6 papers
Graded Algebras over Polynomial Rings
Martin Kreuzer, Lorenzo Robbiano
Given a trivially graded polynomial ring over a field and a positively graded polynomial ring , we study graded rings , where $I…
Re-Embeddings of Special Border Basis Schemes
Martin Kreuzer, Lorenzo Robbiano
Border basis schemes are open subschemes of the Hilbert scheme of points in an affine space . They have easily describable systems of generators of their vanishi…
Efficiently Checking Separating Indeterminates
Bernhard Andraschko, Martin Kreuzer, Le Ngoc Long
In this paper we continue the development of a new technique for computing elimination ideals by substitution which has been called -separating re-embeddings. Given an ideal …
SAT Solving Using XOR-OR-AND Normal Forms
Bernhard Andraschko, Julian Danner, Martin Kreuzer
This paper introduces the XOR-OR-AND normal form (XNF) for logical formulas. It is a generalization of the well-known Conjunctive Normal Form (CNF) where literals are replaced by X…
Computing the unit group of a commutative finite -algebra
Martin Kreuzer, Florian Walsh
For a commutative finite -algebra, i.e., for a commutative ring whose additive group is finitely generated, it is known that the group of units of is finitely g…
Efficient Algorithms for Finite -Algebras
Martin Kreuzer, Florian Walsh
For a finite -algebra , i.e., for a -algebra which is a finitely generated -module, we assume that is explicitly given by a system of $\m…