𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Differential Equations and Algebraic Relations

✍ Scribed by Elie Compoint

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
542 KB
Volume
25
Category
Article
ISSN
0747-7171

No coin nor oath required. For personal study only.

✦ Synopsis

We consider a linear differential equation Ly = 0 of order n with coefficients in C(z) whose differential Galois group G is supposed to be reductive and unimodular. We give an algorithm for the construction of a system of generators of the ideal of algebraic relations, with coefficients in C(z), among the entries of a fundamental matrix of solutions of Ly = 0, starting from the data of a C-algebra basis of the G invariant polynomials with coefficients in C in n vector variables.

πŸ“œ SIMILAR VOLUMES

Asymptotic Forms and Algebraic Different
Asymptotic Forms and Algebraic Differential Equations
✍ John Shackell; Bruno Salvy πŸ“‚ Article πŸ“… 1995 πŸ› Elsevier Science 🌐 English βš– 301 KB

We analyse the complexity of a simple algorithm for computing asymptotic solutions of algebraic differential equations. This analysis is based on a computation of the number of possible asymptotic monomials of a certain order, and on the study of the growth of this number as the order of the equatio