multiplex (version 1.5)

cngr: Congruence Relations

Description

Find the congruence relations of a given abstract or a partially ordered semigroup.

Usage

cngr(S, PO = NULL, unique = FALSE)

Arguments

S

an object from the `Semigroup' class.

PO

(optional) the partial order table

unique

(logical) whether or not return the unique congruence relations

Value

• An object of `Congruence' class. The items included are:
• S
  semigroup of relations
• PO
  partial order table (if specified)
• clu
  congruence classes

Details

Congruences are equivalence relations that preserve the operation between the correspondent classes in the algebraic structure. In this case the different congruence classes are based on the substitution property of the semigroup object.

References

Hartmanis, J. and R.E. Stearns Algebraic Structure Theory of Sequential Machines. Prentice-Hall. 1966.

See Also

decomp, pacnet

Examples

## Create the semigroup object
arr <- round( replace( array(runif(18), c(3,3,2)), array(runif(18),
       c(3,3,2))>.5, 1 ) )
#
S <- semigroup(arr)

## look at the congruences in S
cngr(S, PO=NULL)