5 papers
Segre-Driven Radicality Testing
Martin Helmer, Elias Tsigaridas
We present a probabilistic algorithm to test if a homogeneous polynomial ideal defining a scheme in is radical using Segre classes and other geometric notion…
Probabilistic Saturations and Alt's Problem
Jonathan D. Hauenstein, Martin Helmer
Alt's problem, formulated in 1923, is to count the number of four-bar linkages whose coupler curve interpolates nine general points in the plane. This problem can be phrased as cou…
Families of Toric Chemical Reaction Networks
Michael F. Adamer, Martin Helmer
We study families of chemical reaction networks whose positive steady states are toric, and therefore can be parameterized by monomials. Families are constructed algorithmically fr…
Multistationarity and Bistability for Fewnomial Chemical Reaction Networks
Elisenda Feliu, Martin Helmer
Bistability and multistationarity are properties of reaction networks linked to switch-like responses and connected to cell memory and cell decision making. Determining whether and…
Segre Class Computation and Practical Applications
Corey Harris, Martin Helmer
Let be closed (possibly singular) subschemes of a smooth projective toric variety . We show how to compute the Segre class as a class in the Chow group of…