abelianize {freegroup}

Abelianization of free group elements

Description

Function abelianize() returns a word that is equivalent to its argument under assumption of Abelianness. The symbols are placed in alphabetical order.

Usage

  abelianize(x)
  is.abelian(x)

Arguments

x

An object of class free

Details

Abelianizing a free group element means that the symbols can commute past one another. Abelianization is vectorized.

Function is.abelian() is trivial: it just checks to see whether argument x has its symbols in alphabetical order. It might have been better to call this abelianized().

Package frab presents extensive R-centric functionality for dealing with the free Abelian group. It is much more efficient than this package for Abelian operations, and contains bespoke methods for working with a range of applications such as tables of counts.

Author(s)

Robin K. S. Hankin

Examples

x <- as.free("aabAA")
x
abelianize(x)

x <- rfree(10,10,2)
x
abelianize(x)

abelianize(.[rfree(),rfree()])


p <- free(rbind(rep(1:5,4),rep(1:4,5)))
p
abelianize(p)