decomp:
Decomposition of a Semigroup Structure
Description
A function to perform the decomposition of a semigroup structure
Usage
decomp(S, x, type = c("mc", "pi", "cc"), reduc = FALSE)
Arguments
S
an object of a `Semigroup' class
x
either an object of a `Congruence' class or an object of a `Pi.rels' class
type
whether the reduction is based on a a congruence class or rather on a $\pi$-relation or a meet-complement in the `Pi.rels' class
reduc
(logical) does the return object should include the reduced structures?
Value
An object of `Decomp' class having:
Details
The decomp function is a reduction form of an algebraic structure like the semigroup that verifies which of the class members in the system are congruent to each other. The decomposed object then is made of congruent elements, which form part of the lattice of congruence classes in the algebraic structure. In case that the input data comes from the Pacnet program, then such elements are in form of $\pi$-relations or the meet-complements of the atoms; otherwise these are simply equivalent elements satisfying the substitution property.
References
Pattison, Philippa E. Algebraic Models for Social Networks. Cambridge University Press. 1993.