How can I avoid errors when using equations in German text?

[StrawberryOwl]

I am writing a quite long document using a lot of mathematical equations, mostly inside equation and align environments. The problem is that I always get the error "Außer am Satzanfang werden nur Nomen und Eigennamen großgeschrieben. – DE_CASE" (I am writing the document in German) when I start a sentence after an equation. So it wants me to start the new line with a small letter because it sees the equation as part of a sentence which I didn't finish with a dot. But the equation is no sentence (I have a sentence above ending with a dot) and I want to start a new sentence.
I already tried using the ignore setting (ltex.latex.environments and there set environment, align and environment* and align* to "ignore") but this doesn't change anything. When I end the equation with a dot, the error disappears. This doesn't seem right to me and I do not want to hide them all as false positives (as it appears to be a systematic error).
Am I using the settings wrong or this a bug?

[valentjn]

I need an example for the alleged false positive diagnostic. Otherwise, I'd say this is desired behavior of LT_EX.

According to DIN 1338 Formelschreibweise und Formelsatz (see 4.7.2 in this excerpt) and most typographically good examples from literature, equations and formulas, even and especially when “displayed” (i.e., not inline), are in most cases to be treated as part of a sentence, except in some special cases, for example, if formulas are listed in a table. Just a formula on its own is not a sentence, just like a very long number on its own isn't, but a text body (i.e., your document minus headings, floats, headers/footers, etc.) should only consist of sentences. This means you can't just put a formula in your text body, but you should incorporate it into a sentence, e.g., by ending the previous sentence with a colon (just like this sentence now):

Der Beweis basiert auf folgender langer Rechnung:
\begin{equation}
  E = mc^2.
\end{equation}
Hier haben wir die Äquivalenz von Energie und Masse verwendet.

This is also better from a stylistic/semantic point of view, as you shouldn't just dump stuff like an equation into the text body, but interact with it, i.e., reference it (like folgender Rechnung) and explain its purpose (like in the second sentence).

Regarding ltex.latex.environments, the docs say that this setting only affects environments that are not already handled by default, but equations environments are. As a workaround, you can either define your own alias environments for align etc. via \newenvironment and add them to ltex.latex.environments, or you can use magic comments, which would be more tedious of course. But I wouldn't recommend either of the workarounds, for the reasons I've explained above.

[StrawberryOwl]

Thank you for your very detailed answer! I didn't even know that there was a DIN norm for this (although I probably should have suspected).
Then I will just get used to writing a dot after my equations and enjoy using your amazing spell checker even more!