Ask Your Question

How does one tell if a number field contains a certain element?

asked 2012-06-19 01:32:47 -0500

anonymous user


Suppose I have a number field K, in SAGE how would can see if something like \sqrt[4]{29} is contained in this number field?

edit retag flag offensive close merge delete

1 answer

Sort by ยป oldest newest most voted

answered 2012-06-22 17:42:23 -0500

benjaminfjones gravatar image

I think your question is not well-defined. If you had a number field $K$ along with an embedding $K \to \mathbb{C}$ then the question makes sense. When you construct a number field in Sage I believe it is an abstract field since there may be many different embeddings of $K$ into $\mathbb{C}$.

Now, if your field $K$ is the splitting field of an irreducible polynomial $f$ over $\mathbb{Q}$ then you could test if $f(\sqrt[4]{29})$ is zero or not.

edit flag offensive delete link more

Your Answer

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

Add Answer

Question Tools


Asked: 2012-06-19 01:32:47 -0500

Seen: 168 times

Last updated: Jun 22 '12