IsPerfect - Maple Help
For the best experience, we recommend viewing online help using Google Chrome or Microsoft Edge.

Online Help

All Products    Maple    MapleSim


DerivedAlgebra

calculate the derived algebra of a LAVF object.

IsPerfect

check if a LAVF object is perfect.

 

Calling Sequence

Parameters

Description

Examples

Compatibility

Calling Sequence

DerivedAlgebra ( obj)

IsPerfect( obj)

Parameters

obj

-

a LAVF object that is a Lie algebra i.e. IsLieAlgebra(obj) returns true, see IsLieAlgebra.

Description

• 

Let L be a LAVF object which is a Lie algebra. Then DerivedAlgebra method returns the derived algebra  of L, as a LAVF object.

• 

Let L be a LAVF object and is Lie algebra. Then IsPerfect(L) returns true if and only if DerivedAlgebra(L) = L.

• 

These methods are associated with the LAVF object. For more detail, see Overview of the LAVF object.

Examples

(1)

(2)

We first construct a LAVF object for E(2).

(3)

(4)

(5)

Since L and DL are not the same, therefore L is not perfect.

(6)

Compatibility

• 

The DerivedAlgebra and IsPerfect commands were 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]

IsLieAlgebra

 


Download Help Document