aequationes mathematicae

, Volume 38, Issue 1, pp 86–98 | Cite as

A computation of the Witt index for rational quadratic forms

  • Stephen Beale
  • D. K. Harrison
Research Papers


This paper adds the finishing touches to an algorithmic treatment of quadratic forms over the rational numbers. The Witt index of a rational quadratic form is explicitly computed. When combined with a recent adjustment in the Haase invariants, this gives a complete set of invariants for rational quadratic forms, a set which can be computed and which respects all of the standard natural operations (including the tensor product) for quadratic forms. The overall approach does not use (at least explicitly) anyp-adic methods, but it does give the Witt ring of thep-adics as well as the Witt ring of the rationals.

AMS (1980) subject classification

Primary 11E81 


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  1. [1]
    DeMeyer, F., Harrison, D., andMiranda, R.,Quadratic forms over Q and Galois extensions of commutative rings. Mem. Amer. Math. Soc., Nr. 77. Amer. Math. Soc., Providence, RI, 1989.Google Scholar
  2. [2]
    Lam, T. Y.,The algebraic theory of quadratic forms. W.A. Benjamin Inc., Reading, MA, 1973.Google Scholar

Copyright information

© Birkhäuser Verlag 1989

Authors and Affiliations

  • Stephen Beale
    • 1
  • D. K. Harrison
    • 1
  1. 1.Department of MathematicsUniversity of OregonEugeneUSA

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