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Multivariate Laurent series

asked 2015-10-01 18:55:04 -0500

Earthling gravatar image

updated 2015-10-16 12:17:44 -0500

FrédéricC gravatar image

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.)

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answered 2015-10-04 03:26:53 -0500

This is right.Multivariate Laurent series are not implemented in Sage at the moment.

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Comments

Adding them is tracked at Sage Trac ticket 19343.

slelievre gravatar imageslelievre ( 2019-04-22 06:58:53 -0500 )edit
0

answered 2019-04-22 07:07:39 -0500

slelievre gravatar image

If only one of the variables needs to be invertible, one could work with Laurent series in one variable over a power series ring in the other variable; or conversely, power series in one variable over a Laurent series ring in the other variable:

sage: L.<z> = LaurentSeriesRing(QQ)
sage: P.<u> = PowerSeriesRing(L)

or

sage: P.<u> = PowerSeriesRing(QQ)
sage: L.<z> = LaurentSeriesRing(P)

In some cases it might be enough to use a polynomial ring or a Laurent polynomial ring for one of the variables.

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Asked: 2015-10-01 18:55:04 -0500

Seen: 324 times

Last updated: Apr 22