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Dear Thomas,
I'm using your package to compute HNF matrices, but somehow in one exceptional instance I get a wrong result:
In [28]: Diophantine.lllhermite( array([[ 1, -1, 5], [-1, 1, 5], [-1, -1, 7]]))

Out[28]: (Matrix([ [1, 1, 3], [0, 2, -2], [0, 0, 10]]), Matrix([ [1, 1, -1], [0, 1, -1], [1, 1, 0]]), 3)
The output is not in Hermite normal form (one negative index), and the A matrix is definitely not unimodular... Any idea what the problem is? Thanks!
Best,
Pierre

Also, I noticed that it is unable to find zero-valued solutions. Am I missing something?
Thanks!

I believe there is a bug in the code:
lllhermite(sympy.Matrix([[0,1,0,1],[-1,0,1,0]])
throws an exception. I believe this is because

def lllhermite(G, m1=1, n1=1):
    """
    Input: integer mxn matrix A, nonzero, at least two rows+
    Output: small unimodular matrix B and HNF(A), such that BA=HNF(A)+
    The Havas, Majewski, Matthews LLL method is used+
    We usually take alpha=m1/n1, with (m1,n1)=(1,1) to get best results+
    """
    m = G.shape[0]
    n = G.shape[1]
    A, B, L, D = initialise_working_matrices(G)
    if first_nonzero_is_negative(A):
        B[m, m] = -1
        A[m, :] *= -1

should be:

m = G.shape[0]
n = G.shape[1]
A, B, L, D = initialise_working_matrices(G)
if first_nonzero_is_negative(A):
    B[m-1, m-1] = -1
    A[m-1, :] *= -1

What do you think?