fix

Author: kotapiku

nons-test/new-tensor.egi

@@ -1,29 +1,40 @@
 ;;;
 ;;; Parameters
 ;;;
+
 x = [| θ, φ |]
+
 X = [| r * sin(θ) * cos(φ), ; = x
-     r * sin(θ) * sin(φ), ; = y
-     r * cos(θ)         ; = z
+     r * sin(θ) * sin(φ),   ; = y
+     r * cos(θ)             ; = z
      |]
-X = [r * sin(θ) * cos(φ), r * sin(θ) * sin(φ), r * cos(θ)]
+
 ;;
 ;; Local basis
 ;;
+
 e_i_j = ∂/∂(X_j, x~i)
-e_i_j; [| [| (* r (cos θ) (cos φ)) (* r (cos θ) (sin φ)) (* -1 r (sin θ)) |] [| (* -1 r (sin θ) (sin φ)) (* r (sin θ) (cos φ)) 0 |] |]_i_j
+e_i_j
+; [| [| (* r (cos θ) (cos φ)) (* r (cos θ) (sin φ)) (* -1 r (sin θ)) |]
+; [| (* -1 r (sin θ) (sin φ)) (* r (sin θ) (cos φ)) 0 |]
+; |]_i_j
 
 ;;
 ;; Metric tensor
 ;;
+
 g__ = generateTensor(2#(V.*(e_%1_#, e_%2_#)), [2, 2])
 g~~ = M.inverse(g_#_#)
+
 g_#_#;[| [| r^2 0 |] [| 0 (* r^2 (sin θ)^2) |] |]_#_#
 g~#~#;[| [| (/ 1 r^2) 0 |] [| 0 (/ 1 (* r^2 (sin θ)^2)) |] |]~#~#
+
 ;;
 ;; Christoffel symbols of the first kind
 ;;
+
 Γ_j_k_l = (1/2) * (∂/∂(g_j_l, x~k) + ∂/∂(g_j_k, x~l) - ∂/∂(g_k_l, x~j))
+
 Γ_#_#_#
 Γ_1_#_#
 Γ_2_#_#

sample/math/geometry/riemann-curvature-tensor-of-S2.egi

@@ -17,7 +17,7 @@
 e_i_j
 ;[|[|(* r (cos θ) (cos φ)) (* r (cos θ) (sin φ)) (* -1 r (sin θ)) |]
 ;  [|(* -1 r (sin θ) (sin φ)) (* r (sin θ) (cos φ)) 0 |]
-;  |]_#_#
+;  |]_i_j
 
 ;;
 ;; Metric tensor