multiplex (version 3.7)

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

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

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

Author

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

Details

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

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 of relations
S <- semigroup(arr)

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

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