infolevel[appfac] := 0 randp := proc(vars::list, list_deg_factor::list, N::integer, e::integer, dn) local i, f0, fac, pert_pol, res, deg_pert, dd; if nops([args]) = 4 then dd := 1 else dd := dn end if; deg_pert := convert(list_deg_factor, `+`); f0 := 1; for i to nops(list_deg_factor) do fac := randpoly(vars, degree = list_deg_factor[i], coeffs = rand(-N .. N), dense); f0 := fac*f0 end do; dd := round(nops(convert(expand(f0), list))*dd); print('noise_terms' = dd); pert_pol := randpoly(vars, degree = deg_pert, coeffs = rand(-10^e .. 10^e), terms = dd); return f0, '`*`'(10^(-e)*norm(expand(f0), 2)/norm(pert_pol, 2), pert_pol) end proc N := 200 agr := [9, 7], 5, 4 noise_terms = 38 ` the biggest gap, the last r-th singular values and the number of factors `, 525.7788139, .5911278389e-5, 2 ` The time for computing the number of factors*****`, 16.759 `The time for the entire factorization******`, 133.840 i = 1, Min = 133.849, Med = 133.849, Max = 133.849 noise_terms = 37 ` the biggest gap, the last r-th singular values and the number of factors `, 527.5126827, .9809025443e-5, 2 ` The time for computing the number of factors*****`, 16.771 `The time for the entire factorization******`, 143.261 i = 2, Min = 133.849, Med = 138.5550000, Max = 143.261 noise_terms = 38 ` the biggest gap, the last r-th singular values and the number of factors `, 690.0511654, .1200678249e-4, 2 ` The time for computing the number of factors*****`, 17.141 `The time for the entire factorization******`, 136.231 i = 3, Min = 133.849, Med = 136.240, Max = 143.261 noise_terms = 37 ` the biggest gap, the last r-th singular values and the number of factors `, 551.0934024, .6592517783e-5, 2 ` The time for computing the number of factors*****`, 16.620 `The time for the entire factorization******`, 136.290 i = 4, Min = 133.849, Med = 136.2650000, Max = 143.261 noise_terms = 38 ` the biggest gap, the last r-th singular values and the number of factors `, 533.8719959, .1094816683e-4, 2 ` The time for computing the number of factors*****`, 16.980 `The time for the entire factorization******`, 148.500 i = 5, Min = 133.849, Med = 136.290, Max = 148.500 noise_terms = 38 ` the biggest gap, the last r-th singular values and the number of factors `, 743.0225450, .1021375536e-4, 2 ` The time for computing the number of factors*****`, 17.059 `The time for the entire factorization******`, 216.849 i = 6, Min = 133.849, Med = 139.7755000, Max = 216.849 noise_terms = 38 ` the biggest gap, the last r-th singular values and the number of factors `, 419.4609584, .8152071449e-5, 2 ` The time for computing the number of factors*****`, 16.909 `The time for the entire factorization******`, 128.340 i = 7, Min = 128.340, Med = 136.290, Max = 216.849 noise_terms = 38 ` the biggest gap, the last r-th singular values and the number of factors `, 544.4550049, .1444951474e-4, 2 ` The time for computing the number of factors*****`, 16.869 `The time for the entire factorization******`, 140.619 i = 8, Min = 128.340, Med = 138.4595000, Max = 216.849 noise_terms = 38 ` the biggest gap, the last r-th singular values and the number of factors `, 778.8652825, .1141364670e-4, 2 ` The time for computing the number of factors*****`, 16.800 `The time for the entire factorization******`, 132.240 i = 9, Min = 128.340, Med = 136.290, Max = 216.849 noise_terms = 38 ` the biggest gap, the last r-th singular values and the number of factors `, 303.3999064, .1027804053e-4, 2 ` The time for computing the number of factors*****`, 16.780 `The time for the entire factorization******`, 147.800 i = 10, Min = 128.340, Med = 138.4595000, Max = 216.849 noise_terms = 38 ` the biggest gap, the last r-th singular values and the number of factors `, 626.3485916, .1117234163e-4, 2 ` The time for computing the number of factors*****`, 16.970 `The time for the entire factorization******`, 190.349 i = 11, Min = 128.340, Med = 140.629, Max = 216.849 noise_terms = 38 ` the biggest gap, the last r-th