Junpei Tsuji junpeitsuji
junpeitsuji
/ box_muller.rb
Last active
December 9, 2017 09:24
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| # coding: utf-8 | |
| # Box=Muller 法に基づいて, 平均 0.0 分散 1.0 の正規乱数を発生させる | |
| def box_muller | |
| x = Random.rand(1.0) | |
| y = Random.rand(1.0) | |
| z = Math.sqrt(-2.0 * Math.log(x)) * Math.cos(2.0*Math::PI*y) | |
| w = Math.sqrt(-2.0 * Math.log(x)) * Math.sin(2.0*Math::PI*y) # not use |
junpeitsuji
/ fermat_descent2.rb
Last active
December 7, 2017 05:15
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| require 'prime' | |
| # 無限降下法 (descent) | |
| # | |
| # input: (x, y, k, p) s.t. kp = x^2 + x^2 | |
| # output: (x, y, k, p) s.t. p = x^2 + x^2, k = 1 | |
| def descent(x, y, k, p) | |
| if k == 1 |
junpeitsuji
/ fermat_descent.rb
Created
December 6, 2017 07:56
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| # 無限降下法 (descent) | |
| # | |
| # input: (x, y, k, p) s.t. kp = x^2 + x^2 | |
| # output: (x, y, k, p) s.t. p = x^2 + x^2, k = 1 | |
| def descent(x, y, k, p) | |
| if k == 1 | |
| return [x, y, 1, p] | |
| else |
junpeitsuji
/ gaussian_period_result.txt
Created
October 6, 2017 11:15
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| # The Gaussian periods modulo 65537 | |
| p = 65537 | |
| g = 3 (primitive root modulo 65537) | |
| Z/pZ := [1, 3, 9, 27, 81, 243, 729, 2187, 6561, 19683, 59049, 46073, 7145, 21435, 64305, 61841, 54449, 32273, 31282, 28309, 19390, 58170, 43436, 64771, 63239, 58643, 44855, 3491, 10473, 31419, 28720, 20623, 61869, 54533, 32525, 32038, 30577, 26194, 13045, 39135, 51868, 24530, 8053, 24159, 6940, 20820, 62460, 56306, 37844, 47995, 12911, 38733, 50662, 20912, 62736, 57134, 40328, 55447, 35267, 40264, 55255, 34691, 38536, 50071, 19139, 57417, 41177, 57994, 42908, 63187, 58487, 44387, 2087, 6261, 18783, 56349, 37973, 48382, 14072, 42216, 61111, 52259, 25703, 11572, 34716, 38611, 50296, 19814, 59442, 47252, 10682, 32046, 30601, 26266, 13261, 39783, 53812, 30362, 25549, 11110, 33330, 34453, 37822, 47929, 12713, 38139, 48880, 15566, 46698, 9020, 27060, 15643, 46929, 9713, 29139, 21880, 103, 309, 927, 2781, 8343, 25029, 9550, 28650, 20413, 61239, 52643, 26855, 15028, 45084, 4178, 12534, 37602, 47269, 10733, 32199, 31060, 27643, 17392, 5 |
junpeitsuji
/ gaussian_period.rb
Created
October 6, 2017 11:13
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| # coding: utf-8 | |
| # ガウス周期の大きさ（複素数）を数値的に計算して，正負の判定を行う | |
| require 'set' | |
| require 'prime' | |
| require 'complex' | |
| # 原始根を計算する | |
| # prime |
junpeitsuji
/ The_Gaussian_periods_modulo_65537.txt
Created
August 18, 2017 11:37
The Gaussian periods modulo 65537. See https://en.wikipedia.org/wiki/Gaussian_period
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| # The Gaussian periods modulo 65537 | |
| p = 65537 | |
| g = 3 (primitive root modulo 65537) | |
