Differential algebraic geometry is an area of
differential algebra
In mathematics, differential algebra is, broadly speaking, the area of mathematics consisting in the study of differential equations and differential operators as algebraic objects in view of deriving properties of differential equations and op ...
that adapts concepts and methods from
algebraic geometry
Algebraic geometry is a branch of mathematics which uses abstract algebraic techniques, mainly from commutative algebra, to solve geometry, geometrical problems. Classically, it studies zero of a function, zeros of multivariate polynomials; th ...
and applies them to systems of
differential equations, especially
algebraic differential equation
In mathematics, an algebraic differential equation is a differential equation that can be expressed by means of differential algebra. There are several such notions, according to the concept of differential algebra used.
The intention is to i ...
s.
Another way of generalizing ideas from algebraic geometry is
diffiety theory.
References
Differential algebraic geometry (three parts in one pdf) part of th
*, Henri Gillet (2000)
Differential algebra - A Scheme Theory Approach Differential algebra and related topics: proceedings of the International Workshop, Newark Campus of Rutgers, The State University of New Jersey, 2-3 November 2000, Editors Li Guo, William F. Keigher, World Scientific,
Differential algebra
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