fact: Factorisation of semigroup structures

In multiplex: Algebraic Tools for the Analysis of Multiple Social Networks

Factorisation of semigroup structures

Description

A function to decompose partially ordered semigroups

Usage

fact(S, P, uniq = TRUE, fac, atoms, mca, atmc, patm, k)

Arguments

S	The semigroup object
P	The partial order structure associada to S
uniq	(logical) whether the factorisation include the unique induced inclusions
fac	the ‘factor’ to be factorised, in case that input factorised partially ordered structures
atoms	(logical) whether or not include the atoms in the output
mca	(logical) whether or not include the meet-complements of atoms in the output
atmc	(logical) whether or not include the atoms' meet-complements in the output
patm	(logical) whether or not include the potential atoms in the output
k	the length of the induced inclusion (only relevant if patm is activated)

Details

The factorisation is part of the decomposition process for partially ordered semigroups.

Value

An object of "Ind.incl" class having:

po	the partial order table
iin	list of induced inclusions pairwise listed
niin	length of the induced inclusion
patm	(optional) a vector with the potential atoms
atm	(optional) a vector with the atoms
atmc	(optional) array with meet-complements of atoms
mc	(optional) meet-complements
note	(optional) induced inclusions without the substitution property

Author(s)

Antonio Rivero Ostoic (based on the algorithm described in Ardu, 1995)

References

Ardu, S. ASNET – Algebraic and Statistical Network Analysis. User Manual. University of Melbourne. 1995.

See Also

decomp, cngr, pacnet

Examples

## Create a partially ordered semigroup
arr <- round( replace( array(runif(18), c(3,3,2)), array(runif(18),
       c(3,3,2))>.5, 1 ) )
# semigroup
S <- semigroup(arr)
# string relations
St <- strings(arr)
# partial order
P <- partial.order(St)

## Perform the factorisation of PO S
fact(S, P)

multiplex documentation built on Nov. 16, 2023, 5:08 p.m.