>>
>>> Off topic: d_dx is the unit vector along x. It needs better name. (in
>>> latex it is \frac{\part}{\part x})
>>
>> I'm rather confused by your explanations. You seem to alternate between
>> describing it as a simple vector (but in which space?) and a differential
>> operator. These seem to be completely different things to me.
>
> Welcome to the very confusing world of differential geometry. The
> field is mired with tons of very confusing abuses of notation. I think
> the main thing to remember is that the isomorphism from a vector space
> and its second dual is taken as exact equality, so that a vector (or
> covector) is always considered also as a functional on its
> corresponding convector (or vector).
>I was not speaking about this (and I do not assume the isomorphism). Also, vector spaces are not discussed at all (the existence of some nice tangent space to points of the manifold is implicit in the code). First and foremost a vector field is a differential operator over scalar fields. This is how it is defined. -- You received this message because you are subscribed to the Google Groups "sympy" group. To post to this group, send email to [email protected]. To unsubscribe from this group, send email to [email protected]. For more options, visit this group at http://groups.google.com/group/sympy?hl=en.
