Computing in Algebraic Geometry

A Quick Start using SINGULAR

Wolfram Decker, Christoph Lossen (Autoren)

Buch | Softcover

XVI, 328 Seiten

2010 | Softcover reprint of hardcover 1st ed. 2006
Springer Berlin (Verlag)
978-3-642-06701-3 (ISBN)

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lt;p>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.

Wolfram Decker is professor of mathematics at the Universität des Saarlandes, Saarbrücken, Germany. His fields of interest are algebraic geometry and computer algebra. From 1996-2004, he was the responsible overall organizer of the schools and conferences of two European networks in algebraic geometry, EuroProj and EAGER. He himself gave courses in a number of international schools on computer algebra methods in algebraic geometry, with theoretical and practical sessions: Zürich (Switzerland, 1994), Cortona (Italy, 1995), Nordfjordeid (Norway, 1999), Roma (Italy, 2001), Villa Hermosa (Mexico, 2002), Allahabad (India, 2003), Torino (Italy, 2004). He has managed several successful projects in computer algebra, involving undergraduate and graduate students, thus making contributions to two major computer algebra systems for algebraic geometers, SINGULAR and MACAULAY II.

Introductory 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.

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 Sertöz, Mathematical Reviews, Issue 2007 b)

Erscheint lt. Verlag	12.2.2010
Reihe/Serie	Algorithms and Computation in Mathematics
Zusatzinfo	XVI, 328 p.
Verlagsort	Berlin
Sprache	englisch
Maße	155 x 235 mm
Gewicht	521 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
Schlagworte	computational algebraic geometry • Computational commutative algebra • computer algebra system • Gröbner Bases • Mathematica • polynomial equations • Symbolic Computation
ISBN-10	3-642-06701-8 / 3642067018
ISBN-13	978-3-642-06701-3 / 9783642067013
Zustand	Neuware