clifford (version 1.0-2)

antivector: Antivectors or pseudovectors

Description

Antivectors or pseudovectors

Usage

antivector(v, n = length(v))
is.antivector(C, include.pseudoscalar=FALSE)

Arguments

v

Numeric vector

n

Integer

C

Clifford object

include.pseudoscalar

Boolean: should the pseudoscalar be considered an antivector?

Details

An antivector is an \(n\)-dimensional Clifford object of all of whose terms are of grade \(n-1\).

The pseudoscalar is a peculiar edge case. Consider:

  A <- clifford(list(c(1,2,3)))
  B <- A + clifford(list(c(1,2,4)))
> is.antivector(A)
[1] FALSE
> is.antivector(B)
[1] TRUE
> is.antivector(A,include.pseudoscalar=TRUE)
[1] TRUE
> is.antivector(B,include.pseudoscalar=TRUE)
[1] TRUE

One could argue that A should be an antivector as it is a term in B, which is definitely an antivector. Use include.pseudoscalar=TRUE to ensure consistency in this case.

References

Wikipedia contributors. (2018, July 20). “Antivector”. In Wikipedia, The Free Encyclopedia. Retrieved 19:06, January 27, 2020, from https://en.wikipedia.org/w/index.php?title=Antivector&oldid=851094060

Examples

# NOT RUN {
antivector(1:5)
# }