Profile cover photo
Profile photo
Fredrik Johansson
151 followers
151 followers
About
Fredrik's posts

Post has attachment

Post has attachment
Brilliant anti-computer chess strategy (from 2008).

https://www.youtube.com/watch?v=2k4V_LJTvqM

Post has shared content
Here is some fantastic news about a huge new grant, part of which will fund a new Open Source Computer Algebra System for up to 12 years.

https://wbhart.blogspot.de/2016/11/new-computer-algebra-system-oscar_20.html

Please bear in mind the blog is written from my personal point of view as a participant in the project and is focused on what I hope to contribute to the project.

Obviously the only official source of information on OSCAR will be the OSCAR website when it goes live.

Post has attachment

Post has attachment
https://arxiv.org/abs/1611.02831


Here is a new preprint about Arb, describing the library's overall
scope and goals, precision semantics, and how numbers are implemented
at a low level. This paper is meant to supersede my extended abstract
from ISSAC'13 ("Arb: a C library for ball arithmetic") which now is
completely out of date.

Post has attachment

Post has attachment

Post has attachment
http://arxiv.org/abs/1606.06977

Just finished writing this paper which describes the methods for hypergeometric functions in Arb. Check out the benchmarks section!

Abstract: We present an efficient implementation of hypergeometric functions in arbitrary-precision interval arithmetic. The functions 0F1, 1F1, 2F1 and 2F0 (or the Kummer U-function) are supported for unrestricted complex parameters and argument, and by extension, we cover exponential and trigonometric integrals, error functions, Fresnel integrals, incomplete gamma and beta functions, Bessel functions, Airy functions, Legendre functions, Jacobi polynomials, complete elliptic integrals, and other special functions. The output can be used directly for interval computations or to generate provably correct floating-point approximations in any format. Performance is competitive with earlier arbitrary-precision software, and sometimes orders of magnitude faster. We also partially cover the generalized hypergeometric function pFq and computation of high-order parameter derivatives.

Post has attachment
https://youtu.be/GErUYzzpHTQ

Music for a Zelda-like game? Source MIDI file at https://github.com/fredrik-johansson/midi

Post has attachment
"Hypergeometric functions in Arb" - slides from my talk today at the FastRelax meeting in Toulouse: http://fredrikj.net/math/laas20160525.pdf
Wait while more posts are being loaded