Software For Algebraic Geometry

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Software for Algebraic Geometry

Michael E. Stillman,Nobuki Takayama,Jan Verschelde
Software for Algebraic Geometry Book PDF

Author : Michael E. Stillman,Nobuki Takayama,Jan Verschelde
Publisher : Springer Science & Business Media
Page : 176 pages
File Size : 46,6 Mb
Release : 2008-05-29
Category : Mathematics
ISBN : 9780387781334

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Software for Algebraic Geometry by Michael E. Stillman,Nobuki Takayama,Jan Verschelde Pdf

Algorithms in algebraic geometry go hand in hand with software packages that implement them. Together they have established the modern field of computational algebraic geometry which has come to play a major role in both theoretical advances and applications. Over the past fifteen years, several excellent general purpose packages for computations in algebraic geometry have been developed, such as, CoCoA, Singular and Macaulay 2. While these packages evolve continuously, incorporating new mathematical advances, they both motivate and demand the creation of new mathematics and smarter algorithms. This volume reflects the workshop “Software for Algebraic Geometry” held in the week from 23 to 27 October 2006, as the second workshop in the thematic year on Applications of Algebraic Geometry at the IMA. The papers in this volume describe the software packages Bertini, PHClab, Gfan, DEMiCs, SYNAPS, TrIm, Gambit, ApaTools, and the application of Risa/Asir to a conjecture on multiple zeta values. They offer the reader a broad view of current trends in computational algebraic geometry through software development and applications.

Algebra, Geometry and Software Systems

Michael Joswig,Nobuki Takayama
Algebra Geometry and Software Systems Book PDF

Author : Michael Joswig,Nobuki Takayama
Publisher : Springer Science & Business Media
Page : 332 pages
File Size : 50,8 Mb
Release : 2013-03-14
Category : Mathematics
ISBN : 9783662051481

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Algebra, Geometry and Software Systems by Michael Joswig,Nobuki Takayama Pdf

A collection of surveys and research papers on mathematical software and algorithms. The common thread is that the field of mathematical applications lies on the border between algebra and geometry. Topics include polyhedral geometry, elimination theory, algebraic surfaces, Gröbner bases, triangulations of point sets and the mutual relationship. This diversity is accompanied by the abundance of available software systems which often handle only special mathematical aspects. This is why the volume also focuses on solutions to the integration of mathematical software systems. This includes low-level and XML based high-level communication channels as well as general frameworks for modular systems.

Software for Algebraic Geometry

Michael E. Stillman,Nobuki Takayama,Jan Verschelde
Software for Algebraic Geometry Book PDF

Author : Michael E. Stillman,Nobuki Takayama,Jan Verschelde
Publisher : Springer
Page : 0 pages
File Size : 43,7 Mb
Release : 2008-11-01
Category : Mathematics
ISBN : 0387523367

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Software for Algebraic Geometry by Michael E. Stillman,Nobuki Takayama,Jan Verschelde Pdf

Algorithms in algebraic geometry go hand in hand with software packages that implement them. Together they have established the modern field of computational algebraic geometry which has come to play a major role in both theoretical advances and applications. Over the past fifteen years, several excellent general purpose packages for computations in algebraic geometry have been developed, such as, CoCoA, Singular and Macaulay 2. While these packages evolve continuously, incorporating new mathematical advances, they both motivate and demand the creation of new mathematics and smarter algorithms. This volume reflects the workshop “Software for Algebraic Geometry” held in the week from 23 to 27 October 2006, as the second workshop in the thematic year on Applications of Algebraic Geometry at the IMA. The papers in this volume describe the software packages Bertini, PHClab, Gfan, DEMiCs, SYNAPS, TrIm, Gambit, ApaTools, and the application of Risa/Asir to a conjecture on multiple zeta values. They offer the reader a broad view of current trends in computational algebraic geometry through software development and applications.

