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.. _credits:
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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+).
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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.
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Contributors
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The following people (among others) have contributed patches or bug reports.
* Jonathan Bober
* Yuri Matiyasevich
* Abhinav Baid
* Ondřej Čertík
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* Andrew Booker
* Francesco Biscani
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* Clemens Heuberger
2015-01-28 14:54:30 +01:00
* Pascal Molin
* Ricky Farr
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* Marcello Seri
2015-10-02 09:46:02 +02:00
* Tommy Hofmann
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Software
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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
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* Pari/GP (The Pari group), http://pari.math.u-bordeaux.fr/
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* 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
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* CM (Andreas Enge), http://www.multiprecision.org/index.php?prog=cm
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Citing Arb
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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}
}
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Bibliography
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.. [Arn2010] \J. Arndt, *Matters Computational* , Springer (2010), http://www.jjj.de/fxt/#fxtbook
2013-05-12 19:36:58 +01:00
.. [BBC1997] \D. H. Bailey, J. M. Borwein and R. E. Crandall, "On the Khintchine constant", Mathematics of Computation 66 (1997) 417-431
2012-12-12 10:18:08 +01:00
2013-05-12 19:36:58 +01:00
.. [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
2012-10-11 13:09:44 +02:00
2013-05-12 19:36:58 +01:00
.. [BZ1992] _ \J. Borwein and I. Zucker, "Fast evaluation of the gamma function for small rational fractions using complete elliptic integrals of the first kind", IMA Journal of Numerical Analysis 12 (1992) 519-526
2012-10-11 13:09:44 +02:00
2013-05-12 19:36:58 +01:00
.. [Bor1987] _ \P. Borwein, "Reduced complexity evaluation of hypergeometric functions", Journal of Approximation Theory 50:3 (1987)
2012-10-11 13:09:44 +02:00
2014-08-26 16:23:38 +02:00
.. [Bor2000] \P. Borwein, "An Efficient Algorithm for the Riemann Zeta Function", Constructive experimental and nonlinear analysis, CMS Conference Proc. 27 (2000) 29-34, http://www.cecm.sfu.ca/personal/pborwein/PAPERS/P155.pdf
2012-10-11 13:09:44 +02:00
2013-12-03 16:06:25 +01:00
.. [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.
2012-10-11 13:09:44 +02:00
2013-12-03 16:06:25 +01:00
.. [Bre1978] \R. P. Brent, "A Fortran multiple-precision arithmetic package", ACM Transactions on Mathematical Software, 4(1):57– 70, March 1978.
2013-01-15 12:16:20 +01:00
2013-12-03 16:06:25 +01:00
.. [Bre2010] \R. P. Brent, "Ramanujan and Euler's Constant", http://wwwmaths.anu.edu.au/~brent/pd/Euler_CARMA_10.pdf
2012-10-11 13:09:44 +02:00
2013-12-03 16:06:25 +01:00
.. [BJ2013] \R. P. Brent and F. Johansson, "A bound for the error term in the Brent-McMillan algorithm", preprint (2013), http://arxiv.org/abs/1312.0039
.. [BZ2011] \R. P. Brent and P. Zimmermann, *Modern Computer Arithmetic* , Cambridge University Press (2011), http://www.loria.fr/~zimmerma/mca/pub226.html
2012-10-11 13:09:44 +02:00
2013-05-12 19:36:58 +01:00
.. [CP2005] \R. Crandall and C. Pomerance, *Prime Numbers: A Computational Perspective* , second edition, Springer (2005).
2012-10-11 13:09:44 +02:00
2015-07-13 17:23:34 +02:00
.. [EM2004] \O. Espinosa and V. Moll, "A generalized polygamma function", Integral Transforms and Special Functions (2004), 101-115.
