Bruno Buchberger Authors: Add personal information
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Despite these commonalities, the two communities are currently only weakly connected. We introduce a new project SC 2 to build a joint ... 2 July 2015 Journal of Symbolic Computation: Volume 69 Issue C, July 2015 Publisher: Academic Press, Inc. Bibliometrics: Citation Count: 0 3 June 2012 Journal of Symbolic Computation: Volume 47 Issue 6, June, 2012 Publisher: Academic Press, Inc. Bibliometrics: Citation Count: 0 In this paper, we summarize our recent work on establishing, for the first time, an algorithm for the symbolic solution of linear boundary problems. We put our work in the frame of Wen-Tsun Wu?s approach to algorithmic problem solving in analysis, geometry, and logic by mapping the significant aspects of ... Keywords: Symbolic analysis, Theorema, Baxter algebras, Groebner bases, Linear boundary problems, Algorithmic functors, Integro-differential algebras, Wen-Tsun Wu, Wolfgang Groebner 4 September 2010 ICMS'10: Proceedings of the Third international congress conference on Mathematical software Publisher: Springer-Verlag Bibliometrics: Citation Count: 0 5 October 2009 CASC '09: Proceedings of the 11th International Workshop on Computer Algebra in Scientific Computing Publisher: Springer-Verlag Bibliometrics: Citation Count: 7 We describe a symbolic framework for treating linear boundary problems with a generic implementation in the Theorema system. For ordinary differential equations, the operations implemented include computing Green's operators, composing boundary problems and integro-differential operators, and factoring boundary problems. Based on our factorization approach, we also present some first steps ... Keywords: Green's operator, Integro-Differential Operator, Ordinary Differential Equation, Wave Equation, Linear boundary problem 6 August 2009 Bibliometrics: Citation Count: 0 This book is a synopsis of the basic and applied research carried out at the various research institutions of Softwarepark Hagenberg in Austria. Started in 1987, following a decision of the government of Upper Austria to create a scientific, technological, and economic impulse for the region and for the international ... 7 April 2009 Mathematics and Computers in Simulation: Volume 79 Issue 8, April, 2009 Publisher: Elsevier Science Publishers B. V. Bibliometrics: Citation Count: 0 PCS (Proving-Computing-Solving) introduced by B. Buchberger in 2001 and S-Decomposition, introduced by T. Jebelean in 2001, are strategies for handling proof problems by combining logic inference steps (e.g., modus ponens, Skolemization, instantiation) with rewriting steps (application of definitions) and solving procedures based on algebraic techniques (e.g., Groebner Bases, Cylindrical Algebraic ... Keywords: Automated theorem proving, 68T15, Extended quantifier elimination, 03C10, 03B35, CAD, Groebner Bases 8 February 2009 ACM Communications in Computer Algebra: Volume 42 Issue 3, September 2008 Publisher: ACM Bibliometrics: Citation Count: 3 Downloads (6 Weeks): 0,   Downloads (12 Months): 1,   Downloads (Overall): 102 Full text available: PDF 9 September 2007 SYNASC '07: Proceedings of the Ninth International Symposium on Symbolic and Numeric Algorithms for Scientific Computing Publisher: IEEE Computer Society Bibliometrics: Citation Count: 0 As in any other scientific field, the quality control (by peer reviewing), archiving and distribution of knowledge in mathematics is organized by journals. Currently, mathematical journals represent huge chunks of knowledge that sit passively on a shelf and wait for a human user to read or query them. In contrast, ... 10 September 2006 SYNASC '06: Proceedings of the Eighth International Symposium on Symbolic and Numeric Algorithms for Scientific Computing Publisher: IEEE Computer Society Bibliometrics: Citation Count: 0 Mathematics is characterized by its method of gaining knowledge, namely reasoning. The automation of reasoning has seen significant advances over the past decades and, thus, the expectation was that these advances would also have significant impact on the practice of doing mathematics. However, so far, this impact is small. We ... 