Numerical homotopies from Khovanskii bases Institutional Repository Document uri icon

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.

author list (cited authors)

  • Burr, M., Sottile, F., & Walker, E.

complete list of authors

  • Burr, Michael||Sottile, Frank||Walker, Elise

publication date

  • August 2020