DART XII

Kassel (Germany) April 9^{th} - 12^{th} 2024

XII. Conference on Differential Algebra and Related Topics

April 9^{th} - 12^{th} 2024

Kassel University, Germany

Here, we consider general equilibria. That is, we study positive solutions to parametrized systems of generalized polynomial equations (with real exponents). We identify the relevant geometric objects of the problem, namely the coefficient polytope and the monomial difference and monomial dependency subspaces. As our main result, we rewrite the polynomial equations in terms of binomial equations on the coefficient polytope. Notably, polynomial inequalities (arising from stability or multistationarity considerations) are also covered by our result.

Joint work with Georg Regensburger.