Corresponding to a lattice L(α1,⋯,αn) in Z[τ] there is a matrix (a1⋯anb1⋯bn) with αi=ai+biτ as in Lemma 8.24. Show that the three operations of adding a multiple of one column to another, changing the sign of a column, and permuting columns do not change the greatest common divisor of the numbers in each row of the matrix. Deduce from this that if a,b+cτ is the reduced basis for the lattice then c is the greatest common divisor of the entries in the second row of the matrix.