--
-- Vectors
--

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

def V.* := dotProduct

def 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|]

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

def div %A %xs := trace (∇ A xs)

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