LieAlgebrasOfVectorFields[EliminationSystem] - Maple Programming Help

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LieAlgebrasOfVectorFields[EliminationSystem]

construct a LHPDE object that only contain some specific variables from a given DEs system.

EliminationSystem

construct a LHPDE object that only contain some specific variables from a given LHPDE object

 

Calling Sequence

Parameters

Description

Examples

Compatibility

Calling Sequence

EliminationSystem(system, dvars, varsToKeep, indep = ivars)

EliminationSystem(obj, varsToKeep)

Parameters

system

-

a list or set of linear homogeneous PDEs or ODEs

dvars

-

a list of dependent variables from the system, as functions or names

varsToKeep

-

a list of dependent variable names that are to be kept after elimination in the system

ivars

-

(optional) a list of independent variables from the system

obj

-

a LHPDE object

Description

• 

The EliminationSystem command finds a LHPDE object that only contain some specific variables from a given LHPDEs system.

• 

The command returns a LHPDE object that is in rif-reduced form (see IsRifReduced), and with varsToKeep as the dependent variables.

• 

The command computes a differentially reduced form for the elimination module with respect to some specific variables, this is achieved by performing rif-reduce on a LHPDE object (see RifReduce) with a block ranking.

• 

In the first sequence, the command is part of the LieAlgebrasOfVectorFields package. For more detail, see Overview of the LieAlgebrasOfVectorFields package.

• 

This command can be used in the form LHPDE(...) only after executing the command with(LieAlgebrasOfVectorFields), but can always be used by executing LieAlgebrasOfVectorFields:-LHPDE(...).

• 

The second calling sequence is an extension of the first, so that the command works for a LHPDE object. That is, a call EliminationSystem(obj, varsToKeep) is equivalent to EliminationSystem(GetSystem(obj), GetDependents(obj), varsToKeep, indep = GetIndependents(obj)).

• 

In the second calling sequence, the method is associated with the LHPDE object. For more detail, see Overview of the LHPDE object.

Examples

withLieAlgebrasOfVectorFields:

Typesetting:-Settingsuserep=true:

Typesetting:-Suppressη,ξx,y:

DEsdiffξx,y,x=0,diffηx,y,y=0,diffξx,y,y+diffηx,y,x=0,diffξx,y,y,y=0,diffηx,y,x,x=0

DEsξx=0,ηy=0,ξy+ηx=0,ξy,y=0,ηx,x=0

(1)

The variable eta is eliminated from the system. The system only contains xi.

EliminationSystemDEs,ξx,y,ηx,y,ξ

ξy,y=0,ξx=0,indep=x,y,dep=ξ

(2)

SLHPDEDEs,dep=ξ,η,indep=x,y

Sξx=0,ηy=0,ξy+ηx=0,ξy,y=0,ηx,x=0,indep=x,y,dep=ξ,η

(3)

Similar output, but the input argument is now a LHPDE object.

EliminationSystemS,ξ

ξy,y=0,ξx=0,indep=x,y,dep=ξ

(4)

Compatibility

• 

The LieAlgebrasOfVectorFields[EliminationSystem] and EliminationSystem commands were introduced in Maple 2020.

• 

For more information on Maple 2020 changes, see Updates in Maple 2020.

See Also

LieAlgebrasOfVectorFields

LHPDE (Object overview)

LieAlgebrasOfVectorFields[LHPDE]

IsRifReduced

RifReduce