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.Sun, 30 Jan 2022 12:28:10 +0100Ideals in the Group Algebra C[GL(2,R)]https://ask.sagemath.org/question/60868/ideals-in-the-group-algebra-cgl2r/I was hoping to use Sage to determine whether some element is generated by given generators in the group algebra C[GL(2,R)]. However, it went completely wrong when I tried the following naive thing.
sage: G=GL(2,RR)
sage: R=GroupAlgebra(G,CC)
sage: T=R(G([[1,1],[0,1]]))
sage: I=[T-1]*R;
sage: J=[T-1,(T-1)^2]*R;
sage: I==J
False
I thought I defined the ideals in the wrong way so I tried the following as well, which worked out great.
sage: var('t')
sage: R=PolynomialRing(QQ, 't')
sage: I=[R(t)]*R
sage: J=[R(t),R(t^2)]*R;
sage: I==J
True
I was wondering whether I indeed did something wrong or this is just a bug of Sage, and whether there is a way to fix it or bypass it. Thank you so much!
EDIT: There are in fact two issues going around. When I typed this into the Sage (version 8.7) on my computer, it came out as written above. However, when I tried this on the webpage version of Sage, there is this 'is_commutative' error as mentioned by tmonteil in the comment, and I don't know how this error comes up either. In any case, it seems to be impossible to compute ideals in this group algebra.Sun, 30 Jan 2022 00:21:43 +0100https://ask.sagemath.org/question/60868/ideals-in-the-group-algebra-cgl2r/Comment by chbe for <p>I was hoping to use Sage to determine whether some element is generated by given generators in the group algebra C[GL(2,R)]. However, it went completely wrong when I tried the following naive thing.</p>
<pre><code>sage: G=GL(2,RR)
sage: R=GroupAlgebra(G,CC)
sage: T=R(G([[1,1],[0,1]]))
sage: I=[T-1]*R;
sage: J=[T-1,(T-1)^2]*R;
sage: I==J
False
</code></pre>
<p>I thought I defined the ideals in the wrong way so I tried the following as well, which worked out great.</p>
<pre><code>sage: var('t')
sage: R=PolynomialRing(QQ, 't')
sage: I=[R(t)]*R
sage: J=[R(t),R(t^2)]*R;
sage: I==J
True
</code></pre>
<p>I was wondering whether I indeed did something wrong or this is just a bug of Sage, and whether there is a way to fix it or bypass it. Thank you so much!</p>
<p>EDIT: There are in fact two issues going around. When I typed this into the Sage (version 8.7) on my computer, it came out as written above. However, when I tried this on the webpage version of Sage, there is this 'is_commutative' error as mentioned by tmonteil in the comment, and I don't know how this error comes up either. In any case, it seems to be impossible to compute ideals in this group algebra.</p>
https://ask.sagemath.org/question/60868/ideals-in-the-group-algebra-cgl2r/?comment=60876#post-id-60876@tmonteil Thanks for the comment! The version of my Sage is 8.7. I actually also discovered this 'is_commutative' error when I tried it on the online version of Sage. I have edited my question to include this. Thanks!Sun, 30 Jan 2022 12:28:10 +0100https://ask.sagemath.org/question/60868/ideals-in-the-group-algebra-cgl2r/?comment=60876#post-id-60876Comment by tmonteil for <p>I was hoping to use Sage to determine whether some element is generated by given generators in the group algebra C[GL(2,R)]. However, it went completely wrong when I tried the following naive thing.</p>
<pre><code>sage: G=GL(2,RR)
sage: R=GroupAlgebra(G,CC)
sage: T=R(G([[1,1],[0,1]]))
sage: I=[T-1]*R;
sage: J=[T-1,(T-1)^2]*R;
sage: I==J
False
</code></pre>
<p>I thought I defined the ideals in the wrong way so I tried the following as well, which worked out great.</p>
<pre><code>sage: var('t')
sage: R=PolynomialRing(QQ, 't')
sage: I=[R(t)]*R
sage: J=[R(t),R(t^2)]*R;
sage: I==J
True
</code></pre>
<p>I was wondering whether I indeed did something wrong or this is just a bug of Sage, and whether there is a way to fix it or bypass it. Thank you so much!</p>
<p>EDIT: There are in fact two issues going around. When I typed this into the Sage (version 8.7) on my computer, it came out as written above. However, when I tried this on the webpage version of Sage, there is this 'is_commutative' error as mentioned by tmonteil in the comment, and I don't know how this error comes up either. In any case, it seems to be impossible to compute ideals in this group algebra.</p>
https://ask.sagemath.org/question/60868/ideals-in-the-group-algebra-cgl2r/?comment=60875#post-id-60875On Sage `9.5.rc0`, for the line
sage: I=[T-1]*R;
i got an error:
AttributeError: 'GroupAlgebra_class_with_category' object has no attribute 'is_commutative'
Is your example self-contained ? If yes, which version of Sage are you running ?Sun, 30 Jan 2022 10:47:16 +0100https://ask.sagemath.org/question/60868/ideals-in-the-group-algebra-cgl2r/?comment=60875#post-id-60875Comment by slelievre for <p>I was hoping to use Sage to determine whether some element is generated by given generators in the group algebra C[GL(2,R)]. However, it went completely wrong when I tried the following naive thing.</p>
<pre><code>sage: G=GL(2,RR)
sage: R=GroupAlgebra(G,CC)
sage: T=R(G([[1,1],[0,1]]))
sage: I=[T-1]*R;
sage: J=[T-1,(T-1)^2]*R;
sage: I==J
False
</code></pre>
<p>I thought I defined the ideals in the wrong way so I tried the following as well, which worked out great.</p>
<pre><code>sage: var('t')
sage: R=PolynomialRing(QQ, 't')
sage: I=[R(t)]*R
sage: J=[R(t),R(t^2)]*R;
sage: I==J
True
</code></pre>
<p>I was wondering whether I indeed did something wrong or this is just a bug of Sage, and whether there is a way to fix it or bypass it. Thank you so much!</p>
<p>EDIT: There are in fact two issues going around. When I typed this into the Sage (version 8.7) on my computer, it came out as written above. However, when I tried this on the webpage version of Sage, there is this 'is_commutative' error as mentioned by tmonteil in the comment, and I don't know how this error comes up either. In any case, it seems to be impossible to compute ideals in this group algebra.</p>
https://ask.sagemath.org/question/60868/ideals-in-the-group-algebra-cgl2r/?comment=60874#post-id-60874Welcome to Ask Sage! Thank you for your question.Sun, 30 Jan 2022 09:38:19 +0100https://ask.sagemath.org/question/60868/ideals-in-the-group-algebra-cgl2r/?comment=60874#post-id-60874