Bibliographic Details
| Title: |
Numerical homotopies from Khovanskii bases. |
| Authors: |
Burr, M.1 (AUTHOR), Sottile, F.2 (AUTHOR), Walker, E.2 (AUTHOR) |
| Source: |
Mathematics of Computation. Sep2023, Vol. 92 Issue 343, p2333-2353. 21p. |
| Subjects: |
Projective spaces, Toric varieties, Equations |
| 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 modification of the toric homotopy. Our algorithms are illustrated on several examples using Macaulay2. [ABSTRACT FROM AUTHOR] |
|
Copyright of Mathematics of Computation is the property of American Mathematical Society and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) |
| Database: |
Engineering Source |
