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

\usepackage{mathtools, array, varioref}
\usepackage[british]{babel}
%\usepackage[default,defaultsans]{lato}
\usepackage{fontspec}
\begin{filecontents}{Lato.fontspec}
\defaultfontfeatures[Lato]
  {
   UprightFont       = Lato-Regular.ttf ,
   BoldFont          = Lato-Bold.ttf ,
   ItalicFont        = Lato-Italic.ttf ,
   BoldItalicFont    = Lato-BoldItalic.ttf ,
 }
\end{filecontents}
\setmainfont{Lato}
\setsansfont{Lato}
\usepackage{realscripts}
\usepackage{fourier-orns}
\usepackage{lete-sans-math}
\setmonofont{Inconsolatazi4}[Scale=MatchLowercase, StylisticSet={2,3}]
\usepackage{subfig}
\captionsetup[subtable]{position=top}
\usepackage{microtype}
\usepackage{setspace}
\setstretch{1.10}
\usepackage{hyperref}
\hypersetup{pdftitle={Lete Sans Math User’s Guide},
            pdfauthor={Chenjing Bu \& Daniel Flipo},
            bookmarksopen,
            colorlinks
            }
\newcommand*{\hlabel}[1]{\phantomsection\label{#1}}

\newcommand*{\LAotf}{Lete~Sans~Math}
\newcommand*{\pkg}[1]{\texttt{#1}}
\newcommand*{\file}[1]{\texttt{#1}}
\newcommand*{\ttbold}[1]{\texttt{\textbf{#1}}}
\newcommand*{\opt}[1]{\texttt{#1}}
\newcommand*{\cmd}[1]{\texttt{\textbackslash #1}}
\newcommand*{\scmd}[1]{\texttt{\small\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\,\LAotf\,\decofourright}
\author{Chenjing Bu --- Daniel Flipo\\
        \url{https://github.com/abccsss/LeteSansMath}}

\newcommand*{\version}{0.60}
\setlength{\parindent}{0pt}
\setlength{\parskip}{12pt plus 3pt minus 3pt}

\begin{document}
\maketitle

\section{What is \LAotf{}?}

\LAotf{} is an OpenType maths font
meant to be used with the Lato fonts, or other sans-serif text fonts.
It requires LuaTeX or XeTeX as engine and the \pkg{unicode-math}
package\footnote{Please read the documentation \file{unicode-math.pdf}.}.

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!

Some examples%
\footnote{The second one is borrowed from the LaTeX Companion,
  3\textsuperscript{rd} edition.}:
\[
    \int_0^1 \frac{1}{x^x} \, \symup{d} x =
    \sum_{n=1}^{\infty} \frac{1}{n^n}
\]

\begin{equation*} \begin{split}
  \iiiint\limits_{\symbf{Q}}  f(w,x,y,z)\,\symup{d}w\,\symup{d}x\,\symup{d}y
                                       \,\symup{d}z
  &\leq \oint_{\symbf{\partial Q}} f'
          \left( \max \left\lbrace
            \frac{\lVert w \rVert}{\lvert w^{2} + x^{2} \rvert} ;
            \frac{\lVert z \rVert}{\lvert y^{2} + z^{2} \rvert} ;
            \frac{\lVert w \oplus z \rVert}{\lvert x \oplus y \rvert}
           \right\rbrace \right)                                    \\
  &\precapprox \biguplus_{\mathbb{Q} \Subset \bar{\symbf{Q}}}
    \left[ f^{\ast}
      \left(
        \frac{\left\lmoustache\mathbb{Q}(t)\right\rmoustache}{\sqrt{1 - t^{2}}}
      \right)
    \right]_{t=\alpha}^{t=\vartheta} - ( \Delta + \nu -v )^{3}
\end{split} \end{equation*}

\section{Usage}

\subsection{Calling \cmd{setmathfont}}

A basic call for \LAotf{} would be:
\begin{verbatim}
\usepackage{unicode-math}
\setmathfont{LeteSansMath.otf}  % Call by file name or
\setmathfont{Lete Sans Math}    % Call by font name
\end{verbatim}
this loads \LAotf{} 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.

