  Recent ideas based on the properties of assemblies of frictionless particles
in mechanical equilibrium provide a perspective of amorphous systems different
from that offered by the traditional approach originating in liquid theory. The
relation, if any, between these two points of view, and the relevance of the
former to the glass phase, has been difficult to ascertain. In this paper we
introduce a model for which both theories apply strictly: it exhibits on the
one hand an ideal glass transition and on the other `jamming' features
(fragility, soft modes) virtually identical to that of real systems. This
allows us to disentangle the different contents and domains of applicability of
the two physical phenomena.
