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5

Caution: Opinion based answer ahead ;-) The command argument specification is a very powerful feature of xparse and its \NewDocumentCommand (and the other ones, like \DeclareDocumentCommand etc.) macro. (\NewDocumentCommand stands here for the whole bundle of such commands!) The question if they are better (safer?) than \newcommand - defined macros is ...

3

Do you want an equation? Then use equation or \[ .. \] (or equation* if you want it not to be numbered). Do you want more than one equation together with no text in between? Then use gather(*) (if no alignment is necessary) or align(*) if you want to align them at certain points. To me that's the way of deciding what to use. Now, if it's a single equation ...

6

Reading the amsmath package documentation you'll find that split (only usable within another environment) is for splitting a single equation on more than one line (e.g. when the equation is too long), while the align environment is for typesetting multiple equation (possibly related to one another) aligned in the same display environment I think this ...

17

For the typographic comparison you're looking to make, we need to distinguish between two groups of environments that generate display-style equations: Methods for generating (mostly) single-line equations, such as the \[ ... \] approach and the displaymath, equation, and equation* environments. Methods for generating multi-line equations (although they ...

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