Fredrik Johansson's website
I'm interested in the theory and implementation of fast algorithms for arbitrary-precision arithmetic, polynomial arithmetic, and computation of special functions. More broadly, I'm interested in computational mathematics and computational science.
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 Brent, preprint, 2013, submitted)
- Evaluating parametric holonomic sequences using rectangular splitting (preprint, 2013, submitted)
- Using functional equations to enumerate 1324-avoiding permutations (with Brian Nakamura, preprint, 2013, under review)
- Rigorous high-precision computation of the Hurwitz zeta function and its derivatives (preprint, 2013, under review)
- Ore polynomials in Sage (with Manuel Kauers and Maximilian Jaroschek, preprint, 2013, accepted)
- 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 Mathematics, 2012)
- A fast algorithm for reversion of power series (preprint, 2011, to appear in Mathematics of Computation)
Main author or coauthor
- A Python library for arbitrary-precision floating-point arithmetic with support for numerical approximation of special functions, integrals, infinite series, etc. Notably, the library of special functions with full support for complex arguments and arbitrary-precision evaluation may be the most extensive in any currently available open source library, comparable to Mathematica and Maple (see DLMF).
Mpmath has been cited in numerous publications. I started mpmath in 2007 and have written the majority of the code, with important contributions made by various other authors.
- A C library for rigorous, high-performance arbitrary-precision ball (interval) arithmetic with support for complex numbers, polynomials, power series, matrices, and special functions. Author, started in 2012.
- 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, general optimizations to the code, and other features. I have a page with some benchmarks. Coauthor (about 1/3 of the code), joined 2010.
- A Sage package for holonomic functions. Developed by Manuel Kauers, Maximilian Jaroschek, and myself.
- A computer algebra system which provides a unified Python-based interface to a large number of mathematical packages, plus a comprehensive library of its own. My main contribution has been to integrate mpmath and write Cython extension code to speed up mpmath, though I've also worked on other bits and pieces. Contributor since 2009. I've attended Sage Days 15, 23, 24, 35.
- A computer algebra system written in pure Python. I've worked on various modules (special functions, number theory, statistics, physics) as well as core symbolics and arithmetic. Contributor since 2007, no longer actively involved.
Talks and presentations
- 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
- December 2012: 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.
My Doom maps and related information.