singular values and the number of factors `, 675.1655177, .1178322143e-4, 2 ` The time for computing the number of factors*****`, 16.921 `The time for the entire factorization******`, 213.520 i = 12, Min = 128.340, Med = 141.9450000, Max = 216.849 noise_terms = 38 ` the biggest gap, the last r-th singular values and the number of factors `, 735.5847804, .8601783395e-5, 2 ` The time for computing the number of factors*****`, 16.629 `The time for the entire factorization******`, 143.240 i = 13, Min = 128.340, Med = 143.250, Max = 216.849 noise_terms = 37 ` the biggest gap, the last r-th singular values and the number of factors `, 309.8594012, .1537801216e-4, 2 ` The time for computing the number of factors*****`, 16.649 `The time for the entire factorization******`, 463.830 i = 14, Min = 128.340, Med = 143.2555000, Max = 463.830 noise_terms = 38 ` the biggest gap, the last r-th singular values and the number of factors `, 607.7581510, .8411061625e-5, 2 ` The time for computing the number of factors*****`, 16.821 `The time for the entire factorization******`, 135.770 i = 15, Min = 128.340, Med = 143.250, Max = 463.830 noise_terms = 37 ` the biggest gap, the last r-th singular values and the number of factors `, 517.2989966, .7198632515e-5, 2 ` The time for computing the number of factors*****`, 16.750 `The time for the entire factorization******`, 134.070 i = 16, Min = 128.340, Med = 141.9395000, Max = 463.830 noise_terms = 38 ` the biggest gap, the last r-th singular values and the number of factors `, 697.1219215, .8707053173e-5, 2 ` The time for computing the number of factors*****`, 17.000 `The time for the entire factorization******`, 151.870 i = 17, Min = 128.340, Med = 143.250, Max = 463.830 noise_terms = 37 ` the biggest gap, the last r-th singular values and the number of factors `, 330.7341214, .1581037557e-4, 2 ` The time for computing the number of factors*****`, 16.770 `The time for the entire factorization******`, 214.930 i = 18, Min = 128.340, Med = 143.2555000, Max = 463.830 noise_terms = 38 ` the biggest gap, the last r-th singular values and the number of factors `, 510.8610629, .9323229384e-5, 2 ` The time for computing the number of factors*****`, 16.709 `The time for the entire factorization******`, 142.399 i = 19, Min = 128.340, Med = 143.250, Max = 463.830 noise_terms = 38 ` the biggest gap, the last r-th singular values and the number of factors `, 480.2606316, .8883803155e-5, 2 ` The time for computing the number of factors*****`, 16.681 `The time for the entire factorization******`, 138.791 i = 20, Min = 128.340, Med = 142.8300000, Max = 463.830 noise_terms = 37 ` the biggest gap, the last r-th singular values and the number of factors `, 346.7732806, .1216773703e-4, 2 ` The time for computing the number of factors*****`, 16.841 i = 21, Min = 128.340, Med = 142.8300000, Max = 463.830 noise_terms = 38 ` the biggest gap, the last r-th singular values and the number of factors `, 499.1888695, .1528665893e-4, 2 ` The time for computing the number of factors*****`, 16.869 `The time for the entire factorization******`, 133.500 i = 22, Min = 128.340, Med = 142.410, Max = 463.830 noise_terms = 38 ` the biggest gap, the last r-th singular values and the number of factors `, 466.4804909, .1314519769e-4, 2 ` The time for computing the number of factors*****`, 16.841 `The time for the entire factorization******`, 132.491 i = 23, Min = 128.340, Med = 141.5195000, Max = 463.830 noise_terms = 37 ` the biggest gap, the last r-th singular values and the number of factors `, 344.3697459, .1021703177e-4, 2 ` The time for computing the number of factors*****`, 16.810 `The time for the entire factorization******`, 226.790 i = 24, Min = 128.340, Med = 142.410, Max = 463.830 noise_terms = 38 ` the biggest gap, the last r-th singular values and the number of factors `, 430.3767224, .1120997418e-4, 2 ` The time for computing the number of factors*****`, 17.151 `The time for the entire