The act of praising someone or something highly and publicly; enthusiastic and public approval or admiration.
Derived from extoll with the noun suffix -ation, following the pattern of Latin-based English nouns that convert verbs to abstract nouns describing the action or state.
The noun 'extollation' is quite rare in modern English, replaced by simpler words like 'praise' or 'extolling'—it's the kind of formal, grandiose word Victorian authors loved, which is why you'll find it mostly in historical literature rather than contemporary writing.
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