Title: Applications of Transcendental Zero Bounds to Geometric Computation
Sung Woo Choi
Abstract:
The zero problem is to determine whether a given numerical expression
is zero or not. It is central to many areas which need exact
qualititive decisions. So far the results on the zero problem have
been rather succesful for so called 'algebraic expressions', which
involve only the basic operations +,-,x,/,RoofOf(). These
developments, especially in Exact Geometric Computation, are
theoretically due to systematic use of various bounds for roots of
polynomials away from zero. Recently, there appeared a few concrete
results concerning the zero problem for 'transcendental expressions',
ie, expressions which involve more than just the basic operations so
that they contain Exp or Log for example. In this talk, we present
two specific results on geometric computation, whose solution uses a
variant of the renowned Baker's theorem which provides effective
bounds for a transcendental expression called 'linear forms in
logarithms'.