liesymm - Maple Help

Online Help

All Products    Maple    MapleSim


Home : Support : Online Help : Mathematics : Differential Equations : Lie Symmetry Method : liesymm : liesymm/Eta

liesymm

  

Eta

  

Compute the coefficients of the generator of a finite point transformation

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

Eta(f, x)

Eta[1](f, x)

Eta[2](f, x, y)

Eta[3](f, x, y, z)

Parameters

f

-

named partial in the sense of depvars()

x, y, z

-

Independent variable in the sense of indepvars()

Description

• 

This is a special differential operator defined in terms of TD. The result is an inert expression reported in terms of Diff procedure.  The result can be forced to evaluate further by use of dvalue() or value(), but any variable dependencies for unknown functions must be defined prior to such evaluation. Such variable dependencies can be explicitly specified by use of vfix().

• 

It arises in the course of extending the generator for the finite point transformations to the partial derivatives and is in fact computes the coefficient of the various partials in that generator.

• 

This routine is part of the liesymm package and is ordinarily loaded via with(liesymm). It can also be called via the ``package style'' name liesymm[Eta].

Examples

withliesymm:

indepvarsx,y

x,y

(1)

depvarsf,g

f,g

(2)

Ηf,x

xV3+w1fV3+w3gV3w1xV1+w1fV1+w3gV1w2xV2+w1fV2+w3gV2

(3)

w1=Difftranslatew1

w1=xf

(4)

Η[2]g,x,y

yxV4+w1fV4+w3gV4w3xV1+w1fV1+w3gV1w4xV2+w1fV2+w3gV2+w2fxV4+w1fV4+w3gV4w3xV1+w1fV1+w3gV1w4xV2+w1fV2+w3gV2+w4gxV4+w1fV4+w3gV4w3xV1+w1fV1+w3gV1w4xV2+w1fV2+w3gV2+w6w1xV4+w1fV4+w3gV4w3xV1+w1fV1+w3gV1w4xV2+w1fV2+w3gV2+w8w2xV4+w1fV4+w3gV4w3xV1+w1fV1+w3gV1w4xV2+w1fV2+w3gV2+w10w3xV4+w1fV4+w3gV4w3xV1+w1fV1+w3gV1w4xV2+w1fV2+w3gV2+w12w4xV4+w1fV4+w3gV4w3xV1+w1fV1+w3gV1w4xV2+w1fV2+w3gV2w9yV1+w2fV1+w4gV1+w6w1V1+w8w2V1+w10w3V1+w12w4V1w10yV2+w2fV2+w4gV2+w6w1V2+w8w2V2+w10w3V2+w12w4V2

(5)

See Also

liesymm

liesymm[setup]

with

 


Download Help Document

Was this information helpful?



Please add your Comment (Optional)
E-mail Address (Optional)
What is ? This question helps us to combat spam