path: root/Master/texmf-dist/doc/fonts/erewhon-math/Erewhon-Math.ltx

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

\usepackage{mathtools, array, varioref}
\usepackage[british]{babel}
\usepackage{fourier-otf}
\setsansfont{Cabin}[Scale=MatchLowercase]
\setmonofont{Inconsolatazi4}[Scale=MatchLowercase,
                             HyphenChar=None,StylisticSet={2,3}]
\usepackage{subfig}
\captionsetup[subtable]{position=top}
\usepackage{realscripts}
\usepackage{microtype}
\usepackage{hyperref}
\hypersetup{pdftitle={Erewhon-Math User’s Guide},
            pdfauthor={Daniel FLIPO},
            bookmarksopen,
            colorlinks
            }
\newcommand*{\hlabel}[1]{\phantomsection\label{#1}}

\newcommand*{\FGUT}{Fourier-GUT\textit{enberg}}
\newcommand*{\FOTF}{Erewhon-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{\decofourleft\,\FOTF\,\decofourright}
\author{Daniel Flipo \\ \texttt{daniel.flipo@free.fr}}

\newcommand*{\version}{0.66}

\begin{document}
\maketitle

\section{What is \FOTF{}?}

\FOTF{} is an Utopia based OpenType maths font.
The maths symbols and Greek letters are borrowed or derived from
Michel Bovani’s \FGUT, Latin letters and digits are borrowed from
Michael Shape’s Erewhon font.

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

It is meant to be used with Utopia based OpenType text fonts like {Erewhon}.
For \FGUT{} users who want to switch to LuaLaTeX or XeLaTeX, the
file \file{fourier-otf.sty} can be used as a replacement of \file{fourier.sty}.

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!

\section{Usage}

\subsection{Calling \cmd{setmathfont}}

A basic call for \FOTF{} would be:
\begin{verbatim}
\usepackage{unicode-math}
\setmathfont{Erewhon-Math.otf} % Call by file name or
\setmathfont{Erewhon Math}     % Call by font name
\end{verbatim}
this loads \FOTF{} 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~\vref{ssection-um},
\vref{ssection-cv} and~\vref{ssection-ss} for customisation.

Please note that the three sets of text fonts have to be chosen separately,
f.i.:%\\[.25\baselineskip]

\pagebreak[4]
\noindent\verb+\setmainfont{erewhon}+%
\footnote{\texttt{Erewhon} (with capital E) is fine with LuaTeX but
  would fail with XeTeX (\file{erewhon.fontspec} not found).}%
\hspace{62mm}\texttt{\% rm}\\
\verb+\setsansfont{Cabin}[Scale=MatchLowercase]          % sf+\\
\verb+\setmonofont{Inconsolatazi4}[Scale=MatchLowercase] % tt+\\[.25\baselineskip]
otherwise you would get Latin Modern for text fonts.

\subsection{Calling \pkg{fourier-otf.sty} (recommended)}

As an alternative to load \FOTF{} you can type:\\[.5\baselineskip]
\verb+\usepackage[ +\textit{options}
\footnote{Possible \textit{options} are \opt{loose}, \opt{no-text}, \opt{Scale=}
  or any of the options described in sections \ref{ssection-um} to
  \ref{ssec-other-features}.}%
\verb+ ]{fourier-otf}+\\[.5\baselineskip]
it loads \pkg{unicode-math} with the default options, sets Erewhon-Math
as maths font and Erewhon Text fonts as Roman fonts
(families \textit{sf} and \textit{tt} left unchanged) but does a bit more:
\begin{enumerate}
\item it loads \pkg{realscripts.sty} for better superscripts and footnote calls;
\item it loads \pkg{fourier-orns.sty}, providing many text ornaments;
\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 specific maths characters like \showmchar{Bbbbackslash},
  \showmchar{varemptyset}, \linebreak[4]
  \showmchar{parallelslant},
  \showmchar{shortparallelslant}, etc.;
\item it reduces spacing in maths mode: \cmd{thinmuskip}, \cmd{medmuskip}
  and \cmd{thickmuskip} are reduced as in \file{fourier.sty}.
%  \verb+\thinmuskip=2mu+,\\
%  \verb+\medmuskip=2.5mu plus 1mu minus 2.5mu+,\\
%  \verb+\thickmuskip=3.5mu plus 2.5mu+.\\
  The option \opt{loose} disables these settings.
\end{enumerate}

Apart from the \opt{loose} option mentioned above, \pkg{fourier-otf.sty}
provides two options \opt{no-text} and \opt{Scale=}\textsl{<decimal>} meant to
be used to load the \FOTF{} font together with roman text fonts other than
Erewhon, while keeping the advantages 1. to 5. pointed in the preceding list,
f.i.\quad \verb+\usepackage[no-text,Scale=0.98]{fourier-otf}+

Please note that the fonts loaded by \pkg{fourier-otf.sty} are about 2\%
larger than those loaded by \pkg{fourier.sty}: the Erewhon text fonts are
based on Utopia reduced à 94\%, while the fourier fonts are based on
Utopia reduced à 92\%. Option \verb+Scale=0.98+ can be used to mimic the
output produced by the \pkg{fourier.sty} package.

Option \opt{no-text} can also be useful if Erewhon is to be loaded with
specific options, f.i. \\
\verb+\usepackage[no-text]{fourier-otf}+\\
\verb|\setmainfont{erewhon}[RawFeature=+onum;+ss01]|

\section{What is provided?}

\FOTF{} provides all glyphs supplied by \FGUT{} plus all glyphs available in
the \pkg{amssymb} and \pkg{latexsym} packages and many more.  Therefore, these
two packages \emph{should not} be loaded as they might override \FOTF{} glyphs.

Sans-serif, typewriter and fraktur styles are borrowed from Latin Modern fonts.
See in section~\vref{ssec-math-alphabets} how to choose
from other maths fonts for these styles.

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

\subsection{Upright or slanted?}
\label{ssection-um}

Package \pkg{unicode-math} follows \TeX{} conventions for Latin and Greek
letters: in maths mode, the default option (\opt{math-style=TeX}) prints
Latin letters $a$…$z$ $A$…$Z$ and lowercase greek letters $\alpha$…$\omega$
slanted (italic) while uppercase greek letters $\Alpha \Beta \Gamma$…$\Omega$
are printed upright.
This can be changed by option \opt{math-style} as shown in
table~\vref{math-style}.

\begin{table}[ht]
  \centering
  \caption{Effects of the \opt{math-style} package option.}
  \hlabel{math-style}
  \begin{tabular}{@{}>{\ttfamily}lcc@{}}
    \hline
      \rmfamily Package option & Latin & Greek \\
    \hline
      math-style=ISO & $(a,z,B,X)$ & $\symit{(\alpha,\beta,\Gamma,\Xi)}$ \\
      math-style=TeX & $(a,z,B,X)$ & $(\symit\alpha,\symit\beta,\symup\Gamma,\symup\Xi)$ \\
      math-style=french & $(a,z,\symup B,\symup X)$ & $(\symup\alpha,\symup\beta,\symup\Gamma,\symup\Xi)$ \\
      math-style=upright & $(\symup a,\symup z,\symup B,\symup X)$ & $(\symup\alpha,\symup\beta,\symup\Gamma,\symup\Xi)$ \\
    \hline
  \end{tabular}
\end{table}

Bold letters are printed upright except lowercase Greek letters
which are slanted (the default option is \opt{bold-style=TeX}). This can be
changed by option \opt{bold-style} as shown in table~\vref{bold-style}.

\begin{table}[ht]
  \centering
  \caption{Effects of the \opt{bold-style} package option.}
  \hlabel{bold-style}
  \begin{tabular}{@{}>{\ttfamily}lcc@{}}
    \hline
      \rmfamily Package option & Latin & Greek \\
    \hline
      bold-style=ISO & $(\symbfit a, \symbfit z, \symbfit B, \symbfit X)$ & $(\symbfit\alpha, \symbfit\beta, \symbfit\Gamma, \symbfit\Xi)$ \\
      bold-style=TeX & $(\symbfup a,\symbfup z,\symbfup B,\symbfup X)$ & $(\symbfit\alpha, \symbfit\beta,\symbfup \Gamma,\symbfup \Xi)$ \\
      bold-style=upright & $(\symbfup a,\symbfup z,\symbfup B,\symbfup X)$ & $(\symbfup \alpha,\symbfup \beta,\symbfup \Gamma,\symbfup \Xi)$ \\
    \hline
  \end{tabular}
\end{table}

Other possible customisation: $\nabla$ is printed upright and $\partial$ is
printed slanted by default, but \opt{nabla=italic} and
\opt{partial=upright} can change this.

