# Truncations

Let $\Gamma(X,\sim,t,I)$ be an incidence geometry and let $J$ be a subset of $I$. Then the *J–truncation* of $\Gamma$ is the geometry whose set of elements is $t^{-1}(J)$, together with the restricted type function and incidence relation.

Let $J \subseteq I$. The *J–truncation* of the coset geometry $\Gamma(G;(G_i)_{i \in I})$ is the coset geometry $\Gamma( G; (G_j)_{j\in J})$.

## `Truncation(D, t): IncGeom, Set -> IncGeom`

Given an incidence geometry $D$ and $t$ a subset of the set of types of $D$, return the *t–truncation* of $D$ as an incidence geometry.

## `Truncation(C, t): CosetGeom, Set -> CosetGeom`

Given a coset geometry $C$ and $t$ a subset of the set of types of $C$, return the *t–truncation* of $C$ as a coset geometry.