Choice of character to denote multiplication

LoupVaillant / elligator

Mirror of a website on Elligator by Daniel J. Bernstein, Mike Hamburg, Anna Krasnova, and Tanja Lange

https://elligator.org

16 stars 1 forks source link

Choice of character to denote multiplication #6

Closed LoupVaillant closed 3 years ago

LoupVaillant commented 3 years ago

Currently, multiplication is denoted by the "·" (mid point) character. It took me a while to pick up on that, and expect readers to be equally puzzled. My first instinct is that I don't like this choice, and would like to propose two other alternatives:

The "×" character (don't know if it has an HTML markup for it), which most people will understand means multiplication without needing to be explained.
Nothing at all, following established mathematical convention, but perhaps might hurt readability for programmers. It's still workable if we stick to one letter variables, but I don't like the syntactic ambiguity with function calls (which admittedly only happens with the legendre symbol.

If there's a justification for using the mid point that I'd miss, I'd be willing to keep it, but then we should add a quick note that explains what it means.

fscoto commented 3 years ago

I picked · because that's what I was taught in school for multiplication. Since we have two different kinds of multiplication (scalar–point multiplication and integer multiplication), I felt that e. g. just writing two characters next to each other would be ambiguous.

× is already used to signify the cross product and would thus be misleading to adopt for integer multiplication. If accuracy is a goal, this does not seem to be the way to go to me.

LoupVaillant commented 3 years ago

Hmm, I was taught "×" for multiplication…

Okay, then how about nothing for integer multiplication, and the dot for scalar multiplication? In the overview section (which I'm rearranging, but mostly keeping), we describe curve equations, and those already use nothing to denote multiplication.

If that's not readable enough, there's one thing that can help: explicit or semi-explicit formulas in pseudo-code, or even Python. We may want to show that code right next to the clean, academic looking, formulas from the paper.

fscoto commented 3 years ago

Do you mean · for scalar multiplication or . for scalar multiplication? The former I'm heavily against, the latter I'm okay with.

LoupVaillant commented 3 years ago

Oh, I didn't make such a difference. I originally meant the mid point, but I honestly don't care, as long as we have some symbol for scalar multiplication. The regular "." sounds good, actually.