(A few years ago, I had to develop a macro for putting a circle round an expression, when I was teaching a course on games theory. The solutions sheets for the homework exercises had to include things like .)
Looking at this again, I can see another way in which it needs tweaking. Ideally, the vertical arrow on the left should be aligned with the product signs above and below it; and the vertical arrow on the right should similarly be aligned under the above it. You can achieve that quite easily by using the \llap and \rlap commands. These produce boxes of zero width whose contents overlap to the left or right respectively.
Originally Posted by Bacterius
Interesting diagram, although the horizontal lines look a bit jagged and blurred on my computer, anyone got the same artifact ?
Yes, that is an artefact caused by the fact that TeX does not have ready-made glyphs for long horizontal arrows. Instead, it constructs them on the fly by joining a sequence of short dashes to an arrowhead. The effect on the screen looks a bit uneven, though the printed version would probably be smoother.