Characterization and Existence of Gröbner Bases

MATH536A Paper: Gröbner Bases

An introduction to Gröbner bases and some of their uses in affine algebraic geometry.

Universal Gröbner Bases in Orlik-solomon Algebras

, the Z-algebra OS(M) is isomorphic to the cohomology Z-algebra of the manifold M= C \ ⋃n i=1 Ker(θi). For every term order of the monoids of E, we construct the corresponding reduced Gröbner basis of the Orlik-Solomon ideal I(M). We prove that the set of circuit boundaries is a universal Gröbner basis of I(M). Every ordering of the elements of M determines a canonical basis of OS(M) (termed in...

A characterization of L-dual frames and L-dual Riesz bases

This paper is an investigation of $L$-dual frames with respect to a function-valued inner product, the so called $L$-bracket product on $L^{2}(G)$, where G is a locally compact abelian group with a uniform lattice $L$. We show that several well known theorems for dual frames and dual Riesz bases in a Hilbert space remain valid for $L$-dual frames and $L$-dual Riesz bases in $L^{2}(G)$.

Automatic Geometric Theorem Proving using Gröbner Bases

On Gröbner Bases in Monoid and Group Rings