Differential algebraic geometry is an area of
differential algebra that adapts concepts and methods from
algebraic geometry
Algebraic geometry is a branch of mathematics, classically studying zeros of multivariate polynomials. Modern algebraic geometry is based on the use of abstract algebraic techniques, mainly from commutative algebra, for solving geometrical ...
and applies them to systems of
differential equation
In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, an ...
s, 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 in ...
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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