All these options are offered by the \pkg{unicode-math} package but they can
be added to the \cmd{setmathfont} call%
\footnote{IMHO it is easier to add \emph{all options} to the \cmd{setmathfont}
  command.}, for example:

\verb+\setmathfont{Erewhon-Math.otf}[math-style=french,partial=upright]+\\
will print for the code
\begin{verbatim}
\[ \frac{\partial f}{\partial x} = \alpha \symbf{V} + a\nabla\Gamma
                                 + \symbf{\beta}\symbf{M} \]
\end{verbatim}
\setmathfont{Erewhon-Math.otf}[math-style=french,partial=upright]
\[\frac{\partial f}{\partial x} = \alpha \symbf{V} + a\nabla\Gamma +
              \symbf{\beta}\symbf{M} \]
while the default settings would print
\setmathfont{Erewhon-Math.otf}[math-style=TeX,partial=italic]
\[\frac{\partial f}{\partial x} = \alpha \symbf{V} + a\nabla\Gamma +
              \symbf{\beta}\symbf{M} \]

Both shapes remain available anytime: \verb+$\uppi,\itpi$+
prints $\uppi, \itpi$.

If your text editor is able to handle Greek letters or maths symbols, they can
be entered in the code instead control sequences (i.e.
$\symup{α}$, $\symup{β}$, $\symup{Γ}$,… for \cmd{alpha}, \cmd{beta},
\cmd{Gamma},…).

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

\FOTF{} provides fourteen ``Character Variants’’ options, listed on
table~\vref{cv}, to choose between different glyphs for Greek characters
and some others. Alternative calligraphic capitals have been added for E, Q
and T in version~0.50.

\begin{table}[ht]
  \centering  \caption{Character variants.}
  \hlabel{cv}
  \begin{tabular}{@{}>{\ttfamily}lccl@{}}
    \hline
           & Default       & Variant          & Name\\
    \hline
      cv00 & $0$           & $\mupvarzero$    &  0 \\
      cv01 & $\hslash$     & $\mithbar$       & \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} \\
      cv07 & $\rho$        & $\varrho$        & \cmd{rho} \\
      cv08 & $\sigma$      & $\varsigma$      & \cmd{sigma} \\
      cv09 & $\theta$      & $\vartheta$      & \cmd{theta} \\
      cv10 & $\Theta$      & $\varTheta$      & \cmd{Theta}\\
      cv11 & $\mitpartial$ & $\mitvarpartial$ & \cmd{partial}\\
      cv20 & $\symscr{E}$  & $\varsymscrE$    & \cmd{symcal\{E\}}\\
      cv21 & $\symscr{Q}$  & $\varsymscrQ$    & \cmd{symcal\{Q\}}\\
      cv22 & $\symscr{T}$  & $\varsymscrT$    & \cmd{symcal\{T\}}\\
    \hline
  \end{tabular}
\end{table}

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

This  works for all shapes and weights of these characters: f.i.\ %
\verb+$\symbf{\epsilon}$+, \verb+$\symbf{\phi}$+ are output as
\setmathfont{Erewhon-Math.otf}[CharacterVariant={3,6}]$\symbf{\epsilon}$,
$\symbf{\phi}$ instead of
\setmathfont{Erewhon-Math.otf}$\symbf{\epsilon}$, $\symbf{\phi}$.

Similarly with \opt{math-style=french}, \verb+\epsilon+ and \verb+\phi+
are output as $\symup{\varepsilon}$ and $\symup{\varphi}$ (upright).

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

Note about \cmd{hbar} (v\,0.43): \pkg{unicode-math} defines \cmd{hbar} as
\cmd{hslash} (U+210F) while \pkg{amsmath} provides two different glyphs
(italic h with horizontal or diagonal stroke).\\
\pkg{Erewhon Math} now follows \pkg{unicode-math}; the italic h with horizontal
stroke can be printed using \cmd{hslash} or \cmd{hbar} together with character
variant \texttt{cv01} or with \cmd{mithbar} (replacement for AMS’ command
\cmd{hbar}).


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

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

\verb+StylisticSet=4+, alias%
\footnote{These \texttt{Style} aliases are provided by \file{fourier-otf.sty}.}
 \verb+Style=leqslant+, converts (large) inequalities into their slanted
 variants, see table~\vref{ss04}.

\verb+StylisticSet=5+, alias \verb+Style=smaller+, converts some symbols into
their smaller variants, see table~\vref{ss05}.
\begin{table}[ht]
  \centering
  \caption{Stylistic Sets 4 and 5}
  \subfloat[\texttt{Style=leqslant\quad (+ss04)}]{\hlabel{ss04}%
  \begin{tabular}[t]{@{}lcc@{}}
    \hline
      Command           & Default         & Variant \\
    \hline
      \cmd{leq}         & $\leq$         & $\leqslant$ \\
      \cmd{geq}         & $\geq$         & $\geqslant$ \\
      \cmd{nleq}        & $\nleq$        & $\nleqslant$ \\
      \cmd{ngeq}        & $\ngeq$        & $\ngeqslant$ \\
      \cmd{leqq}        & $\leqq$        & $\leqqslant$ \\
      \cmd{geqq}        & $\geqq$        & $\geqqslant$ \\
      \cmd{eqless}      & $\eqless$      & $\eqslantless$ \\
      \cmd{eqgtr}       & $\eqgtr$       & $\eqslantgtr$ \\
      \cmd{lesseqgtr}   & $\lesseqgtr$   & $\lesseqslantgtr$ \\
      \cmd{gtreqless}   & $\gtreqless$   & $\gtreqslantless$ \\
      \cmd{lesseqqgtr}  & $\lesseqqgtr$  & $\lesseqqslantgtr$ \\
      \cmd{gtreqqless}  & $\gtreqqless$  & $\gtreqqslantless$ \\
   \hline
  \end{tabular}
  }\hspace{10mm} % eof subfloat
  \subfloat[\texttt{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}        & $\nparallel$        & $\nshortparallel$ \\
      \cmd{parallelslant}    & $\parallelslant$    & $\shortparallelslant$ \\
      \cmd{nparallelslant}   & $\nparallelslant$   & $\nshortparallelslant$ \\
   \hline
  \end{tabular}
  }% eof subfloat
\end{table}

\verb+StylisticSet=6+, alias \verb+Style=subsetneq+, converts some inclusion
symbols, see table~\vref{ss06}.

\verb+StylisticSet=7+, alias \verb+Style=parallelslant+, converts
``parallel’’ symbols into their slanted variants, see table~\vref{ss07}.
\begin{table}[ht]
  \centering
  \caption{Stylistic Sets 6 and 7}
  \subfloat[\texttt{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}
  }\hspace{10mm} % eof subfloat
  \subfloat[\texttt{Style=parallelslant\quad (+ss07)}]{\hlabel{ss07}%
  \begin{tabular}[t]{@{}lcc@{}}
    \hline
      Command               & Default            & Variant \\
    \hline
      \cmd{parallel}        & $\parallel$        & $\parallelslant$ \\
      \cmd{nparallel}       & $\nparallel$       & $\nparallelslant$ \\
      \cmd{shortparallel}   & $\shortparallel$   & $\shortparallelslant$ \\
      \cmd{nshortparallel}  & $\nshortparallel$  & $\nshortparallelslant$ \\
   \hline
  \end{tabular}
  } % eof subfloat
\end{table}

To enable Stylistic Sets 4, 6 and 7 for \FOTF{}, you should enter
\begin{verbatim}
\setmathfont{Erewhon-Math.otf}[StylisticSet={4,6,7}]  or
\usepackage[Style={leqslant,subsetneq,parallelslant}]{fourier-otf}
\end{verbatim}
then, \verb+\[x\leq y \quad A \subsetneq B\quad D \parallel D' \]+
will print as
\setmathfont{Erewhon-Math.otf}[StylisticSet={4,6,7}]
\[x\leq y \quad A \subsetneq B\quad D \parallel D' \]
instead of
\setmathfont{Erewhon-Math.otf}
\[x\leq y \quad A \subsetneq B\quad D \parallel D' \]

