Since the coefficient of A and O are integers, the computed solution P is always in M n,3 ( ) with the additional constraint that one of the vertices u be placed at the origin. The exact solution with coefficients in is actually necessary for the subsequent computations and not an approximation, so the resolution of the system must be exact. This turns out to be a very costly operation: it requires storing integers of arbitrary size, which are computationally far more expensive than fixed-width machine integers.