Differential Galois theory information

In mathematics, differential Galois theory studies the Galois groups of differential equations. Whereas algebraic Galois theory studies extensions of...

geometry. Galois group for more examples Fundamental theorem of Galois theory Differential Galois theory for a Galois theory of differential equations...

Picard–Vessiot theory which was initiated by Émile Picard and Ernest Vessiot, and whose recent developments are called differential Galois theory. The impossibility...

hypergeometric equation. In differential Galois theory the case of algebraic solutions is that in which the differential Galois group G is finite (equivalently...

Évariste Galois coined the term "group" and established a connection, now known as Galois theory, between the nascent theory of groups and field theory. In...

problem of Galois theory Given a group G, find an extension of the rational number or other field with G as Galois group. Differential Galois theory The subject...

commutative algebra, Galois theory of rings, algebraic geometry, algebraic groups, representations of groups and differential Galois theory. He has also published...

involving a given set of operations Differential Galois theory – Study of Galois symmetry groups of differential fields Elementary function arithmetic –...

set of operations Differential Galois theory – Study of Galois symmetry groups of differential fields Liouville's theorem (differential algebra) – Says...

was to the theory of differential equations. On the model of Galois theory and polynomial equations, the driving conception was of a theory capable of...

as a fallback Differential Galois theory – Study of Galois symmetry groups of differential fields Differentially closed field Differential graded algebra –...

x^{x}\,\mathrm {d} x.} For a more detailed discussion, see also Differential Galois theory. Finding antiderivatives of elementary functions is often considerably...

References Galois cohomology an application of homological algebra, it is the study of group cohomology of Galois modules. Galois theory named after...

[F(x) : F(y)]. This extension is generally not Galois but has Galois closure L(f). The associated Galois group of the extension [L(f) : F(y)] is called...

variety Theta function Grassmannian Flag manifold Weil restriction Differential Galois theory Prime ideal Valuation (algebra) Krull dimension Regular local...

closed-form antiderivatives; this study forms the subject of differential Galois theory, which was initially developed by Joseph Liouville in the 1830s...

was to the theory of differential equations. On the model of Galois theory and polynomial equations, the driving conception was of a theory capable of...

algebraic, differential, discrete and Euclidean geometries, graph theory, group theory, model theory, number theory, set theory, Ramsey theory, dynamical...

algebraic differential operators can also be defined. They are studied in a purely algebraic setting in differential Galois theory and the theory of D-modules...

the same as cohomology theories?". MathOverflow. Switzer 1975, 7.68. Dieudonné, Jean (1989), History of Algebraic and Differential Topology, Birkhäuser...