Since being introduced by Collins in the 1970s Cylindrical Algebraic Decomposition has found many applications. We focus on its use to decomposition the parameter space of a parametric system of polynomial equations, and possibly some polynomial inequality constraints, with respect to the number of real solutions that the system attains. Previous studies simplify the CAD computation by first computing the discriminant variety of the system, which usually involves Gr¨obner Basis computation. However, on some even very small applied examples this itself can become expensive. Thus we consider development of new algorithms to reduce the complexity of this approach, by adopting numerical ideas and some recent technical developments in CAD theory. In this extended abstract we outline our recent progress as evaluated on an example from population dynamics with the Allee effect.
|Number of pages||4|
|Publication status||Published - 14 Sep 2021|
|Event||23rd International Workshop on Computer Algebra in Scientific Computing - Sochi, Russian Federation|
Duration: 13 Sep 2021 → 17 Sep 2021
|Conference||23rd International Workshop on Computer Algebra in Scientific Computing|
|Abbreviated title||CASC 2021|
|Period||13/09/21 → 17/09/21|