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\documentclass[a4paper]{article}
% \usepackage{textcomp}
\usepackage{hyperref,bookmark}
\usepackage{parskip}

\usepackage{fontspec}
% \usepackage{libertineotf}
\setmainfont{Linux Libertine O}
\setsansfont{Linux Biolinum O}
% \setmainfont{DejaVu Serif}

% Declare the font encoding and Greek LICR definitions:
\usepackage{textalpha}[2013/09/11]

\usepackage[greek,english]{babel}
\languageattribute{greek}{polutoniko}

\DeclareTextCommandDefault{\ensuregreek}{\textgreek}

\begin{document}


\section*{Greek support for Babel with XeTeX/LuaTeX}

The babel option ``greek'' activates the support for the Greek language
defined in the file ``greek.ldf'' (source ``greek.dtx'').

Typesetting Greek texts requires a font containing Greek letters. With the
XeTeX or LuaTeX engines, the user should ensure that the choosen font
contains the required glyphs (the default Latin Modern fonts miss them).
Examples for suitable fonts are the ``Deja Vu'', ``Linux Libertine'', or
``Free Serif'' OpenType fonts.

\section{Language Switch}

The declaration \verb|\selectlanguage| switches between languages.


\begin{quote}
  \selectlanguage{greek}
  Τί φήις;  ̔Ιδὼν ἐνθέδε παῖδ’ ἐλευθέραν
  τὰς πλησίον Νύμφας στεφανοῦσαν, Σώστρατε,
  ἐρῶν άπῆλθες εὐθύς;
\end{quote}

The macro \verb|\foreignlanguage| sets its second argument in the specified
language. This is intended for short text parts like
\foreignlanguage{greek}{Βιβλιοθήκη}.

\section{Font Encoding}

In Greek text parts, the font encoding is automatically set to LGR if an
8-bit TeX engine is used. With XeTeX or LuaTeX, the macros
\verb|\greektext| and \verb|\textgreek| don't change the font encoding.
Latin characters can be used in Greek text parts,
input via the Latin transcription defined in LGR is not possible.%
\footnote{%
  The \emph{xunicode} package provides with the \texttt{tipa} emulation an
  example how this could be achieved if really required.
  }

\begin{quote}
  \greektext Φίλων τοῦ \textlatin{TeX} (ΕΦΤ) --
  \latintext Friends (\textgreek{F\'ilwn}) of TeX.%
  \footnote{Compare the printout to the similar example in test-greek.pdf.}
\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, e.g.
\ensuregreek{μαΐστρος $\mapsto$ \MakeUppercase{μαΐστρος}}.

Tonos and dasia mark a \emph{hiatus} (break-up of a diphthong) if placed on
the first vowel of a diphtong ((άι, άυ, έι, ἄι, ἄυ, ἔι). A dialytika must be
placed on the second vowel if they are dropped. This does not work (yet?)
with Unicode literals (\foreignlanguage{greek}{\MakeUppercase{άι, άυ, έι,
ἄι, ἄυ, ἔι}}). (See section «hiatus» below for a test with LICR macros.)

The following subsections test MakeUppercase and MakeLowercase with all
characters defined in lgrenc.dfu:

\subsection{Greek and Coptic}

\newcommand{\GreekAndCoptic}{
ʹ͵ͺ; ΄ ΅Ά·ΈΉΊΌΎΏΐΑΒΓΔΕΖΗΘΙΚΛΜΝΞΟΠΡΣΤΥΦΧΨΩΪΫϘϚϜϠ}
\newcommand{\greekandcoptic}{
άέήίΰαβγδεζηθικλμνξοπρςστυφχψωϊϋόύώϙϛϝϟϡ}

Characters of the Greek and Coptic Unicode Block:

\begin{quote}
  \GreekAndCoptic\\
  \greekandcoptic
\end{quote}

MakeUppercase:

\begin{quote}
  \MakeUppercase{\GreekAndCoptic}\\
  \MakeUppercase{\greekandcoptic}
\end{quote}

Letters upcased, diacritics except dialytika dropped. OK.

