R: The Free Group

# The Free Group

## Documentation for package ‘freegroup’ version 1.2-0

- DESCRIPTION file
- User guides, package vignettes and other documentation
- Package NEWS
- Package README

## Help Pages

A B C D E F G I J K L N O P R S T V misc

freegroup-package | The Free Group

## -- A --

abc | Alphabetical free group elements
abelianize | Abelianization of free group elements
abelianized | Abelianization of free group elements
abs | Absolute value of a 'free' object
abs.free | Absolute value of a 'free' object
allconj | Cyclic reductions of a word
alpha | Alphabetical free group elements
alphabet | Alphabetical free group elements
as.character_free | Print free objects
as.cyclically_reduced | Cyclic reductions of a word
as.free | Objects of class 'free'
automorphism | Outer automorphisms of the free group
automorphisms | Outer automorphisms of the free group
autosub | Outer automorphisms of the free group
autosub_lowlevel | Outer automorphisms of the free group

## -- B --

backwards | Write free objects backwards
bigness | Bignesses of a free object

## -- C --

c | Concatenation of free objects
c.free | Concatenation of free objects
char_to_free | Convert character vectors to free objects
char_to_matrix | Convert character vectors to free objects
commutator | Class "dot"
conjugate | Cyclic reductions of a word
consolidate | Reduction of a word to reduced form
cumsum | Cumulative sum
cumsum.free | Cumulative sum
cyclic | Cyclic reductions of a word
cyclically | Cyclic reductions of a word
cyclically_reduce | Cyclic reductions of a word
cyclically_reduced | Cyclic reductions of a word
cyclically_reduce_tietze | Cyclic reductions of a word
cyclic_reduction | Cyclic reductions of a word
cycred | Cyclic reductions of a word

## -- D --

discard | Keep or drop symbols
donames | Names attributes of free group elements
dot | Class "dot"
dot-class | Class "dot"
dot_error | Class "dot"
drop | Keep or drop symbols
drop.free | Keep or drop symbols

## -- E --

extract | Class "dot"
Extract.free | Extract or replace parts of a free group object

## -- F --

flip | Substitute and invert symbols
free | Objects of class 'free'
free-class | Objects of class 'free'
freegroup | The Free Group
freeprod | Repeated summation by concatenation
free_equal | Arithmetic Ops methods for the free group
free_power | Arithmetic Ops methods for the free group
free_repeat | Arithmetic Ops methods for the free group

## -- G --

getlet | Get letters of a freegroup object

## -- I --

id | The identity element
identity | The identity element
inverse | Arithmetic Ops methods for the free group
inverse.free | Arithmetic Ops methods for the free group
inverse.matrix | Arithmetic Ops methods for the free group
is.abelian | Abelianization of free group elements
is.conjugate | Cyclic reductions of a word
is.conjugate.free | Cyclic reductions of a word
is.conjugate_single | Cyclic reductions of a word
is.cyclically.reduced | Cyclic reductions of a word
is.cyclically_reduced | Cyclic reductions of a word
is.free | Objects of class 'free'
is.id | The identity element
is.id.free | The identity element
is.identity | The identity element
is.power | Primitive elements of the free algebra
is.primitive | Primitive elements of the free algebra
is_proper | Reduction of a word to reduced form
is_reduced | Reduction of a word to reduced form

## -- J --

jacobi | Class "dot"
juxtapose | Arithmetic Ops methods for the free group

## -- K --

keep | Keep or drop symbols

## -- L --

list_to_free | Objects of class 'free'

## -- N --

names | Names attributes of free group elements
neutral | The identity element
nielsen | Outer automorphisms of the free group
number | Bignesses of a free object

## -- O --

ops | Arithmetic Ops methods for the free group
Ops.free | Arithmetic Ops methods for the free group
outer | Outer automorphisms of the free group

## -- P --

permsymb | Outer automorphisms of the free group
permsymb_single_f | Outer automorphisms of the free group
permsymb_single_X | Outer automorphisms of the free group
permsymb_vec | Outer automorphisms of the free group
primitive | Primitive elements of the free algebra
print.free | Print free objects
print.freegroup | Print free objects
prodfree | Repeated summation by concatenation

## -- R --

reduce | Reduction of a word to reduced form
remove_zero_powers | Reduction of a word to reduced form
rep.free | Concatenation of free objects
retain | Keep or drop symbols
rfree | Random free objects
rfreee | Random free objects
rfreeee | Random free objects

## -- S --

shift | Permute elements of a vector in a cycle
size | Bignesses of a free object
subs | Substitute and invert symbols
subsu | Substitute and invert symbols
sum | Repeated summation by concatenation
sum.free | Repeated summation by concatenation

## -- T --

Tietze | Tietze form for free group objects
tietze | Tietze form for free group objects
tietze.free | Tietze form for free group objects
tietze.matrix | Tietze form for free group objects
total | Bignesses of a free object

## -- V --

vec_to_matrix | Tietze form for free group objects

## -- misc --

%~% | Cyclic reductions of a word
. | Class "dot"
[-method | Class "dot"
[.dot | Class "dot"
[.free | Extract or replace parts of a free group object
[<-.free | Extract or replace parts of a free group object