"An einem heißem, aber glücklichem Dienstag"-is this correct? [duplicate]

Question

So I'm making my first tentative steps with German output and thus, have been trying to generate sentences of my own. Here is one

An einem heißem, aber glücklichem Dienstag während des Sommers stieg ich aus dem Zug aus.

DeepL gives a similar translation but it instead uses "heißen" and "glücklichen" while leaving "einem" intact. Why is that?

Answer 1

This is because declension in German can be either strong or weak. If you have both a determiner and adjectives in a noun phrase, the determiner has a strong pattern showing the case, and the adjectives get a weak pattern (-e or -en) that just shows that this is a declined adjective rather than an undeclined one, and singular vs plural.

But that's only the general idea. German adjective declination is tricky. Here's a recipe but even that recipe is not 100% correct. It fails for genitive singular of masculine and neuter nouns without a determiner, where the adjective ending is -en instead of the expected -es.

Oh, and if you ask yourself why there's a weak adjective declination instead of just no declination: you need it because undeclined adjectives (or rather: adverbs) in a noun phrase modify the following declined adjective rather than the noun.

Answer 2

That's just how the declension works (indefinite article). For clarity I only choose to show that with the adjective 'heiß'. It works the same with 'glücklich' or both of them:

ein heißer Tag
eines heißen Tages
einem heißen Tag
einen heißen Tag

heiße Tage
heißer Tage
heißen Tagen
heiße Tage.

One remark though: "ein glücklicher Tag" does not work, it sounds off. A day doesn't have emotions, thus in German it cannot be happy or lucky, only you can be happy or lucky. In this context the proper word you look for might be 'fröhlich' instead of 'glücklich'. So one would rephrase it somewhat:

An einem heißen aber schönen Dienstag während des Sommers stieg ich aus dem Zug (aus). (it's a hot and nice day, you debark the train)

An einem heißen Dienstag während des Sommerst stieg ich fröhlich aus dem Zug aus. (a hot day, you are happy and debark the train)