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VectorCalculus[VectorSpace] - create a tangent vector space at a given point in a given coordinate system
Calling Sequence
VectorSpace(c, origin)
Parameters
c
-
(optional) symbol or symbol[name, name, ...]; specify the coordinate system, possibly indexed by the coordinate names
origin
Vector or list; free or position Vector or list; specify the root point of the tangent vector space
Description
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:
GetRootPoint
Return the root point of the vector space
GetCoordinates
Return the coordinate system of the vector space
Vector(comps)
Create a rooted Vector based on the vector space, with components comps. comps is expected to be of type list(algebraic).
Examples
See Also
attributes, VectorCalculus, VectorCalculus[About], VectorCalculus[GetCoordinates], VectorCalculus[GetRootPoint], VectorCalculus[GetSpace], VectorCalculus[MapToBasis], VectorCalculus[RootedVector], VectorCalculus[Vector]
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