rev: Reverse of a Clifford object

Description Usage Arguments Author(s) See Also Examples

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

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

Arguments

x

Clifford object

Author(s)

Robin K. S. Hankin

See Also

grade,Conj

Examples

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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

clifford documentation built on March 13, 2020, 3:19 a.m.