R16_8=ZE3modnZObj(6+12ω,16):2有零因子交換無幺環,1,0,16,1,7,7,128,15,16
[1] => [1] 是理想 ,商環: [[1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16]]
[R16Add]
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
2 4 6 7 8 10 5 11 12 13 14 15 9 1 16 3
3 6 5 10 9 8 13 12 1 11 15 2 14 16 4 7
4 7 10 5 11 13 8 14 15 9 1 16 12 2 3 6
5 8 9 11 1 12 14 2 3 15 4 6 16 7 10 13
6 10 8 13 12 11 9 15 2 14 16 4 1 3 7 5
7 5 13 8 14 9 11 1 16 12 2 3 15 4 6 10
8 11 12 14 2 15 1 4 6 16 7 10 3 5 13 9
9 12 1 15 3 2 16 6 5 4 10 8 7 13 11 14
10 13 11 9 15 14 12 16 4 1 3 7 2 6 5 8
11 14 15 1 4 16 2 7 10 3 5 13 6 8 9 12
12 15 2 16 6 4 3 10 8 7 13 11 5 9 14 1
13 9 14 12 16 1 15 3 7 2 6 5 4 10 8 11
14 1 16 2 7 3 4 5 13 6 8 9 10 11 12 15
15 16 4 3 10 7 6 13 11 5 9 14 8 12 1 2
16 3 7 6 13 5 10 9 14 8 12 1 11 15 2 4
[R16Mul]
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 3 5 5 1 9 9 3 5 1 5 9 3 9 1 3
1 5 1 1 1 5 5 5 1 1 1 5 5 5 1 5
1 5 1 1 1 5 5 5 1 1 1 5 5 5 1 5
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 9 5 5 1 3 3 9 5 1 5 3 9 3 1 9
1 9 5 5 1 3 3 9 5 1 5 3 9 3 1 9
1 3 5 5 1 9 9 3 5 1 5 9 3 9 1 3
1 5 1 1 1 5 5 5 1 1 1 5 5 5 1 5
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 5 1 1 1 5 5 5 1 1 1 5 5 5 1 5
1 9 5 5 1 3 3 9 5 1 5 3 9 3 1 9
1 3 5 5 1 9 9 3 5 1 5 9 3 9 1 3
1 9 5 5 1 3 3 9 5 1 5 3 9 3 1 9
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 3 5 5 1 9 9 3 5 1 5 9 3 9 1 3
[2] => [1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16] 是理想 ,是中心 ,商環: [[1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16]]
[R1Add]
1
[R1Mul]
1
[3] => [1 3 5 9] 是理想 ,商環: [[1 3 5 9] [2 6 8 12] [4 10 11 15] [7 13 14 16]]
[R4Add]
1 2 3 4
2 3 4 1
3 4 1 2
4 1 2 3
[R4Mul]
1 1 1 1
1 1 1 1
1 1 1 1
1 1 1 1
[4] => [1 4 5 11] 是理想 ,商環: [[1 4 5 11] [2 7 8 14] [3 9 10 15] [6 12 13 16]]
[R4Add]
1 2 3 4
2 1 4 3
3 4 1 2
4 3 2 1
[R4Mul]
1 1 1 1
1 3 1 3
1 1 1 1
1 3 1 3
[5] => [1 5] 是理想 ,商環: [[1 5] [2 8] [3 9] [4 11] [6 12] [7 14] [10 15] [13 16]]
[R8Add]
1 2 3 4 5 6 7 8
2 4 5 6 7 1 8 3
3 5 1 7 2 8 4 6
4 6 7 1 8 2 3 5
5 7 2 8 4 3 6 1
6 1 8 2 3 4 5 7
7 8 4 3 6 5 1 2
8 3 6 5 1 7 2 4
[R8Mul]
1 1 1 1 1 1 1 1
1 3 1 1 3 3 1 3
1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1
1 3 1 1 3 3 1 3
1 3 1 1 3 3 1 3
1 1 1 1 1 1 1 1
1 3 1 1 3 3 1 3
[10] => [1 10] 是理想 ,商環: [[1 10] [2 13] [3 11] [4 9] [5 15] [6 14] [7 12] [8 16]]
[R8Add]
1 2 3 4 5 6 7 8
2 4 6 7 8 1 5 3
3 6 5 1 4 8 2 7
4 7 1 5 3 2 8 6
5 8 4 3 1 7 6 2
6 1 8 2 7 3 4 5
7 5 2 8 6 4 3 1
8 3 7 6 2 5 1 4
[R8Mul]
1 1 1 1 1 1 1 1
1 3 5 5 1 4 4 3
1 5 1 1 1 5 5 5
1 5 1 1 1 5 5 5
1 1 1 1 1 1 1 1
1 4 5 5 1 3 3 4
1 4 5 5 1 3 3 4
1 3 5 5 1 4 4 3
[15] => [1 15] 是理想 ,商環: [[1 15] [2 16] [3 4] [5 10] [6 7] [8 13] [9 11] [12 14]]
[R8Add]
1 2 3 4 5 6 7 8
2 3 5 6 4 7 8 1
3 5 4 7 6 8 1 2
4 6 7 1 8 2 3 5
5 4 6 8 7 1 2 3
6 7 8 2 1 3 5 4
7 8 1 3 2 5 4 6
8 1 2 5 3 4 6 7
[R8Mul]
1 1 1 1 1 1 1 1
1 3 4 1 7 3 4 7
1 4 1 1 4 4 1 4
1 1 1 1 1 1 1 1
1 7 4 1 3 7 4 3
1 3 4 1 7 3 4 7
1 4 1 1 4 4 1 4
1 7 4 1 3 7 4 3
[3 4] => [1 3 4 5 9 10 11 15] 是理想 ,商環: [[1 3 4 5 9 10 11 15] [2 6 7 8 12 13 14 16]]
[R2Add]
1 2
2 1
[R2Mul]
1 1
1 1
8 階子環:
[R8Add]
1 2 3 4 5 6 7 8
2 4 6 5 1 7 8 3
3 6 4 7 8 5 1 2
4 5 7 1 2 8 3 6
5 1 8 2 4 3 6 7
6 7 5 8 3 1 2 4
7 8 1 3 6 2 4 5
8 3 2 6 7 4 5 1
[R8Mul]
1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1
[5 10] => [1 5 10 15] 是理想 ,商環: [[1 5 10 15] [2 8 13 16] [3 4 9 11] [6 7 12 14]]
[R4Add]
1 2 3 4
2 3 4 1
3 4 1 2
4 1 2 3
[R4Mul]
1 1 1 1
1 3 1 3
1 1 1 1
1 3 1 3
time consume: 2.188321149s
R16_7=ZimodnZObj(1+2i,4+4i):1有零因子交換幺環,1,1,8,2,3,7,64,7,16
8階商環:R8_3、R8_21、R8_3
8階理想子環:R8_16
8階非理想子環:R8_3
[1] => [1] 是理想 ,商環: [[1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16]]
[R16Add]
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
2 4 5 7 8 9 11 12 1 13 14 15 3 6 16 10
3 5 6 8 9 10 12 1 13 11 15 2 14 16 4 7
4 7 8 11 12 1 14 15 2 3 6 16 5 9 10 13
5 8 9 12 1 13 15 2 3 14 16 4 6 10 7 11
6 9 10 1 13 11 2 3 14 15 4 5 16 7 8 12
7 11 12 14 15 2 6 16 4 5 9 10 8 1 13 3
8 12 1 15 2 3 16 4 5 6 10 7 9 13 11 14
9 1 13 2 3 14 4 5 6 16 7 8 10 11 12 15
10 13 11 3 14 15 5 6 16 4 8 9 7 12 1 2
11 14 15 6 16 4 9 10 7 8 1 13 12 2 3 5
12 15 2 16 4 5 10 7 8 9 13 11 1 3 14 6
13 3 14 5 6 16 8 9 10 7 12 1 11 15 2 4
14 6 16 9 10 7 1 13 11 12 2 3 15 4 5 8
15 16 4 10 7 8 13 11 12 1 3 14 2 5 6 9
16 10 7 13 11 12 3 14 15 2 5 6 4 8 9 1
[R16Mul]
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 3 2 6 5 4 10 9 8 7 11 13 12 15 14 16
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
1 6 4 11 1 11 4 6 4 6 1 11 11 6 4 1
1 5 5 1 1 1 5 5 5 5 1 1 1 5 5 1
1 4 6 11 1 11 6 4 6 4 1 11 11 4 6 1
1 10 7 4 5 6 3 14 15 2 11 12 13 8 9 16
1 9 8 6 5 4 14 3 2 15 11 13 12 7 10 16
1 8 9 4 5 6 15 2 3 14 11 12 13 10 7 16
1 7 10 6 5 4 2 15 14 3 11 13 12 9 8 16
1 11 11 1 1 1 11 11 11 11 1 1 1 11 11 1
1 13 12 11 1 11 12 13 12 13 1 11 11 13 12 1
1 12 13 11 1 11 13 12 13 12 1 11 11 12 13 1
1 15 14 6 5 4 8 7 10 9 11 13 12 3 2 16
1 14 15 4 5 6 9 10 7 8 11 12 13 2 3 16
1 16 16 1 1 1 16 16 16 16 1 1 1 16 16 1
[2] => [1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16] 是理想 ,是中心 ,商環: [[1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16]]
[R1Add]
1
[R1Mul]
1
[3] => [1 3 4 6 8 10 11 15] 不是理想
8 階子環:
[R8Add]
1 2 3 4 5 6 7 8
2 4 5 6 1 7 8 3
3 5 7 1 8 2 4 6
4 6 1 7 2 8 3 5
5 1 8 2 3 4 6 7
6 7 2 8 4 3 5 1
7 8 4 3 6 5 1 2
8 3 6 5 7 1 2 4
[R8Mul]
1 1 1 1 1 1 1 1
1 2 3 4 5 6 7 8
1 3 7 7 4 4 1 3
1 4 7 7 3 3 1 4
1 5 4 3 2 8 7 6
1 6 4 3 8 2 7 5
1 7 1 1 7 7 1 7
1 8 3 4 6 5 7 2
[4] => [1 4 6 11] 是理想 ,商環: [[1 4 6 11] [2 7 9 14] [3 8 10 15] [5 12 13 16]]
[R4Add]
1 2 3 4
2 1 4 3
3 4 1 2
4 3 2 1
[R4Mul]
1 1 1 1
1 3 2 4
1 2 3 4
1 4 4 1
[5] => [1 5] 是理想 ,商環: [[1 5] [2 8] [3 9] [4 12] [6 13] [7 15] [10 14] [11 16]]
[R8Add]
1 2 3 4 5 6 7 8
2 4 1 6 3 8 5 7
3 1 5 2 7 4 8 6
4 6 2 8 1 7 3 5
5 3 7 1 8 2 6 4
6 8 4 7 2 5 1 3
7 5 8 3 6 1 4 2
8 7 6 5 4 3 2 1
[R8Mul]
1 1 1 1 1 1 1 1
1 3 2 5 4 7 6 8
1 2 3 4 5 6 7 8
1 5 4 8 8 4 5 1
1 4 5 8 8 5 4 1
1 7 6 4 5 3 2 8
1 6 7 5 4 2 3 8
1 8 8 1 1 8 8 1
[11] => [1 11] 是理想 ,商環: [[1 11] [2 14] [3 15] [4 6] [5 16] [7 9] [8 10] [12 13]]
[R8Add]
1 2 3 4 5 6 7 8
2 4 5 6 7 1 8 3
3 5 4 7 6 8 1 2
4 6 7 1 8 2 3 5
5 7 6 8 1 3 2 4
6 1 8 2 3 4 5 7
7 8 1 3 2 5 4 6
8 3 2 5 4 7 6 1
[R8Mul]
1 1 1 1 1 1 1 1
1 3 2 4 5 7 6 8
1 2 3 4 5 6 7 8
1 4 4 1 1 4 4 1
1 5 5 1 1 5 5 1
1 7 6 4 5 3 2 8
1 6 7 4 5 2 3 8
1 8 8 1 1 8 8 1
[12] => [1 11 12 13] 是理想 ,商環: [[1 11 12 13] [2 3 14 15] [4 5 6 16] [7 8 9 10]]
[R4Add]
1 2 3 4
2 3 4 1
3 4 1 2
4 1 2 3
[R4Mul]
1 1 1 1
1 2 3 4
1 3 1 3
1 4 3 2
[16] => [1 16] 是理想 ,商環: [[1 16] [2 10] [3 7] [4 13] [5 11] [6 12] [8 14] [9 15]]
[R8Add]
1 2 3 4 5 6 7 8
2 4 5 3 7 8 6 1
3 5 6 7 8 2 1 4
4 3 7 5 6 1 8 2
5 7 8 6 1 4 2 3
6 8 2 1 4 5 3 7
7 6 1 8 2 3 4 5
8 1 4 2 3 7 5 6
[R8Mul]
1 1 1 1 1 1 1 1
1 3 2 6 5 4 8 7
1 2 3 4 5 6 7 8
1 6 4 5 1 5 6 4
1 5 5 1 1 1 5 5
1 4 6 5 1 5 4 6
1 8 7 6 5 4 3 2
1 7 8 4 5 6 2 3
[4 5] => [1 4 5 6 11 12 13 16] 是理想 ,商環: [[1 4 5 6 11 12 13 16] [2 3 7 8 9 10 14 15]]
[R2Add]
1 2
2 1
[R2Mul]
1 1
1 2
8 階子環:
[R8Add]
1 2 3 4 5 6 7 8
2 5 6 1 4 8 3 7
3 6 1 7 8 2 4 5
4 1 7 5 2 3 8 6
5 4 8 2 1 7 6 3
6 8 2 3 7 5 1 4
7 3 4 8 6 1 5 2
8 7 5 6 3 4 2 1
[R8Mul]
1 1 1 1 1 1 1 1
1 5 1 5 1 5 5 1
1 1 1 1 1 1 1 1
1 5 1 5 1 5 5 1
1 1 1 1 1 1 1 1
1 5 1 5 1 5 5 1
1 5 1 5 1 5 5 1
1 1 1 1 1 1 1 1
[5 11] => [1 5 11 16] 是理想 ,商環: [[1 5 11 16] [2 8 10 14] [3 7 9 15] [4 6 12 13]]
[R4Add]
1 2 3 4
2 4 1 3
3 1 4 2
4 3 2 1
[R4Mul]
1 1 1 1
1 3 2 4
1 2 3 4
1 4 4 1
time consume: 2.06552835s
R16_109=ZimodnZObj(1+i,4+4i):2有零因子交換無幺環,1,0,16,1,3,7,80,15,16
