VectorField & OneForm Object Overloaded builtins - Maple Programming Help

Online Help

All Products    Maple    MapleSim


Home : Support : Online Help : Mathematics : Differential Equations : Lie Symmetry Method : Commands for PDEs (and ODEs) : LieAlgebrasOfVectorFields : VectorField : LieAlgebrasOfVectorFields/VectorField/Builtins

VectorField & OneForm Object Overloaded builtins

overview of overloaded builtins for VectorField & OneForm objects

 

Description

Examples

Compatibility

Description

• 

The functionalities of some Maple builtin commands are extended for use on VectorField and OneForm objects.

• 

The following builtins have been overloaded for this purpose: map, subs, normal, expand, simplify, indets, has, type, hastype

• 

The map, subs, normal, expand, simplify builtin commands accept a VectorField or a OneForm object and apply their methods onto the components of the object. Then they return a VectorField or a OneForm object with new components.

• 

Let V be a VectorField (respectively OneForm) object.

• 

(i) The call type(V, t) returns true if t is any of the following types: module, object, anything, VectorField (respectively OneForm), appliable, and indexable. See examples below.

• 

(ii) The call type(V,indexable(t)) returns true if the components of V are of type t. See example below.

• 

(iii) The call type(V, dependent(x)) and type(V, freeof(x)) respectively return true if the components and space coordinates of V contain (respectively don't contain) x. See example below.

• 

The indets, has, hastype builtin commands accept a VectorField or a OneForm object and apply their methods onto the space coordinate variables and the components of the object.

• 

These overloaded builtins are associated with the VectorField and OneForm objects. For more detail, see Overview of the VectorField object, Overview of the OneForm object.

Examples

withLieAlgebrasOfVectorFields:

 

map, subs

XVectorFieldξx,yDx+ηx,yDy

Xξx,yx+ηx,yy

(1)

Rsubsξx,y=y,ηx,y=x,X

Ryx+xy

(2)

mapz2z,R

2yx+2xy

(3)

normal, expand, simplify

XVectorFieldxx1x2,x,cosa2+sina2,y

Xxx1x2x+cosa2+sina2y

(4)

normalX

xx+cosa2+sina2y

(5)

expandX

xx+cosa2+sina2y

(6)

simplifyX

xx+y

(7)

type

XVectorFieldξx,yDx+ηx,yDy

Xξx,yx+ηx,yy

(8)

typeX,VectorField,typeX,object,typeX,`module`

true,true,true

(9)

Checking type of the vector field's components, they are functions but not positive integers.

typeX,indexablefunction,typeX,indexableposint

true,false

(10)

The vector field contains x.

typeX,dependentx,typeX,freeofx

true,false

(11)

indets, has, hastype

XVectorField1,x,sina,y,cosa,z

Xx+sinay+cosaz

(12)

The indets of X includes all space variables as well as the indets occurring in the components of X.

indetsX

a,x,y,z,cosa,sina

(13)

hasX,ξ,hasX,sin,hasX,z

false,true,true

(14)

hastypeX,function

true

(15)

hastypeX,float

false

(16)

Compatibility

• 

The VectorField & OneForm Object Overloaded builtins command was introduced in Maple 2020.

• 

For more information on Maple 2020 changes, see Updates in Maple 2020.

See Also

VectorField (Object overview)

OneForm (Object overview)

LieAlgebrasOfVectorFields[VectorField]

LieAlgebrasOfVectorFields[OneForm]