Fredrik Johansson

Fredrik Johansson


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I'm a researcher at INRIA Bordeaux and Institut de Mathématiques de Bordeaux, working in the LFANT team headed by Andreas Enge.

I'm interested in fast and reliable algorithms for computer algebra. I mainly work on arbitrary-precision arithmetic and rigorous numerical computing, with emphasis on provably correct methods for complex analysis and numerical evaluation of special functions (including hypergeometric functions, L-functions, and modular forms).

A big part of my work is to develop free scientific software. My main project since 2012 is Arb, a C library for arbitrary-precision ball arithmetic. I'm also the main author of the arbitrary-precision Python library mpmath, and coauthor of the C number theory library FLINT. All three libraries are standard components of SageMath. See below for other software I've contributed to.

Academic history


This list is also available in BibTeX format (txt file).

  1. F. Johansson. Numerical integration in arbitrary-precision ball arithmetic. Preprint, 2018. [arXiv] [HAL]
  2. F. Johansson, M. Mezzarobba. Fast and rigorous arbitrary-precision computation of Gauss-Legendre quadrature nodes and weights. Preprint, 2018. [arXiv] [HAL]
  3. F. Johansson. Computing the Lambert W function in arbitrary-precision complex interval arithmetic. Preprint, 2017. [arXiv] [HAL]
  4. C. Fieker, W. Hart, T. Hofmann, F. Johansson. Nemo/Hecke: computer algebra and number theory packages for the Julia programming language. ISSAC 2017. [arXiv] [HAL]
  5. F. Johansson. Arb: efficient arbitrary-precision midpoint-radius interval arithmetic. IEEE Transactions on Computers, vol 66, issue 8, 2017, 1281-1292. [DOI] [PDF] [arXiv] [HAL]
  6. A. Enge, W. Hart, F. Johansson. Short addition sequences for theta functions. Journal of Integer Sequences, vol 21, 2018, article 18.2.4. [arXiv] [HAL]
  7. F. Johansson. Computing hypergeometric functions rigorously. Preprint, June 2016, submitted. [PDF] [arXiv] [HAL]
  8. A. Meurer et al. SymPy: Symbolic computing in Python. PeerJ Computer Science 3:e103, 2017. [DOI] [HAL]
  9. F. Johansson. Efficient implementation of elementary functions in the medium-precision range. 22nd IEEE Symposium on Computer Arithmetic (ARITH22), 2015, 83-89. [PDF] [arXiv] [DOI]
  10. R. P. Brent, F. Johansson. A bound for the error term in the Brent-McMillan algorithm. Mathematics of Computation, vol 84, 2015, 2351-2359. [PDF] [arXiv] [DOI]
  11. F. Johansson. A fast algorithm for reversion of power series. Mathematics of Computation, vol 84, 2015, 475-484. [PDF] [arXiv] [DOI] [info]
  12. F. Johansson. Fast and rigorous computation of special functions to high precision. PhD thesis, RISC, Johannes Kepler University, Linz, 2014. [PDF] [info]
  13. F. Johansson. Evaluating parametric holonomic sequences using rectangular splitting. ISSAC 2014, 256-263. [PDF] [slides] [arXiv] [DOI] [info]
  14. F. Johansson, B. Nakamura. Using functional equations to enumerate 1324-avoiding permutations. Advances in Applied Mathematics, vol 56, 2014, 20-34. [PDF] [arXiv] [DOI] [info]
  15. F. Johansson. Rigorous high-precision computation of the Hurwitz zeta function and its derivatives. Numerical Algorithms, vol 69, issue 2, 2015, 253-270. [PDF] [arXiv] [DOI] [info]
  16. M. Kauers, M. Jaroschek, F. Johansson. Ore polynomials in Sage. Computer Algebra and Polynomials, 2015, 105-125, Springer Lecture Notes in Computer Science. [PDF] [arXiv] [DOI] [info]
  17. F. Johansson. Arb: a C library for ball arithmetic. ACM Communications in Computer Algebra, vol 47, issue 4, December 2013, 166-169. [PDF] [slides] [DOI] [info]
  18. F. Johansson, M. Kauers, M. Mezzarobba. Finding hyperexponential solutions of linear ODEs by numerical evaluation. ISSAC 2013, 211-218. [PDF] [arXiv] [DOI] [info]
  19. F. Johansson. Efficient implementation of the Hardy-Ramanujan-Rademacher formula. LMS Journal of Computation and Mathematics, vol 15, 2012, 341-359. [PDF] [arXiv] [DOI] [info]
  20. F. Johansson. Simulation of the Maxwell-Dirac and Schrödinger-Poisson systems. Master's thesis, Chalmers University of Technology, Gothenburg, 2010.

Trivia: my Erdős number is 3 (0-1, 1-2, 2-3).

Mathematical software

I've taken part in Google Summer of Code once as a student and three times as a mentor:

In summer 2009 and 2010, I worked on Sage and mpmath as a contractor for the American Institute of Mathematics, thanks to funding provided by William Stein.

The mpmath library is quite widely used; it has been cited in over 100 papers in applications such as stellar astrophysics, quantum field theory, antenna design, image processing and computational biology.

Both mpmath and Arb have been used for some rather interesting computations. My own record computation of the partition function with Arb is a fun, if not very practically useful, achievement.




My Doom maps and related information.