"Maxwell in tensor form"

clear

--Maxwell equations in tensor form.
--See the book Gravitation p. 81.
--
--   F     + F     + F     = 0
--    ab,c    bc,a    ca,b
--
--    ab           a
--   F     = 4 pi J
--      ,b
--
--For this demo, use circular polarized light.
--
EX = sin(t+z)
EY = cos(t+z)
EZ = 0
BX = cos(t+z)
BY = -sin(t+z)
BZ = 0
FDD = ((  0, -EX, -EY, -EZ),
       ( EX,   0,  BZ, -BY),
       ( EY, -BZ,   0,  BX),
       ( EZ,  BY, -BX,   0))   --See p. 74. Here, DD means "down down" indices.
X = (t,x,y,z)   --Coordinate system
FDDD = d(FDD,X)   --Gradient of F
T1 = transpose(transpose(FDDD,2,3),1,2)   --Transpose bca to abc
T2 = transpose(transpose(FDDD,1,2),2,3)   --Transpose cab to abc
check(FDDD + T1 + T2 = 0)
guu = ((-1,0,0,0),(0,1,0,0),(0,0,1,0),(0,0,0,1))
FDDU = contract(outer(FDDD,guu),3,4)   --Easier to make FDDU than FUUD.
check(contract(FDDU,2,3) = 0)   --For light J is zero.
