fact: Factorisation of Semigroup Structures

In mplex/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	semigroup object
P	partial order structure associated to S
uniq	(logical) whether factorisation should include unique induced inclusions
fac	‘factor’ to be factorised, in case that input factorised partially ordered structures
atoms	(logical) whether or not include in output atoms
mca	(logical) whether or not include in output meet-complements of atoms
atmc	(logical) whether or not include in output atoms' meet-complements
patm	(logical) whether or not include in output potential atoms
k	(for patm) length of induced inclusion

Details

The factorisation is part of decomposition for partially ordered semigroups, and function fact allows to obtain elements generated in this process.

Value

An object of 'Ind.incl' class having:

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

Note

Data objects imported with pacnet are compatible for further factorisation.

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 and partial order
P <- strings(arr) |> 
  partial.order()

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

mplex/multiplex documentation built on Aug. 3, 2024, 3:32 a.m.