Fredrik Johansson's website
I'm interested in arbitrary-precision arithmetic, polynomial arithmetic, and computation of special functions.
I'm currently a PhD student in symbolic computation at RISC in Hagenberg, Austria, where I'm a member of Peter Paule's Algorithmic Combinatorics group (my advisor is Manuel Kauers). My page at RISC contains some more information. I was born in Sweden and obtained my MSc in engineering physics from Chalmers in 2010.
Occasional development updates appear on my blog. For code, see my GitHub account or the links below.
- A bound for the error term in the Brent-McMillan algorithm (with Richard P. Brent), 2013 preprint, to appear in
Mathematics of Computation
- Evaluating parametric holonomic sequences using rectangular splitting, 2013 preprint, submitted
- Using functional equations to enumerate 1324-avoiding permutations (with Brian Nakamura), 2013 preprint, to appear in Advances in Applied Mathematics
- Rigorous high-precision computation of the Hurwitz zeta function and its derivatives, 2013 preprint, submitted
- Ore polynomials in Sage (with Manuel Kauers and Maximilian Jaroschek), 2013 preprint, to appear in a Springer LNCS volume titled Computer Algebra and Polynomials
- Arb: a C library for ball arithmetic, published in ACM Communications in Computer Algebra, 2013
- Finding hyperexponential solutions of linear ODEs by numerical evaluation (with Manuel Kauers and Marc Mezzarobba),
published in the Proceedings of ISSAC 2013
- Efficient implementation of the Hardy-Ramanujan-Rademacher formula, published in LMS Journal of Computation and
- A fast algorithm for reversion of power series, 2011 preprint, to appear in Mathematics of Computation
My most well-known project is probably mpmath, a Python library for arbitrary-precision floating-point arithmetic with support for complex numbers, special functions, numerical integration, linear algebra, etc. Notably, the selection of special functions may be the most extensive in any currently available open source project, comparable to Mathematica and Maple (see DLMF). The mpmath library has been cited in numerous publications. I started mpmath in 2007 and have written the majority of the code (various other people have made significant contributions).
I'm the author of Arb, a C library for asymptotically fast numerical computation with rigorous error bounds, using the concept of ball arithmetic. Arb supports complex numbers, polynomials, power series, matrices, and some special functions. I started developing Arb in 2012.
I'm a coauthor (since 2010) of FLINT, a C library for computational number theory with emphasis on asymptotically fast polynomial arithmetic. My work includes power series functions, exact linear algebra, number-theoretic special functions, and general optimizations.
In 2013, I helped develop ore_algebra, a Sage package for holonomic functions, together with Manuel Kauers and Maximilian Jaroschek. I've contributed to the Sage project since 2009, mainly by writing wrapper code for mpmath and FLINT. I attended Sage Days 15, 23, 24, 35. I also contributed extensively to the pure-Python computer algebra system SymPy from around 2007 to 2008, and designed SymPy's logo, but I'm no longer actively involved in that project.
- October 2013: Progress on algorithms for high-precision evaluation of special functions, Algorithmic Combinatorics Seminar, RISC, Hagenberg
- July 2013: Efficient implementation of the Hardy-Ramanujan-Rademacher formula, 2013 SIAM Annual Meeting, San Diego, CA
- June 2013: Arb: a C library for ball arithmetic, ISSAC 2013, Boston, MA
- June 2013: Finding Hyperexponential Solutions of Linear ODEs by Numerical Evaluation, ISSAC 2013, Boston, MA
- March 2013: Fast, rigorous, arbitrary precision numerics with ball arithmetic, Algorithmic Combinatorics Seminar, RISC, Hagenberg
- November 2012: Algorithms for hyperexponential solutions of differential equations, Algorithmic Combinatorics Seminar, RISC, Hagenberg
- May 2012: Fast special function computations with
FLINT, RISC-DESY Workshop, RISC, Hagenberg.
- December 2011: Fast combinatorial special functions, Sage Days 35: Algorithms in Number Theory and FLINT, University of Warwick
- November 2011: Partitions in the quintillions or Billions of congruences, Algorithmic Combinatorics Seminar, RISC, Hagenberg
- November 2011: Fast reversion of power series, Algorithmic Combinatorics Seminar, RISC, Hagenberg
- July 2010: Computation of special functions in mpmath, Sage Days 24: Symbolic Computation in Differential Algebra and Special Functions, RISC, Hagenberg
- July 2010: Computation of special functions in mpmath, Sage Days 23: Number Theory and Algebra, Lorentz Center, Leiden
- May 2009: mpmath: arbitrary-precision floating-point arithmetic and special functions, Sage Days 15, University of Washington, Seattle, WA
I compose MIDI music. I also have a YouTube channel with some recordings.
On the off chance that you want to know what I'm listening to at the moment, check my last.fm account.
My Doom maps and related information.