Using SAGBI Bases to Compute Rings of Invariants

  • H. E. A. Eddy CampbellEmail author
  • David L. Wehlau
Part of the Encyclopaedia of Mathematical Sciences book series (EMS, volume 139)


In (Shank, 1998), Shank constructed generating sets, in fact, SAGBI bases, for the rings \(\mathbb{F}[V_{4}]^{C_{p}}\) and \(\mathbb{F}[V_{5}]^{C_{p}}\) for all primes p≥5. Of course, for the primes p=2,3, the corresponding actions are actions of \(C_{p^{2}}\) or \(C_{p^{3}}\), not C p . The rings of invariants \(\mathbb{F}[V_{4}]^{C_{4}}\), \(\mathbb{F}[V_{4}]^{C_{9}}\), \(\mathbb{F}[V_{5}]^{C_{8}}\) and \(\mathbb{F}[V_{5}]^{C_{9}}\) are all easily computed by computer, for example, using MAGMA.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 98.
    R. James Shank, S.A.G.B.I. bases for rings of formal modular seminvariants, Comment. Math. Helv. 73 (1998), no. 4, 548–565. MR 2000a:13016 zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  1. 1.Sir Howard Douglas Hall, Dept. MathematicsUniversity of New BrunswickFrederictonCanada
  2. 2.Dept. Mathematics & Computer ScienceRoyal Military College of CanadaKingstonCanada

Personalised recommendations