(define $N 3)
(define $params [| x y z |])
(define $g [| [| 1 0 0 |] [| 0 1 0 |] [| 0 0 1 |] |])

(define $wedge
  (lambda [%X %Y]
    !(. X Y)))

(define $dx [| 1 0 0 |])
(define $dy [| 0 1 0 |])
(define $dz [| 0 0 1 |])

(wedge dx dy)
;[| [| 0 1 0 |] [| 0 0 0 |] [| 0 0 0 |] |]

(df-normalize (wedge dx dy))
;[| [| 0 (/ 1 2) 0 |] [| (/ -1 2) 0 0 |] [| 0 0 0 |] |]

(wedge dz dz)
;[| [| 0 0 0 |] [| 0 0 0 |] [| 0 0 1 |] |]

(df-normalize (wedge dz dz))
;[| [| 0 0 0 |] [| 0 0 0 |] [| 0 0 0 |] |]