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+\documentclass{article}
+\usepackage{cmap} % fix search and cut-and-paste in PDF
+\usepackage{parskip}
+\usepackage{textcomp}
+\usepackage{amsmath}
+\usepackage{fixmath}
+\usepackage{lmodern}
+% \usepackage{gfsdidot}
+% \usepackage{kerkis}
+\usepackage[T1]{fontenc}
+\usepackage[utf8]{inputenc}
+\usepackage[colorlinks=true,linkcolor=blue,urlcolor=blue]{hyperref}
+\hypersetup{unicode=true}
+\usepackage{bookmark}
+% No section numbers but PDF bookmarks for sections
+\setcounter{secnumdepth}{0}
+
+
+% load alphabeta after math setup and encoding setup!
+\usepackage{alphabeta}
+
+\begin{document}
+
+\section{Test the \emph{alphabeta} package}
+
+With the \emph{alphabeta} package, you can write Greek letters ``by name" in
+both, text and math. The mode determines whether the letters are taken
+from the text or math font. Just like Latin letters, the Greek counterparts
+are by default italic in math (capital letters upright without
+\emph{fixmath} or \emph{isomath}) and upright in text:
+
+Text: L \Lambda{} l \lambda, math: $ L \ \Lambda \ l \ \lambda $,
+emphasized: \emph{L \Lambda{} l \lambda}
+
+\section{Greek alphabet}
+
+Greek letters via Latin transscription in LGR font encoding:
+
+\begin{quotation}
+ \TextGreek{A B G D E Z H J I K L M N X O P R S T U F Q Y W}\\
+ \TextGreek{a b g d e z h j i k l m n x o p r s c t u f q y w}
+\end{quotation}
+
+Greek letters via default macros in LGR font encoding:
+
+\begin{quotation} \TextGreek{
+ \Alpha{} \Beta{} \Gamma{} \Delta{} \Epsilon{} \Zeta{} \Eta{} \Theta{}
+ \Iota{} \Kappa{} \Lambda{} \Mu{} \Nu{} \Xi{} \Omicron{} \Pi{} \Rho{}
+ \Sigma{} \Tau{} \Upsilon{} \Phi{} \Chi{} \Psi{} \Omega{}
+
+ \alpha{} \beta{} \gamma{} \delta{} \epsilon{} \zeta{} \eta{} \theta{}
+ \iota{} \kappa{} \lambda{} \mu{} \nu{} \xi{} \omicron{} \pi{} \rho{}
+ \sigma{} \varsigma{} \tau{} \upsilon{} \phi{} \chi{} \psi{} \omega{}
+ }
+\end{quotation}
+
+Greek letters via default macros in other font encoding (here T1):
+
+\begin{quotation}
+ \Alpha{} \Beta{} \Gamma{} \Delta{} \Epsilon{} \Zeta{} \Eta{} \Theta{}
+ \Iota{} \Kappa{} \Lambda{} \Mu{} \Nu{} \Xi{} \Omicron{} \Pi{} \Rho{}
+ \Sigma{} \Tau{} \Upsilon{} \Phi{} \Chi{} \Psi{} \Omega{}
+
+ \alpha{} \beta{} \gamma{} \delta{} \epsilon{} \zeta{} \eta{} \theta{}
+ \iota{} \kappa{} \lambda{} \mu{} \nu{} \xi{} \omicron{} \pi{} \rho{}
+ \sigma{} \varsigma{} \tau{} \upsilon{} \phi{} \chi{} \psi{} \omega{}
+\end{quotation}
+
+
+Greek letters in math (with ``fixmath") (there are no math macros for Greek
+letters wich exist with similar shape in the Latin alphabet):
+
+\[
+ % \Alpha{} \Beta{}
+ \Gamma{} \Delta{}
+ % \Epsilon{} \Zeta{} \Eta{}
+ \Theta{}
+ % \Iota{} \Kappa{}
+ \Lambda{}
+ % \Mu{} \Nu{}
+ \Xi{}
+ % \Omicron{}
+ \Pi{}
+ % \Rho{}
+ \Sigma{}
+ % \Tau{}
+ \Upsilon{} \Phi{}
+ % \Chi{}
+ \Psi{} \Omega{}
+\]
+\[
+ \alpha{} \beta{} \gamma{} \delta{} \epsilon{} \zeta{} \eta{} \theta{}
+ \iota{} \kappa{} \lambda{} \mu{} \nu{} \xi{}
+ % \omicron{}
+ \pi{} \rho{}
+ \sigma{} \varsigma{} \tau{} \upsilon{} \phi{} \chi{} \psi{} \omega{}
+\]
+
+So you can easily write a single Greek symbol (like \Psi{} or \mu{})
+or \lambda\omicron\gamma\omicron\varsigma{} in non-Greek text as well as
+ISO-conforming formulas with an upright pi symbol like
+$A = \text{\pi} r^2$ instead of $A = \pi r^2$.
