\DocumentMetadata{pdfstandard=A-2b, lang=en-GB}
\documentclass[a4paper,12pt]{scrartcl}

\usepackage{mathtools, array, varioref}
\usepackage[british]{babel}
\usepackage{fourier-orns}
\usepackage{euler-math}
\setmainfont{cmunorm.otf}
    [BoldFont =       cmunobx.otf ,
     ItalicFont =     cmunoti.otf ,
     BoldItalicFont = cmunobi.otf
    ]
\setsansfont{Cabin}[Scale=MatchLowercase]
\setmonofont{Inconsolatazi4}[Scale=MatchLowercase,StylisticSet={2,3}]
\usepackage{subfig}
\captionsetup[subtable]{position=top}
\usepackage{realscripts}
\usepackage{microtype}
\usepackage{hyperref}
\hypersetup{pdftitle={Euler-Math User’s Guide},
            pdfauthor={Daniel FLIPO},
            bookmarksopen,
            colorlinks
            }
\newcommand*{\hlabel}[1]{\phantomsection\label{#1}}

\newcommand*{\NEOTF}{Euler-Math}
\newcommand*{\pkg}[1]{\texttt{#1}}
\newcommand*{\file}[1]{\texttt{#1}}
\newcommand*{\opt}[1]{\texttt{#1}}
\newcommand*{\cmd}[1]{\texttt{\textbackslash #1}}\newcommand*{\showtchar}[1]{\cmd{#1}~\csname #1\endcsname}
\newcommand*{\showmchar}[1]{\cmd{#1}~$(\csname #1\endcsname)$}
\newcommand*{\showmchardollar}[1]{\texttt{\$\cmd{#1}\$}~$(\csname #1\endcsname)$}

\renewcommand{\labelitemi}{\lefthand}

\title{Euler Math font, OTF version}
\author{Daniel Flipo \\ \texttt{daniel.flipo@free.fr}}

\newcommand*{\version}{0.61}

\begin{document}
\maketitle

\section{What is \NEOTF{}?}

\NEOTF{} is a fork of the Euler project initiated by Khaled Hosny in 2009
and abandoned in 2016%
\footnote{See \url{https://github.com/aliftype/euler-otf}}.
The original font name `Neo~Euler’, has been changed to `Euler~Math’, the file
name is now \file{Euler-Math.otf}.

\file{Euler-Math.otf} is an OpenType version of Hermann Zapf’s Euler maths font,
as the original font it contains three alphabets $Euler Roman$,
$\symscr{SCRIPT}$ and $\symfrak{Euler Fraktur}$ (none of them being suitable
for typesetting text) and has some specificities:
\begin{itemize}
\item it is an \emph{upright} maths font, Latin and Greek letters are
  \emph{not available} in italic or bold italic shape (only upright and bold) ;
\item integral symbols are upright too;
\item all inequalities symbols are \emph{slanted}, so \cmd{leq} and geq are
  printed as $\leq$ and $\geq$ (same as \cmd{leqslant} and \cmd{geqslant}).
\end{itemize}

\NEOTF{} requires LuaTeX or XeTeX as engine and the \pkg{unicode-math} package%
\footnote{Please read the documentation \file{unicode-math.pdf}.}.

Coverage: currently, all Plain, LaTeX and AMS maths symbols are provided;
sans-serif (Latin, Greek, digits) and typewriter (Latin, digits) defaults
are included.

Please note that the current version (\version) is \emph{experimental,
do expect metrics and glyphs to change} until version 1.0 is reached.
Comments, suggestions and bug reports are welcome!