factorization******`, 135.761 i = 25, Min = 128.340, Med = 141.5195000, Max = 463.830 noise_terms = 38 ` the biggest gap, the last r-th singular values and the number of factors `, 615.2165543, .1165968377e-4, 2 ` The time for computing the number of factors*****`, 17.020 `The time for the entire factorization******`, 177.380 i = 26, Min = 128.340, Med = 142.410, Max = 463.830 noise_terms = 38 ` the biggest gap, the last r-th singular values and the number of factors `, 551.0245475, .8534871286e-5, 2 ` The time for computing the number of factors*****`, 17.200 `The time for the entire factorization******`, 133.231 i = 27, Min = 128.340, Med = 141.5195000, Max = 463.830 noise_terms = 38 ` the biggest gap, the last r-th singular values and the number of factors `, 520.2903635, .1054753523e-4, 2 ` The time for computing the number of factors*****`, 17.179 `The time for the entire factorization******`, 140.269 i = 28, Min = 128.340, Med = 140.629, Max = 463.830 noise_terms = 38 ` the biggest gap, the last r-th singular values and the number of factors `, 314.5099346, .1217151234e-4, 2 ` The time for computing the number of factors*****`, 17.011 `The time for the entire factorization******`, 150.710 i = 29, Min = 128.340, Med = 141.5195000, Max = 463.830 noise_terms = 38 ` the biggest gap, the last r-th singular values and the number of factors `, 642.8253546, .9022396291e-5, 2 ` The time for computing the number of factors*****`, 17.080 `The time for the entire factorization******`, 135.580 i = 30, Min = 128.340, Med = 140.629, Max = 463.830 noise_terms = 38 ` the biggest gap, the last r-th singular values and the number of factors `, 544.4109605, .4517938691e-5, 2 ` The time for computing the number of factors*****`, 16.811 `The time for the entire factorization******`, 132.220 i = 31, Min = 128.340, Med = 140.4490000, Max = 463.830 noise_terms = 38 ` the biggest gap, the last r-th singular values and the number of factors `, 571.4885797, .1304894749e-4, 2 ` The time for computing the number of factors*****`, 17.030 `The time for the entire factorization******`, 138.170 i = 32, Min = 128.340, Med = 140.269, Max = 463.830 noise_terms = 38 ` the biggest gap, the last r-th singular values and the number of factors `, 946.1855079, .9174767149e-5, 2 ` The time for computing the number of factors*****`, 17.019 `The time for the entire factorization******`, 133.279 i = 33, Min = 128.340, Med = 139.5300000, Max = 463.830 noise_terms = 37 ` the biggest gap, the last r-th singular values and the number of factors `, 509.0304030, .8294173803e-5, 2 ` The time for computing the number of factors*****`, 16.309 `The time for the entire factorization******`, 257.849 i = 34, Min = 128.340, Med = 140.269, Max = 463.830 noise_terms = 38 ` the biggest gap, the last r-th singular values and the number of factors `, 295.4333330, .9657780969e-5, 2 ` The time for computing the number of factors*****`, 17.220 `The time for the entire factorization******`, 181.489 i = 35, Min = 128.340, Med = 140.4490000, Max = 463.830 noise_terms = 37 ` the biggest gap, the last r-th singular values and the number of factors `, 441.8490294, .1007009031e-4, 2 ` The time for computing the number of factors*****`, 16.149 `The time for the entire factorization******`, 129.849 i = 36, Min = 128.340, Med = 140.269, Max = 463.830 noise_terms = 38 ` the biggest gap, the last r-th singular values and the number of factors `, 647.5665010, .1026312447e-4, 2 ` The time for computing the number of factors*****`, 16.800 `The time for the entire factorization******`, 197.210 i = 37, Min = 128.340, Med = 140.4490000, Max = 463.830 noise_terms = 38 ` the biggest gap, the last r-th singular values and the number of factors `, 504.0920805, .7206494961e-5, 2 ` The time for computing the number of factors*****`, 16.680 `The time for the entire factorization******`, 179.290 i = 38, Min = 128.340, Med = 140.629, Max = 463.830 noise_terms = 37 ` the biggest gap, the