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References
 

[0] Falkoff, A.D., and Kenneth E. Iverson, The Design of APL, IBM Journal of Research and Development, volume 17, number 4, 1973-07.
[0a] Ibid., §1.
[0b] Ibid., §4.
[1] Hardy, G.H., A Mathematician’s Apology, Cambridge University Press, 1940-11.
[2] Keenan, Tom, IT seeks to recapture lustre in career market, BusinessEdge, volume 4, number 39, 2004-11-04 to -10.
[3] Iverson, Kenneth E., Notation as a Tool of Thought, Communications of the ACM, volume 23, number 8, 1980-08.
[3a] Ibid., equation A.3.
[3b] Ibid., §3.3.
[4] Hui, Roger K.W., Sixteen APL Amuse-Bouches, Vector, volume 26, number 4, 2016-03.
[5] Hui, Roger K.W., A Tour (de Force) of APL in 16 Expressions, Dyalog User Meeting, 2016-10-09.
[6] Hui, Roger K.W., A Tour (de Force) of APL in 16 Expressions, Functional Conf 2016, 2016-10-15. (slides, video)
[7] Jsoftware, J Wiki Essays, 2007-2016.
[8] Iverson, Kenneth E., A Programming Language, Wiley, 1962-05.
[8a] Ibid., §1.4.
[8b] Ibid., §1.9.
[9] Knuth, Donald E., Two Notes on Notation, American Mathematical Monthly, volume 99, number 5, 1992-05-01.
[10] Scholes, John, Data-driven Conditionals, Dyalog Blog, 2014-10-13.
[11] Hui, Roger K.W., Phil Last, and John Scholes, e-mail discussion, 2014-10-18 to -20.
[12] Hui, Roger K.W., editor, Ken Iverson Quotations and Anecdotes, 2014-10-10.
[12a] Ibid., #implementers2.
[12b] Ibid., #Maple.
[13] Hui, Roger K.W., On Average, Vector, volume 24, number 2&3, 2010-08.
[14] Azzarello, Arlene, editor, APL QUOTE-QUAD: The Early Years, APL Press, Palo Alto, 1982-11.
[15] Hui, Roger K.W., Index-Of, A 30-Year Quest, J Conference 2014, 2014-07-25.
[15a] Ibid., §16.
[16] Hui, Roger K.W., and John Scholes, Dyalog Potential v14.0 Language Features, Dyalog Conference, 2012-10-15.
[17] Hui, Roger K.W., A Speed-Up Story, Dyalog Blog, 2014-11-05.
[18] Hui, Roger K.W., Rank & Friends, Dyalog Conference, 2013-10-22.
[19] Smillie, Keith W., STATPACK: An APL Statistical Package, University of Alberta, 1968.
[20] Iverson, Kenneth E., APL in Exposition, IBM Corporation, 1972-01; p.13
[21] Smillie, Keith W., Kenneth Iverson, APL and J: Some Personal Recollections, Vector, volume 22, number 3, 2006-08.
[22] Perlis, Alan J., Almost Perfect Artifacts Improve only in Small Ways: APL is more French than English, APL78, 1978-03-29.
[23] Hui, Roger K.W., An Amuse-Bouche from APL History, 2014-10-25.
[24] Thomson, Norman, Jottings 43: A Rippling Good Yarn!, Vector, volume 21, number 3, 2005-05.
[25] Scholes, John, ripple, D-Functions, 2007-03-05.
[26] OEIS, Sequence A024222, On-line Encyclopedia of Integer Sequences, 2014.
[27] Hui, Roger K.W., Quicksort, J Wiki Essay, 2005-09-28.
[28] Hui, Roger K.W., Quicksort in APL, Dyalog Blog, 2014-12-11.
[29] Hui, Roger K.W., Quicksort in APL Revisited, Dyalog Blog, 2016-02-29.
[30] Hui, Roger K.W., Order Statistics, J Wiki Essay, 2008-03-23.
[31] Aho, A.V., J.E. Hopcroft, and J.D. Ullman, The Design and Analysis of Computer Algorithms, Addison-Wesley, 1974; §3.7.
[32] Hui, Roger K.W., Pascal’s Triangle, J Wiki Essay, 2005-09-28.
