Hans-Gert Gräbe

Hans-Gert Gräbe
University of Leipzig · Institute of Computer Science

Professor

About

56
Publications
4,642
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292
Citations
Introduction
Hans-Gert Gräbe currently works at the Institute of Computer Science, University of Leipzig. Hans-Gert does research in Computer Algebra, Semantic Web Technologies and Philosohical Aspects of Digital Change. He is currently involved with the 'SymbolicData Project' (Computer Algebra) and the 'Leipzig Data Project' (Semantic Web).

Publications

Publications (56)
Chapter
After a short recapitulation of the concepts, developed in an earlier paper in more detail, I show by an example, to what extent also TRIZ benefits from precise notions and what is the impact on modelling for the scope of (abstract) solution models, from which a real-world solution is to be developed. In the second part, a series of links between t...
Chapter
With the concept of a technical system the whole TRIZ theory corpus revolves around a term that is not very precisely defined in the TRIZ literature, but left to a “common sense”. In this paper an attempt is made to determine how far a notion of technical system takes in this theoretical context and how it can be related to approaches from neighbor...
Article
The SymbolicData Project on testing an benchmarking Computer Algebra software grew up from the Special Session on Benchmarking at the 1998 ISSAC conference. During 20 years we collected reserach data and meta information, developed a test framework along the "cross cutting concerns" of modern software engineering and experimented with semantic tech...
Conference Paper
One of the goals of the SymbolicData Project is to set up a navigational structure on the research data associated with the project. In 2009 we started to refactor the data and metadata along standard semantic web concepts based on the Resource Description Framework (RDF) thus opening the door to the Linked Open Data world. One of the main metadata...
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We report on some experience with a parallel version of the Grobner basis algorithm with factorization, implemented in the REDUCE package CALI (4). It is based on a coarse grain parallel master-slave model with distributed memory. This model was realized on an HP workstation cluster both with a disk remote connection based on (ordinary) REDUCE (9)...
Conference Paper
Full-text available
We report about a complete redesign of the tools and data of the SymbolicData project according to RDF technologies and Linked Data principles that proved to be powerful within modern semantic web approaches. During that redesign the focus of the project changed from a mere data store towards the vision of a Computer Algebra Social Network (CASN) t...
Article
Full-text available
There are many good reasons to teach a course on a systematic introduction to sym- bolic methods not only to students of mathematics but also to those of technical sciences. The design of such a course meets an essential diculty since the principles to be demon- strated appear only in nontrivial applications in a convincing way, but there is usuall...
Conference Paper
Full-text available
Die Systemsimulation ist für das Testen von eventbasierten Komponenten eines eingebetteten Systems nicht immer hinreichend genau. Es werden zusätzliche Strategien benötigt, um automatisiert und umfassend testen zu können. Mit dieser Arbeit wird ein modellbasierter Ansatz in Verbindung mit Unittest-Frameworks aufgezeigt.
Chapter
Full-text available
Zusammenfassung: Die Systemsimulation ist für das Testen von eventbasierten Komponenten eines eingebetteten Systems nicht immer hinreichend genau. Es werden zusätzliche Strategien benötigt, um automatisiert und umfassend testen zu können. Mit dieser Arbeit wird ein modellbasierter Ansatz in Verbindung mit Unittest-Frameworks aufgezeigt.
Conference Paper
Formalized proof schemes are the starting point for testing, comparing, and benchmarking of different geometry theorem proving approaches and provers. To automatize such tests it is desirable to collect a common data base of proof schemes, and to develop tools to extract examples, prepare them for input to different provers, and run them "in bulk"....
Chapter
Full-text available
Short descriptions of computer algebra systems are presented in three sections: major systems, special purpose systems, and packages. However, the separation between special purpose systems and packages is not to be taken too literally. An older survey is the paper by Calmet and van Hulzen in [Buchberger et al. 1982]. There is now an excellent new...
Conference Paper
Formalized proof schemes are the starting point for testing, comparing, and benchmarking of different geometry theorem proving approaches and provers. To automatize such tests it is desirable to collect a common data base of proof schemes, and to develop tools to extract examples, prepare them for input to different provers, and run them “in bulk”....
Article
This paper explains, that constructive problems from very different areas of commutative algebra can be formulated in a unified way as the computation of a basis for the intersection of the kernels of a finite number of linear functionals generating a dual S-module. Our implementation honours this point of view, presenting two general drivers dualb...
Article
Given a bialgebra B we present a unifying approach to deformations of associative algebras A with a left B-module algebra structure. Special deformations of the comultiplication of B yield universal deformation formulas, i.e. define deformations of the multiplicative structure for all B-module algebras A. This allows to derive known formulas of Moy...
Article
This paper continues our study of applications of factorized Gröbner basis computations in [8] and [9]. We describe a way tointerweave factorized Grobner bases and the ideas in [5] that leads to a significant speed up in the computation of isolated primes for well splitting examples. Based on that observation we generalize the algorithm presented i...
