Implement the mathematical identities of different calculus objects

[saidctb]

The following identities should be implemented:

• grad(dot(F,G)) == convect(F, G) + convect(G, F) + cross(F, curl(G)) - cross(curl(F), G)
• div(cross(F,G)) == -dot(F, curl(G)) + dot(G, curl(F))
• curl(cross(F,G)) == F*div(G) - G*div(F) - convect(F, G) + convect(G, F)
• curl(f*F) == f*curl(F) + cross(grad(f), F)
• laplace(f*g) == f*laplace(g) + g*laplace(f) + 2*dot(grad(f), grad(g))
• div(cross(F,G)) == -dot(F, curl(G)) + dot(G, curl(F))
• div(f*F) == f*div(F) + dot(F, grad(f))
• div(cross(grad(f), grad(g))) == 0
• curl(curl(F)) == grad(div(F)) - laplace(F)
• curl(f*grad(g)) == cross(grad(f), grad(g))

These used to be automatically verified because SymPDE was expanding all expressions by default. After PR #71 this is not the case anymore, so we'll need to find an explicit procedure to verify these identities.

[ThatDevShparki]

Hast this issue been claimed already? I'm down to put some work into this issue!