\pagebreak[4]
\section{Usage}

\subsection{Calling \cmd{setmathfont}}

A basic call for \NEOTF{} would be:
\begin{verbatim}
\usepackage[math-style=upright]{unicode-math}
\setmathfont{Euler-Math.otf} % Call by file name or
\setmathfont{Euler Math}     % Call by font name or
\end{verbatim}
this loads \NEOTF{} as maths font%
\footnote{Both calls work equally well with LuaTeX; with XeTeX a call by font
  name will fail unless the font is declared as a \emph{system font}.}
 with the default options, see subsections~\ref{ssection-cv},
 \ref{ssection-ss} and~\ref{ssec-other-features} for customisation.

Please note that the three sets of text fonts have to be chosen separately.

\subsection{Calling \pkg{euler-math.sty} (recommended)}

As an alternative to load \NEOTF{} you can type:\\[.5\baselineskip]
\verb+\usepackage{euler-math}+\\[.5\baselineskip]
\verb+\usepackage[ +\textit{options}
\footnote{Possible \textit{options} are \opt{Scale=} or any of the options
  described in sections \ref{ssection-cv}, \ref{ssection-ss} and
  \ref{ssec-other-features}.}%
\verb+ ]{euler-math}+\\[.5\baselineskip]
it loads \pkg{unicode-math} with the \opt{math-style=upright} option and
sets Euler-Math as maths font but does a bit more:
\begin{enumerate}
\item it checks at \verb+\begin{document}+ if packages \pkg{amssymb} or
  \pkg{latexsym} are loaded and issues warnings in case they are;
\item it provides aliases for glyphs named differently in Unicode, so that
  \pkg{latexsym} or AMS names are also available;
\item it defines some specific maths characters \showmchar{varemptyset}, etc.
\end{enumerate}

The \pkg{euler-math.sty} package is meant to replace the \pkg{eulervm.sty}
package for users switching from pdfLaTeX to LuaLaTeX or XeLaTeX.
It does not interfere with text fonts which have to be chosen separately.

\section{What is provided?}

\NEOTF{} provides all glyphs available in the \pkg{amssymb} and \pkg{latexsym}
packages and many more, f.i. lots of extensible accents and arrows.

These two packages \emph{should not} be loaded as they might override \NEOTF{}
glyphs.

As mentioned above, there is neither italic nor bold italic shapes; for user’s
convenience, these slots are filled with their upright analogs.
Sans-serif (Latin, Greek, digits) and typewriter (Latin, digits) alphabets,
Fraktur and Blackboard Bold styles are included.

A full list of available glyphs is shown in file \file{unimath-euler.pdf}.

\subsection{Character variants}
\label{ssection-cv}

\NEOTF{} provides fourteen ``Character Variants’’ options, listed on
table~\vref{cv}, to choose between different glyphs for Greek characters
and some others.
\begin{table}[ht]
  \centering  \caption{Character variants.}
  \hlabel{cv}
  \begin{tabular}{@{}>{\ttfamily}lccl@{}}
    \hline
           & Default       & Variant          & Name\\
    \hline
      cv01 & $\hslash$     & $\muphbar$       & \cmd{hslash} \\
      cv02 & $\emptyset$   & $\varemptyset$   & \cmd{emptyset} \\
      cv03 & $\epsilon$    & $\varepsilon$    & \cmd{epsilon} \\
      cv04 & $\kappa$      & $\varkappa$      & \cmd{kappa} \\
      cv05 & $\pi$         & $\varpi$         & \cmd{pi} \\
      cv06 & $\phi$        & $\varphi$        & \cmd{phi} \\
      cv09 & $\theta$      & $\vartheta$      & \cmd{theta} \\
      cv10 & $\Theta$      & $\varTheta$      & \cmd{Theta}\\
    \hline
  \end{tabular}
\end{table}

For instance, to get \cmd{epsilon} and \cmd{phi} typeset as $\varepsilon$
and $\varphi$ instead of $\epsilon$ and $\phi$ (with matching bold variants
$\symbf{\varepsilon}$ and $\symbf{\varphi}$), you can
add option \verb+CharacterVariant={3,6}+ to the \cmd{setmathfont} call:
\begin{verbatim}
\setmathfont{Euler-Math.otf}[CharacterVariant={3,6}]
\end{verbatim}

Please note that curly braces are mandatory whenever more than one
``Character Variant’’ is selected.

