evitaicossa-package {evitaicossa}

Antiassociative Algebra

Description

Methods to deal with the free antiassociative algebra over the reals with an arbitrary number of indeterminates. Antiassociativity means that (xy)z = -x(yz). Antiassociative algebras are nilpotent with nilindex four (Remm, 2022, <doi:10.48550/arXiv.2202.10812>) and this drives the design and philosophy of the package. Methods are defined to create and manipulate arbitrary elements of the antiassociative algebra, and to extract and replace coefficients. A vignette is provided.

Details

The DESCRIPTION file:

Package:	evitaicossa
Type:	Package
Title:	Antiassociative Algebra
Version:	0.0-1
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]>
Description:	Methods to deal with the free antiassociative algebra over the reals with an arbitrary number of indeterminates. Antiassociativity means that (xy)z = -x(yz). Antiassociative algebras are nilpotent with nilindex four (Remm, 2022, <doi:10.48550/arXiv.2202.10812>) and this drives the design and philosophy of the package. Methods are defined to create and manipulate arbitrary elements of the antiassociative algebra, and to extract and replace coefficients. A vignette is provided.
License:	GPL (>= 2)
Depends:	R (>= 3.5.0)
Suggests:	knitr, markdown, rmarkdown, testthat, mvtnorm, covr
VignetteBuilder:	knitr
Imports:	Rcpp (>= 1.0-7), disordR (>= 0.9-8-2), methods, Rdpack
LinkingTo:	Rcpp
URL:	https://github.com/RobinHankin/evitaicossa
BugReports:	https://github.com/RobinHankin/evitaicossa/issues
RdMacros:	Rdpack
Author:	Robin K. S. Hankin [aut, cre] (<https://orcid.org/0000-0001-5982-0415>)

Index of help topics:

aaa                     Function to create objects of class 'aaa'
aaa-class               Class '"aaa"'
allsymbols              All symbols in an aaa object
Arith-methods           Arithmetic methods for 'aaa' objects
Compare-methods         Comparison methods for antiassociative algebra
evitaicossa-package     Antiassociative Algebra
linear                  Linear functions
raaa                    Random elements of the free antiassociative
                        algebra
s1                      Extract or Replace Parts of 'aaa' objects
show                    Print method for antiassociative algebra
                        objects
zero                    The additive zero in antiassociative algebras

Functionality to work with the free antiassociative algebra in R. The hex sticker features an image taken from Hoffnung (1959) in which musical concepts [pizzicato, crescendo, etc] are given whimsical visual form. The character on the hex sticker is captioned “A Discord”: Hoffnung's interpretation of the musical concept of dissonance. In the book, the preceding image was a “chord”, evoking harmony. The discord, on the other hand, embodies–for me at least–antiassociativity: everything is wrong, wrong, wrong.

Author(s)

Robin K. S. Hankin [aut, cre] (<https://orcid.org/0000-0001-5982-0415>)

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

References

Hoffnung G (1959). Hoffnung's Acoustics. Dobson.

See Also

aaa

Examples

x <- raaa()
x
y <- raaa()

x+y
x*y