On 2014-10-25, Jason Grout <jason-s...@creativetrax.com> wrote:
> http://www.ams.org/notices/201410/rnoti-p1249.pdf
> P.S. It would be interesting to see if Sage can do the calculation they
> identified as buggy in mathematica. That would make for a cool
> follow-up editorial.
I've reimplemnted the buggy determinant calculation in Maxima.
Presumably from this it would be easy to redo it in any other system;
I don't know how Sage manages such calculations.
I am happy to report that Maxima, despite its many and varied bugs,
doesn't have this particular one:
bfloat (determinant (big_matrix));
=> 1.951242191319868b9762
Reported value in paper is 1.95124219131987 * 10^9762.
Script is attached as a PS. The function foo(n) can be used to generate
random examples, as the authors did to find one which tickles the bug.
All in good fun,
Robert Dodier
PS.
basic_matrix : matrix
([-32, 69, 89, -60, -83, -22, -14, -58, 85, 56, -65, -30, -86, -9],
[6, 99, 11, 57, 47, -42, -48, -65, 25, 50, -70, -3, -90, 31],
[78, 38, 12, 64, -67, -4, -52, -65, 19, 71, 38, -17, 51, -3],
[-93, 30, 89, 22, 13, 48, -73, 93, 11, -97, -49, 61, -25, -4],
[54, -22, 54, -53, -52, 64, 19, 1, 81, -72, -11, 50, 0, -81],
[65, -58, 3, 57, 19, 77, 76, -57, -80, 22, 93, -85, 67, 58],
[29, -58, 47, 87, 3, -6, -81, 5, 98, 86, -98, 51, -62, -66],
[93, -77, 16, -64, 48, 84, 97, 75, 89, 63, 34, -98, -94, 19],
[45, -99, 3, -57, 32, 60, 74, 4, 69, 98, -40, -69, -28, -26],
[-13, 51, -99, -2, 48, 71, -81, -32, 78, 27, -28, -22, 22, 94],
[11, 72, -74, 86, 79, -58, -89, 80, 70, 55, -49, 51, -42, 66],
[-72, 53, 49, -46, 17, -22, -48, -40, -28, -85, 88, -30, 74, 32],
[-92, -22, -90, 67, -25, -28, -91, -8, 32, -41, 10, 6, 85, 21],
[47, -73, -30, -60, 99, 9, -86, -70, 84, 55, 19, 69, 11, -84]) $
small_matrix : matrix
([528, 853, -547, -323, 393, -916, -11, -976, 279, -665, 906, -277, 103, -485],
[878, 910, -306, -260, 575, -765, -32, 94, 254, 276, -156, 625, -8, -566],
[-357, 451, -475, 327, -84, 237, 647, 505, -137, 363, -808, 332, 222, -998],
[-76, 26, -778, 505, 942, -561, -350, 698, -532, -507, -78, -758, 346, -545],
[-358, 18, -229, -880, -955, -346, 550, -958, 867, -541, -962, 646, 932, 168],
[192, 233, 620, 955, -877, 281, 357, -226, -820, 513, -882, 536, -237, 877],
[-234, -71, -831, 880, -135, -249, -427, 737, 664, 298, -552, -1, -712, -691],
[80, 748, 684, 332, 730, -111, -643, 102, -242, -82, -28, 585, 207, -986],
[967, 1, -494, 633, 891, -907, -586, 129, 688, 150, -501, -298, 704, -68],
[406, -944, -533, -827, 615, 907, -443, -350, 700, -878, 706, 1, 800, 120],
[33, -328, -543, 583, -443, -635, 904, -745, -398, -110, 751, 660, 474, 255],
[-537, -311, 829, 28, 175, 182, -930, 258, -808, -399, -43, -68, -553, 421],
[-373, -447, -252, -619, -418, 764, 994, -543, -37, -845, 30, -704, 147,
-534],
[638, -33, 932, -335, -75, -676, -934, 239, 210, 665, 414, -803, 564, -805]);
powers_list : [10^123,
10^152, 10^185, 10^220, 10^397, 10^449,
10^503, 10^563, 10^979, 10^1059, 10^1143,
10^1229, 10^1319, 10^1412];
powers_matrix : apply (diag_matrix, powers_list);
big_matrix : basic_matrix . powers_matrix + small_matrix;
bfloat (determinant (big_matrix));
foo (n) := block ([basic_matrix, powers_matrix, small_matrix, big_matrix, a, b],
basic_matrix : genmatrix (lambda ([i, j], random (2 * 99 + 1) - 99), n, n),
powers_matrix : apply (diag_matrix, rest (powers_list, n - length
(powers_list))),
small_matrix : genmatrix (lambda ([i, j], random (2 * 999 + 1) - 999), n, n),
big_matrix : basic_matrix . powers_matrix + small_matrix,
a : determinant (big_matrix),
b : determinant (big_matrix),
is (a = b)) $
set_random_state (make_random_state (1729)) $
foo (4);
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