construct the canonical projection map between jet spaces of a fiber bundle - Maple Help

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JetCalculus[ProjectionTransformation] - construct the canonical projection map between jet spaces of a fiber bundle

Calling Sequences

    ProjectionTransformation(n, m)

Parameters

     n         - a non-negative integer, the order for the domain jet space

     m         - a non-negative integer, the order for the range jet space, m n

 

Description

Examples

Description

• 

Let π: EM be a fiber bundle.Then ProjectionTransformation(n, m) defines the canonical projection map of the jet space JnE to JmE. 

• 

The command ProjectionTransformation is part of the DifferentialGeometry:-JetCalculus package. It can be used in the form ProjectionTransformation(...) only after executing the commands with(DifferentialGeometry) and with(JetCalculus), but can always be used by executing DifferentialGeometry:-JetCalculus:-ProjectionTransformation(...).

Examples

withDifferentialGeometry:withJetCalculus:

 

Example 1.

Define the 6-th order jet bundle J6E for E = ℝ2 ×ℝ with coordinates x,y, u x,y. 

DGsetupx,y,u,E,6:

 

Define the canonical projection from J6(E) to J3E.

E > 

Π1ProjectionTransformation6,3

Π1:=x=x,y=y,u=u,u1=u1,u2=u2,u1,1=u1,1,u1,2=u1,2,u2,2=u2,2,u1,1,1=u1,1,1,u1,1,2=u1,1,2,u1,2,2=u1,2,2,u2,2,2=u2,2,2

(2.1)
E > 

Tools:-DGinfoΠ1,DomainFrame,Tools:-DGinfoΠ1,DomainOrder

E,6

(2.2)
E > 

Tools:-DGinfoΠ1,RangeFrame,Tools:-DGinfoΠ1,RangeOrder

E,3

(2.3)

See Also

DifferentialGeometry

JetCalculus

DGinfo

Pullback

Transformation

 


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