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2010-01-22, 19:49   #5
maxal

Feb 2005

22×32×7 Posts

Quote:
 Originally Posted by jasonp So how does one compute a basis for the intersection of two shifted 3x3 lattices?
If I got the problem correctly, you need first to find a common shift S by solving a system of congruences (using CRT):
S == R0_1 (mod p_1^{k_1})
S == R0_2 (mod p_2^{k_2})
...
with respect to S.
Then you rewrite you matrix equation as:
Code:
| C - S |   | p^k  -r_i  -r_i^2 | | i |
|   Y   | = |  0     1      0   | | j |
|   Z   |   |  0     0      1   | | k |
(where C,Y,Z,S are the same for all p^k) and proceed as if there were no shifts at all.