4 citations · 10 across the 14 of their papers we have counts for
15 papers
On the De Rham Cohomology of Zero-Dimensional Schemes
Martin Kreuzer, Le Ngoc Long
The (naive) de Rham cohomology of a zero-dimensional scheme is the homology of the Kähler differential algebra of its coordinate ring, viewed as a complex. Since it is well-known t…
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 , wher…
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 vanishin…
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 …
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…
Elimination by Substitution
Martin Kreuzer, Lorenzo Robbiano
Let be a field and . The technique of elimination by substitution is based on discovering a coherently -separating tuple of polynomials $…
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…
Decomposing Finite -Algebras
Martin Kreuzer, Alexei Miasnikov, Florian Walsh
For a finite -algebra , i.e., for a ring which is not necessarily associative or unitary, but whose additive group is finitely generated, we construct a decompositio…
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…
Computing the Binomial Part of a Polynomial Ideal
Martin Kreuzer, Florian Walsh
Given an ideal in a polynomial ring over a field , we present a complete algorithm to compute the binomial part of , i.e., the subideal …
Re-embeddings of Affine Algebras Via Gröbner Fans of Linear Ideals
Martin Kreuzer, Le Ngoc Long, Lorenzo Robbiano
Given an affine algebra over a field , where is an ideal in the polynomial ring , we examine the task of effectively calculating r…
Differential theory of zero-dimensional schemes
Martin Kreuzer, Tran N. K. Linh, Le N. Long
For a 0-dimensional scheme in over a perfect field , we first embed the homogeneous coordinate ring into its truncated integral closure $\widetil…
Optimal Re-Embeddings of Border Basis Schemes
Martin Kreuzer, Le Ngoc Long, Lorenzo Robbiano
Border basis schemes are open subschemes of Hilbert schemes parametrizing 0-dimensional subschemes of of given length. They yield open coverings and are easy to desc…
Restricted Gröbner fans and re-embeddings of affine algebras
Martin Kreuzer, Le Ngoc Long, Lorenzo Robbiano
In this paper we continue the study of good re-embeddings of affine K-algebras started in [KLR]. The idea is to use special linear projections to find isomorphisms between a given…
Determinantal schemes and Buchsbaum-Rim sheaves
M. Kreuzer, J. C. Migliore, U. Nagel +1
Let be a generically surjective morphism between direct sums of line bundles on $\proj{n}$ and assume that the degeneracy locus, , of has the expected codimension. We ca…