+
+\section{
+ \TextGreek{\<\Epsilon\lambda\lambda\eta\nu\iota\kappa\'\alpha{} (Ἑλληνικά)}
+ in PDF strings}
+
+With the alphabeta package, you get Greek letters in both, the document body
+and PDF metadata generated by hyperref if the input uses Unicode literals or
+macros. Wrapping in \verb+\TextGreek+ ensures the right placement of the
+accents and breathings (before, not above capital letters).
+As the hyperref packages "PU" encoding uses the \verb+\text...+ macros,
+some diacritics are missing in the PDF data if the short macros are used
+(dasia dropped at the start of the heading in the PDF toc).
+
+The generic macros result in warnings like
+%
+\begin{verbatim}
+Package hyperref Warning: Token not allowed in a PDF string (Unicode):
+(hyperref) removing `\TextOrMath ' on input line 109.
+
+
+Package hyperref Warning: Token not allowed in a PDF string (Unicode):
+(hyperref) removing `\mathlambda' on input line 109.
+\end{verbatim}
+%
+that can savely be ignored.
+
+\subsection{Greek in math $\sin^2\alpha$}
+
+Ensure Greek in math continues to work in both text and PDF metadata:
+$\Gamma = \frac{\sin\alpha}{\cos{\beta}}$.
+
+\section{Limitations}
+
+\subsection{Kerning}
+
+There is no kerning between Greek letters, if the font encoding is not LGR:
+compare \TextGreek{AUA} (LGR) to \textAlpha\textUpsilon\textAlpha (T1).
+Because of this (and for proper hyphenation), use of the Babel package and
+correct language setting is recommended for Greek quotes.
+
+\subsection{Diacritics}
+
+In LGR encoding, shortcuts as well as named macros are set up for use with
+the Latin transcription.
+
+Composition of diacritics (like \verb+\Dasia\Tonos+) fails in other
+font encodings. Long names (like \verb+\DasiaOxia+) work, however they
+do not select precomposed characters (the difference becomes obvious
+if you drag-and-drop text from the PDF version of this document):
+%
+\TextGreek{\<'\alpha{} \Dasia\Tonos\alpha{} \DasiaOxia\alpha{}} \\
+\DasiaOxia\alpha
+
+Diacritics (except the dialytika) should placed
+before capital letters and dropped with MakeUppercase:
+
+\TextGreek{
+\<{\alpha} \>{\epsilon} \"'{\iota} \`>{\eta}
+\'<{\omicron} \~<{\upsilon} \~>{\omega}
+\\
+\<{\Alpha} \>{\Epsilon} \"'{\Iota} \`>{\Eta}
+\'<{\Omicron} \~<{\Upsilon} \~>{\Omega}
+\\
+\MakeUppercase{%
+ \<{\alpha} \>{\epsilon} \"'{\iota} \`>\eta{}
+ \'<{\omicron} \~<{\upsilon} \~>{\omega}
+}}
+
+However, this does not work with the generic macros (yet), as there are no
+TextCompositeCommand declarations for them in lgrxenc.def.
+TODO: add them in alphabeta.sty.
+
+No kerning: (\TextGreek{ΑΥΑ} vs. ΑΥΑ), misplaced multiple (\TextGreek{ἅ} vs.
+ἅ) or Titlecase accents (\TextGreek{Ά Έ Ή Ί} vs. Ά Έ Ή Ί) and strange effects
+with MakeUppercase:
+
+\MakeUppercase{%
+ \<{\alpha} \>{\epsilon} \"'{\iota} \`>\eta{}
+ \'<{\omicron} \~<{\upsilon} \~>{\omega}
+}
+
+The \verb+\TextGreek+ TextCommandDefault ensures that the argument is
+typeset with an LGR encoded font. This works with the Babel transscription
+(\TextGreek{logos}), keeps kerning (if the kerning pair is inside the
+argument, \TextGreek{\Alpha\Upsilon\Alpha}), and allows iterative accent
+macros where pre-composed characters are selected
+(\TextGreek{\DasiaOxia\alpha} or \TextGreek{\Dasia\Tonos\alpha}).
+
+The Unicode definitions in lgrenc.dfu use this to fix the handling of
+diacritics in pre-composed accented Unicode literals (see greek-unicode.pdf).
+
+\end{document}