[33] Falkoff, A.D., and Kenneth E. Iverson, The APL\360 Terminal System, Research Report RC-1922, IBM, 1967-10-16; Fig.1.
[34] Hui, Roger K.W., Kenneth E. Iverson, Eugene McDonnell, and Arthur Whitney, APL\?, APL90, APL Quote Quad, volume 20, number 4, 1990-07.
[34a] Ibid., Appendix Gc and Gd.
[34b] Ibid., Appendix Le.
[35] Iverson, Kenneth E., Elementary Functions: An Algorithmic Treatment, Science Research Associates, Inc., 1966; p.69.
[36] Falkoff, A.D. and Kenneth E. Iverson, APL\360 User’s Manual, IBM Corporation, 1968-08; A.5.
[37] Iverson, Kenneth E., Algebra: An Algorithmic Treatment, Addison-Wesley, 1972; p.141.
[38] Iverson, Kenneth E., Introducing APL to Teachers, IBM Corporation, 1972-07; p.22.
[39] Iverson, Kenneth E., An Introduction to APL for Scientists and Engineers, IBM Corporation, 1973-03; p.19.
[40] Iverson, Kenneth E., Elementary Analysis, APL Press, 1976; ex.1.68.
[41] Iverson, Kenneth E., Programming Style in APL, 1978 APL Users Meeting Proceedings, 1978-09-18; §6.
[42] Iverson, Kenneth E., A Dictionary of APL, APL Quote Quad, volume 18, number 1, 1987-09.
[42a] Ibid., m∇n
[43] Hui, Roger K.W., Fibonacci Sequence, J Wiki Essay, 2005-09-26.
[44] Hui, Roger K.W., Newton’s Method, J Wiki Essay, 2005-10-15.
[45] Iverson, Kenneth E., A Dictionary of J, Vector, volume 7, number 2, 1990-10.
[46] Hui, Roger K.W., f/ .g Improved, J 5.04 Release Notes, Jsoftware, 2004-09-01.
[47] Hui, Roger K.W., Inner Product — An Old/New Problem, 2009-06-07.
[48] Hui, Roger K.W., editor, APL Quotations and Anecdotes, 2014; #IC2013.
[49] Hui, Roger K.W., Some Uses of { and } , APL87, APL Quote Quad, volume 17, number 4, 1987-05.
[49a] Ibid., §4.4.
[49b] Ibid., §1.2.
[49c] Ibid., §4.3.
[49d] Ibid., §4.1.
[49e] Ibid., §2.2.
[49f ] Ibid., §3.1.
[50] Hui, Roger K.W., Symmetries of the Square, J Wiki Essay, 2005-11-07.
[51] Hui, Roger K.W., and Kenneth E. Iverson, J Introduction and Dictionary, 2011-05-03.
[51a] Ibid., /:
[51b] Ibid., I.
[51c] Ibid., M.
[51d] Ibid., for.
[51e] Ibid., ^:
[51f ] Ibid., \.
[51g] Ibid., p:
[51h] Ibid., &.
[51i ] Ibid., :.
[52] Hui, Roger K.W., and John Scholes, New Primitive Functions and Operators, Dyalog User Meeting, 2016-10-10.
[53] Scholes, John, le, D-Functions, 2016-08-16.
[54] Brown, Matthew, The Man Who Knew Infinity, 2016.
[55] Wolfram, Stephen, Who was Ramanujan?, Back Channel, 2016-04-27.
[56] Hardy, G.H., and S. Ramanujan, Asymptotic Formulæ in Combinatory Analysis, Proceedings of the London Mathematics Society, volume 17, number 2, 1918.
[57] Hui, Roger K.W., Partitions, J Wiki Essay, 2005-11-19.
[58] Weisstein, Eric W., Partition Function P, MathWorld, A Wolfram Web Resource, 2016.
[59] Hui, Roger K.W., M. Implemented, J 6.02 Release Notes, Jsoftware, 2006-09-06.
[60] Scholes, John, memo , D-Functions, 2014-05-20.
[61] Hui, Roger K.W., A Memo Operator, BAA Seminar, Royal Society of Arts, 2016-05-20.
[62] Hardy, G.H., Obituary Notices: Srinivasa Ramanujan, Proceedings of the London Mathematical Society, volume 19, 1921; page lvii.
