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Toom-Cook用の係数行列の例. http://xn--w6q13e505b.jp/method/toomcook.html においてToom-4の係数が一部間違っているので検算. https://drive.google.com/file/d/0B7v2yL5QFp_gVzJLVkxCMkxMeXM/view?usp=sharing
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require "matrix" | |
def BaseWrap(x) | |
[[1, 0]] + x.reverse.map(&:to_r).map{|e| [e.numerator, e.denominator] } | |
end | |
def GenBase(t) | |
l = t * 2 - 2 | |
x = [0, -1, 1] | |
0.upto(l) do |i| | |
break if x.size >= l | |
b = 2 << i | |
x = x + [-b, b, "-1/#{b}", "1/#{b}"] | |
end | |
BaseWrap(x.first(l)) | |
end | |
def ToomMat(x) | |
l = x.size | |
# header | |
print "** Toom-", (l + 1) * 0.5, " ", x.map{|e| "#{e[0]}/#{e[1]}" }, " : ", | |
(((l + 2) >> 1)..([l - 1, (l + 2) >> 1].max)).map{|i| "#{i}*#{l+1-i}"}.join(", "), "\n" | |
y = Matrix.build(l) {|i, j| x[i][0] ** (l - j - 1) * x[i][1] ** j }.map(&:to_r).inverse # 逆行列の計算 | |
# 行ごとの通分(整数の要素は除外) | |
print Matrix.rows(y.row_vectors.map{|v| | |
lcm = 1; v.each{|e| lcm = e.denominator.lcm(lcm) }; | |
v.map{|e| e.denominator == 1? e.to_i: "#{(e * lcm).to_i}/#{lcm}" }.to_a | |
}), "\n" | |
# 行列全体の通分(整数の要素も通分) | |
lcm = 1; y.each{|e| lcm = e.denominator.lcm(lcm) } | |
print (lcm == 1? "": "1/#{lcm} * "), (y * lcm).map(&:to_i), "\n" | |
end | |
# http://xn--w6q13e505b.jp/method/toomcook.html の検算 | |
ToomMat([[-1, 2], [-2, 1], [-1, 1], [0, 1], [1, 1], [2, 1], [1, 0]]) | |
# Toom-1.0, Toom-1.5, ..., Toom-16.0, Toom-16.5 | |
1.0.step(16.5, 0.5){|t| ToomMat(GenBase(t)) } | |
# other base | |
ToomMat(BaseWrap([0, -1, 1, -2, 2, "-1/2", "1/2", -3, 3, "-1/3", "1/3", "-3/2", "3/2", "-2/3", "2/3"])) # Toom-8.5 | |
ToomMat(BaseWrap([0, -1, 1, -2, 2, "-1/2", "1/2", -3, 3, "-1/3", "1/3", "-3/2", "3/2", "-2/3", "2/3", -4, 4, "-1/4", "1/4", "-4/3", "4/3", "-3/4", "3/4"])) # Toom-12.5 | |
ToomMat(BaseWrap([0, -1, 1, -2, 2, "-1/2", "1/2", -3, 3, "-1/3", "1/3", "-3/2", "3/2", "-2/3", "2/3", -4, 4, "-1/4", "1/4", "-4/3", "4/3", "-3/4", "3/4", -5, 5, "-1/5", "1/5", "-5/2", "5/2", "-2/5", "2/5"])) # Toom-16.5 | |
ToomMat(BaseWrap([0, -1, 1, -2, 2, "-1/2", "1/2", -3, 3, "-1/3", "1/3", "-3/2", "3/2", "-2/3", "2/3", -4, 4, "-1/4", "1/4", "-4/3", "4/3", "-3/4", "3/4", -5, 5, "-1/5", "1/5", "-5/2", "5/2", "-2/5", "2/5", "-5/3", "5/3", "-3/5", "3/5", "-5/4", "5/4", "-4/5", "4/5"])) # Toom-20.5 |
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** Toom-4.0 ["-1/2", "-2/1", "-1/1", "0/1", "1/1", "2/1", "1/0"] : 4*4, 5*3, 6*2 | |
Matrix[[0, 0, 0, 0, 0, 0, 1], [-2/180, -5/180, 60/180, 90/180, -20/180, 3/180, 90/180], [0, 1/24, -4/24, 6/24, -4/24, 1/24, -5], [1/18, 1/18, -27/18, -45/18, 7/18, 0, -45/18], [0, -1/24, 16/24, -30/24, 16/24, -1/24, 4], [-8/180, -5/180, 120/180, 2, 40/180, -3/180, 2], [0, 0, 0, 1, 0, 0, 0]] | |
1/360 * Matrix[[0, 0, 0, 0, 0, 0, 360], [-4, -10, 120, 180, -40, 6, 180], [0, 15, -60, 90, -60, 15, -1800], [20, 20, -540, -900, 140, 0, -900], [0, -15, 240, -450, 240, -15, 1440], [-16, -10, 240, 720, 80, -6, 720], [0, 0, 0, 360, 0, 0, 0]] | |
** Toom-1.0 ["1/0"] : 1*1 | |
Matrix[[1]] | |
Matrix[[1]] | |
** Toom-1.5 ["1/0", "0/1"] : 2*1 | |
Matrix[[1, 0], [0, 1]] | |
Matrix[[1, 0], [0, 1]] | |
** Toom-2.0 ["1/0", "-1/1", "0/1"] : 2*2 | |
Matrix[[1, 0, 0], [1, -1, 1], [0, 0, 1]] | |
Matrix[[1, 0, 0], [1, -1, 1], [0, 0, 1]] | |
** Toom-2.5 ["1/0", "1/1", "-1/1", "0/1"] : 3*2 | |
Matrix[[1, 0, 0, 0], [0, 1/2, 1/2, -1], [-1, 1/2, -1/2, 0], [0, 0, 0, 1]] | |
1/2 * Matrix[[2, 0, 0, 0], [0, 1, 1, -2], [-2, 1, -1, 0], [0, 0, 0, 2]] | |
** Toom-3.0 ["1/0", "-2/1", "1/1", "-1/1", "0/1"] : 3*3, 4*2 | |
Matrix[[1, 0, 0, 0, 0], [2, -1/6, 1/6, 3/6, -3/6], [-1, 0, 1/2, 1/2, -1], [-2, 1/6, 2/6, -1, 3/6], [0, 0, 0, 0, 1]] | |
1/6 * Matrix[[6, 0, 0, 0, 0], [12, -1, 1, 3, -3], [-6, 0, 3, 3, -6], [-12, 1, 2, -6, 3], [0, 0, 0, 0, 6]] | |
** Toom-3.5 ["1/0", "2/1", "-2/1", "1/1", "-1/1", "0/1"] : 4*3, 5*2 | |
Matrix[[1, 0, 0, 0, 0, 0], [0, 1/24, 1/24, -4/24, -4/24, 6/24], [-5, 1/12, -1/12, -2/12, 2/12, 0], [0, -1/24, -1/24, 16/24, 16/24, -30/24], [4, -1/12, 1/12, 8/12, -8/12, 0], [0, 0, 0, 0, 0, 1]] | |
1/24 * Matrix[[24, 0, 0, 0, 0, 0], [0, 1, 1, -4, -4, 6], [-120, 2, -2, -4, 4, 0], [0, -1, -1, 16, 16, -30], [96, -2, 2, 16, -16, 0], [0, 0, 0, 0, 0, 24]] | |
** Toom-4.0 ["1/0", "-1/2", "2/1", "-2/1", "1/1", "-1/1", "0/1"] : 4*4, 5*3, 6*2 | |
Matrix[[1, 0, 0, 0, 0, 0, 0], [90/180, -2/180, 3/180, -5/180, -20/180, 60/180, 90/180], [-5, 0, 1/24, 1/24, -4/24, -4/24, 6/24], [-45/18, 1/18, 0, 1/18, 7/18, -27/18, -45/18], [4, 0, -1/24, -1/24, 16/24, 16/24, -30/24], [2, -8/180, -3/180, -5/180, 40/180, 120/180, 2], [0, 0, 0, 0, 0, 0, 1]] | |
1/360 * Matrix[[360, 0, 0, 0, 0, 0, 0], [180, -4, 6, -10, -40, 120, 180], [-1800, 0, 15, 15, -60, -60, 90], [-900, 20, 0, 20, 140, -540, -900], [1440, 0, -15, -15, 240, 240, -450], [720, -16, -6, -10, 80, 240, 720], [0, 0, 0, 0, 0, 0, 360]] | |
** Toom-4.5 ["1/0", "1/2", "-1/2", "2/1", "-2/1", "1/1", "-1/1", "0/1"] : 5*4, 6*3, 7*2 | |
Matrix[[1, 0, 0, 0, 0, 0, 0, 0], [0, 1/180, 1/180, 2/180, 2/180, -40/180, -40/180, -1], [-1890/360, 1/360, -1/360, 8/360, -8/360, -80/360, 80/360, 0], [0, -2/72, -2/72, -1/72, -1/72, 68/72, 68/72, 378/72], [378/72, -1/72, 1/72, -2/72, 2/72, 68/72, -68/72, 0], [0, 8/360, 8/360, 1/360, 1/360, -80/360, -80/360, -1890/360], [-1, 2/180, -2/180, 1/180, -1/180, -40/180, 40/180, 0], [0, 0, 0, 0, 0, 0, 0, 1]] | |
