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+\documentclass[a4paper]{article}
+% \usepackage{textcomp}
+\usepackage{hyperref}
+% \usepackage{bookmark}
+\usepackage{parskip}
+
+% Declare the font encoding and Greek LICR definitions:
+\usepackage[LGR]{fontenc}
+
+% Set up Latin Modern OpenType unicode font
+\usepackage{fontspec}
+
+\usepackage[greek,english]{babel}
+% \languageattribute{greek}{polutoniko}
+% \languageattribute{greek}{ancient}
+
+% use LGR (8-bit CB-fonts) instead of Unicode fonts for Greek:
+\addto{\extrasgreek}{\greektext}
+% Alternative:
+% \renewcommand*{\greekscript}{\fontencoding{LGR}\selectfont}
+
+\begin{document}
+
+\title{XeTeX/LuaTeX with LGR fonts}
+\author{Günter Milde}
+\date{2020/11/10}
+\maketitle
+
+The babel option «greek» activates the support for the Greek language
+defined in «greek.ldf» (source «greek.dtx»).
+
+Typesetting Greek texts requires a font containing Greek letters. With the
+XeTeX or LuaTeX engines, the user must ensure that the selected font
+contains the required glyphs (the default Latin Modern fonts miss them).
+
+Latin Modern can be combined with the matching CB-Greek 8-bit font. For the
+setup, see the preamble of this document \texttt{test-unicode-lgr.tex}
+
+Caveat: Currently, hyphenation does not work with this setup. Use it only
+for short Greek quotes or as a last ressort.
+
+\section{Language Switch}
+
+The declaration \verb|\selectlanguage| switches between languages. With
+XeTeX or LuaTeX and LGR as \verb|\greekfontencoding|, Unicode input is not
+possible. Instead, use the Latin transliteration or LICR macros:
+
+\begin{quote}
+  \selectlanguage{greek}
+  T'i f'hic? <Id`wn >enj'ede pa~id'' >eleuj'eran\\
+  t`ac plhs'ion N'umfac stefano~usan, S'wstrate,\\
+  >er~wn 'ap~hljec e>uj'uc?
+\end{quote}
+
+The macro \verb|\foreignlanguage| sets its second argument in the specified
+language. This is intended for short text parts like
+\foreignlanguage{greek}{Biblioj'hkh}.
+
+\section{Font Encoding}
+
+Switching to a font encoding supporting the Greek script is possible without
+switching the text language using the declarations \verb|\greekscript| or
+\verb|\greektext| (always LGR) and the macros \verb|\ensuregreek| or
+\verb|\textgreek|. These commands do not start a new paragraph.
+
+The Babel core defines the declaration \verb|\latintext| and the command
+\verb|\textlatin| to switch to the T1 or OT1 font encoding or typeset the
+argument using this encoding. \texttt{greek.ldf} adds a test for the Unicode
+font encodings TU, EU1, and EU2. Here, \verb|\latinencoding| is
+\latinencoding.
+
+With Unicode fonts, the macros \verb|\greektext| and \verb|\textgreek| are
+only defined, if the LGR font encoding is loaded via the \texttt{fontenc}
+package (see test-unicode-lgr.tex).
+
+% don't change the font encoding.
+With LGR, Latin characters in Greek text parts are typeset as Greek characters
+according to the Latin transcription defined in LGR.%
+
+\begin{quote}
+  \greektext F\'ilwn to\~u \textlatin{TeX} (EFT) --
+  \latintext{Friends (\textgreek{F\'ilwn}) of TeX.}%
+\end{quote}
+
+\section{MakeUppercase, MakeLowercase}
+
+Capital Greek letters have diacritics (except the dialytika and sub-iota) to
+the left (instead of above) and drop them in uppercase.
+
+Tonos and dasia mark a \emph{hiatus} (break-up of a diphthong) if placed on
+the first vowel of a diphthong (\textgreek{\'ai, \'au, \'ei, \'>ai, \'>au,
+\'>ei}). A dialytika must be placed on the second vowel if they are dropped.
+(\foreignlanguage{greek}{\MakeUppercase{\'ai, \'au, \'ei, \'>ai, \'>au,
+\'>ei}}).
+
+\section{LICR Macros}
+
+Babel defines macros for several autogenerated strings so that they may
+appear in the choosen language. \emph{babel-greek} uses LICR macros in
+order to let the string macros work independent of the font encoding.
+
+If \texttt{fontspec} is loaded before babel, babel-greek loads Greek LICR
+for TU from the file \texttt{tuenc-greek.def} provided with
+\emph{greek-fontenc} since version~0.14 (2020-02-28).
