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 parameterization by a Khovanskii basis, e.g., a Grassmannian in its Plücker embedding. This generalizes established algorithms for toric varieties, and introduces the effective use of Khovanskii bases in computer algebra. We investigate regularity questions and discuss several applications.

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Journal of Symbolic Computation
Centrum Wiskunde & Informatica, Amsterdam (CWI), The Netherlands

Betti, B., van Krieken, S., & Telen, S. J. L. (2025). Solving equations using Khovanskii bases. Journal of Symbolic Computation, 126, 102340:1–102340:21. doi:10.1016/j.jsc.2024.102340