Geodesic
Note on two compatibility criteria: Jacobi--Mayer bracket vs.\ differential Gr\"obner basis
Lobachevskii journal of mathematics, Tome 23 (2006), pp. 57-70

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We compare two compatibility criteria for overdetermined PDEs: one via geometric theory of differential equations and another via differential algebra approach. Whenever both are applicable, we show that the former is more effective, though in some very special cases they are equivalent.
Keywords: compatibility of differential equations, Jacobi bracket, Mayer bracket, differential Gröbner basis, Kolchin–Ritt algorithm. 
@article{LJM_2006_23_a2,
     author = {B. S. Kruglikov},
     title = {Note on two compatibility criteria: {Jacobi--Mayer} bracket vs.\ differential {Gr\"obner} basis},
     journal = {Lobachevskii journal of mathematics},
     pages = {57--70},
     publisher = {mathdoc},
     volume = {23},
     year = {2006},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/LJM_2006_23_a2/}
}
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B. S. Kruglikov. Note on two compatibility criteria: Jacobi--Mayer bracket vs.\ differential Gr\"obner basis. Lobachevskii journal of mathematics, Tome 23 (2006), pp. 57-70. http://geodesic.mathdoc.fr/item/LJM_2006_23_a2/