# 円分体上の Galois 群

・サンプル番号
・入力多項式 上の分解体の primitive element の 上の最小多項式の次数
・同じく円分体上の最小多項式の（主係数についての）次数
・各中間体の拡大次数のリスト
・組成列までの処理時間（秒）
・冪根拡大の処理時間（秒）
のリストです．

[1,x^2-2,2,2,,0.152,0.002]
[2,x^3-3*x-1,3,3,,0.137,0.003]
[3,x^4-2,8,8,[2,2,2],0.184,0.006]
[4,x^4+x^2-1,8,8,[2,2,2],0.163,0.007]
[5,x^4-2*x^3+2*x^2+2,12,12,[3,2,2],0.181,0.03]
[6,x^4+2*x^3+3*x^2+4*x+5,24,24,[2,3,2,2],0.275,0.125]
[7,x^4+x+1,24,24,[2,3,2,2],0.234,0.089]
[8,x^5-2,20,5,,0.209,0.002]
[9,x^5-5*x+12,10,10,[2,5],0.205,0.022]
[10,x^5+20*x+32,10,10,[2,5],0.192,0.027]
[11,x^5+11*x+44,10,10,[2,5],0.166,0.026]
[12,x^5+x^4-4*x^3-3*x^2+3*x+1,5,5,,0.172,0.009]
[13,x^5+100*x^2+1000,20,5,,0.21,0.012]
[14,x^6+x^3+1,6,3,,0.144,0.003]
[15,x^6-2,12,6,[2,3],0.184,0.004]
[16,x^5-5*x^3+5*x-5,20,10,[2,5],0.19,0.022]
[17,x^6+x^3+7,18,9,[3,3],0.166,0.011]
[18,x^6-3*x^4+1,24,24,[2,3,2,2],0.266,0.061]
[19,x^6+x^4-9,24,24,[2,3,2,2],0.219,0.083]
[20,x^6+x^4-8,48,48,[2,2,3,2,2],0.611,0.703]
[21,x^7+7*x^3+7*x^2+7*x-1,14,7,,0.184,0.039]
[22,x^7-14*x^5+56*x^3-56*x+22,21,7,,0.19,0.033]
[23,x^7-2,42,7,,0.21,0.004]
[24,x^8-2*x^6-x^4+7*x^2-5*x+1,16,16,[2,2,2,2],0.28,0.034]
[25,x^9+x^8+3*x^6+3*x^3-3*x^2+5*x-1,18,18,[2,3,3],0.253,0.049]
[26,x^12-3,24,12,[2,2,3],0.516,0.009]
[27,x^7-14*x^5+56*x^3-56*x+22,21,7,,0.192,0.029]
[28,
x^15-x^14-14*x^13+13*x^12+78*x^11-66*x^10-220*x^9+165*x^8+330*x^7-210*x^6
-252*x^5+126*x^4+84*x^3-28*x^2-8*x+1,15,15,[3,5],0.606,0.182]

<permutation group with 72 generators>
Welcome to Nemo version 0.13.5
0.634780 seconds (798.89 k allocations: 42.184 MiB, 1.88% gc time)
3.561398 seconds (3.36 M allocations: 1014.657 MiB, 2.55% gc time)
[29,x^6+x^4-x^2+5*x-5,72,72,[2,2,2,3,3],4.496,15.317]
*** nfisincl: Warning: increasing stack size to 16000000.
*** write: Warning: increasing stack size to 16000000.
<permutation group with 13 generators>
Welcome to Nemo version 0.13.5
0.729594 seconds (834.13 k allocations: 43.711 MiB, 8.42% gc time)
0.795107 seconds (1.01 M allocations: 50.953 MiB, 1.18% gc time)
[30,2*(x+1)^13-x^13,156,13,,12.036,12.616]
*** nfisincl: Warning: increasing stack size to 16000000.
<permutation group with 49 generators>
Welcome to Nemo version 0.13.5
0.632685 seconds (811.09 k allocations: 42.324 MiB, 9.44% gc time)
0.994494 seconds (1.16 M allocations: 75.809 MiB, 1.63% gc time)
Welcome to Nemo version 0.13.5
0.639144 seconds (811.09 k allocations: 42.326 MiB, 9.76% gc time)
0.808816 seconds (1.01 M allocations: 51.011 MiB, 1.18% gc time)
[31,
x^14+28*x^11+28*x^10-28*x^9+140*x^8+360*x^7+147*x^6+196*x^5+336*x^4-546*x^3
-532*x^2+896*x+823,98,49,[7,7],5.772,33.549]

*** nfisincl: Warning: increasing stack size to 16000000.
*** write: Warning: increasing stack size to 16000000.
<permutation group with 75 generators>
Welcome to Nemo version 0.13.5
0.635679 seconds (802.47 k allocations: 41.997 MiB, 1.84% gc time)
3.301811 seconds (2.28 M allocations: 812.627 MiB, 2.59% gc time)
Welcome to Nemo version 0.13.5
0.688764 seconds (802.47 k allocations: 41.997 MiB, 8.95% gc time)
1.009562 seconds (1.17 M allocations: 82.609 MiB, 1.53% gc time)
Welcome to Nemo version 0.13.5
0.690487 seconds (802.47 k allocations: 41.997 MiB, 8.90% gc time)
0.809244 seconds (1.01 M allocations: 50.949 MiB, 1.17% gc time)
[32,
x^15-470*x^13-305*x^12+71840*x^11+85357*x^10-4292700*x^9-3714805*x^8
+119761820*x^7+25284495*x^6-1542190154*x^5+717324725*x^4+7178878600*x^3
-5452953875*x^2-7998223215*x+4461221029,75,75,[3,5,5],15.793,132.7]

Evaluation took 180.3810 seconds (240.6020 elapsed) using 74460.010 MB.

