View in EDS

Numerical homotopies from Khovanskii bases.

Saved in:
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
FullText Text:
  Availability: 0
Header DbId: egs
DbLabel: Engineering Source
An: 163884667
AccessLevel: 6
PubType: Academic Journal
PubTypeId: academicJournal
PreciseRelevancyScore: 0
IllustrationInfo
Items – Name: Title
  Label: Title
  Group: Ti
  Data: Numerical homotopies from Khovanskii bases.
– Name: Author
  Label: Authors
  Group: Au
  Data: <searchLink fieldCode="AR" term="%22Burr%2C+M%2E%22">Burr, M.</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Sottile%2C+F%2E%22">Sottile, F.</searchLink><relatesTo>2</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Walker%2C+E%2E%22">Walker, E.</searchLink><relatesTo>2</relatesTo> (AUTHOR)
– Name: TitleSource
  Label: Source
  Group: Src
  Data: <searchLink fieldCode="JN" term="%22Mathematics+of+Computation%22">Mathematics of Computation</searchLink>. Sep2023, Vol. 92 Issue 343, p2333-2353. 21p.
– Name: Subject
  Label: Subjects
  Group: Su
  Data: <searchLink fieldCode="DE" term="%22Projective+spaces%22">Projective spaces</searchLink><br /><searchLink fieldCode="DE" term="%22Toric+varieties%22">Toric varieties</searchLink><br /><searchLink fieldCode="DE" term="%22Equations%22">Equations</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: 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]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>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.</i> (Copyright applies to all Abstracts.)
PLink https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=egs&AN=163884667
RecordInfo BibRecord:
  BibEntity:
    Identifiers:
      – Type: doi
        Value: 10.1090/mcom/3689
    Languages:
      – Code: eng
        Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 21
        StartPage: 2333
    Subjects:
      – SubjectFull: Projective spaces
        Type: general
      – SubjectFull: Toric varieties
        Type: general
      – SubjectFull: Equations
        Type: general
    Titles:
      – TitleFull: Numerical homotopies from Khovanskii bases.
        Type: main
  BibRelationships:
    HasContributorRelationships:
      – PersonEntity:
          Name:
            NameFull: Burr, M.
      – PersonEntity:
          Name:
            NameFull: Sottile, F.
      – PersonEntity:
          Name:
            NameFull: Walker, E.
    IsPartOfRelationships:
      – BibEntity:
          Dates:
            – D: 01
              M: 09
              Text: Sep2023
              Type: published
              Y: 2023
          Identifiers:
            – Type: issn-print
              Value: 00255718
          Numbering:
            – Type: volume
              Value: 92
            – Type: issue
              Value: 343
          Titles:
            – TitleFull: Mathematics of Computation
              Type: main
ResultId 1