Note about \cmd{hbar}: \pkg{unicode-math} defines \cmd{hbar} as
\cmd{hslash} (U+210F) while \pkg{amsmath} provides two different glyphs
(h with horizontal or diagonal stroke).\\
\pkg{euler-math} follows \pkg{unicode-math}; the h with horizontal
stroke can be printed using \cmd{hslash} or \cmd{hbar} together with character
variant \opt{cv01} or with \cmd{muphbar} (replacement for AMS’ command
\cmd{hbar}).

\subsection{Stylistic sets}
\label{ssection-ss}

\NEOTF{} provides two ``Stylistic Sets’’ options to choose between different
glyphs for families of maths symbols.

\verb+StylisticSet=5+, alias \verb+Style=smaller+, converts some symbols into
their smaller variants, see table~\vref{ss05}.

\verb+StylisticSet=6+, alias \verb+Style=subsetneq+, converts some inclusion
symbols, see table~\vref{ss06}.
\begin{table}[ht]
  \centering
  \caption{Stylistic Sets 5 and 6}
  \subfloat[\opt{Style=smaller\quad (+ss05)}]{\hlabel{ss05}%
  \begin{tabular}[t]{@{}lcc@{}}
    \hline
      Command           & Default         & Variant \\
    \hline
      \cmd{in}               & $\in$               & $\smallin$ \\
      \cmd{ni}               & $\ni$               & $\smallni$ \\
      \cmd{mid}              & $\mid$              & $\shortmid$ \\
      \cmd{nmid}             & $\nmid$             & $\nshortmid$ \\
      \cmd{parallel}         & $\parallel$         & $\shortparallel$ \\
      \cmd{nparallel}        & $\nparallel$        & $\nshortparallel$ \\
    \hline
  \end{tabular}
  }\hspace{10mm} % eof subfloat
  \subfloat[\opt{Style=subsetneq\quad (+ss06)}]{\hlabel{ss06}%
  \begin{tabular}[t]{@{}lcc@{}}
    \hline
      Command                & Default             & Variant \\
    \hline
      \cmd{subsetneq}   & $\subsetneq$    & $\varsubsetneq$ \\
      \cmd{supsetneq}   & $\supsetneq$    & $\varsupsetneq$ \\
      \cmd{subsetneqq}  & $\subsetneqq$   & $\varsubsetneqq$ \\
      \cmd{supsetneqq}  & $\supsetneqq$   & $\varsupsetneqq$ \\
    \hline
  \end{tabular}
  }% eof subfloat
\end{table}


To enable Stylistic Sets 5 and 6 for \NEOTF{}, you should enter
\begin{verbatim}
\setmathfont{Euler-Math.otf}[StylisticSet={5,6}]  or
\usepackage[Style={smaller,subsetneq}]{Euler-Math.otf}
\end{verbatim}
{\samepage then, \verb+\[A \subsetneq B\quad x \in E \quad D \parallel D' \]+
will print as
\setmathfont{Euler-Math.otf}[StylisticSet={5,6}]
\[A \subsetneq B\quad x \in E \quad D \parallel D' \]
instead of
\setmathfont{Euler-Math.otf}
\[A \subsetneq B\quad x \in E \quad D \parallel D' \]
}

\subsection{Other font features}
\label{ssec-other-features}

To get oldstyle numbers in maths, the feature \opt{+onum} is available:
\begin{verbatim}
\setmathfont{Euler-Math.otf}[Numbers=OldStyle]  or
\usepackage[Style={fulloldstyle}]{euler-math}
\end{verbatim}

\setmathfont{Euler-Math.otf}[Numbers=OldStyle]
$0123456789, \symbf{0123456789}$
\setmathfont{Euler-Math.otf}

\subsection{Standard \LaTeX{} math commands}
\label{ssec-math-commands}

All standard \LaTeX{} maths commands, all \pkg{amssymb} commands and all
\pkg{latexsym} commands are supported by \NEOTF{}, for some of them loading
\pkg{euler-math.sty} is required.

