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Jonathan M. Borwein Commemorative Conference

JBCC 2017: From Analysis to Visualization pp 407–421Cite as

Extending the PSLQ Algorithm to Algebraic Integer Relations

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Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 313))

Abstract

The pslq algorithm computes integer relations for real numbers and Gaussian integer relations for complex numbers. We endeavour to extend pslq to find integer relations consisting of algebraic integers from some quadratic extension fields (in both the real and complex cases). We outline the algorithm, discuss the required modifications for handling algebraic integers, problems that have arisen, experimental results, and challenges to further work.

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References

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Author information

Authors and Affiliations

  1. School of Mathematical and Physical Sciences, Centre for Computer-Assisted Research Mathematics and its Applications (CARMA), The University of Newcastle, Newcastle, NSW, Australia

    Matthew P. Skerritt

  2. Department of Mathematical and Computational Sciences, University of Toronto, Mississauga, ON, Canada

    Paul Vrbik

Authors
  1. Matthew P. Skerritt
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  2. Paul Vrbik
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Corresponding author

Correspondence to Matthew P. Skerritt .

Editor information

Editors and Affiliations

  1. Lawrence Berkeley National Laboratory, Berkeley, CA, USA

    David H. Bailey

  2. Western University, London, ON, Canada

    Naomi Simone Borwein

  3. Mathematical Sciences Institute, Australian National University, Canberra, ACT, Australia

    Richard P. Brent

  4. School of IT and Mathematical Sciences, University of South Australia, Mawson Lakes, SA, Australia

    Regina S. Burachik

  5. School of Mathematical and Physical Sciences, University of Newcastle, Callaghan, NSW, Australia

    Judy-anne Heather Osborn

  6. School of Mathematical and Physical Sciences, University of Newcastle, Callaghan, NSW, Australia

    Brailey Sims

  7. Department of Mathematics, Western Michigan University, Kalamazoo, MI, USA

    Qiji J. Zhu

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Skerritt, M.P., Vrbik, P. (2020). Extending the PSLQ Algorithm to Algebraic Integer Relations. In: Bailey, D., et al. From Analysis to Visualization. JBCC 2017. Springer Proceedings in Mathematics & Statistics, vol 313. Springer, Cham. https://doi.org/10.1007/978-3-030-36568-4_26

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