last r-th singular values and the number of factors `, 462.2410800, .1161976619e-4, 2 ` The time for computing the number of factors*****`, 16.471 `The time for the entire factorization******`, 204.960 i = 39, Min = 128.340, Med = 141.5195000, Max = 463.830 noise_terms = 37 ` the biggest gap, the last r-th singular values and the number of factors `, 306.0747199, .1220711623e-4, 2 ` The time for computing the number of factors*****`, 16.450 `The time for the entire factorization******`, 278.399 i = 40, Min = 128.340, Med = 142.410, Max = 463.830 noise_terms = 38 ` the biggest gap, the last r-th singular values and the number of factors `, 476.1860620, .8078815477e-5, 2 ` The time for computing the number of factors*****`, 16.650 `The time for the entire factorization******`, 132.421 i = 41, Min = 128.340, Med = 141.5195000, Max = 463.830 noise_terms = 38 ` the biggest gap, the last r-th singular values and the number of factors `, 362.2820641, .1000035937e-4, 2 ` The time for computing the number of factors*****`, 16.740 `The time for the entire factorization******`, 173.990 i = 42, Min = 128.340, Med = 142.410, Max = 463.830 noise_terms = 38 ` the biggest gap, the last r-th singular values and the number of factors `, 464.1069175, .1139295001e-4, 2 ` The time for computing the number of factors*****`, 17.040 `The time for the entire factorization******`, 138.141 i = 43, Min = 128.340, Med = 141.5195000, Max = 463.830 noise_terms = 38 ` the biggest gap, the last r-th singular values and the number of factors `, 354.3889260, .8098530195e-5, 2 ` The time for computing the number of factors*****`, 17.049 `The time for the entire factorization******`, 135.349 i = 44, Min = 128.340, Med = 140.629, Max = 463.830 noise_terms = 37 ` the biggest gap, the last r-th singular values and the number of factors `, 785.2393760, .8006335702e-5, 2 ` The time for computing the number of factors*****`, 16.580 `The time for the entire factorization******`, 182.950 i = 45, Min = 128.340, Med = 141.5195000, Max = 463.830 noise_terms = 38 ` the biggest gap, the last r-th singular values and the number of factors `, 443.8021120, .7450872103e-5, 2 ` The time for computing the number of factors*****`, 16.901 `The time for the entire factorization******`, 142.760 i = 46, Min = 128.340, Med = 142.410, Max = 463.830 noise_terms = 37 ` the biggest gap, the last r-th singular values and the number of factors `, 664.2767788, .9901496393e-5, 2 ` The time for computing the number of factors*****`, 16.920 `The time for the entire factorization******`, 138.359 i = 47, Min = 128.340, Med = 141.5195000, Max = 463.830 noise_terms = 38 ` the biggest gap, the last r-th singular values and the number of factors `, 594.9215735, .6730799501e-5, 2 ` The time for computing the number of factors*****`, 17.009 `The time for the entire factorization******`, 141.899 i = 48, Min = 128.340, Med = 141.899, Max = 463.830 noise_terms = 37 ` the biggest gap, the last r-th singular values and the number of factors `, 404.9820397, .1543810866e-4, 2 ` The time for computing the number of factors*****`, 16.939 `The time for the entire factorization******`, 154.410 i = 49, Min = 128.340, Med = 142.1545000, Max = 463.830 noise_terms = 38 ` the biggest gap, the last r-th singular values and the number of factors `, 317.9551687, .8049073737e-5, 2 ` The time for computing the number of factors*****`, 16.510 `The time for the entire factorization******`, 133.410 i = 50, Min = 128.340, Med = 141.899, Max = 463.830 noise_terms = 38 ` the biggest gap, the last r-th singular values and the number of factors `, 429.2166975, .1476431590e-4, 2 ` The time for computing the number of factors*****`, 16.981 `The time for the entire factorization******`, 282.031 i = 51, Min = 128.340, Med = 142.1545000, Max = 463.830 noise_terms = 38 ` the biggest gap, the last r-th singular values and the number of factors `, 608.2551406, .1247862564e-4, 2 ` The time for computing the