Hildenbrand's 5D conformal geometric algebra

[RobinHankin]

(see page 27 et seq) is easy to set up with the clifford package:

> signature(4)
[1] 4
> e1 <- basis(1)
> e2 <- basis(2)
> e3 <- basis(3)
> eplus <- basis(4)
> eminus <- basis(5) 
> e0 <- (basis(5)-basis(4))/2
> einf <- basis(4) +basis(5)
> e0^2
Element of a Clifford algebra, equal to
the zero clifford element (0)

> einf^2
Element of a Clifford algebra, equal to
the zero clifford element (0)

> e0 %.% einf
Element of a Clifford algebra, equal to
scalar ( -1 )

> einf*e0
Element of a Clifford algebra, equal to
- 1 + 1e_45

> e0 * einf
Element of a Clifford algebra, equal to
- 1 - 1e_45

but this could use some polishing and (e.g.) a nicer print method

[RobinHankin]

Perhaps inst/conformal_algebra.R should be a nice rmarkdown document