The method VectorField.__call__ implements the action v(f) of a vector field v on a scalar field f, as a derivation. It is reimplemented here to simply return df(v), i.e. the differential of f acting on v as a 1-form. Actually, the current code of this method contains the comment:

        #!# Could it be simply
        # return scalar.differential()(self)
        # ?

git blame reveals that this comment dates back to 2015. It is time to make the change, thereby simplifying the code and avoiding some code duplication.

CC: @tscrim @mjungmath

Component: manifolds

Keywords: vector field, scalar field

Author: Eric Gourgoulhon

Branch/Commit: bc25781

Reviewer: Michael Jung

Issue created by migration from https://trac.sagemath.org/ticket/31633