--
-- Exterior Derivative
--

declare symbol x, y, z : MathExpr

def N : Integer := 3

def params : Vector MathExpr := [|x, y, z|]

def g : Matrix Integer := [|[|1, 0, 0|], [|0, 1, 0|], [|0, 0, 1|]|]

def d {a} (X: a) : DiffForm a := !(flip ∂/∂) params X


--def f : MathExpr := function (x, y, z)
def f := x ^ 2 + y ^ 2 + z ^ 2

-- The exterior derivative of f is the gradient 1-form
d f

-- The exterior derivative of d(f) is 0 (d^2 = 0)
d (d f)
dfNormalize (d (d f))