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Ball Arithmetic as a Tool in Computer Algebra

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Book cover Maple in Mathematics Education and Research (MC 2019)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 1125))

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Abstract

This presentation gives an overview of ball arithmetic as a tool for computing with real numbers in the context of computer algebra, and discusses recent development to the Arb library.

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References

  1. van der Hoeven, J.: Ball arithmetic (2009). http://hal.archives-ouvertes.fr/hal-00432152/fr/

  2. Johansson, F.: Arb: efficient arbitrary-precision midpoint-radius interval arithmetic. IEEE Trans. Comput. 66, 1281–1292 (2017). https://doi.org/10.1109/TC.2017.2690633

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  5. Johansson, F.: Numerical integration in arbitrary-precision ball arithmetic. In: Davenport, J.H., Kauers, M., Labahn, G., Urban, J. (eds.) ICMS 2018. LNCS, vol. 10931, pp. 255–263. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-96418-8_30

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  7. Geulig, I., Krämer, W., Grimmer, M.: intpakX 1.2. http://www2.math.uni-wuppertal.de/org/WRST/software/intpakX/

  8. Revol, N., Rouillier, F.: Motivations for an arbitrary precision interval arithmetic and the MPFI library. Reliab. Comput. 11(4), 275–290 (2005). https://doi.org/10.1007/s11155-005-6891-y

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Author information

Authors and Affiliations

  1. Inria Bordeaux, Talence, France

    Fredrik Johansson

Authors
  1. Fredrik Johansson
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Correspondence to Fredrik Johansson .

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Editors and Affiliations

  1. Maplesoft, Waterloo, ON, Canada

    Jürgen Gerhard

  2. Wilfrid Laurier University, Waterloo, ON, Canada

    Ilias Kotsireas

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Johansson, F. (2020). Ball Arithmetic as a Tool in Computer Algebra. In: Gerhard, J., Kotsireas, I. (eds) Maple in Mathematics Education and Research. MC 2019. Communications in Computer and Information Science, vol 1125. Springer, Cham. https://doi.org/10.1007/978-3-030-41258-6_26

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  • DOI: https://doi.org/10.1007/978-3-030-41258-6_26

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-41257-9

  • Online ISBN: 978-3-030-41258-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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