%\enlargethispage*{1.0\baselineskip}
Please note that the text fonts have to be chosen separately, f.i.:
\label{sec:setfont}
\begin{verbatim}
\setsansfont{Lato}[Extension = .ttf,
    UprightFont =     *-Regular,
    BoldFont =        *-Bold,
    ItalicFont =      *-Italic,
    BoldItalicFont =  *-BoldItalic]
\end{verbatim}
otherwise you would get Latin Modern for text fonts.

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

As an alternative to load \LAotf{} you can type:\\[.5\baselineskip]
\verb+\usepackage[ +\textit{options}
\footnote{Possible \textit{options} are \opt{tight}, \opt{Scale=} or
  any of the options described in sections~\ref{ssection-um},
  \ref{ssection-cv} and \ref{ssection-ss}.}%
\verb+ ]{lete-sans-math}+\\[.5\baselineskip]
it loads \pkg{unicode-math} with the default options, sets \LAotf{}
as maths font and 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
  all \pkg{latexsym} or AMS commands are also available;
\item it defines specific maths characters like \showmchar{BbbDelta},
  \showmchar{parallelslant},
  \showmchar{shortparallelslant}, etc.;
\item it provides an option \opt{tight} which reduces spacing
  (\cmd{thinmuskip}, \cmd{medmuskip} and \cmd{thickmuskip}) in maths mode.
\end{enumerate}

Please note that the \pkg{lete-sans-math} package does not load any text fonts.
The Lato text fonts can be loaded directly (see section~\ref{sec:setfont}),
or via the \pkg{lato} package%
\footnote{The \pkg{lato} package loads all available weights,
  \texttt{Hairline} to \texttt{Black}, hence loading takes significantly
  longer…}
---see this package’s documentation, file \file{lato.pdf}, for all the
available options: \\
\verb+\usepackage[default]{lato}+\\
will load the Lato text fonts as main (roman) font while \\
\verb+\usepackage[defaultsans]{lato}+\\
will load the Lato text fonts as sans font (use both options if necessary).
Consider loading \pkg{realscripts.sty} which
redefines \verb+\textsuperscript+ to output the \emph{real} superscripts
available with the Lato fonts: M\textsuperscript{r}, M\textsuperscript{lle},
N\textsuperscript{2} instead of \emph{faked} ones,
M\fakesuperscript{r}, M\fakesuperscript{lle}, N\fakesuperscript{2}.

The \pkg{lete-sans-math} also provides a \opt{Scale=}\textsl{<decimal>} option
meant to be used to load the \LAotf{} font together with text fonts other
than Lato, while keeping the advantages 1. to~4. pointed in the preceding
list, f.i.

\verb+\usepackage[Scale=0.98]{lete-sans-math}+


\section{What is provided?}

\LAotf{} provides all common \pkg{unicode-math} glyphs plus all glyphs
available in the \pkg{amssymb} and \pkg{latexsym} packages.  Therefore,
the latter two packages \emph{should not} be loaded as they might override
\LAotf{} glyphs.

A full list of available glyphs is shown in file \file{unimath-lete.pdf} which
also shows the coverage of other sans-serif maths fonts compared to
the serif maths fonts NewComputerModern and Cambria.

\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, they can
be added to the \cmd{setmathfont} call as well%
\footnote{IMHO it is easier to add \emph{all options} to the \cmd{setmathfont}
  command.}, for example:

\verb+\setmathfont{LeteSansMath.otf}[math-style=french,partial=upright]+

will print for the code

\verb|\[ \frac{\partial f}{\partial x} = \alpha \symbf{V} + a\nabla\Gamma|\\
\verb|                                 + \symbf{\beta}\symbf{M} \]|

\setmathfont{LeteSansMath.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{LeteSansMath.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}

\LAotf{} provides nine ``Character Variants'' options, listed on
table~\vref{cv}, to choose between different glyphs for Greek characters
and some others.

