Algorithms and Computation in Mathematics

Computing in Algebraic Geometry

A Quick Start using SINGULAR

Authors: Decker, Wolfram, Lossen, Christoph

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About the authors

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.

Christoph Lossen is assistant professor (C2) of mathematics at the University of Kaiserslautern. His fields of interest are singularity theory and computer algebra. Since 2000, he is a member of the SINGULAR development team. He taught several courses on computer algebra methods with special emphasis on the needs of singularity theory, including international schools at Sao Carlos (Brazil, 2002), Allahabad (India, 2003) and Oberwolfach (Germany, 2003).

Reviews

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)


Table of contents (15 chapters)

Table of contents (15 chapters)
  • Introductory Remarks on Computer Algebra

    Pages 1-9

  • Basic Notations and Ideas: A Historical Account

    Pages 11-35

  • Basic Computational Problems and Their Solution

    Pages 37-61

  • An Introduction to SINGULAR

    Pages 63-124

  • Practical Session I

    Pages 125-126

Buy this book

eBook $54.99
price for USA in USD
  • ISBN 978-3-540-28993-7
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
  • Institutional customers should get in touch with their account manager
Hardcover $79.99
price for USA in USD
Softcover $69.99
price for USA in USD
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Bibliographic Information

Bibliographic Information
Book Title
Computing in Algebraic Geometry
Book Subtitle
A Quick Start using SINGULAR
Authors
Series Title
Algorithms and Computation in Mathematics
Series Volume
16
Copyright
2006
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
Distribution Rights
Distribution rights for India: Hindustan Book Agency, New Delhi, India
eBook ISBN
978-3-540-28993-7
DOI
10.1007/3-540-28993-3
Hardcover ISBN
978-3-540-28992-0
Softcover ISBN
978-3-642-06701-3
Series ISSN
1431-1550
Edition Number
1
Number of Pages
XVI, 328
Topics