poseticDataAnalysis (version 1.0.0)

IntersectionPOSet: Computing the intersection of a collection of posets.

Description

Computes the poset \((V, \leq_{\cap})=(V, \leq_1)\cap\cdots\cap(V,\leq_k)\).

Usage

IntersectionPOSet(poset1, poset2, ...)

Value

The intersection poset, an object of S4 class POSet.

Arguments

poset1

An object of S4 class POSet. Argument poset1 must be created by using any function contained in the package aimed at building object of S4 class POSet (e.g. POSet(), LinearPOSet(), ProductPOSet(), ...) .

poset2

An object of S4 class POSet. Argument poset2 must be created by using any function contained in the package aimed at building object of S4 class POSet (e.g. POSet(), LinearPOSet(), ProductPOSet(), ...) .

...

Optional additional objects of S4 class POSet. Optional arguments must be created by using any function contained in the package aimed at building object of S4 class POSet (e.g. POSet(), LinearPOSet(), ProductPOSet(), ...) .

Details

Let \(P_1 = (V, \leq_1),\cdots, P_k = (V, \leq_k)\) be \(k\) posets on the same set \(V\). The intersection poset \(P_{\cap}=P_1 \cap\cdots\cap P_k\) is the poset \((V, \leq_{\cap})\) where \(a\leq_{\cap} b\) if and only if \(a\leq_i b\) for all \(i=1\cdots k\).

Examples

elems <- c("a", "b", "c", "d")

dom1 <- matrix(c(
  "a", "b",
  "c", "b",
  "b", "d"
), ncol = 2, byrow = TRUE)

dom2 <- matrix(c(
  "a", "b",
  "b", "c",
  "b", "d"
), ncol = 2, byrow = TRUE)

pos1 <- POSet(elements = elems, dom = dom1)

pos2 <- POSet(elements = elems, dom = dom2)

pos_int <- IntersectionPOSet(pos1, pos2)