ウェッジ積

Nov 20 2017
--
-- Wedge Product
--

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 wedge {a} (X: DiffForm a) (Y: DiffForm a) : DiffForm a := X !. Y

def dx : DiffForm Integer := [|1, 0, 0|]
def dy : DiffForm Integer := [|0, 1, 0|]
def dz : DiffForm Integer := [|0, 0, 1|]

assertEqual "dx ∧ dy"
  (wedge dx dy)
  [| [| 0, 1, 0 |], [| -1, 0, 0 |], [| 0, 0, 0 |] |]

assertEqual "dx ∧ dy (normalized)"
  (dfNormalize (wedge dx dy))
  [| [| 0, 1, 0 |], [| 0, 0, 0 |], [| 0, 0, 0 |] |]

assertEqual "dz ∧ dz"
  (wedge dz dz)
  [| [| 0, 0, 0 |], [| 0, 0, 0 |], [| 0, 0, 0 |] |]

assertEqual "dz ∧ dz (normalized) = 0"
  (dfNormalize (wedge dz dz))
  [| [| 0, 0, 0 |], [| 0, 0, 0 |], [| 0, 0, 0 |] |]
リンク

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