## Symbolic Exploitation of Symmetry in Numerical Path-following.

• Parameter-dependent systems of nonlinear equations with symmetry are treated by a combination of symbolic and numerical computations. In the symbolic part of the algorithm the complete analysis of the symmetry occurs, and it is here where symmetrical normal forms, symmetry reduced systems, and block diagonal Jacobians are computed. Given a particular problem, the symbolic algorithm can create and compute through the list of possible bifurcations thereby forming a so-called tree of decisions correlated to the different types of symmetry breaking bifurcation points. The remaining part of the algorithm deals with the numerical pathfollowing based on the implicit reparametrisation as suggested and worked out by Deuflhard/Fiedler/Kunkel. The symmetry preserving bifurcation points are computed using recently developed augmented systems incorporating the use of symmetry. {\bf Keywords:} pathfollowing, mixed symbolic-numeric algorithm, parameter-dependent, nonlinear systems, linear representations.

Author: Karin Gatermann, Andreas Hohmann ZIB-Report linear representations; mixed symbolic-numeric algorithm; nonlinear systems; parameter dependent; pathfollowing 1990/11/12 ZIB-Report (SC-90-11) No preprint available; the article appeared in: IMPACT Comput. Sci. Eng. 3 (1991) pp. 330-365 Appeared in: IMPACT Comput. Sci. Eng. 3 (1991) pp. 330-365