"Geometry and Polynomial Systems - Theory and  Application"
  Peter F. Stiller
  stiller@alggeo.math.tamu.edu


Dr. Peter F. Stiller
Professor of Mathematics and Computer Science and
Assistant Director of the Institute for Scientific Computation
Texas A&M University
College Station, TX   77843-3368  USA
stiller@alggeo.math.tamu.edu



We discuss some general geometric aspects of polynomial systems and  
their solution by computer algebra systems.  This includes a  
discussion of certain anomalies that can be introduced when solving  
certain systems.  If time permits, we will also discuss some  
applications of computer algebra to solving systems that arise in  
dexterous manipulation planning problems in robotics and in the  
problem of indexing geometric databases for content-based retrieval  
(for example image databases.)  In the first case, the polynomial  
systems characterize the so-called contact formation cells of a  
manipulator system.  These are constraint varieties in configuration  
space that reflect a particular type of grasp.  In the second case,  
we are concerned with generating the equations that define the  
correspondence (in the sense of algebraic geometry) between the  
geometric invariants of certain features of a set of objects and the  
invariants of the images of those features.