[63] Hui, Roger K.W., Unforgettable Numbers, J Wiki Essay, 2009-08-22.
[64] Hui, Roger K.W., Unforgettable Numbers, Dyalog Blog, 2015-03-30.
[65] Nikitin, Andrew, 88 Hats, J General Forum, 2007-06-06.
[66] Randall, John, 88 Hats, J General Forum, 2007-06-07.
[67] Hui, Roger K.W., 88 Hats, Jwiki Essay, 2007-06-08.
[68] Hui, Roger K.W., The “88 Hats” Puzzle, Vector, volume 25, number 4, 2012-11.
[69] McDonnell, Eugene, The Magical Matrix, Vector, volume 20, number 2, 2003-10.
[70] Hui, Roger K.W., The N Queens Problem, APL Quote Quote, volume 11, number 3, 1981-03.
[71] Hui, Roger K.W., Permutations, J Wiki Essay, 2005-10-31.
[72] Scholes, John, pmat, D-Functions, 2008.
[73] Hui, Roger K.W., Permutations, Dyalog Blog, 2015-07-20.
[74] Foad, Jay, and Roger K.W. Hui, Performance: The Neverending Story, Dyalog User Meeting, 2016-10-11.
[75] McDonnell, Eugene, Representing a Permutation, At Play With J, Vector, volume 12, number 1, 1995-07.
[76] Hui, Roger K.W., Implementing @:, comp.lang.apl, 1991-04-21.
[77] Hui, Roger K.W., Permutation Index, J Wiki Essay, 2005-10-11.
[78] Gilman, Leonard, and Allen J. Rose, APL: An Interactive Approach, second edition, Wiley, 1974.
[79] Hui, Roger K.W., Combination Index, J Wiki Essay, 2005-11-11.
[80] Murray, Kip, Testing Whether an Array is Symmetric, J Programming Forum, 2003-08-03.
[81] Herstein, I.N., Topics in Algebra, Second Edition, Xerox College Publishing, 1975; ex.2.10.11.
[82] Hui, Roger K.W., Testing Whether an Array is Symmetric, J Programming Forum, 2003-08-10.
[83] Hui, Roger K.W., Symmetric Array, J Wiki Essay, 2005-09-29.
[84] Hui, Roger K.W., Queens and Knights, J Wiki Essay, 2005-09-29.
[85] Hui, Roger K.W., N Queens Problem, J Wiki Essay, 2008-11-27.
[86] Hui, Roger K.W., Knight’s Tour, J Wiki Essay, 2010-07-22.
[87] Scholes, John, kt , D-Functions, 2013-05-22.
[88] Hui, Roger K.W., moo, J Wiki Essay, 2006-07-24.
[89] Scholes, John, pco , D-Functions, 2014-05-20.
[90] Hui, Roger K.W., Odometer, J Wiki Essay, 2005-11-18.
[91] Hui, Roger K.W., What is an Array?, Vector, volume 25, number 3, 2012-03.
[92] Berry, Paul C., SHARP APL Reference Manual, I.P. Sharp Associates Limited, 1979-03.
[93] Nickolov, Nick, Compiling APL to Javascript, Vector, volume 26, number 1, 2013-09.
[94] Hui, Roger K.W., Inverted Table, J Wiki Essay, 2007-05-08.
[95] Hui, Roger K.W., Rank & Friends, Dyalog Conference, 2013-10-22.
[96] Hui, Roger K.W., A Letter from Dijkstra on APL, Vector, volume 26, number 2, 2014-09.
[97] Rich, Henry, Convolution using FFT, J Programming Forum, 2010-12-27.
[98] Hui, Roger K.W., Rational Numbers in Dyalog APL, Dyalog Conference, 2011-10-02 to -05.
[99] Graham, R.L., D.E. Knuth, and O. Patashnik, Concrete Mathematics, Addison-Wesley, 1989.
[100]  Falkoff, A.D., Kenneth E. Iverson, and E.H. Sussenguth, A Formal Description of System/360, IBM Systems Journal, volume 3, number 3, 1964; Table 1, pp. 200-201.
[101] Hui, Roger K.W., Three Combinatoric Puzzles, Vector, volume 9, number 2, 1992-10.
[102] Hui, Roger K.W., Repeated Squaring, J Wiki Essay, 2005-09-28.
