Differential equations | Differential algebra

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 include equations formed by means of differential operators, in which the coefficients are rational functions of the variables (e.g. the hypergeometric equation). Algebraic differential equations are widely used in computer algebra and number theory. A simple concept is that of a polynomial vector field, in other words a vector field expressed with respect to a standard co-ordinate basis as the first partial derivatives with polynomial coefficients. This is a type of first-order algebraic differential operator. (Wikipedia).

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Differential operator | Differential algebra | Differential equation | Rational function | Jet (mathematics) | Éléments de géométrie algébrique | Differential calculus | Invariant theory | Transcendental function | Riemann surface | Differential Galois theory | Mathematics | D-module | Algebraic geometry | Algebraic function | Vector bundle | Number theory | Weyl algebra | System of differential equations | Computer algebra | Vector field | Commutative ring