Complexity of Irreducibility Testing for a System of Linear Ordinary Differential Equations

Let a system of linear ordinary differential equations of the first order Y' = AY be given, where A is n x n matrix over a field F(X), assume that the degree degx(A) < d and the size of any coefficient occuring in A is at most M. The system Y' = AY is called reducible if it is equivalent (over the field F(X)) to a system Y{ = AIYl with a matrix A1 of the form Al = ALI0 A2,1 A2,2 An algorithm is described for testing irreducibility of the system with the running time exp(M(d2")d2").

• Type: Conference
• Year: 1990
• Where: ISSAC
• Authors: Dima Grigoriev
• Keywords: Coefficient Occuring, ISSAC 1990, Mathematics, Matrix, Order Y