References

[AbbottBronsteinMulders1999] Fast deterministic computation of determinants of dense matrices, ACM International Symposium on Symbolic and Algebraic Computation (1999)
[Abe1973] O. Aberth. Iteration methods for finding all zeros of a polynomial simultaneously. Mathematics of Computation 27 (1973), 339–344. https://doi.org/10.1090/S0025-5718-1973-0329236-7
[ABH2010] M. Albrecht, G. Bard and W. Hart, "Algorithm 898: Efficient multiplication of dense matrices over GF(2)", ACM Transactions on Mathematical Software 37:1 (2010), article 9, https://doi.org/10.1145/1644001.1644010
[ADKF1970] V. L. Arlazarov, E. A. Dinic, M. A. Kronrod and I. A. Faradžev, "On economical construction of the transitive closure of an oriented graph", Soviet Mathematics Doklady 11 (1970), 1209-1210
[ADL2006] N. B. Atti, G. M. Diaz-Toca and H. Lombardi. The Berlekamp–Massey algorithm revisited. Applicable Algebra in Engineering, Communication and Computing 17 (2006), 75–82. https://doi.org/10.1007/s00200-005-0190-z
[AJ2025] A. Ahlbäck and F. Johansson. Fast basecases for arbitrary-size multiplication. 2025 IEEE 32nd Symposium on Computer Arithmetic (ARITH 2025), 53–60. https://doi.org/10.1109/ARITH64983.2025.00018 (preprint: https://hal.science/hal-04861755)
[AlfPom1995] W. R. Alford and C. Pomerance. Implementing the self-initializing quadratic sieve on a distributed network. In: Number Theoretic and Algebraic Methods in Computer Science (Moscow, 1993), World Scientific, 1995, 163–174.
[All2002] B. Allombert. Explicit computation of isomorphisms between finite fields. Finite Fields and Their Applications 8:3 (2002), 332–342.
[Andrews1976] G. E. Andrews, The Theory of Partitions, Encyclopedia of Mathematics and its Applications 2, Addison-Wesley, 1976.
[Apery1979] R. Apéry. Irrationalité de ζ(2) et ζ(3). Astérisque 61 (1979), 11–13.
[Apo1976] T. M. Apostol, Introduction to Analytic Number Theory, Undergraduate Texts in Mathematics, Springer, 1976. https://doi.org/10.1007/978-1-4757-5579-4
[Apostol1997] Apostol, Tom : Modular functions and Dirichlet series in number theory, Springer (1997)
[APR1983] L. M. Adleman, C. Pomerance and R. S. Rumely. On distinguishing prime numbers from composite numbers. Annals of Mathematics 117 (1983), 173–206.
[Ari2011] J. Arias de Reyna, "High precision computation of Riemann’s zeta function by the Riemann-Siegel formula, I", Mathematics of Computation 80 (2011), 995-1009
[Ari2012] J. Arias de Reyna, "Programs for Riemann's zeta function", (J. A. J. van Vonderen, Ed.) Leven met getallen : liber amicorum ter gelegenheid van de pensionering van Herman te Riele CWI (2012) 102-112, https://ir.cwi.nl/pub/19724
[Ari2020] J. Arias de Reyna, "Computation of the secondary zeta function", https://arxiv.org/abs/2006.04869
[Arn2010] J. Arndt, Matters Computational, Springer (2010), https://www.jjj.de/fxt/#fxtbook
[Arn2012] J. Arndt, "On computing the generalized Lambert series", https://arxiv.org/abs/1202.6525
[Arn2013] A. Arnold. A new truncated Fourier transform algorithm. ISSAC 2013, 15–22.
[ArnoldMonagan2011] Arnold, Andrew and Monagan, Michael : Calculating cyclotomic polynomials, Mathematics of Computation 80:276 (2011) 2359–2379
[ASU1975] A. V. Aho, K. Steiglitz and J. D. Ullman. Evaluating polynomials at fixed sets of points. SIAM Journal on Computing 4 (1975), 533–539.
[ASV2008] A. G. Akritas, A. W. Strzeboński and P. S. Vigklas. Improving the performance of the continued fractions method using new bounds of positive roots. Nonlinear Analysis: Modelling and Control 13 (2008), 265–279.
[Atk1992] A. O. L. Atkin, "Probabilistic primality testing", summary by F. Morain, in Algorithms Seminar 1991–1992, INRIA Research Report 1779 (1992), 159–163
[AtkMor1993] A. O. L. Atkin and F. Morain. Elliptic curves and primality proving. Mathematics of Computation 61 (1993), 29–68.
[Ax1971] J. Ax. On Schanuel's conjectures. Annals of Mathematics 93:2 (1971), 252–268. https://doi.org/10.2307/1970774
[BA2008] H.-J. Boehm and S. V. Adve, "Foundations of the C++ concurrency memory model", Proceedings of the 29th ACM SIGPLAN Conference on Programming Language Design and Implementation (PLDI 2008), 68–78
[Bach1990] E. Bach, "Explicit bounds for primality testing and related problems", Mathematics of Computation 55 (1990), 355–380. https://doi.org/10.1090/S0025-5718-1990-1023756-8
[BacSch1998] O. Bachmann and H. Schönemann. Monomial representations for Gröbner bases computations. Proceedings of ISSAC 1998, ACM, 309–316. https://doi.org/10.1145/281508.281657
[Bai1990] D. H. Bailey. FFTs in external or hierarchical memory. The Journal of Supercomputing 4 (1990), 23–35.
[BaiWag1980] Robert Baillie; Samuel S. Wagstaff, Jr. (October 1980). "Lucas Pseudoprimes". Mathematics of Computation. 35 (152): 1391–1417.
[Bar1968] E. H. Bareiss, "Sylvester's identity and multistep integer-preserving Gaussian elimination", Mathematics of Computation 22 (1968), 565–578. https://doi.org/10.1090/S0025-5718-1968-0226829-0
[Bar1987] P. Barrett, "Implementing the Rivest Shamir and Adleman public key encryption algorithm on a standard digital signal processor", Advances in Cryptology – CRYPTO '86, LNCS 263 (1987), 311–323
[BB2009] T. J. Boothby and R. W. Bradshaw, "Bitslicing and the method of four Russians over larger finite fields", arXiv:0901.1413 (2009), https://arxiv.org/abs/0901.1413
[BBC1997] D. H. Bailey, J. M. Borwein and R. E. Crandall, "On the Khintchine constant", Mathematics of Computation 66 (1997) 417-431
[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
[BBK2014] D. H. Bailey, J. M. Borwein and A. D. Kaiser. "Automated simplification of large symbolic expressions". Journal of Symbolic Computation Volume 60, January 2014, Pages 120-136. https://doi.org/10.1016/j.jsc.2013.09.001
[BCOSSS2007] A. Bostan, F. Chyzak, F. Ollivier, B. Salvy, É. Schost, A. Sedoglavic. "Fast computation of power series solutions of systems of differential equations". Proceedings of the Eighteenth Annual ACM-SIAM Symposium on Discrete Algorithms (2007) 1012-1021
[BCS1997] P. Bürgisser, M. Clausen and M. A. Shokrollahi, Algebraic Complexity Theory, Grundlehren der mathematischen Wissenschaften 315, Springer (1997)
[BCS1997b] W. Bosma, J. Cannon and A. Steel. Lattices of compatibly embedded finite fields. Journal of Symbolic Computation 24:3–4 (1997), 351–369.
[BD1992] D. Buchmann and S. Düllmann. "Distributed class group computation." Informatik: Festschrift zum 60. Geburtstag von Günter Hotz (1992): 69-79.
[BDS1993] E. Bach, J. Driscoll and J. Shallit. Factor refinement. Journal of Algorithms 15 (1993), 199–222.
[BenOr1981] M. Ben-Or. Probabilistic algorithms in finite fields. 22nd Annual Symposium on Foundations of Computer Science (FOCS 1981), IEEE, 394–398.
[BenOrTiw1988] M. Ben-Or and P. Tiwari. A deterministic algorithm for sparse multivariate polynomial interpolation. Proceedings of STOC 1988, ACM, 301–309. https://doi.org/10.1145/62212.62241
[Ber1967] E. R. Berlekamp. Factoring polynomials over finite fields. Bell System Technical Journal 46 (1967), 1853–1859.
[Ber1968] E. R. Berlekamp. Algebraic Coding Theory. McGraw-Hill, 1968.
[Ber1970] E. R. Berlekamp. Factoring polynomials over large finite fields. Mathematics of Computation 24 (1970), 713–735.
[Ber1984] S. J. Berkowitz, "On computing the determinant in small parallel time using a small number of processors", Information Processing Letters 18 (1984), 147-150
[Ber2001] D. J. Bernstein. Multidigit multiplication for mathematicians. Preprint, 2001, https://cr.yp.to/papers/m3.pdf
[Ber2004] D. J. Bernstein. Scaled remainder trees. Preprint, 2004. https://cr.yp.to/arith/scaledmod-20040820.pdf
[Ber2008] D. J. Bernstein, "Fast multiplication and its applications", in Algorithmic Number Theory, MSRI Publications 44 (2008), 325–384
[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
[BF2020] F. Beukers and J. Forsgård. "Gamma-evaluations of hypergeometric series". Preprint, 2020. https://arxiv.org/abs/2004.08117
[BFSS2006] A. Bostan, P. Flajolet, B. Salvy and É. Schost. "Fast computation of special resultants". Journal of Symbolic Computation, 41(1):1–29, January 2006. https://doi.org/10.1016/j.jsc.2005.07.001
[BGS2007] A. Bostan, P. Gaudry and É. Schost, "Linear recurrences with polynomial coefficients and application to integer factorization and Cartier–Manin operator", SIAM Journal on Computing 36 (2007), 1777–1806
[BGY1980] R. P. Brent, F. G. Gustavson and D. Y. Y. Yun, "Fast solution of Toeplitz systems of equations and computation of Padé approximants", Journal of Algorithms 1:3 (1980), 259–295
[BH1974] J. R. Bunch and J. E. Hopcroft, "Triangular factorization and inversion by fast matrix multiplication", Mathematics of Computation 28 (1974), 231-236, https://doi.org/10.1090/S0025-5718-1974-0331751-8
[BHKS2009] K. Belabas, M. van Hoeij, J. Klüners and A. Steel. Factoring polynomials over global fields. Journal de Théorie des Nombres de Bordeaux 21 (2009), 15–39. https://doi.org/10.5802/jtnb.655
[Bin1996] D. A. Bini, "Numerical computation of polynomial zeros by means of Aberth's method". Numerical algorithms 13 (1996): 179-200. https://doi.org/10.1007/BF02207694
[BJ2013] R. P. Brent and F. Johansson, "A bound for the error term in the Brent-McMillan algorithm", preprint (2013), https://arxiv.org/abs/1312.0039
[BKM1994] J.-C. Bajard, S. Kla and J.-M. Muller. BKM: a new hardware algorithm for complex elementary functions. IEEE Transactions on Computers 43:8 (1994), 955–963. https://doi.org/10.1109/12.295857
[BL1994] B. Beckermann and G. Labahn, "A uniform approach for the fast computation of matrix-type Padé approximants", SIAM Journal on Matrix Analysis and Applications 15:3 (1994), 804–823. https://doi.org/10.1137/S0895479892230031
[Bla1976] J. M. Blair, C. A. Edwards and J. H. Johnson. Rational Chebyshev approximations for the inverse of the error function. Mathematics of Computation 30 (1976), 827–830. https://doi.org/10.1090/S0025-5718-1976-0421040-7
[Blo2009] R. Bloemen, "Even faster zeta(2n) calculation!", https://web.archive.org/web/20141101133659/http://xn--2-umb.com/09/11/even-faster-zeta-calculation
[BLS1975] J. Brillhart, D. H. Lehmer and J. L. Selfridge, "New primality criteria and factorizations of 2^m ± 1", Mathematics of Computation 29 (1975), 620–647
[BLS2003] A. Bostan, G. Lecerf and É. Schost, "Tellegen's principle into practice", ISSAC 2003, 37–44
[Blu1970] L. I. Bluestein. A linear filtering approach to the computation of discrete Fourier transform. IEEE Transactions on Audio and Electroacoustics 18:4 (1970), 451–455. https://doi.org/10.1109/TAU.1970.1162132
[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.
[Bod2007] M. Bodrato. Towards optimal Toom-Cook multiplication for univariate and multivariate polynomials in characteristic 2 and 0. Arithmetic of Finite Fields (WAIFI 2007), Lecture Notes in Computer Science 4547, Springer, 2007, 116–133. https://doi.org/10.1007/978-3-540-73074-3_10
[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
[Boe2020] H. Boehm. "Towards an API for the real numbers". PLDI 2020: Proceedings of the 41st ACM SIGPLAN Conference on Programming Language Design and Implementation, June 2020, Pages 562-576. https://doi.org/10.1145/3385412.3386037
[Bog2012] I. Bogaert, B. Michiels and J. Fostier, "O(1) computation of Legendre polynomials and Gauss-Legendre nodes and weights for parallel computing", SIAM Journal on Scientific Computing 34:3 (2012), C83-C101
[Bol1887] O. Bolza, "Darstellung der rationalen ganzen Invarianten der Binärform sechsten Grades durch die Nullwerthe der zugehörigen Theta-Functionen", Math. Ann. 30:4 (1887), 478–495. https://doi.org/10.1007/BF01444091
[Boo2006] A. R. Booker. Artin's conjecture, Turing's method, and the Riemann hypothesis. Experimental Mathematics 15:4 (2006), 385–407. https://doi.org/10.1080/10586458.2006.10128976
[Bor1987] P. Borwein, "Reduced complexity evaluation of hypergeometric functions", Journal of Approximation Theory 50:3 (1987)
[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
[BorMoe1974] A. Borodin and R. Moenck, "Fast modular transforms", Journal of Computer and System Sciences 8:3 (1974), 366–386
[BPR2006] S. Basu, R. Pollack and M.-F. Roy. Algorithms in Real Algebraic Geometry, second edition. Springer, 2006. https://doi.org/10.1007/3-540-33099-2
[Bre1976] R. P. Brent. The complexity of multiple-precision arithmetic. In R. S. Anderssen and R. P. Brent (eds.), The Complexity of Computational Problem Solving, University of Queensland Press, 1976, 126–165.
