Math notation: multi-letter variables

[Danijel Gorupec]

What is your opinion on using multi-letter variables in math formulas? Should they be used more often or avoided?

 

If I use a quantity called 'Gross Domestic Product' in a formula, I might want to use 'GDP' as the variable name representing it. But this actually seems as a rare example - I cannot think of many such examples, can you?

 

Should I better come up with a single letter representing some money quantity (like 'M') and then use the 'GDP' description in its index? That is what I usually do when I have several quantities of the same type in the same formula (for example, to represent a current through resistor R1 and a current through resistor R2 I might use indexed variables i_R1 and i_R2).

 

If I still use multi-letter variables, should I always explicitly use the multiplying dot (cdot) between any two variables or is the 'invisible times' still appropriate?

 

We already use multi-letter function names often. There are also some multi-letter measurement units (mol, cd).

 

In my opinion, there are some examples where typing whole words might be beneficial. Like when you state a definition or a law... In the following three examples, I find example #2 to be the clearest:

Example1: a distance equals to the product of speed and time

Example2: distance = speed x time

Example3: s = v t

 

When using computers, multi-letter variables might be easier to type than indexed variables. On the other hand, computer monitors are of limited width so one might prefer single-letter variables.

 

I am posting this into the lounge because I am mostly interested in your personal opinions and aesthetics.

[Sensei]

In my C/C++ programs I use single letters for loop counters, like i,j,k,l,...

 

For coords primary are x,y,z, then x0,y0,z0, then x1,y2,z2 etc.

 

For other variables multi-letter name immediately identifying what variable contains.

 

Couple examples from my currently opened project in Visual Studio:

position, position0, position1, position2,

normal, normal0, normal1, normal2,

polygon_list, polygon, polygon_count,

point_list, point_count, point,

cursor_position, origin, font_scale, metrics,

segment_length

Edited December 25, 2015 by Sensei

[fiveworlds]

To borrow from programming a abit. When writing a section of code all variables should be written in a form such that on returning to a section of code or when somebody new looks at your code your variables should be easily recognizable and not confusing without a long winded explanation. For instance the variable device_width_in_pixels should contain the device width in pixels.

 

 

If I still use multi-letter variables, should I always explicitly use the multiplying dot (cdot) between any two variables or is the 'invisible times' still appropriate?

 

It should be written in a clear and concise manner at all times. For instance.

 

3 + 4 * 5

 

This is unclear and ambiguous unless standards tell you to do things a certain way you should describe the order of precedence in some manner. In javascript it would be evaluated as 23 in another language it could be evaluated as 35

 

(3 + (4 * 5))

 

This is better using brackets to denote precedence. Thus evaluating to 23 and

 

((3 + 4) * 5)

 

evaluating to 35.

[ajb]

I would want to avoid 'AB' being mistaken for 'A times B' (whatever times means here) in a paper. I would not worry about this for certain maps that are well knows, like Tr or Det or Span etc.

 

 

For programming, I would worry less as clarity of the inputs is important.

[Greg H.]

In programming, minified code often uses indexed variables, but it makes it nearly impossible for a human to follow the code and debug issues. Minified code is often generated as a way to save space, especially in javascript, however.

 

The standard in our shop is to use camel case for anything that isn't a constant, and all upper case for constants. So you would have:

 

DAYS_PER_WEEK and currentDayOfTheWeek for example.

[Danijel Gorupec]

Ok, I see that you are not very crazy about using multi-letter variables inside math formulas. This is understandable, some people say that using single-letter variables makes it easier to see the equation structure. I agree.

 

Also, copying line after line of math is easier if variables are shorter.

 

I tried to write the Pythagorean theorem using names BC, AB and AC for triangle sides (instead of a, b and c): AC^2=BC^2+AB^2... This looked very weird at first, but after I was looking at it for some longer time it settled down. The important thing imo is that if you ever decide to use multi-letter variables in your math formulas, then you should always use cdot (and keep this consistent through the whole paper).

 

Multi-letter function names are often cast in some different font to reduce ambiguity. Also, function names are often standard and well known.

 

(Ajb, I noticed that you used capital first letter in your function names - Is this Mathematica influence or your suggestion?)

 

...

 

Regarding programming, I would generally allow single-letter variables only for a very short scope (several lines). Very few exceptions from that. (Unless, of course, the intention is to make sw unreadable).... Interesting is this difference between multi-letter variable usage in pen-written math and keyboard-written software.

[ajb]

I noticed that you used capital first letter in your function names - Is this Mathematica influence or your suggestion?

I tend to use capitals (and a font change), I am not sure why, but you are right that Mathematica typically requires this.