Fredrik Johansson
Contact: fredrik.johansson@gmail.com
I'm a mathematician at INRIA Bordeaux-Sud-Ouest and Institut de MathÃ©matiques de Bordeaux, working in the LFANT team headed by Andreas Enge. My research interests include arbitrary-precision arithmetic, interval arithmetic, computational number theory, computer algebra, and special functions.
I'm a permanent researcher (CR2) at INRIA since October 2015, after previously having been employed as a postdoc for one year. 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.
Research
I'm interested in computer algebra, in the broad sense meaning software and algorithms for doing mathematics. I've come to focus on two aspects:
- Asymptotic and practical efficiency of core routines for computer algebra, such as arbitrary-precision arithmetic and polynomial manipulation.
- Reliable numerical computing, for example based on interval arithmetic, and applications in fields such as number theory.
In particular, I've been working quite extensively on methods for computing special functions (hypergeometric functions, the gamma function, the Riemann zeta function, modular forms, and so forth) with arbitrary precision and rigorous error bounds.
I care a lot about developing practical, robust and maintainable free software. My central project over the last couple of years has been to create Arb, a C library for arbitrary-precision interval arithmetic (and much more besides basic arithmetic) using an efficient midpoint-radius representation of real numbers. I'm also the main author of the arbitrary-precision Python library mpmath, and coauthor of the C library FLINT which does number theory and fast arithmetic over many exact domains. 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. Software that I developed has been cited by other scientists in well over 100 papers, in applications such as stellar astrophysics, quantum field theory, antenna design, image processing and computational biology.
Updates
Publications
This list is also available in BibTeX format (txt file).
- 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.
Talks
- 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.