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发表于 2011-7-20 14:52
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[讨论]偏序集运算和格初步
[这个贴子最后由cjsh在 2011/07/20 02:57pm 第 1 次编辑]
http://www.math.rwth-aachen.de/~Gabriele.Nebe/LATTICES/index.html
The root lattices An and their duals for 1 ≤n ≤24
The root lattices Dn and their duals for 1 ≤n ≤24
The root lattices En and their duals for 6 ≤n ≤8
The laminated lattices Λn for 1 ≤n ≤24 including the 16-dimensional Barnes-Wall lattice Λ16 and the Leech lattice Λ24
The Kappa-lattices Kn and their duals for 7 ≤n ≤13 including the Coxeter-Todd lattice K12
The perfect lattices up to dimension 7
The 3-dimensional Bravais lattices
Various interesting lattices in dimensions 20, 24, 28, 32, 40, 80, 105 including, e.g., some of the densest known lattices in dimension 32.
Given a family name X as a string which is one of "A", "B", "C", "D", "E", "F", "G", "Kappa" or "Lambda", together with an integer n, construct a lattice subject to the following specifications:
A:The root lattice An which is the zero-sum lattice in Qn + 1.
B:n ≥2: The root lattice Bn which is the standard lattice of dimension n.
C:n ≥3: The root lattice Cn which is the even sublattice of Zn and is equal to Dn.
D:n ≥3: The root lattice Dn which is the even sublattice of Zn, also called the checkerboard lattice.
E:6 ≤n ≤8: The root lattice En, also called Gosset lattice.
F:n = 4: The root lattice F4 which is equal to D4.
G:n = 2: The root lattice G2 which is equal to A2.
Kappa:1 ≤n ≤13: The Kappa-lattice Kn. For n = 12 this is the Coxeter-Todd lattice.
Lambda:1 ≤n ≤31: The laminated lattice Λn. For n = 16 this is the Barnes-Wall lattice, for n = 24 the Leech lattice. |
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