Editing Differential Galois theory (section)

{{Use American English|date = January 2019}}
{{Short description|Study of Galois symmetry groups of differential fields}}
{{Refimprove| date = January 2023}}
In mathematics, '''differential Galois theory''' is the field that studies extensions of [[differential field]]s.

Whereas algebraic [[Galois theory]] studies extensions of [[field (mathematics)|algebraic fields]], differential Galois theory studies extensions of [[differential field]]s, i.e. fields that are equipped with a [[derivation (abstract algebra)|derivation]], ''D''. Much of the theory of differential Galois theory is parallel to algebraic Galois theory. One difference between the two constructions is that the Galois groups in differential Galois theory tend to be matrix [[Lie group]]s, as compared with the finite groups often encountered in algebraic Galois theory.