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Intersection

calculate intersection of distributions

VectorSpaceSum

calculate vector space sum of distributions

 

Calling Sequence

Parameters

Description

Examples

Compatibility

Calling Sequence

Intersection(dist1, ...)

VectorSpaceSum(dist1, ...)

Parameters

dist1, ...

-

sequence of Distribution objects.

Description

• 

The Intersection method returns a Distribution object representing the intersection of the input Distribution objects.  More precisely, the result is a distribution such that at each point, the subspace of tangent space is the intersection of the subspaces spanned by the input distributions.

• 

Similarly, the VectorSpaceSum command returns a Distribution object representing the vector space sum of the input Distribution objects.  More precisely, the result is a distribution such that at each point, the subspace of tangent space is the vector space sum of the subspaces spanned by the input distributions.

• 

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

Examples

withLieAlgebrasOfVectorFields:

Build vector fields...

TxVectorFieldDx,space=x,y,z

Txx

(1)

TyVectorFieldDy,space=x,y,z

Tyy

(2)

TzVectorFieldDz,space=x,y,z

Tzz

(3)

RVectorFieldyDx+xDy,space=x,y,z

Ryx+xy

(4)

Construct two distributions...

ΣDistributionTz,R

Σyxx+y,z

(5)

GammaDistributionTx,Ty

Γx,y

(6)

Intersection and sum...

IntersectionGamma,Σ

yxx+y

(7)

VectorSpaceSumΣ,Gamma

x,y,z

(8)

Compatibility

• 

The Intersection and VectorSpaceSum commands were introduced in Maple 2020.

• 

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

See Also

Distribution (Object overview)

LieAlgebrasOfVectorFields[Distribution]

VectorField (Object overview)

LieAlgebrasOfVectorFields[VectorField]

LieAlgebrasOfVectorFields (Package overview)