Computations in Algebraic Geometry with Macaulay 2

David Eisenbud,Daniel R. Grayson,Mike Stillman,Bernd Sturmfels
Computations in Algebraic Geometry with Macaulay 2 Book PDF

Author : David Eisenbud,Daniel R. Grayson,Mike Stillman,Bernd Sturmfels
Publisher : Springer Science & Business Media
Page : 335 pages
File Size : 54,7 Mb
Release : 2013-03-14
Category : Mathematics
ISBN : 9783662048511

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Computations in Algebraic Geometry with Macaulay 2 by David Eisenbud,Daniel R. Grayson,Mike Stillman,Bernd Sturmfels Pdf

This book presents algorithmic tools for algebraic geometry, with experimental applications. It also introduces Macaulay 2, a computer algebra system supporting research in algebraic geometry, commutative algebra, and their applications. The algorithmic tools presented here are designed to serve readers wishing to bring such tools to bear on their own problems. The first part of the book covers Macaulay 2 using concrete applications; the second emphasizes details of the mathematics.

Computer Algebra Handbook

Johannes Grabmeier,Erich Kaltofen,Volker Weispfenning
Computer Algebra Handbook Book PDF

Author : Johannes Grabmeier,Erich Kaltofen,Volker Weispfenning
Publisher : Springer Science & Business Media
Page : 656 pages
File Size : 48,7 Mb
Release : 2012-12-06
Category : Computers
ISBN : 9783642558269

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Computer Algebra Handbook by Johannes Grabmeier,Erich Kaltofen,Volker Weispfenning Pdf

This Handbook gives a comprehensive snapshot of a field at the intersection of mathematics and computer science with applications in physics, engineering and education. Reviews 67 software systems and offers 100 pages on applications in physics, mathematics, computer science, engineering chemistry and education.

Computing in Algebraic Geometry

Wolfram Decker,Christoph Lossen
Computing in Algebraic Geometry Book PDF

Author : Wolfram Decker,Christoph Lossen
Publisher : Springer Science & Business Media
Page : 328 pages
File Size : 50,8 Mb
Release : 2006-05-01
Category : Mathematics
ISBN : 9783540289937

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Computing in Algebraic Geometry by Wolfram Decker,Christoph Lossen Pdf

This book provides a quick access to computational tools for algebraic geometry, the mathematical discipline which handles solution sets of polynomial equations. Originating from a number of intense one week schools taught by the authors, the text is designed so as to provide a step by step introduction which enables the reader to get started with his own computational experiments right away. The authors present the basic concepts and ideas in a compact way.

Mathematical Software -- ICMS 2014

Hoon Hong,Chee Yap
Mathematical Software ICMS 2014 Book PDF

Author : Hoon Hong,Chee Yap
Publisher : Springer
Page : 762 pages
File Size : 40,9 Mb
Release : 2014-08-01
Category : Computers
ISBN : 9783662441992

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Mathematical Software -- ICMS 2014 by Hoon Hong,Chee Yap Pdf

This book constitutes the proceedings of the 4th International Conference on Mathematical Software, ICMS 2014, held in Seoul, South Korea, in August 2014. The 108 papers included in this volume were carefully reviewed and selected from 150 submissions. The papers are organized in topical sections named: invited; exploration; group; coding; topology; algebraic; geometry; surfaces; reasoning; special; Groebner; triangular; parametric; interfaces and general.

Mathematical Software - ICMS 2006

Andres Iglesias,Nobuki Takayama
Mathematical Software ICMS 2006 Book PDF

Author : Andres Iglesias,Nobuki Takayama
Publisher : Springer
Page : 467 pages
File Size : 53,6 Mb
Release : 2006-08-31
Category : Computers
ISBN : 9783540380863

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Mathematical Software - ICMS 2006 by Andres Iglesias,Nobuki Takayama Pdf

This book constitutes the refereed proceedings of the Second International Congress on Mathematical Software, ICMS 2006. The book presents 45 revised full papers, carefully reviewed and selected for presentation. The papers are organized in topical sections on new developments in computer algebra packages, interfacing computer algebra in mathematical visualization, software for algebraic geometry and related topics, number-theoretical software, methods in computational number theory, free software for computer algebra, and general issues.