\verb+StylisticSet=3+, alias%
\footnote{These \texttt{Style} aliases are provided by \file{fourier-otf.sty}.}
\verb+Style=upint+, converts integrals signs into their upright
variants, see table~\vref{ss03}.
\begin{table}[ht]
  \let\DS\displaystyle
  \centering
  \caption{Style=upint\quad  (+ss03)}\hlabel{ss03}
  \begin{tabular}[t]{@{}l*{8}c@{}}
    \hline
    Command   &\cmd{int}   &\cmd{iint}  &\cmd{iiint} &\cmd{iiiint}
                   &\cmd{oint}  &\cmd{oiint} &\cmd{oiiint} \\
    \hline
    Default\rule[-15pt]{0pt}{35pt}   &$\DS\int$ &$\DS\iint$ &$\DS\iiint$ &$\DS\iiiint$
                   &$\DS\oint$ &$\DS\oiint$ &$\DS\oiint$ &$\DS\oiiint$
    \\[\baselineskip]
    \setmathfont{Erewhon-Math.otf}[Style=upint]
    Upright\rule[-15pt]{0pt}{30pt}   &$\DS\int$ &$\DS\iint$  &$\DS\iiint$ &$\DS\iiiint$
                   &$\DS\oint$ &$\DS\oiint$  &$\DS\oiint$ &$\DS\oiiint$ \\
    \hline
  \end{tabular}\\[\baselineskip]
  \setmathfont{Erewhon-Math.otf}
  \begin{tabular}[t]{@{}l*{4}c@{}}
    \hline
    Command  &\cmd{intclockwise}  &\cmd{awint}
                   &\cmd{varointclockwise}  &\cmd{ointctrclockwise} \\
    \hline
    Default\rule[-15pt]{0pt}{35pt} &$\DS\intclockwise$ &$\DS\awint$
                   &$\DS\varointclockwise$ &$\DS\ointctrclockwise$ \\
    \setmathfont{Erewhon-Math.otf}[Style=upint]
    Upright\rule[-15pt]{0pt}{30pt}  &$\DS\intclockwise$ &$\DS\awint$
                   &$\DS\varointclockwise$  &$\DS\ointctrclockwise$ \\
    \hline
  \end{tabular}
\end{table}
\setmathfont{Erewhon-Math.otf}

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

\subsubsection{Oldstyle numbers}

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

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

\subsubsection{Delimiters’ size}

When switching from Type\,1 to OpenType, Adobe has significantly increased%
\footnote{Actually +21\% both in height and thickness!}
the sizes of Utopia’s delimiters `()’, `[]’ and `\{\}’.  Erewhon-Math has been
built from Fourier (Utopia’s Type\,1 type faces%
\footnote{Scaled at 94\% instead of 92\% to match Erewhon text fonts.}),
while the Erewhon text fonts have been built from the OpenType version;
the difference was visible on examples like \verb|($P(n)$)| which has been
typeset as%
\setmathfont{Erewhon-Math.otf}[Style=smalldelim] ($P(n)$)
by versions up to~0.53.%
\setmathfont{Erewhon-Math.otf}

This glitch is now fixed, you get now ($P(n)$), [$P[n]$], \{$P\{n\}$\}.
An option \opt{Style=smalldelim} (\opt{+ss09}),
which can be passed either to the \pkg{fourier-otf} package or to the
\verb|\setmathfont| command, has been added in version~0.54 for backward
compatibility: it reverts to the former behaviour.

\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 \FOTF{}, for some of them loading
\pkg{fourier-otf.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}
  \[\overparen{x}\quad \overparen{xy}\quad \overparen{xyz}\quad
    \mathring{\overparen{A\cup B}}\quad
    \overparen{A\cup (B\cap C)\cup D}^{\smwhtcircle}\quad
    \overparen{x+y}^{2}\quad \overparen{a+b+...+z}^{26}\]
\[\underparen{x}\quad \underparen{xz} \quad \underparen{xyz}
  \quad \underparen{x+z}_{2}\quad \underparen{a+b+...+z}_{26}\]

