On Mar 30, 2010, at 10:18 AM, Santanu Sarkar wrote:

Suppose L is a lattice generated by b_1, b_2, \ldots, b_m for example
say b_1=(1,2,3), b_2=(2,3,4). Is there any function in Sage
by which one can find orthogonal lattice of L?

An orthogonal lattice might not exist in general, but you can use LLL to get close (and, perhaps, hit it right on).

sage: m = matrix([[1,2,3],[2,3,4]])
sage: m.LLL()
[-1  0  1]
[ 1  1  1]

- Robert

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