dimahphone's profile - activity

Case closed, I finally use CyclotomicField(8) and it works.

Do you mean "real need" is what I need on that code? Sorry if I am wrong understanding your comment.

Thank you for the suggestion. It works. But, I still have problem when I use QQbar. I can not do anything for groups I get. For example, I can not know the element order of the group. By hand, I get that the order is 8. Do you have any suggestion? Thank you very much. Sorry if it disturbs your time.

I have problem on generate matrix group over symbolic ring.

First, I define

eta=I;
eta2=(1+I)*sqrt(2)/2;

Then, define a generator matrix

T=matrix(SR,4,[eta**(i*j)*eta2/2 for i in range(4) for j in range(4)]);

I try to make a matrix group by

G=MatrixGroup(T);

What I get is only very long computation that does not give any result. Can somebody help me? Thank you very much.

I have checked the order of T, I got 8 since T**8=I where I is identity matrix.

I am not good on Algebra, exactly on representation theory, but In my understanding, that is always. It means all finite groups can be represented by matrix group. Perhaps, link below may be able to help you. Sorry if it does not help you. https://math.stackexchange.com/questions/85308/can-every-group-be-represented-by-a-group-of-matrices (link text)