I'm wondering if there is existing terminology to describe fields $F$ with the properties below. I don't have a completely precise description of the concept I have in mind, but hopefully this will be enough.

- Every element of $F$ requires only a finite amount of information to describe (so that it can be stored in a computer in some way).
- There exist (finite) algorithms which can be used implement the field operations of $F$.

For example, the field $\mathbb Q$ (and any finite extension of it) has these properties, but the fields $\mathbb R$ and $\mathbb Q_p$ (where $p$ is prime) do not. I would appreciate any help in formulating my question more precisely, and any references which might discuss this concept.