Ask Your Question
3

Compute radical and idempotents of a quotient algebra

asked 2013-07-12 03:50:17 -0500

Bern gravatar image

updated 2015-02-16 07:55:59 -0500

slelievre gravatar image

I tried the following:

R.<x,y>=PolynomialRing(QQ,2)
I=Ideal(x^2,y^2)
S=R.quotient(I)

I have the following question:

I would like to compute with SAGE the Jacobson radical of the algebra S, all primitive orthogonal idempotents and the central idempotents.

Of course, you can compute this by hand, but I am interested in more complicated examples, too (also in matrix algebras), but wanted to start with this simple example.

Since I am relatively new to Sage, I unfortunately do not know how to compute this.

I would be grateful for any help.

edit retag flag offensive close merge delete

1 answer

Sort by ยป oldest newest most voted
1

answered 2018-01-20 08:42:39 -0500

Bern gravatar image

In the meantime I have learned that these things can be done with the aid of the GAP-package QPA. This also works in SAGE via letting GAP be the intermediator.

edit flag offensive delete link more

Comments

Thanks for reporting that you found a solution. I turned your comment into an answer.

Could you edit your answer to include code to perform these computations?

It would be interesting to see how you do it in GAP, but also how to do it in Sage.

slelievre gravatar imageslelievre ( 2018-01-20 23:33:21 -0500 )edit

Your Answer

Please start posting anonymously - your entry will be published after you log in or create a new account.

Add Answer

Question Tools

Stats

Asked: 2013-07-12 03:50:17 -0500

Seen: 197 times

Last updated: Feb 16 '15