# Compute radical and idempotents of a quotient algebra

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 close merge delete

Sort by » oldest newest most voted

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.

more

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.

( 2018-01-20 23:33:21 -0600 )edit