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2024-02-09 13:45:13 +0200	received badge	● Popular Question (source)
2021-07-31 19:22:35 +0200	received badge	● Student (source)
2021-07-30 14:40:45 +0200	marked best answer	How do I use sage to check differential vector identities? Do I need to create an operator? Hi! I would like to check some differential vector 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(sff, name = 'sff') sfg = E.scalar_field(sfg, name = 'sfg') sffg = E.scalar_field(sffg, name = 'sffg') grad(sffg) == grad(sff) * sfg + sff * grad(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.
2021-07-30 14:40:45 +0200	received badge	● Scholar (source)
2021-07-30 14:40:29 +0200	commented answer	How do I use sage to check differential vector identities? Do I need to create an operator? Thank you a lot, Eric! This is what I was searching for.
2021-07-29 22:30:53 +0200	edited question	How do I use sage to check differential vector identities? Do I need to create an operator? How do I use sage to check differential vector identities? Do I need to create an operator? Hi! I would like to check so
2021-07-29 22:29:25 +0200	edited question	How do I use sage to check differential vector identities? Do I need to create an operator? How do I use sage to check differential vector identities? Do I need to create an operator? Hi! I would like to check so
2021-07-29 22:28:26 +0200	received badge	● Editor (source)
2021-07-29 22:28:26 +0200	edited question	How do I use sage to check differential vector identities? Do I need to create an operator? How do I use sage to check differential vector identities? Do I need to create an operator? Hi! I would like to check so
2021-07-29 22:20:05 +0200	asked a question	How do I use sage to check differential vector identities? Do I need to create an operator? How do I use sage to check differential vector identities? Do I need to create an operator? Hi! I would like to check so