antivector {clifford} R Documentation

## Antivectors or pseudovectors

### Description

Antivectors or pseudovectors

### Usage

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


### Arguments

 v Numeric vector n Integer specifying dimensionality of underlying vector space C Clifford object include.pseudoscalar Boolean: should the pseudoscalar be considered an antivector?

### Details

An antivector is an $$n$$-dimensional Clifford object, all of whose terms are of grade $$n-1$$. An antivector has $$n$$ degrees of freedom. Function antivector(v,n) interprets v[i] as the coefficient of $$e_1e_2\ldots e_{i-1}e_{i+1}\ldots e_n$$.

Function as.antivector() is a convenience wrapper, coercing its argument to an antivector of minimal dimension (zero entries are interpreted consistently).

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.

Compare as.1vector(), which returns a clifford object of grade 1.

### Note

An antivector is always a blade.

### Author(s)

Robin K. S. Hankin

### 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

as.1vector
antivector(1:5)