Skip to contents

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: This package was not yet installed at build time.
Index: This package was not yet installed at build time.

Functionality to work with the free antiassociative algebra in R. The hex sticker features an image taken from hoffnung1959;textualevitaicossa 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

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

Maintainer: Robin K. S. Hankin <hankin.robin@gmail.com>

References

See also

Examples

x <- raaa()
x
#> free antiassociative algebra element:
#> +5c +2d +4b.b +1c.c +4d.d +4(b.c)c +1(b.c)d +3(c.d)d
y <- raaa()

x+y
#> free antiassociative algebra element:
#> +2a +1b +6c +2d +2b.a +4b.b +1c.c +4d.a +7d.d +3(a.c)b +1(b.b)b +4(b.c)c
#> +1(b.c)d +2(c.d)c +3(c.d)d
x*y
#> free antiassociative algebra element:
#> +10c.a +5c.b +5c.c +4d.a +2d.b +2d.c +8(b.b)a +4(b.b)b +4(b.b)c -10(c.b)a
#> +2(c.c)a +1(c.c)b +1(c.c)c -20(c.d)a -15(c.d)d -4(d.b)a +4(d.d)b +4(d.d)c
#> -6(d.d)d