1/360 * Matrix[[360, 0, 0, 0, 0, 0, 0, 0], [0, 2, 2, 4, 4, -80, -80, -360], [-1890, 1, -1, 8, -8, -80, 80, 0], [0, -10, -10, -5, -5, 340, 340, 1890], [1890, -5, 5, -10, 10, 340, -340, 0], [0, 8, 8, 1, 1, -80, -80, -1890], [-360, 4, -4, 2, -2, -80, 80, 0], [0, 0, 0, 0, 0, 0, 0, 360]] | |
** Toom-5.0 ["1/0", "-4/1", "1/2", "-1/2", "2/1", "-2/1", "1/1", "-1/1", "0/1"] : 5*5, 6*4, 7*3, 8*2 | |
Matrix[[1, 0, 0, 0, 0, 0, 0, 0, 0], [4, -1/11340, 7/11340, 9/11340, 21/11340, 63/11340, -504/11340, -840/11340, -2835/11340], [-1890/360, 0, 1/360, 1/360, 4/360, 4/360, -80/360, -80/360, -1], [-21, 1/2160, -4/2160, -12/2160, 27/2160, -111/2160, 24/2160, 1320/2160, 2835/2160], [378/72, 0, -1/72, -1/72, -1/72, -1/72, 68/72, 68/72, 378/72], [21, -1/2160, -8/2160, 24/2160, -39/2160, 123/2160, 1536/2160, -2880/2160, -2835/2160], [-1, 0, 4/360, 4/360, 1/360, 1/360, -80/360, -80/360, -1890/360], [-4, 1/11340, 56/11340, -72/11340, 42/11340, -126/11340, -2016/11340, 3360/11340, 2835/11340], [0, 0, 0, 0, 0, 0, 0, 0, 1]] | |
1/45360 * Matrix[[45360, 0, 0, 0, 0, 0, 0, 0, 0], [181440, -4, 28, 36, 84, 252, -2016, -3360, -11340], [-238140, 0, 126, 126, 504, 504, -10080, -10080, -45360], [-952560, 21, -84, -252, 567, -2331, 504, 27720, 59535], [238140, 0, -630, -630, -630, -630, 42840, 42840, 238140], [952560, -21, -168, 504, -819, 2583, 32256, -60480, -59535], [-45360, 0, 504, 504, 126, 126, -10080, -10080, -238140], [-181440, 4, 224, -288, 168, -504, -8064, 13440, 11340], [0, 0, 0, 0, 0, 0, 0, 0, 45360]] | |
** Toom-5.5 ["1/0", "4/1", "-4/1", "1/2", "-1/2", "2/1", "-2/1", "1/1", "-1/1", "0/1"] : 6*5, 7*4, 8*3, 9*2 | |
Matrix[[1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1/90720, 1/90720, -8/90720, -8/90720, -84/90720, -84/90720, 1344/90720, 1344/90720, 5670/90720], [-481950/22680, 1/22680, -1/22680, -1/22680, 1/22680, -42/22680, 42/22680, 336/22680, -336/22680, 0], [0, -1/17280, -1/17280, 32/17280, 32/17280, 276/17280, 276/17280, -5184/17280, -5184/17280, -22950/17280], [385560/4320, -1/4320, 1/4320, 4/4320, -4/4320, 138/4320, -138/4320, -1296/4320, 1296/4320, 0], [0, 1/17280, 1/17280, -128/17280, -128/17280, -324/17280, -324/17280, 17664/17280, 17664/17280, 96390/17280], [-85, 1/4320, -1/4320, -16/4320, 16/4320, -162/4320, 162/4320, 4416/4320, -4416/4320, 0], [0, -1/90720, -1/90720, 512/90720, 512/90720, 336/90720, 336/90720, -21504/90720, -21504/90720, -481950/90720], [16, -1/22680, 1/22680, 64/22680, -64/22680, 168/22680, -168/22680, -5376/22680, 5376/22680, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1]] | |
1/362880 * Matrix[[362880, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 4, 4, -32, -32, -336, -336, 5376, 5376, 22680], [-7711200, 16, -16, -16, 16, -672, 672, 5376, -5376, 0], [0, -21, -21, 672, 672, 5796, 5796, -108864, -108864, -481950], [32387040, -84, 84, 336, -336, 11592, -11592, -108864, 108864, 0], [0, 21, 21, -2688, -2688, -6804, -6804, 370944, 370944, 2024190], [-30844800, 84, -84, -1344, 1344, -13608, 13608, 370944, -370944, 0], [0, -4, -4, 2048, 2048, 1344, 1344, -86016, -86016, -1927800], [5806080, -16, 16, 1024, -1024, 2688, -2688, -86016, 86016, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 362880]] | |
** Toom-6.0 ["1/0", "-1/4", "4/1", "-4/1", "1/2", "-1/2", "2/1", "-2/1", "1/1", "-1/1", "0/1"] : 6*6, 7*5, 8*4, 9*3, 10*2 | |
Matrix[[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1445850/5783400, -2/5783400, 15/5783400, -17/5783400, -340/5783400, 1020/5783400, -2380/5783400, 3060/5783400, 68544/5783400, -114240/5783400, 1445850/5783400], [-1927800/90720, 0, 1/90720, 1/90720, -4/90720, -4/90720, -84/90720, -84/90720, 1344/90720, 1344/90720, 5670/90720], [-1445850/272160, 2/272160, -3/272160, 5/272160, 334/272160, -1014/272160, 1876/272160, -2556/272160, -64512/272160, 110208/272160, -1445850/272160], [1542240/17280, 0, -1/17280, -1/17280, 16/17280, 16/17280, 276/17280, 276/17280, -5184/17280, -5184/17280, -22950/17280], [722925/32400, -1/32400, 0, -1/32400, -155/32400, 495/32400, -155/32400, 495/32400, 24552/32400, -47400/32400, 722925/32400], [-85, 0, 1/17280, 1/17280, -64/17280, -64/17280, -324/17280, -324/17280, 17664/17280, 17664/17280, 96390/17280], [-5783400/272160, 8/272160, 3/272160, 5/272160, 856/272160, -3576/272160, -686/272160, -2034/272160, 4032/272160, 178752/272160, -5783400/272160], [16, 0, -1/90720, -1/90720, 256/90720, 256/90720, 336/90720, 336/90720, -21504/90720, -21504/90720, -481950/90720], [4, -32/5783400, -15/5783400, -17/5783400, 2720/5783400, 8160/5783400, 4760/5783400, 6120/5783400, -274176/5783400, -456960/5783400, 4], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]] | |
1/92534400 * Matrix[[92534400, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [23133600, -32, 240, -272, -5440, 16320, -38080, 48960, 1096704, -1827840, 23133600], [-1966356000, 0, 1020, 1020, -4080, -4080, -85680, -85680, 1370880, 1370880, 5783400], [-491589000, 680, -1020, 1700, 113560, -344760, 637840, -869040, -21934080, 37470720, -491589000], [8258695200, 0, -5355, -5355, 85680, 85680, 1477980, 1477980, -27760320, -27760320, -122897250], [2064673800, -2856, 0, -2856, -442680, 1413720, -442680, 1413720, 70120512, -135374400, 2064673800], [-7865424000, 0, 5355, 5355, -342720, -342720, -1735020, -1735020, 94590720, 94590720, 516168450], [-1966356000, 2720, 1020, 1700, 291040, -1215840, -233240, -691560, 1370880, 60775680, -1966356000], [1480550400, 0, -1020, -1020, 261120, 261120, 342720, 342720, -21934080, -21934080, -491589000], [370137600, -512, -240, -272, 43520, 130560, 76160, 97920, -4386816, -7311360, 370137600], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 92534400]] | |
