This program simply computes the symmetrized covariant derivative of T with respect to the Christoffel symbols of the metric g or the connection C, that is, it computes the Killing tensor equation for T.

This command is part of the DifferentialGeometry:-Tensor package, and so can be used in the form CheckKillingTensor(...) only after executing the commands with(DifferentialGeometry), with(Tensor) in that order.  It can always be used in the long form DifferentialGeometry:-Tensor:CheckKillingTensor.

with(DifferentialGeometry): with(Tensor):

DGsetup([x, y], M):

g := evalDG((1/y)*dx &t dx + 1/x*dy &t dy);

K1 := evalDG((1/y^3)*dx &t dx &t dx - (1/x^3)*dy &t dy &t dy);

CheckKillingTensor(g, K1);

K2 := evalDG(A(y)*dx &t dx &t dx + B(x)*dy &t dy &t dy);

P := CheckKillingTensor(g, K2);

Tools:-DGinfo(P, "CoefficientSet");