def differential(self, place):
hom = Hom(self.sheaf_at(place), self.sheaf_at(place + 1))
if place not in self._diff:
return hom.zero()
return hom(self._diff[place],
name="differential of {} at degree {}".format(
self._name, place))
def _composition_free_module_morphism(psi, phi):
"""
Returns the composition of two compasable morphisms of free modules of
finite rank over the same base ring.
"""
hom = Hom(phi.domain(), psi.codomain())
if phi.is_zero() or psi.is_zero():
return hom.zero()
return hom(psi.matrix() * phi.matrix())
def _cover_relation_to_restriction(self, relation):
"""
Returns the restriction morphism associated to a cover relation of the domain
poset of ``self``.
"""
hom = Hom(self.stalk(relation[0]), self.stalk(relation[1]))
if self._res_dict[relation] == 0:
return hom.zero()
elif self._res_dict[relation] == 1:
return hom(identity_matrix(self._stalk_dict[relation[0]]))
else:
return hom(self._res_dict[relation])
def component(self, point):
h = Hom(self.domain().stalk(point), self.codomain().stalk(point))
if self._components[point] == 0:
phi = h.zero()
elif self._components[point] == 1:
phi = h(
identity_marix(self._base_ring,
self.domain()._stalk_dict[point]))
else:
phi = h(self._components[point])
phi._name = "Component of {} at {}".format(self._name, point)
return phi
