freealg-package {freealg}

The Free Algebra

Description

The free algebra in R with non-commuting indeterminates. Uses 'disordR' discipline (Hankin, 2022, <doi:10.48550/ARXIV.2210.03856>). To cite the package in publications please use Hankin (2022) <doi:10.48550/ARXIV.2211.04002>.

Details

The DESCRIPTION file:

Package:	freealg
Type:	Package
Title:	The Free Algebra
Version:	1.1-1
Authors@R:	person(given=c("Robin", "K. S."), family="Hankin", role = c("aut","cre"), email="[e-mail]", comment = c(ORCID = "0000-0001-5982-0415"))
Maintainer:	Robin K. S. Hankin <[e-mail]>
Depends:	R (>= 3.5.0), methods
Description:	The free algebra in R with non-commuting indeterminates. Uses 'disordR' discipline (Hankin, 2022, <doi:10.48550/ARXIV.2210.03856>). To cite the package in publications please use Hankin (2022) <doi:10.48550/ARXIV.2211.04002>.
License:	GPL (>= 2)
LazyData:	yes
Imports:	Rcpp (>= 1.0-7), partitions (>= 1.9-22), mathjaxr, disordR (>= 0.9)
LinkingTo:	Rcpp
Suggests:	knitr,testthat,magrittr,markdown,rmarkdown
VignetteBuilder:	knitr
URL:	https://github.com/RobinHankin/freealg
BugReports:	https://github.com/RobinHankin/freealg/issues
RdMacros:	mathjaxr
Author:	Robin K. S. Hankin [aut, cre] (<https://orcid.org/0000-0001-5982-0415>)

Index of help topics:

Ops.freealg             Arithmetic Ops methods for the the free algebra
abelianize              Abelianize a 'freealg' object
accessor                Accessor methods for freealg objects
adjoint                 The adjoint map
constant                The constant term
deriv                   Differentiation of 'freealg' objects
dot-class               Class "dot"
drop                    Drop redundant information
freealg                 The free algebra
freealg-package         The Free Algebra
grade                   The grade (or degree) of terms in a 'freealg'
                        object
horner                  Horner's method
linear                  A simple free algebra object
nterms                  Number of terms in a freealg object
pepper                  Combine variables in every possible order
print.freealg           Print freealg objects
rfalg                   Random free algebra objects
subs                    Substitution
zero                    The zero algebraic object

Author(s)

NA

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

Examples

a <- as.freealg("x+xyx")
b <- as.freealg("4x +XyX")  # upper-case interpreted as inverse

a+b
stopifnot(a+b==b+a)   # should be TRUE

a*b ==b*a # FALSE; noncommutative algebra

as.freealg("1+X+xy")^3

rfalg()
rfalg()^2