rev: Reverse of a Clifford object In clifford: Arbitrary Dimensional Clifford Algebras

Description

The “reverse” of a term is simply the basis vectors written in reverse order; this changes the sign of the term if the number of basis vectors is 2 or 3 (modulo 4). Taking the reverse is a linear operation.

Both Hestenes and Chisholm use a dagger to denote the reverse of A, as in omitted. But both Perwass and Dorst use a tilde, as in omitted.

omitted

where <A> is the grade operator; and it is easy to prove that

omitted

We can also show that

≤ft<AB\right>_r=(-1)^{r(r-1)/2}≤ft<B^\dag A^\dag\right>_r

Usage

 1 2 ## S3 method for class 'clifford' rev(x) 

Arguments

 x Clifford object

Author(s)

Robin K. S. Hankin

grade,Conj
 1 2 3 4 5 6 7 8 x <- rcliff() rev(x) A <- rblade(g=3) B <- rblade(g=4) rev(A %^% B) == rev(B) %^% rev(A) # should be small rev(A * B) == rev(B) * rev(A) # should be small