8階商環:R8_24
8階理想子環:R8_23
[1] => [1] 是理想 ,商環: [[1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16]]
[R16Add]
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
2 4 6 8 9 11 12 1 7 14 15 5 16 13 3 10
3 6 7 11 10 12 13 15 14 4 5 16 1 8 9 2
4 8 11 1 7 15 5 2 12 13 3 9 10 16 6 14
5 9 10 7 1 14 4 12 2 3 13 8 11 6 16 15
6 11 12 15 14 5 16 3 13 8 9 10 2 1 7 4
7 12 13 5 4 16 1 9 8 11 10 2 3 15 14 6
8 1 15 2 12 3 9 4 5 16 6 7 14 10 11 13
9 7 14 12 2 13 8 5 4 6 16 1 15 11 10 3
10 14 4 13 3 8 11 16 6 7 1 15 5 12 2 9
11 15 5 3 13 9 10 6 16 1 7 14 4 2 12 8
12 5 16 9 8 10 2 7 1 15 14 4 6 3 13 11
13 16 1 10 11 2 3 14 15 5 4 6 7 9 8 12
14 13 8 16 6 1 15 10 11 12 2 3 9 5 4 7
15 3 9 6 16 7 14 11 10 2 12 13 8 4 5 1
16 10 2 14 15 4 6 13 3 9 8 11 12 7 1 5
[R16Mul]
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 3 5 7 7 10 1 13 13 4 4 3 5 11 11 10
1 5 7 1 1 4 1 5 5 7 7 5 7 4 4 4
1 7 1 1 1 7 1 7 7 1 1 7 1 7 7 7
1 7 1 1 1 7 1 7 7 1 1 7 1 7 7 7
1 10 4 7 7 13 1 11 11 5 5 10 4 3 3 13
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 13 5 7 7 11 1 3 3 4 4 13 5 10 10 11
1 13 5 7 7 11 1 3 3 4 4 13 5 10 10 11
1 4 7 1 1 5 1 4 4 7 7 4 7 5 5 5
1 4 7 1 1 5 1 4 4 7 7 4 7 5 5 5
1 3 5 7 7 10 1 13 13 4 4 3 5 11 11 10
1 5 7 1 1 4 1 5 5 7 7 5 7 4 4 4
1 11 4 7 7 3 1 10 10 5 5 11 4 13 13 3
1 11 4 7 7 3 1 10 10 5 5 11 4 13 13 3
1 10 4 7 7 13 1 11 11 5 5 10 4 3 3 13
[2] => [1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16] 是理想 ,是中心 ,商環: [[1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16]]
[R1Add]
1
[R1Mul]
1
[3] => [1 3 7 13] 不是理想
[4] => [1 4] 不是理想
[5] => [1 5] 不是理想
[7] => [1 7] 是理想 ,商環: [[1 7] [2 12] [3 13] [4 5] [6 16] [8 9] [10 11] [14 15]]
[R8Add]
1 2 3 4 5 6 7 8
2 4 5 6 7 1 8 3
3 5 1 7 2 8 4 6
4 6 7 1 8 2 3 5
5 7 2 8 4 3 6 1
6 1 8 2 3 4 5 7
7 8 4 3 6 5 1 2
8 3 6 5 1 7 2 4
[R8Mul]
1 1 1 1 1 1 1 1
1 3 4 1 7 3 4 7
1 4 1 1 4 4 1 4
1 1 1 1 1 1 1 1
1 7 4 1 3 7 4 3
1 3 4 1 7 3 4 7
1 4 1 1 4 4 1 4
1 7 4 1 3 7 4 3
[10] => [1 7 10 11] 不是理想
[3 4] => [1 3 4 5 7 10 11 13] 是理想 ,商環: [[1 3 4 5 7 10 11 13] [2 6 8 9 12 14 15 16]]
[R2Add]
1 2
2 1
[R2Mul]
1 1
1 1
8 階子環:
[R8Add]
1 2 3 4 5 6 7 8
2 5 7 6 8 3 4 1
3 7 1 5 4 8 2 6
4 6 5 1 3 2 8 7
5 8 4 3 1 7 6 2
6 3 8 2 7 5 1 4
7 4 2 8 6 1 5 3
8 1 6 7 2 4 3 5
[R8Mul]
1 1 1 1 1 1 1 1
1 5 1 1 1 5 5 5
1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1
1 5 1 1 1 5 5 5
1 5 1 1 1 5 5 5
1 5 1 1 1 5 5 5
[4 5] => [1 4 5 7] 是理想 ,商環: [[1 4 5 7] [2 8 9 12] [3 10 11 13] [6 14 15 16]]
[R4Add]
1 2 3 4
2 1 4 3
3 4 1 2
4 3 2 1
[R4Mul]
1 1 1 1
1 3 1 3
1 1 1 1
1 3 1 3
time consume: 2.056919909s
環R16_389的結構不變量n0,bA,bO,n1,n2,n4,n5,n6,n7,n8=2,1,1,未知,4,0,0,49,6,16
單個生成元子環的階的分布:[ 1, 2, 2, 2, 4, 4, 4, 4, 4, 4, 4, 4, 8, 8, 8, 8 ]
8階商環:無
8階理想子環:無
8階非理想子環:R8_51、R8_51
[1] => [1] 是理想 ,商環: [[1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16]]
[R16Add]
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
2 1 4 3 6 5 8 7 10 9 12 11 14 13 16 15
3 4 1 2 7 8 5 6 11 12 9 10 15 16 13 14
4 3 2 1 8 7 6 5 12 11 10 9 16 15 14 13
5 6 7 8 1 2 3 4 13 14 15 16 9 10 11 12
6 5 8 7 2 1 4 3 14 13 16 15 10 9 12 11
7 8 5 6 3 4 1 2 15 16 13 14 11 12 9 10
8 7 6 5 4 3 2 1 16 15 14 13 12 11 10 9
9 10 11 12 13 14 15 16 1 2 3 4 5 6 7 8
10 9 12 11 14 13 16 15 2 1 4 3 6 5 8 7
11 12 9 10 15 16 13 14 3 4 1 2 7 8 5 6
12 11 10 9 16 15 14 13 4 3 2 1 8 7 6 5
13 14 15 16 9 10 11 12 5 6 7 8 1 2 3 4
14 13 16 15 10 9 12 11 6 5 8 7 2 1 4 3
15 16 13 14 11 12 9 10 7 8 5 6 3 4 1 2
16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1
[R16Mul]
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 2 3 4 2 1 4 3 3 4 1 2 4 3 2 1
1 3 4 2 3 1 2 4 4 2 1 3 2 4 3 1
1 4 2 3 4 1 3 2 2 3 1 4 3 2 4 1
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
1 1 1 1 6 6 6 6 11 11 11 11 16 16 16 16
1 4 2 3 7 6 8 5 12 9 11 10 14 15 13 16
1 3 4 2 8 6 5 7 10 12 11 9 15 13 14 16
1 3 4 2 9 11 12 10 13 15 16 14 5 7 8 6
1 4 2 3 10 11 9 12 15 14 16 13 8 5 7 6
1 1 1 1 11 11 11 11 16 16 16 16 6 6 6 6
1 2 3 4 12 11 10 9 14 13 16 15 7 8 5 6
1 4 2 3 13 16 14 15 5 8 6 7 9 12 10 11
1 3 4 2 14 16 15 13 7 5 6 8 12 10 9 11
1 2 3 4 15 16 13 14 8 7 6 5 10 9 12 11
1 1 1 1 16 16 16 16 6 6 6 6 11 11 11 11
[2] => [1 2] 不是理想
[3] => [1 2 3 4] 是理想 ,商環: [[1 2 3 4] [5 6 7 8] [9 10 11 12] [13 14 15 16]]
[R4Add]
1 2 3 4
2 1 4 3
3 4 1 2
4 3 2 1
[R4Mul]
1 1 1 1
1 2 3 4
1 3 4 2
1 4 2 3
[5] => [1 5] 不是理想
[6] => [1 6] 不是理想
[7] => [1 2 3 4 5 6 7 8] 不是理想
8 階子環:
[R8Add]
1 2 3 4 5 6 7 8
2 1 4 3 6 5 8 7
3 4 1 2 7 8 5 6
4 3 2 1 8 7 6 5
5 6 7 8 1 2 3 4
6 5 8 7 2 1 4 3
7 8 5 6 3 4 1 2
8 7 6 5 4 3 2 1
[R8Mul]
1 1 1 1 1 1 1 1
1 2 3 4 2 1 4 3
1 3 4 2 3 1 2 4
1 4 2 3 4 1 3 2
1 2 3 4 5 6 7 8
1 1 1 1 6 6 6 6
1 4 2 3 7 6 8 5
1 3 4 2 8 6 5 7
[9] => [1 5 9 13] 不是理想
[10] => [1 5 10 14] 不是理想
[11] => [1 6 11 16] 是理想 ,商環: [[1 6 11 16] [2 5 12 15] [3 8 9 14] [4 7 10 13]]
[R4Add]
1 2 3 4
2 1 4 3
3 4 1 2
4 3 2 1
[R4Mul]
1 1 1 1
1 2 3 4
1 3 4 2
1 4 2 3
[12] => [1 2 5 6 11 12 15 16] 不是理想
8 階子環:
[R8Add]
1 2 3 4 5 6 7 8
2 1 4 3 6 5 8 7
3 4 1 2 7 8 5 6
4 3 2 1 8 7 6 5
5 6 7 8 1 2 3 4
6 5 8 7 2 1 4 3
7 8 5 6 3 4 1 2
8 7 6 5 4 3 2 1
[R8Mul]
1 1 1 1 1 1 1 1
1 2 2 1 1 2 2 1
1 2 3 4 5 6 7 8
1 1 4 4 5 5 8 8
1 1 5 5 8 8 4 4
1 2 6 5 8 7 3 4
1 2 7 8 4 3 6 5
1 1 8 8 4 4 5 5
[2 5] => [1 2 5 6] 不是理想
[2 9] => [1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16] 是理想 ,是中心 ,商環: [[1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16]]
[R1Add]
1
[R1Mul]
1
time consume: 1.701732687s
環R16_388的結構不變量n0,bA,bO,n1,n2,n4,n5,n6,n7,n8=2,1,1,未知,4,0,0,45,8,16
單個生成元子環的階的分布:[ 1, 2, 2, 2, 8, 8, 8, 8, 8, 8, 16, 16, 16, 16, 16, 16 ]
8階商環:R8_52
8階理想子環:R8_52
8階非理想子環:無
[1] => [1] 是理想 ,商環: [[1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16]]
[R16Add]
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
2 1 4 3 6 5 8 7 10 9 12 11 14 13 16 15
3 4 1 2 7 8 5 6 11 12 9 10 15 16 13 14
4 3 2 1 8 7 6 5 12 11 10 9 16 15 14 13
5 6 7 8 1 2 3 4 13 14 15 16 9 10 11 12
6 5 8 7 2 1 4 3 14 13 16 15 10 9 12 11
7 8 5 6 3 4 1 2 15 16 13 14 11 12 9 10
8 7 6 5 4 3 2 1 16 15 14 13 12 11 10 9
9 10 11 12 13 14 15 16 1 2 3 4 5 6 7 8
10 9 12 11 14 13 16 15 2 1 4 3 6 5 8 7
11 12 9 10 15 16 13 14 3 4 1 2 7 8 5 6
12 11 10 9 16 15 14 13 4 3 2 1 8 7 6 5
13 14 15 16 9 10 11 12 5 6 7 8 1 2 3 4
14 13 16 15 10 9 12 11 6 5 8 7 2 1 4 3
15 16 13 14 11 12 9 10 7 8 5 6 3 4 1 2
16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1
[R16Mul]
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 7 8 2 6 4 3 5 2 8 7 1 5 3 4 6
1 8 6 3 2 7 5 4 3 6 8 1 4 5 7 2
1 2 3 4 5 6 7 8 4 3 2 1 8 7 6 5
1 6 2 5 3 8 4 7 5 2 6 1 7 4 8 3
1 4 7 6 8 5 2 3 6 7 4 1 3 2 5 8
1 3 5 7 4 2 8 6 7 5 3 1 6 8 2 4
1 5 4 8 7 3 6 2 8 4 5 1 2 6 3 7
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
1 8 6 3 2 7 5 4 10 15 13 12 9 16 14 11
1 7 8 2 6 4 3 5 11 13 14 12 16 10 9 15
1 1 1 1 1 1 1 1 12 12 12 12 12 12 12 12
1 5 4 8 7 3 6 2 13 9 16 12 11 15 10 14
1 3 5 7 4 2 8 6 14 16 10 12 15 13 11 9
1 4 7 6 8 5 2 3 15 14 9 12 10 11 16 13
1 6 2 5 3 8 4 7 16 11 15 12 14 9 13 10
[2] => [1 2 3 4 5 6 7 8] 是理想 ,商環: [[1 2 3 4 5 6 7 8] [9 10 11 12 13 14 15 16]]
[R2Add]
1 2
2 1
[R2Mul]
1 1
1 2
8 階子環:
[R8Add]
1 2 3 4 5 6 7 8
2 1 4 3 6 5 8 7
3 4 1 2 7 8 5 6
4 3 2 1 8 7 6 5
5 6 7 8 1 2 3 4
6 5 8 7 2 1 4 3
7 8 5 6 3 4 1 2
8 7 6 5 4 3 2 1
[R8Mul]
1 1 1 1 1 1 1 1
1 7 8 2 6 4 3 5
1 8 6 3 2 7 5 4
1 2 3 4 5 6 7 8
1 6 2 5 3 8 4 7
1 4 7 6 8 5 2 3
1 3 5 7 4 2 8 6
1 5 4 8 7 3 6 2
[4] => [1 4] 不是理想
[9] => [1 9] 不是理想
[10] => [1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16] 是理想 ,是中心 ,商環: [[1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16]]
[R1Add]
1
[R1Mul]
1
[12] => [1 12] 是理想 ,商環: [[1 12] [2 11] [3 10] [4 9] [5 16] [6 15] [7 14] [8 13]]
[R8Add]
1 2 3 4 5 6 7 8
2 1 4 3 6 5 8 7
3 4 1 2 7 8 5 6
4 3 2 1 8 7 6 5
5 6 7 8 1 2 3 4
6 5 8 7 2 1 4 3
7 8 5 6 3 4 1 2
8 7 6 5 4 3 2 1
[R8Mul]
1 1 1 1 1 1 1 1
1 7 8 2 6 4 3 5
1 8 6 3 2 7 5 4
1 2 3 4 5 6 7 8
1 6 2 5 3 8 4 7
1 4 7 6 8 5 2 3
1 3 5 7 4 2 8 6
1 5 4 8 7 3 6 2
[4 9] => [1 4 9 12] 不是理想
time consume: 1.714077595s
環R16_387的結構不變量n0,bA,bO,n1,n2,n4,n5,n6,n7,n8=2,1,1,未知,8,0,0,63,12,16
單個生成元子環的階的分布:[ 1, 2, 2, 2, 2, 2, 2, 2, 4, 4, 8, 8, 8, 8, 8, 8 ]
8階商環:R8_51、R8_51
8階理想子環:R8_51、R8_51
8階非理想子環:R8_51、R8_50
[1] => [1] 是理想 ,商環: [[1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16]]
[R16Add]
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
2 1 4 3 6 5 8 7 10 9 12 11 14 13 16 15
3 4 1 2 7 8 5 6 11 12 9 10 15 16 13 14
4 3 2 1 8 7 6 5 12 11 10 9 16 15 14 13
5 6 7 8 1 2 3 4 13 14 15 16 9 10 11 12
6 5 8 7 2 1 4 3 14 13 16 15 10 9 12 11
7 8 5 6 3 4 1 2 15 16 13 14 11 12 9 10
8 7 6 5 4 3 2 1 16 15 14 13 12 11 10 9
9 10 11 12 13 14 15 16 1 2 3 4 5 6 7 8
10 9 12 11 14 13 16 15 2 1 4 3 6 5 8 7
11 12 9 10 15 16 13 14 3 4 1 2 7 8 5 6
12 11 10 9 16 15 14 13 4 3 2 1 8 7 6 5
13 14 15 16 9 10 11 12 5 6 7 8 1 2 3 4
14 13 16 15 10 9 12 11 6 5 8 7 2 1 4 3
15 16 13 14 11 12 9 10 7 8 5 6 3 4 1 2
16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1
[R16Mul]
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 2 3 4 5 6 7 8 2 1 4 3 6 5 8 7
1 3 5 7 2 4 6 8 3 1 7 5 4 2 8 6
1 4 7 6 6 7 4 1 4 1 6 7 7 6 1 4
1 5 2 6 3 7 4 8 5 1 6 2 7 3 8 4
1 6 4 7 7 4 6 1 6 1 7 4 4 7 1 6
1 7 6 4 4 6 7 1 7 1 4 6 6 4 1 7
1 8 8 1 8 1 1 8 8 1 1 8 1 8 8 1
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
1 1 1 1 1 1 1 1 10 10 10 10 10 10 10 10
1 4 7 6 6 7 4 1 11 10 13 16 16 13 10 11
1 3 5 7 2 4 6 8 12 10 16 14 11 9 15 13
1 6 4 7 7 4 6 1 13 10 16 11 11 16 10 13
1 5 2 6 3 7 4 8 14 10 13 9 16 12 15 11
1 8 8 1 8 1 1 8 15 10 10 15 10 15 15 10
1 7 6 4 4 6 7 1 16 10 11 13 13 11 10 16
[2] => [1 2] 不是理想
[3] => [1 2 3 4 5 6 7 8] 是理想 ,商環: [[1 2 3 4 5 6 7 8] [9 10 11 12 13 14 15 16]]
[R2Add]
1 2
2 1
[R2Mul]
1 1
1 2
8 階子環:
[R8Add]
1 2 3 4 5 6 7 8
2 1 4 3 6 5 8 7
3 4 1 2 7 8 5 6
4 3 2 1 8 7 6 5
5 6 7 8 1 2 3 4
6 5 8 7 2 1 4 3
7 8 5 6 3 4 1 2
8 7 6 5 4 3 2 1
[R8Mul]
1 1 1 1 1 1 1 1
1 2 3 4 5 6 7 8
1 3 5 7 2 4 6 8
1 4 7 6 6 7 4 1
1 5 2 6 3 7 4 8
1 6 4 7 7 4 6 1
1 7 6 4 4 6 7 1
1 8 8 1 8 1 1 8
[4] => [1 4 6 7] 是理想 ,商環: [[1 4 6 7] [2 3 5 8] [9 12 14 15] [10 11 13 16]]
[R4Add]
1 2 3 4
2 1 4 3
3 4 1 2
4 3 2 1
[R4Mul]
1 1 1 1
1 2 2 1
1 2 3 4
1 1 4 4
[7] => [1 7] 不是理想
[8] => [1 8] 是理想 ,商環: [[1 8] [2 7] [3 6] [4 5] [9 16] [10 15] [11 14] [12 13]]
[R8Add]
1 2 3 4 5 6 7 8
2 1 4 3 6 5 8 7
3 4 1 2 7 8 5 6
4 3 2 1 8 7 6 5
5 6 7 8 1 2 3 4
6 5 8 7 2 1 4 3
7 8 5 6 3 4 1 2
8 7 6 5 4 3 2 1
[R8Mul]
1 1 1 1 1 1 1 1
1 2 3 4 2 1 4 3
1 3 4 2 3 1 2 4
1 4 2 3 4 1 3 2
1 2 3 4 5 6 7 8
1 1 1 1 6 6 6 6
1 4 2 3 7 6 8 5
1 3 4 2 8 6 5 7
[9] => [1 9] 不是理想
[10] => [1 10] 是理想 ,商環: [[1 10] [2 9] [3 12] [4 11] [5 14] [6 13] [7 16] [8 15]]
[R8Add]
1 2 3 4 5 6 7 8
2 1 4 3 6 5 8 7
3 4 1 2 7 8 5 6
4 3 2 1 8 7 6 5
5 6 7 8 1 2 3 4
6 5 8 7 2 1 4 3
7 8 5 6 3 4 1 2
8 7 6 5 4 3 2 1
[R8Mul]
1 1 1 1 1 1 1 1
1 2 3 4 5 6 7 8
1 3 5 7 2 4 6 8
1 4 7 6 6 7 4 1
1 5 2 6 3 7 4 8
1 6 4 7 7 4 6 1
1 7 6 4 4 6 7 1
1 8 8 1 8 1 1 8
[11] => [1 4 6 7 10 11 13 16] 是理想 ,商環: [[1 4 6 7 10 11 13 16] [2 3 5 8 9 12 14 15]]
[R2Add]
1 2
2 1
[R2Mul]
1 1
1 2
8 階子環:
[R8Add]
1 2 3 4 5 6 7 8
2 1 4 3 6 5 8 7
3 4 1 2 7 8 5 6
4 3 2 1 8 7 6 5
5 6 7 8 1 2 3 4
6 5 8 7 2 1 4 3
7 8 5 6 3 4 1 2
8 7 6 5 4 3 2 1
[R8Mul]
1 1 1 1 1 1 1 1
1 3 4 2 1 3 4 2
1 4 2 3 1 4 2 3
1 2 3 4 1 2 3 4
1 1 1 1 5 5 5 5
1 3 4 2 5 7 8 6
1 4 2 3 5 8 6 7
1 2 3 4 5 6 7 8
[12] => [1 4 6 7 9 12 14 15] 不是理想
8 階子環:
[R8Add]
1 2 3 4 5 6 7 8
2 1 4 3 6 5 8 7
3 4 1 2 7 8 5 6
4 3 2 1 8 7 6 5
5 6 7 8 1 2 3 4
6 5 8 7 2 1 4 3
7 8 5 6 3 4 1 2
8 7 6 5 4 3 2 1
[R8Mul]
1 1 1 1 1 1 1 1
1 3 4 2 2 4 3 1
1 4 2 3 3 2 4 1
1 2 3 4 4 3 2 1
1 2 3 4 5 6 7 8
1 4 2 3 6 7 5 8
1 3 4 2 7 5 6 8
1 1 1 1 8 8 8 8
[15] => [1 15] 不是理想
[16] => [1 16] 不是理想
[2 7] => [1 2 7 8] 不是理想
[2 9] => [1 2 9 10] 不是理想
[3 9] => [1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16] 是理想 ,是中心 ,商環: [[1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16]]
[R1Add]
1
[R1Mul]
1
[7 9] => [1 7 9 15] 不是理想
[8 9] => [1 8 9 16] 不是理想
[7 10] => [1 7 10 16] 不是理想
[8 10] => [1 8 10 15] 是理想 ,商環: [[1 8 10 15] [2 7 9 16] [3 6 12 13] [4 5 11 14]]
[R4Add]
1 2 3 4
2 1 4 3
3 4 1 2
4 3 2 1
[R4Mul]
1 1 1 1
1 2 3 4
1 3 4 2
1 4 2 3
[2 15] => [1 2 7 8 9 10 15 16] 不是理想
8 階子環:
[R8Add]
1 2 3 4 5 6 7 8
2 1 4 3 6 5 8 7
3 4 1 2 7 8 5 6
4 3 2 1 8 7 6 5
5 6 7 8 1 2 3 4
6 5 8 7 2 1 4 3
7 8 5 6 3 4 1 2
8 7 6 5 4 3 2 1
[R8Mul]
1 1 1 1 1 1 1 1
1 2 3 4 2 1 4 3
1 3 3 1 3 1 1 3
1 4 1 4 4 1 4 1
1 2 3 4 5 6 7 8
1 1 1 1 6 6 6 6
1 4 1 4 7 6 7 6
1 3 3 1 8 6 6 8
time consume: 1.732554626s
環R16_384的結構不變量n0,bA,bO,n1,n2,n4,n5,n6,n7,n8=2,1,1,未知,4,3,3,64,11,16
單個生成元子環的階的分布:[ 1, 2, 2, 2, 2, 2, 2, 4, 4, 4, 4, 4, 4, 4, 8, 8 ]
8階商環:R8_48、R8_48
8階理想子環:R8_35、R8_35
8階非理想子環:R8_48、R8_48、R8_45
[1] => [1] 是理想 ,商環: [[1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16]]
[R16Add]
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
2 1 4 3 6 5 8 7 10 9 12 11 14 13 16 15
3 4 1 2 7 8 5 6 11 12 9 10 15 16 13 14
4 3 2 1 8 7 6 5 12 11 10 9 16 15 14 13
5 6 7 8 1 2 3 4 13 14 15 16 9 10 11 12
6 5 8 7 2 1 4 3 14 13 16 15 10 9 12 11
7 8 5 6 3 4 1 2 15 16 13 14 11 12 9 10
8 7 6 5 4 3 2 1 16 15 14 13 12 11 10 9
9 10 11 12 13 14 15 16 1 2 3 4 5 6 7 8
10 9 12 11 14 13 16 15 2 1 4 3 6 5 8 7
11 12 9 10 15 16 13 14 3 4 1 2 7 8 5 6
12 11 10 9 16 15 14 13 4 3 2 1 8 7 6 5
13 14 15 16 9 10 11 12 5 6 7 8 1 2 3 4
14 13 16 15 10 9 12 11 6 5 8 7 2 1 4 3
15 16 13 14 11 12 9 10 7 8 5 6 3 4 1 2
16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1
[R16Mul]
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 3 2 4 3 1 4 2 2 4 1 3 4 2 3 1
1 2 3 4 2 1 4 3 3 4 1 2 4 3 2 1
1 4 4 1 4 1 1 4 4 1 1 4 1 4 4 1
1 3 2 4 3 1 4 2 5 7 6 8 7 5 8 6
1 1 1 1 1 1 1 1 6 6 6 6 6 6 6 6
1 4 4 1 4 1 1 4 7 6 6 7 6 7 7 6
1 2 3 4 2 1 4 3 8 7 6 5 7 8 5 6
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
1 4 4 1 7 6 6 7 10 11 11 10 16 13 13 16
1 1 1 1 6 6 6 6 11 11 11 11 16 16 16 16
1 3 2 4 8 6 7 5 12 10 11 9 13 15 14 16
1 4 4 1 7 6 6 7 13 16 16 13 11 10 10 11
1 2 3 4 5 6 7 8 14 13 16 15 10 9 12 11
1 3 2 4 8 6 7 5 15 13 16 14 10 12 9 11
1 1 1 1 6 6 6 6 16 16 16 16 11 11 11 11
[2] => [1 2 3 4] 是理想 ,商環: [[1 2 3 4] [5 6 7 8] [9 10 11 12] [13 14 15 16]]
[R4Add]
1 2 3 4
2 1 4 3
3 4 1 2
4 3 2 1
[R4Mul]
1 1 1 1
1 1 2 2
1 2 3 4
1 2 4 3
[3] => [1 3] 不是理想
[4] => [1 4] 是理想 ,商環: [[1 4] [2 3] [5 8] [6 7] [9 12] [10 11] [13 16] [14 15]]
[R8Add]
1 2 3 4 5 6 7 8
2 1 4 3 6 5 8 7
3 4 1 2 7 8 5 6
4 3 2 1 8 7 6 5
5 6 7 8 1 2 3 4
6 5 8 7 2 1 4 3
7 8 5 6 3 4 1 2
8 7 6 5 4 3 2 1
[R8Mul]
1 1 1 1 1 1 1 1
1 2 2 1 2 1 1 2
1 2 2 1 3 4 4 3
1 1 1 1 4 4 4 4
1 2 3 4 5 6 7 8
1 1 4 4 6 6 7 7
1 1 4 4 7 7 6 6
1 2 3 4 8 7 6 5
[5] => [1 2 3 4 5 6 7 8] 是理想 ,商環: [[1 2 3 4 5 6 7 8] [9 10 11 12 13 14 15 16]]
[R2Add]
1 2
2 1
[R2Mul]
1 1
1 2
8 階子環:
[R8Add]
1 2 3 4 5 6 7 8
2 1 4 3 6 5 8 7
3 4 1 2 7 8 5 6
4 3 2 1 8 7 6 5
5 6 7 8 1 2 3 4
6 5 8 7 2 1 4 3
7 8 5 6 3 4 1 2
8 7 6 5 4 3 2 1
[R8Mul]
1 1 1 1 1 1 1 1
1 3 2 4 3 1 4 2
1 2 3 4 2 1 4 3
1 4 4 1 4 1 1 4
1 3 2 4 3 1 4 2
1 1 1 1 1 1 1 1
1 4 4 1 4 1 1 4
1 2 3 4 2 1 4 3
[6] => [1 6] 是理想 ,商環: [[1 6] [2 5] [3 8] [4 7] [9 14] [10 13] [11 16] [12 15]]
