test a given symmetry - Maple Help

Online Help

All Products    Maple    MapleSim


Home : Support : Online Help : Mathematics : Differential Equations : Lie Symmetry Method : Commands for ODEs : DEtools/symtest

DEtools[symtest] - test a given symmetry

Calling Sequence

symtest(sym, ode, y(x))

Parameters

sym

-

list of the coefficients of a symmetry generator

ode

-

ordinary differential equation

y(x)

-

(optional) indeterminate function of the ODE

Description

• 

The symtest command checks whether a given pair of infinitesimals (coefficients of the symmetry generator) leave the given ODE invariant; that is, whether the given "symmetry" is actually a symmetry of the ODE. Similar to odetest, symtest returns 0 when the result is valid or returns an algebraic expression obtained after simplifying the PDE for the infinitesimals associated with the given ODE.

• 

If the result returned by symtest is not zero, the symmetry is not necessarily wrong. Sometimes, with further simplification, you can obtain the desired 0 using commands such as expand, combine, and so on.

• 

This function is part of the DEtools package, and so it can be used in the form symtest(..) only after executing the command with(DEtools). However, it can always be accessed through the long form of the command by using DEtools[symtest](..).

Examples

An ODE with an arbitrary function F

withDEtools,symgen,symtest

symgen,symtest

(1)

ode:=ⅆⅆxyx=Fyxxlnxx+lnx

ode:=ⅆⅆxyx=Fyxxlnxx+lnx

(2)

A pair of infinitesimals for the ODE above

sym:=symgenode

sym:=_ξ=x,_η=x+y

(3)

Testing these infinitesimals

symtestsym,ode

0

(4)

A second order ODE

ode:=ⅆ2ⅆx2yx=1_F1ⅆⅆxyxxyxyxx2

ode:=ⅆ2ⅆx2yx=_F1ⅆⅆxyxxyxyxx2

(5)

sym:=symgenode

sym:=_ξ=0,_η=y,_ξ=x,_η=0

(6)

mapsymtest,sym,ode

0,0

(7)

See Also

DEtools, dsolve,Lie, equinv, PDEtools, symgen


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