CDE: A REDUCE PACKAGE FOR INTEGRABILITY OF PDES VERSION 2.0

The Reduce package CDE is devoted to integrability of general differential equations (i.e., not necessarily in evolution form) with an arbitrary number of dependent and independent variables. It can compute linearization and adjoints of differential operators in total derivatives, generalized symmetries, conservation laws, Hamiltonian, symplectic and recursion operators, with local and nonlocal coordinates. Schouten brackets between local Hamiltonian operators, also in multidimensions, can be computed. The simplecticity tests for local operators can also be computed. The extension of the Schouten bracket to nonlocal operators is currently under development, as well as symplecticity and hereditariety properties for nonlocal operators. CDE is part of the official Reduce distribution, and can be obtained here, click on the more recent snapshot directory. It is distributed in different binary files for various operating systems (Windows, macOS, Linux).