Differential algebra is a field of mathematics that attempts to use methods from abstract algebra to study solutions of systems
of polynomial nonlinear ordinary
and partial differential equations.
It is a generalization of classical commutative
algebra and is primarily based on the work of Ritt (1950) and Kolchin (1973).
Mansfield (1991) gave a terminating algorithm for differential Gröbner bases,
which are differential analogs of polynomial Gröbner
bases.
The theory of symbolic integration in finite terms is a classical application of differential algebra. Liouville's
principle describes the form of elementary antiderivatives when they exist, and
the Risch algorithm gives a decision procedure
for elementary integration in differential fields.
