On Tue, May 29, 2012 at 1:19 PM, krastanov.ste...@gmail.com
<krastanov.ste...@gmail.com> wrote:
>>>
>>>> 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).Oh, I don't know how things will work in your code. I was referring to differential geometry as I learned it. You always have a vector space any time you have something linear (a vector space just means that you can add elements and multiply them by scalars). > > First and foremost a vector field is a differential operator over > scalar fields. This is how it is defined. This is again due to implicit isomorphism. See http://planetmath.org/encyclopedia/VectorField.html (second paragraph on the section on manifolds). Aaron Meurer -- You received this message because you are subscribed to the Google Groups "sympy" group. To post to this group, send email to sympy@googlegroups.com. To unsubscribe from this group, send email to sympy+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/sympy?hl=en.
