f******r
发帖数: 2975 | 1 Lattice is a discrete subgroup of Euclidean Space
Suppose I have one lattice L now,
choose some deep holes of the lattice P0,P1,..Pn
Construct L'= L+a_0P0+a_1P1+...+a_nPn
where a_0,a_1,...a_n are either 0 or 1.
Now I am thinking whether L' is a lattice
I guess it is but I don't know how to prove it
Here is my step for addition
Let L1,L2 be two points of the lattice L
L1'=L1+a_0P0+a_1P1+...+a_nPn
L2'=L2+b_0P0+b_1P1+...+b_nPn
L1'+L2' = L1+a_0P0+a_1P1+...+a_nPn+L2+b_0P0+b_1P1+...+b_nPn
then I don't | l*****e
发帖数: 65 | 2
i don't get your question, but i would like suggest that you may consider
first the case n=0. and a_0=1. then try to draw some conclusion.
hope it helps.
【在 f******r 的大作中提到】
: Lattice is a discrete subgroup of Euclidean Space
: Suppose I have one lattice L now,
: choose some deep holes of the lattice P0,P1,..Pn
: Construct L'= L+a_0P0+a_1P1+...+a_nPn
: where a_0,a_1,...a_n are either 0 or 1.
: Now I am thinking whether L' is a lattice
: I guess it is but I don't know how to prove it
: Here is my step for addition
: Let L1,L2 be two points of the lattice L
: L1'=L1+a_0P0+a_1P1+...+a_nPn
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