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Session S34 - Symbolic and Numerical Computation with Polynomials

Friday, July 16, 12:30 ~ 13:00 UTC-3

Numerical homotopies from Khovanskii bases

Elise Walker

Texas A&M University, USA   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

Homotopies are useful numerical methods for solving systems of polynomial equations. Embedded toric degenerations are one source for homotopy algorithms. In particular, if a projective variety has a toric degeneration, then linear sections of that variety can be optimally computed using the polyhedral homotopy. Any variety whose coordinate ring has a finite Khovanskii basis is known to have a toric degeneration. We provide embeddings for this Khovanskii toric degeneration and use the resulting homotopy to compute general linear sections of the variety.

Joint work with Michael Burr (Clemson University, USA) and Frank Sottile (Texas A&M University, USA).

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