How to symbolically calculate the curl of a vector

so basically i want to do this:

syms E1(x,y,z) E2(x,y,z) E3(x,y,z)
Ecurl=symcurl(x,y,z,E1,E2,E3)

function Ecurl = symcurl(x,y,z,E1,E2,E3)
Ecurl1 = diff(E2,z)-diff(E3,y)
Ecurl2 = diff(E3,x)-diff(E1,z)
Ecurl3 = diff(E1,y)-diff(E2,x)
Ecurl=[Ecurl1 Ecurl2 Ecurl3]
end

with the builtin curl function of matlab. When i try it like this:

syms x y z E1 E2 E3
curl([x,y,z],[E1,E2,E3])

i get a zero vector. And like this:

syms E1(x,y,z) E2(x,y,z) E3(x,y,z)
curl([x,y,z],[E1,E2,E3])

i get an error message that the second argument must be a vector of three variables. In the end i want to be able to use the subs command to assign a specific function to E1 E2 E3 at a later time. Thanks.

Answer 1

[David Goodmanson]

Hi Max, this appears to work.

>> minusdBdt = curl([E1,E2,E3],[x,y,z])

minusdBdt(x, y, z) =

   diff(E3(x, y, z), y) - diff(E2(x, y, z), z)
   diff(E1(x, y, z), z) - diff(E3(x, y, z), x)
   diff(E2(x, y, z), x) - diff(E1(x, y, z), y)

(It's correct for a right hand coordinate system and opposite in sign from symcurl above)

>>