Algebra, Geometry and Software Systems

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Author: Michael Joswig,Nobuki Takayama

Publisher: Springer Science & Business Media

ISBN: 3662051486

Category: Mathematics

Page: 332

View: 5622

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.

Algorithms in Algebraic Geometry

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Author: Alicia Dickenstein,Frank-Olaf Schreyer,Andrew J. Sommese

Publisher: Springer Science & Business Media

ISBN: 9780387751559

Category: Mathematics

Page: 162

View: 6680

In the last decade, there has been a burgeoning of activity in the design and implementation of algorithms for algebraic geometric computation. The workshop on Algorithms in Algebraic Geometry that was held in the framework of the IMA Annual Program Year in Applications of Algebraic Geometry by the Institute for Mathematics and Its Applications on September 2006 is one tangible indication of the interest. This volume of articles captures some of the spirit of the IMA workshop.

Topics in Algebraic Geometry and Geometric Modeling

Workshop on Algebraic Geometry and Geometric Modeling, July 29-August 2, 2002, Vilnius University, Lithuania

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Author: Ron Goldman,Rimvydas Krasauskas

Publisher: American Mathematical Soc.

ISBN: 0821834207

Category: Mathematics

Page: 366

View: 1522

Algebraic geometry and geometric modeling both deal with curves and surfaces generated by polynomial equations. Algebraic geometry investigates the theoretical properties of polynomial curves and surfaces; geometric modeling uses polynomial, piecewise polynomial, and rational curves and surfaces to build computer models of mechanical components and assemblies for industrial design and manufacture. The NSF sponsored the four-day ``Vilnius Workshop on Algebraic Geometry and Geometric Modeling'', which brought together some of the top experts in the two research communities to examine a wide range of topics of interest to both fields. This volume is an outgrowth of that workshop. Included are surveys, tutorials, and research papers. In addition, the editors have included a translation of Minding's 1841 paper, ``On the determination of the degree of an equation obtained by elimination'', which foreshadows the modern application of mixed volumes in algebraic geometry. The volume is suitable for mathematicians, computer scientists, and engineers interested in applications of algebraic geometry to geometric modeling.

Algorithmic and Experimental Methods in Algebra, Geometry, and Number Theory

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Author: Gebhard Böckle,Wolfram Decker,Gunter Malle

Publisher: Springer

ISBN: 3319705660

Category: Mathematics

Page: 763

View: 3378

This book presents state-of-the-art research and survey articles that highlight work done within the Priority Program SPP 1489 “Algorithmic and Experimental Methods in Algebra, Geometry and Number Theory”, which was established and generously supported by the German Research Foundation (DFG) from 2010 to 2016. The goal of the program was to substantially advance algorithmic and experimental methods in the aforementioned disciplines, to combine the different methods where necessary, and to apply them to central questions in theory and practice. Of particular concern was the further development of freely available open source computer algebra systems and their interaction in order to create powerful new computational tools that transcend the boundaries of the individual disciplines involved. The book covers a broad range of topics addressing the design and theoretical foundations, implementation and the successful application of algebraic algorithms in order to solve mathematical research problems. It offers a valuable resource for all researchers, from graduate students through established experts, who are interested in the computational aspects of algebra, geometry, and/or number theory.

Mathematical Tools for Physicists

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Author: Michael Grinfeld

Publisher: John Wiley & Sons

ISBN: 3527684271

Category: Science

Page: 632

View: 7124

The new edition is significantly updated and expanded. This unique collection of review articles, ranging from fundamental concepts up to latest applications, contains individual contributions written by renowned experts in the relevant fields. Much attention is paid to ensuring fast access to the information, with each carefully reviewed article featuring cross-referencing, references to the most relevant publications in the field, and suggestions for further reading, both introductory as well as more specialized. While the chapters on group theory, integral transforms, Monte Carlo methods, numerical analysis, perturbation theory, and special functions are thoroughly rewritten, completely new content includes sections on commutative algebra, computational algebraic topology, differential geometry, dynamical systems, functional analysis, graph and network theory, PDEs of mathematical physics, probability theory, stochastic differential equations, and variational methods.

Software for Algebraic Geometry

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Author: Michael E. Stillman,Nobuki Takayama,Jan Verschelde

Publisher: Springer Science & Business Media

ISBN: 0387781331

Category: Mathematics

Page: 176

View: 2786

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.

Interactions of Classical and Numerical Algebraic Geometry

A Conference in Honor of Andrew Sommese : Interactions of Classical and Numerical Algebraic Geometry, May 22-24, 2008, University of Notre Dame, Notre Dame, Indiana

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Author: Daniel James Bates

Publisher: American Mathematical Soc.

ISBN: 0821847465

Category: Mathematics

Page: 362

View: 1228

This volume contains the proceedings of the conference on Interactions of Classical and Numerical Algebraic Geometry, held May 22-24, 2008, at the University of Notre Dame, in honor of the achievements of Professor Andrew J. Sommese. While classical algebraic geometry has been studied for hundreds of years, numerical algebraic geometry has only recently been developed. Due in large part to the work of Andrew Sommese and his collaborators, the intersection of these two fields is now ripe for rapid advancement. The primary goal of both the conference and this volume is to foster the interaction between researchers interested in classical algebraic geometry and those interested in numerical methods. The topics in this book include (but are not limited to) various new results in complex algebraic geometry, a primer on Seshadri constants, analyses and presentations of existing and novel numerical homotopy methods for solving polynomial systems, a numerical method for computing the dimensions of the cohomology of twists of ideal sheaves, and the application of algebraic methods in kinematics and phylogenetics.

Geometric Algebra: An Algebraic System for Computer Games and Animation

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Author: John A. Vince

Publisher: Springer Science & Business Media

ISBN: 9781848823792

Category: Computers

Page: 195

View: 8629

Geometric algebra is still treated as an obscure branch of algebra and most books have been written by competent mathematicians in a very abstract style. This restricts the readership of such books especially by programmers working in computer graphics, who simply want guidance on algorithm design. Geometric algebra provides a unified algebraic system for solving a wide variety of geometric problems. John Vince reveals the beauty of this algebraic framework and communicates to the reader new and unusual mathematical concepts using colour illustrations, tabulations, and easy-to-follow algebraic proofs. The book includes many worked examples to show how the algebra works in practice and is essential reading for anyone involved in designing 3D geometric algorithms.

Connections Between Algebra, Combinatorics, and Geometry

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Author: Susan M. Cooper,Sean Sather-Wagstaff

Publisher: Springer

ISBN: 1493906267

Category: Mathematics

Page: 317

View: 3078

Commutative algebra, combinatorics, and algebraic geometry are thriving areas of mathematical research with a rich history of interaction. Connections Between Algebra and Geometry contains lecture notes, along with exercises and solutions, from the Workshop on Connections Between Algebra and Geometry held at the University of Regina from May 29-June 1, 2012. It also contains research and survey papers from academics invited to participate in the companion Special Session on Interactions Between Algebraic Geometry and Commutative Algebra, which was part of the CMS Summer Meeting at the University of Regina held June 2–3, 2012, and the meeting Further Connections Between Algebra and Geometry, which was held at the North Dakota State University February 23, 2013. This volume highlights three mini-courses in the areas of commutative algebra and algebraic geometry: differential graded commutative algebra, secant varieties, and fat points and symbolic powers. It will serve as a useful resource for graduate students and researchers who wish to expand their knowledge of commutative algebra, algebraic geometry, combinatorics, and the intricacies of their intersection.

Serre's Problem on Projective Modules

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Author: T.Y. Lam

Publisher: Springer Science & Business Media

ISBN: 9783540233176

Category: Mathematics

Page: 404

View: 7031

An invaluable summary of research work done in the period from 1978 to the present

Analysis of Dirac Systems and Computational Algebra

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Author: Fabrizio Colombo,Irene Sabadini,Franciscus Sommen,Daniele C. Struppa

Publisher: Springer Science & Business Media

ISBN: 9780817642556

Category: Mathematics

Page: 332

View: 1771

* The main treatment is devoted to the analysis of systems of linear partial differential equations (PDEs) with constant coefficients, focusing attention on null solutions of Dirac systems * All the necessary classical material is initially presented * Geared toward graduate students and researchers in (hyper)complex analysis, Clifford analysis, systems of PDEs with constant coefficients, and mathematical physics

Algebraic Methodology and Software Technology

6th International Conference, AMAST '97, Sydney, Australia, Dezember 13-17, 1997. Proceedings

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Author: Michael Johnson

Publisher: Springer Science & Business Media

ISBN: 9783540638889

Category: Computers

Page: 594

View: 1946

This book constitutes the refereed proceedings of the 6th International Conference on Algebraic Methodology and Software Engineering, AMAST'97, held in Sydney, Australia, in December 1997. The volume presents 48 revised full papers selected from an unusually high number of submissions. One of the outstanding features of AMAST is its mix of serious mathematical development of formal methods in software engineering with practical concerns, tools, case studies, and industrial development. The volume addresses all current aspects of formal methods in software engineering and programming methodology, with a certain emphasis on algebraic and logical foundations.

Software for Algebraic Geometry

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Author: Kurt Weichselberger,Sigrid Pöhlmann

Publisher: Springer

ISBN: N.A

Category: Computers

Page: 132

View: 9746

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.

Algebraic Methodology and Software Technology

5th International Conference, AMAST '96 Munich, Germany, July 1996. Proceedings

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Author: Martin Wirsing,Maurice Nivat

Publisher: Springer Science & Business Media

ISBN: 9783540614630

Category:

Page: 640

View: 9825

Geometric Computing for Perception Action Systems

Concepts, Algorithms, and Scientific Applications

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Author: Eduardo Bayro Corrochano

Publisher: Springer Science & Business Media

ISBN: 1461301777

Category: Computers

Page: 235

View: 2532

After an introduction to geometric algebra, and the necessary math concepts that are needed, the book examines a variety of applications in the field of cognitive systems using geometric algebra as the mathematical system. There is strong evidence that geobetric albegra can be used to carry out efficient computations at all levels in the cognitive system. Geometric algebra reduces the complexity of algebraic expressions and as a result, it improves algorithms both in speed and accuracy. The book is addressed to a broad audience of computer scientists, cyberneticists, and engineers. It contains computer programs to clarify and demonstrate the importance of geometric algebra in cognitive systems.

Geometric Modeling and Algebraic Geometry

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Author: Bert Jüttler,Ragni Piene

Publisher: Springer Science & Business Media

ISBN: 9783540721857

Category: Mathematics

Page: 231

View: 2526

Geometric Modeling and Algebraic Geometry, though closely related, are traditionally represented by two almost disjoint scientific communities. Both fields deal with objects defined by algebraic equations, but the objects are studied in different ways. In 12 chapters written by leading experts, this book presents recent results which rely on the interaction of both fields. Some of these results have been obtained from a major European project in geometric modeling.

Algorithms In Algebraic Geometry And Applications

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Author: Laureano Gonzalez-Vega

Publisher: Springer Science & Business Media

ISBN: 9783764352745

Category: Computers

Page: 399

View: 6649

This volume arises from the contributions presented at the MEGA 94 Con­ ference (Metodos Efectivos en Geomctria Algebraica = Effective Methods in Algebraic Geometry), held at the University of Cantabria (Santander, Spain) April 59, 1994. Previous sessions of this biannual conference had taken place in Castiglioncello (Livorno, Italy, 1990) and in Nice (France, 1992) and the cor­ responding proceedings have been published in the Birkhauser series Progress in Mathematics. volumes no. 94 and 109, respectively. The present collection consists of twenty articles involvillg miscellaneous topics concerning algorithms in algebra, algebraic geometry and related appli­ cations. Fourteen of these papers correspond to the contents of the Conference's regular scientific program and have been selected, by the MEGA Committee, from the submitted contributions after a very rigorous refereeing procedure entailing an average of three independent reports per paper and two Program Committee panel discussions before and after the Conference. The remaining six papers (by S. Beck & M. Kreuzer, M. Bronstein, E. V. Flvnn. 1. Itenberg, J.-P. Merlet and 1\1. Seppala) correspond to invited talks and have also been subject to a post-conference refereeing procedure.

Algebraic and Geometric Ideas in the Theory of Discrete Optimization

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Author: JesÏs A. De Loera,Raymond Hemmecke,Matthias KÓppe

Publisher: SIAM

ISBN: 1611972434

Category: Mathematics

Page: 333

View: 9740

In recent years, many new techniques have emerged in the mathematical theory of discrete optimization that have proven to be effective in solving a number of hard problems. This book presents these recent advances, particularly those that arise from algebraic geometry, commutative algebra, convex and discrete geometry, generating functions, and other tools normally considered outside of the standard curriculum in optimization. These new techniques, all of which are presented with minimal prerequisites, provide a transition from linear to nonlinear discrete optimization. This book can be used as a textbook for advanced undergraduates or first-year graduate students in mathematics, computer science or operations research. It is also appropriate for mathematicians, engineers, and scientists engaged in computation who wish to gain a deeper understanding of how and why algorithms work.

Computations in Algebraic Geometry with Macaulay 2

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Author: David Eisenbud,Daniel R. Grayson,Mike Stillman,Bernd Sturmfels

Publisher: Springer Science & Business Media

ISBN: 3662048515

Category: Mathematics

Page: 329

View: 1736

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.

Physik und Informatik — Informatik und Physik

Arbeitsgespräch, München, 21./22. November 1991 Proceedings

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Author: D. Krönig,M. Lang

Publisher: Springer-Verlag

ISBN: 3642773826

Category: Technology & Engineering

Page: 326

View: 6670

Proceedings