Projections methods for the topology of algebraic curves and <br/><br/>surfaces

Tuesday, September 19, 2006 - 1:40pm - 2:30pm
EE/CS 3-180
Bernard Mourrain (Institut National de Recherche en Informatique Automatique (INRIA))
We described algorithms for computing the topology of real algebraic
implicit curves and surfaces in dimension 3, based on projections
techniques, starting with the algorithm for implicit planar curves.
Then we consider curves in dimension 3. Next we describe an algorithm
for computing the topology of a general real algebraic surface S. The
approach is based on tools from stratification theory and the
construction of an explicit Whitney stratification of S.
We show how these methods can be turned into effective
algorithms, using resultant ans subresultant computations
and discussed the problem of iterated resultants and discriminants, for
which we give some explicit formula.
MSC Code: