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.

See also

Abstract Algebra, Commutative Algebra, Differential, Differential-Algebraic Equation, Gröbner Basis

This entry contributed by Bhuvanesh Bhatt

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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.

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Differential Algebra

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Bhatt, Bhuvanesh. "Differential Algebra." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein.

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