** Toom-6.5 ["1/0", "1/4", "-1/4", "4/1", "-4/1", "1/2", "-1/2", "2/1", "-2/1", "1/1", "-1/1", "0/1"] : 7*6, 8*5, 9*4, 10*3, 11*2 | |
Matrix[[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1/5783400, 1/5783400, 4/5783400, 4/5783400, -680/5783400, -680/5783400, -1360/5783400, -1360/5783400, 91392/5783400, 91392/5783400, -1], [-493034850/23133600, 1/23133600, -1/23133600, 64/23133600, -64/23133600, -1360/23133600, 1360/23133600, -10880/23133600, 10880/23133600, 365568/23133600, -365568/23133600, 0], [0, -1/272160, -1/272160, -1/272160, -1/272160, 674/272160, 674/272160, 1108/272160, 1108/272160, -87360/272160, -87360/272160, 5800410/272160], [98606970/1088640, -1/1088640, 1/1088640, -16/1088640, 16/1088640, 1348/1088640, -1348/1088640, 8864/1088640, -8864/1088640, -349440/1088640, 349440/1088640, 0], [0, 4/259200, 4/259200, 1/259200, 1/259200, -2600/259200, -2600/259200, -1300/259200, -1300/259200, 287808/259200, 287808/259200, -23477850/259200], [-23477850/259200, 1/259200, -1/259200, 4/259200, -4/259200, -1300/259200, 1300/259200, -2600/259200, 2600/259200, 287808/259200, -287808/259200, 0], [0, -16/1088640, -16/1088640, -1/1088640, -1/1088640, 8864/1088640, 8864/1088640, 1348/1088640, 1348/1088640, -349440/1088640, -349440/1088640, 98606970/1088640], [5800410/272160, -1/272160, 1/272160, -1/272160, 1/272160, 1108/272160, -1108/272160, 674/272160, -674/272160, -87360/272160, 87360/272160, 0], [0, 64/23133600, 64/23133600, 1/23133600, 1/23133600, -10880/23133600, -10880/23133600, -1360/23133600, -1360/23133600, 365568/23133600, 365568/23133600, -493034850/23133600], [-1, 4/5783400, -4/5783400, 1/5783400, -1/5783400, -1360/5783400, 1360/5783400, -680/5783400, 680/5783400, 91392/5783400, -91392/5783400, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]] | |
1/92534400 * Matrix[[92534400, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 16, 16, 64, 64, -10880, -10880, -21760, -21760, 1462272, 1462272, -92534400], [-1972139400, 4, -4, 256, -256, -5440, 5440, -43520, 43520, 1462272, -1462272, 0], [0, -340, -340, -340, -340, 229160, 229160, 376720, 376720, -29702400, -29702400, 1972139400], [8381592450, -85, 85, -1360, 1360, 114580, -114580, 753440, -753440, -29702400, 29702400, 0], [0, 1428, 1428, 357, 357, -928200, -928200, -464100, -464100, 102747456, 102747456, -8381592450], [-8381592450, 357, -357, 1428, -1428, -464100, 464100, -928200, 928200, 102747456, -102747456, 0], [0, -1360, -1360, -85, -85, 753440, 753440, 114580, 114580, -29702400, -29702400, 8381592450], [1972139400, -340, 340, -340, 340, 376720, -376720, 229160, -229160, -29702400, 29702400, 0], [0, 256, 256, 4, 4, -43520, -43520, -5440, -5440, 1462272, 1462272, -1972139400], [-92534400, 64, -64, 16, -16, -21760, 21760, -10880, 10880, 1462272, -1462272, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 92534400]] | |
** Toom-7.0 ["1/0", "-8/1", "1/4", "-1/4", "4/1", "-4/1", "1/2", "-1/2", "2/1", "-2/1", "1/1", "-1/1", "0/1"] : 7*7, 8*6, 9*5, 10*4, 11*3, 12*2 | |
Matrix[[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [8, -1/5916418200, 31/5916418200, 33/5916418200, 341/5916418200, 1023/5916418200, -40920/5916418200, -46376/5916418200, -139128/5916418200, -231880/5916418200, 10388224/5916418200, 13356288/5916418200, -739552275/5916418200], [-493034850/23133600, 0, 1/23133600, 1/23133600, 16/23133600, 16/23133600, -1360/23133600, -1360/23133600, -5440/23133600, -5440/23133600, 365568/23133600, 365568/23133600, -1], [-47331345600/277603200, 1/277603200, -28/277603200, -36/277603200, 427/277603200, -1791/277603200, 32760/277603200, 54536/277603200, 8568/277603200, 362440/277603200, -6001408/277603200, -17743104/277603200, 739552275/277603200], [98606970/1088640, 0, -1/1088640, -1/1088640, -4/1088640, -4/1088640, 1348/1088640, 1348/1088640, 4432/1088640, 4432/1088640, -349440/1088640, -349440/1088640, 23201640/1088640], [47331345600/65318400, -1/65318400, 16/65318400, 48/65318400, -619/65318400, 1983/65318400, -480/65318400, -86816/65318400, 392712/65318400, -763720/65318400, -10578176/65318400, 34322688/65318400, -739552275/65318400], [-23477850/259200, 0, 1/259200, 1/259200, 1/259200, 1/259200, -1300/259200, -1300/259200, -1300/259200, -1300/259200, 287808/259200, 287808/259200, -23477850/259200], [-47331345600/65318400, 1/65318400, 32/65318400, -96/65318400, 667/65318400, -2031/65318400, -122880/65318400, 210176/65318400, -516072/65318400, 887080/65318400, 62139392/65318400, -85883904/65318400, 739552275/65318400], [23201640/1088640, 0, -4/1088640, -4/1088640, -1/1088640, -1/1088640, 4432/1088640, 4432/1088640, 1348/1088640, 1348/1088640, -349440/1088640, -349440/1088640, 98606970/1088640], [47331345600/277603200, -1/277603200, -224/277603200, 288/277603200, -679/277603200, 2043/277603200, 524160/277603200, -611456/277603200, 548352/277603200, -919360/277603200, -78718976/277603200, 102463488/277603200, -739552275/277603200], [-1, 0, 16/23133600, 16/23133600, 1/23133600, 1/23133600, -5440/23133600, -5440/23133600, -1360/23133600, -1360/23133600, 365568/23133600, 365568/23133600, -493034850/23133600], [-8, 1/5916418200, 992/5916418200, -1056/5916418200, 682/5916418200, -2046/5916418200, -654720/5916418200, 742016/5916418200, -556512/5916418200, 927520/5916418200, 83105792/5916418200, -106850304/5916418200, 739552275/5916418200], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]] | |
1/378650764800 * Matrix[[378650764800, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [3029206118400, -64, 1984, 2112, 21824, 65472, -2618880, -2968064, -8904192, -14840320, 664846336, 854802432, -47331345600], [-8069994424800, 0, 16368, 16368, 261888, 261888, -22260480, -22260480, -89041920, -89041920, 5983617024, 5983617024, -378650764800], [-64559955398400, 1364, -38192, -49104, 582428, -2442924, 44684640, 74387104, 11686752, 494368160, -8185920512, -24201593856, 1008749303100], [34297476305400, 0, -347820, -347820, -1391280, -1391280, 468861360, 468861360, 1541538240, 1541538240, -121542220800, -121542220800, 8069994424800], [274379810443200, -5797, 92752, 278256, -3588343, 11495451, -2782560, -503272352, 2276551464, -4427284840, -61321686272, 198968622336, -4287184538175], [-34297476305400, 0, 1460844, 1460844, 1460844, 1460844, -1899097200, -1899097200, -1899097200, -1899097200, 420442589952, 420442589952, -34297476305400], [-274379810443200, 5797, 185504, -556512, 3866599, -11773707, -712335360, 1218390272, -2991669384, 5142402760, 360222055424, -497868991488, 4287184538175], [8069994424800, 0, -1391280, -1391280, -347820, -347820, 1541538240, 1541538240, 468861360, 468861360, -121542220800, -121542220800, 34297476305400], [64559955398400, -1364, -305536, 392832, -926156, 2786652, 714954240, -834025984, 747952128, -1254007040, -107372683264, 139760197632, -1008749303100], [-378650764800, 0, 261888, 261888, 16368, 16368, -89041920, -89041920, -22260480, -22260480, 5983617024, 5983617024, -8069994424800], [-3029206118400, 64, 63488, -67584, 43648, -130944, -41902080, 47489024, -35616768, 59361280, 5318770688, -6838419456, 47331345600], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 378650764800]] | |
** Toom-7.5 ["1/0", "8/1", "-8/1", "1/4", "-1/4", "4/1", "-4/1", "1/2", "-1/2", "2/1", "-2/1", "1/1", "-1/1", "0/1"] : 8*7, 9*6, 10*5, 11*4, 12*3, 13*2 | |
Matrix[[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1/94662691200, 1/94662691200, -16/94662691200, -16/94662691200, -1364/94662691200, -1364/94662691200, 43648/94662691200, 43648/94662691200, 371008/94662691200, 371008/94662691200, -23744512/94662691200, -23744512/94662691200, 1479104550/94662691200], [-2018977710750/23665672800, 2/23665672800, -2/23665672800, -1/23665672800, 1/23665672800, -1364/23665672800, 1364/23665672800, 5456/23665672800, -5456/23665672800, 185504/23665672800, -185504/23665672800, -5936128/23665672800, 5936128/23665672800, 0], [0, -1/4441651200, -1/4441651200, 64/4441651200, 64/4441651200, 4436/4441651200, 4436/4441651200, -174208/4441651200, -174208/4441651200, -1415488/4441651200, -1415488/4441651200, 93933568/4441651200, 93933568/4441651200, -5920755750/4441651200], [807591084300/555206400, -1/555206400, 1/555206400, 2/555206400, -2/555206400, 2218/555206400, -2218/555206400, -10888/555206400, 10888/555206400, -353872/555206400, 353872/555206400, 11741696/555206400, -11741696/555206400, 0], [0, 1/1045094400, 1/1045094400, -256/1045094400, -256/1045094400, -5204/1045094400, -5204/1045094400, 690688/1045094400, 690688/1045094400, 4625728/1045094400, 4625728/1045094400, -359206912/1045094400, -359206912/1045094400, 23752678950/1045094400], [-769134366000/130636800, 1/130636800, -1/130636800, -8/130636800, 8/130636800, -2602/130636800, 2602/130636800, 43168/130636800, -43168/130636800, 1156432/130636800, -1156432/130636800, -44900864/130636800, 44900864/130636800, 0], [0, -1/1045094400, -1/1045094400, 1024/1045094400, 1024/1045094400, 5396/1045094400, 5396/1045094400, -2664448/1045094400, -2664448/1045094400, -5612608/1045094400, -5612608/1045094400, 1184186368/1045094400, 1184186368/1045094400, -96141795750/1045094400], [760085726400/130636800, -1/130636800, 1/130636800, 32/130636800, -32/130636800, 2698/130636800, -2698/130636800, -166528/130636800, 166528/130636800, -1403152/130636800, 1403152/130636800, 148023296/130636800, -148023296/130636800, 0], [0, 1/4441651200, 1/4441651200, -4096/4441651200, -4096/4441651200, -5444/4441651200, -5444/4441651200, 9084928/4441651200, 9084928/4441651200, 5870848/4441651200, 5870848/4441651200, -1449459712/4441651200, -1449459712/4441651200, 403795542150/4441651200], [-1365, 1/555206400, -1/555206400, -128/555206400, 128/555206400, -2722/555206400, 2722/555206400, 567808/555206400, -567808/555206400, 1467712/555206400, -1467712/555206400, -181182464/555206400, 181182464/555206400, 0], [0, -1/94662691200, -1/94662691200, 16384/94662691200, 16384/94662691200, 5456/94662691200, 5456/94662691200, -11173888/94662691200, -11173888/94662691200, -5936128/94662691200, -5936128/94662691200, 1519648768/94662691200, 1519648768/94662691200, -2018977710750/94662691200], [64, -1/11832836400, 1/11832836400, 512/11832836400, -512/11832836400, 2728/11832836400, -2728/11832836400, -698368/11832836400, 698368/11832836400, -1484032/11832836400, 1484032/11832836400, 189956096/11832836400, -189956096/11832836400, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]] | |
1/6058412236800 * Matrix[[6058412236800, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 64, 64, -1024, -1024, -87296, -87296, 2793472, 2793472, 23744512, 23744512, -1519648768, -1519648768, 94662691200], [-516858293952000, 512, -512, -256, 256, -349184, 349184, 1396736, -1396736, 47489024, -47489024, -1519648768, 1519648768, 0], [0, -1364, -1364, 87296, 87296, 6050704, 6050704, -237619712, -237619712, -1930725632, -1930725632, 128125386752, 128125386752, -8075910843000], [8812433911881600, -10912, 10912, 21824, -21824, 24202816, -24202816, -118809856, 118809856, -3861451264, 3861451264, 128125386752, -128125386752, 0], [0, 5797, 5797, -1484032, -1484032, -30167588, -30167588, 4003918336, 4003918336, 26815345216, 26815345216, -2082322468864, -2082322468864, 137694279873150], [-35669375357616000, 46376, -46376, -371008, 371008, -120670352, 120670352, 2001959168, -2001959168, 53630690432, -53630690432, -2082322468864, 2082322468864, 0], [0, -5797, -5797, 5936128, 5936128, 31280612, 31280612, -15445805056, -15445805056, -32536288576, -32536288576, 6864728375296, 6864728375296, -557333989962750], [35249735647526400, -46376, 46376, 1484032, -1484032, 125122448, -125122448, -7722902528, 7722902528, -65072577152, 65072577152, 6864728375296, -6864728375296, 0], [0, 1364, 1364, -5586944, -5586944, -7425616, -7425616, 12391841792, 12391841792, 8007836672, 8007836672, -1977063047168, -1977063047168, 550777119492600], [-8269732703232000, 10912, -10912, -1396736, 1396736, -29702464, 29702464, 6195920896, -6195920896, 16015673344, -16015673344, -1977063047168, 1977063047168, 0], [0, -64, -64, 1048576, 1048576, 349184, 349184, -715128832, -715128832, -379912192, -379912192, 97257521152, 97257521152, -129214573488000], [387738383155200, -512, 512, 262144, -262144, 1396736, -1396736, -357564416, 357564416, -759824384, 759824384, 97257521152, -97257521152, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6058412236800]] | |
** Toom-8.0 ["1/0", "-1/8", "8/1", "-8/1", "1/4", "-1/4", "4/1", "-4/1", "1/2", "-1/2", "2/1", "-2/1", "1/1", "-1/1", "0/1"] : 8*8, 9*7, 10*6, 11*5, 12*4, 13*3, 14*2 | |
Matrix[[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [6056933132250/48455465058000, -2/48455465058000, 63/48455465058000, -65/48455465058000, -5460/48455465058000, 16380/48455465058000, -169260/48455465058000, 180180/48455465058000, 17873856/48455465058000, -29789760/48455465058000, 89369280/48455465058000, -101285184/48455465058000, -10803752960/48455465058000, 13890539520/48455465058000, 6056933132250/48455465058000], [-8075910843000/94662691200, 0, 1/94662691200, 1/94662691200, -4/94662691200, -4/94662691200, -1364/94662691200, -1364/94662691200, 21824/94662691200, 21824/94662691200, 371008/94662691200, 371008/94662691200, -23744512/94662691200, -23744512/94662691200, 1479104550/94662691200], [-6056933132250/567976147200, 2/567976147200, -15/567976147200, 17/567976147200, 5454/567976147200, -16374/567976147200, 136524/567976147200, -147444/567976147200, -17808384/567976147200, 29724288/567976147200, -84917184/567976147200, 96833088/567976147200, 10661285888/567976147200, -13748072448/567976147200, -6056933132250/567976147200], [6460728674400/4441651200, 0, -1/4441651200, -1/4441651200, 16/4441651200, 16/4441651200, 4436/4441651200, 4436/4441651200, -87104/4441651200, -87104/4441651200, -1415488/4441651200, -1415488/4441651200, 93933568/4441651200, 93933568/4441651200, -5920755750/4441651200], [6056933132250/33312384000, -2/33312384000, 3/33312384000, -5/33312384000, -5430/33312384000, 16350/33312384000, -36180/33312384000, 47100/33312384000, 17547216/33312384000, -29463120/33312384000, 68136960/33312384000, -80052864/33312384000, -10099251200/33312384000, 13186037760/33312384000, 6056933132250/33312384000], [-6153074928000/1045094400, 0, 1/1045094400, 1/1045094400, -64/1045094400, -64/1045094400, -5204/1045094400, -5204/1045094400, 345344/1045094400, 345344/1045094400, 4625728/1045094400, 4625728/1045094400, -359206912/1045094400, -359206912/1045094400, 23752678950/1045094400], [-3028466566125/4115059200, 1/4115059200, 0, 1/4115059200, 2667/4115059200, -8127/4115059200, 2667/4115059200, -8127/4115059200, -8257032/4115059200, 14214984/4115059200, -8257032/4115059200, 14214984/4115059200, 3987499264/4115059200, -5530892544/4115059200, -3028466566125/4115059200], [6080685811200/1045094400, 0, -1/1045094400, -1/1045094400, 256/1045094400, 256/1045094400, 5396/1045094400, 5396/1045094400, -1332224/1045094400, -1332224/1045094400, -5612608/1045094400, -5612608/1045094400, 1184186368/1045094400, 1184186368/1045094400, -96141795750/1045094400], [24227732529000/33312384000, -8/33312384000, -3/33312384000, -5/33312384000, -19800/33312384000, 63480/33312384000, 10950/33312384000, 32730/33312384000, 50263104/33312384000, -97926720/33312384000, -326640/33312384000, -47336976/33312384000, -5469071360/33312384000, 17816217600/33312384000, 24227732529000/33312384000], [-1365, 0, 1/4441651200, 1/4441651200, -1024/4441651200, -1024/4441651200, -5444/4441651200, -5444/4441651200, 4542464/4441651200, 4542464/4441651200, 5870848/4441651200, 5870848/4441651200, -1449459712/4441651200, -1449459712/4441651200, 403795542150/4441651200], [-96910930116000/567976147200, 32/567976147200, 15/567976147200, 17/567976147200, 54624/567976147200, -229344/567976147200, -76446/567976147200, -98274/567976147200, 4452096/567976147200, 186202368/567976147200, 71560896/567976147200, 119093568/567976147200, -12489613312/567976147200, -36898971648/567976147200, -96910930116000/567976147200], [64, 0, -1/94662691200, -1/94662691200, 4096/94662691200, 4096/94662691200, 5456/94662691200, 5456/94662691200, -5586944/94662691200, -5586944/94662691200, -5936128/94662691200, -5936128/94662691200, 1519648768/94662691200, 1519648768/94662691200, -2018977710750/94662691200], [8, -128/48455465058000, -63/48455465058000, -65/48455465058000, 174720/48455465058000, 524160/48455465058000, 338520/48455465058000, 360360/48455465058000, -285981696/48455465058000, -476636160/48455465058000, -357477120/48455465058000, -405140736/48455465058000, 86430023680/48455465058000, 111124316160/48455465058000, 8], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]] | |
1/24809198109696000 * Matrix[[24809198109696000, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [3101149763712000, -1024, 32256, -33280, -2795520, 8386560, -86661120, 92252160, 9151414272, -15252357120, 45757071360, -51858014208, -5531521515520, 7111956234240, 3101149763712000], [-2116534713733440000, 0, 262080, 262080, -1048320, -1048320, -357477120, -357477120, 5719633920, 5719633920, 97233776640, 97233776640, -6222961704960, -6222961704960, 387643720464000], [-264566839216680000, 87360, -655200, 742560, 238230720, -715216320, 5963368320, -6440353920, -777870213120, 1298356899840, -3709182597120, 4229669283840, 465684967587840, -600515804528640, -264566839216680000], [36086916869155152000, 0, -5585580, -5585580, 89369280, 89369280, 24777632880, 24777632880, -486526360320, -486526360320, -7906321463040, -7906321463040, 524673458749440, 524673458749440, -33070854902085000], [4510864608644394000, -1489488, 2234232, -3723720, -4043959920, 12176564400, -26944837920, 35077442400, 13068183832704, -21942481841280, 50744592138240, -59618890146816, -7521356735692800, 9820222505533440, 4510864608644394000], [-146066092089437520000, 0, 23738715, 23738715, -1519277760, -1519277760, -123536272860, -123536272860, 8198022792960, 8198022792960, 109808838659520, 109808838659520, -8527110509998080, -8527110509998080, 563858076080549250], [-18258261511179690000, 6028880, 0, 6028880, 16079022960, -48996707760, 16079022960, -48996707760, -49780655084160, 85700432737920, -49780655084160, 85700432737920, 24040154562744320, -33345087440670720, -18258261511179690000], [144347667476620608000, 0, -23738715, -23738715, 6077111040, 6077111040, 128094106140, 128094106140, -31625285852160, -31625285852160, -133236101718720, -133236101718720, 28111062696837120, 28111062696837120, -2282282688897461250], [18043458434577576000, -5957952, -2234232, -3723720, -14745931200, 47276349120, 8154946800, 24375471120, 37433145125376, -72930337159680, -243263180160, -35253928854144, -4073058080931840, 13268521160294400, 18043458434577576000], [-33864555419735040000, 0, 5585580, 5585580, -5719633920, -5719633920, -30407897520, -30407897520, 25372296069120, 25372296069120, 32792091171840, 32792091171840, -8096073178152960, -8096073178152960, 2255432304322197000], [-4233069427466880000, 1397760, 655200, 742560, 2385976320, -10017745920, -3339161280, -4292608320, 194467553280, 8133319434240, 3125779937280, 5202007050240, -545546309468160, -1611747081584640, -4233069427466880000], [1587788679020544000, 0, -262080, -262080, 1073479680, 1073479680, 1429908480, 1429908480, -1464226283520, -1464226283520, -1555740426240, -1555740426240, 398269549117440, 398269549117440, -529133678433360000], [198473584877568000, -65536, -32256, -33280, 89456640, 268369920, 173322240, 184504320, -146422628352, -244037713920, -183028285440, -207432056832, 44252172124160, 56895649873920, 198473584877568000], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 24809198109696000]] | |
** Toom-8.5 ["1/0", "1/8", "-1/8", "8/1", "-8/1", "1/4", "-1/4", "4/1", "-4/1", "1/2", "-1/2", "2/1", "-2/1", "1/1", "-1/1", "0/1"] : 9*8, 10*7, 11*6, 12*5, 13*4, 14*3, 15*2 | |
Matrix[[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1/48455465058000, 1/48455465058000, 8/48455465058000, 8/48455465058000, -10920/48455465058000, -10920/48455465058000, -43680/48455465058000, -43680/48455465058000, 23831808/48455465058000, 23831808/48455465058000, 47663616/48455465058000, 47663616/48455465058000, -12347146240/48455465058000, -12347146240/48455465058000, -1], [-33076911835217250/387643720464000, 1/387643720464000, -1/387643720464000, 512/387643720464000, -512/387643720464000, -21840/387643720464000, 21840/387643720464000, -1397760/387643720464000, 1397760/387643720464000, 95327232/387643720464000, -95327232/387643720464000, 762617856/387643720464000, -762617856/387643720464000, -98777169920/387643720464000, 98777169920/387643720464000, 0], [0, -1/567976147200, -1/567976147200, -2/567976147200, -2/567976147200, 10914/567976147200, 10914/567976147200, 35496/567976147200, 35496/567976147200, -23766336/567976147200, -23766336/567976147200, -45437568/567976147200, -45437568/567976147200, 12204679168/567976147200, 12204679168/567976147200, 48464339685300/567976147200], [6615382367043450/4543809177600, -1/4543809177600, 1/4543809177600, -128/4543809177600, 128/4543809177600, 21828/4543809177600, -21828/4543809177600, 1135872/4543809177600, -1135872/4543809177600, -95065344/4543809177600, 95065344/4543809177600, -727001088/4543809177600, 727001088/4543809177600, 97637433344/4543809177600, -97637433344/4543809177600, 0], [0, 2/66624768000, 2/66624768000, 1/66624768000, 1/66624768000, -21780/66624768000, -21780/66624768000, -20820/66624768000, -20820/66624768000, 47010336/66624768000, 47010336/66624768000, 74094912/66624768000, 74094912/66624768000, -23285288960/66624768000, -23285288960/66624768000, -96999741452250/66624768000], [-1575091039772250/266499072000, 1/266499072000, -1/266499072000, 32/266499072000, -32/266499072000, -21780/266499072000, 21780/266499072000, -333120/266499072000, 333120/266499072000, 94020672/266499072000, -94020672/266499072000, 592759296/266499072000, -592759296/266499072000, -93141155840/266499072000, 93141155840/266499072000, 0], [0, -8/65840947200, -8/65840947200, -1/65840947200, -1/65840947200, 86352/65840947200, 86352/65840947200, 21588/65840947200, 21588/65840947200, -179776128/65840947200, -179776128/65840947200, -89888064/65840947200, -89888064/65840947200, 76147134464/65840947200, 76147134464/65840947200, 389140139237850/65840947200], [389140139237850/65840947200, -1/65840947200, 1/65840947200, -8/65840947200, 8/65840947200, 21588/65840947200, -21588/65840947200, 86352/65840947200, -86352/65840947200, -89888064/65840947200, 89888064/65840947200, -179776128/65840947200, 179776128/65840947200, 76147134464/65840947200, -76147134464/65840947200, 0], [0, 32/266499072000, 32/266499072000, 1/266499072000, 1/266499072000, -333120/266499072000, -333120/266499072000, -21780/266499072000, -21780/266499072000, 592759296/266499072000, 592759296/266499072000, 94020672/266499072000, 94020672/266499072000, -93141155840/266499072000, -93141155840/266499072000, -1575091039772250/266499072000], [-96999741452250/66624768000, 1/66624768000, -1/66624768000, 2/66624768000, -2/66624768000, -20820/66624768000, 20820/66624768000, -21780/66624768000, 21780/66624768000, 74094912/66624768000, -74094912/66624768000, 47010336/66624768000, -47010336/66624768000, -23285288960/66624768000, 23285288960/66624768000, 0], [0, -128/4543809177600, -128/4543809177600, -1/4543809177600, -1/4543809177600, 1135872/4543809177600, 1135872/4543809177600, 21828/4543809177600, 21828/4543809177600, -727001088/4543809177600, -727001088/4543809177600, -95065344/4543809177600, -95065344/4543809177600, 97637433344/4543809177600, 97637433344/4543809177600, 6615382367043450/4543809177600], [48464339685300/567976147200, -2/567976147200, 2/567976147200, -1/567976147200, 1/567976147200, 35496/567976147200, -35496/567976147200, 10914/567976147200, -10914/567976147200, -45437568/567976147200, 45437568/567976147200, -23766336/567976147200, 23766336/567976147200, 12204679168/567976147200, -12204679168/567976147200, 0], [0, 512/387643720464000, 512/387643720464000, 1/387643720464000, 1/387643720464000, -1397760/387643720464000, -1397760/387643720464000, -21840/387643720464000, -21840/387643720464000, 762617856/387643720464000, 762617856/387643720464000, 95327232/387643720464000, 95327232/387643720464000, -98777169920/387643720464000, -98777169920/387643720464000, -33076911835217250/387643720464000], [-1, 8/48455465058000, -8/48455465058000, 1/48455465058000, -1/48455465058000, -43680/48455465058000, 43680/48455465058000, -10920/48455465058000, 10920/48455465058000, 47663616/48455465058000, -47663616/48455465058000, 23831808/48455465058000, -23831808/48455465058000, -12347146240/48455465058000, 12347146240/48455465058000, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]] | |
1/24809198109696000 * Matrix[[24809198109696000, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 512, 512, 4096, 4096, -5591040, -5591040, -22364160, -22364160, 12201885696, 12201885696, 24403771392, 24403771392, -6321738874880, -6321738874880, -24809198109696000], [-2116922357453904000, 64, -64, 32768, -32768, -1397760, 1397760, -89456640, 89456640, 6100942848, -6100942848, 48807542784, -48807542784, -6321738874880, 6321738874880, 0], [0, -43680, -43680, -87360, -87360, 476723520, 476723520, 1550465280, 1550465280, -1038113556480, -1038113556480, -1984712970240, -1984712970240, 533100386058240, 533100386058240, 2116922357453904000], [36119987724057237000, -5460, 5460, -698880, 698880, 119180880, -119180880, 6201861120, -6201861120, -519056778240, 519056778240, -3969425940480, 3969425940480, 533100386058240, -533100386058240, 0], [0, 744744, 744744, 372372, 372372, -8110262160, -8110262160, -7752785040, -7752785040, 17505332836992, 17505332836992, 27590870571264, 27590870571264, -8670789620613120, -8670789620613120, -36119987724057237000], [-146629950165518069250, 93093, -93093, 2978976, -2978976, -2027565540, 2027565540, -31011140160, 31011140160, 8752666418496, -8752666418496, 55181741142528, -55181741142528, -8670789620613120, 8670789620613120, 0], [0, -3014440, -3014440, -376805, -376805, 32537865360, 32537865360, 8134466340, 8134466340, -67740543911040, -67740543911040, -33870271955520, -33870271955520, 28692621001707520, 28692621001707520, 146629950165518069250], [146629950165518069250, -376805, 376805, -3014440, 3014440, 8134466340, -8134466340, 32537865360, -32537865360, -33870271955520, 33870271955520, -67740543911040, 67740543911040, 28692621001707520, -28692621001707520, 0], [0, 2978976, 2978976, 93093, 93093, -31011140160, -31011140160, -2027565540, -2027565540, 55181741142528, 55181741142528, 8752666418496, 8752666418496, -8670789620613120, -8670789620613120, -146629950165518069250], [-36119987724057237000, 372372, -372372, 744744, -744744, -7752785040, 7752785040, -8110262160, 8110262160, 27590870571264, -27590870571264, 17505332836992, -17505332836992, -8670789620613120, 8670789620613120, 0], [0, -698880, -698880, -5460, -5460, 6201861120, 6201861120, 119180880, 119180880, -3969425940480, -3969425940480, -519056778240, -519056778240, 533100386058240, 533100386058240, 36119987724057237000], [2116922357453904000, -87360, 87360, -43680, 43680, 1550465280, -1550465280, 476723520, -476723520, -1984712970240, 1984712970240, -1038113556480, 1038113556480, 533100386058240, -533100386058240, 0], [0, 32768, 32768, 64, 64, -89456640, -89456640, -1397760, -1397760, 48807542784, 48807542784, 6100942848, 6100942848, -6321738874880, -6321738874880, -2116922357453904000], [-24809198109696000, 4096, -4096, 512, -512, -22364160, 22364160, -5591040, 5591040, 24403771392, -24403771392, 12201885696, -12201885696, -6321738874880, 6321738874880, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 24809198109696000]] | |
** Toom-9.0 ["1/0", "-16/1", "1/8", "-1/8", "8/1", "-8/1", "1/4", "-1/4", "4/1", "-4/1", "1/2", "-1/2", "2/1", "-2/1", "1/1", "-1/1", "0/1"] : 9*9, 10*8, 11*7, 12*6, 13*5, 14*4, 15*3, 16*2 | |
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** Toom-9.5 ["1/0", "16/1", "-16/1", "1/8", "-1/8", "8/1", "-8/1", "1/4", "-1/4", "4/1", "-4/1", "1/2", "-1/2", "2/1", "-2/1", "1/1", "-1/1", "0/1"] : 10*9, 11*8, 12*7, 13*6, 14*5, 15*4, 16*3, 17*2 | |
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** Toom-10.0 ["1/0", "-1/16", "16/1", "-16/1", "1/8", "-1/8", "8/1", "-8/1", "1/4", "-1/4", "4/1", "-4/1", "1/2", "-1/2", "2/1", "-2/1", "1/1", "-1/1", "0/1"] : 10*10, 11*9, 12*8, 13*7, 14*6, 15*5, 16*4, 17*3, 18*2 | |
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** Toom-10.5 ["1/0", "1/16", "-1/16", "16/1", "-16/1", "1/8", "-1/8", "8/1", "-8/1", "1/4", "-1/4", "4/1", "-4/1", "1/2", "-1/2", "2/1", "-2/1", "1/1", "-1/1", "0/1"] : 11*10, 12*9, 13*8, 14*7, 15*6, 16*5, 17*4, 18*3, 19*2 | |
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** Toom-11.0 ["1/0", "-32/1", "1/16", "-1/16", "16/1", "-16/1", "1/8", "-1/8", "8/1", "-8/1", "1/4", "-1/4", "4/1", "-4/1", "1/2", "-1/2", "2/1", "-2/1", "1/1", "-1/1", "0/1"] : 11*11, 12*10, 13*9, 14*8, 15*7, 16*6, 17*5, 18*4, 19*3, 20*2 | |
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** Toom-11.5 ["1/0", "32/1", "-32/1", "1/16", "-1/16", "16/1", "-16/1", "1/8", "-1/8", "8/1", "-8/1", "1/4", "-1/4", "4/1", "-4/1", "1/2", "-1/2", "2/1", "-2/1", "1/1", "-1/1", "0/1"] : 12*11, 13*10, 14*9, 15*8, 16*7, 17*6, 18*5, 19*4, 20*3, 21*2 | |
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** Toom-12.0 ["1/0", "-1/32", "32/1", "-32/1", "1/16", "-1/16", "16/1", "-16/1", "1/8", "-1/8", "8/1", "-8/1", "1/4", "-1/4", "4/1", "-4/1", "1/2", "-1/2", "2/1", "-2/1", "1/1", "-1/1", "0/1"] : 12*12, 13*11, 14*10, 15*9, 16*8, 17*7, 18*6, 19*5, 20*4, 21*3, 22*2 | |
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** Toom-12.5 ["1/0", "1/32", "-1/32", "32/1", "-32/1", "1/16", "-1/16", "16/1", "-16/1", "1/8", "-1/8", "8/1", "-8/1", "1/4", "-1/4", "4/1", "-4/1", "1/2", "-1/2", "2/1", "-2/1", "1/1", "-1/1", "0/1"] : 13*12, 14*11, 15*10, 16*9, 17*8, 18*7, 19*6, 20*5, 21*4, 22*3, 23*2 | |
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** Toom-13.0 ["1/0", "-64/1", "1/32", "-1/32", "32/1", "-32/1", "1/16", "-1/16", "16/1", "-16/1", "1/8", "-1/8", "8/1", "-8/1", "1/4", "-1/4", "4/1", "-4/1", "1/2", "-1/2", "2/1", "-2/1", "1/1", "-1/1", "0/1"] : 13*13, 14*12, 15*11, 16*10, 17*9, 18*8, 19*7, 20*6, 21*5, 22*4, 23*3, 24*2 | |
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** Toom-13.5 ["1/0", "64/1", "-64/1", "1/32", "-1/32", "32/1", "-32/1", "1/16", "-1/16", "16/1", "-16/1", "1/8", "-1/8", "8/1", "-8/1", "1/4", "-1/4", "4/1", "-4/1", "1/2", "-1/2", "2/1", "-2/1", "1/1", "-1/1", "0/1"] : 14*13, 15*12, 16*11, 17*10, 18*9, 19*8, 20*7, 21*6, 22*5, 23*4, 24*3, 25*2 | |
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** Toom-14.0 ["1/0", "-1/64", "64/1", "-64/1", "1/32", "-1/32", "32/1", "-32/1", "1/16", "-1/16", "16/1", "-16/1", "1/8", "-1/8", "8/1", "-8/1", "1/4", "-1/4", "4/1", "-4/1", "1/2", "-1/2", "2/1", "-2/1", "1/1", "-1/1", "0/1"] : 14*14, 15*13, 16*12, 17*11, 18*10, 19*9, 20*8, 21*7, 22*6, 23*5, 24*4, 25*3, 26*2 | |
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** Toom-14.5 ["1/0", "1/64", "-1/64", "64/1", "-64/1", "1/32", "-1/32", "32/1", "-32/1", "1/16", "-1/16", "16/1", "-16/1", "1/8", "-1/8", "8/1", "-8/1", "1/4", "-1/4", "4/1", "-4/1", "1/2", "-1/2", "2/1", "-2/1", "1/1", "-1/1", "0/1"] : 15*14, 16*13, 17*12, 18*11, 19*10, 20*9, 21*8, 22*7, 23*6, 24*5, 25*4, 26*3, 27*2 | |
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** Toom-15.0 ["1/0", "-128/1", "1/64", "-1/64", "64/1", "-64/1", "1/32", "-1/32", "32/1", "-32/1", "1/16", "-1/16", "16/1", "-16/1", "1/8", "-1/8", "8/1", "-8/1", "1/4", "-1/4", "4/1", "-4/1", "1/2", "-1/2", "2/1", "-2/1", "1/1", "-1/1", "0/1"] : 15*15, 16*14, 17*13, 18*12, 19*11, 20*10, 21*9, 22*8, 23*7, 24*6, 25*5, 26*4, 27*3, 28*2 | |
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** Toom-15.5 ["1/0", "128/1", "-128/1", "1/64", "-1/64", "64/1", "-64/1", "1/32", "-1/32", "32/1", "-32/1", "1/16", "-1/16", "16/1", "-16/1", "1/8", "-1/8", "8/1", "-8/1", "1/4", "-1/4", "4/1", "-4/1", "1/2", "-1/2", "2/1", "-2/1", "1/1", "-1/1", "0/1"] : 16*15, 17*14, 18*13, 19*12, 20*11, 21*10, 22*9, 23*8, 24*7, 25*6, 26*5, 27*4, 28*3, 29*2 | |
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** Toom-16.0 ["1/0", "-1/128", "128/1", "-128/1", "1/64", "-1/64", "64/1", "-64/1", "1/32", "-1/32", "32/1", "-32/1", "1/16", "-1/16", "16/1", "-16/1", "1/8", "-1/8", "8/1", "-8/1", "1/4", "-1/4", "4/1", "-4/1", "1/2", "-1/2", "2/1", "-2/1", "1/1", "-1/1", "0/1"] : 16*16, 17*15, 18*14, 19*13, 20*12, 21*11, 22*10, 23*9, 24*8, 25*7, 26*6, 27*5, 28*4, 29*3, 30*2 | |
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** Toom-16.5 ["1/0", "1/128", "-1/128", "128/1", "-128/1", "1/64", "-1/64", "64/1", "-64/1", "1/32", "-1/32", "32/1", "-32/1", "1/16", "-1/16", "16/1", "-16/1", "1/8", "-1/8", "8/1", "-8/1", "1/4", "-1/4", "4/1", "-4/1", "1/2", "-1/2", "2/1", "-2/1", "1/1", "-1/1", "0/1"] : 17*16, 18*15, 19*14, 20*13, 21*12, 22*11, 23*10, 24*9, 25*8, 26*7, 27*6, 28*5, 29*4, 30*3, 31*2 | |
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