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Mar 17 at 13:24 comment added Felipe @MichaelWeyrauch As you said, "most people", I am just not one of those people. I am like those people that if you want them to learn math you put a little history in between, but what I need is a general guiding principle (looking back I think that is why I went to physics not engineering lol). Just learning what functions Mathematica has for me is like "learning" calculus by looking at an Integral table. I loved that my calculus professor made me proof a bunch of theorems, and went deep into the nasty stuff lol.
Mar 17 at 11:01 comment added Michael Weyrauch It would be interesting to understand why this lack of explanation makes Mathematica frustrating for you. The essential point for most people is that it just works as documented and as efficiently as possible. To understand it in total detail (in particular the evaluation process) would be extremely demanding, and in most cases not necessary. Similarly, pilots of a Boeing 747 airplane do typically not understand in detail how the engines of the aircraft are constructed and how they work in detail, but still successfully transport people around the world.
Mar 16 at 23:44 comment added Felipe Thanks. Yeah, that was the question how this optimization works. I think this should be documented, it is a part of the evaluation process. Mathematica has nice sintaxe and structure, but this lack of a clear explanation of how things work makes it very frustrating.
Mar 16 at 23:05 comment added Lukas Lang Rereading your question, I think I misunderstood it slightly... Maybe this answers it more directly: You can think of the system re-evaluating every expression after every replacement. And no, the system doesn't actually do this: As you note, it would be very inefficient to try and re-evaluate a list of numbers at every step, because obviously nothing will happen. This optimization of what to actually re-check for evaluation is done fully automatically (your functions also benefit from this), and you can't really affect this. That being said, there is Update, but I never had any use for it.
Mar 16 at 21:59 comment added Felipe I am sorry, but what do you mean by "the system at this point will only check for each step where there are any rules to be applied to a list of real numbers"
Mar 16 at 21:51 history answered Lukas Lang CC BY-SA 4.0