Cardo Wong's problem

------------

>> m=[1,1,1,1,1,1,1,1,1,1;120,148,175,204,232,260,288,316,343,371;14400,21904,30625,41616,53824,67600,82944,99856,117649,137641;1728000,3241792,5359375,8489664,12487168,17576000,23887872,31554496,40353607,51064811;207360000,479785216,937890625,1731891456,2897022976,4569760000,6879707136,9971220736,13841287201,18945044881;24883200000,71008211968,164130859375,353305857024,672109330432,1188137600000,1981355655168,3150905752576,4747561509943,7028611650851;2985984000000,10509215371264,28722900390625,72074394832896,155929364660224,308915776000000,570630428688384,995686217814016,1628413597910449,2607614922465721;358318080000000,1555363874947072,5026507568359375,14703176545910784,36175612601171968,80318101760000000,164341563462254592,314636844829229056,558545864083284007,967425136234782491;42998169600000000,230193853492166656,879638824462890625,2999448015365799936,8392742123471896576,20882706457600000000,47330370277129322496,99425242966036381696,191581231380566414401,358914725543104304161];
>> rank(m)

ans =

     5

>> m

m =

   1.0e+20 *

    0.0000    0.0000    0.0000    0.0000    0.0000    0.0000    0.0000    0.0000    0.0000    0.0000
    0.0000    0.0000    0.0000    0.0000    0.0000    0.0000    0.0000    0.0000    0.0000    0.0000
    0.0000    0.0000    0.0000    0.0000    0.0000    0.0000    0.0000    0.0000    0.0000    0.0000
    0.0000    0.0000    0.0000    0.0000    0.0000    0.0000    0.0000    0.0000    0.0000    0.0000
    0.0000    0.0000    0.0000    0.0000    0.0000    0.0000    0.0000    0.0000    0.0000    0.0000
    0.0000    0.0000    0.0000    0.0000    0.0000    0.0000    0.0000    0.0000    0.0000    0.0000
    0.0000    0.0000    0.0000    0.0000    0.0000    0.0000    0.0000    0.0000    0.0000    0.0000
    0.0000    0.0000    0.0001    0.0001    0.0004    0.0008    0.0016    0.0031    0.0056    0.0097
    0.0004    0.0023    0.0088    0.0300    0.0839    0.2088    0.4733    0.9943    1.9158    3.5891

>> 

-------------


sage: print cols
[[1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [120, 148, 175, 204, 232, 260, 288, 316, 343, 371], [14400, 21904, 30625, 41616, 53824, 67600, 82944, 99856, 117649, 137641], [1728000, 3241792, 5359375, 8489664, 12487168, 17576000, 23887872, 31554496, 40353607, 51064811], [207360000, 479785216, 937890625, 1731891456, 2897022976, 4569760000, 6879707136, 9971220736, 13841287201, 18945044881], [24883200000, 71008211968, 164130859375, 353305857024, 672109330432, 1188137600000, 1981355655168, 3150905752576, 4747561509943, 7028611650851], [2985984000000, 10509215371264, 28722900390625, 72074394832896, 155929364660224, 308915776000000, 570630428688384, 995686217814016, 1628413597910449, 2607614922465721], [358318080000000, 1555363874947072, 5026507568359375, 14703176545910784, 36175612601171968, 80318101760000000, 164341563462254592, 314636844829229056, 558545864083284007, 967425136234782491], [42998169600000000, 230193853492166656, 879638824462890625, 2999448015365799936, 8392742123471896576, 20882706457600000000, 47330370277129322496, 99425242966036381696, 191581231380566414401, 358914725543104304161]]
sage: m = matrix(RDF, cols)
sage: m.rank()
9
sage: m.nrows()
9