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Software for Algebraic Geometry

  • Book
  • © 2008

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Editors:
  1. Michael Stillman

    1. Department of Mathematics, Cornell University, Ithaca, USA

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    You can also search for this editor in PubMed   Google Scholar

  2. Jan Verschelde

    1. Department of Mathematics, University of Illinois, Chicago, USA

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    You can also search for this editor in PubMed   Google Scholar

  3. Nobuki Takayama

    1. Department of Mathematics, Kobe University, Kobe, Japan

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    You can also search for this editor in PubMed   Google Scholar

Part of the book series: The IMA Volumes in Mathematics and its Applications (IMA, volume 148)

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Table of contents (9 chapters)

  1. Front Matter

    Pages i-ix
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  2. Software for Numerical Algebraic Geometry: A Paradigm and Progress Towards its Implementation

    • Daniel J. Bates, Jonathan D. Hauenstein, Andrew J. Sommese, Charles W. Wampler II
    Pages 1-14

  3. PHClab: A MATLAB/Octave Interface to PHCpack

    • Yun Guan, Jan Verschelde
    Pages 15-32

  4. Computing Gröbner Fans and Tropical Varieties in Gfan

    • Anders Nedergaard Jensen
    Pages 33-46

  5. On a Conjecture for the Dimension of the Space of the Multiple Zeta Values

    • Masanobu Kaneko, Masayuki Noro, Ken’Ichi Tsurumaki
    Pages 47-58

  6. DEMiCs: A Software Package for Computing the Mixed Volume Via Dynamic Enumeration of all Mixed Cells

    • Tomohiko Mizutani, Akiko Takeda
    Pages 59-79

  7. SYNAPS: A Library for Dedicated Applications in Symbolic Numeric Computing

    • Bernard Mourrain, Jean-Pascal Pavone, Philippe Trebuchet, Elias P. Tsigaridas, Julien Wintz
    Pages 81-109

  8. Tropical Implicitization and Mixed Fiber Polytopes

    • Bernd Sturmfels, Josephine Yu
    Pages 111-131

  9. Towards a Black-Box Solver for Finite Games: Computing All Equilibria With Gambit and PHCpack

    • Theodore L. Turocy
    Pages 133-147

  10. ApaTools: A Software Toolbox for Approximate Polynomial Algebra

    • Zhonggang Zeng
    Pages 149-167

  11. Back Matter

    Pages 169-172
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Keywords

About this book

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.

Editors and Affiliations

  • Department of Mathematics, Cornell University, Ithaca, USA

    Michael Stillman

  • Department of Mathematics, University of Illinois, Chicago, USA

    Jan Verschelde

  • Department of Mathematics, Kobe University, Kobe, Japan

    Nobuki Takayama

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