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.