Mathematical Software - ICMS 2006

Andres Iglesias,Nobuki Takayama
Mathematical Software ICMS 2006 Book PDF

Author : Andres Iglesias,Nobuki Takayama
Publisher : Springer
Page : 0 pages
File Size : 41,9 Mb
Release : 2006-08-31
Category : Computers
ISBN : 3540380868

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Mathematical Software - ICMS 2006 by Andres Iglesias,Nobuki Takayama Pdf

This book constitutes the refereed proceedings of the Second International Congress on Mathematical Software, ICMS 2006. The book presents 45 revised full papers, carefully reviewed and selected for presentation. The papers are organized in topical sections on new developments in computer algebra packages, interfacing computer algebra in mathematical visualization, software for algebraic geometry and related topics, number-theoretical software, methods in computational number theory, free software for computer algebra, and general issues.

Ideals, Varieties, and Algorithms

David A. Cox,John Little,Donal O'Shea
Ideals Varieties and Algorithms Book PDF

Author : David A. Cox,John Little,Donal O'Shea
Publisher : Springer
Page : 664 pages
File Size : 42,6 Mb
Release : 2015-04-30
Category : Mathematics
ISBN : 9783319167213

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Ideals, Varieties, and Algorithms by David A. Cox,John Little,Donal O'Shea Pdf

This text covers topics in algebraic geometry and commutative algebra with a strong perspective toward practical and computational aspects. The first four chapters form the core of the book. A comprehensive chart in the Preface illustrates a variety of ways to proceed with the material once these chapters are covered. In addition to the fundamentals of algebraic geometry—the elimination theorem, the extension theorem, the closure theorem and the Nullstellensatz—this new edition incorporates several substantial changes, all of which are listed in the Preface. The largest revision incorporates a new Chapter (ten), which presents some of the essentials of progress made over the last decades in computing Gröbner bases. The book also includes current computer algebra material in Appendix C and updated independent projects (Appendix D). The book may serve as a first or second course in undergraduate abstract algebra and with some supplementation perhaps, for beginning graduate level courses in algebraic geometry or computational algebra. Prerequisites for the reader include linear algebra and a proof-oriented course. It is assumed that the reader has access to a computer algebra system. Appendix C describes features of MapleTM, Mathematica® and Sage, as well as other systems that are most relevant to the text. Pseudocode is used in the text; Appendix B carefully describes the pseudocode used. Readers who are teaching from Ideals, Varieties, and Algorithms, or are studying the book on their own, may obtain a copy of the solutions manual by sending an email to [email protected]. From the reviews of previous editions: “...The book gives an introduction to Buchberger’s algorithm with applications to syzygies, Hilbert polynomials, primary decompositions. There is an introduction to classical algebraic geometry with applications to the ideal membership problem, solving polynomial equations and elimination theory. ...The book is well-written. ...The reviewer is sure that it will be an excellent guide to introduce further undergraduates in the algorithmic aspect of commutative algebra and algebraic geometry.” —Peter Schenzel, zbMATH, 2007 “I consider the book to be wonderful. ... The exposition is very clear, there are many helpful pictures and there are a great many instructive exercises, some quite challenging ... offers the heart and soul of modern commutative and algebraic geometry.” —The American Mathematical Monthly

Automated Practical Reasoning

Jochen Pfalzgraf
Automated Practical Reasoning Book PDF

Author : Jochen Pfalzgraf
Publisher : Springer Science & Business Media
Page : 244 pages
File Size : 47,9 Mb
Release : 1995-03
Category : Computers
ISBN : 3211826009

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Automated Practical Reasoning by Jochen Pfalzgraf Pdf

This book presents a collection of articles on the general framework of mechanizing deduction in the logics of practical reasoning. Topics treated are novel approaches in the field of constructive algebraic methods (theory and algorithms) to handle geometric reasoning problems, especially in robotics and automated geometry theorem proving; constructive algebraic geometry of curves and surfaces showing some new interesting aspects; implementational issues concerning the use of computer algebra systems to deal with such algebraic methods. Besides work on nonmonotonic logic and a proposed approach for a unified treatment of critical pair completion procedures, a new semantical modeling approach based on the concept of fibered structures is discussed; an application to cooperating robots is demonstrated.

