Algorithms for symbolic and numeric manipulation of systems are needed for basic symbolic, numeric and geometric computations and their application to problems in graphics, geometric modeling, robotics, vision and engineering. This research takes a three-fold approach to these problems using multipolynomial resultants: (1) Develop better algorithms for symbolic resultant computation and solving nonlinear polynomial equations using resultants and matrix computations. Algorithms are being developed in the context of exact arithmetic as well as floating point arithmetic. It involves better formulations of resultants in terms of matrices and determinants and use of symbolic and numeric algorithms making use of the matrix formulation. (2) Specialize these algorithms to applications in computer graphics, geometric modeling and robotics by making use of the specific polynomial systems arising in these applications. (3) Develop a library of routines, ELIMPACK, for symbolic resultant computation and finding roots of polynomial equations (in exact and floating point arithmetic). This package is of great utility to symbolic computation, numerical computation, geometric applications and the engineering community. The results also help in understanding the complexity of geometric problems described in terms of polynomial equations.
