A Comparison of Two Methods to Calculate Conservation Laws of PDE systems Thomas Wolf Queen Mary and Westfield College, London email: tw@maths.qmw.ac.uk The methods of calculating conservation laws either directly or through the calculation of their characteristic function are compared concerning the the invariance of the result they provide and their complexity. Two corresponding computer algebra programs are compared concerning the range of problems they are applicable to and their efficiency. Applications are given including a conservation law of an evolutionary system of equations known from plasma physics with a conserved density depending explicitly on the independent variables.