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.Tue, 19 Jun 2018 04:48:42 +0200Quotient ring involving Laurent polynomialshttps://ask.sagemath.org/question/42650/quotient-ring-involving-laurent-polynomials/Hi all,
I have actually two closely related questions:
Q1
Below is a working code that involves no Laurent polynomials:
sage: P = PolynomialRing(ZZ,'t0,t1')
sage: A.<T0,T1> = QuotientRing(P,[t0^2-1, t1^2-1])
sage: T0^2
sage: T1^2
The output is
1
1
I want to make a q-analog of it so it will produce its (Q,q)-deformation:
(Q-1)*T0 + Q
(q-1)*T1 + q
My attempt below didn't compile, and I'm wondering if there's a good solution to it.
sage: R = LaurentPolynomialRing(ZZ,'Q,q')
sage: P = PolynomialRing(R,'t0,t1')
sage: A.<T0,T1> = QuotientRing(P,[t0^2-1, t1^2-1])
sage: T0^2
sage: T1^2
Q2
I'm trying to implement the most general Hecke algebra of type B2 with unequal parameters for the two nodes. This is labeled as a TODO in the Sage Reference Manual (cannot post direct link due too low karma):
doc.sagemath.org/html/en/reference/algebras/sage/algebras/iwahori_hecke_algebra.html
Does anyone know any update to this?Mon, 18 Jun 2018 21:35:35 +0200https://ask.sagemath.org/question/42650/quotient-ring-involving-laurent-polynomials/Comment by CJLai for <p>Hi all,
I have actually two closely related questions:</p>
<p>Q1
Below is a working code that involves no Laurent polynomials:</p>
<pre><code>sage: P = PolynomialRing(ZZ,'t0,t1')
sage: A.<T0,T1> = QuotientRing(P,[t0^2-1, t1^2-1])
sage: T0^2
sage: T1^2
</code></pre>
<p>The output is </p>
<pre><code>1
1
</code></pre>
<p>I want to make a q-analog of it so it will produce its (Q,q)-deformation:</p>
<pre><code>(Q-1)*T0 + Q
(q-1)*T1 + q
</code></pre>
<p>My attempt below didn't compile, and I'm wondering if there's a good solution to it.</p>
<pre><code>sage: R = LaurentPolynomialRing(ZZ,'Q,q')
sage: P = PolynomialRing(R,'t0,t1')
sage: A.<T0,T1> = QuotientRing(P,[t0^2-1, t1^2-1])
sage: T0^2
sage: T1^2
</code></pre>
<p>Q2
I'm trying to implement the most general Hecke algebra of type B2 with unequal parameters for the two nodes. This is labeled as a TODO in the Sage Reference Manual (cannot post direct link due too low karma): </p>
<p>doc.sagemath.org/html/en/reference/algebras/sage/algebras/iwahori_hecke_algebra.html</p>
<p>Does anyone know any update to this?</p>
https://ask.sagemath.org/question/42650/quotient-ring-involving-laurent-polynomials/?comment=42659#post-id-42659Regarding Q1:
Just after posting the question I realized that T0 and T1 commute in the ring in Q1, which is not my intended object. However, it's still a question I'd like to ask.
If any of you is interested, for the Hecke algebra I end up using free algebra quotientTue, 19 Jun 2018 04:48:42 +0200https://ask.sagemath.org/question/42650/quotient-ring-involving-laurent-polynomials/?comment=42659#post-id-42659