[1,x^2-2,2,2,,0.133,0.001]
[2,x^3-3*x-1,3,3,,0.169,0.003]
[3,x^4-2,8,8,[2,2,2],0.168,0.005]
[4,x^4+x^2-1,8,8,[2,2,2],0.16,0.007]
[5,x^4-2*x^3+2*x^2+2,12,12,[3,2,2],0.174,0.029]
[6,x^4+2*x^3+3*x^2+4*x+5,24,24,[2,3,2,2],0.273,0.126]
[7,x^4+x+1,24,24,[2,3,2,2],0.224,0.087]
[8,x^5-2,20,5,,0.182,0.002]
[9,x^5-5*x+12,10,10,[2,5],0.18,0.023]
[10,x^5+20*x+32,10,10,[2,5],0.163,0.032]
[11,x^5+11*x+44,10,10,[2,5],0.146,0.025]
[12,x^5+x^4-4*x^3-3*x^2+3*x+1,5,5,,0.141,0.008]
[13,x^5+100*x^2+1000,20,5,,0.161,0.012]
[14,x^6+x^3+1,6,3,,0.139,0.002]
[15,x^6-2,12,6,[2,3],0.167,0.004]
[16,x^5-5*x^3+5*x-5,20,10,[2,5],0.171,0.023]
[17,x^6+x^3+7,18,9,[3,3],0.162,0.009]
[18,x^6-3*x^4+1,24,24,[2,3,2,2],0.243,0.061]
[19,x^6+x^4-9,24,24,[2,3,2,2],0.218,0.083]
[20,x^6+x^4-8,48,48,[2,2,3,2,2],0.612,0.702]
[21,x^7+7*x^3+7*x^2+7*x-1,14,7,,0.17,0.04]
[22,x^7-14*x^5+56*x^3-56*x+22,21,7,,0.175,0.028]
[23,x^7-2,42,7,,0.185,0.004]
[24,x^8-2*x^6-x^4+7*x^2-5*x+1,16,16,[2,2,2,2],0.274,0.033]
[25,x^9+x^8+3*x^6+3*x^3-3*x^2+5*x-1,18,18,[2,3,3],0.241,0.048]
[26,x^12-3,24,12,[2,2,3],0.52,0.009]
[27,x^7-14*x^5+56*x^3-56*x+22,21,7,,0.177,0.029]
[28,
x^15-x^14-14*x^13+13*x^12+78*x^11-66*x^10-220*x^9+165*x^8+330*x^7-210*x^6
-252*x^5+126*x^4+84*x^3-28*x^2-8*x+1,15,15,[3,5],0.605,0.189]

<permutation group with 72 generators>
// Using locale /usr/share/locale/
// ja_JP.UTF-8
// /usr/share/locale/
// giac
// UTF-8
// Maximum number of parallel threads 2

Evaluation time: 8.8
"Done","Done","Done","Done"
// Time 8.8
// Total time 8.8
[29,x^6+x^4-x^2+5*x-5,72,72,[2,2,2,3,3],4.448,15.771]
*** nfisincl: Warning: increasing stack size to 16000000.
*** write: Warning: increasing stack size to 16000000.
<permutation group with 13 generators>
// Using locale /usr/share/locale/
// ja_JP.UTF-8
// /usr/share/locale/
// giac
// UTF-8
// Maximum number of parallel threads 2
"Done","Done","Done","Done"
// Time 0
// Total time 0
[30,2*(x+1)^13-x^13,156,13,,12.067,8.419]
*** nfisincl: Warning: increasing stack size to 16000000.
<permutation group with 49 generators>
// Using locale /usr/share/locale/
// ja_JP.UTF-8
// /usr/share/locale/
// giac
// UTF-8
// Maximum number of parallel threads 2

Evaluation time: 0.43
"Done","Done","Done","Done"
// Time 0.43
// Total time 0.43
// Using locale /usr/share/locale/
// ja_JP.UTF-8
// /usr/share/locale/
// giac
// UTF-8
// Maximum number of parallel threads 2
"Done","Done","Done","Done"
// Time 0
// Total time 0
[31,
x^14+28*x^11+28*x^10-28*x^9+140*x^8+360*x^7+147*x^6+196*x^5+336*x^4-546*x^3
-532*x^2+896*x+823,98,49,[7,7],5.794,25.028]

*** nfisincl: Warning: increasing stack size to 16000000.
*** write: Warning: increasing stack size to 16000000.
<permutation group with 75 generators>
// Using locale /usr/share/locale/
// ja_JP.UTF-8
// /usr/share/locale/
// giac
// UTF-8
// Maximum number of parallel threads 2

Evaluation time: 8.13
"Done","Done","Done","Done"
// Time 8.13
// Total time 8.13
// Using locale /usr/share/locale/
// ja_JP.UTF-8
// /usr/share/locale/
// giac
// UTF-8
// Maximum number of parallel threads 2
"Done","Done","Done","Done"
// Time 0.35
// Total time 0.35
// Using locale /usr/share/locale/
// ja_JP.UTF-8
// /usr/share/locale/
// giac
// UTF-8
// Maximum number of parallel threads 2
Evaluation took 179.0620 seconds (218.4700 elapsed) using 74669.995 MB.