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IsRifReduced

check if a LHPDEs system is in rif-reduced form

IsTotalDegreeRanking

check if a LHPDEs system is rif-reduced with respect to a total degree ranking

 

Calling Sequence

Parameters

Description

Examples

Compatibility

Calling Sequence

IsRifReduced( obj)

IsTotalDegreeRanking( obj)

Parameters

obj

-

a LHPDE object

Description

• 

The IsRifReduced method returns true if a LHPDE object is in rif-reduced form, false otherwise. It returns FAIL if the status is unknown.

• 

Let S be a LHPDE object. The IsTotalDegreeRanking method checks if S is rif-reduced with respect to a total degree ranking (see ranking for more detail). It returns FAIL if S is not in rif-reduced form.

• 

For setting a LHPDEs system as being in a rif-reduced form, see LieAlgebrasOfVectorFields[LHPDE]. And, to rif-reduce a LHPDE object, see the RifReduce method.

• 

These methods are associated with the LHPDE object. For more detail, see Overview of the LHPDE object.

Examples

withLieAlgebrasOfVectorFields:

Typesetting:-Suppressξx,y,ηx,y:

Typesetting:-Settingsuserep=true:

SLHPDEdiffξx,y,y,y=0,diffηx,y,x+diffξx,y,y=0,diffηx,y,y=0,diffξx,y,x=0,diffηx,y,x,x=0,indep=x,y,dep=ξ,η

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

(1)

SRifReduceS

Sξy,y=0,ξx=0,ηx=ξy,ηy=0,indep=x,y,dep=ξ,η

(2)

IsRifReducedS

true

(3)

IsTotalDegreeRankingS

true

(4)

The status of S1 for being a rif-reduced form is not known:

S1LHPDEdiffξx,y,x=0,ηx,y=0,indep=x,y,dep=ξ,η

S1ξx=0,η=0,indep=x,y,dep=ξ,η

(5)

Therefore, information will not be available..

IsRifReducedS1

FAIL

(6)

IsTotalDegreeRankingS1

FAIL

(7)

Compatibility

• 

The IsRifReduced and IsTotalDegreeRanking commands were introduced in Maple 2020.

• 

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

See Also

LHPDE (Object overview)

LieAlgebrasOfVectorFields[LHPDE]

RifReduce

ranking