# Variable naming convention in mathematical modeling

Is there a guide or source of inspiration I can use when picking variable and constant names for a mathematical formula? I'm in the process of converting a poorly written technical document into something cleaner, and I'm faced with garbage like this:

$HWP\_cur_x=Cut\_cur\times\sum^{ru\left(\frac{yr\_cur-start\_date}{Freq\_cur_x}\right)}_{t=0}f(Decay\_cur_x;yr\_cur-start\_date_x)$

I have a background in scientific computing, so I can appreciate an elegantly constructed formula, but I've always wondered how a good mathematician would choose variable names.

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With so many variables, it's probably not a bad idea to short names (as is done here) instead of single letters. Your foremost concern should be ease of reading, not adherence to mathematical convention for it's own sake. – Austin Mohr Nov 27 '11 at 5:31
@AustinMohr That's a good point. Any chance you could point me to a published reference that does this? I've got all kinds of heavy books spread out on my table and I have yet to see a single equation that has a variable or function longer than two letters. – Rich Nov 27 '11 at 5:36
Nothing springs to my mind, though I am under the impression that it is fairly common practice in computer science and engineering. – Austin Mohr Nov 27 '11 at 5:41
@AustinMohr Thanks. Unfortunately there's nothing like that in my finite element or signal processing references. I'll check my Art of Computer Programming tomorrow at the office. – Rich Nov 27 '11 at 5:51
See this post. – Zev Chonoles Nov 27 '11 at 8:01

If you're going to introduce single-letter variable names, it's important that (a) you only do it when it really will make the expression clearer, and (b) you provide full explanations for what your variables are? For example:

Let

\begin{align} \tau & = \textrm{year} - \textrm{start date} \\ f & = \rm frequency \\ r & = \textrm{...description of what ru is} \\ T & = {r\tau/f} \\ d & = \rm decay \end{align}

then

$$HWP={\rm cut} \times \sum^{T}_{t=0} f(d;\tau)$$

Here I followed the common convention of using $t$-like variables ($t$, $T$, $\tau$) to represent times and $f$ to represent a frequency. For the other variables I used the first letter of their names.

Note that this equation doesn't really make sense - the dummy variable in the summation is $t$, but $t$ doesn't appear anywhere in the summand. That should be fixed.

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