Ϡ (Sampi) $\mapsto$ \MakeUppercase{Ϡ} (Kappa) and
ϡ (sampi) $\mapsto$ \MakeUppercase{ϡ} (Rho) is a bug
in xgreek-fixes.def from the polyglossia package.
% This is fixed in xgreek.sty and reported to the polyglossia author.

MakeLowercase:

\begin{quote}
  \MakeLowercase{\GreekAndCoptic}\\
  \MakeLowercase{\greekandcoptic}
\end{quote}

The lowercase of Σ is σ (GREEK SMALL LETTER SIGMA).\footnote{%
With LGR, it is \texttt{\textbackslash textautosigma}.}
The lowercase of Ϛ (GREEK LETTER STIGMA) is \MakeLowercase{Ϛ}.

% \newpage

\subsection{Greek extended}

Characters of the Greek extended Unicode block:

\selectlanguage{greek}
ἀ ἁ ἂ ἃ ἄ ἅ ἆ ἇ Ἀ Ἁ Ἂ Ἃ Ἄ Ἅ Ἆ Ἇ \\
ἐ ἑ ἒ ἓ ἔ ἕ     Ἐ Ἑ Ἒ Ἓ Ἔ Ἕ     \\
ἠ ἡ ἢ ἣ ἤ ἥ ἦ ἧ Ἠ Ἡ Ἢ Ἣ Ἤ Ἥ Ἦ Ἧ \\
ἰ ἱ ἲ ἳ ἴ ἵ ἶ ἷ Ἰ Ἱ Ἲ Ἳ Ἴ Ἵ Ἶ Ἷ \\
ὀ ὁ ὂ ὃ ὄ ὅ     Ὀ Ὁ Ὂ Ὃ Ὄ Ὅ     \\
ὐ ὑ ὒ ὓ ὔ ὕ ὖ ὗ   Ὑ   Ὓ   Ὕ   Ὗ \\
ὠ ὡ ὢ ὣ ὤ ὥ ὦ ὧ Ὠ Ὡ Ὢ Ὣ Ὤ Ὥ Ὦ Ὧ \\
ὰ ά ὲ έ ὴ ή ὶ ί ὸ ό ὺ ύ ὼ ώ     \\
ᾀ ᾁ ᾂ ᾃ ᾄ ᾅ ᾆ ᾇ ᾈ ᾉ ᾊ ᾋ ᾌ ᾍ ᾎ ᾏ \\
ᾐ ᾑ ᾒ ᾓ ᾔ ᾕ ᾖ ᾗ ᾘ ᾙ ᾚ ᾛ ᾜ ᾝ ᾞ ᾟ \\
ᾠ ᾡ ᾢ ᾣ ᾤ ᾥ ᾦ ᾧ ᾨ ᾩ ᾪ ᾫ ᾬ ᾭ ᾮ ᾯ \\
ᾰ ᾱ ᾲ ᾳ ᾴ   ᾶ ᾷ Ᾰ Ᾱ Ὰ Ά ᾼ ᾽ ι ᾿ \\
῀ ῁ ῂ ῃ ῄ   ῆ ῇ Ὲ Έ Ὴ Ή ῌ ῍ ῎ ῏ \\
ῐ ῑ ῒ ΐ     ῖ ῗ Ῐ Ῑ Ὶ Ί   ῝ ῞ ῟ \\
ῠ ῡ ῢ ΰ ῤ ῥ ῦ ῧ Ῠ Ῡ Ὺ Ύ Ῥ ῭ ΅ ` \\
    ῲ ῳ ῴ   ῶ ῷ Ὸ Ό Ὼ Ώ ῼ ´ ῾
\selectlanguage{english}

MakeUppercase:

