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.Wed, 19 Jul 2017 21:25:49 +0200Computations on U and V when they do not commute.https://ask.sagemath.org/question/29846/computations-on-u-and-v-when-they-do-not-commute/We have $f= U + U^{-1} + V + V^{-1}$. Exp is the exponential map: $e^{f}=\Sigma_{m=0}^{\infty} \frac{f^{n}}{n!} $. U and V do not commute and we have $U^{m}V^{n}= e^{imn}V^{n}U^{m}$ for any m,n integer. I want to find the constant term for the expression $\partial_{2}e^{-f/2} \partial_{2}e^{f}$. We have $\partial_{2}f= V - V^{-1}$.
Is there any program in which I can compute it?Thu, 08 Oct 2015 19:00:09 +0200https://ask.sagemath.org/question/29846/computations-on-u-and-v-when-they-do-not-commute/Comment by dan_fulea for <p>We have $f= U + U^{-1} + V + V^{-1}$. Exp is the exponential map: $e^{f}=\Sigma_{m=0}^{\infty} \frac{f^{n}}{n!} $. U and V do not commute and we have $U^{m}V^{n}= e^{imn}V^{n}U^{m}$ for any m,n integer. I want to find the constant term for the expression $\partial_{2}e^{-f/2} \partial_{2}e^{f}$. We have $\partial_{2}f= V - V^{-1}$.</p>
<p>Is there any program in which I can compute it?</p>
https://ask.sagemath.org/question/29846/computations-on-u-and-v-when-they-do-not-commute/?comment=38333#post-id-38333What is (mathematically) $\partial_2$? Is it a derivation? (So that we can formally extend it to a polynomial to a series in $f$...) Is there really $\exp(imn)$ the twisting factor?Wed, 19 Jul 2017 21:25:49 +0200https://ask.sagemath.org/question/29846/computations-on-u-and-v-when-they-do-not-commute/?comment=38333#post-id-38333