Abstract: We report, through different examples, the current development in GeoGebra, a widespread
Dynamic Geometry software, of geometric automated reasoning tools by means of computational
algebraic geometry algorithms. Then we introduce and analyze the case of the degeneracy conditions
that so often arise in the automated deduction in geometry context, proposing two different ways
for dealing with them. One is working with the saturation of the hypotheses ideal with respect
to the ring of geometrically independent variables, as a way to globally handle the statement
over all non-degenerate components. The second is considering the reformulation of the given
hypotheses ideal?considering the independent variables as invertible parameters?and developing
and exploiting the specific properties of this zero-dimensional case to analyze individually the truth
of the statement over the different non-degenerate components
