Differential algebraic geometry
Encyclopedia
Differential algebraic geometry is an area of differential algebra
that adapts concepts and methods from algebraic geometry
and applies them to systems of differential equation
s/algebraic differential equation
s.
Another way of generalizing ideas from algebraic geometry is diffiety theory
.
Differential algebra
In mathematics, differential rings, differential fields, and differential algebras are rings, fields, and algebras equipped with a derivation, which is a unary function that is linear and satisfies the Leibniz product law...
that adapts concepts and methods from algebraic geometry
Algebraic geometry
Algebraic geometry is a branch of mathematics which combines techniques of abstract algebra, especially commutative algebra, with the language and the problems of geometry. It occupies a central place in modern mathematics and has multiple conceptual connections with such diverse fields as complex...
and applies them to systems of differential equation
Differential equation
A differential equation is a mathematical equation for an unknown function of one or several variables that relates the values of the function itself and its derivatives of various orders...
s/algebraic differential equation
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....
s.
Another way of generalizing ideas from algebraic geometry is diffiety theory
Diffiety
In mathematics a diffiety, is a geometrical object introduced by playing the same role in the modern theory of partial differential equations as algebraic varieties play for algebraic equations....
.