[Bre1976agm] R. P. Brent. Fast multiple-precision evaluation of elementary functions. Journal of the ACM 23:2 (1976), 242–251. https://doi.org/10.1145/321941.321944
[Bre1976b] R. P. Brent. The complexity of multiple-precision evaluation of elementary functions. In J. F. Traub (ed.), Analytic Computational Complexity, Academic Press, 1976, 151–176.
[Bre1978] R. P. Brent, "A Fortran multiple-precision arithmetic package", ACM Transactions on Mathematical Software, 4(1):57–70, March 1978.
[Bre1979] R. P. Brent, "On the Zeros of the Riemann Zeta Function in the Critical Strip", Mathematics of Computation 33 (1979), 1361-1372, https://doi.org/10.1090/S0025-5718-1979-0537983-2
[Bre1980] R. P. Brent, "An improved Monte Carlo factorization algorithm", BIT 20 (1980), 176–184
[Bre2010] R. P. Brent, "Ramanujan and Euler's Constant", http://wwwmaths.anu.edu.au/~brent/pd/Euler_CARMA_10.pdf
[Bre2016] R. P. Brent. Asymptotic approximation of central binomial coefficients with rigorous error bounds. Preprint, 2016. https://arxiv.org/abs/1608.04834
[BrentHarvey2013] R. P. Brent and D. Harvey, "Fast computation of Bernoulli, tangent and secant numbers", in Computational and Analytical Mathematics, Springer Proceedings in Mathematics & Statistics 50 (2013), 127–142. https://doi.org/10.1007/978-1-4614-7621-4_8
[BrentKung1978] Brent, R. P. and Kung, H. T. : Fast Algorithms for Manipulating Formal Power Series, J. ACM 25:4 (1978) 581–595
[Bro1971] W. S. Brown. On Euclid's algorithm and the computation of polynomial greatest common divisors. Journal of the ACM 18:4 (1971), 478–504. https://doi.org/10.1145/321662.321664
[BroPet1996] M. Bronstein and M. Petkovšek. An introduction to pseudo-linear algebra. Theoretical Computer Science 157 (1996), 3–33. https://doi.org/10.1016/0304-3975(95)00173-5
[BS2005] A. Bostan and É. Schost. Polynomial evaluation and interpolation on special sets of points. Journal of Complexity 21 (2005), 420–446.
[BT1971] W. S. Brown and J. F. Traub. On Euclid's algorithm and the theory of subresultants. Journal of the ACM 18 (1971), 505–514. https://doi.org/10.1145/321662.321665
[Buc1965] B. Buchberger. Ein Algorithmus zum Auffinden der Basiselemente des Restklassenringes nach einem nulldimensionalen Polynomideal. PhD thesis, University of Innsbruck, 1965.
[Buell1989] D. A. Buell, Binary Quadratic Forms: Classical Theory and Modern Computations, Springer, 1989. https://doi.org/10.1007/978-1-4612-4542-1
[BuhlerCrandallSompolski1992] Buhler, J.P. and Crandall, R.E. and Sompolski, R.W. : Irregular primes to one million : Math. Comp. 59:2000 (1992) 717–722
[BurZie1998] C. Burnikel and J. Ziegler. Fast recursive division. Max-Planck-Institut für Informatik, Research Report MPI-I-98-1-022, 1998.
[But1997] D. R. Butenhof, Programming with POSIX Threads, Addison-Wesley (1997)
[BW1993] T. Becker and V. Weispfenning, Gröbner Bases: A Computational Approach to Commutative Algebra, Graduate Texts in Mathematics 141, Springer-Verlag (1993). https://doi.org/10.1007/978-1-4612-0913-3
[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
[BZ2007] M. Bodrato and A. Zanoni. Integer and polynomial multiplication: towards optimal Toom-Cook matrices. ISSAC 2007, 17–24. https://doi.org/10.1145/1277548.1277552
[BZ2011] R. P. Brent and P. Zimmermann, Modern Computer Arithmetic, Cambridge University Press (2011), http://www.loria.fr/~zimmerma/mca/pub226.html
[CA1976] G. E. Collins and A. G. Akritas. Polynomial real root isolation using Descartes' rule of signs. SYMSAC 1976, 272–275. https://doi.org/10.1145/800205.806346
[Cab1971] S. Cabay, "Exact solution of linear equations", Proceedings of the Second ACM Symposium on Symbolic and Algebraic Manipulation (1971) 392-398
[CalkinWilf2000] N. Calkin and H. S. Wilf, "Recounting the rationals", American Mathematical Monthly 107:4 (2000), 360–363. https://doi.org/10.2307/2589182
[CanZas1981] D. G. Cantor and H. Zassenhaus. A new algorithm for factoring polynomials over finite fields. Mathematics of Computation 36 (1981), 587–592. https://doi.org/10.1090/S0025-5718-1981-0606517-5
[Car1995] B. C. Carlson, "Numerical computation of real or complex elliptic integrals". Numerical Algorithms, 10(1):13-26 (1995).
[Car2004] J. Carette. "Understanding expression simplification." ISSAC '04: Proceedings of the 2004 international symposium on Symbolic and algebraic computation, pp. 72-79. 2004. https://doi.org/10.1145/1005285.1005298
[Car2017] X. Caruso. Computations with p-adic numbers. Les cours du CIRM 5 (2017), Journées Nationales de Calcul Formel. https://arxiv.org/abs/1701.06794
[CC1988] D. V. Chudnovsky and G. V. Chudnovsky. Approximations and complex multiplication according to Ramanujan. In Ramanujan Revisited, Academic Press, 1988, 375–472.
[CC1990] D. V. Chudnovsky and G. V. Chudnovsky. Computer algebra in the service of mathematical physics and number theory. In Computers in Mathematics (Stanford, 1986), Lecture Notes in Pure and Applied Mathematics 125, Dekker, 1990, 109–232.
[CF1994] R. Crandall and B. Fagin. Discrete weighted transforms and large-integer arithmetic. Mathematics of Computation 62 (1994), 305–324.
[CFG2017] F. Cléry, C. Faber, and G. van der Geer. "Covariants of binary sextics and vector-valued Siegel modular forms of genus two", Math. Ann. 369 (2017), 1649–1669. https://doi.org/10.1007/s00208-016-1510-2
[CFG2019] F. Cléry, C. Faber, and G. van der Geer. "Covariants of binary sextics and modular forms of degree 2 with character", Math. Comp. 88 (2019), 2423–2441. https://doi.org/10.1090/mcom/3412
[CGG1989] B. W. Char, K. O. Geddes and G. H. Gonnet. GCDHEU: heuristic polynomial GCD algorithm based on integer GCD computation. Journal of Symbolic Computation 7 (1989), 31–48. https://doi.org/10.1016/S0747-7171(89)80004-6
[CGHJK1996] R. M. Corless, G. H. Gonnet, D. E. Hare, D. J. Jeffrey and D. E. Knuth, "On the Lambert W function", Advances in Computational Mathematics, 5(1) (1996), 329-359
[CGVW1998] J. Cherly, L. Gallardo, L. Vaserstein and E. Wheland. Solving quadratic equations over polynomial rings of characteristic two. Publicacions Matemàtiques 42:1 (1998), 131–142.
[Chen2003] Zhuo Chen and John Greene : Some Comments on Baillie–PSW Pseudoprimes, The Fibonacci Quarterly 41:4 (2003) 334–344
[CheSto2005] Z. Chen and A. Storjohann, "A BLAS based C library for exact linear algebra on integer matrices", Proceedings of the 2005 International Symposium on Symbolic and Algebraic Computation (ISSAC) (2005) 92-99
[Chi1964] R. T. Chien. Cyclic decoding procedures for Bose–Chaudhuri–Hocquenghem codes. IEEE Transactions on Information Theory 10 (1964), 357–363.
[Cho1999] T. Chow. "What is a closed-form number?". The American Mathematical Monthly Volume 106, 1999 - Issue 5. https://doi.org/10.1080/00029890.1999.12005066
[CHTZZ2007] H. Cheng, G. Hanrot, E. Thomé, E. Zima and P. Zimmermann. Time- and space-efficient evaluation of some hypergeometric constants. ISSAC 2007, 85–91. https://doi.org/10.1145/1277548.1277561
[CL1984] H. Cohen and H. W. Lenstra, Jr. Primality testing and Jacobi sums. Mathematics of Computation 42 (1984), 297–330.
[CL1987] H. Cohen and A. K. Lenstra. Implementation of a new primality test. Mathematics of Computation 48 (1987), 103–121.
[ClaHug2000] K. Claessen and J. Hughes. QuickCheck: a lightweight tool for random testing of Haskell programs. ICFP 2000, 268–279. https://doi.org/10.1145/351240.351266
[CLO2015] D. Cox, J. Little and D. O'Shea. Ideals, Varieties, and Algorithms, fourth edition. Undergraduate Texts in Mathematics, Springer, 2015. https://doi.org/10.1007/978-3-319-16721-3
[Coh1996] Cohen, Henri : A course in computational algebraic number theory, Springer, 1996
[Coh2000] H. Cohen. Advanced topics in computational number theory. Springer, 2000. https://doi.org/10.1007/978-1-4419-8489-0
[Coh2007b] H. Cohen, Number Theory, Volume II: Analytic and Modern Tools, Graduate Texts in Mathematics 240, Springer, 2007. https://doi.org/10.1007/978-0-387-49894-2
[Col1967] G. E. Collins. Subresultants and reduced polynomial remainder sequences. Journal of the ACM 14 (1967), 128–142. https://doi.org/10.1145/321371.321381
[Col1971] Collins, George E. : The Calculation of Multivariate Polynomial Resultants, SYMSAC '71, ACM 1971 212–222
[CollinsEncarnacion1995] G. E. Collins and M. J. Encarnación, "Efficient rational number reconstruction", Journal of Symbolic Computation 20:3 (1995), 287–297. https://doi.org/10.1006/jsco.1995.1051
[Comtet1974] L. Comtet, Advanced Combinatorics: The Art of Finite and Infinite Expansions, D. Reidel, 1974.
[Con1997] S. P. Contini. Factoring integers with the self-initializing quadratic sieve. Master's thesis, University of Georgia, 1997.
[Coo1966] S. A. Cook. On the minimum computation time of functions. PhD thesis, Harvard University, 1966.
[Cow2009] M. F. Cowlishaw. General Decimal Arithmetic Specification, version 1.70. IBM, 2009. https://speleotrove.com/decimal/decarith.html
[Cox2013] D. A. Cox, Primes of the Form x^2 + ny^2: Fermat, Class Field Theory, and Complex Multiplication, second edition, Wiley, 2013.
[CP1978] R. Caviness and M. J. Prelle. A note on algebraic independence of logarithmic and exponential constants. ACM SIGSAM Bulletin 12:2 (1978), 18–20. https://doi.org/10.1145/1088276.1088280
[CraPom2005] R. Crandall and C. Pomerance, Prime Numbers: A Computational Perspective, second edition, Springer (2005).
[CT1965] J. W. Cooley and J. W. Tukey. An algorithm for the machine calculation of complex Fourier series. Mathematics of Computation 19 (1965), 297–301.
[Dan1937] A. M. Danilevsky, "On the numerical solution of the secular equation" (in Russian), Matematicheskii Sbornik 2(44):1 (1937), 169-171
[DDDD1985] J. Della Dora, C. Dicrescenzo and D. Duval. About a new method for computing in algebraic number fields. EUROCAL '85, Lecture Notes in Computer Science 204, Springer, 1985, 289–290. https://doi.org/10.1007/3-540-15984-3_279
[deB1958] N. G. de Bruijn, Asymptotic Methods in Analysis, North-Holland, 1958 (§6.2: Bell numbers).
[Dek1971] T. J. Dekker. A floating-point technique for extending the available precision. Numerische Mathematik 18 (1971), 224–242. https://doi.org/10.1007/BF01397083
[DelegliseNicolasZimmermann2009] Deleglise, Marc and Niclas, Jean-Louis and Zimmermann, Paul : Landau's function for one million billions, J. Théor. Nombres Bordeaux 20:3 (2009) 625–671
[DFRR2019] L. De Feo, H. Randriam and É. Rousseau. Standard lattices of compatibly embedded finite fields. Proceedings of ISSAC 2019, ACM, 122–130.
