Gröbner Bases for the Rings of Special Orthogonal and 2×2 Matrix Invariants

Pivoting in Extended Rings for Computing Approximate Gröbner Bases

It is well known that in the computation of Gröbner bases arbitrarily small perturbations in the coefficients of polynomials may lead to a completely different staircase, even if the solutions of the polynomial system change continuously. This phenomenon is called artificial discontinuity in Kondratyev’s Ph.D. thesis. We show how such phenomenon may be detected and even “repaired” by using a ne...

Utilizing Moment Invariants and Gröbner Bases to Reason About Shapes

Shapes such as triangles or rectangles can be defined in terms of geometric properties invariant under a group of transformations. Complex shapes can be described by logic formulae w i th simpler shapes as the atoms. A standard technique for computing invariant properties of simple shapes is the method of moment invariants, known since the early sixties. We generalize this technique to shapes d...

Sagbi Bases in Rings of Multiplicative Invariants

Let k be a field and G be a finite subgroup of GLn(Z). We show that the ring of multiplicative invariants k[x±1 1 , . . . , x ±1 n ] G has a finite SAGBI basis if and only if G is generated by reflections.

On Gröbner bases in monoid and group rings

Multiplicative Bases, Gröbner Bases, and Right Gröbner Bases

Before surveying the results of the paper, we introduce path algebras. Path algebras play a central role in the representation theory of finite-dimensional algebras (Gabriel, 1980; Auslander et al., 1995; Bardzell, 1997) and the theory of Gröbner bases (Bergman, 1978; Mora, 1986; Farkas et al., 1993) has been an important tool in some results (Feustel et al., 1993; Green and Huang, 1995; Bardze...