# Ambiguous Function Notation

Say you see this:

$$f(x-y)$$

Does this mean that the function $f$ is *evaluated* at $x-y$? Or does that mean
that some $f$ *times* $(x-y)$? Perhaps for the case $f(x-y)$ it is clear, but
what about the time evolution operator $\exp(-\mathrm i H(t - t_0) / \hbar)$?
The Hamiltonian $H$ 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.

## Solutions

### C and other Programming Languages

The evaluation in C is writen like so:

```
f(x-y)
```

Whereas the multiplication is denoted like so:

```
f*(x-y)
```

This is fine, but has one problem. If you want to denote $\omega R C$, you would have to write every single multiplication sign:

```
omega * R * C
```

This is unacceptable for normal formulas, since it has way to many "$\cdot$" in it.

### Mathematica

Mathematica has its very own solution to this. It denotes function calls with
`[]`

and multiplication with `()`

. That way, it is clear what is meant.

Function call:

```
f[x-y]
```

Multiplication:

```
f(x-y)
```

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 Theorie 3.

## My Ideas

### The dot

To use the unambiguous way the C language does it, without too many "$\cdot$" in it, I now write a "$\cdot$" in front of every "$($" if I mean a multiplication. So the examples from "The Problem" become:

$$f(x-y)$$$$f \cdot (x-y)$$

### 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:

$$f(x-y)$$$$f[x-y]$$

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.