[DGP2002] J.-G. Dumas, T. Gautier and C. Pernet, "Finite field linear algebra subroutines", Proceedings of the 2002 International Symposium on Symbolic and Algebraic Computation (ISSAC) (2002), 63-74, https://doi.org/10.1145/780506.780515
[DGP2008] J.-G. Dumas, P. Giorgi and C. Pernet, "Dense linear algebra over word-size prime fields: the FFLAS and FFPACK packages", ACM Transactions on Mathematical Software 35:3 (2008), 1-42, https://doi.org/10.1145/1391989.1391992
[DH1984] P. Duhamel and H. Hollmann. Split radix FFT algorithm. Electronics Letters 20:1 (1984), 14–16. https://doi.org/10.1049/el:19840012
[DHBHS2004] B. Deconinck, M. Heil, A. Bobenko, M. van Hoeij, and M. Schmies, "Computing Riemann theta functions", Math. Comp. 73:247 (2004), 1417–1442. https://arxiv.org/abs/nlin/0206009
[Dix1982] J. D. Dixon, "Exact solution of linear equations using p-adic expansions", Numerische Mathematik 40 (1982) 137-141
[dKMW2005] J. de Kleine, M. Monagan and A. Wittkopf. Algorithms for the non-monic case of the sparse modular GCD algorithm. Proceedings of ISSAC 2005, ACM, 124–131. https://doi.org/10.1145/1073884.1073903
[Dob1877] G. Dobiński, "Summirung der Reihe \sum n^m/n! für m = 1, 2, 3, 4, 5, \ldots", Archiv der Mathematik und Physik 61 (1877), 333–336.
[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
[DPS2017] J.-G. Dumas, C. Pernet and Z. Sultan, "Fast computation of the rank profile matrix and the generalized Bruhat decomposition", Journal of Symbolic Computation 83 (2017), 187-210
[DPW2005] J.-G. Dumas, C. Pernet and Z. Wan, "Efficient computation of the characteristic polynomial", Proceedings of the 2005 International Symposium on Symbolic and Algebraic Computation (ISSAC) (2005), 140-147
[DPZ2009] J.-G. Dumas, C. Pernet and W. Zhou, "Memory efficient scheduling of Strassen-Winograd's matrix multiplication algorithm", Proceedings of the 2009 International Symposium on Symbolic and Algebraic Computation (ISSAC) (2009), 135-143, https://doi.org/10.1145/1576702.1576713
[Duc2000] L. Ducos. Optimizations of the subresultant algorithm. Journal of Pure and Applied Algebra 145 (2000), 149–163. https://doi.org/10.1016/S0022-4049(98)00081-4
[Dum2007] J.-G. Dumas, "Bounds on the coefficients of the characteristic and minimal polynomials", Journal of Inequalities in Pure and Applied Mathematics 8:2 (2007), article 31.
[Dup2006] R. Dupont. "Moyenne arithmético-géométrique, suites de Borchardt et applications." These de doctorat, École polytechnique, Palaiseau (2006). http://www.lix.polytechnique.fr/Labo/Regis.Dupont/these_soutenance.pdf
[Dur1960] E. Durand. Solutions numériques des équations algébriques, tome I. Masson, Paris, 1960.
[Dur1964] R. Durstenfeld. Algorithm 235: Random permutation. Communications of the ACM 7(7), 420, 1964.
[Dus1999] P. Dusart, "The k^{th} prime is greater than k(\ln k+\ln \ln k-1) for k \ge 2," Math. Comp., 68:225 (January 1999) 411–415.
[DV1990] P. Duhamel and M. Vetterli. Fast Fourier transforms: a tutorial review and a state of the art. Signal Processing 19:4 (1990), 259–299. https://doi.org/10.1016/0165-1684(90)90158-U
[DYF1999] A. Dzieciol, S. Yngve and P. O. Fröman, "Coulomb wave functions with complex values of the variable and the parameters", J. Math. Phys. 40, 6145 (1999), https://doi.org/10.1063/1.533083
[EGV2000] W. Eberly, M. Giesbrecht and G. Villard, "On computing the determinant and Smith form of an integer matrix", Proceedings of the 41st Annual Symposium on Foundations of Computer Science (FOCS 2000), 675–685. https://doi.org/10.1109/SFCS.2000.892335
[EHJ2016] A. Enge, W. Hart and F. Johansson, "Short addition sequences for theta functions", preprint (2016), https://arxiv.org/abs/1608.06810
[EK2025] N. D. Elkies and J. Kieffer, "A uniform quasi-linear time algorithm for evaluating theta functions in any dimension", in preparation.
[EM2004] O. Espinosa and V. Moll, "A generalized polygamma function", Integral Transforms and Special Functions (2004), 101-115.
[Enge2009] A. Enge. The complexity of class polynomial computation via floating point approximations. Mathematics of Computation 78 (2009), 1089–1107. https://doi.org/10.1090/S0025-5718-08-02200-X
[Enge2024] A. Enge, "FastECPP over MPI", Mathematical Software - ICMS 2024: 8th International Conference, Durham, UK, July 22-25, 2024, Proceedings, Springer-Verlag, Berlin, Heidelberg, 36-45. https://doi.org/10.1007/978-3-031-64529-7_4
[EngeCM] A. Enge, CM - a library for the computation of class polynomials and elliptic curve primality proving, https://www.multiprecision.org/cm/
[EngeMorain2003] A. Enge and F. Morain, "Fast decomposition of polynomials with known Galois group", Applied Algebra, Algebraic Algorithms and Error-Correcting Codes (AAECC-15), LNCS 2643, Springer (2003), 254-264
[FadSom1972] D. K. Faddeev and I. S. Sominsky. Problems in Higher Algebra. Mir Publishers, Moscow, 1972 (translated from the Russian edition of 1954). The method of Le Verrier and Faddeev for the characteristic polynomial.
[FB1992] H. R. P. Ferguson and D. H. Bailey. A polynomial time, numerically stable integer relation algorithm. RNR Technical Report RNR-91-032, NASA Ames Research Center, 1992.
[FeiGal2013] J. Feitsma and W. Galway, "Tables of pseudoprimes and related data", http://www.cecm.sfu.ca/Pseudoprimes/index-2-to-64.html
[FHHJ2017] C. Fieker, W. Hart, T. Hofmann and F. Johansson. Nemo/Hecke: computer algebra and number theory packages for the Julia programming language. ISSAC 2017, 157–164. https://doi.org/10.1145/3087604.3087611
[Fid1972] C. M. Fiduccia, "Polynomial evaluation via the division algorithm: the fast Fourier transform revisited", Proceedings of the 4th Annual ACM Symposium on Theory of Computing (STOC 1972), 88–93
[Fie2007] C. Fieker, "Sparse representation for cyclotomic fields". Experiment. Math. Volume 16, Issue 4 (2007), 493-500. https://doi.org/10.1080/10586458.2007.10129012
[FieHof2014] Fieker C. and Hofmann T.: "Computing in quotients of rings of integers" LMS Journal of Computation and Mathematics, 17(A), 349-365
[Fil1992] S. Fillebrown, "Faster Computation of Bernoulli Numbers", Journal of Algorithms 13 (1992) 431-445
[FJ2005] M. Frigo and S. G. Johnson. The design and implementation of FFTW3. Proceedings of the IEEE 93:2 (2005), 216–231. https://doi.org/10.1109/JPROC.2004.840301
[FKMW2004] J. Franke, T. Kleinjung, F. Morain and T. Wirth, "Proving the primality of very large numbers with fastECPP", Algorithmic Number Theory (ANTS-VI), LNCS 3076, Springer (2004), 194-207
[FLPR1999] M. Frigo, C. E. Leiserson, H. Prokop and S. Ramachandran. Cache-oblivious algorithms. 40th Annual Symposium on Foundations of Computer Science (FOCS 1999), 285–297. https://doi.org/10.1109/SFFCS.1999.814600
[For1965] G. D. Forney. On decoding BCH codes. IEEE Transactions on Information Theory 11 (1965), 549–557.
[ForJan2015] M. Forisek and J. Jancina, "Fast Primality Testing for Integers That Fit into a Machine Word", SOFSEM 2015, https://ceur-ws.org/Vol-1326/020-Forisek.pdf
[Fru1977] M. A. Frumkin, "Polynomial time algorithms in the theory of linear diophantine equations", Fundamentals of Computation Theory (FCT 1977), Lecture Notes in Computer Science 56 (1977), 386–392. https://doi.org/10.1007/3-540-08442-8_106
[Fuj1916] M. Fujiwara. Über die obere Schranke des absoluten Betrages der Wurzeln einer algebraischen Gleichung. Tôhoku Mathematical Journal 10 (1916), 167–171.
[Fungrim] F. Johansson. Fungrim: the Mathematical Functions Grimoire. https://fungrim.org
[Fur2009] M. Fürer. Faster integer multiplication. SIAM Journal on Computing 39 (2009), 979–1005.
[Gao2001] S. Gao. Absolute irreducibility of polynomials via Newton polytopes. Journal of Algebra 237 (2001), 501–520. https://doi.org/10.1006/jabr.2000.8586
[Gao2003] S. Gao. A new algorithm for decoding Reed–Solomon codes. In Communications, Information and Network Security, Kluwer, 2003, 55–68.
[GaoLau2001] S. Gao and A. G. B. Lauder. Decomposition of polytopes and polynomials. Discrete and Computational Geometry 26 (2001), 89–104. https://doi.org/10.1007/s00454-001-0024-0
[GaoPan1997] S. Gao and D. Panario. Tests and constructions of irreducible polynomials over finite fields. In Foundations of Computational Mathematics (F. Cucker, M. Shub, eds.), Springer, 1997, 346–361.
[Gar1959] H. L. Garner. The residue number system. IRE Transactions on Electronic Computers EC-8:2 (1959), 140–147. https://doi.org/10.1109/TEC.1959.5219515
[Gas2018] D. Gaspard, "Connection formulas between Coulomb wave functions" (2018), https://arxiv.org/abs/1804.10976
[GatSho1992] J. von zur Gathen and V. Shoup, "Computing Frobenius maps and factoring polynomials", Computational Complexity 2 (1992), 187-224. https://doi.org/10.1007/BF01272074
[GCL1992] K. O. Geddes, S. R. Czapor and G. Labahn. Algorithms for computer algebra. Springer, 1992. https://doi.org/10.1007/b102438
[GG1997] J. von zur Gathen and J. Gerhard. Fast algorithms for Taylor shifts and certain difference equations. ISSAC 1997, 40–47.
[GG2003] J. von zur Gathen and J. Gerhard, Modern Computer Algebra, second edition, Cambridge University Press (2003)
[Gie1995] M. Giesbrecht, "Fast computation of the Smith normal form of an integer matrix", Proceedings of the 1995 International Symposium on Symbolic and Algebraic Computation (ISSAC 1995), 110–118. https://doi.org/10.1145/220346.220361
[GieLobSau1998] M. Giesbrecht, A. Lobo and B. D. Saunders, "Certifying inconsistency of sparse linear systems", Proceedings of the 1998 International Symposium on Symbolic and Algebraic Computation (ISSAC) (1998) 113-119
[GJV2003] P. Giorgi, C.-P. Jeannerod and G. Villard, "On the complexity of polynomial matrix computations", Proceedings of the 2003 International Symposium on Symbolic and Algebraic Computation (ISSAC 2003), 135–142. https://doi.org/10.1145/860854.860889
[GKP1994] R. L. Graham, D. E. Knuth and O. Patashnik, Concrete Mathematics, second edition, Addison-Wesley, 1994.
[GKZ2007] P. Gaudry, A. Kruppa and P. Zimmermann. A GMP-based implementation of Schönhage-Strassen's large integer multiplication algorithm. ISSAC 2007, 167–174.
[Gly2010] D. G. Glynn, "The permanent of a square matrix", European Journal of Combinatorics, Volume 31, Issue 7, October 2010, Pages 1887-1891, https://doi.org/10.1016/j.ejc.2010.01.010
[GM1988] R. Gebauer and H. M. Möller. On an installation of Buchberger's algorithm. Journal of Symbolic Computation 6:2–3 (1988), 275–286.
[GMP] T. Granlund and the GMP development team. GNU MP: The GNU Multiple Precision Arithmetic Library, version 6.3.0. Manual, 2023. https://gmplib.org/manual/
[GolKil1986] S. Goldwasser and J. Kilian. Almost all primes can be quickly certified. Proceedings of the 18th Annual ACM Symposium on Theory of Computing (STOC 1986), 316–329.
[Goo1958] I. J. Good. The interaction algorithm and practical Fourier analysis. Journal of the Royal Statistical Society, Series B 20:2 (1958), 361–372.
[Gos1974] R. W. Gosper, "Acceleration of series", MIT AI Memo no.304, (March-1974). https://dspace.mit.edu/handle/1721.1/6088
[Got1959] E. Gottschling, "Explizite Bestimmung der Randflächen es Fundamentalbereiches der Modulgruppe zweiten Grades'', Math. Annalen 138 (1959), 103–124. https://doi.org/10.1007/BF01342938
[Gou1997] F. Q. Gouvêa. p-adic Numbers: An Introduction. Universitext, Springer, second edition, 1997. https://doi.org/10.1007/978-3-642-59058-0
[GowWag2008] Jason Gower and Sam Wagstaff : "Square form factoring" Math. Comp. 77, 2008, pp 551-588, https://doi.org/10.1090/S0025-5718-07-02010-8
[GraMol2010] N. Möller and T. Granlund, "Improved division by invariant integers", IEEE Transactions on Computers 60 (2011), 165–175, https://gmplib.org/~tege/division-paper.pdf
[GraMon1994] Törbjorn Granlund and Peter L. Montgomery : Division by Invariant Integers using Multiplication https://gmplib.org/~tege/divcnst-pldi94.pdf
[Grosswald1985] E. Grosswald, Representations of Integers as Sums of Squares, Springer, 1985. https://doi.org/10.1007/978-1-4613-8566-0
[GS1966] W. M. Gentleman and G. Sande. Fast Fourier transforms – for fun and profit. AFIPS Fall Joint Computer Conference 29 (1966), 563–578.