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

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

\item \cmd{overrightarrow} and \cmd{overleftarrow}
  \[\overrightarrow{v}\quad \overrightarrow{M}\quad \overrightarrow{vv}
  \quad \overrightarrow{AB}\quad \overrightarrow{ABC}
  \quad \overrightarrow{ABCD} \quad \overrightarrow{ABCDEFGH}.
  \]
  \[\overleftarrow{v}\quad \overleftarrow{M}\quad \overleftarrow{vv}
  \quad \overleftarrow{AB}\quad \overleftarrow{ABC}
  \quad \overleftarrow{ABCD} \quad \overleftarrow{ABCDEFGH}\]

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

\item \cmd{underrightarrow} and \cmd{underleftarrow}
  \[\underrightarrow{v}\quad \underrightarrow{M}\quad \underrightarrow{vv}
  \quad \underrightarrow{AB}\quad \underrightarrow{ABC}
  \quad \underrightarrow{ABCD} \quad \underrightarrow{ABCDEFGH}.
  \]
  \[\underleftarrow{v}\quad \underleftarrow{M}\quad \underleftarrow{vv}
  \quad \underleftarrow{AB}\quad \underleftarrow{ABC}
  \quad \underleftarrow{ABCD} \quad \underleftarrow{ABCDEFGH}\]

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

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

All the extensible arrows provided by the \pkg{mathtools} package are
available in the \FOTF{} font (loading \pkg{fourier-otf.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 italic, upright, bold
  and bold italic via the \verb+\symit{}+, \verb+\symup{}+, \verb+\symbf{}+
  and \verb+\symbfit{}+ 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):

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

\item Fraktur alphabet is borrowed from Latin Modern,

  $\symfrak{ABCDEFGHIJKLMNOPQRSTUVWXYZ abcdefghijklmnopqrstuvwxyz}$

  but this can overwritten, i.e.
\begin{verbatim}
\setmathfont{Asana-Math.otf}[range=frak,Scale=MatchUppercase]
$\symfrak{ABCDEFGHIJKL...XYZ abcdefghijkl...xyz}$
\end{verbatim}
\setmathfont{Asana-Math.otf}[range=frak,Scale=MatchUppercase]
$\symfrak{ABCDEFGHIJKLMNOPQRSTUVWXYZ abcdefghijklmnopqrstuvwxyz}$

\item Sans serif alphabet is borrowed from Latin Modern,

$\symsfup{ABCDEFGHIJKLM abcdefghijk}\quad\symsfit{NOPQRSTUVWXYZ mnopqrstuvwxyz}$

  but it can be borrowed from another maths font, i.e.
\begin{verbatim}
\setmathfont{STIXTwoMath-Regular.otf}[range={sfup,sfit},
                            Scale=MatchUppercase]
$\symsfup{ABCD...klm}\quad\symsfit{NOPQ...xyz}$
\end{verbatim}
\setmathfont{STIXTwoMath-Regular.otf}[range={sfup,sfit},Scale=MatchUppercase]
$\symsfup{ABCDEFGHIJKLM abcdefghijklm}\quad
    \symsfit{NOPQRSTUVWXYZ nopqrstuvwxyz}$

\item Typewriter alphabet is borrowed from Latin Modern,

  $\symtt{ABCDEFGHIJKLMNOPQRSTUVWXYZ abcdefghijklmnopqrstuvwxyz}$

but it can be borrowed from  another Math font, i.e.
\begin{verbatim}
\setmathfont{STIXTwoMath-Regular.otf}[range=tt,Scale=MatchUppercase]
$\symtt{ABCDE...XYZ abcde...xyz}$
\end{verbatim}
\setmathfont{STIXTwoMath-Regular.otf}[range=tt,Scale=MatchUppercase]
$\symtt{ABCDEFGHIJKLMNOPQRSTUVWXYZ abcdefghijklmnopqrstuvwxyz}$
\end{itemize}

Like Latin Modern, Erewhon-Math provides only four lowercase Latin letters in
script (or calligraphic) shape:  $\mscre$, $\mscrg$, $\ell$, $\mscro$
(\verb+\mscre+, \verb+\mscrg+, \verb+\ell+, \verb+\mscro+).

