Function `signature()` in the `clifford` package
In clifford: Arbitrary Dimensional Clifford Algebras

set.seed(0)
library("clifford")
options(rmarkdown.html_vignette.check_title = FALSE)
knitr::opts_chunk$set(echo = TRUE)
knit_print.function <- function(x, ...){dput(x)}
registerS3method(
  "knit_print", "function", knit_print.function,
  envir = asNamespace("knitr")
)

knitr::include_graphics(system.file("help/figures/clifford.png", package = "clifford"))
knitr::include_graphics(system.file("help/figures/lorentz.png", package = "lorentz"))

signature

To cite the clifford package in publications please use @hankin2022_clifford. This short document discusses signature() in the clifford R package. As an example we might wish to work in $\operatorname{Cl}(1,2)$:

signature(1,2)

Thus $e_1^2=+1$, and $e_2^2=e_3^2=-1$:

c(drop(e(1)^2),drop(e(2)^2),drop(e(3)^2))

We might ask what $e_4$ would evaluate to, and this is assumed to be zero as is $e_i^2$ for $i\geqslant 4$:

c(drop(e(4)^2),drop(e(100)^2))

If we wish to set paranoid-level safety measures, we would set option maxdim to prevent accidentally working with too-large values of $i$:

options(maxdim = 4)

Now we work with a four-dimensional vector space in which $e_1^2=+1,e_2^2=e_3^2=-1,e_4^2=0$, but now $e_5$ is undefined:

c(drop(e(1)^2),drop(e(2)^2),drop(e(3)^2),drop(e(4)^2))
e(5)

The operation of signature() is modelled on the sol() function in the lorentz package [@hankin2022_lorentz]. Thus, if given no arguments we return the signature:

signature()

However, the default value is to use an infinite signature which corresponds to $e_i^2=1\forall i$:

options(maxdim=NULL)
signature(Inf)
signature()

Function signature() returns an object of (trivial) class sigobj which has a bespoke print method, print.sigobj(). For technical reasons an infinite signature is not allowed but is represented internally by a near-infinite integer, specifically .Machine$integer.max: