@article{berman_singer_1999, title={Calculating the Galois group of L-1(L-2(y))=0, L-1,L-2 completely reducible operators}, volume={139}, ISSN={["0022-4049"]}, DOI={10.1016/S0022-4049(99)00003-1}, abstractNote={In Calculating Galois groups of completely reducible linear operators, Compoint and Singer describe a decision procedure that computes the Galois group of a completely reducible linear differential operator with rational or algebraic function coefficients (i.e., a linear differential operator that is the least common left multiple of irreducible operators or, equivalently, one whose Galois group is a reductive group). At present, it is unknown how to calculate the Galois group of a general operator. In this paper, we push beyond the completely reducible case by showing how to compute the Galois group of an operator of the form L1∘L2 where L1 and L2 are completely reducible and have rational function coefficients. We begin by showing how to compute the Galois group of an equation of the form L(y)=b with L completely reducible. This corresponds to the case of L1∘L2 where L1=D−b′/b. We then show how one can reduce the general case to the above case and give several examples.}, number={1-3}, journal={JOURNAL OF PURE AND APPLIED ALGEBRA}, author={Berman, PH and Singer, MF}, year={1999}, month={Jun}, pages={3–23} }