# Matrix transformation of a LLL reduced basis

Dear Sage Community,

I am trying the way to obtain the matrix transformation of a LLL reduced basis, that is a matrix that gives the expression of the new lattice basis in terms of the old.

In particular, I have a matrix X and the LLL reduced base Y (obtain by the LLL function of Sage: Y=X.LLL()) and I want a matrix T such that TX=Y.

I try to solve the problem using solve.left() but the result is different from Magma. With a matrix X=[5 2] [1 4] [2 3],

the T matrix in Sage is [ 0 0 0] [ 2/9 -1/9 0] [ 1/18 -5/18 0] while in Magma is [ -3 -6 10] [ -3 -7 11] [ -5 -11 18]

Please could anyone help me to understand a way to have in SAGE the same result of Magma?