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Algorithms for quadratic forms over real function fields

Volume 108 / 2016

Konrad Jałowiecki, Przemysław Koprowski Banach Center Publications 108 (2016), 133-141 MSC: 11E25, 14P05, 14Q99, 68W30. DOI: 10.4064/bc108-0-10

Abstract

This paper presents algorithms for quadratic forms over a formally real algebraic function field $K$ of one variable over a fixed real closed field~$\bf k$. The algorithms introduced in the paper solve the following problems: test whether an element is a square, respectively a local square, compute Witt index of a quadratic form and test if a form is isotropic/hyperbolic. Finally, we remark on a method for testing whether two function fields are Witt equivalent.

Authors

  • Konrad JałowieckiInstitute of Mathematics
    University of Silesia
    Bankowa 14
    40-007 Katowice, Poland
    e-mail
  • Przemysław KoprowskiInstitute of Mathematics
    University of Silesia
    Bankowa 14
    40-007 Katowice, Poland
    e-mail

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