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:

\verb+\setmathfont{LeteSansMath.otf}[CharacterVariant={3,6}]+

\begin{table}[ht]
  \centering  \caption{Character variants.}
  \hlabel{cv}
  \begin{tabular}{@{}>{\ttfamily}lccl@{}}
    \hline
           & Default       & Variant          & Name\\
    \hline
      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 & $g$           & $\mitvarg$       & g \\
    \hline
  \end{tabular}
\end{table}

This  works for all shapes and weights of these characters: f.i.\ %
\verb+$\symbf{\epsilon}$+, \verb+$\symbf{\phi}$+ are output as
\setmathfont{LeteSansMath.otf}[CharacterVariant={3,6}]$\symbf{\epsilon}$,
$\symbf{\phi}$ instead of
\setmathfont{LeteSansMath.otf}$\symbf{\epsilon}$, $\symbf{\phi}$.
If \opt{math-style=french} has been chosen, \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}: \pkg{amsmath} provides two different glyphs
(italic $h$ with horizontal or diagonal stroke) while \pkg{unicode-math}
defines \cmd{hbar} as \cmd{hslash} (U+210F).
\pkg{lete-sans-math} 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}

\LAotf{} provides seven ``Stylistic Sets'' options to choose between different
glyphs for families of maths symbols.

\ttbold{StylisticSet=1}, alias%
\footnote{These \texttt{Style} aliases are provided by
\file{lete-sans-math.sty}.}
\setmathfont{LeteSansMath}[range={cal,bfcal},StylisticSet=1]
\ttbold{Style=mathcal} is new to version~0.60.
It forces commands \verb|\mathcal{}| and \verb|\mathscr{}|
to print $\mathcal{ABC}$ (former shape) instead of $\mathscr{ABC}$
(the new default in v.~0.60).
Please note that \pkg{unicode-math} recommends to use \cmd{symcal} and
\cmd{symscr} instead of \cmd{mathcal} and \cmd{mathscr}.

If you want to use both commands \verb|$\symcal{ABC}$| and
\verb|$\symscr{ABC}$| to print $\symcal{ABC}$ and $\symscr{ABC}$
respectively, you can use \pkg{unicode-math}’s option \verb|range| this way%
\footnote{The \pkg{unicode-math} package is not yet able to make use of Unicode
Variation Selectors U+FE00 and U+FE01 to switch between `cal’ and `scr’
variants but these selectors are already implemented in \LAotf.}%
:\\
\verb|\setmathfont{LeteSansMath}[|\textit{your options}\verb|]|\\
\verb|\setmathfont{LeteSansMath}[range={cal,bfcal},StylisticSet=1]|\\
Both lines are mandatory: the first one loads {\LAotf} while the
second one modifies \verb|\mathcal| and \verb|\symcal| commands’ output.

\addtocounter{footnote}{-1}
\ttbold{StylisticSet=4}, alias\footnotemark{}
\ttbold{Style=leqslant}, converts inequalities into their slanted  variants,
see table~\vref{ss04}.

\addtocounter{footnote}{-1}
\ttbold{StylisticSet=5}, alias\footnotemark{}
\ttbold{Style=smaller}, converts some symbols
into their smaller variants, see table~\vref{ss05}.
\begin{table}[ht]
  \centering
  \caption{Stylistic Sets 4 and 5}
  \addtocounter{table}{-1}% \subfloat steps counter table?
  \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{nleqq}       & $\nleqq$       & $\nleqqslant$ \\
      \cmd{ngeqq}       & $\ngeqq$       & $\ngeqqslant$ \\
      \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}
\stepcounter{table}% \subfloat steps counter table?

\addtocounter{footnote}{-1}
\ttbold{StylisticSet=6}, alias\footnotemark{}
\ttbold{Style=subsetneq}, converts some
inclusion symbols, as shown in table~\vref{ss06}.

