Software For Algebraic Geometry
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Author | : David Eisenbud |
Publisher | : Springer Science & Business Media |
Total Pages | : 335 |
Release | : 2013-03-14 |
Genre | : Mathematics |
ISBN | : 3662048515 |
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.
Author | : Michael E. Stillman |
Publisher | : Springer Science & Business Media |
Total Pages | : 176 |
Release | : 2008-05-29 |
Genre | : Mathematics |
ISBN | : 0387781331 |
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.
Author | : Michael Joswig |
Publisher | : Springer Science & Business Media |
Total Pages | : 332 |
Release | : 2013-03-14 |
Genre | : Mathematics |
ISBN | : 3662051486 |
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.
Author | : Leo Dorst |
Publisher | : Elsevier |
Total Pages | : 664 |
Release | : 2010-07-26 |
Genre | : Juvenile Nonfiction |
ISBN | : 0080553109 |
Until recently, almost all of the interactions between objects in virtual 3D worlds have been based on calculations performed using linear algebra. Linear algebra relies heavily on coordinates, however, which can make many geometric programming tasks very specific and complex-often a lot of effort is required to bring about even modest performance enhancements. Although linear algebra is an efficient way to specify low-level computations, it is not a suitable high-level language for geometric programming. Geometric Algebra for Computer Science presents a compelling alternative to the limitations of linear algebra. Geometric algebra, or GA, is a compact, time-effective, and performance-enhancing way to represent the geometry of 3D objects in computer programs. In this book you will find an introduction to GA that will give you a strong grasp of its relationship to linear algebra and its significance for your work. You will learn how to use GA to represent objects and perform geometric operations on them. And you will begin mastering proven techniques for making GA an integral part of your applications in a way that simplifies your code without slowing it down. * The first book on Geometric Algebra for programmers in computer graphics and entertainment computing * Written by leaders in the field providing essential information on this new technique for 3D graphics * This full colour book includes a website with GAViewer, a program to experiment with GA
Author | : David Cox |
Publisher | : Springer Science & Business Media |
Total Pages | : 523 |
Release | : 2013-04-17 |
Genre | : Mathematics |
ISBN | : 1475721811 |
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. Contains a new section on Axiom and an update about MAPLE, Mathematica and REDUCE.
Author | : Wolfram Decker |
Publisher | : Cambridge University Press |
Total Pages | : 127 |
Release | : 2013-02-07 |
Genre | : Computers |
ISBN | : 1107612535 |
A quick guide to computing in algebraic geometry with many explicit computational examples introducing the computer algebra system Singular.
Author | : Johannes Grabmeier |
Publisher | : Springer Science & Business Media |
Total Pages | : 656 |
Release | : 2012-12-06 |
Genre | : Computers |
ISBN | : 3642558267 |
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.
Author | : Wolfram Decker |
Publisher | : Springer Science & Business Media |
Total Pages | : 331 |
Release | : 2006-05-01 |
Genre | : Mathematics |
ISBN | : 3540289933 |
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.
Author | : David Eisenbud |
Publisher | : Springer Science & Business Media |
Total Pages | : 784 |
Release | : 2013-12-01 |
Genre | : Mathematics |
ISBN | : 1461253500 |
This is a comprehensive review of commutative algebra, from localization and primary decomposition through dimension theory, homological methods, free resolutions and duality, emphasizing the origins of the ideas and their connections with other parts of mathematics. The book gives a concise treatment of Grobner basis theory and the constructive methods in commutative algebra and algebraic geometry that flow from it. Many exercises included.
Author | : Michael E. Stillman |
Publisher | : Springer |
Total Pages | : 0 |
Release | : 2008-11-01 |
Genre | : Mathematics |
ISBN | : 9780387523361 |
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.