79 citations · 407 across the 53 of their papers we have counts for
6 papers · 1 filter
Numerical computation of Galois groups
Jonathan D. Hauenstein, Jose Israel Rodriguez, Frank Sottile
The Galois/monodromy group of a family of geometric problems or equations is a subtle invariant that encodes the structure of the solutions. Computing monodromy permutations using…
Computing complex and real tropical curves using monodromy
Daniel A. Brake, Jonathan D. Hauenstein, Cynthia Vinzant
Tropical varieties capture combinatorial information about how coordinates of points in a classical variety approach zero or infinity. We present algorithms for computing the rays…
Decomposing the parameter space of biological networks via a numerical discriminant approach
Heather A. Harrington, Dhagash Mehta, Helen M. Byrne +1
Many systems in biology, physics and engineering can be described by systems of ordinary differential equation containing many parameters. When studying the dynamic behavior of the…
Investigating the Maximum Number of Real Solutions to the Power Flow Equations: Analysis of Lossless Four-Bus Systems
Daniel K. Molzahn, Matthew Niemerg, Dhagash Mehta +1
The power flow equations model the steady-state relationship between the power injections and voltage phasors in an electric power system. By separating the real and imaginary comp…
Numerically validating the completeness of the real solution set of a system of polynomial equations
Daniel A. Brake, Jonathan D. Hauenstein, Alan C. Liddell
Computing the real solutions to a system of polynomial equations is a challenging problem, particularly verifying that all solutions have been computed. We describe an approach tha…
On deflation and multiplicity structure
Jonathan D. Hauenstein, Bernard Mourrain, Agnes Szanto
This paper presents two new constructions related to singular solutions of polynomial systems. The first is a new deflation method for an isolated singular root. This construction…