References
------------

.. [AbbottBronsteinMulders1999] Fast deterministic computation of determinants of dense matrices ACM International Symposium on Symbolic and Algebraic Computation 1999

.. [Apostol1997] Apostol, Tom : Modular functions and Dirichlet series in number theory, Springer (1997)

.. [ArnoldMonagan2011] Arnold, Andrew and Monagan, Michael : Calculating cyclotomic polynomials, Mathematics of Computation 80:276 (2011) 2359--2379

.. [BaiWag1980] Robert Baillie; Samuel S. Wagstaff, Jr. (October 1980). "Lucas Pseudoprimes". Mathematics of Computation. 35 (152): 1391–1417. 

.. [BerTas2010] D. Berend and T. Tassa : Improved bounds on Bell numbers and on moments of sums of random variables, Probability and Mathematical Statistics vol. 30 (2010) 185--205
.. [Bodrato2010] Bodrato, Marco A Strassen-like Matrix Multiplication Suited for Squaring and Higher Power Computation. Proceedings of the ISSAC 2010 München, Germany, 25-28 July, 2010

.. [BrentKung1978] Brent, R. P. and Kung, H. T. : Fast Algorithms for Manipulating Formal Power Series, J. ACM 25:4 (1978) 581--595

.. [BuhlerCrandallSompolski1992] Buhler, J.P. and Crandall, R.E. and Sompolski, R.W. : Irregular primes to one million : Math. Comp. 59:2000 (1992) 717--722

.. [Chen2003] Zhuo Chen and John Greene : Some Comments on {Baillie--PSW} Pseudoprimes, The Fibonacci Quaterly 41:4 (2003) 334--344

.. [Coh1996] Cohen, Henri : A course in computational algebraic number theory, Springer, 1996 

.. [Col1971] Collins, George E. : The Calculation of Multivariate Polynomial Resultants, SYMSAC '71, ACM 1971 212--222

.. [CraPom2005] Richard Crandall and Carl Pomerance: Prime numbers: a computational perspective. 2005.

.. [DelegliseNicolasZimmermann2009] Deleglise, Marc and Niclas, Jean-Louis and Zimmermann, Paul : Landau's function for one million billions, J. Th\'eor. Nombres Bordeaux 20:3 (2009) 625--671

.. [DomKanTro1987] Domich, P. D. and Kannan, R. and Trotter, L. E. Jr. : Hermite Normal Form Computation Using Modulo Determinant Arithmetic, Math. Operations Res. (12) 1987 50-59

.. [Dus1999] P. Dusart, "The kth prime is greater than k(ln k+ln ln k-1) for k> 2," Math. Comp., 68:225 (January 1999) 411--415.

.. [FieHof2014] Fieker C. and Hofmann T.: "Computing in quotients of rings of integers" LMS Journal of Computation and Mathematics, 17(A), 349-365

.. [GraMol2010] Torbjorn Granlund and Niels Moller : Improved Division by Invariant Integers https://gmplib.org/~tege/division-paper.pdf

.. [GowWag2008] Jason Gower and Sam Wagstaff : "Square form factoring" Math. Comp. 77, 2008, pp 551-588, http://www.ams.org/mcom/2008-77-261/S0025-5718-07-02010-8/home.html

.. [HanZim2004] Guillaume Hanrot and Paul Zimmermann : Newton Iteration Revisited (2004) http://www.loria.fr/~zimmerma/papers/fastnewton.ps.gz

.. [Har2012] Hart, William B.. (2012) A one line factoring algorithm. Journal of the Australian Mathematical Society, Volume 92 (Number 1). pp. 61-69.

.. [Iliopoulos1989] Iliopoulos, C. S., Worst-Case Complexity Bounds on Algorithms for Computing the Canonical Structure of Finite Abelian Groups and the Hermite and Smith Normal Forms of an Integer Matrix : SIAM J. Computation 18:4 (1989) 658

.. [KanBac1979] Kannan, R. and Bachem, A. : Polynomial algorithms for computing and the Smith and Hermite normal forms of an integer matrix, SIAM J. Computation vol. 9 (1979) 499--507

.. [Kahan1991] Kahan, William: Computing a Real Cube Root. https://csclub.uwaterloo.ca/~pbarfuss/qbrt.pdf

.. [LukPatWil1996] R. F. Lukes and C. D. Patterson and H. C. Williams "Some results on pseudosquares" Math. Comp. 1996, no. 65, 361--372

.. [MasRob1996] J. Massias and G. Robin, "Bornes effectives pour certaines fonctions concernant les nombres premiers," J. Theorie Nombres Bordeaux, 8 (1996) 215-242.

.. [NakTurWil1997] Nakos, George and Turner, Peter and Williams, Robert : Fraction-free algorithms for linear and polynomial equations, ACM SIGSAM Bull. 31 (1997) 3 11--19

.. [Mul2000] Thom Mulders : On Short Multiplications and Divisions, AAECC vol. 11 (2000) 69--88

.. [Paterson1973] Michael S. Paterson and Larry J. Stockmeyer : On the number of nonscalar multiplications necessary to evaluate polynomials, SIAM Journal on Computing (1973)

.. [PernetStein2010] Pernet, C. and Stein, W. : Fast computation of Hermite normal forms of random integer matrices ,J. Number Theory 130:17 (2010) 1675--1683

.. [Rademacher1937] Rademacher, Hans : On the partition function `p(n)` Proc. London Math. Soc vol. 43 (1937) 241--254

.. [RosSch1962] Rosser, J. Barkley; Schoenfeld, Lowell: Approximate formulas for some functions of prime numbers. Illinois J. Math. 6 (1962), no. 1, 64--94. 

.. [SorWeb2016] Sorenson, Jonathan and Webster, Jonathan : Strong pseudoprimes to twelve prime bases. Math. Comp. 86 (2017), 985-1003, https://doi.org/10.1090/mcom/3134 

.. [Stehle2010] Stehl\'e, Damien : Floating-Point LLL: Theoretical and Practical Aspects, in Nguyen, Phong Q. and Vall\'ee, Brigitte : The LLL Algorithm: Survey and Applications (2010) 179--213

.. [Stein2007] Stein, William A.: Modular forms, a computational approach. American Mathematical Society. 2007

.. [StoMul1998] Storjohann, Arne and Mulders, Thom : Fast algorithms for linear algebra modulo :math:`N` : Algorithms---{ESA} '98 (Venice), Lecture Notes in Comput. Sci. 1461 139--150

.. [ThullYap1990] Thull, K. and Yap, C. : A Unified Approach to {HGCD} Algorithms for Polynomials and Integers, (1990)

.. [Villard2007] Villard, Gilles :  Certification of the QR Factor R and of Lattice Basis Reducedness, In proceedings of ACM International Symposium on Symbolic and Algebraic Computation (2007) 361--368 ACM Press. 

.. [WaktinsZeitlin1993] Watkins, W. and Zeitlin, J. : The minimal polynomial of $\cos(2\pi/n)$ The American Mathematical Monthly 100:5 (1993) 471--474

.. [Whiteman1956] Whiteman, A. L. : A sum connected with the series for the partition function, Pacific Journal of Mathematics 6:1 (1956) 159--176

