Fredrik Johansson
Contact: fredrik.johansson@gmail.com
I'm a researcher at INRIA Bordeaux and Institut de MathÃ©matiques de Bordeaux, working in the LFANT team headed by Andreas Enge.
I'm interested in fast and reliable algorithms for computer algebra. My main focus is on arbitrary-precision arithmetic and rigorous numerical computing, in particular methods for rigorous numerical evaluation of special functions (hypergeometric functions, L-functions, modular forms, and so on).
I have a permanent position as a junior research scientist (chargÃ© de recherche) at INRIA since October 2015, following a one-year postdoc term. From October 2010 to March 2014, I did my PhD in symbolic computation at RISC in Linz, Austria, where Manuel Kauers was my advisor. I grew up in Sweden, and have an MSc (2010) in engineering physics from Chalmers University of Technology, Gothenburg.
Developing free software for mathematics is a big part of my work. My main project since 2012 is Arb, a C library for arbitrary-precision interval arithmetic. I'm also the main author of the arbitrary-precision Python library mpmath, and coauthor of the C library FLINT which covers computational number theory and polynomial arithmetic. All three libraries are standard components of SageMath. See below for other software I've contributed to.
My record computation of the partition function is a fun, if not very practically useful, achievement.
Updates
Publications
This list is also available in BibTeX format (txt file).
- F. Johansson. Computing the Lambert W function in arbitrary-precision complex interval arithmetic. Preprint, 2017. [arXiv] [HAL]
- 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]
- 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]
- A. Enge, W. Hart, F. Johansson. Short addition sequences for theta functions. Preprint, August 2016, submitted. [arXiv]
- F. Johansson. Computing hypergeometric functions rigorously. Preprint, June 2016, submitted. [PDF] [arXiv] [HAL]
- A. Meurer et al. SymPy: Symbolic computing in Python. PeerJ Computer Science 3:e103, 2017. [DOI] [HAL]
- 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]
- 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]
- F. Johansson. A fast algorithm for reversion of power series. Mathematics of Computation, vol 84, 2015, 475-484. [PDF] [arXiv] [DOI] [info]
- F. Johansson. Fast and rigorous computation of special functions to high precision. PhD thesis, RISC, Johannes Kepler University, Linz, 2014. [PDF] [info]
- F. Johansson. Evaluating parametric holonomic sequences using rectangular splitting. ISSAC 2014, 256-263. [PDF] [slides] [arXiv] [DOI] [info]
- 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]
- 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]
- 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]
- 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]
- F. Johansson, M. Kauers, M. Mezzarobba. Finding hyperexponential solutions of linear ODEs by numerical evaluation. ISSAC 2013, 211-218. [PDF] [arXiv] [DOI] [info]
- 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]
Trivia: my Erdős number is 3 (0-1, 1-2, 2-3).
Mathematical software
- Nemo - Julia computer algebra package (coauthor, since 2015)
- mpmath - Python library for arbitrary-precision floating-point arithmetic (main author, since 2007)
- Arb - C library for arbitrary-precision interval arithmetic (main author, since 2012)
- FLINT - C library for number theory (coauthor, since 2010)
- ore_algebra - SageMath package for holonomic functions (coauthor, 2013)
- SageMath (miscellaneous contributions since 2009)
- SymPy (miscellaneous contributions 2007-2008, designed the logo)
I've taken part in Google Summer of Code once as a student and three times as a mentor:
- 2015: mentored Anubhav Srivastava who implemented BLAS wrappers for linear algebra in FLINT
- 2014: mentored Alex Best who implemented Hermite and Smith normal form computation in FLINT
- 2012: mentored Lina Kulakova who implemented algorithms for polynomial factorization in FLINT
- 2008: implemented numerical evaluation in SymPy, mentored by Ondrej Certik
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.
