Lattice LAMBDA(S3)
格目录中的条目,这是一个联合项目
Gabriele Nebe,亚琛RWTH大学(nebe@math.rwth-aachen.de)和
尼尔·J·A·斯隆(njasloane@gmail.com)
上次修改时间:2014年7月18日星期五13:17:50 CEST
索引文件|缩写
此文件的内容
名称
尺寸
格拉姆
DET公司
最小_形式
MINVECS公司
亲吻_编号
密度
HERMITE_NUMBER公司
组订单(_O)
发电机组
学士_心理学
属性
参考文献
笔记
最后一行
-
名称
兰巴达(S3)
-
尺寸
32
-
格拉姆
32 0
4
0 4
0 -1 4
1 0 1 4
0 0 -1 -1 4
0 0 0 1 0 4
0 1 -1 0 0 0 4
1 -1 0 0 -1 -2 0 4
0 1 0 -1 -1 0 1 0 4
-1 0 -1 -1 0 1 0 0 1 4
1 1 0-1 0 0 0 0 1 0 4
-1 1 -1 0 1 1 1 -2 0 0 -1 4
1 0 0 0 -1 -1 0 2 0 0 1 -2 4
1 -1 1 1 -1 0 0 0 -1 -1 0 0 -1 4
1 0 0 0 0 1 -1 0 1 1 -1 0 -1 -1 4
0 0 0 0 1-1 0-1 0 0 0-1 0 4
0 0 -1 0 1 -1 1 0 0 0 0 1 0 0 -1 0 4
1 0 0 1 1 0 -1 0 -1 0 -1 1 -1 0 1 2 -1 4
1 -1 1 0 1 1 -1 -1 0 0 0 0 -1 0 1 1 -1 2 4
-1 0 0 0 1 2 -1 -2 0 1 0 1 -1 0 0 -1 -1 0 0 4
2 0 1 0 -1 -1 0 1 0 -2 1 -1 0 1 0 1 -1 1 1 -2 4
0 -1 -1 0 0 0 0 1 -1 1 -1 0 0 1 0 -1 2 -1 -1 -1 -1 4
0 -2 0 1 -1 0 0 2 -1 0 -1 -1 0 1 0 -1 0 0 -1 0 0 1 4
-1 1 1 0 1 0 -1 -2 0 -1 0 1 -1 0 0 0 0 0 0 1 -1 -1 -2 4
0 -2 2 0 -1 1 0 0 0 0 0 -1 -1 2 0 -1 -1 -1 1 0 1 1 1 -1 4
1 1 1 1 0 2 -1 -2 0 0 1 0 0 0 1 0 -1 0 1 1 0 -1 -2 2 0 4
2 0 0 1 1 0 0 0 -2 -2 0 0 0 1 0 1 0 1 1 -1 2 0 0 0 0 1 4
1 -1 1 1 0 -1 0 1 -2 -2 1 -1 1 2 -2 0 1 -1 -1 -1 1 1 1 0 1 0 2 4
0 0 1 1 1 1 -1 -2 -1 -1 1 1 -1 1 -1 1 -1 1 1 2 0 -2 -1 2 0 2 1 1 4
0 2 -1 0 0 0 1 -1 1 0 2 1 1 -1 -1 0 1 -1 -1 0 -1 -1 -2 1 -2 1 -1 0 1 4
0 0 -2 -2 1 -2 1 1 0 0 1 0 1 0 -2 0 2 -1 -1 -1 0 1 0 -1 -1 -2 0 1 -1 1 4
-2 -1 0 0 1 1 1 -1 0 1 -1 1 -1 0 -1 -1 1 -1 -1 2 -2 1 1 0 1 -1 -1 0 0 -1 0 4
-
DET公司
1
-
最小_形式
4
-
MINVECS公司
-
亲吻_编号
146880
-
密度
-
HERMITE_NUMBER公司
4
-
组订单(_O)
2^16 3^4 5
-
发电机组
13
32 32
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32 32
0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 -1 0 1 -1 -1 -1 -1 -1 -1 1 0 1 0 0 0 0 0
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1 0 0 1 1 0 -1 0 0 1 0 1 0 0 -1 0 0 -1 -1 -1 -1 -2 0 0 1 0 0 0 -1 -1 0 -1
0 1 0 0 1-1 0 0 0-1 1 2 2 2-3 3 4 1 4 3 3 1-3 1-2 1-1 3 0 3
0 -1 0 0 -1 1 0 0 0 0 1 -1 -1 -1 0 -2 1 2 -2 -1 -2 -1 -3 -1 0 -1 1 0 1 -2 0 -1
0 -1 0 1 0 0 0 -1 0 1 1 0 0 -1 -1 -1 1 1 -2 -1 -1 -1 -1 0 1 -1 1 -1 1 -2 0 -2
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32 32
0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 -1 0 0 -1 -2 -1 -1 -1 -1 0 0 0 0 1 -1 0 0
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32 32
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32 32
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32 32
0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 -1 0 1 -1 -1 -1 -1 -1 -1 1 0 1 0 0 0 0 0
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1 0 -2 1 -1 1 -2 1 -2 1 1 0 0 -1 0 -2 3 2 -3 -2 -2 -5 -3 1 5 -2 1 -1 0 -1 0 0
