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Isotropic vectors over global fields.

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Title: Isotropic vectors over global fields.
Authors: Koprowski, Przemysław1 (AUTHOR)
Source: Mathematics of Computation. May2026, Vol. 95 Issue 359, p1541-1567. 27p.
Subjects: Quadratic forms, Algorithms, Algebraic field theory, Vector algebra, Computational mathematics
Abstract: An isotropic vector of a given quadratic form is a nonzero vector where the form vanishes. Geometrically, it is a vector that is self-orthogonal with respect to this form. On the other hand, from the arithmetical point of view, an isotropic vector forms a solution to a multivariate quadratic equation. The problem of constructing isotropic vectors is one of the leading forces in the computational theory of quadratic forms. In this paper, we present algorithms for finding isotropic vectors of quadratic forms (of any dimension) over an arbitrary global field of characteristic distinct from 2. [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: 191660138
AccessLevel: 6
PubType: Academic Journal
PubTypeId: academicJournal
PreciseRelevancyScore: 0
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  Data: Isotropic vectors over global fields.
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  Data: <searchLink fieldCode="JN" term="%22Mathematics+of+Computation%22">Mathematics of Computation</searchLink>. May2026, Vol. 95 Issue 359, p1541-1567. 27p.
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  Data: An isotropic vector of a given quadratic form is a nonzero vector where the form vanishes. Geometrically, it is a vector that is self-orthogonal with respect to this form. On the other hand, from the arithmetical point of view, an isotropic vector forms a solution to a multivariate quadratic equation. The problem of constructing isotropic vectors is one of the leading forces in the computational theory of quadratic forms. In this paper, we present algorithms for finding isotropic vectors of quadratic forms (of any dimension) over an arbitrary global field of characteristic distinct from 2. [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.)
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RecordInfo BibRecord:
  BibEntity:
    Identifiers:
      – Type: doi
        Value: 10.1090/mcom/4165
    Languages:
      – Code: eng
        Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 27
        StartPage: 1541
    Subjects:
      – SubjectFull: Quadratic forms
        Type: general
      – SubjectFull: Algorithms
        Type: general
      – SubjectFull: Algebraic field theory
        Type: general
      – SubjectFull: Vector algebra
        Type: general
      – SubjectFull: Computational mathematics
        Type: general
    Titles:
      – TitleFull: Isotropic vectors over global fields.
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          Name:
            NameFull: Koprowski, Przemysław
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          Dates:
            – D: 01
              M: 05
              Text: May2026
              Type: published
              Y: 2026
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              Value: 95
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              Value: 359
          Titles:
            – TitleFull: Mathematics of Computation
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