freegroup-package {freegroup}

The Free Group

Description

The free group in R; juxtaposition is represented by a plus. Includes inversion, multiplication by a scalar, group-theoretic power operation, and Tietze forms. To cite the package in publications please use Hankin (2022) <doi:10.48550/ARXIV.2212.05883>.

Details

The DESCRIPTION file:

Package:	freegroup
Type:	Package
Title:	The Free Group
Version:	1.1-8
Authors@R:	c(person(c("Robin", "K. S. "), "Hankin", role=c("aut","cre"), email="[e-mail]", comment = c(ORCID = "0000-0001-5982-0415")))
Maintainer:	Robin K. S. Hankin <[e-mail]>
Description:	The free group in R; juxtaposition is represented by a plus. Includes inversion, multiplication by a scalar, group-theoretic power operation, and Tietze forms. To cite the package in publications please use Hankin (2022) <doi:10.48550/ARXIV.2212.05883>.
Depends:	methods, plyr, R (>= 3.5.0)
Suggests:	knitr, rmarkdown, permutations, testthat
LazyData:	yes
Imports:	freealg (>= 1.0-4), magic (>= 1.5-9), magrittr
VignetteBuilder:	knitr
License:	GPL-2
URL:	https://github.com/RobinHankin/freegroup
BugReports:	https://github.com/RobinHankin/freegroup/issues
Author:	Robin K. S. Hankin [aut, cre] (<https://orcid.org/0000-0001-5982-0415>)

Index of help topics:

abelianize              Abelianization of free group elements
abs.free                Absolute value of a 'free' object
alpha                   Alphabetical free group elements
backwards               Write free objects backwards
c                       Concatenation of free objects
char_to_free            Convert character vectors to free objects
cumsum                  Cumulative sum
cycred                  Cyclic reductions of a word
donames                 Names attributes of free group elements
dot-class               Class "dot"
Extract.free            Extract or replace parts of a free group object
free                    Objects of class 'free'
freegroup-package       The Free Group
getlet                  Get letters of a freegroup object
identity                The identity element
keep                    Keep or drop symbols
nielsen                 Outer automorphisms of the free group
Ops.free                Arithmetic Ops methods for the free group
print.free              Print free objects
reduce                  Reduction of a word to reduced form
rfree                   Random free objects
shift                   Permute elements of a vector in a cycle
size                    Bignesses of a free object
subs                    Substitute and invert symbols
sum                     Repeated summation by concatenation
tietze                  Tietze form for free group objects

Author(s)

NA

Maintainer: Robin K. S. Hankin <[e-mail]>

Examples

p <- rfree(10,6,3)
x <- as.free('x')

p+x

p^x

sum(p)

abelianize(p)

subsu(p,"ab","z")
subs(p,a='z')


discard(p+x,'a')