𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Note on Kovacic's Algorithm

✍ Scribed by FELIX ULMER; JACQUES-ARTHUR WEIL

Publisher
Elsevier Science
Year
1996
Tongue
English
Weight
688 KB
Volume
22
Category
Article
ISSN
0747-7171

No coin nor oath required. For personal study only.

✦ Synopsis

Algorithms exist to find Liouvillian solutions of second order homogeneous linear differential equations (Kovacic, 1986, Singer andUlmer, 1993b). In this paper, we show how, by carefully combining the techniques of those algorithms, one can find the Liouvillian solutions of an irreducible second order linear differential equation by computing only rational solutions of some associated linear differential equations. The result is an easyto-implement simplified version of the Kovacic algorithm, based as much as possible on the computation of rational solutions of linear differential equations.

πŸ“œ SIMILAR VOLUMES

Coefficient Fields of Solutions in Kovac
Coefficient Fields of Solutions in Kovacic's Algorithm
✍ Alexey Zharkov πŸ“‚ Article πŸ“… 1995 πŸ› Elsevier Science 🌐 English βš– 188 KB

In this paper we prove the following theorem: if the Riccati equation \(w^{\prime}+w^{2}=R(x), R \in\) \(Q(x)\), has algebraic solutions, then there exists a minimum polynomial defining such a solution whose coefficients lie at most in a cubic extension of the field \(Q\). In Zharkov (1992), the sam

A note on the ace algorithm
A note on the ace algorithm
✍ Stena Kettl πŸ“‚ Article πŸ“… 1989 πŸ› Elsevier Science 🌐 English βš– 179 KB
A note on Winkler's algorithm for factor
A note on Winkler's algorithm for factoring a connected graph
✍ Bernhard Hochstrasser πŸ“‚ Article πŸ“… 1992 πŸ› Elsevier Science 🌐 English βš– 529 KB

Hochstrasser, B., A note on Winkler's algorithm for factoring a connected graph, Discrete Mathematics 109 (1992) 127-132. Let the connected graph G be canonically embedded into a Cartesian product fl,,, CF. We improve a method of Winkler (1987) for partitioning I in a way suitable for finding the un