--
-- Vectors
--

dotProduct %v1 %v2 := withSymbols [i] v1~i . v2_i

V.* := dotProduct

crossProduct/fn fn %a %b :=
  [|fn a_2 b_3 - fn a_3 b_2, fn a_3 b_1 - fn a_1 b_3, fn a_1 b_2 - fn a_2 b_1|]

crossProduct %a %b := crossProduct/fn (*) a b

div %A %xs := trace (∇ A xs)

rot %A %xs := crossProduct/fn ∂/∂ A xs