Talks
- October 2017: Numerics of classical elliptic functions, elliptic integrals and modular forms, Elliptic Integrals, Elliptic Functions and Modular Forms in Quantum Field Theory, DESY, Zeuthen, Germany
- August 2017: Fundamental algorithms in Arb, OSCAR : Antic workshop, TU Kaiserslautern, Germany
- July 2017: Arb: efficient arbitrary-precision midpoint-radius interval arithmetic, ARITH24, Imperial College London, UK
- June 2016: Fast reversion of formal power series, RAIM 2016, Banyuls-sur-mer, France
- May 2016: Hypergeometric functions in Arb, FastRelax meeting, LAAS-CNRS, Toulouse, France
- November 2015: Taking precision to the limit, Unithe ou cafe, INRIA, Bordeaux, France
- October 2015: Computing transcendental functions with error bounds, LFANT seminar, IMB, Bordeaux, France
- September 2015: Addition sequences and numerical evaluation of modular forms, DK Statusseminar, Strobl, Austria
- June 2015: Efficient implementation of elementary functions in the medium-precision range, ARITH22, ENS Lyon, France
- June 2015: Fast arbitrary-precision evaluation of special functions in the Arb library, OPSFA13, NIST, Gaithersburg, MD, USA
- May 2015: High-precision methods for zeta functions. Part 3: fast evaluation of sequences, UNCG Summer School in Computational Number Theory, Greensboro, NC, USA
- May 2015: High-precision methods for zeta functions. Part 2: derivatives, UNCG Summer School in Computational Number Theory, Greensboro, NC, USA
- May 2015: High-precision methods for zeta functions. Part 1: functions, formulas, UNCG Summer School in Computational Number Theory, Greensboro, NC, USA
- May 2015: Special functions in arbitrary-precision interval arithmetic, CAPA seminar, Uppsala University, Sweden
- March 2015: Special functions in the Arb library, AriC seminar, LIP, ENS Lyon, France
- March 2015: Special functions in the Arb library, Pequan seminar, LIP6, UPMC, Paris, France
- March 2015: Special functions in the Arb library, SpecFun seminar, INRIA Saclay Ile-de-France, Palaiseau, France
- September 2014: Reliable multiprecision arithmetic for number theory, LFANT seminar, IMB, Bordeaux, France
- July 2014: Evaluating parametric holonomic sequences using rectangular splitting, ISSAC 2014, Kobe University, Japan
- May 2014: Making change for 10^{20}, computer algebra seminar, TU Kaiserslautern, Germany
- March 2014: Making change for 10^{20}, Algorithmic Combinatorics Seminar, RISC, Hagenberg, Austria
- October 2013: Progress on algorithms for high-precision evaluation of special functions, Algorithmic Combinatorics Seminar, RISC, Hagenberg, Austria
- July 2013: Efficient implementation of the Hardy-Ramanujan-Rademacher formula, 2013 SIAM Annual Meeting, San Diego, CA, USA
- June 2013: Arb: a C library for ball arithmetic, ISSAC 2013, Boston, MA, USA [Received the ISSAC 2013 Distinguished Software Presentation Award]
- June 2013: Finding Hyperexponential Solutions of Linear ODEs by Numerical Evaluation, ISSAC 2013, Boston, MA, USA
- March 2013: Fast, rigorous, arbitrary precision numerics with ball arithmetic, Algorithmic Combinatorics Seminar, RISC, Hagenberg, Austria
- November 2012: Algorithms for hyperexponential solutions of differential equations, Algorithmic Combinatorics Seminar, RISC, Hagenberg, Austria
- May 2012: Fast special function computations with FLINT, RISC-DESY Workshop, RISC, Hagenberg, Austria
- December 2011: Fast combinatorial special functions, Sage Days 35: Algorithms in Number Theory and FLINT, University of Warwick, UK
- November 2011: Partitions in the quintillions or Billions of congruences, Algorithmic Combinatorics Seminar, RISC, Hagenberg, Austria
- November 2011: Fast reversion of power series, Algorithmic Combinatorics Seminar, RISC, Hagenberg, Austria
- July 2010: Computation of special functions in mpmath, Sage Days 24: Symbolic Computation in Differential Algebra and Special Functions, RISC, Hagenberg, Austria
- July 2010: Computation of special functions in mpmath, Sage Days 23: Number Theory and Algebra, Lorentz Center, Leiden, Netherlands
- May 2009: mpmath: arbitrary-precision floating-point arithmetic and special functions, Sage Days 15, University of Washington, Seattle, WA, USA
Music
- I compose MIDI music.
- What I'm listening to: my last.fm account.
Doom
My Doom maps and related information.