Thanks for your reply! I now know more about the motivations and backend of LaTeX.
Ok, so \atop (and \atopwithdelims) are how \choose, in particular, is made - and based on what the linked document says, this is exactly why people prefer \binom now.
Maybe I should not be so cagey about what I'm trying to do though, as I don't really need to recreate the \choose function, so much as get a new command that takes input in the same way as \choose or \atop: one input from the left, one from the right. I think I understand the risks involved re: formatting, but I'm working toward a pretty specialized purpose where I'm not so concerned about this:
I hate all the examples I've found online of drawing logic circuits: the simple gated ones, where you have labels of things like "p" or "~q", where series means "and" and parallel means "or". I'm still pretty new to LaTeX, and have just been drawing everything by hand, point-by-point, in tikz. I'd really love to instead make a very user-friendly code that anyone (in particular, the other instructors in my department) can copy/paste into their quizzes/tests/example sheets. My vision is that a statement that you'd write out as "(p V ~q) ^ r" could be displayed in circuit-form by
instead of
(yes I know \not already means something else... still trying to decide if, for the purposes of this one class, we care little enough about the original \not that I can \renewcommand it, or whether I should just do \n or something)
What I'm aiming for is something that reads like how you'd actually write the statement, so that a frazzled instructor on a deadline who isn't necessarily that comfortable with LaTeX but using it nonetheless can diagram the circuit they want to ask their class about without much of any learning curve. The idea is to get things to nest like here:
http://www.texample.net/tikz/examples/s ... -diagrams/
but of course, with that charming one-input-from-each-side. Which I can't figure out how to get. Which may still be inadvisable, but I think that since the inputs are only every going to be single letters or \not{} where the input of not is a single letter, it shouldn't be too bad.
Augh and now this is ridiculously detailed and babbly. Thanks so much if you've read this far! I really appreciate the above information, and welcome further thoughts on how to get a new command to take inputs from the left.