# 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.

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:

14J80

Keywords: