About this product

Product Identifiers

PublisherSpringer Berlin / Heidelberg

ISBN-103540289925

ISBN-139783540289920

eBay Product ID (ePID)49212252

Product Key Features

Number of PagesXvi, 328 Pages

Publication NameComputing in Algebraic Geometry : a Quick Start Using Singular

LanguageEnglish

SubjectAlgebra / Abstract, Mathematical & Statistical Software, Geometry / General, Geometry / Algebraic

Publication Year2006

TypeTextbook

Subject AreaMathematics, Computers

AuthorWolfram Decker, Christoph Lossen

SeriesAlgorithms and Computation in Mathematics Ser.

FormatHardcover

Dimensions

Item Weight51.1 Oz

Item Length9.3 in

Item Width6.1 in

Additional Product Features

Intended AudienceScholarly & Professional

LCCN2005-938498

Dewey Edition22

ReviewsFrom the reviews: "Algebraic geometry generally studies the properties of solution sets of systems of polynomial equations without direct reference to the actual polynomials used in these systems. ... This is especially desirable for classwork where the development of the abstract machinery generally outlasts the patience of the students, except possibly the most motivated ones. ... However, the book can ... be used in an introductory algebraic geometry course where the students will have the advantage of experimenting with examples as their knowledge grows." (A. Sinan Sertöz, Mathematical Reviews, Issue 2007 b), From the reviews:"Algebraic geometry generally studies the properties of solution sets of systems of polynomial equations without direct reference to the actual polynomials used in these systems. â€¦ This is especially desirable for classwork where the development of the abstract machinery generally outlasts the patience of the students, except possibly the most motivated ones. â€¦ However, the book can â€¦ be used in an introductory algebraic geometry course where the students will have the advantage of experimenting with examples as their knowledge grows." (A. Sinan SertÃ¶z, Mathematical Reviews, Issue 2007 b), From the reviews: "Algebraic geometry generally studies the properties of solution sets of systems of polynomial equations without direct reference to the actual polynomials used in these systems. ... This is especially desirable for classwork where the development of the abstract machinery generally outlasts the patience of the students, except possibly the most motivated ones. ... However, the book can ... be used in an introductory algebraic geometry course where the students will have the advantage of experimenting with examples as their knowledge grows." (A. Sinan Sertz, Mathematical Reviews, Issue 2007 b), From the reviews: "Algebraic geometry generally studies the properties of solution sets of systems of polynomial equations without direct reference to the actual polynomials used in these systems. a? This is especially desirable for classwork where the development of the abstract machinery generally outlasts the patience of the students, except possibly the most motivated ones. a? However, the book can a? be used in an introductory algebraic geometry course where the students will have the advantage of experimenting with examples as their knowledge grows." (A. Sinan Sert'z, Mathematical Reviews, Issue 2007 b)

Series Volume Number16

Number of Volumes1 vol.

IllustratedYes

Dewey Decimal516.35

Table Of ContentIntroductory Remarks on Computer Algebra.- Basic Notations and Ideas: A Historical Account.- Basic Computational Problems and Their Solution.- An Introduction to SINGULAR.- Practical Session I.- Practical Session II.- Constructive Module Theory and Homological Algebra I.- Homological Algebra II.- Practical Session III.- Solving Systems of Polynomial Equations.- Primary Decomposition and Normalization.- Practical Session IV.- Algorithms for Invariant Theory.- Computing in Local Rings.- Practical Session V.

SynopsisSystems of polynomial equations are central to mathematics and its appli- tion to science and engineering. Their solution sets, called algebraic sets, are studied in algebraic geometry, a mathematical discipline of its own. Algebraic geometry has a rich history, being shaped by di'erent schools. We quote from Hartshorne's introductory textbook (1977): "Algebraic geometry has developed in waves, each with its own language and point of view. The late nineteenth century saw the function-theoretic approach of Brill and Noether, and the purely algebraic approach of K- necker, Dedekind, and Weber. The Italian school followed with Cast- nuovo, Enriques, and Severi, culminating in the classi'cation of algebraic surfaces. Then came the twentieth-century "American school" of Chow, Weil, and Zariski, which gave ?rm algebraic foundations to the Italian - tuition. Mostrecently,SerreandGrothendieck initiatedthe Frenchschool, which has rewritten the foundations of algebraic geometry in terms of schemes and cohomology, and which has an impressive record of solving old problems with new techniques. Each of these schools has introduced new concepts and methods. " As a result of this historical process, modern algebraic geometry provides a multitude oftheoreticalandhighly abstracttechniques forthe qualitativeand quantitative study of algebraic sets, without actually studying their de'ning equations at the ?rst place. On the other hand, due to the development of powerful computers and e'ectivecomputer algebraalgorithmsatthe endof the twentiethcentury,it is nowadayspossibletostudyexplicitexamplesviatheirequationsinmanycases ofinterest. Inthisway,algebraicgeometrybecomes accessibleto experiments. Theexperimentalmethod,whichhasproventobehighlysuccessfulinnumber theory, now also adds to the toolbox of the algebraic geometer., 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.

LC Classification NumberQA564-609