The VectorSpace(c, origin) command returns a module representing the tangent vector space rooted at point origin in c coordinates.

The order of the arguments may be reversed. If no coordinate system argument is present, the current coordinate system is used.

The root point origin can be specified as a free or position Vector or as a list of coordinates. If it is a free or position Vector, the coordinate system attribute is checked and conversion done accordingly. If it is a list, the components are expected to be in c coordinates.

Once coordinates c are specified, the unit basis vectors are evaluated at the point origin. If any of the unit basis vectors evaluate to zero an error is raised.

The returned module is a valid right hand side for the space attribute on Vectors. If this attribute is present, it qualifies the Vector as a rooted Vector, and determines its root point and coordinate system.

The module itself has 3 exports: