Bruno Buchberger - Böcker

The theory of Gröbner bases, invented by Bruno Buchberger, is a general method by which many fundamental problems in various branches of mathematics and engineering can be solved by structurally simple algorithms. The method is now available in all major mathematical software systems. This book provides a short and easy-to-read account of the theory of Gröbner bases and its applications. It is in two parts, the first consisting of tutorial lectures, beginning with a general introduction. The subject is then developed in a further twelve tutorials, written by leading experts, on the application of Gröbner bases in various fields of mathematics. In the second part are seventeen original research papers on Gröbner bases. An appendix contains the English translations of the original German papers of Bruno Buchberger in which Gröbner bases were introduced.

The papers in this volume aim at obtaining a common understanding of the challenging research questions in web applications comprising web information systems, web services, and web interoperability; obtaining a common understanding of verification needs in web applications; achieving a common understanding of the available rigorous approaches to system development, and the cases in which they have succeeded; identifying how rigorous software engineering methods can be exploited to develop suitable web applications; and at developing a European-scale research agenda combining theory, methods and tools that would lead to suitable web applications with the potential to implement systems for computation in the public domain.

The papers in this volume aim at obtaining a common understanding of the challenging research questions in web applications comprising web information systems, web services, and web interoperability; obtaining a common understanding of verification needs in web applications; achieving a common understanding of the available rigorous approaches to system development, and the cases in which they have succeeded; identifying how rigorous software engineering methods can be exploited to develop suitable web applications; and at developing a European-scale research agenda combining theory, methods and tools that would lead to suitable web applications with the potential to implement systems for computation in the public domain.

This volume contains the proceedings of theSecondInternationalConferenceon MathematicalKnowledgeManagement (MKM 2003), held 16-18 February 2003 in Bertinoro, Italy. Mathematical Knowledge Management is an exciting new ?eld at the int- section between mathematics and computer science. We need e?cient, new te- niques, based on sophisticated formal mathematics and software technology, to exploit the enormous knowledge available in current mathematical sources and to organize mathematical knowledge in a new way. On the other side, due to its verynature,therealmofmathematicalinformationlookslikethebestcandidate for testing innovative theoretical and technological solutions for content-based systems, interoperability, management of machine-understandable information, and the Semantic Web. The organizers are grateful to Dana Scott and Massimo Marchiori for agr- ing to give invited talks at MKM 2003. November 2002 AndreaAsperti BrunoBuchberger JamesDavenport Conference Organization Andrea Asperti (Program Chair) Luca Padovani (Organizing Chair) Program Commitee A. Asperti (Bologna) P. D. F. Ion (Michigan) B. Buchberger (RISC Linz) Z. Luo (Durham) J. Caldwell (Wyoming) R.Nederpelt (Eindhoven) O. Caprotti (RISC Linz) M. Sofroniou (Wolfram Research Inc. ) J. Davenport (Bath) N. Soi?er (Wolfram Research Inc. ) W. M. Farmer (McMaster Univ. ) M. Suzuki (Kyushu) H. Geuvers (Nijmegen) N. Takayama (Kobe) T. Hardin (Paris 6) A. Trybulec (Bialystok) M. Hazewinkel (CWI Amsterdam) S. M. Watt (UWO) M. Kohlhase (CMU) B. Wegner (Berlin) Invited Speakers Massimo Marchiori (W3C, University of Venezia) Dana Scott (CMU) Additional Referees G. Bancerek R. Gamboa G. Jojgov P. Callaghan B. Han V. Prevosto D. Doligez Table of Contents Regular Contributions Digitisation,Representation,andFormalisation (DigitalLibrariesofMathematics) ...1 Andrew A. Adams MKMfromBooktoComputer:ACaseStudy ...

