>> 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). > I am not sure that we speak about the same things. There is the isomorphism between vectors and forms (i.e. vector and form fields *evaluated at a point*). But the fact that a vector field (not a vector) is an operator over scalar fields (not a single value, but a field) is not concerned with this isomorphism.
Just to be clear (you already mentioned it in a different way): It is true that a vector field is a vector in "the space of vector fields", but this is not the tangent space to the manifold (the vector space in which the vector field has its values) and we are not really interested in it. -- 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.
