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https://github.com/vale981/arb
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73 lines
4.7 KiB
ReStructuredText
73 lines
4.7 KiB
ReStructuredText
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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Software
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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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* 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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Bibliography
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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.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.Brent, "A Fortran multiple-precision arithmetic package", ACM Transactions on Mathematical Software, 4(1):57–70, March 1978.
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.. [Bre2010] R.Brent, "Ramanujan and Euler's Constant", http://wwwmaths.anu.edu.au/~brent/pd/Euler_CARMA_10.pdf
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.. [BZ2011] R.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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.. [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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.. [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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.. [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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