Shadows

Let \(\Gamma(X,\sim,t,I)\) be an incidence geometry. Let \(J\) be a subset of \(I\) and let \(F\) be a flag of \(\Gamma\) such that \(t(F) \cap J = \emptyset\). The \(J\)-shadow of the flag \(F\), denoted by \(\sigma_J(F)\), is the set of flags of type \(J\) in the residue of the flag \(F\).

Shadow(D, I, F): IncGeom, Set, Set -> SetIndx

Given an incidence geometry \(D\), a subset \(I\) of the set of types of \(D\) and a flag \(F\) of \(D\), return the \(I\)-shadow of the flag \(F\) as an indexed set of subsets of points of \(D\).