All Questions

I am looking for a computer algebra system that checks if the splitting fields of two polynomials over a $p$-number field are the same or not. At least, knowing their splitting fields are isomorphic ...

Actually I am interested in degree $ 8 $ cyclic extension over $ \mathbb{Q} $. Let $ L $ be such extension. At first I was thinking to take basis as normal basis, as we can determine the galois group ...

I am looking to find real quadratic fields whose Hilbert class field is abelian over $\Bbb Q$. Then I learned about genus numbers and genus field of the number field. It is enough to find a number ...