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This book constitutes the thoroughly refereed and revised post-workshop proceedings of the International Workshop on Automated Deduction in Geometry, held in Toulouse, France, in September 1996. The revised extended papers accepted for inclusion in the volume were selected on the basis of double reviewing. Among the topics covered are automated geometric reasoning and the deduction applied to Dixon resultants, Gröbner bases, characteristic sets, computational geometry, algebraic geometry, and planet motion; furthermore the system REDLOG is demonstrated and the verification of geometric statements as well as the automated production of proof in Euclidean Geometry are present.
Computer science. --- Programming languages (Electronic computers). --- Computers. --- Mathematical logic. --- Artificial intelligence. --- Computer graphics. --- Algorithms. --- Computer Science. --- Theory of Computation. --- Programming Languages, Compilers, Interpreters. --- Artificial Intelligence (incl. Robotics). --- Mathematical Logic and Formal Languages. --- Computer Graphics. --- Automatic theorem proving --- Congresses --- Logic [Symbolic and mathematical ] --- Geometry --- Information theory. --- Artificial Intelligence. --- Algorism --- Algebra --- Arithmetic --- Automatic drafting --- Graphic data processing --- Graphics, Computer --- Computer art --- Graphic arts --- Electronic data processing --- Engineering graphics --- Image processing --- AI (Artificial intelligence) --- Artificial thinking --- Electronic brains --- Intellectronics --- Intelligence, Artificial --- Intelligent machines --- Machine intelligence --- Thinking, Artificial --- Bionics --- Cognitive science --- Digital computer simulation --- Logic machines --- Machine theory --- Self-organizing systems --- Simulation methods --- Fifth generation computers --- Neural computers --- Informatics --- Science --- Communication theory --- Communication --- Cybernetics --- Foundations --- Digital techniques --- Algebra of logic --- Logic, Universal --- Mathematical logic --- Symbolic and mathematical logic --- Symbolic logic --- Mathematics --- Algebra, Abstract --- Metamathematics --- Set theory --- Syllogism --- Computer languages --- Computer program languages --- Computer programming languages --- Machine language --- Languages, Artificial --- Automatic computers --- Automatic data processors --- Computer hardware --- Computing machines (Computers) --- Electronic calculating-machines --- Electronic computers --- Hardware, Computer --- Computer systems --- Calculators --- Cyberspace
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Polynomial Elimination at Work; The Epsilon Library; The CharSets Package; The TriSys and SiSys Modules; The GEOTHER Environment; Relevant Elimination Tools; Solving Polynomial Systems; Automated Theorem Proving and Discovering in Geometry; Symbolic Geometric Computation; Selected Problems in Computer Mathematics
Elimination. --- Polynomials. --- Algebra --- Computer algorithms. --- Differential equations, Nonlinear. --- Nonlinear differential equations --- Nonlinear theories --- Algorithms --- Resultants --- Data processing.
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Presents tackling differential equations using advanced methods and software tools of symbolic computation. This book focuses on the symbolic-computational aspects of three kinds of fundamental problems in differential equations: transforming the equations, solving the equations, and studying the structure and properties of their solutions.
Differential equations. --- Differential equations, Partial. --- Algorithms. --- Partial differential equations --- 517.91 Differential equations --- Differential equations --- Algorism --- Algebra --- Arithmetic --- Foundations --- Differential equations, partial. --- Computer science --- Partial Differential Equations. --- Computational Mathematics and Numerical Analysis. --- Mathematics. --- Computer mathematics --- Discrete mathematics --- Electronic data processing --- Mathematics --- Partial differential equations. --- Computer mathematics.
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The growing demand of speed, accuracy, and reliability in scientific and engineering computing has been accelerating the merging of symbolic and numeric computations, two types of computation coexisting in mathematics yet separated in traditional research of mathematical computation. This book with 23 chapters presents original research and tutorial survey on the integration and interaction of symbolic and numeric computations. It represents the current state of the art and will serve as a valuable reference on the development of algorithms and software packages for hybrid symbolic-numeric computation. The book highlights the interaction between symbolic and numeric computations. It contains tutorial surveys by distinguished experts, covers recent advances on key topics, and provides effective methods illustrated with applications.
Computable functions --- Numerical analysis --- Logic, Symbolic and mathematical --- Data processing --- Computability theory --- Functions, Computable --- Partial recursive functions --- Recursive functions, Partial --- Constructive mathematics --- Decidability (Mathematical logic) --- Numerical analysis. --- Numerical Analysis. --- Mathematical analysis
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This book contains tutorial surveys and original research contributions in geometric computing, modeling, and reasoning. Highlighting the role of algebraic computation, it covers: surface blending, implicitization, and parametrization; automated deduction with Clifford algebra and in real geometry; and exact geometric computation. Basic techniques, advanced methods, and new findings are presented coherently, with many examples and illustrations. Using this book the reader will easily cross the frontiers of symbolic computation, computer aided geometric design, and automated reasoning. The boo
Geometry --- Mathematics --- Euclid's Elements --- Data processing. --- Computer programs. --- Geometric computation
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Partial differential equations --- Computer. Automation --- differentiaalvergelijkingen --- informatica --- wiskunde
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Mathematical logic --- Geometry --- Discrete mathematics --- Mathematical statistics --- Geology. Earth sciences --- Computer science --- Artificial intelligence. Robotics. Simulation. Graphics --- patroonherkenning --- factoranalyse --- discrete wiskunde --- grafische vormgeving --- informatica --- wiskunde --- KI (kunstmatige intelligentie) --- logica --- robots --- geometrie
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Ordered algebraic structures --- Mathematical physics --- Equations --- Automatic theorem proving. --- Numerical solutions --- Data processing. --- Automatic theorem proving --- 519.68 --- 519.68 Computer programming --- Computer programming --- Automated theorem proving --- Theorem proving, Automated --- Theorem proving, Automatic --- Artificial intelligence --- Proof theory --- Algebra --- Mathematics --- Numerical solutions&delete& --- Data processing
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Mathematics Mechanization and Applications provides a uniform presentation of major developments, carried out mostly in Wu's extended Chinese group, on algorithms and software tools for mechanizing algebraic equations solving and geometric theorem proving together with their applications to problems in science and engineering. It is distinguished by its uniform presentation with all-Chinese contributors and a 40-page list of references. There are 20 chapters written by experienced researchers. The book is divided into four parts: polynomial system solving, automated geometric reasoning, algebraic computation, and implementations and applications. Each chapter is devoted to surveying and expounding the main results achieved from one selected subject. The book contains surveys for diverse applications of the theories and methods to real world problems, ranging from the analysis of robotics and mechanisms to nonlinear programming and chemical equilibrium computation. Part of the theoretical and practical work reviewed in the book has been either unpublished or published only in Chinese journals or even only in the Chinese language. This book therefore provides Western readers working in symbolic and algebraic computation, geometric reasoning and modeling, algorithmic mathematics, robotics, CAGD, and other relevant areas with an easily accessible source of references for what the Chinese researchers have been doing under the banner of mathematics mechanization. * Addresses the frontiers of research with original ideas and results * Includes sophisticated, successful applications to scientific and engineering problems * Covers polynomial system solving, geometric reasoning, computer algebra, and mathematical software * Is comprehensive and focused * Contains an extensive bibliography--of high reference value--particularly for western readers.
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