Multivariate Laurent series

edit

I'm trying to perform calculations with two variables $z, u$, one of which, $z$, should be invertible. Apparently Laurent series rings are not yet implemented for multivariate rings. I tried the following

R = QQ[['zed, you, zedi']]
R
Multivariate Power Series Ring in zed, you, zedi over Rational Field

x = R.gens()
x
(zed, you, zedi)

i = x[0]*x[2] - 1
i
-1 + zed*zedi

I = i*R
I
S = QuotientRing(R, I, names="z, u, xi")
S

Principal ideal (-1 + zed*zedi) of Multivariate Power Series Ring in zed, you, zedi over Rational Field  
Quotient of Multivariate Power Series Ring in zed, you, zedi over Rational Field by the ideal (-1 + zed*zedi)

g = S.gens()
g
(zed, you, zedi)

g[0]*g[2]
zed*zedi

Apparently, in the quotient ring I still get that $z z^{-1}$ doesn't simplify to 1. Also, my assigned names aren't recognized. What am I doing wrong? Is this even the best way of dealing with multivariate Laurent polynomials?

Thank you. (This is my first day using sage and my first question here on ask.sagemath.org. Please let me know if I've done something wrong.)