[R8Add]
1 2 3 4 5 6 7 8
2 1 4 3 6 5 8 7
3 4 1 2 7 8 5 6
4 3 2 1 8 7 6 5
5 6 7 8 1 2 3 4
6 5 8 7 2 1 4 3
7 8 5 6 3 4 1 2
8 7 6 5 4 3 2 1
[R8Mul]
1 1 1 1 1 1 1 1
1 3 2 4 2 4 1 3
1 2 3 4 3 4 1 2
1 4 4 1 4 1 1 4
1 2 3 4 5 6 7 8
1 4 4 1 6 7 7 6
1 1 1 1 7 7 7 7
1 3 2 4 8 6 7 5
[7] => [1 7] 不是理想
[8] => [1 3 6 8] 不是理想
[9] => [1 9] 不是理想
[10] => [1 4 10 11] 不是理想
[11] => [1 11] 不是理想
[12] => [1 4 9 12] 不是理想
[13] => [1 4 6 7 10 11 13 16] 是理想 ,商環: [[1 4 6 7 10 11 13 16] [2 3 5 8 9 12 14 15]]
[R2Add]
1 2
2 1
[R2Mul]
1 1
1 2
8 階子環:
[R8Add]
1 2 3 4 5 6 7 8
2 1 4 3 6 5 8 7
3 4 1 2 7 8 5 6
4 3 2 1 8 7 6 5
5 6 7 8 1 2 3 4
6 5 8 7 2 1 4 3
7 8 5 6 3 4 1 2
8 7 6 5 4 3 2 1
[R8Mul]
1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1
1 1 1 1 3 3 3 3
1 1 1 1 3 3 3 3
1 1 3 3 6 6 8 8
1 1 3 3 6 6 8 8
1 1 3 3 8 8 6 6
1 1 3 3 8 8 6 6
[14] => [1 6 9 14] 不是理想
[15] => [1 7 9 15] 不是理想
[16] => [1 6 11 16] 是理想 ,商環: [[1 6 11 16] [2 5 12 15] [3 8 9 14] [4 7 10 13]]
[R4Add]
1 2 3 4
2 1 4 3
3 4 1 2
4 3 2 1
[R4Mul]
1 1 1 1
1 3 2 4
1 2 3 4
1 4 4 1
[4 6] => [1 4 6 7] 是理想 ,商環: [[1 4 6 7] [2 3 5 8] [9 12 14 15] [10 11 13 16]]
[R4Add]
1 2 3 4
2 1 4 3
3 4 1 2
4 3 2 1
[R4Mul]
1 1 1 1
1 2 2 1
1 2 3 4
1 1 4 4
[2 9] => [1 2 3 4 9 10 11 12] 不是理想
8 階子環:
[R8Add]
1 2 3 4 5 6 7 8
2 1 4 3 6 5 8 7
3 4 1 2 7 8 5 6
4 3 2 1 8 7 6 5
5 6 7 8 1 2 3 4
6 5 8 7 2 1 4 3
7 8 5 6 3 4 1 2
8 7 6 5 4 3 2 1
[R8Mul]
1 1 1 1 1 1 1 1
1 3 2 4 2 4 1 3
1 2 3 4 3 4 1 2
1 4 4 1 4 1 1 4
1 2 3 4 5 6 7 8
1 4 4 1 6 7 7 6
1 1 1 1 7 7 7 7
1 3 2 4 8 6 7 5
[3 9] => [1 3 9 11] 不是理想
[5 9] => [1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16] 是理想 ,是中心 ,商環: [[1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16]]
[R1Add]
1
[R1Mul]
1
[8 9] => [1 3 6 8 9 11 14 16] 不是理想
8 階子環:
[R8Add]
1 2 3 4 5 6 7 8
2 1 4 3 6 5 8 7
3 4 1 2 7 8 5 6
4 3 2 1 8 7 6 5
5 6 7 8 1 2 3 4
6 5 8 7 2 1 4 3
7 8 5 6 3 4 1 2
8 7 6 5 4 3 2 1
[R8Mul]
1 1 1 1 1 1 1 1
1 2 1 2 2 1 2 1
1 1 1 1 3 3 3 3
1 2 1 2 4 3 4 3
1 2 3 4 5 6 7 8
1 1 3 3 6 6 8 8
1 2 3 4 7 8 5 6
1 1 3 3 8 8 6 6
[6 12] => [1 4 6 7 9 12 14 15] 不是理想
8 階子環:
[R8Add]
1 2 3 4 5 6 7 8
2 1 4 3 6 5 8 7
3 4 1 2 7 8 5 6
4 3 2 1 8 7 6 5
5 6 7 8 1 2 3 4
6 5 8 7 2 1 4 3
7 8 5 6 3 4 1 2
8 7 6 5 4 3 2 1
[R8Mul]
1 1 1 1 1 1 1 1
1 1 1 1 2 2 2 2
1 1 1 1 3 3 3 3
1 1 1 1 4 4 4 4
1 2 3 4 5 6 7 8
1 2 3 4 6 5 8 7
1 2 3 4 7 8 5 6
1 2 3 4 8 7 6 5
time consume: 1.706511251s
環R16_383的結構不變量n0,bA,bO,n1,n2,n4,n5,n6,n7,n8=2,1,1,未知,2,3,3,40,3,16
單個生成元子環的階的分布:[ 1, 2, 2, 2, 2, 4, 4, 4, 4, 4, 16, 16, 16, 16, 16, 16 ]
S(R16_383)=12,[1,2,2,2,2,4,4,4,4,4,8,16],
N(R16_383)=3,[1,4,16],
R16_383的8階理想子環有0個,8階非理想子環有1個R8_45,8階商環有0個
[1] => [1] 是理想 ,商環: [[1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16]]
[R16Add]
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
2 1 4 3 6 5 8 7 10 9 12 11 14 13 16 15
3 4 1 2 7 8 5 6 11 12 9 10 15 16 13 14
4 3 2 1 8 7 6 5 12 11 10 9 16 15 14 13
5 6 7 8 1 2 3 4 13 14 15 16 9 10 11 12
6 5 8 7 2 1 4 3 14 13 16 15 10 9 12 11
7 8 5 6 3 4 1 2 15 16 13 14 11 12 9 10
8 7 6 5 4 3 2 1 16 15 14 13 12 11 10 9
9 10 11 12 13 14 15 16 1 2 3 4 5 6 7 8
10 9 12 11 14 13 16 15 2 1 4 3 6 5 8 7
11 12 9 10 15 16 13 14 3 4 1 2 7 8 5 6
12 11 10 9 16 15 14 13 4 3 2 1 8 7 6 5
13 14 15 16 9 10 11 12 5 6 7 8 1 2 3 4
14 13 16 15 10 9 12 11 6 5 8 7 2 1 4 3
15 16 13 14 11 12 9 10 7 8 5 6 3 4 1 2
16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1
[R16Mul]
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 9 6 14 11 3 16 8 2 10 5 13 12 4 15 7
1 6 11 16 2 5 12 15 3 8 9 14 4 7 10 13
1 14 16 3 12 7 5 10 4 15 13 2 9 6 8 11
1 11 2 12 3 9 4 10 5 15 6 16 7 13 8 14
1 3 5 7 9 11 13 15 6 8 2 4 14 16 10 12
1 16 12 5 4 13 9 8 7 10 14 3 6 11 15 2
1 8 15 10 10 15 8 1 8 1 10 15 15 10 1 8
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
1 10 8 15 15 8 10 1 10 1 15 8 8 15 1 10
1 5 9 13 6 2 14 10 11 15 3 7 16 12 8 4
1 13 14 2 16 4 3 15 12 8 7 11 5 9 10 6
1 12 4 9 7 14 6 15 13 8 16 5 11 2 10 3
1 4 7 6 13 16 11 10 14 15 12 9 2 3 8 5
1 15 10 8 8 10 15 1 15 1 8 10 10 8 1 15
1 7 13 11 14 12 2 8 16 10 4 6 3 5 15 9
[2] => [1 2 9 10] 不是理想
[3] => [1 3 9 11] 不是理想
[4] => [1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16] 是理想 ,是中心 ,商環: [[1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16]]
[R1Add]
1
[R1Mul]
1
[7] => [1 7 9 15] 不是理想
[8] => [1 8] 不是理想
[9] => [1 9] 不是理想
[10] => [1 10] 不是理想
[15] => [1 15] 不是理想
[16] => [1 8 9 16] 不是理想
[2 7] => [1 2 7 8 9 10 15 16] 不是理想
8 階子環:
[R8Add]
1 2 3 4 5 6 7 8
2 1 4 3 6 5 8 7
3 4 1 2 7 8 5 6
4 3 2 1 8 7 6 5
5 6 7 8 1 2 3 4
6 5 8 7 2 1 4 3
7 8 5 6 3 4 1 2
8 7 6 5 4 3 2 1
[R8Mul]
1 1 1 1 1 1 1 1
1 5 8 4 2 6 7 3
1 8 5 4 3 6 7 2
1 4 4 1 4 1 1 4
1 2 3 4 5 6 7 8
1 6 6 1 6 1 1 6
1 7 7 1 7 1 1 7
1 3 2 4 8 6 7 5
[8 10] => [1 8 10 15] 是理想 ,商環: [[1 8 10 15] [2 7 9 16] [3 6 12 13] [4 5 11 14]]
[R4Add]
1 2 3 4
2 1 4 3
3 4 1 2
4 3 2 1
[R4Mul]
1 1 1 1
1 2 3 4
1 3 4 2
1 4 2 3
time consume: 1.726419508s
環R16_390的結構不變量n0,bA,bO,n1,n2,n4,n5,n6,n7,n8=2,1,1,未知,2,0,0,31,0,16
單個生成元子環的階的分布:[ 1, 2, 4, 4, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16 ]【 這裡所謂的“主理想階”準确應該叫做"單個生成元子環的階",該子環不一定是理想】
S(R16_390)=4,[1,2,4,16],
N(R16_390)=2,[1,16],
R16_390的8階理想子環有0個,8階非理想子環有0個,8階商環有0個
[1] => [1] 是理想 ,商環: [[1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16]]
[R16Add]
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
2 1 4 3 6 5 8 7 10 9 12 11 14 13 16 15
3 4 1 2 7 8 5 6 11 12 9 10 15 16 13 14
4 3 2 1 8 7 6 5 12 11 10 9 16 15 14 13
5 6 7 8 1 2 3 4 13 14 15 16 9 10 11 12
6 5 8 7 2 1 4 3 14 13 16 15 10 9 12 11
7 8 5 6 3 4 1 2 15 16 13 14 11 12 9 10
8 7 6 5 4 3 2 1 16 15 14 13 12 11 10 9
9 10 11 12 13 14 15 16 1 2 3 4 5 6 7 8
10 9 12 11 14 13 16 15 2 1 4 3 6 5 8 7
11 12 9 10 15 16 13 14 3 4 1 2 7 8 5 6
12 11 10 9 16 15 14 13 4 3 2 1 8 7 6 5
13 14 15 16 9 10 11 12 5 6 7 8 1 2 3 4
14 13 16 15 10 9 12 11 6 5 8 7 2 1 4 3
15 16 13 14 11 12 9 10 7 8 5 6 3 4 1 2
16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1
[R16Mul]
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 4 7 6 13 16 11 10 2 3 8 5 14 15 12 9
1 7 13 11 2 8 14 12 3 5 15 9 4 6 16 10
1 6 11 16 14 9 8 3 4 7 10 13 15 12 5 2
1 13 2 14 3 15 4 16 5 9 6 10 7 11 8 12
1 16 8 9 15 2 10 7 6 11 3 14 12 5 13 4
1 11 14 8 4 10 15 5 7 13 12 2 6 16 9 3
1 10 12 3 16 7 5 14 8 15 13 6 9 2 4 11
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
1 3 5 7 9 11 13 15 10 12 14 16 2 4 6 8
1 8 15 10 6 3 12 13 11 14 5 4 16 9 2 7
1 5 9 13 10 14 2 6 12 16 4 8 3 7 11 15
1 14 4 15 7 12 6 9 13 2 16 3 11 8 10 5
1 15 6 12 11 5 16 2 14 4 9 7 8 10 3 13
1 12 16 5 8 13 9 4 15 6 2 11 10 3 7 14
1 9 10 2 12 4 3 11 16 8 7 15 5 13 14 6
[2] => [1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16] 是理想 ,是中心 ,商環: [[1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16]]
[R1Add]
1
[R1Mul]
1
[7] => [1 7 9 15] 不是理想
[9] => [1 9] 不是理想
time consume: 1.646601949s
256階全矩陣環M_2(R4_5)的一個16階子環R16_379:4有零因子非交換無幺環,0,0,16,1,11,15,144,15,4
8階商環:R8_28、R8_31(找到了,還剩11種)、R8_28
8階理想子環:R8_26、R8_25、R8_25
R8_31=[5] => [1 5] 是理想 ,商環: [[1 5] [2 6] [3 7] [4 8] [9 13] [10 14] [11 15] [12 16]]
[1] => [1] 是理想 ,商環: [[1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16]]
[R16Add]
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
2 1 4 3 6 5 8 7 10 9 12 11 14 13 16 15
3 4 1 2 7 8 5 6 11 12 9 10 15 16 13 14
4 3 2 1 8 7 6 5 12 11 10 9 16 15 14 13
5 6 7 8 1 2 3 4 13 14 15 16 9 10 11 12
6 5 8 7 2 1 4 3 14 13 16 15 10 9 12 11
7 8 5 6 3 4 1 2 15 16 13 14 11 12 9 10
8 7 6 5 4 3 2 1 16 15 14 13 12 11 10 9
