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LieAlgebrasOfVectorFields

  

DisplayStructure

  

display the structure constants of a LAVF object

 

Calling Sequence

Parameters

Description

Examples

Compatibility

Calling Sequence

DisplayStructure( L, u, order = n, format = x )

DisplayStructure( C, u, format = x )

Parameters

L

-

a LAVF object

C

-

an array with three indices representing the structure constants of a LAVF (see method StructureConstants)

u

-

a name or a list of names

n

-

(optional) a positive integer or a string "involution"

x

-

(optional) a string: either "commutatorTable", "commutatorList", or "cartan"

Description

• 

The command DisplayStructure(...) displays the structure constants of a LAVF object L as with respect to L's current initial data basis, formatted as a commutator table with the second input argument u as the printed name(s).

• 

The second calling sequence gives alternative way to display the structure constants from the input argument C directly, without needed to know which LAVF object is C from. The structure constants of a LAVF object L can be got by calling StructureConstants(L).

• 

If the second input argument u is a name,then the basis of solution vector fields are printed as X1,X2,,Xr where r is the dimension of the Lie algebra. If u is provided as list of names A,B,C, then these will be taken as names of basis elements. The number of entries in the list must be equivalent to r.

• 

By specifying the option format = "commutatorList" or "cartan", the structure constants cijk can be displayed as commutator lists or cartan format respectively,

• 

This command is part of the LieAlgebrasOfVectorFields package. For more detail, see Overview of the LieAlgebrasOfVectorFields package.

• 

This command can be used in the form DisplayStructure(...) only after executing the command with(LieAlgebrasOfVectorFields), but can always be used in the form :-LieAlgebrasOfVectorFields:-DisplayStructure(...).

Examples

withLieAlgebrasOfVectorFields:

Typesetting:-Settingsuserep=true:

Typesetting:-Suppressξx,y,ηx,y:

VVectorFieldξx,yDx+ηx,yDy,space=x,y

Vξx+ηy

(1)

E2LHPDEdiffξx,y,y,y=0,diffηx,y,x=diffξx,y,y,diffηx,y,y=0,diffξx,y,x=0,indep=x,y,dep=ξ,η

E2ξy,y=0,ηx=ξy,ηy=0,ξx=0,indep=x,y,dep=ξ,η

(2)

LLAVFV,E2

Lξx+ηy&whereξy,y=0,ξx=0,ηx=ξy,ηy=0

(3)

DisplayStructureL,X

00X200X1X2X10

(4)

Or the above step is equivalent to the following two steps.

CijkStructureConstantsL

(5)

DisplayStructureCijk,X

00X200X1X2X10

(6)

Alternative way to display cijk as commutator lists.

DisplayStructureCijk,X,format=commutatorList

X1,X3=X2,X2,X3=X1

(7)

Compatibility

• 

The LieAlgebrasOfVectorFields[DisplayStructure] command was introduced in Maple 2020.

• 

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

See Also

LieAlgebrasOfVectorFields (Package overview)

LAVF (Object overview)

LieAlgebrasOfVectorFields[VectorField]

LieAlgebrasOfVectorFields[LHPDE]

LieAlgebrasOfVectorFields[LAVF]

StructureConstants