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CauchyDistribution

calculate Distribution spanned by Cauchy vector fields of a distribution

 

Calling Sequence

Parameters

Description

Examples

Compatibility

Calling Sequence

CauchyDistribution(dist)

Parameters

dist

-

a Distribution object.

Description

• 

The CauchyDistribution method returns a Distribution object spanned by the Cauchy vector fields of input Distribution dist.

• 

A vector field C is a Cauchy vector field of distribution dist if C within dist, then [C,X] likewise lies within dist.  That is, C lies in dist and is a symmetry of dist. Such vector fields span a distribution, which is always in involution.

• 

This method is of little interest if the input Distribution dist is involutive, since in that case CauchyDistribution(dist) will simply return dist itself.

• 

This use of the term 'Cauchy distribution' is unrelated to its use in statistics (see Statistics[Distributions][Cauchy]).

• 

This method is associated with the Distribution object. For more detail see Overview of the Distribution object.

Examples

withLieAlgebrasOfVectorFields:

Build vector fields...

V1VectorFieldDx,space=x,y,z,w

V1x

(1)

V2VectorFieldDz,space=x,y,z,w

V2z

(2)

V3VectorFieldDy+zDw,space=x,y,z,w

V3y+zw

(3)

Construct the associated distribution...

ΣDistributionV1,V2,V3

Σz,yz+w,x

(4)

Construct Cauchy vectors...

CauchyDistributionΣ

x

(5)

IsInvolutiveΣ

false

(6)

Compatibility

• 

The CauchyDistribution command was 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)