter image description here

\documentclass{article}
\usepackage{newtxtext,newtxmath} % Times Roman clone
\usepackage{mathrsfs} % for fancy script-X symbol (via `\mathscr`)
\usepackage{tipa} % for '\textesh' macro
\newcommand\esh{\text{\textesh}}
\usepackage{graphicx} % for '\rotatebox' macro
\newcommand\rotcup{\rotatebox[origin=b]{-30}{$\cup$}}

\begin{document}

\[
H^{\bullet}_{\mathrm{trad}}
(\mathscr{X},A)
\coloneq
H^{\bullet}_{\mathrm{sing}}
(\esh\rotcup\mathscr{X},A)
\]
\end{document}
2
  • Oh - be sure I do know it's an "esh"! What I hastly meant (in a hurry when writing) was that one can write it as an integralsymbol. A small one 😃...
    – Mikael
    Sep 6 '20 at 14:24
  • Oh - be sure I do know it's an "esh"! What I hastly meant (in a hurry when writing) was that one can write it as an integralsymbol even. A small one 😃... The "tilted" U that was a new one. And I did appreciated your answer. It's rather difficult to keep up with all symbols and how to write them. But interesting! Thank's all for your dedication - and it's really interesting to take part in everyone's writing! Fonts are very funny! Now back to my tikzcd. Anyone who know if tikzcd have an "own" site to ask questions on?
    – Mikael
    Sep 6 '20 at 14:36
6

(I expected @egreg to remark this...)

I don’t know the meaning of this “rotated union symbol”; but assuming it is a binary operator like \cup, \cap, etc., you'd probably want to typeset it as such, and not as an ordinary symbol. You'd also want it to scale correctly in script and scriptscript styles, and to behave well when used with the amsmath package.

Here's how you could do:

\documentclass{article}
\usepackage{newtxtext,newtxmath} % Times Roman clone
\usepackage{mathrsfs} % for fancy script-X symbol (via `\mathscr`)
\usepackage{tipa} % for '\textesh' macro
\usepackage{amsmath} % presumably you'll want this!
\usepackage{graphicx} % for '\rotatebox' macro

\makeatletter

% For added generality, let's show how a general solution can be 
% implemented:
\newcommand*\@my@genrot@x[1]{%
    \mathbin{%
        \mathpalette\@my@genrot@y{#1}%
    }%
}
\newcommand*\@my@genrot@y[2]{\@my@genrot@z #1#2}
\newcommand*\@my@genrot@z[3]{%
    \rotatebox[origin=b]{#2}{$#1#3$}%
}
%
% Now define two similar commands, "\rotcup" and "\rotcap":
\newcommand*\rotcup{%
    \DOTSB % appropriate?
    \@my@genrot@x{{-30}{\cup}}%
}
\newcommand*\rotcap{%
    \DOTSB
    \@my@genrot@x{{30}{\cap}}%
}

\makeatother

\newcommand\esh{\text{\textesh}}



\begin{document}

This text is typeset in \fontname\the\font (\expandafter\string \the\font).
\begin{gather*}
    H^{\bullet}_{\mathrm{trad}}
    (\mathscr{X},A)
    \coloneq
    H^{\bullet}_{\mathrm{sing}}
    (\esh\rotcup\mathscr{X},A) \\
    A\rotcap B
\end{gather*}
Other math styles are now honored:
text style \( \esh\rotcup\mathscr{X} \) (same a display style, in this 
case),
script style \( \scriptstyle \esh\rotcup\mathscr{X} \)
scriptscript style \( \scriptscriptstyle \esh\rotcup\mathscr{X} \).

Also works with \textsf{amsmath}'s \verb|\dots|:
\( A_{1} \rotcup\dots\rotcup A_{n} \).

\end{document}

All this, based on the assumption that LaTeX is still what I remember it was...

Thanks to @Mico (see his answer) and to @egreg (see here).

Output:

Output of the code


Addition

I came to the conclusion that the \rotcup symbol should be an ordinary symbol. Well, in any case it should scale with the math style. This is how I would implement it:

\documentclass[a4paper]{article}
\usepackage{newtxtext,newtxmath} % Times Roman clone
\usepackage{mathrsfs} % for fancy script-X symbol (via `\mathscr`)
\usepackage{tipa} % for '\textesh' macro
\usepackage{amsmath} % presumably you'll want this!
\usepackage{graphicx} % for '\rotatebox' macro

\makeatletter

% Less general than my previous solution, now the rotation angle is 
% fixed once for all to -30 degrees:
\newcommand*\@my@genrot@x[1]{%
    \mathord{% superfluous, but more elegant
        \mathpalette\@my@genrot@y{#1}%
    }%
}
\newcommand*\@my@genrot@y[2]{%
    \rotatebox[origin=c]{-30}{$#1#2$}% note: we rotate around the center
}
%
% Now define two similar commands, "\rotcup" and "\rotvee":
\newcommand*\rotcup{%
    \@my@genrot@x{\cup}%
}
\newcommand*\rotvee{%
    \@my@genrot@x{\vee}%
}

\makeatother

\newcommand\esh{\text{\textesh}}



\begin{document}

For example: $\esh\rotcup\mathscr{X}$ and $\esh\rotvee\mathscr{X}$.
And honors the math style:
text style \( \esh\rotcup\mathscr{X} \) (same as display style, in this 
case),
script style \( \scriptstyle \esh\rotcup\mathscr{X} \)
scriptscript style \( \scriptscriptstyle \esh\rotcup\mathscr{X} \).


Does the current math version ``percolate'' inside \verb|\rotatebox|?
{\bfseries \mathversion{bold}%
Let's see: $A\rotcup B$.}
Yes, it does.

\end{document}

And this is what I getOutput of the second code sample:

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  • HI, and welcome again into the site.
    – Sebastiano
    Sep 5 '20 at 15:15
  • 1
    I was touring in the mountains 🏔 🏍
    – egreg
    Sep 5 '20 at 17:01
  • 1
    I'm not sure it's to be considered a binary operation. My impression is that the integral sign and the rotated cup are a single operator.
    – egreg
    Sep 5 '20 at 17:42
  • 1
    I think there might be too much space around the new symbol in your output. This is just going by the example the OP gave.
    – Anush
    Sep 5 '20 at 18:39
  • @egreg: I agree, perhaps it is not; perhaps it’s an ordinary symbol. Or perhaps the \rotcup symbol should be a subscript to the \esh… I simply don’t know. I just wanted to elaborate on the other answers.
    – GuM
    Sep 5 '20 at 20:25

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