Ambiguous Function Notation¶
Say you see this:
Does this mean that the function is evaluated at ? Or does that mean that some times ? Perhaps for the case it is clear, but what about the time evolution operator ? The Hamiltonian is a function of time in the general case. But here it actually means a multiplication which one can find out by the units as well.
The problem is, that mathematical texts, including physical texts, are not to be interpreted by a computer. I would like this to be very clear cut and unambiguous, so I thought about a solution to this, inspired by other things I saw.
C and other Programming Languages¶
The evaluation in C is writen like so:
Whereas the multiplication is denoted like so:
This is fine, but has one problem. If you want to denote , you would have to write every single multiplication sign:
omega * R * C
This is unacceptable for normal formulas, since it has way to many “” in it.
Mathematica has its very own solution to this. It denotes function calls with
 and multiplication with
(). That way, it is clear what is meant.
It works great for a mathematical programming language, but it is extremely unusual to write it this way. I tried it once, in problem set physik421-10, which you can find at physik421 Theoretische Physik 3.
To use the unambiguous way the C language does it, without too many “” in it, I now write a “” in front of every “” if I mean a multiplication. So the examples from “The Problem” become:
Brackets and parentheses¶
The way it is used in Mathematica is consistent with itself, but very strange for other people.
So I currently use this inverted:
This still has the problem that it is not obvious if you do not know the convention. Also, functional dependencies are sometimes denoted with square brackets. When I switch between Mathematica and this notation, the confusion is maximized. So far, this is the best compromise, I think.