[GS2003] X. Gourdon and P. Sebah, "Numerical evaluation of the Riemann Zeta-function" (2003), http://numbers.computation.free.fr/Constants/Miscellaneous/zetaevaluations.pdf
[GT1996] P. Gianni and B. Trager. Square-free algorithms in positive characteristic. Applicable Algebra in Engineering, Communication and Computing 7 (1996), 1–14.
[GvdG2008] K. Goto and R. A. van de Geijn, "Anatomy of high-performance matrix multiplication", ACM Transactions on Mathematical Software 34:3 (2008), article 12, https://doi.org/10.1145/1356052.1356053
[GVL1996] G. H. Golub and C. F. Van Loan, Matrix Computations, third edition, Johns Hopkins University Press (1996).
[Had1893] J. Hadamard. Résolution d'une question relative aux déterminants. Bulletin des Sciences Mathématiques 17 (1893), 240–246.
[HanZim2004] Guillaume Hanrot and Paul Zimmermann : Newton Iteration Revisited (2004) https://www.loria.fr/~zimmerma/papers/fastnewton.ps.gz
[Har2009] D. Harvey. A cache-friendly truncated FFT. Theoretical Computer Science 410 (2009), 2649–2658.
[Har2009a] D. Harvey, "Faster polynomial multiplication via multipoint Kronecker substitution", Journal of Symbolic Computation 44:10 (2009), 1502–1510
[Har2009b] D. Harvey, "Faster exponentials of power series", preprint (2009), https://arxiv.org/abs/0911.3110
[Har2010] D. Harvey, "A multimodular algorithm for computing Bernoulli numbers" (2010), Mathematics of Computation 79.272: 2361-2370
[Har2011] D. Harvey, "Faster algorithms for the square root and reciprocal of power series", Mathematics of Computation 80 (2011), 387–394
[Har2012] Hart, William B.. (2012) A one line factoring algorithm. Journal of the Australian Mathematical Society, Volume 92 (Number 1). pp. 61-69.
[Har2014] D. Harvey, "Faster arithmetic for number-theoretic transforms", Journal of Symbolic Computation 60 (2014), 113–119, https://doi.org/10.1016/j.jsc.2013.09.002
[Har2015] W. B. Hart. "ANTIC: Algebraic number theory in C". Computeralgebra-Rundbrief: Vol. 56, 2015
[Har2018] W. B. Hart. "Algebraic number theory". Unpublished manuscript, 2018.
[HardyRamanujan1918] G. H. Hardy and S. Ramanujan, "Asymptotic formulae in combinatory analysis", Proceedings of the London Mathematical Society (2) 17 (1918), 75–115.
[Hare1997] D. E. G. Hare. Computing the principal branch of log-Gamma. Journal of Algorithms 25:2 (1997), 221–236. https://doi.org/10.1006/jagm.1997.0881
[Hart2010] W. B. Hart. "Fast library for number theory: an introduction." International Congress on Mathematical Software. Springer, Berlin, Heidelberg, 2010. https://doi.org/10.1007/978-3-642-15582-6_18
[HarveyBern2014] D. Harvey, "A subquadratic algorithm for computing the n-th Bernoulli number", Mathematics of Computation 83 (2014), 2471–2477. https://doi.org/10.1090/S0025-5718-2014-02832-X
[HarWri2008] G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, sixth edition, revised by D. R. Heath-Brown and J. H. Silverman, Oxford University Press, 2008.
[HB1986] M. T. Heideman and C. S. Burrus. On the number of multiplications necessary to compute a length-2^n DFT. IEEE Transactions on Acoustics, Speech, and Signal Processing 34:1 (1986), 91–95. https://doi.org/10.1109/TASSP.1986.1164785
[Hea1963] B. R. Heap. Permutations by interchanges. The Computer Journal 6(3), 293–298, 1963.
[HeaLoe2004] L. S. Heath and N. A. Loehr. New algorithms for generating Conway polynomials over finite fields. Journal of Symbolic Computation 38:2 (2004), 1003–1024.
[Hen1908] K. Hensel. Theorie der algebraischen Zahlen. Teubner, Leipzig, 1908.
[Hen1956] Peter Henrici : "A Subroutine for Computations with Rational Numbers" J. ACM (1956), https://doi.org/10.1145/320815.320818
[Hickerson1977] D. Hickerson, "Continued fractions and density results for Dedekind sums", Journal für die reine und angewandte Mathematik 290 (1977), 113–116.
[Hig2002] N. J. Higham. Accuracy and Stability of Numerical Algorithms, second edition, chapter 24 (The fast Fourier transform and applications). SIAM, 2002. https://doi.org/10.1137/1.9780898718027
[HJ2024] J. van der Hoeven and F. Johansson, "Fast multiple precision exp(x) with precomputations", 2024 IEEE 31st Symposium on Computer Arithmetic (ARITH) (2024), https://hal.science/hal-04454093
[HLB2001] Y. Hida, X. S. Li and D. H. Bailey. Algorithms for quad-double precision floating point arithmetic. Proceedings of the 15th IEEE Symposium on Computer Arithmetic (ARITH-15), 2001, 155–162.
[HLJJTG1996] S. Huss-Lederman, E. M. Jacobson, J. R. Johnson, A. Tsao and T. Turnbull, "Implementation of Strassen's algorithm for matrix multiplication", Proceedings of the 1996 ACM/IEEE Conference on Supercomputing (1996)
[HLQ2016] J. van der Hoeven, G. Lecerf and G. Quintin, "Modular SIMD arithmetic in Mathemagix", ACM Transactions on Mathematical Software 43:1 (2016), article 5, https://doi.org/10.1145/2876503
[HM1991] J. L. Hafner and K. S. McCurley, "Asymptotically fast triangularization of matrices over rings", SIAM Journal on Computing 20:6 (1991), 1068–1083. https://doi.org/10.1137/0220067
[HM2017] J. van der Hoeven and B. Mourrain. "Efficient certification of numeric solutions to eigenproblems", MACIS 2017, 81-94, (2017), https://hal.archives-ouvertes.fr/hal-01579079
[Hoe2001] J. van der Hoeven. "Fast evaluation of holonomic functions near and in regular singularities", Journal of Symbolic Computation, 31(6):717-743 (2001).
[Hoe2009] J. van der Hoeven, "Ball arithmetic", Technical Report, HAL 00432152 (2009), http://www.texmacs.org/joris/ball/ball-abs.html
[Hor1972] Ellis Horowitz : "Algorithms for Rational Function Arithmetic Operations" Annual ACM Symposium on Theory of Computing: Proceedings of the Fourth Annual ACM Symposium on Theory of Computing (Denver) (1972), https://doi.org/10.1145/800152.804903
[How1986] J. A. Howell, "Spans in the module (\mathbb{Z}_m)^s", Linear and Multilinear Algebra 19 (1986), 67-77
[HP1998] B. Haible and T. Papanikolaou, "Fast multiprecision evaluation of series of rational numbers", Algorithmic Number Theory (ANTS-III), LNCS 1423 (1998), 338–350
[HQZ2004] G. Hanrot, M. Quercia and P. Zimmermann, "The middle product algorithm I. Speeding up the division and square root of power series", Applicable Algebra in Engineering, Communication and Computing 14:6 (2004), 415–438
[HR2010] D. Harvey and D. S. Roche. An in-place truncated Fourier transform and applications to polynomial multiplication. ISSAC 2010, 325–329.
[HS1967] E. Hansen and R. Smith, "Interval Arithmetic in Matrix Computations, Part II", SIAM Journal of Numerical Analysis, 4(1):1-9 (1967). https://doi.org/10.1137/0704001
[Hub1990] K. Huber. Some comments on Zech's logarithms. IEEE Transactions on Information Theory 36:4 (1990), 946–950.
[HuMon2016] J. Hu and M. Monagan. A fast parallel sparse polynomial GCD algorithm. Proceedings of ISSAC 2016, ACM, 271–278; full version in Journal of Symbolic Computation 105 (2021), 28–63. https://doi.org/10.1016/j.jsc.2020.06.001
[Hur2022] J. Hurchalla, "An improved integer modular multiplicative inverse (modulo 2^w)", preprint (2022), https://arxiv.org/abs/2204.04342
[HvdH2021] D. Harvey and J. van der Hoeven. Integer multiplication in time O(n \log n). Annals of Mathematics 193 (2021), 563–617.
[HvHN2011] W. Hart, M. van Hoeij and A. Novocin. Practical polynomial factoring in polynomial time. ISSAC 2011, 163–170. https://doi.org/10.1145/1993886.1993915
[HZ2004] G. Hanrot and P. Zimmermann, "Newton Iteration Revisited" (2004), http://www.loria.fr/~zimmerma/papers/fastnewton.ps.gz
[HZ2011] D. Harvey and P. Zimmermann, "Short division of long integers" (2011), Proceedings of the 20th Symposium on Computer Arithmetic (ARITH-20), July 25-27, 2011, pages 7-14. https://web.maths.unsw.edu.au/~davidharvey/research/shortdiv.pdf
[IEEE1788] IEEE Standard for Interval Arithmetic. IEEE Std 1788-2015, 2015. https://doi.org/10.1109/IEEESTD.2015.7140721
[IEEE754] IEEE Standard for Floating-Point Arithmetic. IEEE Std 754-2008, 2008. https://doi.org/10.1109/IEEESTD.2008.4610935
[Igu1972] J.-I. Igusa. Theta functions, Springer, 1972. https://doi.org/10.1007/978-3-642-65315-5
[Igu1979] J.-I. Igusa, "On the ring of modular forms of degree two over Z", Amer. J. Math. 101:1 (1979), 149–183. https://doi.org/10.2307/2373943
[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
[IMH1982] O. H. Ibarra, S. Moran and R. Hui, "A generalization of the fast LUP matrix decomposition algorithm and applications", Journal of Algorithms 3 (1982), 45-56
[IR1990] K. Ireland and M. Rosen, A Classical Introduction to Modern Number Theory, second edition, Graduate Texts in Mathematics 84, Springer, 1990. https://doi.org/10.1007/978-1-4757-2103-4
[JB2018] F. Johansson and I. Blagouchine. "Computing Stieltjes constants using complex integration", preprint (2018), https://arxiv.org/abs/1804.01679
[Jeb1993] T. Jebelean. An algorithm for exact division. Journal of Symbolic Computation 15 (1993), 169–180. https://doi.org/10.1006/jsco.1993.1012
[Jeb1993b] T. Jebelean. Improving the multiprecision Euclidean algorithm. DISCO '93, LNCS 722 (1993), 45–58.
[Jef2010] D. J. Jeffrey, "LU factoring of non-invertible matrices", ACM Communications in Computer Algebra 44:1 (2010), 1–8. https://doi.org/10.1145/1838599.1838602
[JF2007] S. G. Johnson and M. Frigo. A modified split-radix FFT with fewer arithmetic operations. IEEE Transactions on Signal Processing 55:1 (2007), 111–119. https://doi.org/10.1109/TSP.2006.882087
[JM2018] F. Johansson and M. Mezzarobba, "Fast and rigorous arbitrary-precision computation of Gauss-Legendre quadrature nodes and weights", preprint (2018), https://arxiv.org/abs/1802.03948
[JMP2017] M. Joldes, J.-M. Muller and V. Popescu. Tight and rigorous error bounds for basic building blocks of double-word arithmetic. ACM Transactions on Mathematical Software 44:2 (2017), 15:1–15:27. https://doi.org/10.1145/3121432
[JMPT2016] M. Joldes, O. Marty, J.-M. Muller and V. Popescu. Arithmetic algorithms for extended precision using floating-point expansions. IEEE Transactions on Computers 65:4 (2016), 1197–1210. https://doi.org/10.1109/TC.2015.2441714
[Joh1974] S. C. Johnson. Sparse polynomial arithmetic. ACM SIGSAM Bulletin 8:3 (1974), 63–71. https://doi.org/10.1145/1086837.1086847
[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
[Joh2013] F. Johansson, "Rigorous high-precision computation of the Hurwitz zeta function and its derivatives", Numerical Algorithms, http://arxiv.org/abs/1309.2877 https://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. https://fredrikj.net/thesis/
[Joh2014b] F. Johansson, "Evaluating parametric holonomic sequences using rectangular splitting", ISSAC 2014, 256-263. https://doi.org/10.1145/2608628.2608629
[Joh2014c] F. Johansson, "Efficient implementation of elementary functions in the medium-precision range", 22nd IEEE Symposium on Computer Arithmetic (ARITH 22), 83-89 (2015), https://arxiv.org/abs/1410.7176
[Joh2015] F. Johansson, "Computing Bell numbers", https://fredrikj.net/blog/2015/08/computing-bell-numbers/
[Joh2015b] F. Johansson, "A fast algorithm for reversion of power series", Math. Comp. 84 (2015), 475-484, http://doi.org/10.1090/S0025-5718-2014-02857-3
[Joh2016] F. Johansson, "Computing hypergeometric functions rigorously", preprint (2016), https://arxiv.org/abs/1606.06977
[Joh2017] F. Johansson. "Arb: efficient arbitrary-precision midpoint-radius interval arithmetic". IEEE Transactions on Computers, vol 66, issue 8, 2017, pp. 1281-1292. https://doi.org/10.1109/TC.2017.2690633
[Joh2017a] F. Johansson. "Arb: efficient arbitrary-precision midpoint-radius interval arithmetic", IEEE Transactions on Computers, 66(8):1281-1292 (2017). https://doi.org/10.1109/TC.2017.2690633
[Joh2017b] F. Johansson, "Computing the Lambert W function in arbitrary-precision complex interval arithmetic", preprint (2017), https://arxiv.org/abs/1705.03266
[Joh2018a] F. Johansson, "Numerical integration in arbitrary-precision ball arithmetic", preprint (2018), https://arxiv.org/abs/1802.07942
[Joh2018b] F. Johansson and others, "mpmath: a Python library for arbitrary-precision floating-point arithmetic (version 1.1.0)", December 2018. https://mpmath.org/
[Joh2019] F. Johansson. Numerical evaluation of elliptic functions, elliptic integrals and modular forms. In J. Blümlein, C. Schneider and P. Paule (eds.), Elliptic Integrals, Elliptic Functions and Modular Forms in Quantum Field Theory, Texts & Monographs in Symbolic Computation, Springer, 2019, 269–293. https://arxiv.org/abs/1806.06725
[Joh2019dot] F. Johansson. Faster arbitrary-precision dot product and matrix multiplication. Proceedings of the 26th IEEE Symposium on Computer Arithmetic (ARITH-26), 2019, 15–22. https://arxiv.org/abs/1901.04289
[Joh2021calcium] F. Johansson. Calcium: computing in exact real and complex fields. ISSAC 2021, 225–232. https://doi.org/10.1145/3452143.3465513
[Joh2023g] F. Johansson. Arbitrary-precision computation of the gamma function. Maple Transactions 3:1 (2023), article 14591. https://doi.org/10.5206/mt.v3i1.14591 (preprint: https://arxiv.org/abs/2109.08392)
[Joh2025gr] F. Johansson. Generic rings in FLINT. Preprint, 2025. https://fredrikj.net/math/flintgenerics.pdf
[JPS2013] C.-P. Jeannerod, C. Pernet and A. Storjohann, "Rank-profile revealing Gaussian elimination and the CUP matrix decomposition", Journal of Symbolic Computation 56 (2013), 46-68, https://doi.org/10.1016/j.jsc.2013.04.004
[JR1999] D. Jeffrey and A. D. Rich. "Simplifying square roots of square roots by denesting". Computer Algebra Systems: A Practical Guide, M.J. Wester, Ed., Wiley 1999.