Various wide accents are also supported:
\begin{itemize}
\item \cmd{wideoverbar} and \cmd{mathunderbar}%
  \footnote{\cmd{overline} and \cmd{underline} are not font related,
     they are based on \cmd{rule}.}
  \[\wideoverbar{x}\quad \wideoverbar{xy}\quad \wideoverbar{xyz}\quad
    \wideoverbar{A\cup B}\quad \wideoverbar{A\cup (B\cap C)\cup D}\quad
    \mathunderbar{m+n+p}\]

\item \cmd{widehat} and \cmd{widetilde}
\[\widehat{x}\; \widehat{xx} \;\widehat{xxx} \;\widehat{xxxx}\;
  \widehat{xxxxx} \;\widehat{xxxxxx} \;\widetilde{x}\; \widetilde{xx}\;
  \widetilde{xxx} \;\widetilde{xxxx} \;\widetilde{xxxxx}\;
  \widetilde{xxxxxx}\]

\item \cmd{widecheck}  and \cmd{widebreve}
  \[\widecheck{x}\quad \widecheck{xxxx}\quad \widecheck{xxxxxx}\quad
    \widebreve{x}\quad \widebreve{xxxx}\quad \widebreve{xxxxxx}\]

\item \cmd{overparen} and \cmd{underparen}
  \[\overparen{x}\quad \overparen{xy}\quad \overparen{xyz}\quad
    \mathring{\overparen{A\cup B}}\quad
    \overparen{A\cup (B\cap C)\cup D}^{\smwhtcircle}\quad
    \overparen{x+y}^{2}\quad \overparen{a+b+...+z}^{26}\]
\vspace{-\baselineskip}
\[\underparen{x}\quad \underparen{xz} \quad \underparen{xyz}
  \quad \underparen{x+z}_{2}\quad \underparen{a+b+...+z}_{26}\]

\item \cmd{overbrace} and \cmd{underbrace}
  \[\overbrace{a}\quad \overbrace{ab}\quad \overbrace{abc}\quad
  \overbrace{abcd}\quad \overbrace{abcde}\quad
  \overbrace{a+b+c}^{3}\quad \overbrace{ a+b+. . . +z }^{26}\]
  \vspace{-\baselineskip}
  \[\underbrace{a}\quad\underbrace{ab}\quad\underbrace{abc}\quad
  \underbrace{abcd}\quad \underbrace{abcde}\quad
  \underbrace{a+b+c}_{3}  \quad \underbrace{ a+b+...+z }_{26}\]

\item \cmd{overbracket} and \cmd{underbracket}
  \[\overbracket{a}\quad \overbracket{ab}\quad \overbracket{abc}\quad
  \overbracket{abcd}\quad \overbracket{abcde}\quad
  \overbracket{a+b+c}^{3}\quad \overbracket{ a+b+. . . +z }^{26}\]
  \vspace{-\baselineskip}
  \[\underbracket{a}\quad\underbracket{ab}\quad\underbracket{abc}\quad
  \underbracket{abcd}\quad \underbracket{abcde}\quad
  \underbracket{a+b+c}_{3}  \quad \underbracket{ a+b+...+z }_{26}\]

