It is my understanding that if one has a (possibly overdetermined) system of PDEs, one can check for compatibility by applying Cartan's test (see for example [1], Chapter 7). It involves first writing the equations as an Exterior Differential System. My question is this: is there a Computer Algebra system that, given a system of PDEs, can apply this test for you?
[1] Ivey, Thomas Andrew, and Joseph M. Landsberg. Cartan for beginners: differential geometry via moving frames and exterior differential systems. Vol. 61. Providence, RI: American Mathematical Society, 2003.