9 10 11 12 13 14 15 16 1 2 3 4 5 6 7 8
10 9 12 11 14 13 16 15 2 1 4 3 6 5 8 7
11 12 9 10 15 16 13 14 3 4 1 2 7 8 5 6
12 11 10 9 16 15 14 13 4 3 2 1 8 7 6 5
13 14 15 16 9 10 11 12 5 6 7 8 1 2 3 4
14 13 16 15 10 9 12 11 6 5 8 7 2 1 4 3
15 16 13 14 11 12 9 10 7 8 5 6 3 4 1 2
16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1
[R16Mul]
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2
1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2
1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2
1 1 6 6 1 1 6 6 5 5 2 2 5 5 2 2
1 1 6 6 1 1 6 6 5 5 2 2 5 5 2 2
1 1 6 6 1 1 6 6 6 6 1 1 6 6 1 1
1 1 6 6 1 1 6 6 6 6 1 1 6 6 1 1
1 1 6 6 1 1 6 6 5 5 2 2 5 5 2 2
1 1 6 6 1 1 6 6 5 5 2 2 5 5 2 2
1 1 6 6 1 1 6 6 6 6 1 1 6 6 1 1
1 1 6 6 1 1 6 6 6 6 1 1 6 6 1 1
[2] => [1 2] 是理想 ,商環: [[1 2] [3 4] [5 6] [7 8] [9 10] [11 12] [13 14] [15 16]]
[R8Add]
1 2 3 4 5 6 7 8
2 1 4 3 6 5 8 7
3 4 1 2 7 8 5 6
4 3 2 1 8 7 6 5
5 6 7 8 1 2 3 4
6 5 8 7 2 1 4 3
7 8 5 6 3 4 1 2
8 7 6 5 4 3 2 1
[R8Mul]
1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1
1 3 1 3 3 1 3 1
1 3 1 3 3 1 3 1
1 3 1 3 3 1 3 1
1 3 1 3 3 1 3 1
[3] => [1 3] 不是理想
[4] => [1 4] 不是理想
[5] => [1 5] 是理想 ,商環: [[1 5] [2 6] [3 7] [4 8] [9 13] [10 14] [11 15] [12 16]]
[R8Add]
1 2 3 4 5 6 7 8
2 1 4 3 6 5 8 7
3 4 1 2 7 8 5 6
4 3 2 1 8 7 6 5
5 6 7 8 1 2 3 4
6 5 8 7 2 1 4 3
7 8 5 6 3 4 1 2
8 7 6 5 4 3 2 1
[R8Mul]
1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1
1 1 1 1 2 2 2 2
1 1 1 1 2 2 2 2
1 1 2 2 1 1 2 2
1 1 2 2 1 1 2 2
1 1 2 2 2 2 1 1
1 1 2 2 2 2 1 1
[6] => [1 6] 是理想 ,商環: [[1 6] [2 5] [3 8] [4 7] [9 14] [10 13] [11 16] [12 15]]
[R8Add]
1 2 3 4 5 6 7 8
2 1 4 3 6 5 8 7
3 4 1 2 7 8 5 6
4 3 2 1 8 7 6 5
5 6 7 8 1 2 3 4
6 5 8 7 2 1 4 3
7 8 5 6 3 4 1 2
8 7 6 5 4 3 2 1
[R8Mul]
1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1
1 1 1 1 2 2 2 2
1 1 1 1 2 2 2 2
1 1 1 1 2 2 2 2
1 1 1 1 2 2 2 2
1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1
[7] => [1 7] 不是理想
[8] => [1 8] 不是理想
[9] => [1 5 9 13] 不是理想
[10] => [1 5 10 14] 不是理想
[11] => [1 11] 不是理想
[12] => [1 12] 不是理想
[15] => [1 15] 不是理想
[16] => [1 16] 不是理想
[2 3] => [1 2 3 4] 不是理想
[2 5] => [1 2 5 6] 是理想 ,是中心 ,商環: [[1 2 5 6] [3 4 7 8] [9 10 13 14] [11 12 15 16]]
[R4Add]
1 2 3 4
2 1 4 3
3 4 1 2
4 3 2 1
[R4Mul]
1 1 1 1
1 1 1 1
1 1 1 1
1 1 1 1
[3 5] => [1 3 5 7] 不是理想
[4 5] => [1 4 5 8] 不是理想
[3 6] => [1 3 6 8] 不是理想
[4 6] => [1 4 6 7] 不是理想
[2 7] => [1 2 7 8] 不是理想
[2 9] => [1 2 5 6 9 10 13 14] 是理想 ,商環: [[1 2 5 6 9 10 13 14] [3 4 7 8 11 12 15 16]]
[R2Add]
1 2
2 1
[R2Mul]
1 1
1 1
8 階子環:
[R8Add]
1 2 3 4 5 6 7 8
2 1 4 3 6 5 8 7
3 4 1 2 7 8 5 6
4 3 2 1 8 7 6 5
5 6 7 8 1 2 3 4
6 5 8 7 2 1 4 3
7 8 5 6 3 4 1 2
8 7 6 5 4 3 2 1
[R8Mul]
1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1
1 1 1 1 3 3 3 3
1 1 1 1 3 3 3 3
1 1 1 1 3 3 3 3
1 1 1 1 3 3 3 3
[3 9] => [1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16] 是理想 ,商環: [[1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16]]
[R1Add]
1
[R1Mul]
1
[2 11] => [1 2 11 12] 不是理想
[5 11] => [1 5 11 15] 不是理想
[6 11] => [1 6 11 16] 不是理想
[5 12] => [1 5 12 16] 不是理想
[6 12] => [1 6 12 15] 不是理想
[2 15] => [1 2 15 16] 不是理想
[2 3 5] => [1 2 3 4 5 6 7 8] 是理想 ,商環: [[1 2 3 4 5 6 7 8] [9 10 11 12 13 14 15 16]]
[R2Add]
1 2
2 1
[R2Mul]
1 1
1 1
8 階子環:
[R8Add]
1 2 3 4 5 6 7 8
2 1 4 3 6 5 8 7
3 4 1 2 7 8 5 6
4 3 2 1 8 7 6 5
5 6 7 8 1 2 3 4
6 5 8 7 2 1 4 3
7 8 5 6 3 4 1 2
8 7 6 5 4 3 2 1
[R8Mul]
1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1
[2 5 11] => [1 2 5 6 11 12 15 16] 是理想 ,商環: [[1 2 5 6 11 12 15 16] [3 4 7 8 9 10 13 14]]
[R2Add]
1 2
2 1
[R2Mul]
1 1
1 1
8 階子環:
[R8Add]
1 2 3 4 5 6 7 8
2 1 4 3 6 5 8 7
3 4 1 2 7 8 5 6
4 3 2 1 8 7 6 5
5 6 7 8 1 2 3 4
6 5 8 7 2 1 4 3
7 8 5 6 3 4 1 2
8 7 6 5 4 3 2 1
[R8Mul]
1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1
time consume: 2.077338191s
256階全矩陣環M_2(F_2×F_2)的一個16階子環R16_380:3有零因子非交換幺環,0,1,14,12,1,1,78,13,4
8階商環:R8_49、R8_50
8階理想子環:R8_49、R8_41、R8_47
8階非理想子環:R8_49、R8_49、R8_48、R8_50、R8_50
[1] => [1] 是理想 ,商環: [[1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16]]
[R16Add]
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
2 1 4 3 6 5 8 7 10 9 12 11 14 13 16 15
3 4 1 2 7 8 5 6 11 12 9 10 15 16 13 14
4 3 2 1 8 7 6 5 12 11 10 9 16 15 14 13
5 6 7 8 1 2 3 4 13 14 15 16 9 10 11 12
6 5 8 7 2 1 4 3 14 13 16 15 10 9 12 11
7 8 5 6 3 4 1 2 15 16 13 14 11 12 9 10
8 7 6 5 4 3 2 1 16 15 14 13 12 11 10 9
9 10 11 12 13 14 15 16 1 2 3 4 5 6 7 8
10 9 12 11 14 13 16 15 2 1 4 3 6 5 8 7
11 12 9 10 15 16 13 14 3 4 1 2 7 8 5 6
12 11 10 9 16 15 14 13 4 3 2 1 8 7 6 5
13 14 15 16 9 10 11 12 5 6 7 8 1 2 3 4
14 13 16 15 10 9 12 11 6 5 8 7 2 1 4 3
15 16 13 14 11 12 9 10 7 8 5 6 3 4 1 2
16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1
[R16Mul]
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 2 1 2 1 2 1 2 2 1 2 1 2 1 2 1
1 12 3 10 3 10 1 12 3 10 1 12 1 12 3 10
1 11 3 9 3 9 1 11 4 10 2 12 2 12 4 10
1 12 3 10 5 16 7 14 3 10 1 12 7 14 5 16
1 11 3 9 5 15 7 13 4 10 2 12 8 14 6 16
1 1 1 1 7 7 7 7 1 1 1 1 7 7 7 7
1 2 1 2 7 8 7 8 2 1 2 1 8 7 8 7
1 2 3 4 3 4 1 2 9 10 11 12 11 12 9 10
1 1 3 3 3 3 1 1 10 10 12 12 12 12 10 10
1 11 1 11 1 11 1 11 11 1 11 1 11 1 11 1
1 12 1 12 1 12 1 12 12 1 12 1 12 1 12 1
1 11 1 11 7 13 7 13 11 1 11 1 13 7 13 7
1 12 1 12 7 14 7 14 12 1 12 1 14 7 14 7
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
1 1 3 3 5 5 7 7 10 10 12 12 14 14 16 16
[2] => [1 2] 不是理想
[3] => [1 3] 不是理想
[4] => [1 4 9 12] 不是理想
[5] => [1 5] 不是理想
[6] => [1 6 12 15] 不是理想
[7] => [1 7] 是理想 ,商環: [[1 7] [2 8] [3 5] [4 6] [9 15] [10 16] [11 13] [12 14]]
[R8Add]
1 2 3 4 5 6 7 8
2 1 4 3 6 5 8 7
3 4 1 2 7 8 5 6
4 3 2 1 8 7 6 5
5 6 7 8 1 2 3 4
6 5 8 7 2 1 4 3
7 8 5 6 3 4 1 2
8 7 6 5 4 3 2 1
[R8Mul]
1 1 1 1 1 1 1 1
1 2 1 2 2 1 2 1
1 8 3 6 3 6 1 8
1 7 3 5 4 6 2 8
1 2 3 4 5 6 7 8
1 1 3 3 6 6 8 8
1 7 1 7 7 1 7 1
1 8 1 8 8 1 8 1
[8] => [1 8] 不是理想
[9] => [1 9] 不是理想
[10] => [1 10] 不是理想
[11] => [1 11] 不是理想
[12] => [1 12] 是理想 ,商環: [[1 12] [2 11] [3 10] [4 9] [5 16] [6 15] [7 14] [8 13]]
[R8Add]
1 2 3 4 5 6 7 8
2 1 4 3 6 5 8 7
3 4 1 2 7 8 5 6
4 3 2 1 8 7 6 5
5 6 7 8 1 2 3 4
6 5 8 7 2 1 4 3
7 8 5 6 3 4 1 2
8 7 6 5 4 3 2 1
[R8Mul]
1 1 1 1 1 1 1 1
1 2 1 2 1 2 1 2
1 1 3 3 3 3 1 1
1 2 3 4 3 4 1 2
1 1 3 3 5 5 7 7
1 2 3 4 5 6 7 8
1 1 1 1 7 7 7 7
1 2 1 2 7 8 7 8
[13] => [1 13] 不是理想
[14] => [1 7 12 14] 是理想 ,商環: [[1 7 12 14] [2 8 11 13] [3 5 10 16] [4 6 9 15]]
[R4Add]
1 2 3 4
2 1 4 3
3 4 1 2
4 3 2 1
[R4Mul]
1 1 1 1
1 2 1 2
1 1 3 3
1 2 3 4
[15] => [1 15] 不是理想
[16] => [1 16] 不是理想
[2 3] => [1 2 3 4 9 10 11 12] 是理想 ,商環: [[1 2 3 4 9 10 11 12] [5 6 7 8 13 14 15 16]]
[R2Add]
1 2
2 1
[R2Mul]
1 1
1 2
8 階子環:
[R8Add]
1 2 3 4 5 6 7 8
2 1 4 3 6 5 8 7
3 4 1 2 7 8 5 6
4 3 2 1 8 7 6 5
5 6 7 8 1 2 3 4
6 5 8 7 2 1 4 3
7 8 5 6 3 4 1 2
8 7 6 5 4 3 2 1
[R8Mul]
1 1 1 1 1 1 1 1
1 2 1 2 2 1 2 1
1 8 3 6 3 6 1 8
1 7 3 5 4 6 2 8
1 2 3 4 5 6 7 8
1 1 3 3 6 6 8 8
1 7 1 7 7 1 7 1
1 8 1 8 8 1 8 1
[2 5] => [1 2 5 6 11 12 15 16] 不是理想
8 階子環:
[R8Add]
1 2 3 4 5 6 7 8
2 1 4 3 6 5 8 7
3 4 1 2 7 8 5 6
4 3 2 1 8 7 6 5
5 6 7 8 1 2 3 4
6 5 8 7 2 1 4 3
7 8 5 6 3 4 1 2
8 7 6 5 4 3 2 1
[R8Mul]
1 1 1 1 1 1 1 1
1 2 1 2 2 1 2 1
1 6 3 8 1 6 3 8
1 5 3 7 2 6 4 8
1 5 1 5 5 1 5 1
1 6 1 6 6 1 6 1
1 2 3 4 5 6 7 8
1 1 3 3 6 6 8 8
[3 5] => [1 3 5 7] 不是理想
[4 5] => [1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16] 是理想 ,商環: [[1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16]]
[R1Add]
1
[R1Mul]
1
[3 6] => [1 3 6 8 10 12 13 15] 不是理想
8 階子環:
[R8Add]
1 2 3 4 5 6 7 8
2 1 4 3 6 5 8 7
3 4 1 2 7 8 5 6
4 3 2 1 8 7 6 5