\item \cmd{overrightarrow}, \cmd{overleftarrow} and \cmd{overleftrightarrow}
  \[\overrightarrow{v}\quad \overrightarrow{M}\quad \overrightarrow{vv}
  \quad \overrightarrow{AB}\quad \overrightarrow{ABC}
  \quad \overrightarrow{ABCD} \quad \overrightarrow{ABCDEFGH}.
  \]
  \vspace{-\baselineskip}
  \[\overleftarrow{v}\quad \overleftarrow{M}\quad \overleftarrow{vv}
  \quad \overleftarrow{AB}\quad \overleftarrow{ABC}
  \quad \overleftarrow{ABCD} \quad \overleftarrow{ABCDEFGH}\]
  \vspace{-\baselineskip}
  \[\overleftrightarrow{v}\quad \overleftrightarrow{M}\quad
    \overleftrightarrow{vv}\quad
    \overleftrightarrow{AB}\quad \overleftrightarrow{ABC}\quad
    \overleftrightarrow{ABCD} \quad \overleftrightarrow{ABCDEFGH}\]

\item \cmd{overrightharpoon} and \cmd{overleftharpoon}
  \[\overrightharpoon{v}\quad \overrightharpoon{M}\quad \overrightharpoon{vv}
  \quad \overrightharpoon{AB}\quad \overrightharpoon{ABC}
  \quad \overrightharpoon{ABCD} \quad \overrightharpoon{ABCDEFGH}.
  \]
  \vspace{-\baselineskip}
  \[\overleftharpoon{v}\quad \overleftharpoon{M}\quad \overleftharpoon{vv}
  \quad \overleftharpoon{AB}\quad \overleftharpoon{ABC}
  \quad \overleftharpoon{ABCD} \quad \overleftharpoon{ABCDEFGH}\]

\item \cmd{underrightarrow}, \cmd{underleftarrow} and \cmd{underleftrightarrow}
  \[\underrightarrow{v}\quad \underrightarrow{M}\quad \underrightarrow{vv}
  \quad \underrightarrow{AB}\quad \underrightarrow{ABC}
  \quad \underrightarrow{ABCD} \quad \underrightarrow{ABCDEFGH}.
  \]
  \vspace{-\baselineskip}
  \[\underleftarrow{v}\quad \underleftarrow{M}\quad \underleftarrow{vv}
  \quad \underleftarrow{AB}\quad \underleftarrow{ABC}
  \quad \underleftarrow{ABCD} \quad \underleftarrow{ABCDEFGH}\]
  \vspace{-\baselineskip}
  \[\underleftrightarrow{v}\quad \underleftrightarrow{M}\quad
    \underleftrightarrow{vv}\quad
    \underleftrightarrow{AB}\quad \underleftrightarrow{ABC}\quad
    \underleftrightarrow{ABCD} \quad \underleftrightarrow{ABCDEFGH}\]

\item \cmd{underrightharpoondown} and \cmd{underleftharpoondown}
  \[\underrightharpoondown{v} \quad \underrightharpoondown{M}\quad
    \underrightharpoondown{vv}\quad \underrightharpoondown{AB}\quad
    \underrightharpoondown{ABC}\quad \underrightharpoondown{ABCD}
    \quad \underrightharpoondown{ABCDEFGH}.
  \]
  \vspace{-\baselineskip}
  \[\underleftharpoondown{v} \quad \underleftharpoondown{M}\quad
    \underleftharpoondown{vv}\quad \underleftharpoondown{AB}\quad
    \underleftharpoondown{ABC}\quad \underleftharpoondown{ABCD}
    \quad \underleftharpoondown{ABCDEFGH}.
  \]

\item Finally \cmd{widearc} and \cmd{overrightarc} (loading
  \pkg{euler-math.sty} is required)
\[\widearc{AMB}\quad \overrightarc{AMB}\]
\end{itemize}

All the extensible arrows provided by the \pkg{mathtools} package are
available in the \NEOTF{} font (loading \pkg{euler-math.sty} is required),
f.i.:
\[X \xLeftrightarrow{above} Y \xhookrightarrow[under]{} Z\xmapsto{above} W\]


\subsection{Mathematical alphabets}
\label{ssec-math-alphabets}

\begin{itemize}
\item  All Latin and Greek characters are available in upright
  and bold via the \verb+\symup{}+ and \verb+\symbf{}+ commands.

