170514

Ruby


eta products の線形結合

E_6 をeta products の線形結合で表してみた。

def s(k, n)
  s = 0
  (1..n).each{|i| s += i if n % i == 0 && i % k == 0}
  s
end

def A0(n)
  ary = [1]
  a = [0] + (1..n).map{|i| 24 * s(1, i) - 12 * s(2, i)}
  (1..n).each{|i| ary << (1..i).inject(0){|s, j| s - a[j] * ary[-j]} / i}
  ary
end

def A1(n)
  ary = [1]
  a = [0] + (1..n).map{|i| 12 * s(2, i)}
  (1..n).each{|i| ary << (1..i).inject(0){|s, j| s - a[j] * ary[-j]} / i}
  ary
end

def A2(n)
  ary = [1]
  a = [0] + (1..n).map{|i| 12 * s(2, i) + 8 * s(4, i) - 8 * s(1, i)}
  (1..n).each{|i| ary << (1..i).inject(0){|s, j| s - a[j] * ary[-j]} / i}
  ary
end

def A3(n)
  ary = [1]
  a = [0] + (1..n).map{|i| 24 * s(4, i) - 12 * s(2, i)}
  (1..n).each{|i| ary << (1..i).inject(0){|s, j| s - a[j] * ary[-j]} / i}
  ary
end

n = 200
p ary0 = A0(n)
p ary1 = [0] + A1(n)
p ary2 = [0] * 2 + A2(n)
p ary3 = [0] * 3 + A3(n)
p (0..n).map{|i| ary0[i] - 480 * ary1[i] - 16896 * ary2[i] + 8192 * ary3[i]}

出力結果
[1, -24, 264, -1760, 7944, -25872, 64416, -133056, 253704, -472760, 825264, -1297056, 1938336, -2963664, 4437312, -6091584, 8118024, -11368368, 15653352, -19822176, 24832944, -32826112, 42517728, -51425088, 61903776, -78146664, 98021616, -115331264, 133522752, -164079696, 201364416, -229101312, 259776264, -314269824, 374842512, -420258432, 471023592, -554746896, 653690400, -724846144, 793078704, -927125232, 1082704128, -1175873952, 1279397088, -1482713808, 1699194816, -1834739328, 1980797856, -2259791448, 2578950264, -2771448768, 2949559536, -3345875856, 3803764800, -4028054976, 4264256832, -4833186688, 5414943600, -5719271712, 6059238336, -6756214608, 7558096128, -7972913344, 8312839944, -9284959200, 10374325632, -10801349856, 11279351952, -12564531456, 13871037312, -14433084864, 15042871272, -16585653744, 18306804912, -19068642080, 19670138400, -21654935808, 23917274304, -24615220608, 25376943024, -28009137752, 30586037328, -31513408608, 32579551488, -35508322080, 38810229216, -40037878848, 40859536608, -44672951664, 48932378352, -49926264960, 51130316736, -55883287552, 60547082112, -61923031104, 63385408416, -68696763696, 74577903048, -76393194528, 77602957944, -84080984592, 91461572928, -92741489856, 94198772976, -102562521600, 110403610416, -112206096288, 114458740800, -123091514832, 132910417728, -135359463232, 136447747392, -147394340016, 159500457600, -160956544896, 162940575600, -176121743248, 188740015200, -190918949760, 193511203776, -207502774008, 222973423728, -226147998912, 227429983488, -244215894432, 263101540416, -264312339456, 266010877704, -286962805888, 306415571616, -308637532896, 312172889472, -332945133312, 356433028512, -360323811456, 360223654032, -386088721392, 414603535104, -415108384416, 417392122752, -447681704448, 476316548928, -478377518784, 481341997032, -512942325984, 547290900816, -551426235360, 550868402352, -587521351824, 629263864416, -628022995776, 628196474400, -673500182256, 714637972224, -715961510400, 719692526784, -763113874512, 812342889600, -816313861440, 812060601264, -865462338048, 924314846664, -920507154912, 920361668688, -982725974784, 1039906730016, -1039128015552, 1040478667008, -1102867760040, 1171757692512, -1174521854176, 1167835079136, -1239722456016, 1321246238400, -1313545628736, 1307424001248, -1395533705856, 1474191694800, -1470135873888, 1472419748592, -1554105008016, 1647547321728, -1648658651200, 1632926218176, -1734153444192, 1844175455232, -1829372897088, 1821916743552, -1937378426368, 2043436190400, -2033547631104, 2028332946336, -2142281587248, 2267057828112, -2265622499712, 2244116900808, -2373665758992, 2521003646304, -2496637706688, 2478371203704]
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