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Full-text available
We report on some experiences with the general purpose Computer Algebra Systems (CAS) Axiom, Macsyma, Maple, Mathematica, MuPAD, and Reduce solving systems of polynomial equations and the way they present their solutions. This snapshot (taken in the spring 1996) of the current power of the different systems in a special area concentrates both on CP...
Article
We report on some experience with a new version of the well known Gröbner algorithm with factorization and constraint inequalities, implemented in our REDUCE package CALI, [12]. We discuss some of its details and present run time comparisons with other existing implementations on well splitting examples.
Article
In memoriam to Renate. We report on some experiences with the general purpose Computer Algebra Systems (CAS) Axiom, Macsyma, Maple, Mathematica, MuPAD, and Reduce solving systems of polynomial equations and the way they present their solutions. This snapshot (taken in spring 1996) of the current power of the different systems in a special area conc...
Conference Paper
In a preceding paper [9] we reported on some experience with a new version of the well known Gröbner algorithm with factorization and constraint inequalities. Here we discuss, how this approach may be refined to produce triangular systems in the sense of [12] and [13]. Such a refinement guarantees, different to the usual Gröbner factorizer, to prod...
Article
Let k be a field, S = k[xv : v ϵ V] be the polynomial ring over the finite set of variables (xv : v ϵ V), and m = (xv : v ϵ V) the ideal defining the origin of Spec S.It is theoretically known (see e.g. Alonso et el., 1991) that the algorithmic ideas for the computation of ideal (and module) intersections, quotients, deciding radical membership etc...
Article
Solving systems of polynomial equations in an ultimate way means to nd the isolated primes of the associated variety and to present them in a way that is well suited for further computations. [5] proposes an algorithm, that uses several Gr obner basis computations for a dimension reduction argument, delaying factorization to the end of the algo-ri...
Article
Let S:=k[xv: vϵH] be a polynomial ring over the field k. For non-noetherian term orders there are essentially two ways to compute standard sets from a polynomial basis B of an ideal I ⊂ S, one based on Mora's tangent cone algorithm, and another one using Lazard's homogenization approach. The former applies (in its original version) only to inflimit...
Article
In the first part we generalize the notion of strongly independent sets, introduced in [10] for polynomial ideals, to submodules of free modules and explain their computational relevance. We discuss also two algorithms to compute strongly independent sets that rest on the primary decomposition of squarefree monomial ideals. Usually the initial idea...
Article
Winkler (1988) and Pauer (1992) present algorithms for a Hensel lifting of a modular Gröbner basis over lucky primes to a rational one. They have to solve a linear system with modular polynomial entries that requires another (modular) Gröbner basis computation.After an extension of luckiness to arbitrary (commutative noetherian) base rings we show...
Article
The aim of this paper is to prove that many homological properties and estimates of the discrete straightening ring still remain valid for the straightening ring itself. E.g. Cohen-Macaulay property, generalised Cohen-Macaulay property and Serre condition (Sn) (the latter for unmixed discrete straightening rings) transfer. The main technical tool i...
Article
In this paper we give an algorithm to compute an upper bound for the arithmetical rank of squarefree monomial ideals, i.e. the minimal number of hypersurfaces which cut out set-theoretically the variety of such an ideal. An apriori bound N – a=b+2 is obtained, where N means the number of variables, a the lowest degree in the ideal and b the lowest...
Article
In this paper we construct a (multihomogeneous) dualizing complex for A [Δ], the Stanley–Reisner ring of Δ over an arbitrary commutative noetherian ring A with identity, admitting a dualizing complex. In addition, some consequences are discussed.
Article
Full-text available
The SymbolicData project has the following three main goals: 1. to systematically collect existing symbolic computation benchmark data and to produce tools to extend and maintain this collection; 2. to design and implement concepts for trusted benchmarks computations on the collected data; and 3. to provide tools for data access /selection/transfor...
Article
Geometry is not only a part of mathematics with ancient roots but also a vivid area of modern research. Especially the eld of geometry, called by some negligence \el-ementary", continues to attract the attention also of the great community of leisure mathematicians. This is probably due to the small set of prerequisites necessary to formulate the p...
Article
Full-text available
10. Oktober 2003 Anfang August 2002 verbreitete sich die Nachricht, dass einige bis dahin unbekannte Inder einen deterministischen Primzahltest mit polynomialer Laufzeit entdeckt hatten. Die Anerkennung und Beweisglättung durch führende Experten folgte im Laufe einer Woche, so dass damit eines der großen Probleme der Komplexitätstheorie eine Lösung...
Article
Hodge algebras proved to be useful in the investigation of certain important classes of examples arising in commutative algebra and algebraic geometry. Hence it is of some interest to have methods to verify this property. For graded Hodge algebras (all more or less important examples are of this kind) it can be verified by the Gröbner basis method...
Article
Erfurt, Mühlhausen, Pädag. Hochsch., Diss. B, 1988 (Nicht f.d. Austausch).

Projects

Projects (3)
Archived project
Papers on Commutative Algebra and Stanley-Reisner rings
Archived project
Archived project