Differential field

Summary

A differential field is a field with a derivation, an additive map that obeys the product rule, see the definition. It is the algebraic setting for studying differential equations, where solutions are elements of larger differential fields. The field $\C(x)$ of rational functions with $d/dx$ is the basic example. Differential Galois theory and the Liouville theorem on elementary integrals are built on differential fields.