Antiassociative algebra in R: introducing the evitaicossa package
Robin K. S. Hankinn
TL;DR
The paper presents the evitaicossa R package for antiassociative algebras, formalizing the law $u(\mathbf{v}\mathbf{w})=-(\mathbf{u}\mathbf{v})\mathbf{w}$ and noting key properties such as nilpotence of order $4$ and the absence of nonzero scalars. It introduces a concrete representation of free antiassociative elements as tripartite sums of single-, double-, and triple-symbol terms and implements the corresponding arithmetic using a dedicated product formula that encodes antiassociativity. Practical tooling is showcased through functions like $raaa()$, $as.aaa()$, and $aaa()$, along with robust extraction/replacement mechanisms ($single()/double()/triple()$ and square-bracket indexing) for manipulating components. The package also integrates with disordR to track symbol/coefficient metadata and supports a generalized antiassociativity parameter $k$, allowing a continuum between associativity ($k=1$) and antiassociativity ($k=-1$). Together, these contributions enable symbolic exploration and computation of antiassociative algebras directly in R, providing a foundation for further algebraic tooling and research.
Abstract
In this short article I introduce the evitaicossa package which provides functionality for antiassociative algebras in the R programming language; it is available on CRAN at https://CRAN.R-project.org/package=evitaicossa.