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arXiv · 2008.13055

Numerical homotopies from Khovanskii bases

Michael Burr·Frank Sottile·Elise Walker
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Abstract

We present numerical homotopy continuation algorithms for solving systems of equations on a variety in the presence of a finite Khovanskii basis. These take advantage of Anderson's flat degeneration to a toric variety. When Anderson's degeneration embeds into projective space, our algorithm is a special case of a general toric two-step homotopy algorithm. When Anderson's degeneration is embedded in a weighted projective space, we explain how to lift to a projective space and construct an appropriate modification of the toric homotopy. Our algorithms are illustrated on several examples using Macaulay2.

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Michael Burr, Frank Sottile, Elise Walker. 2020-08-29. Numerical homotopies from Khovanskii bases. https://arxiv.org/abs/2008.13055

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