1 | initial version |

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.

Copyright Sage, 2010. Some rights reserved under creative commons license. Content on this site is licensed under a Creative Commons Attribution Share Alike 3.0 license.