Ideals in the Group Algebra C[GL(2,R)]
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
FalseI 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
TrueI 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.
Welcome to Ask Sage! Thank you for your question.
On Sage
9.5.rc0, for the linei got an error:
Is your example self-contained ? If yes, which version of Sage are you running ?
@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!