Credits and references
Arb is licensed GNU General Public License version 2, or any later version.
Arb includes code by Bill Hart and
Sebastian Pancratz taken from FLINT (also licensed GPL 2.0+).
From 2012 to July 2014, Fredrik’s work on Arb was supported by
Austrian Science Fund FWF Grant Y464-N18 (Fast Computer Algebra
for Special Functions).
During that period, he was a PhD student (and briefly a postdoc) at
RISC, Johannes Kepler University, Linz, supervised by Manuel Kauers.
From September 2014 to the present, Fredrik’s work on Arb was supported by
ERC Starting Grant ANTICS 278537 (Algorithmic Number Theory in Computer Science) http://cordis.europa.eu/project/rcn/101288_en.html
During that period, he was a postdoc at INRIA-Bordeaux and IMB, supervised
by Andreas Enge.
Contributors
The following people (among others) have contributed patches or bug reports.
- Jonathan Bober
- Yuri Matiyasevich
- Abhinav Baid
- Ondřej Čertík
- Andrew Booker
- Francesco Biscani
- Clemens Heuberger
- Pascal Molin
- Ricky Farr
- Marcello Seri
Software
The following software has been helpful in the development of Arb.
- GMP (Torbjörn Granlund and others), http://gmplib.org
- MPIR (Brian Gladman, Jason Moxham, William Hart and others), http://mpir.org
- MPFR (Guillaume Hanrot, Vincent Lefèvre, Patrick Pélissier, Philippe Théveny, Paul Zimmermann and others), http://mpfr.org
- FLINT (William Hart, Sebastian Pancratz, Andy Novocin, Fredrik Johansson, David Harvey and others), http://flintlib.org
- Sage (William Stein and others), http://sagemath.org
- Pari/GP (The Pari group), http://pari.math.u-bordeaux.fr/
- SymPy (Ondřej Čertík, Aaron Meurer and others), http://sympy.org
- mpmath (Fredrik Johansson and others), http://mpmath.org
- Mathematica (Wolfram Research), http://www.wolfram.com/mathematica
- HolonomicFunctions (Christoph Koutschan), http://www.risc.jku.at/research/combinat/software/HolonomicFunctions/
- Sphinx (George Brandl and others), http://sphinx.pocoo.org
- CM (Andreas Enge), http://www.multiprecision.org/index.php?prog=cm
Citing Arb
If you wish to cite Arb in a scientific paper, the following reference can be used (you may also cite the manual or the website directly):
F. Johansson. “Arb: a C library for ball arithmetic”, ACM Communications in Computer Algebra, 47(4):166-169, 2013.
In BibTeX format:
@article{Johansson2013arb,
title={{A}rb: a {C} library for ball arithmetic},
author={F. Johansson},
journal={ACM Communications in Computer Algebra},
volume={47},
number={4},
pages={166--169},
year={2013},
publisher={ACM}
}
Bibliography
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[BBC2000] | J. Borwein, D. M. Bradley and R. E. Crandall, “Computational strategies for the Riemann zeta function”, Journal of Computational and Applied Mathematics 121 (2000) 247-296 |
[BM1980] | R. P. Brent and E. M. McMillan, “Some new algorithms for high-precision computation of Euler’s constant”, Mathematics of Computation 34 (1980) 305-312. |
[Bre1978] | R. P. Brent, “A Fortran multiple-precision arithmetic package”, ACM Transactions on Mathematical Software, 4(1):57–70, March 1978. |
[CP2005] | R. Crandall and C. Pomerance, Prime Numbers: A Computational Perspective, second edition, Springer (2005). |
[EM2004] | O. Espinosa and V. Moll, “A generalized polygamma function”, Integral Transforms and Special Functions (2004), 101-115. |
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[GG2003] | J. von zur Gathen and J. Gerhard, Modern Computer Algebra, second edition, Cambridge University Press (2003) |
[Joh2014a] | F. Johansson, Fast and rigorous computation of special functions to high precision, PhD thesis, RISC, Johannes Kepler University, Linz, 2014. http://fredrikj.net/thesis/ |
[NIST2012] | National Institute of Standards and Technology, Digital Library of Mathematical Functions (2012), http://dlmf.nist.gov/ |
[Olv1997] | F. Olver, Asymptotics and special functions, AKP Classics, AK Peters Ltd., Wellesley, MA, 1997. Reprint of the 1974 original. |
[Rad1973] | H. Rademacher, Topics in analytic number theory, Springer, 1973. |
[PS1973] | M. S. Paterson and L. J. Stockmeyer, “On the number of nonscalar multiplications necessary to evaluate polynomials”, SIAM J. Comput (1973) |
[Smi2001] | D. M. Smith, “Algorithm: Fortran 90 Software for Floating-Point Multiple Precision Arithmetic, Gamma and Related Functions”, Transactions on Mathematical Software 27 (2001) 377-387, http://myweb.lmu.edu/dmsmith/toms2001.pdf |