\item Calligraphic alphabet (\cmd{symscr} or \cmd{symcal} or
  \cmd{mathcal} command), uppercase:\\
  $\symscr{ABCDEFGHIJKLMNOPQRSTUVWXYZ}$\\
  also in boldface (\cmd{symbfscr},\cmd{symbfcal} or \cmd{mathbfcal} command):\\
  $\symbfscr{ABCDEFGHIJKLMNOPQRSTUVWXYZ}$

\item Blackboard-bold alphabet (\cmd{symbb} or \cmd{mathbb} command),
  uppercase, lowercase and digits:

  $\symbb{ABCDEFGHIJKLMNOPQRSTUVWXYZ}$

  $\symbb{abcdefghijklmnopqrstuvwxyz\quad 0123456789}$

\item Fraktur alphabet medium and bold
  (\cmd{symfrak}, or \cmd{symbffrak} commands):

  $\symfrak{ABCDEFGHIJKLMNOPQRSTUVWXYZ\quad abcdefghijklmnopqrstuvwxyz}$\\
  $\symbffrak{ABCDEFGHIJKLMNOPQRSTUVWXYZ}$\\
  \hphantom{$\symfrak{ABCDEFGHIJKLMNOPQRSTUVWXYZ\quad}$}%
    $\symbffrak{abcdefghijklmnopqrstuvwxyz}$

\item Sans-serif (Latin and Greek) and Typewriter (Latin) alphabets
  (commands \verb+\symsf{}+, \verb+\symbfsf{}+, \verb+\symtt{}+):

  $\symsf{ABCDEFGHIJKLMNOPQRSTUVWXYZ}\\
   \symsfit{abcdefghijklmnopqrstuvwxyz\quad 0123456789}$

  $\symbfsf{ΑΒΓΔΕΖΗΘΙΚΛΜΝΞΟΠΡΣΤΥΦΧΨΩ}\\
   \symbfsf{αβγδεζηθικλμνξοπρσςτυφχψω}$

  $\symtt{ABCDEFGHIJKLMNOPQRSTUVWXYZ}\\
   \symtt{abcdefghijklmnopqrstuvwxyz\quad 0123456789}$

\end{itemize}


\subsection{Missing symbols}

\NEOTF{} does not aim at being as complete as \file{STIXTwoMath-Regular} or
\file{Cambria}, the current glyph coverage compares with TeXGyre math fonts.
In case some symbols do not show up in the output file, you will see warnings
in the \file{.log} file, for instance:

\setmathfont{STIXTwoMath-Regular.otf}[range={"2964}]
\texttt{Missing character: There is no }$⥤$%
\texttt{ (U+2964) in font Euler Math}

Borrowing them from a more complete font, say \file{Asana-Math},
is a possible workaround:
\verb+\setmathfont{Asana-Math.otf}[range={"2964},Scale=1.02]+\\
scaling is possible, multiple character ranges are separated with commas:\\
\verb+\setmathfont{Asana-Math.otf}[range={"294A-"2951,"2964,"2ABB-"2ABE}]+

Let’s mention \pkg{albatross}, a useful tool to find out the list of fonts
providing a given glyph: f.i. type in a terminal ``\texttt{albatross U+2964}’’,
see the manpage or \file{albatross-manual.pdf}.

\section{Acknowledgements}

Khaled Hosni achieved most of the portage of Hermann Zapf’s Euler font to
Unicode between 2009 and 2016.  After Hermann’s death in 2015, he decided to
stop the project but his \file{euler.otf} font, although not available on CTAN,
continued to be used, see
\href{https://tex.stackexchange.com/questions/425098/which-opentype-math-fonts-are-available}{https://tex.stackexchange.com/questions/425098/}.
I offered Khaled my help to finalise the font, we agreed I would try to
complete the font and maintain it on my own.

\bigskip
\begin{center}\Huge
\decotwo
\end{center}

\end{document}

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