[103] Smith, Bob, Paragraphics Perfected, The I.P. Sharp Newsletter, volume 7, number 2, I.P. Sharp Associates Limited, 1979-03.
[104] Cerovski, Viktor, Silver Ratio, Geometrically Interpreted, J Programming Forum, 2009-05-20.
[105] Kobchenko, Oleg, Base Spectrum, J Wiki Essay, 2005-12-13.
[106] Hui, Roger K.W., and Oleg Kobchenko, Gray Code, J Wiki Essay, 2005-10-16.
[107] Hui, Roger K.W., Tower of Hanoi, Vector, volume 21, number 1, 2004-09.
[108] Hui, Roger K.W., Tower of Hanoi, J Wiki Essay, 2007-12-11.
[109] Hui, Roger K.W., Ackermann’s Function, J Wiki Essay, 2005-10-14.
[110] Hui, Roger K.W., The Halting Problem Rendered in APL, Dyalog Blog, 2016-04-12.
[111] Hui, Roger K.W., Cholesky Decomposition, J Wiki Essay, 2005-10-14.
[112] Hui, Roger K.W., Triangular Matrix Inverse, J Wiki Essay, 2005-10-27.
[113] Hui, Roger K.W., LU Decomposition, J Wiki Essay, 2005-10-31.
[114] Hui, Roger K.W., QR Decomposition, J Wiki Essay, 2005-10-30.
[115] Ibarra, Oscar, Shlomo Moran, and Roger K.W. Hui, A Generalization of the Fast LUP Matrix Decomposition Algorithm and Applications, Journal of Algorithms, volume 3, 1982, pp. 45-56.
[116] Hui, Roger K.W., The Complexity of Some Decompositions in Matrix Algebra, M.Sc. Thesis, University of Toronto, 1981-04.
[117] Hui, Roger K.W., Cholesky Decomposition, Dyalog Blog, 2015-01-08.
[118] Hui, Roger K.W., Minors, J Wiki Essay, 2007-08-18.
[119] Iverson, Kenneth E., Concrete Math Companion, Iverson Software Inc., 1995-05-11; §6A.
[120] Hui, Roger K.W., Stirling Numbers, J Wiki Essay, 2005-09-29.
[121] Hui, Roger K.W., The Ball Clock Problem, Vector, volume 12, number 2, 1995-10.
[122] Hui, Roger K.W., Chinese Remainder Theorem, J Wiki Essay, 2005-10-26.
[123] McDonnell, Eugene, and Jeffrey Shallit, Extending APL to Infinity, APL80, 1980.
[124] Hui, Roger K.W., Some Exercises in APL Language Design, 2016-11-27.
[124a] Ibid., §12.
[124b]  Ibid., §47.
[125] Hui, Roger K.W., Euler’s Identity, J Wiki Essay, 2010-02-04.
[126] Weisstein, Eric W., Bertelsen’s Number, MathWorld, A Wolfram Web Resource, 2016.
[127] Hui, Roger K.W., 50847534, Dyalog Blog, 2016-09-14.
[128] McDonnell, Eugene, Recreational APL: Pyramigram Puzzle, APL Quote Quad, volume 11, number 1, 1980-09.
[129] McDonnell, Eugene, Recreational APL: Pyramigram Solution, APL Quote Quad, volume 11, number 4, 1981-06.
[130] Hoffman, Paul, The Man Who Loved Only Numbers, Hyperion, 1998.
[131] Robinson, Kim Stanley, Sixty Days and Counting, Bantam Spectra, 2007.
[132] Haddon, Mark, The Curious Incident of the Dog in the Night-Time, Doubleday, 2003.
[133] Hui, Roger K.W., The Monty Hall Problem, J Wiki Essay, 2006-09-02.
[134] Hui, Roger K.W., Bring Something Beautiful, Vector, volume 24, number 4, 2010-12.
[135] Hui, Roger K.W., I. Interval Index Implemented, J 6.01 Release Notes, Jsoftware, 2005-07-29.
[136] Dyalog, Dyalog APL Language Reference, Dyalog Limited, 2016.
[137] Hui, Roger K.W., Tests, Derivations, Proofs, Functional Conf 2017, 2017-11-18. (slides, video)
[138] Foad, Jay, Sieve of Eratosthenes, e-mail, 2019-04-29.