An algorithm which transforms any Diophantine equation into an equivalent system of equations of the forms x_i=1, x_i+x_j=x_k, x_i cdot x_j=x_k

We describe an algorithm which transforms any Diophantineequation into an equivalent system of equations of the forms mbox{$x_i=1$},mbox{$x_i+x_j=x_k$}, mbox{$x_i cdot x_j=x_k$}. We apply the algorithmto the polynomial mbox{$x_1 cdot x_2-1$}. This procedure is implementedin {sl MuPAD}, {sl Sage}, and {sl Mathematica}.