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Matters Computational

Ideas, Algorithms, Source Code

  • Jörg Arndt

Table of contents

  1. Front Matter
    Pages i-xiv
  2. Low level algorithms

    1. Front Matter
      Pages 1-1
    2. Jörg Arndt
      Pages 2-101
    3. Jörg Arndt
      Pages 102-133
    4. Jörg Arndt
      Pages 134-152
    5. Jörg Arndt
      Pages 153-170
  3. Combinatorial generation

    1. Front Matter
      Pages 171-171
    2. Jörg Arndt
      Pages 172-175
    3. Jörg Arndt
      Pages 176-193
    4. Jörg Arndt
      Pages 194-201
    5. Jörg Arndt
      Pages 202-216
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      Pages 217-231
    7. Jörg Arndt
      Pages 232-276
    8. Jörg Arndt
      Pages 277-290
    9. Jörg Arndt
      Pages 291-294
    10. Jörg Arndt
      Pages 295-303
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      Pages 304-322
    12. Jörg Arndt
      Pages 323-338
    13. Jörg Arndt
      Pages 339-353
    14. Jörg Arndt
      Pages 354-369
    15. Jörg Arndt
      Pages 370-383
    16. Jörg Arndt
      Pages 384-390
    17. Jörg Arndt
      Pages 391-408
  4. Fast transforms

    1. Front Matter
      Pages 409-409
    2. Jörg Arndt
      Pages 410-439
    3. Jörg Arndt
      Pages 459-496
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      Pages 497-514
    5. Jörg Arndt
      Pages 515-534
    6. Jörg Arndt
      Pages 535-542
    7. Jörg Arndt
      Pages 543-548
  5. Fast arithmetic

    1. Front Matter
      Pages 549-549
    2. Jörg Arndt
      Pages 550-566
    3. Jörg Arndt
      Pages 567-586
    4. Jörg Arndt
      Pages 587-598
    5. Jörg Arndt
      Pages 622-640
    6. Jörg Arndt
      Pages 651-665
    7. Jörg Arndt
      Pages 666-684
    8. Jörg Arndt
      Pages 685-703
    9. Jörg Arndt
      Pages 726-762
  6. Algorithms for finite fields

    1. Front Matter
      Pages 763-763
    2. Jörg Arndt
      Pages 764-821
    3. Jörg Arndt
      Pages 822-863
    4. Jörg Arndt
      Pages 864-885
    5. Jörg Arndt
      Pages 886-920
  7. Back Matter
    Pages 921-966

About this book

Introduction

This book provides algorithms and ideas for computationalists. Subjects treated include low-level algorithms, bit wizardry, combinatorial generation, fast transforms like the Fourier transform, and fast arithmetic for both real numbers and finite fields. Various optimization techniques are described and the actual performance of many given implementations is examined. The focus is on material that does not usually appear in textbooks on algorithms. The implementations are done in C++ and the GP language, written for POSIX-compliant platforms such as the Linux and BSD operating systems.

Keywords

Algorithms Arithmetic Combinatorics Finite fields Fourier transform

Authors and affiliations

  • Jörg Arndt
    • 1
  1. 1.NürnbergGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-14764-7
  • Copyright Information Springer-Verlag Berlin Heidelberg 2011
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Computer Science
  • Print ISBN 978-3-642-14763-0
  • Online ISBN 978-3-642-14764-7
  • Buy this book on publisher's site