On Wednesday, December 19, 2012 11:07:03 PM UTC, William wrote:
>
> > sage: D=Matrix(IntegerModRing(), 
> [[-1,1,0,1,1,0],[1,-3,1,0,0,0],[0,1,-2,0,0,0],[1,0,0,-3,0,0],[1,0,0,0,-4,1],[0,0,0,0,1,-5]]);D
>
> > [-1  1  0  1  1  0]
> > [ 1 -3  1  0  0  0]
> > [ 0  1 -2  0  0  0]
> > [ 1  0  0 -3  0  0]
> > [ 1  0  0  0 -4  1]
> > [ 0  0  0  0  1 -5]
> > sage: X = D.LLL_gram(); 
>

This uses Pari lllgramint(), which assumes that the matrix is positive 
definite. If the matrix is not positive definite, Pari may not return.

sage: D.is_positive_definite()
False


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