Ideals, Varieties, and Algorithms

David Cox,John Little,DONAL OSHEA
Ideals Varieties and Algorithms Book PDF

Author : David Cox,John Little,DONAL OSHEA
Publisher : Springer Science & Business Media
Page : 549 pages
File Size : 45,8 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9781475726930

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Ideals, Varieties, and Algorithms by David Cox,John Little,DONAL OSHEA Pdf

Written at a level appropriate to undergraduates, this book covers such topics as the Hilbert Basis Theorem, the Nullstellensatz, invariant theory, projective geometry, and dimension theory. The book bases its discussion of algorithms on a generalisation of the division algorithm for polynomials in one variable that was only discovered in the 1960's. Although the algorithmic roots of algebraic geometry are old, the computational aspects were neglected earlier in this century. This has changed in recent years, and new algorithms, coupled with the power of fast computers, have let to some interesting applications, for example in robotics and in geometric theorem proving. In preparing this new edition, the authors present an improved proof of the Buchberger Criterion as well as a proof of Bezout's Theorem.

Combinatorial Algebraic Geometry

Gregory G. Smith,Bernd Sturmfels
Combinatorial Algebraic Geometry Book PDF

Author : Gregory G. Smith,Bernd Sturmfels
Publisher : Springer
Page : 390 pages
File Size : 48,5 Mb
Release : 2017-11-17
Category : Mathematics
ISBN : 9781493974863

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Combinatorial Algebraic Geometry by Gregory G. Smith,Bernd Sturmfels Pdf

This volume consolidates selected articles from the 2016 Apprenticeship Program at the Fields Institute, part of the larger program on Combinatorial Algebraic Geometry that ran from July through December of 2016. Written primarily by junior mathematicians, the articles cover a range of topics in combinatorial algebraic geometry including curves, surfaces, Grassmannians, convexity, abelian varieties, and moduli spaces. This book bridges the gap between graduate courses and cutting-edge research by connecting historical sources, computation, explicit examples, and new results.

Computer Algebra and Geometric Algebra with Applications

Hongbo Li
Computer Algebra and Geometric Algebra with Applications Book PDF

Author : Hongbo Li
Publisher : Springer Science & Business Media
Page : 457 pages
File Size : 46,6 Mb
Release : 2005-06-21
Category : Computers
ISBN : 9783540262961

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Computer Algebra and Geometric Algebra with Applications by Hongbo Li Pdf

This book constitutes the thoroughly refereed joint post-proceedings of the 6th International Workshop on Mathematics Mechanization, IWMM 2004, held in Shanghai, China in May 2004 and the International Workshop on Geometric Invariance and Applications in Engineering, GIAE 2004, held in Xian, China in May 2004. The 30 revised full papers presented were rigorously reviewed and selected from 65 presentations given at the two workshops. The papers are devoted to topics such as applications of computer algebra in celestial and engineering multibody systems, differential equations, computer vision, computer graphics, and the theory and applications of geometric algebra in geometric reasoning, robot vision, and computer graphics.

Discovering Mathematics with Magma

Wieb Bosma,John Cannon
Discovering Mathematics with Magma Book PDF

Author : Wieb Bosma,John Cannon
Publisher : Springer Science & Business Media
Page : 364 pages
File Size : 45,5 Mb
Release : 2007-07-10
Category : Computers
ISBN : 9783540376347

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Discovering Mathematics with Magma by Wieb Bosma,John Cannon Pdf

Based on the ontology and semantics of algebra, the computer algebra system Magma enables users to rapidly formulate and perform calculations in abstract parts of mathematics. Edited by the principal designers of the program, this book explores Magma. Coverage ranges from number theory and algebraic geometry, through representation theory and group theory to discrete mathematics and graph theory. Includes case studies describing computations underpinning new theoretical results.