[JvdP2002] M. J. Jacobson Jr. and A. J. van der Poorten. "Computational aspects of NUCOMP." In International Algorithmic Number Theory Symposium, pp. 120-133. Berlin, Heidelberg: Springer Berlin Heidelberg, 2002.
[Kahan1991] Kahan, William: Computing a Real Cube Root. https://csclub.uwaterloo.ca/~pbarfuss/qbrt.pdf
[Kal1985] E. Kaltofen. Sparse Hensel lifting. EUROCAL '85, Lecture Notes in Computer Science 204, Springer, 1985, 4–17. https://doi.org/10.1007/3-540-15984-3_230
[Kal2002] E. Kaltofen, "An output-sensitive variant of the baby steps/giant steps determinant algorithm", Proceedings of the 2002 International Symposium on Symbolic and Algebraic Computation (ISSAC 2002), 138–144. https://doi.org/10.1145/780506.780524
[KalLak1988] E. Kaltofen and Y. N. Lakshman. Improved sparse multivariate polynomial interpolation algorithms. Symbolic and Algebraic Computation (ISSAC '88), Lecture Notes in Computer Science 358, Springer, 1989, 467–474. https://doi.org/10.1007/3-540-51084-2_44
[KalSho1998] E. Kaltofen and V. Shoup, "Subquadratic-time factoring of polynomials over finite fields", Mathematics of Computation 67 (1998), 1179-1197. https://doi.org/10.1090/S0025-5718-98-00944-2
[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
[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
[Ked2001] K. S. Kedlaya. Counting points on hyperelliptic curves using Monsky–Washnitzer cohomology. Journal of the Ramanujan Mathematical Society 16 (2001), 323–338.
[Kei1992] J. B. Keiper. Power series expansions of Riemann's ξ function. Mathematics of Computation 58:198 (1992), 765–773. https://doi.org/10.1090/S0025-5718-1992-1122072-5
[Ker1966] I. O. Kerner. Ein Gesamtschrittverfahren zur Berechnung der Nullstellen von Polynomen. Numerische Mathematik 8 (1966), 290–294. https://doi.org/10.1007/BF02162564
[KG1985] W. Keller-Gehrig, "Fast algorithms for the characteristic polynomial", Theoretical Computer Science 36 (1985), 309-317, https://doi.org/10.1016/0304-3975(85)90049-0
[KL2024] Y. Kinoshita and B. Li, "Power series composition in near-linear time", 2024, https://arxiv.org/abs/2404.05177
[KM1997] A. H. Karp and P. Markstein, "High-precision division and square root", ACM Transactions on Mathematical Software 23:4 (1997), 561–589
[KM1999] E. Kaltofen and M. Monagan. On the genericity of the modular polynomial GCD algorithm. Proceedings of ISSAC 1999, ACM, 59–66.
[Knu1970] D. E. Knuth, "The analysis of algorithms", Actes du Congrès International des Mathématiciens (Nice, 1970), tome 3, Gauthier-Villars (1971), 269–274
[Knu1997] Knuth, D. E. The Art of Computer Programming, volume 2: Seminumerical algorithms, 1997
[KO1962] A. Karatsuba and Yu. Ofman, "Multiplication of multidigit numbers on automata", Doklady Akademii Nauk SSSR 145 (1962), 293–294; English translation in Soviet Physics Doklady 7 (1963), 595–596
[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
[Kra1969] R. Krawczyk. Newton-Algorithmen zur Bestimmung von Nullstellen mit Fehlerschranken. Computing 4 (1969), 187–201. https://doi.org/10.1007/BF02234767
[Kri2013] A. Krishnamoorthy and D. Menon, "Matrix Inversion Using Cholesky Decomposition" Proc. of the International Conference on Signal Processing Algorithms, Architectures, Arrangements, and Applications (SPA-2013), pp. 70-72, 2013.
[Kro1882] L. Kronecker, "Grundzüge einer arithmetischen Theorie der algebraischen Grössen", Journal für die reine und angewandte Mathematik 92 (1882), 1–122
[KU2011] K. S. Kedlaya and C. Umans, "Fast polynomial factorization and modular composition", SIAM Journal on Computing 40:6 (2011), 1767–1802
[Kun1974] H. T. Kung, "On computing reciprocals of power series", Numerische Mathematik 22 (1974), 341–348
[KV2004] E. Kaltofen and G. Villard, "On the complexity of computing determinants", Computational Complexity 13 (2004), 91–130. https://doi.org/10.1007/s00037-004-0185-3
[Lan1966] S. Lang. Introduction to Transcendental Numbers. Addison-Wesley, 1966.
[Lec2006] G. Lecerf. Sharp precision in Hensel lifting for bivariate polynomial factorization. Mathematics of Computation 75 (2006), 921–933.
[Lec2008] G. Lecerf. Fast separable factorization and applications. Applicable Algebra in Engineering, Communication and Computing 19:2 (2008), 135–160.
[Leh1938] D. H. Lehmer, "Euclid's algorithm for large numbers", American Mathematical Monthly 45:4 (1938), 227–233.
[Leh1970] R. S. Lehman, "On the Distribution of Zeros of the Riemann Zeta-Function", Proc. of the London Mathematical Society 20(3) (1970), 303-320, https://doi.org/10.1112/plms/s3-20.2.303
[Leh1974] R. S. Lehman, "Factoring large integers", Mathematics of Computation 28 (1974), 637–646
[Len1984] H. W. Lenstra, Jr. Divisors in residue classes. Mathematics of Computation 42 (1984), 331–340.
[Len1987] H. W. Lenstra, Jr., "Factoring integers with elliptic curves", Annals of Mathematics 126 (1987), 649–673
[Len1991] H. W. Lenstra, Jr. Finding isomorphisms between finite fields. Mathematics of Computation 56 (1991), 329–347.
[LF1995] H.-C. Liao and R. J. Fateman. Evaluation of the heuristic polynomial GCD. ISSAC 1995, 240–247. https://doi.org/10.1145/220346.220376
[Li1997] X.-J. Li. The positivity of a sequence of numbers and the Riemann hypothesis. Journal of Number Theory 65:2 (1997), 325–333. https://doi.org/10.1006/jnth.1997.2137
[LKK2019] D. Lemire, O. Kaser and N. Kurz, "Faster remainder by direct computation: applications to compilers and software libraries", Software: Practice and Experience 49 (2019), 953–970, https://arxiv.org/abs/1902.01961
[LLL1982] A. K. Lenstra, H. W. Lenstra, Jr. and L. Lovász, "Factoring polynomials with rational coefficients", Mathematische Annalen 261 (1982), 515–534. https://doi.org/10.1007/BF01457454
[LMFDB] The LMFDB Collaboration, The L-functions and modular forms database, https://www.lmfdb.org (Dirichlet characters: https://www.lmfdb.org/Character/Dirichlet/).
[LN1997] R. Lidl and H. Niederreiter. Finite Fields. Second edition, Encyclopedia of Mathematics and its Applications 20, Cambridge University Press, 1997.
[Loo1983] R. Loos. Computing in algebraic extensions. In B. Buchberger, G. E. Collins and R. Loos (eds.), Computer Algebra: Symbolic and Algebraic Computation, second edition, Springer, 1983, 173–187. https://doi.org/10.1007/978-3-7091-7551-4_12
[LT2016] H. Labrande and E. Thomé, "Computing theta functions in quasi-linear time in genus 2 and above", ANTS XII, Kaiserslautern, LMS J. Comp. Math 19 (2016), 163–177. https://doi.org/10.1112/S1461157016000309
[LukPatWil1996] R. F. Lukes and C. D. Patterson and H. C. Williams "Some results on pseudosquares" Math. Comp. 1996, no. 65, 361–372
[Lus2008] P. Luschny. Fast factorial functions. Web page, 2008. http://www.luschny.de/math/factorial/FastFactorialFunctions.htm
[Lüb2002] F. Lübeck, "On the computation of elementary divisors of integer matrices", Journal of Symbolic Computation 33:1 (2002), 57–65. https://doi.org/10.1006/jsco.2001.0492
[Lüb2004] F. Lübeck, "Conway polynomials for finite fields", RTWH Aachen, https://www.math.rwth-aachen.de/~Frank.Luebeck/data/ConwayPol/index.html, (accessed 2024-01-12)
[Mah1964] K. Mahler. An inequality for the discriminant of a polynomial. Michigan Mathematical Journal 11:3 (1964), 257–262. https://doi.org/10.1307/mmj/1028999140
[ManWright1994] Y.-K. Man and F. J. Wright. "Fast polynomial dispersion computation and its application to indefinite summation". Proceedings of the International Symposium on Symbolic and Algebraic Computation (1994), 175-180. https://doi.org/10.1145/190347.190413
[Mar2014] D. Marquis. Deterministic factorization of polynomials over finite fields. Master's thesis, Carleton University, 2014.
[Mas1969] J. L. Massey. Shift-register synthesis and BCH decoding. IEEE Transactions on Information Theory 15 (1969), 122–127.
[MasRob1996] J. Massias and G. Robin, "Bornes effectives pour certaines fonctions concernant les nombres premiers," J. Theorie Nombres Bordeaux, 8 (1996) 215-242.
[MB1972] R. Moenck and A. Borodin, "Fast modular transforms via division", Proceedings of the 13th Annual Symposium on Switching and Automata Theory (1972), 90–96
[MBD2018] J.-M. Muller, N. Brunie, F. de Dinechin, C.-P. Jeannerod, M. Joldes, V. Lefèvre, G. Melquiond, N. Revol and S. Torres, Handbook of Floating-Point Arithmetic, second edition, Birkhäuser (2018), https://doi.org/10.1007/978-3-319-76526-6
[MC1979] R. T. Moenck and J. H. Carter, "Approximate algorithms to derive exact solutions to systems of linear equations", Symbolic and Algebraic Computation (EUROSAM 1979), Lecture Notes in Computer Science 72 (1979), 65–73. https://doi.org/10.1007/3-540-09519-5_60
[Mez2010] M. Mezzarobba. NumGfun: a package for numerical and analytic computation with D-finite functions. ISSAC 2010, 139–146. https://doi.org/10.1145/1837934.1837965
[Mic2007] N. Michel, "Precise Coulomb wave functions for a wide range of complex l, eta and z", Computer Physics Communications, Volume 176, Issue 3, (2007), 232-249, https://doi.org/10.1016/j.cpc.2006.10.004
[Mig1974] M. Mignotte. An inequality about factors of polynomials. Mathematics of Computation 28 (1974), 1153–1157. https://doi.org/10.1090/S0025-5718-1974-0354624-3
[Mil1976] G. L. Miller, "Riemann's hypothesis and tests for primality", Journal of Computer and System Sciences 13 (1976), 300–317
[Miy2010] S. Miyajima, "Fast enclosure for all eigenvalues in generalized eigenvalue problems", Journal of Computational and Applied Mathematics, 233 (2010), 2994-3004, https://doi.org/10.1016/j.cam.2009.11.048
[MN2019] P. Molin and C. Neurohr, "Computing period matrices and the Abel–Jacobi map of superelliptic curves", Math. Comp. 88:316 (2019), 847–888.
[Moe1973] R. T. Moenck, "Fast computation of GCDs", Proceedings of the 5th Annual ACM Symposium on Theory of Computing (STOC 1973), 142–151
[Mol1965] O. Møller. Quasi double-precision in floating point addition. BIT 5 (1965), 37–50.
