multiplex (version 3.1.1)

fact: Factorisation of semigroup structures

Description

A function to decompose partially ordered semigroups

Usage

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

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

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)

Author

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

Details

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

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)