# Hans-Gert GräbeUniversity of Leipzig · Institute of Computer Science

Hans-Gert Gräbe

Professor

## About

62

Publications

6,794

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327

Citations

Introduction

Hans-Gert Gräbe is a retired university lecturer at the Institute of Computer Science, University of Leipzig. He did research in Computer Algebra, Semantic Web Technologies, Systematic Innovation Methodology and Philosohical Aspects of Digital Change.

## Publications

Publications (62)

Dialectic played an important role in the transformation of TRIZ as a problem and as a methodological aim. It is argued that this source can be fruitful for the field of social sciences. As a systematic and theoretical topic, TRIZ offers new impulses for further research and for the development of teaching. We will demonstrate that TRIZ in social s...

The concept of systems and problem solving are central to TRIZ. Solving a problem along TRIZ ends in a certain conditional mind game that requires implementation and operation to “change the world” along the proposed solution. In Gräbe (Systems and Systemic Development in TRIZ. Submitted to TFC, 2022) the question is examined more closely how real-...

In TRIZ theory, resources play an important role when it comes to operate a systemic solution. It is only in this phase that the resource identified in the detailed solution plan as “any type of tangible or intangible matter that can be used to solve an inventive problem” must prove itself in practice. Conceptual distinctions such as “role definiti...

Concepts such as “resource” or “system” pose a challenge when it comes to adapting to the context. So the main problem is to adapt the concepts and the development process to the requirements of the users. The user is not only the methodological foundation of the concepts, but also a resource and a component of the system. Therefore, the initial ph...

This text discusses aspects of Human-Machine Interaction from the perspectives of an engineer and a philosopher. Machines are viewed not so much as tools, but more as complex socio-technical systems. On this basis, the relation between production and use of such systems and its influence on the interaction between human and machine is examined. The...

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...

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...

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...

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...

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)...

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...

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...

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.

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.

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"....

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...

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”....

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...

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...

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...

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...

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.

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...

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...

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...

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...

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...

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...

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...

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...

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...

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.

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...

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...

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...

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...

Erfurt, Mühlhausen, Pädag. Hochsch., Diss. B, 1988 (Nicht f.d. Austausch).