2013-05-12 19:36:58 +01:00
.. [Fil1992] \S. Fillebrown, "Faster Computation of Bernoulli Numbers", Journal of Algorithms 13 (1992) 431-445
2012-10-11 13:09:44 +02:00
2013-05-12 19:36:58 +01:00
.. [GG2003] \J. von zur Gathen and J. Gerhard, *Modern Computer Algebra* , second edition, Cambridge University Press (2003)
2012-10-11 13:09:44 +02:00
2013-05-12 19:36:58 +01:00
.. [GS2003] \X. Gourdon and P. Sebah, "Numerical evaluation of the Riemann Zeta-function" (2003), http://numbers.computation.free.fr/Constants/Miscellaneous/zetaevaluations.pdf
2012-10-11 13:09:44 +02:00
2013-05-12 19:36:58 +01:00
.. [HZ2004] \G. Hanrot and P. Zimmermann, "Newton Iteration Revisited" (2004), http://www.loria.fr/~zimmerma/papers/fastnewton.ps.gz
2012-10-11 13:09:44 +02:00
2014-08-26 16:23:38 +02:00
.. [Hoe2009] \J. van der Hoeven, "Ball arithmetic", Technical Report, HAL 00432152 (2009), http://www.texmacs.org/joris/ball/ball-abs.html
2012-10-11 13:09:44 +02:00
2013-05-29 18:07:00 +02:00
.. [Joh2012] \F. Johansson, "Efficient implementation of the Hardy-Ramanujan-Rademacher formula", LMS Journal of Computation and Mathematics, Volume 15 (2012), 341-359, http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=8710297
2014-10-28 14:04:12 +01:00
.. [Joh2013] \F. Johansson, "Rigorous high-precision computation of the Hurwitz zeta function and its derivatives", Numerical Algorithms, http://arxiv.org/abs/1309.2877 http://dx.doi.org/10.1007/s11075-014-9893-1
.. [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/
.. [Joh2014b] \F. Johansson, "Evaluating parametric holonomic sequences using rectangular splitting", ISSAC 2014, 256-263. http://dx.doi.org/10.1145/2608628.2608629
.. [Joh2014c] \F. Johansson, "Efficient implementation of elementary functions in the medium-precision range", http://arxiv.org/abs/1410.7176
2013-09-19 18:15:28 +01:00
2014-08-26 16:23:38 +02:00
.. [Kar1998] \E. A. Karatsuba, "Fast evaluation of the Hurwitz zeta function and Dirichlet L-series", Problems of Information Transmission 34:4 (1998), 342-353, http://www.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=ppi&paperid=425&option_lang=eng
2012-10-11 13:09:44 +02:00
2013-05-12 19:36:58 +01:00
.. [Kob2010] \A. Kobel, "Certified Complex Numerical Root Finding", Seminar on Computational Geometry and Geometric Computing (2010), http://www.mpi-inf.mpg.de/departments/d1/teaching/ss10/Seminar_CGGC/Slides/02_Kobel_NRS.pdf
2013-04-27 17:26:38 +02:00
2012-10-11 13:09:44 +02:00
.. [MPFR2012] The MPFR team, "MPFR Algorithms" (2012), http://www.mpfr.org/algo.html
2013-03-04 12:30:54 +01:00
.. [NIST2012] National Institute of Standards and Technology, *Digital Library of Mathematical Functions* (2012), http://dlmf.nist.gov/
2012-10-11 13:09:44 +02:00
2013-07-19 14:38:38 +02:00
.. [Olv1997] \F. Olver, *Asymptotics and special functions* , AKP Classics, AK Peters Ltd., Wellesley, MA, 1997. Reprint of the 1974 original.
2014-10-14 16:23:46 +02:00
.. [Rad1973] \H. Rademacher, *Topics in analytic number theory* , Springer, 1973.
2013-05-12 19:36:58 +01:00
.. [PS1973] \M. S. Paterson and L. J. Stockmeyer, "On the number of nonscalar multiplications necessary to evaluate polynomials", SIAM J. Comput (1973)
2012-10-11 13:09:44 +02:00
2013-05-12 19:36:58 +01:00
.. [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
2013-03-09 12:32:56 +01:00
2014-08-26 16:23:38 +02:00
.. [Tak2000] \D. Takahashi, "A fast algorithm for computing large Fibonacci numbers", Information Processing Letters 75 (2000) 243-246, http://www.ii.uni.wroc.pl/~lorys/IPL/article75-6-1.pdf
2012-10-11 13:09:44 +02:00