+
+\subsection{Hiatus}
+
+The «hiatus» feature works with macro input:
+
+\selectlanguage{greek}
+% from teubner: άυλος/ΑΫΛΟΣ
+\acctonos\textalpha\textupsilon\textlambda\textomicron\textfinalsigma{}
+$\mapsto$
+\MakeUppercase{\acctonos\textalpha\textupsilon\textlambda\textomicron\textfinalsigma},
+\'>\textalpha\textupsilon\textlambda\textomicron\textfinalsigma{} $\mapsto$
+\MakeUppercase{\'>\textalpha\textupsilon\textlambda\textomicron\textfinalsigma},
+% from http://diacritics.typo.cz/index.php?id=69  μάινα -> ΜΑΪΝΑ
+\textmu\acctonos\textalpha\textiota\textnu\textalpha{} $\mapsto$
+\MakeUppercase{\textmu\acctonos\textalpha\textiota\textnu\textalpha},
+% from  http://de.wikipedia.org/wiki/Neugriechische_Orthographie#Das_Trema
+% κέικ, ἀυπνία/αϋπνία
+\textkappa\acctonos\textepsilon\textiota\textkappa $\mapsto$
+\MakeUppercase{\textkappa\acctonos\textepsilon\textiota\textkappa},
+\accpsili\textalpha\textupsilon\textpi\textnu\'\textiota\textalpha{} $\mapsto$
+\MakeUppercase{\accpsili\textalpha\textupsilon\textpi\textnu\'\textiota\textalpha}.
+\selectlanguage{english}
+
+\subsection{Captions}
+
+\selectlanguage{greek}
+\prefacename,
+\refname,
+\abstractname,
+\bibname,
+\chaptername,
+\appendixname,
+\contentsname,
+\listfigurename ,
+\listtablename,
+\indexname,
+\figurename,
+\tablename,
+\partname,
+\enclname,
+\ccname,
+\headtoname,
+\pagename,
+\seename,
+\alsoname,
+\proofname,
+\glossaryname
+\selectlanguage{english}
+
+Test correct upcasing (dropping of accents):
+
+\selectlanguage{greek}
+\MakeUppercase{
+\prefacename,
+\refname,
+\abstractname,
+\bibname,
+\chaptername,
+\appendixname,
+\contentsname,
+\listfigurename,
+\listtablename,
+\indexname,
+\figurename,
+\tablename,
+\partname,
+\enclname,
+\ccname,
+\headtoname,
+\pagename,
+\seename,
+\alsoname,
+\proofname,
+\glossaryname
+}
+\selectlanguage{english}
+
+\subsection{Months}
+
+\selectlanguage{greek}
+\newcounter{foo}
+\stepcounter{foo} \month=\value{foo} \today \\
+\stepcounter{foo} \month=\value{foo} \today \\
+\stepcounter{foo} \month=\value{foo} \today \\
+\stepcounter{foo} \month=\value{foo} \today \\
+\stepcounter{foo} \month=\value{foo} \today \\
+\stepcounter{foo} \month=\value{foo} \today \\
+\stepcounter{foo} \month=\value{foo} \today \\
+\stepcounter{foo} \month=\value{foo} \today \\
+\stepcounter{foo} \month=\value{foo} \today \\
+\stepcounter{foo} \month=\value{foo} \today \\
+\stepcounter{foo} \month=\value{foo} \today \\
+\stepcounter{foo} \month=\value{foo} \today \\
+\selectlanguage{english}
+
+\section{Greek Numerals}
+
+See greek.pdf for the formation rules of Greek numerals.
+Some examples:
+
+\selectlanguage{greek}
+
+\greeknumeral{1},
+\greeknumeral{2},
+\greeknumeral{3},
+\greeknumeral{4},
+\greeknumeral{5},
+\greeknumeral{6},
+\greeknumeral{7},
+\greeknumeral{8},
+\greeknumeral{9},
+\greeknumeral{10},
+\greeknumeral{11},
+\greeknumeral{12},
+\greeknumeral{20},
+\greeknumeral{345},
+\greeknumeral{500},
+\greeknumeral{1997},
+\greeknumeral{2013},
+
+\Greeknumeral{1},
+\Greeknumeral{2},
+\Greeknumeral{3},
+\Greeknumeral{4},
+\Greeknumeral{5},
+\Greeknumeral{6},
+\Greeknumeral{7},
+\Greeknumeral{8},
+\Greeknumeral{9},
+\Greeknumeral{10},
+\Greeknumeral{11},
+\Greeknumeral{12},
+\Greeknumeral{20},
+\Greeknumeral{345},
+\Greeknumeral{500},
+\Greeknumeral{1997},
+\Greeknumeral{2013},
+
+
+\selectlanguage{english}
+Enumerated lists use Greek characters/numerals in the second and fourth level:
+
+\selectlanguage{greek}
+\begin{enumerate}
+  \item \textlatin{item} 1
+  \begin{enumerate}
+    \item \textlatin{item} 1.1
+    \begin{enumerate}
+      \item \textlatin{item} 1.1.1
+       \begin{enumerate}
+         \item \textlatin{item} 1.1.1.1
+         \item \textlatin{item} 1.1.1.2
+       \end{enumerate}
+      \item \textlatin{item} 1.1.2
+    \end{enumerate}
+  \end{enumerate}
+\end{enumerate}
+\selectlanguage{english}
+
+\end{document}