[Mol2008] N. Möller. On Schönhage's algorithm and subquadratic integer GCD computation. Mathematics of Computation 77 (2008), 589–607. https://doi.org/10.1090/S0025-5718-07-02017-0
[Mon1980] L. Monier, "Evaluation and comparison of two efficient probabilistic primality testing algorithms", Theoretical Computer Science 12 (1980), 97–108
[Mon1985] P. L. Montgomery, "Modular multiplication without trial division", Mathematics of Computation 44 (1985), 519–521
[Mon1987] P. L. Montgomery, "Speeding the Pollard and elliptic curve methods of factorization", Mathematics of Computation 48 (1987), 243-264, https://doi.org/10.1090/S0025-5718-1987-0866113-7
[Mon1995] P. L. Montgomery. A block Lanczos algorithm for finding dependencies over GF(2). Advances in Cryptology – EUROCRYPT '95, Lecture Notes in Computer Science 921, Springer, 1995, 106–120.
[Mon2004] M. Monagan, "Maximal quotient rational reconstruction: an almost optimal algorithm for rational reconstruction", Proceedings of the 2004 International Symposium on Symbolic and Algebraic Computation (ISSAC 2004), 243–249. https://doi.org/10.1145/1005285.1005321
[MonPea2007] M. Monagan and R. Pearce. Polynomial division using dynamic arrays, heaps, and packed exponent vectors. Computer Algebra in Scientific Computing (CASC 2007), Lecture Notes in Computer Science 4770, Springer, 2007, 295–315. https://doi.org/10.1007/978-3-540-75187-8_23
[MonPea2009] M. Monagan and R. Pearce. Parallel sparse polynomial multiplication using heaps. Proceedings of ISSAC 2009, ACM, 263–270. https://doi.org/10.1145/1576702.1576739
[MonPea2010] M. Monagan and R. Pearce. Parallel sparse polynomial division using heaps. Proceedings of PASCO 2010, ACM, 105–111. https://doi.org/10.1145/1837210.1837227
[MonPea2011] M. Monagan and R. Pearce. Sparse polynomial division using a heap. Journal of Symbolic Computation 46:7 (2011), 807–822. https://doi.org/10.1016/j.jsc.2010.08.014
[MonPea2012] M. Monagan and R. Pearce. Sparse polynomial powering using heaps. Computer Algebra in Scientific Computing (CASC 2012), Lecture Notes in Computer Science 7442, Springer, 2012, 236–247. https://doi.org/10.1007/978-3-642-32973-9_20
[MonTun2020] M. Monagan and B. Tuncer. The complexity of sparse Hensel lifting and sparse polynomial factorization. Journal of Symbolic Computation 99 (2020), 189–230. https://doi.org/10.1016/j.jsc.2019.05.001
[Moo1966] R. E. Moore. Interval Analysis. Prentice-Hall, 1966.
[Mor1975] M. A. Morrison. A note on primality testing using Lucas sequences. Mathematics of Computation 29 (1975), 181–182.
[Morain2007] F. Morain, "Implementing the asymptotically fast version of the elliptic curve primality proving algorithm", Mathematics of Computation 76 (2007), 493-505
[Mos1971] J. Moses. "Algebraic simplification - a guide for the perplexed". Proceedings of the second ACM symposium on Symbolic and algebraic manipulation (1971), 282-304. https://doi.org/10.1145/362637.362648
[MosYun1973] J. Moses and D. Y. Y. Yun. The EZ GCD algorithm. Proceedings of the ACM Annual Conference 1973, 159–166. https://doi.org/10.1145/800192.805698
[MP2006] M. Monagan and R. Pearce. "Rational simplification modulo a polynomial ideal". Proceedings of the 2006 international symposium on Symbolic and algebraic computation - ISSAC '06. https://doi.org/10.1145/1145768.1145809
[MPFR2012] The MPFR team, "MPFR Algorithms" (2012), https://www.mpfr.org/algo.html
[Mue2004] S. Müller, "On the computation of square roots in finite fields", Designs, Codes and Cryptography 31 (2004), 301–312, https://doi.org/10.1023/B:DESI.0000015890.44831.e2
[Mul2000] Thom Mulders : On Short Multiplications and Divisions, AAECC vol. 11 (2000) 69–88
[Mul2016] J.-M. Muller. Elementary Functions: Algorithms and Implementation, third edition. Birkhäuser, 2016. https://doi.org/10.1007/978-1-4899-7983-4
[MulSto2004] T. Mulders and A. Storjohann, "Certified dense linear system solving", Journal of Symbolic Computation 37:4 (2004) 485-510
[Mum1983] D. Mumford, Tata Lectures on Theta I, Birkhäuser, 1983. https://doi.org/10.1007/978-1-4899-2843-6
[Mum1984] D. Mumford, Tata Lectures on Theta II, Birkhäuser, 1984. https://doi.org/10.1007/978-0-8176-4578-6
[Mus1971] D. R. Musser. Algorithms for polynomial factorization. PhD thesis, University of Wisconsin, 1971.
[Mus1975] D. R. Musser. Multivariate polynomial factorization. Journal of the ACM 22:2 (1975), 291–308. https://doi.org/10.1145/321879.321890
[MW2001] D. Micciancio and B. Warinschi, "A linear space algorithm for computing the Hermite normal form", Proceedings of the 2001 International Symposium on Symbolic and Algebraic Computation (ISSAC 2001), 231–236. https://doi.org/10.1145/384101.384133
[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
[Neu1990] A. Neumaier. Interval Methods for Systems of Equations. Cambridge University Press, 1990.
[Neu1999] J. Neukirch. Algebraic Number Theory. Grundlehren der mathematischen Wissenschaften 322, Springer, 1999. https://doi.org/10.1007/978-3-662-03983-0
[NIST2012] National Institute of Standards and Technology, Digital Library of Mathematical Functions (2012), https://dlmf.nist.gov/
[Nov2008] A. Novocin. Factoring univariate polynomials over the rationals. PhD thesis, Florida State University, 2008.
[NS2005] P. Q. Nguyen and D. Stehlé, "Floating-point LLL revisited", Advances in Cryptology – EUROCRYPT 2005, Lecture Notes in Computer Science 3494 (2005), 215–233. https://doi.org/10.1007/11426639_13
[NS2009] P. Q. Nguyen and D. Stehlé, "An LLL algorithm with quadratic complexity", SIAM Journal on Computing 39:3 (2009), 874–903. https://doi.org/10.1137/070705702
[NSV2011] A. Novocin, D. Stehlé and G. Villard, "An LLL-reduction algorithm with quasi-linear time complexity", Proceedings of the 43rd ACM Symposium on Theory of Computing (STOC 2011), 403–412. https://doi.org/10.1145/1993636.1993691
[Nus1980] H. J. Nussbaumer. Fast polynomial transform algorithms for digital convolution. IEEE Transactions on Acoustics, Speech and Signal Processing 28 (1980), 205–215.
[Nus1982] H. J. Nussbaumer. Fast Fourier Transform and Convolution Algorithms, second edition. Springer, 1982. https://doi.org/10.1007/978-3-642-81897-4
[NW1978] A. Nijenhuis and H. S. Wilf, Combinatorial Algorithms for Computers and Calculators. 2nd Edition, Academic Press, 1978.
[NZ2004] M. Nüsken and M. Ziegler, "Fast multipoint evaluation of bivariate polynomials", Algorithms – ESA 2004, LNCS 3221 (2004), 544–555
[Obr1963] N. Obreschkoff. Verteilung und Berechnung der Nullstellen reeller Polynome. VEB Deutscher Verlag der Wissenschaften, Berlin, 1963.
[Olv1997] F. Olver, Asymptotics and special functions, AKP Classics, AK Peters Ltd., Wellesley, MA, 1997. Reprint of the 1974 original.
[Ore1933] O. Ore. Theory of non-commutative polynomials. Annals of Mathematics 34 (1933), 480–508. https://doi.org/10.2307/1968173
[ORO2005] T. Ogita, S. M. Rump and S. Oishi. Accurate sum and dot product. SIAM Journal on Scientific Computing 26:6 (2005), 1955–1988. https://doi.org/10.1137/030601818
[OS1988] A. M. Odlyzko and A. Schönhage. Fast algorithms for multiple evaluations of the Riemann zeta function. Transactions of the American Mathematical Society 309 (1988), 797–809. https://doi.org/10.1090/S0002-9947-1988-0961614-2
[Ost1921] A. Ostrowski. Über die Bedeutung der Theorie der konvexen Polyeder für die formale Algebra. Jahresbericht der Deutschen Mathematiker-Vereinigung 30 (1921), 98–99.
[Pal1933] R. E. A. C. Paley, "On orthogonal matrices", Journal of Mathematics and Physics 12 (1933), 311–320. https://doi.org/10.1002/sapm1933121311
[Pan1988] V. Pan, "Computing the determinant and the characteristic polynomial of a matrix via solving linear systems of equations", Information Processing Letters 28:2 (1988), 71–75. https://doi.org/10.1016/0020-0190(88)90166-4
[PARI] The PARI Group, PARI/GP, https://pari.math.u-bordeaux.fr/ ; the primecert implementation of FastECPP is by Jared Asuncion
[Paterson1973] Michael S. Paterson and Larry J. Stockmeyer : On the number of nonscalar multiplications necessary to evaluate polynomials, SIAM Journal on Computing (1973)
[PauSto2013] C. Pauderis and A. Storjohann, "Computing the invariant structure of integer matrices: fast algorithms into practice", Proceedings of the 2013 International Symposium on Symbolic and Algebraic Computation (ISSAC 2013), 307–314. https://doi.org/10.1145/2465506.2465955
[Per2003] C. Percival. Rapid multiplication modulo the sum and difference of highly composite numbers. Mathematics of Computation 72 (2003), 387–395. https://doi.org/10.1090/S0025-5718-02-01419-9
[PernetStein2010] Pernet, C. and Stein, W. : Fast computation of Hermite normal forms of random integer matrices ,J. Number Theory 130:17 (2010) 1675–1683
[Pet1999] K. Petras, "On the computation of the Gauss-Legendre quadrature formula with a given precision", Journal of Computational and Applied Mathematics 112 (1999), 253-267
[Pet2002] K. Petras. Self-validating integration and approximation of piecewise analytic functions. Journal of Computational and Applied Mathematics 145:2 (2002), 345–359. https://doi.org/10.1016/S0377-0427(01)00586-2
[Pla2011] D. J. Platt, "Computing degree 1 L-functions rigorously", Ph.D. Thesis, University of Bristol (2011), https://people.maths.bris.ac.uk/~madjp/thesis5.pdf
[Pla2017] D. J. Platt, "Isolating some non-trivial zeros of zeta", Mathematics of Computation 86 (2017), 2449-2467, https://doi.org/10.1090/mcom/3198
[Poc1914] H. C. Pocklington, "The determination of the prime or composite nature of large numbers by Fermat's theorem", Proceedings of the Cambridge Philosophical Society 18 (1914), 29–30
[PohHel1978] S. C. Pohlig and M. E. Hellman, "An improved algorithm for computing logarithms over GF(p) and its cryptographic significance", IEEE Transactions on Information Theory 24 (1978), 106–110, https://doi.org/10.1109/TIT.1978.1055817
[Pol1971] J. M. Pollard. The fast Fourier transform in a finite field. Mathematics of Computation 25 (1971), 365–374.
[Pol1974] J. M. Pollard, "Theorems on factorization and primality testing", Proceedings of the Cambridge Philosophical Society 76 (1974), 521–528
[Pol1975] J. M. Pollard, "A Monte Carlo method for factorization", BIT 15 (1975), 331–334
[Pol1978] J. M. Pollard, "Monte Carlo methods for index computation (mod p)", Mathematics of Computation 32 (1978), 918–924. https://doi.org/10.1090/S0025-5718-1978-0491431-9
[Pom1985] C. Pomerance. The quadratic sieve factoring algorithm. Advances in Cryptology – EUROCRYPT '84, Lecture Notes in Computer Science 209, Springer, 1985, 169–182.
[PP2010] K. H. Pilehrood and T. H. Pilehrood. "Series acceleration formulas for beta values", Discrete Mathematics and Theoretical Computer Science, DMTCS, 12 (2) (2010), 223-236, https://hal.inria.fr/hal-00990465/
[PreSar1978] F. P. Preparata and D. V. Sarwate. An improved parallel processor bound in fast matrix inversion. Information Processing Letters 7 (1978), 148–150. https://doi.org/10.1016/0020-0190(78)90079-0
[Pri1991] D. M. Priest. Algorithms for arbitrary precision floating point arithmetic. Proceedings of the 10th IEEE Symposium on Computer Arithmetic (ARITH-10), 1991, 132–143.
[PS1973] M. S. Paterson and L. J. Stockmeyer, "On the number of nonscalar multiplications necessary to evaluate polynomials", SIAM J. Comput (1973)
[PS1991] G. Pittaluga and L. Sacripante, "Inequalities for the zeros of the Airy functions", SIAM J. Math. Anal. 22:1 (1991), 260-267.
[PS2007] C. Pernet and A. Storjohann, "Faster algorithms for the characteristic polynomial", Proceedings of the 2007 International Symposium on Symbolic and Algebraic Computation (ISSAC) (2007), 307-314
[PSW1980] C. Pomerance, J. L. Selfridge and S. S. Wagstaff, Jr., "The pseudoprimes to 25·10^9", Mathematics of Computation 35 (1980), 1003–1026
[Rab1980] M. O. Rabin, "Probabilistic algorithm for testing primality", Journal of Number Theory 12 (1980), 128–138
[Rab1980b] M. O. Rabin. Probabilistic algorithms in finite fields. SIAM Journal on Computing 9 (1980), 273–280.
