Complexity of irreducibility testing for a system of linear ordinary differential equations
Dima Yu. Grigoriev · 1990
Let a system of linear ordinary differential equations of the first order Y′ = AY be given, where A is n × n matrix over a field F(X), assume that the degree degX(A) < d and the size of any coefficient occurring 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&prime1 = A1Y1 with a matrix A1 of the form A1 = (A1,1 0) (A2,1 A2,2)