Student/VectorCalculus/VectorSpace

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Student[VectorCalculus][VectorSpace] - creates a vector space at a given point in a given coordinate system

	Calling Sequence
	VectorSpace(c, origin)

Parameters

c	-	name or name[name, name, ...]; specify the coordinate system, possibly indexed by the coordinate variable names
origin	-	free or position Vector or list; root point of the vector space

Description

•	The VectorSpace(c, origin) command returns a module representing the 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, its coordinate system attribute is checked and the Vector will be converted to c coordinates. 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 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

Matrix([[`Type: `, `Vector Space`], [`Coordinates: `, spherical[r, phi, theta]], [`Root Point: `, [1, (1/2)*Pi, (1/2)*Pi]]])

(1)

v := Vector[column]([[0], [1], [0]])

(2)

Matrix([[`Type: `, `Rooted Vector`], [`Components: `, [0, 1, 0]], [`Coordinates: `, spherical[r, phi, theta]], [`Root Point: `, [1, (1/2)*Pi, (1/2)*Pi]]])

(3)

(4)

Matrix([[`Type: `, `Rooted Vector`], [`Components: `, [a, b]], [`Coordinates: `, polar[r, theta]], [`Root Point: `, [(x^2+y^2)^(1/2), arctan(y, x)]]])

(5)

Matrix([[`Type: `, `Vector Space`], [`Coordinates: `, polar[r, theta]], [`Root Point: `, [(x^2+y^2)^(1/2), arctan(y, x)]]])

(6)

	See Also
	attributes, Student[VectorCalculus], Student[VectorCalculus][About], Student[VectorCalculus][GetCoordinates], Student[VectorCalculus][GetRootPoint], Student[VectorCalculus][GetSpace], Student[VectorCalculus][MapToBasis], Student[VectorCalculus][Vector]