Thanks Dima and John, In the meantime, since I have Magma available to me I 
tried to use magma's functions.  What I'm really interested is getting the 
unimodular (when it makes sense to use that term) transition matrix needed 
to put a matrix in reduced form.  It looks like, but correct me if I'm 
wrong, that the only sage function which returns this is LLL_gram.  I 
looked at the Magma documentation, and saw the the LLL function in Magma 
returns 3 things: the reduced matrix, the transition matrix, and the rank.  
However, when I do that I get a traceback from sage, plus at the end

TypeError: Error evaluating Magma code:
IN:_sage[1]:=[_a : _a in _sage[2]];
OUT:
>> _sage_[1]:=[_a : _a in _sage[2]];
                              ^
Runtime error in for: Iteration is not possible over this object

When I look at the returned value of magma.LLL it only has the reduced 
matrix.  Is there a way of getting the entire tuple of returned values from 
magma?

Victor

B,U,rk = magma.LLL(A)

I get a message from sage (it's pretty obscure) saying that it 

On Tuesday, March 19, 2013 2:38:02 PM UTC-4, Victor Miller wrote:
>
> Suppose that A is an m by n integer matrix.  Its Gram matrix is G = 
> A*A^t.  If A is not full rank, then G has some eigenvalues of 0.  If I do 
> G.LLL_gram() I get a somewhat uniformative error message like:
>
> Value Error: ma matrix from Full MatrixSpace of 10 by 2 dense matrices 
> over Integer Ring cannot be converted to a matrix in Full MatrixSpace of 10 
> by 10 dense matrices over Integer Ring!
>
> I understand that pari (which is what I understand, actually computes 
> LLL_gram) doesn't like non-definite matrices.  But, in this case it looks 
> like it returned something to SAGE of lower dimension (what?) and SAGE 
> didn't know what to do with it.  Can the error message at least be changed 
> to something more informative.
>
> I've found a work around for some of my matrices:   Let N be some big 
> integer, and let G'= N*G + identity_matrix(G.nrows()).  This perturbs G a 
> little so that the 0 eigenvalues go away.
>
> Victor
>

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