# Function `signature()` in the `clifford` package

#### Robin K. S. Hankin

    signature

    ## function (p, q = 0)
    ## {
    ##     if (missing(p)) {
    ##         s <- getOption("signature")
    ##         if (is.null(s)) {
    ##             s <- c(.Machine$integer.max, 0)
    ##         }
    ##         showsig(s)
    ##         class(s) <- "sigobj"
    ##         return(s)
    ##     }
    ##     else {
    ##         s <- c(p, q)
    ##         m <- getOption("maxdim")
    ##         if (!is.null(m)) {
    ##             if (p + q > m) {
    ##                 stop("signature requires p+q <= maxdim")
    ##             }
    ##         }
    ##         p <- min(s[1], .Machine$integer.max)
    ##         q <- min(s[2], .Machine$integer.max)
    ##         stopifnot(is_ok_sig(s))
    ##         options(signature = c(p, q))
    ##         showsig(s)
    ##         return(invisible(s))
    ##     }
    ## }

To cite the `clifford` package in publications please use Hankin (2025a). 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))

    ## [1]  1 -1 -1

We might ask what \(e_4^2\) 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))

    ## [1] 0 0

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))

    ## [1]  1 -1 -1  0

    e(5)

    ## Error in `is_ok_clifford()`:
    ## ! option maxdim exceeded

The operation of `signature()` is modelled on the `sol()` function in the `lorentz` package (Hankin 2025b). Thus, if given no arguments we return the signature:

    signature()

    ## [1] 1 2

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

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

    ## [1] Inf   0

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`:

    dput(signature())

    ## structure(c(2147483647, 0), class = "sigobj")

# References

Hankin, R. K. S. 2025a. “Clifford Algebra in R: Introducing the clifford Package.” Advances in Applied Clifford Algebra 35 (51). https://doi.org/https://doi.org/10.1007/s00006-025-01403-9.
———. 2025b. “Special Relativity in R: The Lorentz Package.” Journal of Open Source Education 8 (88): 196. https://doi.org/10.21105/jose.00196.