あと or あとで?

[Leilaure]

Hi everyone!
This is what Bunpro says about あと・で:

Verb + のは + あと・で
Verb[ た ] + あと・で
Noun + の・あと・で

My problem is that I can’t figure out when to use あと and when to use あとで… It’s totally unclear to me. I’ve looked online and found explanations of the difference between あとに and あとで, and others that explain how to use あとで, but none that explained why あと is sometimes used alone, like in the sentences below

勉強べんきょうした あと 、遊あそんでもいいよ

食事しょくじ のあと 、お皿さらを洗あらわなくてはいけない

Thank you in advance!

[TheCodingFox]

I might be wrong, but I think the comma indicates a short pause in speech which clarifies that there’s an omission of で because it’s casual speech.

I’m not sure if the で in あとで is the て form of だ or if it’s the で particle, so I would like to know myself. I’m leaning towards the latter which would probably make more sense.

[anon54313967]

@Leilaure

but none that explained why あと is sometimes used alone, like in the sentences below

勉強べんきょうした あと 、遊あそんでもいいよ

食事しょくじ のあと 、お皿さらを洗あらわなくてはいけない

I see those sentences in Bunpro and they both use 後で. Where did you see them with only 後?

As to the larger question, the で I believe is just a conjunction. Since it’s marking something you’ll do later/after something else (even if the action A is being omitted). To quote a comment on the Maggie Sensei article on 後:

Hi Joey,
後で／後 focusing on the order/what you are going to do after ~
After finishing (A), you do (B)
食事が終わった後／後でテレビを観ます。

後に focusing on the time, the particular time after ~
食事が終わった後に薬を飲まないといけません。

And in response to asking if it can be optional.

Right. You can say both 食事の後／食事の後でテレビを観ます。

http://maggiesensei.com/2018/01/22/how-to-use-後-あと-ato/

The comments to the Maggie Sensei articles contain a lot of these extra clarifications.

I expect the で would be used in areas where you wouldn’t want it confused with 後 (の)?

[Leilaure]

Ah yes I see. I saw that explanation on Maggie Sensei but was wondering if there was another. Those sentences in Bunpro accept both 後 and 後で as correct while others don’t, so I was wondering whether there was an explanation to this… Thanks for your lengthy answer, I’ll go look at the Maggie Sensei article in detail!