\selectlanguage{greek}

\MakeUppercase{ ἀ ἁ ἂ ἃ ἄ ἅ ἆ ἇ Ἀ Ἁ Ἂ Ἃ Ἄ Ἅ Ἆ Ἇ }\\
\MakeUppercase{ ἐ ἑ ἒ ἓ ἔ ἕ     Ἐ Ἑ Ἒ Ἓ Ἔ Ἕ     }\\
\MakeUppercase{ ἠ ἡ ἢ ἣ ἤ ἥ ἦ ἧ Ἠ Ἡ Ἢ Ἣ Ἤ Ἥ Ἦ Ἧ }\\
\MakeUppercase{ ἰ ἱ ἲ ἳ ἴ ἵ ἶ ἷ Ἰ Ἱ Ἲ Ἳ Ἴ Ἵ Ἶ Ἷ }\\
\MakeUppercase{ ὀ ὁ ὂ ὃ ὄ ὅ     Ὀ Ὁ Ὂ Ὃ Ὄ Ὅ     }\\
\MakeUppercase{ ὐ ὑ ὒ ὓ ὔ ὕ ὖ ὗ   Ὑ   Ὓ   Ὕ   Ὗ }\\
\MakeUppercase{ ὠ ὡ ὢ ὣ ὤ ὥ ὦ ὧ Ὠ Ὡ Ὢ Ὣ Ὤ Ὥ Ὦ Ὧ }\\
\MakeUppercase{ ὰ ά ὲ έ ὴ ή ὶ ί ὸ ό ὺ ύ ὼ ώ     }\\
\MakeUppercase{ ᾀ ᾁ ᾂ ᾃ ᾄ ᾅ ᾆ ᾇ ᾈ ᾉ ᾊ ᾋ ᾌ ᾍ ᾎ ᾏ }\\
\MakeUppercase{ ᾐ ᾑ ᾒ ᾓ ᾔ ᾕ ᾖ ᾗ ᾘ ᾙ ᾚ ᾛ ᾜ ᾝ ᾞ ᾟ }\\
\MakeUppercase{ ᾠ ᾡ ᾢ ᾣ ᾤ ᾥ ᾦ ᾧ ᾨ ᾩ ᾪ ᾫ ᾬ ᾭ ᾮ ᾯ }\\
\MakeUppercase{ ᾰ ᾱ ᾲ ᾳ ᾴ   ᾶ ᾷ Ᾰ Ᾱ Ὰ Ά ᾼ ᾽ ι ᾿ }\\
\MakeUppercase{ ῀ ῁ ῂ ῃ ῄ   ῆ ῇ Ὲ Έ Ὴ Ή ῌ ῍ ῎ ῏ }\\
\MakeUppercase{ ῐ ῑ ῒ ΐ     ῖ ῗ Ῐ Ῑ Ὶ Ί   ῝ ῞ ῟ }\\
\MakeUppercase{ ῠ ῡ ῢ ΰ ῤ ῥ ῦ ῧ Ῠ Ῡ Ὺ Ύ Ῥ ῭ ΅ ` }\\
\MakeUppercase{     ῲ ῳ ῴ   ῶ ῷ Ὸ Ό Ὼ Ώ ῼ ´ ῾   }
\selectlanguage{english}

MakeLowercase:

