TITLE: variable update operator , using "correct" mathematical notation
QUESTION [5 upvotes]: In a text describing mathematically an algorithm, there is a vector $y_l$ (local y-axis) which is computed, but must be subsequently adjusted to avoid numerical drift. I've considered a few possibilities to write it:

using APL-like arrow, $ y_l\leftarrow y_l-x_l(y_l\cdot x_l)$,
with Pascalesque $y_l:=y_l-x_l(y_l\cdot x_l)$,
introducing an extra $y_l'$ first, then just say $y_l=y_l'-x_l(y_l'\cdot x_l)$.

I find 1. the most readable, 3. the most correct and I've seen 2. several times. The text does not otherwise use algorithmical notation (such as pseudo-code). Which of them to pick?

REPLY [7 votes]: The problem you are facing is the lack of a widely accepted notation for assignments in mathematical circles. In computer science this problem does not exist, and people happily use '$\leftarrow$' or '$:=$' or even '$=$' for the assignment operator, with what seems to be no risk of confusion.
In computer science journals, I have found that (1) is the most common, followed by (2). In mathematics journals I have seen (3), but normally expressed with the prime on the quantity to be updated:
$$y_l' = y_l - x_l(y_l\cdot x_l)$$
Whatever notation you choose to use, you should explain clearly what you intend the reader to understand from it - this is particularly important if you aren't using the notation anywhere else in your paper.