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.


1. 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).
2. 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.



Representing field elements in a computer
You are looking at a computable field (if your focus is on the field), or a computable presentation of a field (if your focus is on the details of how elements and operations are coded). These objects are studied in computable structure theory.


