Hi!
I would like to check some differential vectorial identities. Any suggestion to achieve this goal would be welcomed.
Example of a case I already worked out: $\vec{\nabla} (fg) = (\vec{\nabla}f) g + f (\vec{\nabla} g)$.
Code (I coudn't manage to put it on a single box, sorry):
from sage.manifolds.operators import
E.<x,y,z>=EuclideanSpace()
f=function('f')(x,y,z)
g=function('g'(x,y,z)
sff=E.scalar_field(fg,name='sff')
sfg=E.scalar_field(fg,name='sfg')
sffg=E.scalar_field(fg,name='sffg')
grad(sffg) == grad(sff)sfg+sffgrad(sfg)
Out: True
Example of what I want to check: $ \vec{\nabla} (\vec{A}\centerdot \vec{B}) = \vec{A}\times(\vec{\nabla} \times \vec{B}) + \vec{B} \times (\vec{\nabla} \times \vec{A}) + (\vec{A} \centerdot \vec{\nabla}) \vec{B} + (\vec{B} \centerdot \vec{\nabla}) \vec{A}. $ I don't know how to came to differential operators of the form $(\vec{A} \centerdot \vec{\nabla})$.
I tried (kind of hopelessly)
newOperator=A.dot(grad())
without success.
How could I put sage to check identities like this one?
Thank you in advance.