#1: " ----------[ D e r i v e ]---------- " User
#2: " ---------- Initialization ---------- " User
#3: " ---------- Tensor Analysis ---------- " User
#4: " Generalized Kronecker delta: delta([j, h], [i, k]) = "User
User
#5: " delta(j, i) delta(h, k) - delta(j, k) delta(h, i). See David
Lovelock and "
User
#6: " Hanno Rund, _Tensors, Differential Forms, & Variational
Principles_, John "
#7: " Wiley & Sons, Inc., 1975, p. 109. " User
#8: GDELTA(2, 2) User
/ / 0 0 \ / 0 1 \ \
| | | | | |
| \ 0 0 / \ -1 0 / |
#9: | | Simp(#8)
| / 0 -1 \ / 0 0 \ |
| | | | | |
\ \ 1 0 / \ 0 0 / /
User
#10: " Levi-Civita symbol: [epsilon(2,1,3), epsilon(1,3,1)] => [-1,
0] "
#11: [EL_E([2, 1, 3]), EL_E([1, 3, 1])] User
#12: [-1, 0] Simp(#11)
User
#13: " Tensor outer product: [[ 5 6] [-10 -12]] "
User
#14: " [1 -2] [ 5 6] [[ -7 8] [ 14 -16]] "
User
#15: " ij ij [3 4] X [-7 8] = [ ] "
User
#16: " c = a b [[ 15 18] [ 20 24]] "
User
#17: " kl kl [[-21 24] [-28 32]] "
/ 1 -2 \
#18: a := | | User
\ 3 4 /
/ 5 6 \
#19: b := | | User
\ -7 8 /
#20: O_T(a, b) User
/ / 5 6 \ / -10 -12 \ \
| | | | | |
| \ -7 8 / \ 14 -16 / |
#21: | | Simp(#20)
| / 15 18 \ / 20 24 \ |
| | | | | |
\ \ -21 24 / \ -28 32 / /
#22: a := User
#23: b := User
User
#24: " Definition of the Christoffel symbol of the first kind (a is
the metric "
#25: " tensor) [Lovelock and Rund, p. 81] " User
#26: " d a d a d a " User
#27: " 1 kh hl lk " User
#28: " Chr1 = - (----- + ----- - -----) " User
#29: " lhk 2 l k h " User
#30: " d x d x d x " User
User
#31: " Partial covariant derivative of a type (1, 1) tensor field
(Chr2 is the "
User
#32: " Christoffel symbol of the second kind) [Lovelock and Rund, p.
77] "
#33: " i d i i m m i " User
#34: " T = ---- T + Chr2 T - Chr2 T " User
#35: " j|k k j m k j j k m " User
#36: " d x " User
T
#37: j User
T
#38: j Simp(#37)
User
#39: " Verify the Bianchi identity for a symmetric connection (K is
the Riemann "
#40: " curvature tensor) [Lovelock and Rund, p. 94] " User
#41: " h h h " User
#42: " K + K + K = 0 " User
#43: " i jk|l i kl|j i lj|k " User
#44: " ---------- Quit ---------- " User