\addtocounter{footnote}{-1}
\ttbold{StylisticSet=7}, alias\footnotemark{}
\ttbold{Style=parallelslant}, converts
``parallel'' symbols into their slanted variants, see table~\vref{ss07}.
\begin{table}[ht]
  \centering
  \caption{Stylistic Sets 6 and 7}
  \addtocounter{table}{-1}% \subfloat steps counter table?
  \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}
\stepcounter{table}% \subfloat steps counter table?

\addtocounter{footnote}{-1}
\ttbold{StylisticSet=8}, alias\footnotemark{}
\ttbold{Style=upint}, converts integrals signs into their upright
variants, see table~\vref{ss08}.
\begin{table}[ht]
  \let\DS\displaystyle
  \centering
  \caption{Style=upint\quad  (+ss08)}\hlabel{ss08}
  \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}   &$\DS\int$ &$\DS\iint$ &$\DS\iiint$ &$\DS\iiiint$
                   &$\DS\oint$ &$\DS\oiint$ &$\DS\oiiint$
    \\[\baselineskip]
    \setmathfont{LeteSansMath.otf}[Style=upint]
    Upright\rule[-15pt]{0pt}{30pt}   &$\DS\int$ &$\DS\iint$  &$\DS\iiint$ &$\DS\iiiint$
                   &$\DS\oint$ &$\DS\oiint$  &$\DS\oiiint$ \\
    \hline
  \end{tabular}\\[\baselineskip]
  \setmathfont{LeteSansMath.otf}
  \begin{tabular}[t]{@{}l*{4}c@{}}
    \hline
    Command  &\scmd{intclockwise}  &\scmd{awint}
                   &\scmd{varointclockwise}  &\scmd{ointctrclockwise} \\
    \hline
    Default\rule[-15pt]{0pt}{35pt} &$\DS\intclockwise$ &$\DS\awint$
                   &$\DS\varointclockwise$ &$\DS\ointctrclockwise$ \\
    \setmathfont{LeteSansMath.otf}[Style=upint]
    Upright\rule[-15pt]{0pt}{30pt}  &$\DS\intclockwise$ &$\DS\awint$
                   &$\DS\varointclockwise$  &$\DS\ointctrclockwise$ \\
    \hline
  \end{tabular}
\end{table}
\setmathfont{LeteSansMath.otf}

To enable Stylistic Sets  4 and 8 for \LAotf{}, you can enter\\
\verb+\setmathfont{LeteSansMath.otf}[StylisticSet={4,8}]  or+\\
\verb+\usepackage[Style={leqslant,upint}]{lete-sans-math}+

then, \verb+\[x\leq y \quad \int_{a}^{b} f(x) \;\symup{d}x\]+
will print as
\setmathfont{LeteSansMath.otf}[StylisticSet={4,8}]
\[x\leq y \quad \int_{a}^{b} f(x) \;\symup{d}x\]
instead of
\setmathfont{LeteSansMath.otf}
\[x\leq y \quad \int_{a}^{b} f(x) \;\symup{d}x\]

\ttbold{StylisticSet=9}, alias%
\footnote{These \texttt{Style} aliases are provided by
\file{lete-sans-math.sty}.}
\ttbold{Style=vertneg}, converts slanted negations into vertical ones.
see table~\vref{ss09}.

