ASKSAGE: Sage Q&A Forum - RSS feedhttps://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Mon, 22 Apr 2019 14:07:39 +0200Multivariate Laurent serieshttps://ask.sagemath.org/question/29669/multivariate-laurent-series/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.)Fri, 02 Oct 2015 01:55:04 +0200https://ask.sagemath.org/question/29669/multivariate-laurent-series/Answer by rws for <p>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</p>
<pre><code>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
</code></pre>
<p>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?</p>
<p>Thank you. (This is my first day using sage and my first question here on <a href="http://ask.sagemath.org">ask.sagemath.org</a>. Please let me know if I've done something wrong.)</p>
https://ask.sagemath.org/question/29669/multivariate-laurent-series/?answer=29750#post-id-29750This is right.Multivariate Laurent series are not implemented in Sage at the moment.Sun, 04 Oct 2015 10:26:53 +0200https://ask.sagemath.org/question/29669/multivariate-laurent-series/?answer=29750#post-id-29750Comment by slelievre for <p>This is right.Multivariate Laurent series are not implemented in Sage at the moment.</p>
https://ask.sagemath.org/question/29669/multivariate-laurent-series/?comment=46307#post-id-46307Adding them is tracked at [Sage Trac ticket 19343](https://trac.sagemath.org/ticket/19343).Mon, 22 Apr 2019 13:58:53 +0200https://ask.sagemath.org/question/29669/multivariate-laurent-series/?comment=46307#post-id-46307Answer by slelievre for <p>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</p>
<pre><code>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
</code></pre>
<p>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?</p>
<p>Thank you. (This is my first day using sage and my first question here on <a href="http://ask.sagemath.org">ask.sagemath.org</a>. Please let me know if I've done something wrong.)</p>
https://ask.sagemath.org/question/29669/multivariate-laurent-series/?answer=46308#post-id-46308If 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.Mon, 22 Apr 2019 14:07:39 +0200https://ask.sagemath.org/question/29669/multivariate-laurent-series/?answer=46308#post-id-46308