Methods And Examples In Mechanical Geometry Theorem Proving
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Mechanical Theorem Proving In Geometries
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Author : Wen-tsün Wu
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Mechanical Theorem Proving In Geometries written by Wen-tsün Wu and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Computers categories.
There seems to be no doubt that geometry originates from such practical activ ities as weather observation and terrain survey. But there are different manners, methods, and ways to raise the various experiences to the level of theory so that they finally constitute a science. F. Engels said, "The objective of mathematics is the study of space forms and quantitative relations of the real world. " Dur ing the time of the ancient Greeks, there were two different methods dealing with geometry: one, represented by the Euclid's "Elements," purely pursued the logical relations among geometric entities, excluding completely the quantita tive relations, as to establish the axiom system of geometry. This method has become a model of deduction methods in mathematics. The other, represented by the relevant work of Archimedes, focused on the study of quantitative re lations of geometric objects as well as their measures such as the ratio of the circumference of a circle to its diameter and the area of a spherical surface and of a parabolic sector. Though these approaches vary in style, have their own features, and reflect different viewpoints in the development of geometry, both have made great contributions to the development of mathematics. The development of geometry in China was all along concerned with quanti tative relations.
Methods And Examples In Mechanical Geometry Theorem Proving
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Author : Shang-ching Chou
language : en
Publisher:
Release Date : 1986
Methods And Examples In Mechanical Geometry Theorem Proving written by Shang-ching Chou and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986 with categories.
Machine Proofs In Geometry
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Author : Shang-Ching Chou
language : en
Publisher: World Scientific
Release Date : 1994
Machine Proofs In Geometry written by Shang-Ching Chou and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Mathematics categories.
This book reports recent major advances in automated reasoning in geometry. The authors have developed a method and implemented a computer program which, for the first time, produces short and readable proofs for hundreds of geometry theorems.The book begins with chapters introducing the method at an elementary level, which are accessible to high school students; latter chapters concentrate on the main theme: the algorithms and computer implementation of the method.This book brings researchers in artificial intelligence, computer science and mathematics to a new research frontier of automated geometry reasoning. In addition, it can be used as a supplementary geometry textbook for students, teachers and geometers. By presenting a systematic way of proving geometry theorems, it makes the learning and teaching of geometry easier and may change the way of geometry education.
A Combination Of Geometry Theorem Proving And Nonstandard Analysis With Application To Newton S Principia
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Author : Jacques Fleuriot
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-09-30
A Combination Of Geometry Theorem Proving And Nonstandard Analysis With Application To Newton S Principia written by Jacques Fleuriot and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-09-30 with Mathematics categories.
Sir Isaac Newton's philosophi Naturalis Principia Mathematica'(the Principia) contains a prose-style mixture of geometric and limit reasoning that has often been viewed as logically vague. In A Combination of Geometry Theorem Proving and Nonstandard Analysis, Jacques Fleuriot presents a formalization of Lemmas and Propositions from the Principia using a combination of methods from geometry and nonstandard analysis. The mechanization of the procedures, which respects much of Newton's original reasoning, is developed within the theorem prover Isabelle. The application of this framework to the mechanization of elementary real analysis using nonstandard techniques is also discussed.
Logic And Software Engineering Proceedings Of The International Workshop In Honor Of Chih Sung Tang
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Author : Amir Pnueli
language : en
Publisher: World Scientific
Release Date : 1996-10-25
Logic And Software Engineering Proceedings Of The International Workshop In Honor Of Chih Sung Tang written by Amir Pnueli and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-10-25 with categories.
This workshop brought together top researchers in logic and software engineering in the unique occasion of celebrating the 70th birthday of Professor C S Tang who has devoted much of his long research career to establishing a solid logic foundation for software engineering.
Computer Algebra In Scientific Computing
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Author : Vladimir P. Gerdt
language : en
Publisher: Springer
Release Date : 2013-08-15
Computer Algebra In Scientific Computing written by Vladimir P. Gerdt and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-08-15 with Computers categories.
This book constitutes the proceedings of the 14th International Workshop on Computer Algebra in Scientific Computing, CASC 2013, held in Berlin, Germany, in September 2013. The 33 full papers presented were carefully reviewed and selected for inclusion in this book. The papers address issues such as polynomial algebra; the solution of tropical linear systems and tropical polynomial systems; the theory of matrices; the use of computer algebra for the investigation of various mathematical and applied topics related to ordinary differential equations (ODEs); applications of symbolic computations for solving partial differential equations (PDEs) in mathematical physics; problems arising at the application of computer algebra methods for finding infinitesimal symmetries; applications of symbolic and symbolic-numeric algorithms in mechanics and physics; automatic differentiation; the application of the CAS Mathematica for the simulation of quantum error correction in quantum computing; the application of the CAS GAP for the enumeration of Schur rings over the group A5; constructive computation of zero separation bounds for arithmetic expressions; the parallel implementation of fast Fourier transforms with the aid of the Spiral library generation system; the use of object-oriented languages such as Java or Scala for implementation of categories as type classes; a survey of industrial applications of approximate computer algebra.
Automated Theorem Proving After 25 Years
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Author : W. W. Bledsoe
language : en
Publisher: American Mathematical Soc.
Release Date : 1984
Automated Theorem Proving After 25 Years written by W. W. Bledsoe and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984 with Mathematics categories.
Automated Deduction In Geometry
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Author : Pascal Schreck
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-11-22
Automated Deduction In Geometry written by Pascal Schreck and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-11-22 with Computers categories.
This book constitutes the thoroughly refereed post-workshop proceedings of the 8th International Workshop on Automated Deduction in Geometry, ADG 2010, held in Munich, Germany in July 2010. The 13 revised full papers presented were carefully selected during two rounds of reviewing and improvement from the lectures given at the workshop. Topics addressed by the papers are incidence geometry using some kind of combinatoric argument; computer algebra; software implementation; as well as logic and proof assistants.
Automated Deduction In Geometry
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Author : Franz Winkler
language : en
Publisher: Springer
Release Date : 2004-05-06
Automated Deduction In Geometry written by Franz Winkler and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-05-06 with Mathematics categories.
This book constitutes the thoroughly refereed post-proceedings of the 4th International Workshop on Automated Deduction in Geometry, ADG 2002, held at Hagenberg Castle, Austria in September 2002. The 13 revised full papers presented were carefully selected during two rounds of reviewing and improvement. Among the issues addressed are theoretical and methodological topics, such as the resolution of singularities, algebraic geometry and computer algebra; various geometric theorem proving systems are explored; and applications of automated deduction in geometry are demonstrated in fields like computer-aided design and robotics.
Differential Geometric Methods In Theoretical Physics Proceedings Of The Xxi International Conference
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Author : Chen Ning Yang
language : en
Publisher: World Scientific
Release Date : 1993-07-31
Differential Geometric Methods In Theoretical Physics Proceedings Of The Xxi International Conference written by Chen Ning Yang and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-07-31 with categories.
This volume contains intense studies on Quantum Groups, Knot Theory, Statistical Mechanics, Conformal Field Theory, Differential Geometry and Differential Equation Methods and so on. It has contributions by renowned experts and covers most of the recent developments in these fields.