All others (range \verb+"1D4B6+ to \verb+"1D4CF+) have to be borrowed
from another maths font if needed, i.e.
\begin{verbatim}
\setmathfont{LibertinusMath-Regular.otf}%
            [range="1D4B6-"1D4CF, Scale=MatchLowercase]
\end{verbatim}

\subsection{Bold variant}

In case short maths formulas have to be printed in section titles,
a \emph{limited} bold variant has been added in version~0.54. Example of usage:\\
\verb+\setmathfont{Erewhon-Math-Bold.otf}[version=bold, +\textit{options}\verb+]+
\\
\verb+\section{\mathversion{bold} Einstein’s equation $E=mc^2$}+

It is also possible to use the \verb+\boldmath+ command:\\
\verb+\setmathfont{Erewhon-Math-Regular.otf}[BoldFont=Erewhon-Math-Bold.otf]+\\
\verb+\section{\boldmath Einstein’s equation $E=mc^2$}+

\subsection{Missing symbols}

\FOTF{} does not aim at being as complete as \file{STIXTwoMath-Regular} or
\file{Cambria}, the current glyph coverage compares with TeXGyre maths 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 ErewhonMath}

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}.

\subsection{Fourier ornaments}

When loaded by \verb+\usepackage{fourier-otf}+, Erewhon-Math loads
\pkg{fourier-orns.sty} which provides all logos and ornaments available
in \FGUT.

\pkg{fourier-orns.sty} as of v2.x automatically fetches its glyphs in
a specific OpenType font with LuaTeX or XeTeX engines and from
a Type\,1 font otherwise (pdfTeX).

\begin{raggedright}
\begin{itemize}

%%%\item \showtchar{textpertenthousand}, \textit{\textpertenthousand},
%%%  \textbf{\textpertenthousand},  \textbf{\textit{\textpertenthousand}}.

\item A variant of the euro symbol: \showtchar{eurologo}, \textit{\eurologo},
  \textbf{\eurologo},  \textbf{\textit{\eurologo}}.

\item Two ``starred'' bullets: \showtchar{starredbullet}, \showtchar{decosix}.

\item Decos and logos: \showtchar{warning}, \showtchar{noway},
  \showtchar{caution}, \showtchar{bomb},\\
  \showtchar{decoone}, \showtchar{decotwo}, \showtchar{decothreeleft},
    \showtchar{decothreeright},
  \showtchar{decofourleft}, \showtchar{decofourright},
  \showtchar{floweroneleft}, \showtchar{floweroneright},\\
  \showtchar{lefthand}, \showtchar{righthand},
  \showtchar{textxswup}, \showtchar{textxswdown}.

\item Smileys: \showtchar{grimace}, \showtchar{textthing}.

\item Leaves: \showtchar{aldineleft}, \showtchar{aldineright},
   \showtchar{aldine}, \showtchar{aldinesmall}, %\\
  \showtchar{leafleft}, \showtchar{leafright}, \showtchar{leafNE},
  \showtchar{leafNW}, \showtchar{leafSE}, \showtchar{leafSW}.

\item Pilcrows: \showtchar{oldpilcrowone}, \showtchar{oldpilcrowtwo},
  \showtchar{oldpilcrowthree}, %\\
  \showtchar{oldpilcrowfour},
  \showtchar{oldpilcrowfive} aaaa, %\\
  \showtchar{oldpilcrowsix} aaaaaaaaaaa.
\end{itemize}
\end{raggedright}

All these logos and ornaments are also available as described in the
\pkg{fournier-orns} documentation: for instance, you could type
\verb+{\FourierOrns E 2 F}+ to get {\FourierOrns E 2 F}.

\vspace{\baselineskip}
Finally, some symbols are also provided in maths mode, with other names:
\begin{itemize}
\item \showmchardollar{forbidden}, \showmchardollar{beware},
      \showmchardollar{boom},
\item \showmchardollar{thething} is a \emph{QED symbol}
  for a false proof. Of course, you don't need it!
\item \showmchardollar{xswordsup} and \showmchardollar{xswordsdown} may be used
  as tags for a debated statement, or for anything else.
\end{itemize}

\section{Acknowledgements}

All glyphs in \FOTF{} are borrowed or derived either from Erewhon fonts or
\FGUT{} package.  Many thanks to Michael Sharpe and Michel Bovani for
providing these.

I am grateful to George Williams and his co-workers for providing and
maintaining FontForge and to Ulrik Vieth for his illuminating paper published
in TUGboat~2009 Volume~30 about Open Type Math.

Thanks to Oliver Natt for providing valuable feedback!

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

\end{document}

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