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

  • Gebhard Böckle
  • Wolfram Decker
  • Gunter Malle

Table of contents

  1. Front Matter
    Pages i-ix
  2. Andreas Bächle, Wolfgang Kimmerle, Leo Margolis
    Pages 1-22
  3. Janko Böhm, Wolfram Decker, Santiago Laplagne, Gerhard Pfister
    Pages 51-96
  4. Michel Börner, Irene I. Bouw, Stefan Wewers
    Pages 97-122
  5. Winfried Bruns, Richard Sieg, Christof Söger
    Pages 123-146
  6. Tommaso Giorgio Centeleghe, Christian Theisen
    Pages 147-175
  7. Michael Dettweiler, Mirjam Jöllenbeck
    Pages 177-197
  8. Bettina Eick, Max Horn, Alexander Hulpke
    Pages 199-211
  9. Anne Frühbis-Krüger, Stefan Wewers
    Pages 231-252
  10. Andreas Gathmann, Dennis Ochse
    Pages 253-286
  11. Andreas Gathmann, Hannah Markwig, Dennis Ochse
    Pages 287-309
  12. Simon Hampe, Michael Joswig
    Pages 361-385
  13. Torsten Hoge, Gerhard Röhrle, Anne Schauenburg
    Pages 403-421
  14. Tilman Möller, Gerhard Röhrle
    Pages 495-501
  15. Markus Kirschmer, Gabriele Nebe
    Pages 503-532
  16. Andreas Paffenholz
    Pages 533-547
  17. Gerhard Pfister, Dorin Popescu
    Pages 549-559
  18. Armin Shalile
    Pages 587-609
  19. Ute Spreckels, Andreas Stein
    Pages 611-622
  20. Michael Stoll
    Pages 623-663
  21. Panagiotis Tsaknias, Gabor Wiese
    Pages 741-763

About this book

Introduction

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.

Keywords

Computer Algebra Computational Group Theory Finite Group Theory Reflection Arrangements Associative Algebras Representation Theory Computational Algebraic Geometry Gröbner Bases Tropical Geometry Polyhedral Geometry Lattices Modular Forms Arithmetic Geometry Jacobians and Abelian Varieties Rational Points Real and Complex Multiplication

Editors and affiliations

  • Gebhard Böckle
    • 1
  • Wolfram Decker
    • 2
  • Gunter Malle
    • 3
  1. 1.IWRHeidelberg UniversityHeidelbergGermany
  2. 2.Department of MathematicsTechnische Universität KaiserslauternKaiserslauternGermany
  3. 3.Department of MathematicsTechnische Universität KaiserslauternKaiserslauternGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-70566-8
  • Copyright Information Springer International Publishing AG, part of Springer Nature 2017
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-70565-1
  • Online ISBN 978-3-319-70566-8
  • Buy this book on publisher's site