1 1 -2 3 0 1 0 -1 -2 2 1 2 2 -1 2 -1 1 -2 0 -2 1 -3 -2 2 1 -2 -4 2 2 -6 2 -1
-1 0 1 -2 0 -1 0 1 1 -1 -1 -1 -1 1 -1 1 -1 1 1 2 0 2 2 0 0 1 3 -1 -2 5 -1 1
2 0 -1 1 -2 2 -2 1 -2 1 1 0 -1 -2 0 -3 3 1 -3 -4 -3 -5 -4 0 3 -2 0 -1 3 -4 2 0
0 0 1 -2 0 0 0 1 1 -1 -1 -1 -1 1 -1 1 -1 0 1 1 0 2 2 0 -1 1 2 -1 -1 4 -1 1
1 1 1 -1 0 -1 1 -1 0 -1 0 0 0 1 1 1 -2 -2 2 -1 1 3 2 -1 -4 1 -2 0 2 0 0 2
2 1 -1 0 -1 0 -1 0 -2 1 0 1 0 0 1 -1 0 -2 1 -3 0 -2 -1 0 -1 -1 -2 1 2 -2 0 2
0 0 1 -2 0 -1 1 0 1 -1 -1 0 -1 1 -1 2 -2 -1 3 2 1 3 3 0 -3 2 0 1 -2 3 -1 1
-1 -1 0 -1 1 -1 0 0 1 0 -1 0 0 1 -1 1 -1 0 1 2 1 1 2 0 0 1 2 0 -3 4 -2 0
0 0 0 0 0 -1 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 -1 0
0 1 -1 1 0 0 0 0 -1 1 0 1 1 0 1 0 0 -2 2 0 2 0 0 1 -1 -1 -2 1 1 -1 0 1
32 32
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
-1 0 0 1 0 -1 1 0 0 0 0 1 1 1 1 2 -1 -1 2 3 2 1 2 2 0 1 0 0 -3 2 1 0
0 0 0 0 1 -1 0 -1 1 1 -1 0 0 0 -1 0 -1 0 0 1 1 1 1 0 0 0 0 1 -1 1 -1 -1
0 0 0 -1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 -1 -1 0 0 0 0 0 -1 0
1 -1 0 1 0 0 0 0 0 1 1 1 -1 -1 -1 0 0 0 -1 0 -1 -1 -1 1 1 -1 1 0 -1 -1 0 -1
0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0
-1 0 0 -1 0 -1 1 0 1 -1 0 0 0 1 0 1 -1 0 2 2 1 2 2 0 -2 2 0 1 -2 2 -1 1
0 0 0 -1 -1 0 0 1 0 -1 0 -1 -1 0 0 0 0 1 0 0 -1 0 -1 -1 -1 1 0 1 0 0 0 1
-1 1 0 -1 1 -2 1 0 1 -1 -2 0 1 2 0 3 -2 -2 4 3 4 4 5 1 -2 3 -1 0 -2 5 -1 2
-1 0 1 0 0 -1 2 0 0 -1 0 0 0 0 0 2 -1 -1 2 3 2 3 2 0 -2 2 -1 0 -1 1 0 0
0 0-1 2 1 0 0 0 1 0 1 1 1 0 0 0-1 0 0 1-1 0 1 1 0-1 0 0-1 1-1
-1 0 0 -1 -1 0 1 0 0 -1 0 -1 0 0 1 0 1 2 0 1 -1 0 0 0 1 0 1 0 0 1 0 0
0 0 1 0 0 -1 1 -1 1 -1 1 0 0 0 0 1 -2 -1 1 0 0 3 1 -1 -3 1 -1 0 1 -1 0 0
0 0 -1 0 0 1 -1 1 -1 0 0 -1 0 0 0 -2 2 2 -2 -1 -1 -3 -2 0 3 -1 1 -1 0 0 0 0
0 1 1 0 1 -1 1 -1 0 0 -1 1 1 1 1 2 -2 -3 3 1 3 3 3 0 -3 1 -2 1 0 1 0 1
0-1 0 1 0 1 0 0 1 0 0 1 0-1 0-1 2 1-3 0-2-2-3 0 2-2 1 0 1-3 0-3
0 0 0 0 0 0 2 0 0 0 0 0 0 0 1 1 -1 -2 2 1 2 2 1 1 -3 0 -2 1 1 -1 0 0
0 0 1 -1 -1 0 0 1 0 -1 0 -1 -1 0 0 0 1 2 -1 1 -2 0 -1 -1 1 0 2 -1 0 1 0 0
1 0 0 0 0 0 -1 0 0 0 0 0 -1 -1 -1 -1 1 1 -2 -1 -2 -1 -1 -1 2 0 1 -1 1 -1 0 -1
0 0 0 0 0 0 0 0 0 0 0 0-1 1 0 1 0 0 1 2 0 1-1-2 2 0 0
0 0-1 0 1-2 1 0 1-1 0 0-2 2 2-2-1-1-3-2 0 3-1 2 0 1 0 0
0 0 0 0 0 0 1 0 -1 0 0 0 0 0 1 0 -1 -2 2 0 2 1 0 0 -3 0 -2 1 1 -1 0 1
0 0 0 -1 -1 1 0 1 0 -1 0 -1 -1 0 0 0 0 1 0 0 -1 0 -1 -1 -1 0 0 1 0 0 0 1
0 0 0 1 1 -1 0 -1 0 1 0 1 1 0 0 0 0 -1 0 0 1 0 1 1 1 -1 0 -1 0 0 0 -1
0 0 -1 0 1 0 -1 0 0 1 -1 0 0 0 -1 -1 0 0 0 0 1 -1 0 0 1 0 0 1 -1 1 -1 0
0 0 0 1 1 -1 0 -1 0 1 0 1 1 0 0 0 0 -1 0 0 1 0 1 0 1 0 0 -1 0 0 0 -1