[Rad1968] C. M. Rader. Discrete Fourier transforms when the number of data samples is prime. Proceedings of the IEEE 56:6 (1968), 1107–1108. https://doi.org/10.1109/PROC.1968.6477
[Rad1973] H. Rademacher, Topics in analytic number theory, Springer, 1973.
[Rademacher1937] Rademacher, Hans : On the partition function p(n) Proc. London Math. Soc vol. 43 (1937) 241–254
[RadGro1972] H. Rademacher and E. Grosswald, Dedekind Sums, Carus Mathematical Monographs 16, Mathematical Association of America, 1972.
[Ram1911] S. Ramanujan, "Some properties of Bernoulli's numbers", Journal of the Indian Mathematical Society 3 (1911), 219–234.
[Rei1997] D. Reischert, "Asymptotically fast computation of subresultants", ISSAC 1997, 233–240
[RenDob1969] B. C. Rennie and A. J. Dobson, "On Stirling numbers of the second kind", Journal of Combinatorial Theory 7:2 (1969), 116–121. https://doi.org/10.1016/S0021-9800(69)80045-1
[RF1994] D. Richardson and J. Fitch. "The identity problem for elementary functions and constants". ISSAC '94: Proceedings of the international symposium on Symbolic and algebraic computation, August 1994, 285-290. https://doi.org/10.1145/190347.190429
[Ric1968] D. Richardson. Some undecidable problems involving elementary functions of a real variable. Journal of Symbolic Logic 33:4 (1968), 514–520. https://doi.org/10.2307/2271358
[Ric1992] D. Richardson. "The elementary constant problem". ISSAC '92: Papers from the international symposium on Symbolic and algebraic computation, August 1992, 108-116. https://doi.org/10.1145/143242.143284
[Ric1995] D. Richardson. "A simplified method of recognizing zero among elementary constants". ISSAC '95: Proceedings of the 1995 international symposium on Symbolic and algebraic computation, April 1995, 104-109. https://doi.org/10.1145/220346.220360
[Ric1997] D. Richardson. "How to recognize zero". Journal of Symbolic Computation 24.6 (1997): 627-645. https://doi.org/10.1006/jsco.1997.0157
[Ric2007] D. Richardson. "Zero tests for constants in simple scientific computation". Mathematics in Computer Science volume 1, pages 21-37 (2007). https://doi.org/10.1007/s11786-007-0002-x
[Ric2009] D. Richardson. "Recognising zero among implicitly defined elementary numbers". Preprint, 2009.
[Rob2000] A. M. Robert. A Course in p-adic Analysis. Graduate Texts in Mathematics 198, Springer, 2000. https://doi.org/10.1007/978-1-4757-3254-2
[Rob2005] A. D. Robison. N-bit unsigned division via N-bit multiply-add. Proceedings of the 17th IEEE Symposium on Computer Arithmetic (ARITH-17), 2005, 131–139.
[Rosowski2023] Rosowski, Andreas. "Fast commutative matrix algorithms". Journal of Symbolic Computation 114 (2023): 302–321.
[RosSch1962] Rosser, J. Barkley; Schoenfeld, Lowell: Approximate formulas for some functions of prime numbers. Illinois J. Math. 6 (1962), no. 1, 64–94.
[RS1960] I. S. Reed and G. Solomon. Polynomial codes over certain finite fields. Journal of the Society for Industrial and Applied Mathematics 8 (1960), 300–304.
[RSR1969] L. R. Rabiner, R. W. Schafer and C. M. Rader. The chirp z-transform algorithm. IEEE Transactions on Audio and Electroacoustics 17:2 (1969), 86–92. https://doi.org/10.1109/TAU.1969.1162034
[Rum1999] S. M. Rump. Fast and parallel interval arithmetic. BIT Numerical Mathematics 39:3 (1999), 534–554. https://doi.org/10.1023/A:1022374804152
[Rum2010] S. M. Rump, "Verification methods: Rigorous results using floating-point arithmetic", Acta Numerica 19 (2010), 287-449.
[Rys1963] H. J. Ryser, Combinatorial Mathematics, The Carus Mathematical Monographs #14, The Mathematical Association of America (1963).
[RZ2004] F. Rouillier and P. Zimmermann. Efficient isolation of polynomial's real roots. Journal of Computational and Applied Mathematics 162 (2004), 33–50. https://doi.org/10.1016/j.cam.2003.08.015
[RZBM2009] S. M. Rump, P. Zimmermann, S. Boldo and G. Melquiond. Computing predecessor and successor in rounding to nearest. BIT Numerical Mathematics 49 (2009), 419–431. https://doi.org/10.1007/s10543-009-0218-z
[Sal1976] E. Salamin. Computation of π using arithmetic-geometric mean. Mathematics of Computation 30:135 (1976), 565–570. https://doi.org/10.2307/2005327
[Sch-mpoly] D. Schultz. Algorithms for multivariate polynomials. Notes in the FLINT source tree, src/mpoly/doc/MPolyAlgorithms.tex.
[Sch1971] A. Schönhage, "Schnelle Berechnung von Kettenbruchentwicklungen", Acta Informatica 1 (1971), 139–144
[Sch1977] A. Schönhage. Schnelle Multiplikation von Polynomen über Körpern der Charakteristik 2. Acta Informatica 7 (1977), 395–398.
[Sch1980] J. T. Schwartz. Fast probabilistic algorithms for verification of polynomial identities. Journal of the ACM 27:4 (1980), 701–717. https://doi.org/10.1145/322217.322225
[Sch1982] A. Schönhage, "Asymptotically fast algorithms for the numerical multiplication and division of polynomials with complex coefficients", Computer Algebra (EUROCAM '82), LNCS 144 (1982), 3–15
[Sch1982b] A. Schönhage. The fundamental theorem of algebra in terms of computational complexity. Technical report, Universität Tübingen, 1982.
[Sch1985] R. Schoof, "Elliptic curves over finite fields and the computation of square roots mod p", Mathematics of Computation 44 (1985), 483–494
[Sch1995] R. Schoof, "Counting points on elliptic curves over finite fields", Journal de Théorie des Nombres de Bordeaux 7 (1995), 219–254
[Sch2000] A. Schinzel. Polynomials with Special Regard to Reducibility. Cambridge University Press, 2000. https://doi.org/10.1017/CBO9780511542916
[Sch2008] R. Schoof. Four primality testing algorithms. In: J. P. Buhler and P. Stevenhagen (eds.), Algorithmic Number Theory, MSRI Publications 44, Cambridge University Press, 2008, 101–126.
[Schertz2002] R. Schertz, "Weber's class invariants revisited", Journal de Theorie des Nombres de Bordeaux 14 (2002), 325-343
[SE1994] C. P. Schnorr and M. Euchner, "Lattice basis reduction: improved practical algorithms and solving subset sum problems", Mathematical Programming 66 (1994), 181–199. https://doi.org/10.1007/BF01581144
[Sha1971] D. Shanks, "Class number, a theory of factorization, and genera", Proc. Symp. Pure Math. 20, American Mathematical Society (1971), 415–440
[Sha1973] D. Shanks, "Five number-theoretic algorithms", Proceedings of the Second Manitoba Conference on Numerical Mathematics, Congressus Numerantium 7 (1973), 51–70
[Sha1989] D. Shanks, "On Gauss and composition I, II", in Number Theory and Applications (R. A. Mollin, ed.), NATO ASI Series C 265, Kluwer, 1989, 163–204.
[ShaSor1993] J. Shallit and J. Sorenson, "A binary algorithm for the Jacobi symbol", ACM SIGSAM Bulletin 27 (1993), 4–11
[She1997] J. R. Shewchuk. Adaptive precision floating-point arithmetic and fast robust geometric predicates. Discrete & Computational Geometry 18 (1997), 305–363. https://doi.org/10.1007/PL00009321
[Sho1994] V. Shoup. Fast construction of irreducible polynomials over finite fields. Journal of Symbolic Computation 17:5 (1994), 371–391.
[Sho1995] V. Shoup, "A new polynomial factorization algorithm and its implementation", Journal of Symbolic Computation 20:4 (1995), 363–397
[Sho1999] V. Shoup. Efficient computation of minimal polynomials in algebraic extensions of finite fields. Proceedings of ISSAC 1999, ACM, 53–58.
[Sho2009] V. Shoup. A Computational Introduction to Number Theory and Algebra. Second edition, Cambridge University Press, 2009. https://shoup.net/ntb/
[Sho2021] V. Shoup, "Arithmetic software libraries", chapter 9 of Computational Cryptography, Cambridge University Press (2021), https://doi.org/10.1017/9781108854207.012
[Sie1972] M. Sieveking, "An algorithm for division of power series", Computing 10 (1972), 153–156
[Sil1987] R. D. Silverman. The multiple polynomial quadratic sieve. Mathematics of Computation 48 (1987), 329–339.
[Sil2009] J. H. Silverman, The Arithmetic of Elliptic Curves, 2nd edition, Graduate Texts in Mathematics 106, Springer (2009)
[SK1982] T. Sasaki and Y. Kanada. Practically fast multiple-precision evaluation of log(x). Journal of Information Processing 5:4 (1982), 247–250.
[SKHN1975] Y. Sugiyama, M. Kasahara, S. Hirasawa and T. Namekawa. A method for solving key equation for decoding Goppa codes. Information and Control 27 (1975), 87–99.
[SL1996] A. Storjohann and G. Labahn, "Asymptotically fast computation of Hermite normal forms of integer matrices", Proceedings of the 1996 International Symposium on Symbolic and Algebraic Computation (ISSAC 1996), 259–266. https://doi.org/10.1145/236869.237083
[Smi1989] D. M. Smith. Efficient multiple-precision evaluation of elementary functions. Mathematics of Computation 52 (1989), 131–134. https://doi.org/10.1090/S0025-5718-1989-0971406-0
[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
[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
[SS1971] A. Schönhage and V. Strassen. Schnelle Multiplikation großer Zahlen. Computing 7 (1971), 281–292.
[SST2003] T. Satoh, B. Skjernaa and Y. Taguchi. Fast computation of canonical lifts of elliptic curves and its application to point counting. Finite Fields and Their Applications 9 (2003), 89–101. https://doi.org/10.1016/S1071-5797(02)00013-8
[Ste1967] J. Stein. Computational problems associated with Racah algebra. Journal of Computational Physics 1 (1967), 397–405. https://doi.org/10.1016/0021-9991(67)90047-2
[Ste1974] P. H. Sterbenz. Floating-Point Computation. Prentice-Hall, 1974.
[Ste2002] A. Steel. "A new scheme for computing with algebraically closed fields". In: Fieker C., Kohel D.R. (eds) Algorithmic Number Theory. ANTS 2002. Lecture Notes in Computer Science, vol 2369. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45455-1_38
[Ste2005] D. Stehlé, "Algorithmique de la réduction de réseaux et application à la recherche de pires cas pour l'arrondi de fonctions mathématiques", Ph.D. thesis, Université Henri Poincaré Nancy 1 (2005).
[Ste2010] A. Steel. "Computing with algebraically closed fields". Journal of Symbolic Computation 45 (2010) 342-372. https://doi.org/10.1016/j.jsc.2009.09.005
[Stef2010] D. E. Steffy, "Exact solutions to linear systems of equations using output sensitive lifting", ACM Communications in Computer Algebra 44:3/4 (2010) 160-182
[Stehle2010] Stehlé, Damien : Floating-Point LLL: Theoretical and Practical Aspects, in Nguyen, Phong Q. and Vallée, Brigitte : The LLL Algorithm: Survey and Applications (2010) 179–213
[Stein2007] Stein, William A.: Modular forms, a computational approach. American Mathematical Society. 2007
[Sto1996] A. Storjohann, "Faster algorithms for integer lattice basis reduction", Technical Report 249, Department of Computer Science, ETH Zürich (1996).
[Sto2000] A. Storjohann, Algorithms for Matrix Canonical Forms, PhD thesis, ETH Zürich (2000), https://doi.org/10.3929/ethz-a-004141007
[Sto2003] A. Storjohann, "High-order lifting and integrality certification", Journal of Symbolic Computation 36:3–4 (2003), 613–648. https://doi.org/10.1016/S0747-7171(03)00097-X
[Sto2005] A. Storjohann, "The shifted number system for fast linear algebra on integer matrices", Journal of Complexity 21:4 (2005), 609–650. https://doi.org/10.1016/j.jco.2005.04.002
[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
[Str1969] V. Strassen, "Gaussian elimination is not optimal", Numerische Mathematik 13 (1969), 354-356, https://doi.org/10.1007/BF02165411
[Str1973] V. Strassen, "Die Berechnungskomplexität von elementarsymmetrischen Funktionen und von Interpolationskoeffizienten", Numerische Mathematik 20 (1973), 238–251
[Str1997] A. Strzebonski. "Computing in the field of complex algebraic numbers". Journal of Symbolic Computation (1997) 24, 647-656. https://doi.org/10.1006/jsco.1997.0158
[Str2012] A. Strzebonski. "Real root isolation for exp-log-arctan functions". Journal of Symbolic Computation 47 (2012) 282–314. https://doi.org/10.1016/j.jsc.2011.11.004
[Str2014] M. Streng, "Computing Igusa class polynomials", Math. Comp. 83:285 (2014), 275–309. https://doi.org/10.1090/S0025-5718-2013-02712-3
[Stu1835] C. Sturm. Mémoire sur la résolution des équations numériques. Mémoires présentés par divers savants étrangers à l'Académie royale des sciences de l'Institut de France 6 (1835), 273–318.