\begin{table}[ht]
  \let\DS\displaystyle
  \centering
  \caption{Style=vertneg\quad  (+ss09)}\hlabel{ss09}
  \begin{tabular}[t]{@{}lcc@{}}
    \hline
      Command        & Default     & Variant \\
    \hline
      \cmd{notin}    & $\notin$    & $\vertnotin$  \\
      \cmd{nni}      & $\nni$      & $\vertnni$  \\
      \cmd{ne}       & $\ne$       & $\vertne$ \\
      \cmd{nequiv}   & $\nequiv$   & $\vertnequiv$ \\
      \cmd{nsim}     & $\nsim$     & $\vertnsim$ \\
      \cmd{nsimeq}   & $\nsimeq$   & $\vertnsimeq$ \\
      \cmd{ncong}    & $\ncong$    & $\vertncong$ \\
      \cmd{nasymp}   & $\nasymp$   & $\vertnasymp$ \\
      \cmd{ngtr}     & $\ngtr$     & $\vertngtr$  \\
      \cmd{nless}    & $\nless$    & $\vertnless$ \\
      \cmd{ngeq}     & $\ngeq$     & $\vertngeq$  \\
      \cmd{nleq}     & $\nleq$     & $\vertnleq$ \\
      \cmd{gneqq}    & $\gneqq$    & $\gvertneqq$ \\
      \cmd{lneqq}    & $\lneqq$    & $\lvertneqq$  \\
  \hline
  \end{tabular}
  \hfill
  \begin{tabular}[t]{@{}lcc@{}}
    \hline
      Command            & Default         & Variant \\
    \hline
      \cmd{ngtrless}     & $\ngtrless$     & $\vertngtrless$ \\
      \cmd{nlessgtr}     & $\nlessgtr$     & $\vertnlessgtr$ \\
      \cmd{nlesssim}     & $\nlesssim$     & $\vertnlesssim$ \\
      \cmd{ngtrsim}      & $\ngtrsim$      & $\vertngtrsim$ \\
      \cmd{nprec}        & $\nprec$        & $\vertnprec$ \\
      \cmd{nsucc}        & $\nsucc$        & $\vertnsucc$ \\
      \cmd{npreccurlyeq} & $\npreccurlyeq$ & $\vertnpreccurlyeq$ \\
      \cmd{nsucccurlyeq} & $\nsucccurlyeq$ & $\vertnsucccurlyeq$ \\
      \cmd{nsubset}      & $\nsubset$      & $\vertnsubset$ \\
      \cmd{nsupset}      & $\nsupset$      & $\vertnsupset$ \\
      \cmd{nsubseteq}    & $\nsubseteq$    & $\vertnsubseteq$ \\
      \cmd{nsupseteq}    & $\nsupseteq$    & $\vertnsupseteq$ \\
      \cmd{ntrianglelefteq}  & $\ntrianglelefteq$  & $\vertntrianglelefteq$ \\
      \cmd{ntrianglerighteq} & $\ntrianglerighteq$ & $\vertntrianglerighteq$ \\
   \hline
  \end{tabular}
\end{table}


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

To get oldstyle numbers in maths, the feature \texttt{+onum} is available:

\verb+\setmathfont{LeteSansMath.otf}[Numbers=OldStyle]  or+\\
\verb+\usepackage[Style=fulloldstyle]{lete-sans-math}+

\setmathfont{LeteSansMath.otf}[Numbers=OldStyle]
$0123456789, \symbf{0123456789}$
\setmathfont{LeteSansMath.otf}

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

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

Various wide accents and extensible arrows 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}
  \[\underrightharpoondown{v}\quad \underrightharpoondown{M}\quad
    \underrightharpoondown{vv}\quad \underrightharpoondown{AB}\quad
    \underrightharpoondown{ABC}\quad \underrightharpoondown{ABCD}\quad
    \underrightharpoondown{ABCDEFGH}.
  \]
  \[\underleftharpoondown{v}\quad \underleftharpoondown{M}\quad
    \underleftharpoondown{vv}\quad \underleftharpoondown{AB}\quad
    \underleftharpoondown{ABC}\quad \underleftharpoondown{ABCD}
    \quad \underleftharpoondown{ABCDEFGH}.
  \]
\end{itemize}