5 6 7 8 1 2 3 4
6 5 8 7 2 1 4 3
7 8 5 6 3 4 1 2
8 7 6 5 4 3 2 1
[R8Mul]
1 1 1 1 1 1 1 1
1 2 5 6 5 6 1 2
1 2 8 7 5 6 4 3
1 1 4 4 1 1 4 4
1 2 2 1 5 6 6 5
1 1 6 6 1 1 6 6
1 1 7 7 1 1 7 7
1 2 3 4 5 6 7 8
[4 6] => [1 4 6 7 9 12 14 15] 不是理想
8 階子環:
[R8Add]
1 2 3 4 5 6 7 8
2 1 4 3 6 5 8 7
3 4 1 2 7 8 5 6
4 3 2 1 8 7 6 5
5 6 7 8 1 2 3 4
6 5 8 7 2 1 4 3
7 8 5 6 3 4 1 2
8 7 6 5 4 3 2 1
[R8Mul]
1 1 1 1 1 1 1 1
1 5 5 1 2 6 6 2
1 5 8 4 2 6 7 3
1 1 4 4 1 1 4 4
1 2 2 1 5 6 6 5
1 6 6 1 6 1 1 6
1 6 7 4 6 1 4 7
1 2 3 4 5 6 7 8
[2 7] => [1 2 7 8] 不是理想
[2 9] => [1 2 9 10] 不是理想
[3 9] => [1 3 9 11] 不是理想
[5 9] => [1 3 5 7 9 11 13 15] 不是理想
8 階子環:
[R8Add]
1 2 3 4 5 6 7 8
2 1 4 3 6 5 8 7
3 4 1 2 7 8 5 6
4 3 2 1 8 7 6 5
5 6 7 8 1 2 3 4
6 5 8 7 2 1 4 3
7 8 5 6 3 4 1 2
8 7 6 5 4 3 2 1
[R8Mul]
1 1 1 1 1 1 1 1
1 2 2 1 2 1 1 2
1 2 3 4 2 1 4 3
1 1 4 4 1 1 4 4
1 2 2 1 5 6 6 5
1 1 1 1 6 6 6 6
1 1 4 4 6 6 7 7
1 2 3 4 5 6 7 8
[7 9] => [1 7 9 15] 不是理想 ,是中心
[8 9] => [1 2 7 8 9 10 15 16] 不是理想
8 階子環:
[R8Add]
1 2 3 4 5 6 7 8
2 1 4 3 6 5 8 7
3 4 1 2 7 8 5 6
4 3 2 1 8 7 6 5
5 6 7 8 1 2 3 4
6 5 8 7 2 1 4 3
7 8 5 6 3 4 1 2
8 7 6 5 4 3 2 1
[R8Mul]
1 1 1 1 1 1 1 1
1 2 1 2 2 1 2 1
1 1 3 3 1 1 3 3
1 2 3 4 2 1 4 3
1 2 1 2 5 6 5 6
1 1 1 1 6 6 6 6
1 2 3 4 5 6 7 8
1 1 3 3 6 6 8 8
[3 10] => [1 3 10 12] 是理想 ,商環: [[1 3 10 12] [2 4 9 11] [5 7 14 16] [6 8 13 15]]
[R4Add]
1 2 3 4
2 1 4 3
3 4 1 2
4 3 2 1
[R4Mul]
1 1 1 1
1 2 1 2
1 1 3 3
1 2 3 4
[5 10] => [1 3 5 7 10 12 14 16] 是理想 ,商環: [[1 3 5 7 10 12 14 16] [2 4 6 8 9 11 13 15]]
[R2Add]
1 2
2 1
[R2Mul]
1 1
1 2
8 階子環:
[R8Add]
1 2 3 4 5 6 7 8
2 1 4 3 6 5 8 7
3 4 1 2 7 8 5 6
4 3 2 1 8 7 6 5
5 6 7 8 1 2 3 4
6 5 8 7 2 1 4 3
7 8 5 6 3 4 1 2
8 7 6 5 4 3 2 1
[R8Mul]
1 1 1 1 1 1 1 1
1 2 2 1 5 6 6 5
1 2 3 4 5 6 7 8
1 1 4 4 1 1 4 4
1 2 2 1 5 6 6 5
1 1 1 1 1 1 1 1
1 1 4 4 1 1 4 4
1 2 3 4 5 6 7 8
[7 10] => [1 7 10 16] 不是理想
[8 10] => [1 8 10 15] 不是理想
[2 11] => [1 2 11 12] 是理想 ,商環: [[1 2 11 12] [3 4 9 10] [5 6 15 16] [7 8 13 14]]
[R4Add]
1 2 3 4
2 1 4 3
3 4 1 2
4 3 2 1
[R4Mul]
1 1 1 1
1 2 2 1
1 2 3 4
1 1 4 4
[5 11] => [1 5 11 15] 不是理想
[7 11] => [1 7 11 13] 不是理想
[8 11] => [1 2 7 8 11 12 13 14] 是理想 ,商環: [[1 2 7 8 11 12 13 14] [3 4 5 6 9 10 15 16]]
[R2Add]
1 2
2 1
[R2Mul]
1 1
1 2
8 階子環:
[R8Add]
1 2 3 4 5 6 7 8
2 1 4 3 6 5 8 7
3 4 1 2 7 8 5 6
4 3 2 1 8 7 6 5
5 6 7 8 1 2 3 4
6 5 8 7 2 1 4 3
7 8 5 6 3 4 1 2
8 7 6 5 4 3 2 1
[R8Mul]
1 1 1 1 1 1 1 1
1 2 1 2 2 1 2 1
1 1 3 3 1 1 3 3
1 2 3 4 2 1 4 3
1 5 1 5 5 1 5 1
1 6 1 6 6 1 6 1
1 5 3 7 5 1 7 3
1 6 3 8 6 1 8 3
[5 12] => [1 5 12 16] 不是理想
[8 12] => [1 8 12 13] 不是理想
[3 13] => [1 3 13 15] 不是理想
[2 15] => [1 2 15 16] 不是理想
time consume: 1.711167172s
256階全矩陣環M_2(2Z/8Z)的一個16階子環R16_200:2有零因子交換無幺環,1,0,16,1,7,15,192,15,16
8階商環有7個:5個均是R_6、R_16、R_23中的一種,R8_26,R8_5
8階理想子環有2個:R_6、R_16、R_23中的一種,R8_25
[1] => [1] 是理想 ,商環: [[1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16]]
[R16Add]
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
2 1 4 3 6 5 8 7 10 9 12 11 14 13 16 15
3 4 6 5 7 8 2 1 11 12 14 13 15 16 10 9
4 3 5 6 8 7 1 2 12 11 13 14 16 15 9 10
5 6 7 8 1 2 3 4 13 14 15 16 9 10 11 12
6 5 8 7 2 1 4 3 14 13 16 15 10 9 12 11
7 8 2 1 3 4 6 5 15 16 10 9 11 12 14 13
8 7 1 2 4 3 5 6 16 15 9 10 12 11 13 14
9 10 11 12 13 14 15 16 1 2 3 4 5 6 7 8
10 9 12 11 14 13 16 15 2 1 4 3 6 5 8 7
11 12 14 13 15 16 10 9 3 4 6 5 7 8 2 1
12 11 13 14 16 15 9 10 4 3 5 6 8 7 1 2
13 14 15 16 9 10 11 12 5 6 7 8 1 2 3 4
14 13 16 15 10 9 12 11 6 5 8 7 2 1 4 3
15 16 10 9 11 12 14 13 7 8 2 1 3 4 6 5
16 15 9 10 12 11 13 14 8 7 1 2 4 3 5 6
[R16Mul]
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 9 9 1 1 9 9 1 1 9 9 1 1 9 9
1 1 9 9 1 1 9 9 1 1 9 9 1 1 9 9
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 9 9 1 1 9 9 1 1 9 9 1 1 9 9
1 1 9 9 1 1 9 9 1 1 9 9 1 1 9 9
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 9 9 1 1 9 9 1 1 9 9 1 1 9 9
1 1 9 9 1 1 9 9 1 1 9 9 1 1 9 9
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 9 9 1 1 9 9 1 1 9 9 1 1 9 9
1 1 9 9 1 1 9 9 1 1 9 9 1 1 9 9
[2] => [1 2] 是理想 ,商環: [[1 2] [3 4] [5 6] [7 8] [9 10] [11 12] [13 14] [15 16]]
[R8Add]
1 2 3 4 5 6 7 8
2 3 4 1 6 7 8 5
3 4 1 2 7 8 5 6
4 1 2 3 8 5 6 7
5 6 7 8 1 2 3 4
6 7 8 5 2 3 4 1
7 8 5 6 3 4 1 2
8 5 6 7 4 1 2 3
[R8Mul]
1 1 1 1 1 1 1 1
1 5 1 5 1 5 1 5
1 1 1 1 1 1 1 1
1 5 1 5 1 5 1 5
1 1 1 1 1 1 1 1
1 5 1 5 1 5 1 5
1 1 1 1 1 1 1 1
1 5 1 5 1 5 1 5
[3] => [1 3 6 8 9 11 14 16] 是理想 ,商環: [[1 3 6 8 9 11 14 16] [2 4 5 7 10 12 13 15]]
[R2Add]
1 2
2 1
[R2Mul]
1 1
1 1
8 階子環:
[R8Add]
1 2 3 4 5 6 7 8
2 3 4 1 6 7 8 5
3 4 1 2 7 8 5 6
4 1 2 3 8 5 6 7
5 6 7 8 1 2 3 4
6 7 8 5 2 3 4 1
7 8 5 6 3 4 1 2
8 5 6 7 4 1 2 3
[R8Mul]
1 1 1 1 1 1 1 1
1 5 1 5 1 5 1 5
1 1 1 1 1 1 1 1
1 5 1 5 1 5 1 5
1 1 1 1 1 1 1 1
1 5 1 5 1 5 1 5
1 1 1 1 1 1 1 1
1 5 1 5 1 5 1 5
[4] => [1 4 6 7 9 12 14 15] 是理想 ,商環: [[1 4 6 7 9 12 14 15] [2 3 5 8 10 11 13 16]]
[R2Add]
1 2
2 1
[R2Mul]
1 1
1 1
8 階子環:
[R8Add]
1 2 3 4 5 6 7 8
2 3 4 1 6 7 8 5
3 4 1 2 7 8 5 6
4 1 2 3 8 5 6 7
5 6 7 8 1 2 3 4
6 7 8 5 2 3 4 1
7 8 5 6 3 4 1 2
8 5 6 7 4 1 2 3
[R8Mul]
1 1 1 1 1 1 1 1
1 5 1 5 1 5 1 5
1 1 1 1 1 1 1 1
1 5 1 5 1 5 1 5
1 1 1 1 1 1 1 1
1 5 1 5 1 5 1 5
1 1 1 1 1 1 1 1
1 5 1 5 1 5 1 5
[5] => [1 5] 是理想 ,商環: [[1 5] [2 6] [3 7] [4 8] [9 13] [10 14] [11 15] [12 16]]
[R8Add]
1 2 3 4 5 6 7 8
2 1 4 3 6 5 8 7
3 4 2 1 7 8 6 5
4 3 1 2 8 7 5 6
5 6 7 8 1 2 3 4
6 5 8 7 2 1 4 3
7 8 6 5 3 4 2 1
8 7 5 6 4 3 1 2
[R8Mul]
1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1
1 1 5 5 1 1 5 5
1 1 5 5 1 1 5 5
1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1
1 1 5 5 1 1 5 5
1 1 5 5 1 1 5 5
[6] => [1 6] 是理想 ,商環: [[1 6] [2 5] [3 8] [4 7] [9 14] [10 13] [11 16] [12 15]]
[R8Add]
1 2 3 4 5 6 7 8
2 1 4 3 6 5 8 7
3 4 1 2 7 8 5 6
4 3 2 1 8 7 6 5
5 6 7 8 1 2 3 4
6 5 8 7 2 1 4 3
7 8 5 6 3 4 1 2
8 7 6 5 4 3 2 1
[R8Mul]
1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1
1 1 5 5 1 1 5 5
1 1 5 5 1 1 5 5
1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1
1 1 5 5 1 1 5 5
1 1 5 5 1 1 5 5
[9] => [1 9] 是理想 ,商環: [[1 9] [2 10] [3 11] [4 12] [5 13] [6 14] [7 15] [8 16]]
[R8Add]
1 2 3 4 5 6 7 8
2 1 4 3 6 5 8 7
3 4 6 5 7 8 2 1
4 3 5 6 8 7 1 2
5 6 7 8 1 2 3 4
6 5 8 7 2 1 4 3
7 8 2 1 3 4 6 5
8 7 1 2 4 3 5 6
[R8Mul]
1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1
[10] => [1 10] 是理想 ,商環: [[1 10] [2 9] [3 12] [4 11] [5 14] [6 13] [7 16] [8 15]]
[R8Add]
1 2 3 4 5 6 7 8
2 1 4 3 6 5 8 7
3 4 6 5 7 8 2 1
4 3 5 6 8 7 1 2
5 6 7 8 1 2 3 4
6 5 8 7 2 1 4 3
7 8 2 1 3 4 6 5
8 7 1 2 4 3 5 6
[R8Mul]
1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1
1 1 2 2 1 1 2 2
1 1 2 2 1 1 2 2
1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1
1 1 2 2 1 1 2 2
1 1 2 2 1 1 2 2
[13] => [1 13] 是理想 ,商環: [[1 13] [2 14] [3 15] [4 16] [5 9] [6 10] [7 11] [8 12]]
[R8Add]
1 2 3 4 5 6 7 8
2 1 4 3 6 5 8 7
3 4 6 5 7 8 2 1
4 3 5 6 8 7 1 2
5 6 7 8 1 2 3 4
6 5 8 7 2 1 4 3
7 8 2 1 3 4 6 5
8 7 1 2 4 3 5 6
[R8Mul]
1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1
1 1 5 5 1 1 5 5
1 1 5 5 1 1 5 5
1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1
1 1 5 5 1 1 5 5
1 1 5 5 1 1 5 5
[14] => [1 14] 是理想 ,商環: [[1 14] [2 13] [3 16] [4 15] [5 10] [6 9] [7 12] [8 11]]
[R8Add]
1 2 3 4 5 6 7 8
2 1 4 3 6 5 8 7
3 4 6 5 7 8 2 1
4 3 5 6 8 7 1 2
5 6 7 8 1 2 3 4
6 5 8 7 2 1 4 3
7 8 2 1 3 4 6 5
8 7 1 2 4 3 5 6
[R8Mul]
1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1
1 1 6 6 1 1 6 6
1 1 6 6 1 1 6 6
1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1
1 1 6 6 1 1 6 6
1 1 6 6 1 1 6 6
