  The algebraic approach to the phase problem for the case of X-ray scattering
from an ideal crystal is extended to the case of the neutron scattering,
overcoming the difficulty related to the non-positivity of the scattering
density. In this way, it is proven that the atomicity is the crucial assumption
while the positiveness of the scattering density only affects the method for
searching the basic sets of reflections. We also report the algebraic
expression of the determinants of the Karle-Hauptman matrices generated by the
basic sets with the most elongated shape along one of the reciprocal
crystallographic axes.