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

A wide range of extensible vertical delimiters is provided:
\[\left/
  \begin{pmatrix}  a_{1} \\ a_{2} \\  a_{3}  \end{pmatrix}
  \begin{bmatrix}  a_{1} \\ a_{2} \\  a_{3}  \end{bmatrix}
  \begin{Bmatrix}  a_{1} \\ a_{2} \\  a_{3}  \end{Bmatrix}
  \begin{vmatrix}  a_{1} \\ a_{2} \\  a_{3}  \end{vmatrix}
  \begin{Vmatrix}  a_{1} \\ a_{2} \\  a_{3}  \end{Vmatrix}
  \left\lVvert\begin{array}{c} a_{1} \\ a_{2} \\  a_{3} \end{array}\right\Vvert
  \left\lceil \begin{array}{c} a_{1} \\ a_{2} \\  a_{3} \end{array}\right\rceil
  \left\lfloor\begin{array}{c} a_{1} \\ a_{2} \\  a_{3} \end{array}\right\rfloor
  \left\lBrack\begin{array}{c} a_{1} \\ a_{2} \\  a_{3} \end{array}\right\rBrack
  \left\langle\begin{array}{c} a_{1} \\ a_{2} \\  a_{3} \end{array}\right\rangle
  \left\lAngle\begin{array}{c} a_{1} \\ a_{2} \\  a_{3} \end{array}\right\rAngle
  \right\backslash \]

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

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

  but this can overwritten, i.e.

\verb+\setmathfont{Asana-Math.otf}[range=frak,Scale=MatchUppercase]+\\
\verb+$\symfrak{ABCDEFGHIJKL...XYZ abcdefghijkl...xyz}$+

%\verb+\setmathfont{Asana-Math.otf}[range=frak,Scale=MatchUppercase]+\\
%\verb+$\symfrak{ABCDEFGHIJKLMNOPQRSTUVWXYZ abcdefghijklmnopqrstuvwxyz}$+

\item Typewriter alphabet is sans-serif: $\symtt{0123456789}$

  $\symtt{ABCDEFGHIJKLMNOPQRSTUVWXYZ abcdefghijklmnopqrstuvwxyz}$

but it can be borrowed from  another maths font.

%\verb+\setmathfont{STIXTwoMath-Regular.otf}[range=tt,+\\
%\verb+                                      Scale=MatchUppercase]+\\
%\verb+$\symtt{ABCDE...XYZ abcde...xyz}$+

%\verb+\setmathfont{STIXTwoMath-Regular.otf}[range=tt,Scale=MatchUppercase]+\\
%\verb+$\symtt{ABCDEFGHIJKLMNOPQRSTUVWXYZ abcdefghijklmnopqrstuvwxyz}$+
\end{itemize}

Like Latin Modern, \pkg{lete-sans-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.

\verb+\setmathfont{LibertinusMath-Regular.otf}%+\\
\verb+            [range="1D4B6-"1D4CF, Scale=MatchLowercase]+

\subsection{Bold variant}

\setmathfont{LeteSansMath.otf}[BoldFont=LeteSansMath-Bold.otf]
In case short maths formulas have to be printed in section titles,
a \emph{limited} bold variant is provided. Example of usage:\quad
\textbf{\boldmath Einstein’s equation $E=mc^2$}

\verb+\setmathfont{LeteSansMath-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%
\footnote{The \cmd{boldmath} command works out of the box when
  \pkg{lete-sans-math.sty} is loaded.}:

\verb+\setmathfont{LeteSansMath.otf}[BoldFont=LeteSansMath-Bold.otf]+\\
\verb+\section{\boldmath Einstein’s equation $E=mc^2$}+

\subsection{Missing symbols}

\LAotf{} is fairly complete (see file \file{unimath-lete.pdf}),
if you happen to need some of the few missing glyphs you can borrow them from
a more complete font, say \file{New Computer Modern}. For instance if you need
Italic Blackboard Bold (U+2145 to U+2149) you could try:

\verb+\setmathfont{NewCMMath-Book.otf}[range={"2145-"2149},Scale=1.05]+

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 -t U+2145}'', see the manpage or \file{albatross-manual.pdf}.

\section{Acknowledgements}

Many thanks to \href{https:www.typoland.com}{Łukasz Dziedzic} for providing
the Lato text fonts in OpenType format.

We are 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 OpenType Maths.


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

\end{document}

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