Let Γ(X, ~, t, I) be an incidence geometry and let F be a flag of Γ (i.e. a clique of the incidence graph of Γ).
We say that an element x ∈F is incident to the flag F if and only if x is incident to all elements in F, and we denote it x ~F.
The residue ΓF of the flag F in Γ is the geometry whose set of elements is { x∈X : x ~F } \ F and whose set of types is I\ t(F), together with the restricted type function and incidence relation.
Let Γ(G;(Gi)i∈I) be a coset geometry and assume that G acts flag--transitively on Γ. Let F be a flag of Γ. The residue of F is the coset geometry ΓF = Γ( ∩j∈F Gj; (Gi∩(∩j∈FGj))i ∈I\ t(F)).
Given an incidence geometry D and a flag f of D, return the residue of the flag f as an incidence geometry.
Given a coset geometry C and a subset f of the set of types of C, return the residue of the flag consisting in the maximal parabolics of C whose type is in f.