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)?



Is there a name for the involution on Laurent polynomials?
I would call it the antipode. If your base ring is commutative, then the Laurent polynomials are the coordinate ring of the multiplicative group, and the antipode gives you the inversion on the group scheme.