number of factors*****`, 16.719 `The time for the entire factorization******`, 163.139 i = 52, Min = 128.340, Med = 142.410, Max = 463.830 noise_terms = 38 ` the biggest gap, the last r-th singular values and the number of factors `, 575.8231857, .1394112287e-4, 2 ` The time for computing the number of factors*****`, 16.731 `The time for the entire factorization******`, 254.950 i = 53, Min = 128.340, Med = 142.5850000, Max = 463.830 noise_terms = 37 ` the biggest gap, the last r-th singular values and the number of factors `, 556.7896018, .6868845473e-5, 2 ` The time for computing the number of factors*****`, 16.409 `The time for the entire factorization******`, 137.639 i = 54, Min = 128.340, Med = 142.410, Max = 463.830 noise_terms = 38 ` the biggest gap, the last r-th singular values and the number of factors `, 553.5968158, .1146933995e-4, 2 ` The time for computing the number of factors*****`, 16.721 `The time for the entire factorization******`, 328.580 i = 55, Min = 128.340, Med = 142.5850000, Max = 463.830 noise_terms = 38 ` the biggest gap, the last r-th singular values and the number of factors `, 415.1497705, .1034673357e-4, 2 ` The time for computing the number of factors*****`, 16.679 `The time for the entire factorization******`, 153.509 i = 56, Min = 128.340, Med = 142.760, Max = 463.830 noise_terms = 38 ` the biggest gap, the last r-th singular values and the number of factors `, 373.3988786, .7975781951e-5, 2 ` The time for computing the number of factors*****`, 17.080 `The time for the entire factorization******`, 159.570 i = 57, Min = 128.340, Med = 143.0050000, Max = 463.830 noise_terms = 37 ` the biggest gap, the last r-th singular values and the number of factors `, 593.1378802, .8604228427e-5, 2 ` The time for computing the number of factors*****`, 16.459 `The time for the entire factorization******`, 132.119 i = 58, Min = 128.340, Med = 142.760, Max = 463.830 noise_terms = 38 ` the biggest gap, the last r-th singular values and the number of factors `, 550.4528337, .7799142897e-5, 2 ` The time for computing the number of factors*****`, 16.971 `The time for the entire factorization******`, 136.250 i = 59, Min = 128.340, Med = 142.5850000, Max = 463.830 noise_terms = 38 ` the biggest gap, the last r-th singular values and the number of factors `, 628.5632466, .1136731815e-4, 2 ` The time for computing the number of factors*****`, 17.039 `The time for the entire factorization******`, 235.599 i = 60, Min = 128.340, Med = 142.760, Max = 463.830 noise_terms = 38 ` the biggest gap, the last r-th singular values and the number of factors `, 322.5207904, .6318605282e-5, 2 ` The time for computing the number of factors*****`, 17.099 `The time for the entire factorization******`, 142.009 i = 61, Min = 128.340, Med = 142.5850000, Max = 463.830 noise_terms = 37 ` the biggest gap, the last r-th singular values and the number of factors `, 421.6847507, .1074186186e-4, 2 ` The time for computing the number of factors*****`, 16.740 `The time for the entire factorization******`, 106.539 i = 62, Min = 106.539, Med = 142.410, Max = 463.830 noise_terms = 38 ` the biggest gap, the last r-th singular values and the number of factors `, 431.0663158, .7548083363e-5, 2 ` The time for computing the number of factors*****`, 16.750 `The time for the entire factorization******`, 141.390 i = 63, Min = 106.539, Med = 142.2095000, Max = 463.830 times6 := [133.849, 143.261, 136.240, 136.290, 148.500, 216.849, 128.340, 140.629, 132.240, 147.811, 190.349, 213.520, 143.250, 463.830, 135.770, 134.070, 151.870, 214.930, 142.410, 138.791, 133.500, 132.491, 226.790, 135.761, 177.380, 133.231, 140.269, 150.721, 135.580, 132.220, 138.179, 133.279, 257.849, 181.489, 129.849, 197.210, 179.290, 204.960, 278.399, 132.421, 173.990, 138.141, 135.349, 182.950, 142.760, 138.359, 141.899, 154.410, 133.410, 282.031, 163.139, 254.950, 137.639, 328.580, 153.509, 159.580, 132.119, 136.250, 235.609, 142.009, 106.539, 141.390]