Student/VectorCalculus/VectorSpace - Maple Help
For the best experience, we recommend viewing online help using Google Chrome or Microsoft Edge.
Our website is currently undergoing maintenance, which may result in occasional errors while browsing. We apologize for any inconvenience this may cause and are working swiftly to restore full functionality. Thank you for your patience.

Online Help

All Products    Maple    MapleSim


Home : Support : Online Help : Student/VectorCalculus/VectorSpace

Student[VectorCalculus]

  

VectorSpace

  

creates a vector space at a given point in a given coordinate system

 

Calling Sequence

Parameters

Description

Examples

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

withStudentVectorCalculus:

vsVectorSpacesphericalr,φ,θ,1,π2,π2:

Aboutvs

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

(1)

vvs:-Vector0,1,0

v010

(2)

Aboutv

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

(3)

MapToBasisv,cartesian

00−1

(4)

vVectorSpacepolarr,θ,x,y:-Vectora,b:

Aboutv

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

(5)

AboutGetSpacev

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