Qualitative symbolic perturbation: two applications of a new geometry-based perturbation framework

In a classical Symbolic Perturbation scheme, degeneracies are handled by substituting some polynomials in $\varepsilon$ for the inputs of a predicate. Instead of a single perturbation, we propose to use a sequence of (simpler) perturbations. Moreover, we look at their effects geometrically instead of algebraically; this allows us to tackle cases that were not tractable with the classical algebraic approach