| # 1 dim'l Gaussian periods: | |
| (65536, 1) = [1]+[3]+[9]+[27]+[81]+[243]+[729]+[2187]+[6561]+[19683]+[59049]+[46073]+[7145]+[21435]+[64305]+[61841]+[54449]+[32273]+[31282]+[28309]+[19390]+[58170]+[43436]+[64771]+[63239]+[58643]+[44855]+[3491]+[10473]+[31419]+[28720]+[20623]+[61869]+[54533]+[32525]+[32038]+[30577]+[26194]+[13045]+[39135]+[51868]+[24530]+[8053]+[24159]+[6940]+[20820]+[62460]+[56306]+[37844]+[47995]+[12911]+[38733]+[50662]+[20912]+[62736]+[57134]+[40328]+[55447]+[35267]+[40264]+[55255]+[34691]+[38536]+[50071]+[19139]+[57417]+[41177]+[57994]+[42908]+[63187]+[58487]+[44387]+[2087]+[6261]+[18783]+[56349]+[37973]+[48382]+[14072]+[42216]+[61111]+[52259]+[25703]+[11572]+[34716]+[38611]+[50296]+[19814]+[59442]+[47252]+[10682]+[32046]+[30601]+[26266]+[13261]+[39783]+[53812]+[30362]+[25549]+[11110]+[33330]+[34453]+[37822]+[47929]+[12713]+[38139]+[48880]+[15566]+[46698]+[9020]+[27060]+[15643]+[46929]+[9713]+[29139]+[21880]+[10 |
junpeitsuji
/ The_Gaussian_periods_modulo_257.txt
Created
August 18, 2017 11:05
The Gaussian periods modulo 257. See https://en.wikipedia.org/wiki/Gaussian_period .
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| # The Gaussian periods modulo 257 | |
| p = 257 | |
| g = 3 (primitive root modulo 257) | |
| # 1 dim'l Gaussian periods: | |
| (256, 1) = [1]+[3]+[9]+[27]+[81]+[243]+[215]+[131]+[136]+[151]+[196]+[74]+[222]+[152]+[199]+[83]+[249]+[233]+[185]+[41]+[123]+[112]+[79]+[237]+[197]+[77]+[231]+[179]+[23]+[69]+[207]+[107]+[64]+[192]+[62]+[186]+[44]+[132]+[139]+[160]+[223]+[155]+[208]+[110]+[73]+[219]+[143]+[172]+[2]+[6]+[18]+[54]+[162]+[229]+[173]+[5]+[15]+[45]+[135]+[148]+[187]+[47]+[141]+[166]+[241]+[209]+[113]+[82]+[246]+[224]+[158]+[217]+[137]+[154]+[205]+[101]+[46]+[138]+[157]+[214]+[128]+[127]+[124]+[115]+[88]+[7]+[21]+[63]+[189]+[53]+[159]+[220]+[146]+[181]+[29]+[87]+[4]+[12]+[36]+[108]+[67]+[201]+[89]+[10]+[30]+[90]+[13]+[39]+[117]+[94]+[25]+[75]+[225]+[161]+[226]+[164]+[235]+[191]+[59]+[177]+[17]+[51]+[153]+[202]+[92]+[19]+[57]+[171]+[256]+[254]+[248]+[230]+[176]+[14]+[42]+[126]+[121]+[106]+[61]+[183]+[35]+[105]+[58]+[174]+[8]+[24]+[72]+[216]+[134]+[145]+[178]+[20]+[60]+[180]+[26]+[78]+[234]+[188]+[50]+[150]+[193]+[65]+[195]+[71] |
junpeitsuji
/ dijkstra.rb
Created
January 26, 2017 07:33
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| module Dijkstra | |
| # ノード全体を格納するクラス | |
| class Nodes | |
| def initialize | |
| @done = false | |
| @map = {} | |
| end |
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| # coding: utf-8 | |
| require 'prime' | |
| # Legendre symbol | |
| def legendre(a, p) | |
| p.times do |x| | |
| if (x*x - a) % p == 0 then | |
| return 1 |
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| # zeta.rb | |
| require 'complex' | |
| LOWER_THRESHOLD = 1.0e-6 | |
| UPPER_BOUND = 1.0e+4 | |
| MAXNUM = 100 | |
| module Zeta |