mirror of
https://github.com/vale981/arb
synced 2025-03-06 09:51:39 -05:00
124 lines
6.8 KiB
ReStructuredText
124 lines
6.8 KiB
ReStructuredText
.. _credits:
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Credits and references
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===============================================================================
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Arb is licensed GNU General Public License version 2, or any later version.
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Fredrik's work on Arb is supported by Austrian Science Fund FWF Grant Y464-N18
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(Fast Computer Algebra for Special Functions).
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Arb includes code by Bill Hart and
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Sebastian Pancratz taken from FLINT (also licensed GPL 2.0+).
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Contributors
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-------------------------------------------------------------------------------
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The following people (among others) have contributed patches or bug reports.
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* Jonathan Bober
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* Yuri Matiyasevich
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* Abhinav Baid
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* Ondřej Čertík
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* Andrew Booker
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* Francesco Biscani
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Software
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-------------------------------------------------------------------------------
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The following software has been helpful in the development of Arb.
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* GMP (Torbjörn Granlund and others), http://gmplib.org
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* MPIR (Brian Gladman, Jason Moxham, William Hart and others), http://mpir.org
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* MPFR (Guillaume Hanrot, Vincent Lefèvre, Patrick Pélissier, Philippe Théveny, Paul Zimmermann and others), http://mpfr.org
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* FLINT (William Hart, Sebastian Pancratz, Andy Novocin, Fredrik Johansson, David Harvey and others), http://flintlib.org
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* 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
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* mpmath (Fredrik Johansson and others), http://mpmath.org
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* Mathematica (Wolfram Research), http://www.wolfram.com/mathematica
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* HolonomicFunctions (Christoph Koutschan), http://www.risc.jku.at/research/combinat/software/HolonomicFunctions/
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* 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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-------------------------------------------------------------------------------
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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):
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\F. Johansson. "Arb: a C library for ball arithmetic", *ACM Communications in Computer Algebra*, 47(4):166-169, 2013.
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In BibTeX format::
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@article{Johansson2013arb,
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title={{A}rb: a {C} library for ball arithmetic},
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author={F. Johansson},
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journal={ACM Communications in Computer Algebra},
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volume={47},
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number={4},
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pages={166--169},
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year={2013},
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publisher={ACM}
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}
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Bibliography
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-------------------------------------------------------------------------------
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.. [Arn2010] \J. Arndt, *Matters Computational*, Springer (2010), http://www.jjj.de/fxt/#fxtbook
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.. [BBC1997] \D. H. Bailey, J. M. Borwein and R. E. Crandall, "On the Khintchine constant", Mathematics of Computation 66 (1997) 417-431
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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
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.. [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
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.. [Bor1987]_ \P. Borwein, "Reduced complexity evaluation of hypergeometric functions", Journal of Approximation Theory 50:3 (1987)
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.. [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
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.. [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.
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.. [Bre1978] \R. P. Brent, "A Fortran multiple-precision arithmetic package", ACM Transactions on Mathematical Software, 4(1):57–70, March 1978.
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.. [Bre2010] \R. P. Brent, "Ramanujan and Euler's Constant", http://wwwmaths.anu.edu.au/~brent/pd/Euler_CARMA_10.pdf
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.. [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
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.. [BZ2011] \R. P. Brent and P. Zimmermann, *Modern Computer Arithmetic*, Cambridge University Press (2011), http://www.loria.fr/~zimmerma/mca/pub226.html
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.. [CP2005] \R. Crandall and C. Pomerance, *Prime Numbers: A Computational Perspective*, second edition, Springer (2005).
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.. [Fil1992] \S. Fillebrown, "Faster Computation of Bernoulli Numbers", Journal of Algorithms 13 (1992) 431-445
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.. [GG2003] \J. von zur Gathen and J. Gerhard, *Modern Computer Algebra*, second edition, Cambridge University Press (2003)
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.. [GS2003] \X. Gourdon and P. Sebah, "Numerical evaluation of the Riemann Zeta-function" (2003), http://numbers.computation.free.fr/Constants/Miscellaneous/zetaevaluations.pdf
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.. [HZ2004] \G. Hanrot and P. Zimmermann, "Newton Iteration Revisited" (2004), http://www.loria.fr/~zimmerma/papers/fastnewton.ps.gz
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.. [Hoe2009] \J. van der Hoeven, "Ball arithmetic", Technical Report, HAL 00432152 (2009), http://www.texmacs.org/joris/ball/ball-abs.html
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.. [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
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.. [Joh2013] \F. Johansson, "Rigorous high-precision computation of the Hurwitz zeta function and its derivatives", preprint (2013), http://arxiv.org/abs/1309.2877
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.. [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
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.. [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
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.. [MPFR2012] The MPFR team, "MPFR Algorithms" (2012), http://www.mpfr.org/algo.html
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.. [NIST2012] National Institute of Standards and Technology, *Digital Library of Mathematical Functions* (2012), http://dlmf.nist.gov/
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.. [Olv1997] \F. Olver, *Asymptotics and special functions*, AKP Classics, AK Peters Ltd., Wellesley, MA, 1997. Reprint of the 1974 original.
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.. [Rad1973] \H. Rademacher, *Topics in analytic number theory*, Springer, 1973.
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.. [PS1973] \M. S. Paterson and L. J. Stockmeyer, "On the number of nonscalar multiplications necessary to evaluate polynomials", SIAM J. Comput (1973)
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.. [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
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.. [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
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