\selectlanguage{greek}
\MakeLowercase{ ἀ ἁ ἂ ἃ ἄ ἅ ἆ ἇ Ἀ Ἁ Ἂ Ἃ Ἄ Ἅ Ἆ Ἇ }\\
\MakeLowercase{ ἐ ἑ ἒ ἓ ἔ ἕ     Ἐ Ἑ Ἒ Ἓ Ἔ Ἕ     }\\
\MakeLowercase{ ἠ ἡ ἢ ἣ ἤ ἥ ἦ ἧ Ἠ Ἡ Ἢ Ἣ Ἤ Ἥ Ἦ Ἧ }\\
\MakeLowercase{ ἰ ἱ ἲ ἳ ἴ ἵ ἶ ἷ Ἰ Ἱ Ἲ Ἳ Ἴ Ἵ Ἶ Ἷ }\\
\MakeLowercase{ ὀ ὁ ὂ ὃ ὄ ὅ     Ὀ Ὁ Ὂ Ὃ Ὄ Ὅ     }\\
\MakeLowercase{ ὐ ὑ ὒ ὓ ὔ ὕ ὖ ὗ   Ὑ   Ὓ   Ὕ   Ὗ }\\
\MakeLowercase{ ὠ ὡ ὢ ὣ ὤ ὥ ὦ ὧ Ὠ Ὡ Ὢ Ὣ Ὤ Ὥ Ὦ Ὧ }\\
\MakeLowercase{ ὰ ά ὲ έ ὴ ή ὶ ί ὸ ό ὺ ύ ὼ ώ     }\\
\MakeLowercase{ ᾀ ᾁ ᾂ ᾃ ᾄ ᾅ ᾆ ᾇ ᾈ ᾉ ᾊ ᾋ ᾌ ᾍ ᾎ ᾏ }\\
\MakeLowercase{ ᾐ ᾑ ᾒ ᾓ ᾔ ᾕ ᾖ ᾗ ᾘ ᾙ ᾚ ᾛ ᾜ ᾝ ᾞ ᾟ }\\
\MakeLowercase{ ᾠ ᾡ ᾢ ᾣ ᾤ ᾥ ᾦ ᾧ ᾨ ᾩ ᾪ ᾫ ᾬ ᾭ ᾮ ᾯ }\\
\MakeLowercase{ ᾰ ᾱ ᾲ ᾳ ᾴ   ᾶ ᾷ Ᾰ Ᾱ Ὰ Ά ᾼ ᾽ ι ᾿ }\\
\MakeLowercase{ ῀ ῁ ῂ ῃ ῄ   ῆ ῇ Ὲ Έ Ὴ Ή ῌ ῍ ῎ ῏ }\\
\MakeLowercase{ ῐ ῑ ῒ ΐ     ῖ ῗ Ῐ Ῑ Ὶ Ί   ῝ ῞ ῟ }\\
\MakeLowercase{ ῠ ῡ ῢ ΰ ῤ ῥ ῦ ῧ Ῠ Ῡ Ὺ Ύ Ῥ ῭ ΅ ` }\\
\MakeLowercase{     ῲ ῳ ῴ   ῶ ῷ Ὸ Ό Ὼ Ώ ῼ ´ ῾   }
\selectlanguage{english}

\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.

Until automatically done by \emph{euenc} for EU1 and EU2 font encodings, the
recommended way to load Greek LICR definitions is via the \emph{textalpha}
or \emph{alphabeta} packages provided with \emph{greek-fontenc} since
version~0.10.

\subsection{Hiatus}

The «hiatus» feature works with macro input:

\selectlanguage{greek}
% from teubner: άυλος/ΑΫΛΟΣ
\acctonos\textalpha\textupsilon λος $\mapsto$
\MakeUppercase{\acctonos\textalpha\textupsilon λος},
\>'\textalpha\textupsilon λος $\mapsto$
\MakeUppercase{\>'\textalpha\textupsilon λος},
% from http://diacritics.typo.cz/index.php?id=69  μάινα -> ΜΑΪΝΑ
m\acctonos\textalpha\textiota να $\mapsto$
\MakeUppercase{m\acctonos\textalpha\textiota να},
% 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},
\>\textalpha\textupsilon πνία $\mapsto$
\MakeUppercase{\>\textalpha\textupsilon πνία}.
\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}


\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},


Enumerated lists use Greek characters/numerals in the second and fourth level.

\selectlanguage{greek}
\begin{enumerate}
  \item item 1
  \begin{enumerate}
    \item item 1.1
    \begin{enumerate}
      \item item 1.1.1
       \begin{enumerate}
         \item item 1.1.1.1
         \item item 1.1.1.2
       \end{enumerate}
      \item item 1.1.2
    \end{enumerate}
  \end{enumerate}
\end{enumerate}
\selectlanguage{english}


\end{document}