KARASOULOU , Anna

The contribution of the thesis is threefold. The first Problem is computing the discriminant, when the system's dimension varies. Thus solving polynomial equations and systems by exploiting the structure and sparseness of them have been studied. Specifically, closed formulas for the degree of the sparse (mixed) discriminant and the sparse...

Given a system of n homogeneous polynomials in n variables which is equivariant with respect to the canonical actions of the symmetric group of n symbols on the variables and on the polynomials, it is proved that its resultant can be decomposed into a product of several smaller resultants that are given in terms of some divided differences. As...

We consider the approximation of two NP-hard problems: Minkowski Decomposition (MinkDecomp) of lattice polygons in the plane and the closely related problem of Multidimensional Subset Sum (kD-SS) in arbitrary dimension. In kD-SS we are given an input set S of k-dimensional vectors, a target vector t and we ask, if there exists a subset of S...