[2 3] => [1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16] 是理想 ,是中心 ,商環: [[1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16]]
[R1Add]
1
[R1Mul]
1
[2 5] => [1 2 5 6] 是理想 ,商環: [[1 2 5 6] [3 4 7 8] [9 10 13 14] [11 12 15 16]]
[R4Add]
1 2 3 4
2 1 4 3
3 4 1 2
4 3 2 1
[R4Mul]
1 1 1 1
1 3 1 3
1 1 1 1
1 3 1 3
[2 9] => [1 2 9 10] 是理想 ,商環: [[1 2 9 10] [3 4 11 12] [5 6 13 14] [7 8 15 16]]
[R4Add]
1 2 3 4
2 3 4 1
3 4 1 2
4 1 2 3
[R4Mul]
1 1 1 1
1 1 1 1
1 1 1 1
1 1 1 1
[5 9] => [1 5 9 13] 是理想 ,商環: [[1 5 9 13] [2 6 10 14] [3 7 11 15] [4 8 12 16]]
[R4Add]
1 2 3 4
2 1 4 3
3 4 2 1
4 3 1 2
[R4Mul]
1 1 1 1
1 1 1 1
1 1 1 1
1 1 1 1
[6 9] => [1 6 9 14] 是理想 ,商環: [[1 6 9 14] [2 5 10 13] [3 8 11 16] [4 7 12 15]]
[R4Add]
1 2 3 4
2 1 4 3
3 4 1 2
4 3 2 1
[R4Mul]
1 1 1 1
1 1 1 1
1 1 1 1
1 1 1 1
[5 10] => [1 5 10 14] 是理想 ,商環: [[1 5 10 14] [2 6 9 13] [3 7 12 16] [4 8 11 15]]
[R4Add]
1 2 3 4
2 1 4 3
3 4 2 1
4 3 1 2
[R4Mul]
1 1 1 1
1 1 1 1
1 1 2 2
1 1 2 2
[6 10] => [1 6 10 13] 是理想 ,商環: [[1 6 10 13] [2 5 9 14] [3 8 12 15] [4 7 11 16]]
[R4Add]
1 2 3 4
2 1 4 3
3 4 1 2
4 3 2 1
[R4Mul]
1 1 1 1
1 1 1 1
1 1 2 2
1 1 2 2
[2 13] => [1 2 13 14] 是理想 ,商環: [[1 2 13 14] [3 4 15 16] [5 6 9 10] [7 8 11 12]]
[R4Add]
1 2 3 4
2 3 4 1
3 4 1 2
4 1 2 3
[R4Mul]
1 1 1 1
1 3 1 3
1 1 1 1
1 3 1 3
[2 5 9] => [1 2 5 6 9 10 13 14] 是理想 ,商環: [[1 2 5 6 9 10 13 14] [3 4 7 8 11 12 15 16]]
[R2Add]
1 2
2 1
[R2Mul]
1 1
1 1
8 階子環:
[R8Add]
1 2 3 4 5 6 7 8
2 1 4 3 6 5 8 7
3 4 1 2 7 8 5 6
4 3 2 1 8 7 6 5
5 6 7 8 1 2 3 4
6 5 8 7 2 1 4 3
7 8 5 6 3 4 1 2
8 7 6 5 4 3 2 1
[R8Mul]
1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1
time consume: 1.938026894s
256階全矩陣環M_2(F_4)的一個16階子環R16_381:4有零因子非交換無幺環,0,0,16,5,3,3,76,3,1
S(R16_381)=21,[1,2,2,2,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,8,16],
N(R16_381)=3,[1,4,16],
R16_381的8階理想子環有0個,R16_381的8階非理想子環有1個R8_30,R16_381的8階商環有0個
[1] => [1] 是理想 ,是中心 ,商環: [[1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16]]
[R16Add]
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
2 1 4 3 6 5 8 7 10 9 12 11 14 13 16 15
3 4 1 2 7 8 5 6 11 12 9 10 15 16 13 14
4 3 2 1 8 7 6 5 12 11 10 9 16 15 14 13
5 6 7 8 1 2 3 4 13 14 15 16 9 10 11 12
6 5 8 7 2 1 4 3 14 13 16 15 10 9 12 11
7 8 5 6 3 4 1 2 15 16 13 14 11 12 9 10
8 7 6 5 4 3 2 1 16 15 14 13 12 11 10 9
9 10 11 12 13 14 15 16 1 2 3 4 5 6 7 8
10 9 12 11 14 13 16 15 2 1 4 3 6 5 8 7
11 12 9 10 15 16 13 14 3 4 1 2 7 8 5 6
12 11 10 9 16 15 14 13 4 3 2 1 8 7 6 5
13 14 15 16 9 10 11 12 5 6 7 8 1 2 3 4
14 13 16 15 10 9 12 11 6 5 8 7 2 1 4 3
15 16 13 14 11 12 9 10 7 8 5 6 3 4 1 2
16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1
[R16Mul]
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 4 2 3 13 16 14 15 5 8 6 7 9 12 10 11
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
1 3 4 2 9 11 12 10 13 15 16 14 5 7 8 6
1 4 2 3 13 16 14 15 5 8 6 7 9 12 10 11
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 3 4 2 9 11 12 10 13 15 16 14 5 7 8 6
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
1 3 4 2 9 11 12 10 13 15 16 14 5 7 8 6
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 4 2 3 13 16 14 15 5 8 6 7 9 12 10 11
1 3 4 2 9 11 12 10 13 15 16 14 5 7 8 6
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
1 4 2 3 13 16 14 15 5 8 6 7 9 12 10 11
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[2] => [1 2 3 4] 不是理想
[3] => [1 3] 不是理想
[5] => [1 5 9 13] 不是理想
[6] => [1 6] 不是理想
[7] => [1 7 12 14] 不是理想
[8] => [1 8] 不是理想
[9] => [1 9] 不是理想
[10] => [1 8 10 15] 不是理想
[11] => [1 11] 不是理想
[14] => [1 14] 不是理想
[16] => [1 16] 不是理想
[2 5] => [1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16] 是理想 ,商環: [[1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16]]
[R1Add]
1
[R1Mul]
1
[3 6] => [1 3 6 8] 不是理想
[3 9] => [1 3 9 11] 不是理想
[6 9] => [1 6 9 14] 不是理想
[8 9] => [1 8 9 16] 不是理想
[6 11] => [1 6 11 16] 是理想 ,商環: [[1 6 11 16] [2 5 12 15] [3 8 9 14] [4 7 10 13]]
[R4Add]
1 2 3 4
2 1 4 3
3 4 1 2
4 3 2 1
[R4Mul]
1 1 1 1
1 4 2 3
1 2 3 4
1 3 4 2
[8 11] => [1 8 11 14] 不是理想
[3 14] => [1 3 14 16] 不是理想
[3 6 9] => [1 3 6 8 9 11 14 16] 不是理想
8 階子環:
[R8Add]
1 2 3 4 5 6 7 8
2 1 4 3 6 5 8 7
3 4 1 2 7 8 5 6
4 3 2 1 8 7 6 5
5 6 7 8 1 2 3 4
6 5 8 7 2 1 4 3
7 8 5 6 3 4 1 2
8 7 6 5 4 3 2 1
[R8Mul]
1 1 1 1 1 1 1 1
1 2 3 4 5 6 7 8
1 1 1 1 1 1 1 1
1 2 3 4 5 6 7 8
1 2 3 4 5 6 7 8
1 1 1 1 1 1 1 1
1 2 3 4 5 6 7 8
1 1 1 1 1 1 1 1
time consume: 1.70606846s
256階全矩陣環M_2(2Z/8Z)的一個16階子環R16_108:4有零因子非交換無幺環,0,0,16,1,7,15,160,15,4
S(R16_108)=15,[1,2,2,2,4,4,4,4,4,4,4,8,8,8,16],
N(R16_108)=11,[1,2,2,2,4,4,4,8,8,8,16],
R16_108的8階理想子環有3個(R8_16、R8_16、R8_5),R16_108的8階非理想子環有0個,R16_108的8階商環有3個(2個均是R8_8、R_10中的一個,R8_16)
[1] => [1] 是理想 ,商環: [[1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16]]
[R16Add]
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
2 3 4 1 6 7 8 5 10 11 12 9 14 15 16 13
3 4 1 2 7 8 5 6 11 12 9 10 15 16 13 14
4 1 2 3 8 5 6 7 12 9 10 11 16 13 14 15
5 6 7 8 9 10 11 12 13 14 15 16 1 2 3 4
6 7 8 5 10 11 12 9 14 15 16 13 2 3 4 1
7 8 5 6 11 12 9 10 15 16 13 14 3 4 1 2
8 5 6 7 12 9 10 11 16 13 14 15 4 1 2 3
9 10 11 12 13 14 15 16 1 2 3 4 5 6 7 8
10 11 12 9 14 15 16 13 2 3 4 1 6 7 8 5
11 12 9 10 15 16 13 14 3 4 1 2 7 8 5 6
12 9 10 11 16 13 14 15 4 1 2 3 8 5 6 7
13 14 15 16 1 2 3 4 5 6 7 8 9 10 11 12
14 15 16 13 2 3 4 1 6 7 8 5 10 11 12 9
15 16 13 14 3 4 1 2 7 8 5 6 11 12 9 10
16 13 14 15 4 1 2 3 8 5 6 7 12 9 10 11
[R16Mul]
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 3 1 3 9 11 9 11 1 3 1 3 9 11 9 11
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 3 1 3 9 11 9 11 1 3 1 3 9 11 9 11
1 3 1 3 9 11 9 11 1 3 1 3 9 11 9 11
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 3 1 3 9 11 9 11 1 3 1 3 9 11 9 11
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 3 1 3 9 11 9 11 1 3 1 3 9 11 9 11
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 3 1 3 9 11 9 11 1 3 1 3 9 11 9 11
1 3 1 3 9 11 9 11 1 3 1 3 9 11 9 11
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 3 1 3 9 11 9 11 1 3 1 3 9 11 9 11
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[2] => [1 2 3 4] 不是理想
[3] => [1 3] 是理想 ,商環: [[1 3] [2 4] [5 7] [6 8] [9 11] [10 12] [13 15] [14 16]]
[R8Add]
1 2 3 4 5 6 7 8
2 1 4 3 6 5 8 7
3 4 5 6 7 8 1 2
4 3 6 5 8 7 2 1
5 6 7 8 1 2 3 4
6 5 8 7 2 1 4 3
7 8 1 2 3 4 5 6
8 7 2 1 4 3 6 5
[R8Mul]
1 1 1 1 1 1 1 1
1 1 5 5 1 1 5 5
1 1 5 5 1 1 5 5
1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1
1 1 5 5 1 1 5 5
1 1 5 5 1 1 5 5
1 1 1 1 1 1 1 1
[5] => [1 5 9 13] 不是理想
[6] => [1 6 11 16] 是理想 ,商環: [[1 6 11 16] [2 7 12 13] [3 8 9 14] [4 5 10 15]]
[R4Add]
1 2 3 4
2 3 4 1
3 4 1 2
4 1 2 3
[R4Mul]
1 1 1 1
1 3 1 3
1 1 1 1
1 3 1 3
[7] => [1 7 9 15] 不是理想
[8] => [1 8 11 14] 是理想 ,商環: [[1 8 11 14] [2 5 12 15] [3 6 9 16] [4 7 10 13]]
[R4Add]
1 2 3 4
2 3 4 1
3 4 1 2
4 1 2 3
[R4Mul]
1 1 1 1
1 3 1 3
1 1 1 1
1 3 1 3
[9] => [1 9] 是理想 ,商環: [[1 9] [2 10] [3 11] [4 12] [5 13] [6 14] [7 15] [8 16]]
[R8Add]
1 2 3 4 5 6 7 8
2 3 4 1 6 7 8 5
3 4 1 2 7 8 5 6
4 1 2 3 8 5 6 7
5 6 7 8 1 2 3 4
6 7 8 5 2 3 4 1
7 8 5 6 3 4 1 2
8 5 6 7 4 1 2 3
[R8Mul]
1 1 1 1 1 1 1 1
1 3 1 3 1 3 1 3
1 1 1 1 1 1 1 1
1 3 1 3 1 3 1 3
1 3 1 3 1 3 1 3
1 1 1 1 1 1 1 1
1 3 1 3 1 3 1 3
1 1 1 1 1 1 1 1
[10] => [1 3 10 12] 不是理想
[11] => [1 11] 是理想 ,商環: [[1 11] [2 12] [3 9] [4 10] [5 15] [6 16] [7 13] [8 14]]
[R8Add]
1 2 3 4 5 6 7 8
2 3 4 1 6 7 8 5
3 4 1 2 7 8 5 6
4 1 2 3 8 5 6 7
5 6 7 8 3 4 1 2
6 7 8 5 4 1 2 3
7 8 5 6 1 2 3 4
8 5 6 7 2 3 4 1
[R8Mul]
1 1 1 1 1 1 1 1
1 3 1 3 3 1 3 1
1 1 1 1 1 1 1 1
1 3 1 3 3 1 3 1
1 3 1 3 3 1 3 1
1 1 1 1 1 1 1 1
1 3 1 3 3 1 3 1
1 1 1 1 1 1 1 1