11 August 2006 IJCAR'06: Proceedings of the Third international joint conference on Automated Reasoning Publisher: Springer-Verlag Bibliometrics: Citation Count: 2 Mathematics is characterized by its method of gaining knowledge, namely reasoning. The automation of reasoning has seen significant advances over the past decades and, thus, the expectation was that these advances would also have significant impact on the practice of doing mathematics. However, so far, this impact is small. We ... 12 March 2006 Journal of Symbolic Computation: Volume 41 Issue 3-4, March, 2006 Publisher: Academic Press, Inc. Bibliometrics: Citation Count: 72 This is the English translation (by Michael P. Abramson) of the PhD thesis of Bruno Buchberger, in which he introduced the algorithmic theory of Grobner bases. Some comments by Buchberger on the translation and the thesis are given in an additional short paper in this issue of the Journal of ... 13 March 2006 Journal of Symbolic Computation: Volume 41 Issue 3-4, March, 2006 Publisher: Academic Press, Inc. Bibliometrics: Citation Count: 1 14 January 2006 The Seventeen Provers of the World Publisher: Springer-Verlag Bibliometrics: Citation Count: 1 Statement Theorem”gsqrt[2 irrational”, ¬ rat$\sqrt{2}$ 15 July 2005 ISSAC '05: Proceedings of the 2005 international symposium on Symbolic and algebraic computation Publisher: ACM Bibliometrics: Citation Count: 0 Downloads (6 Weeks): 0,   Downloads (12 Months): 4,   Downloads (Overall): 249 Full text available: PDF Since approximately 1960, symbolic computation added algebraic algorithms (polynomial algorithms, simplification algorithms for expressions, algorithms for integration, algorithms for the analysis of algebraic structures like groups etc.) to numerics and provided both numerical and algebraic algorithms in the frame of powerful integrated mathematical software systems like Macsyma, Reduce,..., Mathematica, Maple,... ... 16 September 2004 ADG'04: Proceedings of the 5th international conference on Automated Deduction in Geometry Publisher: Springer-Verlag Bibliometrics: Citation Count: 3 Construction of geometrical objects by origami, the Japanese traditional art of paper folding, is enjoyable and intriguing. It attracted the minds of artists, mathematicians and computer scientists for many centuries. Origami will become a more rigorous, effective and enjoyable art if the origami constructions can be visualized on the computer ... 17 May 2003 Annals of Mathematics and Artificial Intelligence: Volume 38 Issue 1-3, May 2003 Publisher: Kluwer Academic Publishers Bibliometrics: Citation Count: 1 18 March 2002 ACM SIGSAM Bulletin: Volume 36 Issue 1, March 2002 Publisher: ACM Bibliometrics: Citation Count: 1 Downloads (6 Weeks): 4,   Downloads (12 Months): 10,   Downloads (Overall): 374 Full text available: PDF Mathematical software systems, such as Mathematica, Maple, Derive, and so on, are substantially based on enormous advances in the area of mathematics known as Computer Algebra or Symbolic Mathematics. In fact, everything taught in high school and in the first semesters of a university mathematical education, is available in these ... 19 October 2001 Multidimensional Systems and Signal Processing: Volume 12 Issue 3, July/October 2001 Publisher: Kluwer Academic Publishers Bibliometrics: Citation Count: 8 20 July 2001 Multidimensional Systems and Signal Processing: Volume 12 Issue 3-4, July-October 2001 Publisher: Kluwer Academic Publishers Bibliometrics: Citation Count: 0 We present the basic concepts and results of Gröbner bases theory for readers working or interested in systems theory. The concepts and methods of Gröbner bases theory are presented by examples. No prerequisites, except some notions of elementary mathematics, are necessary for reading this paper. The two main properties of ... Keywords: syzygies, algebraic algorithms, algorithmic systems theory, computer algebra, polynomial diophantine equations, residue class rings, Gröbner bases, elimination, polynomial ideals