Computing with Hamiltonian operators

Hamiltonian operators for partial differential equations are ubiquitous in mathematical models of theoretical and applied physics. In this paper the new Reduce package CDE for computations with Hamiltonian operators is presented. CDE can verify the Hamiltonian properties of skew-adjointness and vanishing Schouten bracket for a differential operator, as well as the compatibility property of two Hamiltonian operators, and it can compute the Lie derivative of a Hamiltonian operator with respect to a vector field. More generally, it can compute with (variational) multivectors, or functions on supermanifolds. This can open the way to applications in other fields of mathematical or theoretical physics. (C) 2019 Elsevier B.V. All rights reserved.