Symbolic Computation Group

In an earlier talk in September 2003 at ORCCA I showed problems concerning the integrability of Hamiltonian systems that require the solution of large overdetermined systems of bi-linear algebraic equations. Since then it became possible to solve even larger problems involving about 900 conditions for >450 unknowns which could not be solved before. Two new techniques are responsible, one is the dynamic adaptation of solution strategies to the continuing change of the system under investigation. The other one involves the continuous collection, modification and utilization of inequalities which will be the main content of the talk. Other, shorter topics will be programming issues that are also essential for solving large systems of equations.