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+\documentclass{article}
+
+\ifdefined \UnicodeEncodingName
+ \usepackage{fontspec}
+ \setmainfont[Scale=0.92]{DejaVu Serif}
+\fi
+
+% Babel is required for hyphenation and the post-2022/06 \MakeUppercase
+% \usepackage[greek]{babel}
+
+\usepackage{xgreek}
+
+\newcommand*\uppercasetest[1]{\noindent#1 →\par\MakeUppercase{#1}\par}
+
+\begin{document}
+
+% examples from https://icu.unicode.org/design/case/greek-upper
+% See there for the expected output
+\uppercasetest{άδικος, κείμενο, ίριδα}
+\uppercasetest{Πατάτα}
+\uppercasetest{Αέρας, Μυστήριο, Ωραίο}
+\uppercasetest{Μαΐου, Πόρος, Ρύθμιση}
+\uppercasetest{ΰ, Τηρώ, Μάιος}
+\uppercasetest{άυλος}
+\uppercasetest{ΑΫΛΟΣ}
+\uppercasetest{Άκλιτα ρήματα ή άκλιτες μετοχές}
+\uppercasetest{Επειδή η αναγνώριση της αξιοπρέπειας}
+\uppercasetest{νομικού ή διεθνούς}
+\uppercasetest{Ἐπειδὴ ἡ ἀναγνώριση}
+\uppercasetest{νομικοῦ ἢ διεθνοῦς} % I need to look at this one
+\uppercasetest{Νέο, Δημιουργία}
+\uppercasetest{Ελάτε να φάτε τα καλύτερα παϊδάκια!}
+\uppercasetest{Μαΐου, τρόλεϊ}
+\uppercasetest{Το ένα ή το άλλο.}
+\uppercasetest{ρωμέικα}
+
+\end{document}
+
+% from http://www.polytoniko.org/kano.php?newlang=en
+% Words with rough breathing
+αἷμα, Αἷμος, αἵρεση,
+εἱρμός, εὑρετήριο
+υἱός
+
+ρολόι → ΡΟΛΟΪ
+
+If a capitalized word begins with a diphthong, the breathing mark is still
+over the second vowel (Αἰτέω). If the word begins with two vowels that do
+not form a diphthong, the breathing mark stands in front of the capital (
+᾽Ιησοῦς).
+
+
+
+
+If placed over a DIPHTHONG, a breathing mark is always above the SECOND
+vowel (e.g. οἱ, εἰ, and Εὐρώπη).
+<https://pressbooks.pub/ancientgreek/chapter/3/>