Differential Algebra

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.

REFERENCES:

Kolchin, E. R. Differential Algebra and Algebraic Groups. New York: Academic Press, 1973.

Mansfield, E. L. Differential Gröbner Bases. Ph.D. thesis, University of Sydney, 1991.

Ritt, J. F. Differential Algebra. Providence, RI: Amer. Math. Soc., 1950. http://www.ams.org/online_bks/coll33/.