Using SAGBI bases to compute invariants (Q1295793)

In this paper, the authors extend Miller's SAGBI basis theory [\textit{J. L. Miller}, J. Symb. Comput. 21, No. 2, 139-153 (1996; Zbl 0867.13007)]. The paper is organized as follows. In section 2, the authors introduce a SAGBI basis theory for quotients of a polynomial ring by an ideal \(I\) which reduces to the usual SAGBI basis theory when \(I\) is the zero ideal. In section 3, they consider the simplest case of quotient ring SAGBI theory, when \(A\) is a monomial subalgebra over a field and \(I\) is a binomial ideal. They show that a finitely generated monomial subalgebra has a finite SAGBI basis if \(I\) is a lattice ideal. Finally, in section 4, they describe how the quotient ring SAGBI algorithm can be applied to computing invariants. The authors show that the SAGBI algorithm terminates when applied to computing invariants of actions of the torus or a finite abelian group.