An empirical case study of how to embed a fixed polynomial system into a good vertically parametrised family, one whose generic algebraic invariants (dimension and generic root count) match the original. Using every polynomial system in the ODEbase chemical-reaction-network database, transcribed to OSCAR and released as the Julia package OscarODEbase, the authors find that the original parametrised system minimises the number of distinct monomials, and they propose and benchmark a greedy embedding algorithm against the optimum.
Vertically parametrised polynomial systems are a class of parametrised polynomial systems in which much algebraic information is encoded in the system's combinatorics. This paper empirically studies,…