;;; Parameters and metrics (define $N 2) (define $params [|x y|]) (define $g__ [| [| (G_1_1 x y) (G_1_2 x y) |] [| (G_2_1 x y) (G_2_2 x y) |] |]) (define $g~~ [| [| (G~1~1 x y) (G~1~2 x y) |] [| (G~2~1 x y) (G~2~2 x y) |] |]) ;;; Hodge Laplacian (define $d (lambda [%X] !((flip ∂/∂) params X))) (define $hodge (lambda [%A] (let {[$k (df-order A)]} (with-symbols {i j} (* (sqrt (abs (M.det g_#_#))) (foldl . (. (ε' N k)_[i_1]..._[i_N] A..._[j_1]..._[j_k]) (map 1#g~[i_%1]~[j_%1] (between 1 k)))))))) (define $δ (lambda [%A] (let {[$r (df-order A)]} (* (** -1 (+ (* N r) 1)) (hodge (d (hodge A))))))) (define $Δ (lambda [%A] (match (df-order A) integer {[,0 (δ (d A))] [,2 (d (δ A))] [_ (+ (d (δ A)) (δ (d A)))]}))) (d (f x y)) (hodge (d (f x y))) (d (hodge (d (f x y)))) (δ (d (f x y))) (Δ (f x y)) ;