[2 5] => [1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16] 是理想 ,商環: [[1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16]]
[R1Add]
1
[R1Mul]
1
[3 5] => [1 3 5 7 9 11 13 15] 是理想 ,商環: [[1 3 5 7 9 11 13 15] [2 4 6 8 10 12 14 16]]
[R2Add]
1 2
2 1
[R2Mul]
1 1
1 1
8 階子環:
[R8Add]
1 2 3 4 5 6 7 8
2 1 4 3 6 5 8 7
3 4 5 6 7 8 1 2
4 3 6 5 8 7 2 1
5 6 7 8 1 2 3 4
6 5 8 7 2 1 4 3
7 8 1 2 3 4 5 6
8 7 2 1 4 3 6 5
[R8Mul]
1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1
1 1 5 5 1 1 5 5
1 1 5 5 1 1 5 5
1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1
1 1 5 5 1 1 5 5
1 1 5 5 1 1 5 5
[3 6] => [1 3 6 8 9 11 14 16] 是理想 ,商環: [[1 3 6 8 9 11 14 16] [2 4 5 7 10 12 13 15]]
[R2Add]
1 2
2 1
[R2Mul]
1 1
1 1
8 階子環:
[R8Add]
1 2 3 4 5 6 7 8
2 1 4 3 6 5 8 7
3 4 6 5 7 8 2 1
4 3 5 6 8 7 1 2
5 6 7 8 1 2 3 4
6 5 8 7 2 1 4 3
7 8 2 1 3 4 6 5
8 7 1 2 4 3 5 6
[R8Mul]
1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1
[2 9] => [1 2 3 4 9 10 11 12] 是理想 ,商環: [[1 2 3 4 9 10 11 12] [5 6 7 8 13 14 15 16]]
[R2Add]
1 2
2 1
[R2Mul]
1 1
1 1
8 階子環:
[R8Add]
1 2 3 4 5 6 7 8
2 3 4 1 6 7 8 5
3 4 1 2 7 8 5 6
4 1 2 3 8 5 6 7
5 6 7 8 1 2 3 4
6 7 8 5 2 3 4 1
7 8 5 6 3 4 1 2
8 5 6 7 4 1 2 3
[R8Mul]
1 1 1 1 1 1 1 1
1 3 1 3 1 3 1 3
1 1 1 1 1 1 1 1
1 3 1 3 1 3 1 3
1 1 1 1 1 1 1 1
1 3 1 3 1 3 1 3
1 1 1 1 1 1 1 1
1 3 1 3 1 3 1 3
[3 9] => [1 3 9 11] 是理想 ,是中心 ,商環: [[1 3 9 11] [2 4 10 12] [5 7 13 15] [6 8 14 16]]
[R4Add]
1 2 3 4
2 1 4 3
3 4 1 2
4 3 2 1
[R4Mul]
1 1 1 1
1 1 1 1
1 1 1 1
1 1 1 1
time consume: 2.05997964s
[email protected]:/home/hanxiaohua/work1/MathTool/gaptool# g++ -o calRing calRing.cpp
[email protected]:/home/hanxiaohua/work1/MathTool/gaptool# ./calRing /home/cpptest/gotest/R16.txt
R16:2有零因子交換無幺環,1,0,16,1,15,15,256,15,16
這個R16是256階全矩陣環M_2(M_4)的一個16階子環R16_107:2有零因子交換無幺環,1,0,16,1,15,15,256,15,16
[email protected]:/home/cpptest/gotest# ./AllSubRings R16.txt 8
vvA= [[1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16] [2 3 4 1 6 7 8 5 10 11 12 9 14 15 16 13] [3 4 1 2 7 8 5 6 11 12 9 10 15 16 13 14] [4 1 2 3 8 5 6 7 12 9 10 11 16 13 14 15] [5 6 7 8 9 10 11 12 13 14 15 16 1 2 3 4] [6 7 8 5 10 11 12 9 14 15 16 13 2 3 4 1] [7 8 5 6 11 12 9 10 15 16 13 14 3 4 1 2] [8 5 6 7 12 9 10 11 16 13 14 15 4 1 2 3] [9 10 11 12 13 14 15 16 1 2 3 4 5 6 7 8] [10 11 12 9 14 15 16 13 2 3 4 1 6 7 8 5] [11 12 9 10 15 16 13 14 3 4 1 2 7 8 5 6] [12 9 10 11 16 13 14 15 4 1 2 3 8 5 6 7] [13 14 15 16 1 2 3 4 5 6 7 8 9 10 11 12] [14 15 16 13 2 3 4 1 6 7 8 5 10 11 12 9] [15 16 13 14 3 4 1 2 7 8 5 6 11 12 9 10] [16 13 14 15 4 1 2 3 8 5 6 7 12 9 10 11]]
vvM= [[1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1] [1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1] [1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1] [1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1] [1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1] [1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1] [1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1] [1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1] [1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1] [1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1] [1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1] [1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1] [1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1] [1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1] [1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1] [1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]]
AFlagA= [0 16 16]
AFlagM= [0 16 16]
[1] => [1] 是理想 ,商環: [[1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16]]
[R16Add]
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
2 3 4 1 6 7 8 5 10 11 12 9 14 15 16 13
3 4 1 2 7 8 5 6 11 12 9 10 15 16 13 14
4 1 2 3 8 5 6 7 12 9 10 11 16 13 14 15
5 6 7 8 9 10 11 12 13 14 15 16 1 2 3 4
6 7 8 5 10 11 12 9 14 15 16 13 2 3 4 1
7 8 5 6 11 12 9 10 15 16 13 14 3 4 1 2
8 5 6 7 12 9 10 11 16 13 14 15 4 1 2 3
9 10 11 12 13 14 15 16 1 2 3 4 5 6 7 8
10 11 12 9 14 15 16 13 2 3 4 1 6 7 8 5
11 12 9 10 15 16 13 14 3 4 1 2 7 8 5 6
12 9 10 11 16 13 14 15 4 1 2 3 8 5 6 7
13 14 15 16 1 2 3 4 5 6 7 8 9 10 11 12
14 15 16 13 2 3 4 1 6 7 8 5 10 11 12 9
15 16 13 14 3 4 1 2 7 8 5 6 11 12 9 10
16 13 14 15 4 1 2 3 8 5 6 7 12 9 10 11
[R16Mul]
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[2] => [1 2 3 4] 是理想 ,商環: [[1 2 3 4] [5 6 7 8] [9 10 11 12] [13 14 15 16]]
[R4Add]
1 2 3 4
2 3 4 1
3 4 1 2
4 1 2 3
[R4Mul]
1 1 1 1
1 1 1 1
1 1 1 1
1 1 1 1
[3] => [1 3] 是理想 ,商環: [[1 3] [2 4] [5 7] [6 8] [9 11] [10 12] [13 15] [14 16]]
[R8Add]
1 2 3 4 5 6 7 8
2 1 4 3 6 5 8 7
3 4 5 6 7 8 1 2
4 3 6 5 8 7 2 1
5 6 7 8 1 2 3 4
6 5 8 7 2 1 4 3
7 8 1 2 3 4 5 6
8 7 2 1 4 3 6 5
[R8Mul]
1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1
[5] => [1 5 9 13] 是理想 ,商環: [[1 5 9 13] [2 6 10 14] [3 7 11 15] [4 8 12 16]]
[R4Add]
1 2 3 4
2 3 4 1
3 4 1 2
4 1 2 3
[R4Mul]
1 1 1 1
1 1 1 1
1 1 1 1
1 1 1 1
[6] => [1 6 11 16] 是理想 ,商環: [[1 6 11 16] [2 7 12 13] [3 8 9 14] [4 5 10 15]]
[R4Add]
1 2 3 4
2 3 4 1
3 4 1 2
4 1 2 3
[R4Mul]
1 1 1 1
1 1 1 1
1 1 1 1
1 1 1 1
[7] => [1 7 9 15] 是理想 ,商環: [[1 7 9 15] [2 8 10 16] [3 5 11 13] [4 6 12 14]]
[R4Add]
1 2 3 4
2 3 4 1
3 4 1 2
4 1 2 3
[R4Mul]
1 1 1 1
1 1 1 1
1 1 1 1
1 1 1 1
[8] => [1 8 11 14] 是理想 ,商環: [[1 8 11 14] [2 5 12 15] [3 6 9 16] [4 7 10 13]]
[R4Add]
1 2 3 4
2 3 4 1
3 4 1 2
4 1 2 3
[R4Mul]
1 1 1 1
1 1 1 1
1 1 1 1
1 1 1 1
[9] => [1 9] 是理想 ,商環: [[1 9] [2 10] [3 11] [4 12] [5 13] [6 14] [7 15] [8 16]]
[R8Add]
1 2 3 4 5 6 7 8
2 3 4 1 6 7 8 5
3 4 1 2 7 8 5 6
4 1 2 3 8 5 6 7
5 6 7 8 1 2 3 4
6 7 8 5 2 3 4 1
7 8 5 6 3 4 1 2
8 5 6 7 4 1 2 3
[R8Mul]
1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1
[10] => [1 3 10 12] 是理想 ,商環: [[1 3 10 12] [2 4 9 11] [5 7 14 16] [6 8 13 15]]
[R4Add]
1 2 3 4
2 1 4 3
3 4 2 1
4 3 1 2
[R4Mul]
1 1 1 1
1 1 1 1
1 1 1 1
1 1 1 1
[11] => [1 11] 是理想 ,商環: [[1 11] [2 12] [3 9] [4 10] [5 15] [6 16] [7 13] [8 14]]
[R8Add]
1 2 3 4 5 6 7 8
2 3 4 1 6 7 8 5
3 4 1 2 7 8 5 6
4 1 2 3 8 5 6 7
5 6 7 8 3 4 1 2
6 7 8 5 4 1 2 3
7 8 5 6 1 2 3 4
8 5 6 7 2 3 4 1
[R8Mul]
1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1
[2 5] => [1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16] 是理想 ,是中心 ,商環: [[1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16]]
[R1Add]
1
[R1Mul]
1
[3 5] => [1 3 5 7 9 11 13 15] 是理想 ,商環: [[1 3 5 7 9 11 13 15] [2 4 6 8 10 12 14 16]]
[R2Add]
1 2
2 1
[R2Mul]
1 1
1 1
8 階子環:
[R8Add]
1 2 3 4 5 6 7 8
2 1 4 3 6 5 8 7
3 4 5 6 7 8 1 2
4 3 6 5 8 7 2 1
5 6 7 8 1 2 3 4
6 5 8 7 2 1 4 3
7 8 1 2 3 4 5 6
8 7 2 1 4 3 6 5
[R8Mul]
1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1
[3 6] => [1 3 6 8 9 11 14 16] 是理想 ,商環: [[1 3 6 8 9 11 14 16] [2 4 5 7 10 12 13 15]]
[R2Add]
1 2
2 1
[R2Mul]
1 1
1 1
8 階子環:
[R8Add]
1 2 3 4 5 6 7 8
2 1 4 3 6 5 8 7
3 4 6 5 7 8 2 1
4 3 5 6 8 7 1 2
5 6 7 8 1 2 3 4
6 5 8 7 2 1 4 3
7 8 2 1 3 4 6 5
8 7 1 2 4 3 5 6
[R8Mul]
1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1
[2 9] => [1 2 3 4 9 10 11 12] 是理想 ,商環: [[1 2 3 4 9 10 11 12] [5 6 7 8 13 14 15 16]]
[R2Add]
1 2
2 1
[R2Mul]
1 1
1 1
8 階子環:
[R8Add]
1 2 3 4 5 6 7 8
2 3 4 1 6 7 8 5
3 4 1 2 7 8 5 6
4 1 2 3 8 5 6 7
5 6 7 8 1 2 3 4
6 7 8 5 2 3 4 1
7 8 5 6 3 4 1 2
8 5 6 7 4 1 2 3
[R8Mul]
1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1
[3 9] => [1 3 9 11] 是理想 ,商環: [[1 3 9 11] [2 4 10 12] [5 7 13 15] [6 8 14 16]]
[R4Add]
1 2 3 4
2 1 4 3
3 4 1 2
4 3 2 1
[R4Mul]
1 1 1 1
1 1 1 1
1 1 1 1
1 1 1 1
time consume: 1.757249791s