This program first computes all partitions [p1, p2, ... ] of the integer p, that is, all non-decreasing sequences p1, p2, ... with p1 + p2 + p3 + ... = p.  Then, for each partition, all possible rank p symmetric tensors of the form T_1 &s T_2 &s T3 ..., where the tensor T_i is taken from the list K_i, are generated.  From the totality of tensors so obtained a maximal set of linearly independent tensors (over the real numbers) is selected.  Each symmetric tensor in the returned list is a Killing tensor if each of the K_i are.

The independent tensors are generated by a call to the DifferentialGeometry command DGbasis.  For tensors with coefficients which are not rational functions, the DGbasis program may work faster using a Wronskian approach which requires the specification of a list of points on M.

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