2023
DOI: 10.1090/mcom/3689
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Numerical homotopies from Khovanskii bases

Abstract: We present numerical homotopy continuation algorithms for solving systems of equations on a variety in the presence of a finite Khovanskii basis. These homotopies 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… Show more

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Cited by 7 publications
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