AISC 2004, the 7th International Conference on Arti?cial Intelligence and S- bolicComputation,wasthelatestintheseriesofspecializedbiennialconferences foundedin1992byJacquesCalmetoftheUniversitat .. KarlsruheandJohnCa- bell of University College London with the initial title Arti?cial Intelligence and Symbolic Mathematical Computing (AISMC).TheM disappeared from the title between the 1996 and 1998 conferences. As the editors of the AISC 1998 p- ceedings said, the organizers of the current meeting decided to drop the adjective 'mathematical' and toemphasize that the conference is concerned with all aspects of symbolic computation in AI: mathematical foundations, implementations, and applications, including applications in industry and academia. This remains the intended pro?le of the series, and will ?gure in the call for papersfor AISC 2006,whichis intended to takeplaceinChina. Thedistribution of papers in the present volume over all the areas of AISC happens to be rather noticeably mathematical, an e?ect that emerged because we were concerned to select the best relevant papers that were o?ered to us in 2004, irrespective of their particular topics; hence the title on the cover.Nevertheless, we encourage researchersovertheentirespectrumofAISC,asexpressedbythe1998quotation above,to be intouchwith us abouttheir interestsandthe possibility ofeventual submission of papers on their work for the next conference in the series. The papers in the present volume are evidence of the health of the ?eld of AISC. Additionally, there are two reasons for optimism about the continuation of this situation.

This book constitutes the thoroughly refereed post-proceedings of the 8th International Workshop on Computer Aided Systems Theory, EUROCAST 2001, held in Las Palmas de Gran Canaria, Spain in February 2001. The 48 revised full papers presented together with two invited papers were carefully selected during two rounds of reviewing and revision. The book offers topical sections on computer aided systems theory, mathematical and logical formalisms, information and decision, complexity, neural-like computation, automation and control, computer algebra and automated theorem proving, and functional programming and lambda calculus.

BrunoBuchberger This book is a synopsis of basic and applied research done at the various re search institutions of the Softwarepark Hagenberg in Austria. Starting with 15 coworkers in my Research Institute for Symbolic Computation (RISC), I initiated the Softwarepark Hagenberg in 1987 on request of the Upper Aus trian Government with the objective of creating a scienti?c, technological, and economic impulse for the region and the international community. In the meantime, in a joint e?ort, the Softwarepark Hagenberg has grown to the current (2009) size of over 1000 R&D employees and 1300 students in six research institutions, 40 companies and 20 academic study programs on the bachelor, master’s and PhD level. The goal of the Softwarepark Hagenberg is innovation of economy in one of the most important current technologies: software. It is the message of this book that this can only be achieved and guaranteed long term by “watering the root”, namely emphasis on research, both basic and applied. In this book, we summarize what has been achieved in terms of research in the various research institutions in the Softwarepark Hagenberg and what research vision we have for the imminent future. When I founded the Softwarepark Hagenberg, in addition to the “watering the root” principle, I had the vision that such a technology park can only prosper if we realize the “magic triangle”, i.e. the close interaction of research, academic education, and business applications at one site, see Figure 1.

BrunoBuchberger This book is a synopsis of basic and applied research done at the various re search institutions of the Softwarepark Hagenberg in Austria. Starting with 15 coworkers in my Research Institute for Symbolic Computation (RISC), I initiated the Softwarepark Hagenberg in 1987 on request of the Upper Aus trian Government with the objective of creating a scienti?c, technological, and economic impulse for the region and the international community. In the meantime, in a joint e?ort, the Softwarepark Hagenberg has grown to the current (2009) size of over 1000 R&D employees and 1300 students in six research institutions, 40 companies and 20 academic study programs on the bachelor, master’s and PhD level. The goal of the Softwarepark Hagenberg is innovation of economy in one of the most important current technologies: software. It is the message of this book that this can only be achieved and guaranteed long term by “watering the root”, namely emphasis on research, both basic and applied. In this book, we summarize what has been achieved in terms of research in the various research institutions in the Softwarepark Hagenberg and what research vision we have for the imminent future. When I founded the Softwarepark Hagenberg, in addition to the “watering the root” principle, I had the vision that such a technology park can only prosper if we realize the “magic triangle”, i.e. the close interaction of research, academic education, and business applications at one site, see Figure 1.