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math.AG2025
The SagbiHomotopy.jl package for solving polynomial systems
Barbara Betti, Viktoriia Borovik
We present the Julia package SagbiHomotopy.jl for solving systems of polynomial equations using numerical homotopy continuation. The package introduces an optimal choice of a start…
math.AG2024
Proudfoot-Speyer degenerations of scattering equations
Barbara Betti, Viktoriia Borovik, Simon Telen
We study scattering equations of hyperplane arrangements from the perspective of combinatorial commutative algebra and numerical algebraic geometry. We formulate the problem as lin…
math.AG2023
Solving Equations Using Khovanskii Bases
Barbara Betti, Marta Panizzut, Simon Telen
We develop a new eigenvalue method for solving structured polynomial equations over any field. The equations are defined on a projective algebraic variety which admits a rational p…