This note extends the algorithm of [hess] for computing unimodular Galois groups of irreducible differential equations of order four. The main tool is invariant theory.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc58-0-7, author = {Julia Hartmann}, title = {Invariants and differential Galois groups in degree four}, journal = {Banach Center Publications}, volume = {58}, year = {2002}, pages = {79-87}, zbl = {1030.12003}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc58-0-7} }
Julia Hartmann. Invariants and differential Galois groups in degree four. Banach Center Publications, Tome 58 (2002) pp. 79-87. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc58-0-7/