Differential algebraic geometry

Differential algebraic geometry is principally the study of solution sets to systems of algebraic differential equations, differential varieties. More formally, if (K, ∂1, …, ∂n) is a differential field and g1, …, gm is a sequence of differential polynomials over K in l variables, then the (K-points of the) differential variety associated to these data is

{a ∈ Kl | g1(a) = 0 & … & gm(a) = 0}