Symbolic Manipulation of Differential Systems with AXIOM Computer Algebra System

摘要

Advanced symbolic computation methods are needed, when studying formal propertiesof systems of partial differential equations. One suitable tool for this is the computer algebra system AXIOM. The report present new AXIOM structures that can handle quite general differential systems. The main emphasis is in describing the new programs and giving examples of their use, while the mathematical background is only briefly sketched. The algorithms are capable of defining and prolonging differential systems and finding their symbol. The problem of redundant equations found when projecting systems down is solved with Grobner basis algorithms.