hodge-Minkowski.egi

(define $N 4)
(define $params [| t x y z |])
(define $g [| [| -1 0 0 0 |] [| 0 1 0 0 |] [| 0 0 1 0 |] [| 0 0 0 1 |] |])

(define $hodge
  (lambda [%A]
    (let {[$k (df-order A)]}
      (with-symbols {i j}
        (* (sqrt (abs (M.det g_#_#)))
           (foldl . (. (subrefs A (map 1#j_%1 (between 1 k)))
                       (subrefs (ε' N k) (map 1#i_%1 (between 1 N))))
                  (map 1#g~[i_%1]~[j_%1] (between 1 k))))))))

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

(hodge (wedge dt dx))
;[| [| 0 0 0 0 |] [| 0 0 0 0 |] [| 0 0 0 -1 |] [| 0 0 0 0 |] |]
;= (* -1 (wedge dy dz))

(hodge (wedge dy dz))
;[| [| 0 1 0 0 |] [| 0 0 0 0 |] [| 0 0 0 0 |] [| 0 0 0 0 |] |]
;= (wedge dt dx)