• Publications
  • Influence
Liouvillian Solutions of Linear Differential Equations of Order Three and Higher
TLDR
Singer and Ulmer (1997) gave an algorithm to compute Liouvillian (“closed-form") solutions of homogeneous linear differential equations. Expand
  • 63
  • 6
  • PDF
An algorithm for computing invariants of differential Galois groups
This paper presents an algorithm to compute invariants of the differential Galois group of linear differential equations L(y) = 0: if V(L) is the vector space of solutions of L(y) = 0, we show howExpand
  • 59
  • 3
  • PDF
Note on Kovacic's algorithm
TLDR
We compute the liouvillian solutions rn.--1 of L ( y ) = y" r y = 0 by computing the minimal polynomial P ( u ) = u '~ + ~i=0 bi ul of an algebraic solution of R i ( u) = u ~ ao a l u + u s = O. Expand
  • 63
  • 1
Computing closed form solutions of integrable connections
TLDR
We present algorithms for computing rational and hyperexponential solutions of linear D-finite partial differential systems written as integrable connections by adapting existing algorithms handling ordinary linear differential systems. Expand
  • 20
  • 1
  • PDF
Note on Kovacic's Algorithm
TLDR
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. Expand
  • 39
  • 1
Non-integrability of the generalized spring-pendulum problem
We investigate a generalization of the three-dimensional spring-pendulum system. The problem depends on two real parameters (k, a), where k is the Young modulus of the spring and a describes theExpand
  • 19
  • 1
On symmetric powers of differential operators
TLDR
We present alternative algorithms for computing symmetric powers of linear ordinary differential operators with coefficients in arbitrary integral domains and become faster than the traditional methods. Expand
  • 22
  • 1
Solving second order linear differential equations with Klein's theorem
TLDR
We give an algorithm for solving second order differential by pullbacks for a general differential field k by constructing new formulas which rely on invariants only. Expand
  • 27
  • 1
  • PDF
A reduced form for linear differential systems and its application to integrability of Hamiltonian systems
TLDR
We show how to compute reduced forms of some symplectic differential systems, arising as variational equations of Hamiltonian systems. Expand
  • 13
  • 1
  • PDF
Recent Algorithms for Solving Second-Order Dierential Equations
(2) Lry ≡ ∂y − r(x)y = 0 where r(x) = A1 4 + A1 2 −A2 Given two linearly independent solutions of (1), say y1, y2, either formal or actual, the differential fieldK generated byK, y1 and y2 is calledExpand
  • 6
  • 1
  • PDF
...
1
2
3
4
5
...