Abstract
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.
References
A. Suslin. "The projective modules are free over polynomial rings", Doklady-Soviet Math., vol.229, pp.1063–66, 1976.
M.Knebusch, M.Kolster. "Wittrings", Friedr.Vieweg & Sohn, Brauschweig/Wiesbaden, 1982.
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.
G.L.Watson. "Integral Quadratic Forms", Cambridge University Press, 1960.
P.Gianni. "Properties of Gröbner bases under specializations", to be published.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1989 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Juozapavičius, A. (1989). Symbolic computation for Witt rings. In: Gianni, P. (eds) Symbolic and Algebraic Computation. ISSAC 1988. Lecture Notes in Computer Science, vol 358. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-51084-2_25
Download citation
DOI: https://doi.org/10.1007/3-540-51084-2_25
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-51084-0
Online ISBN: 978-3-540-46153-1
eBook Packages: Springer Book Archive