  The fragmentation description is used to analyse calculated neutron
scattering intensities from kagom\'e ice and spin ice systems. The
longitudinal, transverse and harmonic fragments produce independent
contributions to the neutron scattering intensity. This framework is used to
analyse the ordering due to quantum fluctuations in the topologically
constrained phase of kagom\'e ice and the monopole crystal phase of spin ice.
Here, quantum fluctuations are restricted to the transverse fragment and they
drive the system into a double-$q$ structure in which longitudinal and
transverse fragments have a different ordering wave vector. The intensity
reduction of the Bragg peaks for the transverse fragments, compared with known
classical limits can be used as a diagnostic tool for quantum fluctuations.
Published quantum Monte Carlo data for spin ice in a $[111]$ field are
consistent with the proposed protocol.
