This is a simple terminology question: I want to know if the involution $z \mapsto z^{-1}$ on Laurent polynomials (over some ring, I happen to be working over $\mathbb{Z}$ but that's not important) has a special name.

My motivation is perhaps a little unusual for this site. I'm doing some computations that involve manipulating Laurent polynomials and, being a lazy sort of fellow, I'm letting the computer do it. Being extra lazy, I don't particularly want to learn a new programming language to do this so I'm using Perl as it's the only one that I know. However, there my laziness stops as whilst there's a Perl module for ordinary polynomials there isn't one for Laurent polynomials. Still, it wasn't hard to adapt it to Laurent polynomials so I did and the program is chugging away churning out these computations to its heart's content. In writing the methods (meaning, things you can do to a Laurent polynomial), most already have obvious names (add, subtract - actually called `sub_`

, mul(tiplication), and so forth) but I don't know one for the obvious involution $z \mapsto z^{-1}$. `inv`

sounds a little to easy to mistake for `inverse`

.

So, is there a name for this? If not, would anyone like to suggest one (preferably with an unambiguous shortening - I've already gotten fed up of typing `monomial`

every time)?

unitcomplex number. So I see no harm in calling it conjugation. I think I've seen this convention in some knot theory texts. It's also advantageous since it allows for notational sloppiness $z^{-1} = \overline{z}^1$. When you're computing Alexander polynomials and if you have sloppy handwriting, this is a major advantage. – Ryan Budney Dec 10 '10 at 21:27