I'm working with Vectors type in Mathematica 9. For this purpose I use the following command:

Assumptions = v ϵ Vectors[3]


Now I want to find gradient from the next vector expression: $\vec{v}/\mid \vec{v}\mid$, but the usual Grad function doesn't work with Vectors. I tried this:

Grad[v/Norm[v], v]


Question: Is it possible to find Grad or at least Norm from variables of Vectors type?

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Not sure what you expect, but it seems like it works but with warnings. Eg TensorRank[Grad[v/Norm[v] , v]] -> 2. Maybe all you need is to surpress the warnings. Otherwise give more detail of what you are trying to do. – george2079 Dec 20 '13 at 19:53
Note the difference between $Assumptions and Assumptions. – Szabolcs Dec 21 '13 at 4:02 I hope to get something like $${\bigtriangledown}^{}_{v} \vec{v} / \mid \vec{v} \mid = \frac{1}{\mid \vec{v} \mid}[{\bigtriangledown}^{}_{v} \vec{v}-({\bigtriangledown}^{}_{v} \vec{v}* \frac{\vec{v}}{\mid \vec{v} \mid}) \otimes (\frac{\vec{v}}{\mid \vec{v} \mid})]$$ I know it is possible to do with Mathematica, but it seems like I chose the wrong functions for this purpose. – Stepan Loginov Dec 23 '13 at 8:21 It seems unlikely in the best case mathematica would do that expansion for you. Can you proove it to be true using lists (show code) then see what you get with abstract vectors? – george2079 Dec 23 '13 at 14:42 Also, I'm Assuming the lack of a $ on \$Assumptions is a typo in your post, but you might want to edit that. – george2079 Dec 23 '13 at 14:45