Function `getcoeffs()` in the `clifford` package

getcoeffs

## function (C, B) 
## {
##     out <- c_getcoeffs(L = terms(C), c = coeffs(C), m = maxyterm(C), 
##         B = list_modifier(B))
##     names(out) <- lapply(B, catterm)
##     return(out)
## }

To cite the clifford package in publications please use Hankin (2022). This short document discusses function getcoeffs() in the clifford R package which, as its name suggests, retrieves specific coefficients from a clifford object. It is a relatively low-level helper function that is a wrapper for a C routine. It takes as arguments a clifford object and a list of terms:

set.seed(0)
(a <- rcliff())

## Element of a Clifford algebra, equal to
## + 5 + 6e_1 - 9e_12 - 3e_14 + 3e_26 - 6e_126 + 1e_236 - 1e_56 + 4e_156

getcoeffs(a,list(1:2, 0, c(2,5), c(1,5,6), c(2,6), 1:2))

##  e_12   e_0  e_25 e_156  e_26  e_12 
##    -9     5     0     4     3    -9

Note that the first and last element of the returned vector are both the coefficient of \(e_{12}\), viz. -9. The coefficients are returned in the form of a numeric vector [not a disord object: the order of the elements is determined by the order of argument B]. Compare standard extraction, e.g. a[index], which returns a clifford object. Also, compare coeffs() which extracts all coefficients of a clifford object:

coeffs(a)

## A disord object with hash 95062597dd6246faa022dc8f8a57947483f5ba60 and elements
## [1]  5  6 -9 -3  3 -6  1 -1  4
## (in some order)

The index for the constant is formally list(numeric(0)), but this is a pain to type, so there is special dispensation for argument B having list elements of zero, which are translated by helper function list_modifier() to numeric(0) and listified if necessary. The upshot is that a zero list element in argument B works as expected extracting the constant. Also, passing B=0 works as expected, returning the constant (there is no need to coerce to a list: coercion is performed by list_modifier). A similar scheme is used in the square bracket extraction and replacement methods

Attempting to extract a coefficient of a term that includes a negative index will throw an error. The coefficient of a term including an index larger than indicated by maxyterm() will return zero.

References

Hankin, R. K. S. 2022. “Clifford Algebra in R.” arXiv. https://doi.org/10.48550/ARXIV.2209.13659.

Robin K. S. Hankin

References