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VectorCalculus

  

VectorSpace

  

create a tangent vector space at a given point in a given coordinate system

 

Calling Sequence

Parameters

Description

Examples

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 useful 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

withVectorCalculus:

vsVectorSpacesphericalr,φ,θ,1,Pi2,Pi2

vs:=modulelocal_origin,_coords,_coords_dim;exportGetCoordinates,GetRootPoint,Vector,eval;end module

(1)

Aboutvs

Type: Vector SpaceCoordinates: sphericalr,φ,θRoot Point: 1,π2,π2

(2)

vvs:-Vector0,1,0

v010

(3)

Aboutv

Type: Rooted VectorComponents: 0,1,0Coordinates: sphericalr,φ,θRoot Point: 1,π2,π2

(4)

MapToBasisv,'cartesian'

00−1

(5)

vVectorSpacepolarr,θ,x,y:-Vectora,b:

Aboutv

Type: Rooted VectorComponents: a,bCoordinates: polarr,θRoot Point: x2+y2,arctany,x

(6)

AboutGetSpacev

Type: Vector SpaceCoordinates: polarr,θRoot Point: x2+y2,arctany,x

(7)

See Also

attributes

VectorCalculus

VectorCalculus[About]

VectorCalculus[GetCoordinates]

VectorCalculus[GetRootPoint]

VectorCalculus[GetSpace]

VectorCalculus[MapToBasis]

VectorCalculus[RootedVector]

VectorCalculus[Vector]