Symbolic computation for Witt rings

  • Algimantas Juozapavičius
Algorithmic Number Theory
Part of the Lecture Notes in Computer Science book series (LNCS, volume 358)


In this paper we consider bilinear and quadratic forms over polynomial rings, such that they can carry linear discrete orderings. We define the notion of reduced form and present theorems concerning equivalence of forms to their reduced presentation. The proofs of these statements are based on the Buchberger's algorithms and their modifications to Gröbner bases.


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  1. 1.
    A. Suslin. "The projective modules are free over polynomial rings", Doklady-Soviet Math., vol.229, pp.1063–66, 1976.Google Scholar
  2. 2.
    M.Knebusch, M.Kolster. "Wittrings", Friedr.Vieweg & Sohn, Brauschweig/Wiesbaden, 1982.Google Scholar
  3. 3.
    B.Buchberger. "Gröbner bases: an algorithmic method in polynomial ideal theory", in N.K.Bose (ed.): Recent trends in multidimensional systems theory, D.Rheidel Publ. Comp., chapter 6.Google Scholar
  4. 4.
    G.L.Watson. "Integral Quadratic Forms", Cambridge University Press, 1960.Google Scholar
  5. 5.
    P.Gianni. "Properties of Gröbner bases under specializations", to be published.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1989

Authors and Affiliations

  • Algimantas Juozapavičius
    • 1
  1. 1.Department of MathematicsVilnius State UniversityVilnius, LithuaniaU.S.S.R.

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