[Sut2007] A. V. Sutherland. "Order computations in generic groups." PhD diss., Massachusetts Institute of Technology, 2007.
[Suy1985] H. Suyama. Informal preliminary report (8). Letter to R. P. Brent, 1985.
[Swa1962] R. G. Swan. Factorization of polynomials over finite fields. Pacific Journal of Mathematics 12 (1962), 1099–1106.
[Syl1867] J. J. Sylvester, "Thoughts on inverse orthogonal matrices, simultaneous sign successions, and tessellated pavements in two or more colours, with applications to Newton's rule, ornamental tile-work, and the theory of numbers", Philosophical Magazine 34 (1867), 461–475.
[SZ2004] D. Stehlé and P. Zimmermann. A binary recursive gcd algorithm. Algorithmic Number Theory (ANTS VI), LNCS 3076 (2004), 411–425. https://doi.org/10.1007/978-3-540-24847-7_31
[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
[Tan1989] P. T. P. Tang. Table-driven implementation of the exponential function in IEEE floating-point arithmetic. ACM Transactions on Mathematical Software 15:2 (1989), 144–157. https://doi.org/10.1145/63522.214389
[Tar1972] R. E. Tarjan. Depth-first search and linear graph algorithms. SIAM Journal on Computing 1(2), 146–160, 1972.
[Tho1963] L. H. Thomas. Using a computer to solve problems in physics. In Applications of Digital Computers, Ginn, Boston, 1963, 44–45.
[Tho2002] E. Thomé, "Subquadratic computation of vector generating polynomials and improvement of the block Wiedemann algorithm", Journal of Symbolic Computation 33:5 (2002), 757–775
[ThullYap1990] Thull, K. and Yap, C. : A Unified Approach to HGCD Algorithms for Polynomials and Integers, (1990)
[Ton1891] A. Tonelli, "Bemerkung über die Auflösung quadratischer Congruenzen", Nachrichten von der Königlichen Gesellschaft der Wissenschaften und der Georg-Augusts-Universität zu Göttingen (1891), 344–346
[Too1963] A. L. Toom. The complexity of a scheme of functional elements realizing the multiplication of integers. Soviet Mathematics Doklady 3 (1963), 714–716.
[Tre2008] L. N. Trefethen, "Is Gauss Quadrature Better than Clenshaw-Curtis?", SIAM Review, 50:1 (2008), 67-87, https://doi.org/10.1137/060659831
[Tre2013] L. N. Trefethen. Approximation Theory and Approximation Practice. SIAM, 2013.
[Tru2011] T. S. Trudgian, "Improvements to Turing's method", Mathematics of Computation 80 (2011), 2259-2279, https://doi.org/10.1090/S0025-5718-2011-02470-1
[Tru2014] T. S. Trudgian, "An improved upper bound for the argument of the Riemann zeta-function on the critical line II", Journal of Number Theory 134 (2014), 280-292, https://doi.org/10.1016/j.jnt.2013.07.017
[Tuc2011] W. Tucker. Validated Numerics: A Short Introduction to Rigorous Computations. Princeton University Press, 2011.
[Tur1953] A. M. Turing, "Some Calculations of the Riemann Zeta-Function", Proc. of the London Mathematical Society 3(3) (1953), 99-117, https://doi.org/10.1112/plms/s3-3.1.99
[Val1979] L. G. Valiant. The complexity of computing the permanent. Theoretical Computer Science 8 (1979), 189–201. https://doi.org/10.1016/0304-3975(79)90044-6
[vdH1995] J. van der Hoeven, "Automatic numerical expansions". Proc. of the conference Real numbers and computers (1995), 261-274. https://www.texmacs.org/joris/ane/ane-abs.html
[vdH1999] J. van der Hoeven. Fast evaluation of holonomic functions. Theoretical Computer Science 210:1 (1999), 199–215. https://doi.org/10.1016/S0304-3975(98)00102-9
[vdH2004] J. van der Hoeven, "Truncated FFTs", ISSAC 2004 notes, https://www.texmacs.org/joris/issac04/issac04.html
[vdH2005] J. van der Hoeven. Notes on the truncated Fourier transform. Technical report 2005-5, Université Paris-Sud, Orsay, 2005.
[vdH2006] J. van der Hoeven, "Computations with effective real numbers". Theoretical Computer Science, Volume 351, Issue 1, 14 February 2006, Pages 52-60. https://doi.org/10.1016/j.tcs.2005.09.060
[vdH2008] J. van der Hoeven. Making fast multiplication of polynomials numerically stable. Technical report 2008-02, Université Paris-Sud, Orsay, 2008.
[vdH2010] J. van der Hoeven, "Newton's method and FFT trading", Journal of Symbolic Computation 45:8 (2010), 857–878
[vHN2010] M. van Hoeij and A. Novocin, "Gradual sub-lattice reduction and a new complexity for factoring polynomials", LATIN 2010, Lecture Notes in Computer Science 6034 (2010), 539–553. https://doi.org/10.1007/978-3-642-12200-2_47
[vHo2002] M. van Hoeij. Factoring polynomials and the knapsack problem. Journal of Number Theory 95 (2002), 167–189. https://doi.org/10.1006/jnth.2001.2763
[vHP2012] M. van Hoeij and V. Pal. "Isomorphisms of algebraic number fields". Journal de Théorie des Nombres de Bordeaux, Vol. 24, No. 2 (2012), pp. 293-305. https://doi.org/10.2307/43973105
[Vil1997] G. Villard, "A study of Coppersmith's block Wiedemann algorithm using matrix polynomials", Rapport de recherche 975-IM, LMC-IMAG, Grenoble (1997).
[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.
[VZvdG2015] F. G. Van Zee and R. A. van de Geijn, "BLIS: A framework for rapidly instantiating BLAS functionality", ACM Transactions on Mathematical Software 41:3 (2015), 1-33, https://doi.org/10.1145/2764454
[Waksman1970] Waksman, Abraham, "On Winograd's algorithm for inner products", IEEE Transactions on Computers 19.04 (1970): 360-361.
[WaktinsZeitlin1993] Watkins, W. and Zeitlin, J. : The minimal polynomial of \cos(2\pi/n) The American Mathematical Monthly 100:5 (1993) 471–474
[Wal1999] C. D. Walter, "Montgomery exponentiation needs no final subtractions", Electronics Letters 35 (1999), 1831–1832, https://doi.org/10.1049/el:19991230
[Wan1978] P. S. Wang. An improved multivariate polynomial factoring algorithm. Mathematics of Computation 32 (1978), 1215–1231. https://doi.org/10.1090/S0025-5718-1978-0568284-3
[Wan1980] P. S. Wang. The EEZ-GCD algorithm. ACM SIGSAM Bulletin 14:2 (1980), 50–60. https://doi.org/10.1145/1089220.1089228
[WanRot1975] P. S. Wang and L. P. Rothschild. Factoring multivariate polynomials over the integers. Mathematics of Computation 29 (1975), 935–950. https://doi.org/10.1090/S0025-5718-1975-0396471-3
[War1962] S. Warshall. A theorem on Boolean matrices. Journal of the ACM 9(1), 11–12, 1962.
[Was1997] L. C. Washington. Introduction to Cyclotomic Fields, second edition. Graduate Texts in Mathematics 83, Springer, 1997. https://doi.org/10.1007/978-1-4612-1934-7
[Wei1891] K. Weierstrass. Neuer Beweis des Satzes, dass jede ganze rationale Function einer Veränderlichen dargestellt werden kann als ein Product aus linearen Functionen derselben Veränderlichen. Sitzungsberichte der Königlich Preussischen Akademie der Wissenschaften zu Berlin, 1891, 1085–1101.
[Wei2000] A. Weilert, "(1+i)-ary GCD computation in Z[i] as an analogue to the binary GCD algorithm", Journal of Symbolic Computation 30.5 (2000): 605-617, https://doi.org/10.1006/jsco.2000.0422
[WGD1982] P. S. Wang, M. J. T. Guy and J. H. Davenport, "P-adic reconstruction of rational numbers", ACM SIGSAM Bulletin 16:2 (1982), 2–3. https://doi.org/10.1145/1089292.1089293
[Whiteman1956] Whiteman, A. L. : A sum connected with the series for the partition function, Pacific Journal of Mathematics 6:1 (1956) 159–176
[Wil1965] J. H. Wilkinson. The Algebraic Eigenvalue Problem. Clarendon Press, Oxford, 1965.
[Wil1982] H. C. Williams, "A p+1 method of factoring", Mathematics of Computation 39 (1982), 225–234
[Win1968] S. Winograd. A new algorithm for inner product. IEEE Transactions on Computers C-17 (1968), 693–694. https://doi.org/10.1109/TC.1968.227420
[Win1971] S. Winograd, "On multiplication of 2 × 2 matrices", Linear Algebra and its Applications 4 (1971), 381-388, https://doi.org/10.1016/0024-3795(71)90009-7
[Win1978] S. Winograd. On computing the discrete Fourier transform. Mathematics of Computation 32 (1978), 175–199. https://doi.org/10.1090/S0025-5718-1978-0468306-4
[WQ3a] The Wolfram Functions Site, formula 07.11.26.0033.01. http://functions.wolfram.com/07.11.26.0033.01
[WQ3b] The Wolfram Functions Site, formula 07.12.27.0014.01. http://functions.wolfram.com/07.12.27.0014.01
[WQ3c] The Wolfram Functions Site, formula 07.12.26.0003.01. http://functions.wolfram.com/07.12.26.0003.01
[WQ3d] The Wolfram Functions Site, formula 07.12.26.0088.01. http://functions.wolfram.com/07.12.26.0088.01
[Yan1998] T. Yan. The geobucket data structure for polynomials. Journal of Symbolic Computation 25:3 (1998), 285–293. https://doi.org/10.1006/jsco.1997.0176
[Yan2009] S. Yang. Computing the greatest common divisor of multivariate polynomials over finite fields. MSc thesis, Simon Fraser University, 2009.
[Yap2000] C. K. Yap. Fundamental Problems of Algorithmic Algebra. Oxford University Press, 2000.
[Yav1968] R. Yavne. An economical method for calculating the discrete Fourier transform. AFIPS Fall Joint Computer Conference (1968), 115–125. https://doi.org/10.1145/1476589.1476610
[Yee2025] A. J. Yee. y-cruncher: a multi-threaded pi-program, and its formula collection. http://www.numberworld.org/y-cruncher/ and https://github.com/Mysticial/y-cruncher-Formulas
[YuiZagier1997] N. Yui and D. Zagier, "On the singular values of Weber modular functions", Mathematics of Computation 66 (1997), 1645-1662
[Yun1976] D. Y. Y. Yun. On square-free decomposition algorithms. Proceedings of the 1976 ACM Symposium on Symbolic and Algebraic Computation (SYMSAC '76), 26–35. https://doi.org/10.1145/800205.806320
[Zas1969] H. Zassenhaus. On Hensel factorization, I. Journal of Number Theory 1 (1969), 291–311. https://doi.org/10.1016/0022-314X(69)90047-X
[ZD2006] P. Zimmermann and B. Dodson, "20 years of ECM", Algorithmic Number Theory (ANTS VII), LNCS 4076 (2006), 525–542
[Zei1995] D. Zeilberger. The J. C. P. Miller recurrence for exponentiating a polynomial, and its q-analog. Journal of Difference Equations and Applications 1 (1995), 57–60. https://doi.org/10.1080/10236199508808006
[Zim1999] P. Zimmermann. Karatsuba square root. INRIA Research Report RR-3805, 1999.
[Zip1979] R. Zippel. Probabilistic algorithms for sparse polynomials. Symbolic and Algebraic Computation (EUROSAM 1979), Lecture Notes in Computer Science 72, Springer, 1979, 216–226. https://doi.org/10.1007/3-540-09519-5_73
[Zip1981] R. Zippel. Newton's iteration and the sparse Hensel algorithm. Proceedings of SYMSAC 1981, ACM, 68–72. https://doi.org/10.1145/800206.806373
[Zip1985] R. Zippel. "Simplification of expressions involving radicals". Journal of Symbolic Computation (1985) 1, 189-210. https://doi.org/10.1016/S0747-7171(85)80014-6
[Ziv1991] A. Ziv. Fast evaluation of elementary mathematical functions with correctly rounded last bit. ACM Transactions on Mathematical Software 17:3 (1991), 410–423. https://doi.org/10.1145/114697.116813
[Zun2023] J. Zuniga, "Catalan's constant fast convergent series", https://mathoverflow.net/q/424055
[Zun2023b] J. Zuniga, "Are these fast convergent series for log(2) and log(3) already known and proven?", https://math.stackexchange.com/q/4854073
[Zun2025] J. Zuniga, "Fast Ramanujan-type Series for Logarithms. Part I", 2025, https://arxiv.org/abs/2506.08245
[Zun2025b] J. Zuniga, "Fast Ramanujan-type Series for Logarithms. Part II", 2025, https://arxiv.org/abs/2506.10321
[ZZ2020] D. Zeilberger and W. Zudilin. The irrationality measure of π is at most 7.103205334137... Moscow Journal of Combinatorics and Number Theory 9:4 (2020), 407–419. https://doi.org/10.2140/moscow.2020.9.407

Cite this page

The FLINT team, “References,” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/references.html (generated 2026-10-20).

@misc{flint-doc-references,
  author       = {{The FLINT team}},
  title        = {{References}},
  howpublished = {FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev},
  year         = {2026},
  url          = {https://flintlib.org/doc/references.html},
  note         = {Generated 2026-10-20}
}

Edit this page · PDF version · Built with fdoc from f12f9f517b