0 -1 -1 1 0 1 -1 0 0 1 1 0 0 -1 0 -2 2 2 -3 -1 -2 -3 -3 0 3 -2 2 0 0 -2 0 -2
0 -1 -1 1 0 1 0 0 0 1 1 0 0 -1 0 -2 1 1 -2 -1 -1 -2 -3 0 1 -2 0 1 1 -3 0 -2
0 -1 -1 1 0 1 -1 0 0 1 1 0 0 -1 -1 -2 3 3 -4 -1 -3 -4 -3 0 5 -2 2 -1 0 -2 0 -3
0 0 0 1 0 0 1 -1 0 0 1 1 1 0 1 0 0 -1 0 -1 0 0 0 0 -1 0 -2 0 2 -3 1 -1
0 -1 0 0 -1 1 0 1 0 -1 1 -1 -1 -1 0 -1 1 2 -2 -1 -2 -1 -2 0 1 0 1 -1 1 -1 1 0
-1 0 0 -1 1 -1 1 0 1 0 -1 0 0 1 -1 2 -2 -1 3 3 3 3 3 1 -2 1 0 1 -3 4 -2 1
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学士_心理学
1 32
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
x ^5220*12 x ^5124*24 x ^5112*4 x ^5064*24 x×^5040*16 x ^4968*4 x×^4944*96 x ^4932*36 x ^4920*12 x^4872*12 x×^4869*64 x ^4860*384 x ^4848*48 x ^4824*288 x ^4773*192 x ^4740*24(5760x)
1 32
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0
x ^5193*2 x ^5124*30 x ^5076*20 x ^5028*6 x ^4857*90 x ^4833*532 x ^4824*480 x ^4752*20 x×^4740*60(4608x)
1 32
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 -1 0 0 0 0
x ^5544*8 x ^5400*16 x ^5208*48 x ^5160*48 x×^5076*128 x ^5064*96 x ^4908*384 x ^4896*384 x^4752*128(360 x)
1 32
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 -1 0 0 -1 1 0
x ^5076*16 x ^4992*6 x ^4944*18 x ^4917*144 x ^4896*8 x ^4884*288 x ^ 4860*96 x ^4845*288 x^4836*144 x^4833*96 x×^4824*120 x ^4725*16(46080 x)
1 32
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0
x ^5157*2 x ^5148*2 x×^5040*12 x ^5004*6 x ^4968*36 x ^4944*72 x ^4941*30 x ^4917*216 x ^ 4908*36 x×^4869*12 x^4848*36 x*4845*432 x ^4824*144 x ^4773*144 x×^4725*24 x ^4701*36(15360x)
1 32个
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 -1 0 0 0 0 1 -1 0 0 0
x ^5304*16 x ^5208*32 x ^5160*24 x ^5124*64 x ^5112*48 x ^4992*128 x ^4968*256 x ^4944*384 x ^4908*128 x
1 32
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 -1 0 0 0
x ^5688*8 x ^5304*120 x ^5160*120 x ^5112*160 x ^5028*192 x ^5004*640(72 x)
1 32
0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 -1 0 0 0 -1 0 0 -1 -1 -1 0 -1 1 1 -1 0 0
x ^5832*2 x ^5448*18 x ^5148*128 x ^5064*324 x ^4968*96 x ^4920*288 x ^4896*384(120 x)
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属性
单一模块=1
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参考文献
H.Koch、B.B.Venkov,
\“Uber ganzzahlige unimodulare euklidische记事本。
Mathematik杂志398(1989),144-168
H.Koch,B.B.Venkov,“Uber gerade unimodulare”
Gitter der Dimension 32,III型
马瑟姆。纳克里斯。152 (1991), 191-213
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笔记
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最后一行
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