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DifferentialAlgebra[Tools]

  

ToJet

  

rewrite in jet notation a mathematical expression written in function notation

  

FromJet

  

rewrite in function notation a mathematical expression written in jet notation

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

ToJet(expr, DepVars, notation = ...)

FromJet(expr, DepVars, differentiationnotation = ...)

Parameters

expr

-

algebraic expression or equation

DepVars

-

function or list of functions indicating the dependent variables of the problem

differentiationnotation = ...

-

(optional) can be diff (default), Diff, or D; specifies the derivative notation to return

notation = ...

-

(optional) can be jet (default), tjet, diff, or Diff; specifies the jet notation to return

Description

• 

The ToJet and FromJet commands rewrite mathematical expressions back and forth using jet and function notation respectively.

• 

For ToJet, the option notation can be used to select the jet notation. The possible values are jet and tjet, respectively corresponding to the notations jetvariables and jetvariableswithbrackets explained in the help page of the equivalent PDEtools[ToJet] command.

• 

For FromJet, the option differentiationnotation can be used to select the notation used for derivatives.  The possible values are diff, Diff and D, explained in the help page of the equivalent PDEtools[FromJet] command.

Examples

withDifferentialAlgebra:-Tools,ToJet,FromJet

ToJet,FromJet

(1)

DepVarsux,t,vt,wy

DepVars:=ux,t,vt,wy

(2)

PDExux,tvtwy+2ytux,tvtwy

PDE:=xux,tvtwy+tux,tvtⅆⅆywy+ux,tⅆⅆtvtⅆⅆywy

(3)

The following is PDE in jet notation

jet_PDEToJetPDE,DepVars

jet_PDE:=uvtwy+vwux+vutwy

(4)

This is PDE in tjet notation, or jet notation with brackets

tjet_PDEToJetPDE,DepVars,notation=tjet

tjet_PDE:=u[]vtwy+utv[]wy+uxv[]w[]

(5)

You can express jet_PDE and tjet_PDE in function notation, using diff, Diff, or D for expression the derivatives. By default diff notation is used.

FromJetjet_PDE,DepVars

xux,tvtwy+tux,tvtⅆⅆywy+ux,tⅆⅆtvtⅆⅆywy

(6)

FromJetjet_PDE,DepVars,differentiationnotation='Diff'

xux,tvtwy+tux,tvtⅆⅆywy+ux,tⅆⅆtvtⅆⅆywy

(7)

FromJetjet_PDE,DepVars,differentiationnotation='D'

D1ux,tvtwy+D2ux,tvtDwy+ux,tDvtDwy

(8)

See Also

DifferentialAlgebra

PDEtools[FromJet]

PDEtools[ToJet]

 


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