Quote:
Originally Posted by jasonp
So how does one compute a basis for the intersection of two shifted 3x3 lattices?
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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.