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
IsRifReduced( obj)
IsTotalDegreeRanking( obj)
obj
-
a LHPDE object
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.
withLieAlgebrasOfVectorFields:
Typesetting:-Suppressξx,y,ηx,y:
Typesetting:-Settingsuserep=true:
S≔LHPDEdiffξx,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
S≔ξy,y=0,ηx+ξy=0,ηy=0,ξx=0,ηx,x=0,indep=x,y,dep=ξ,η
S≔RifReduceS
S≔ξy,y=0,ξx=0,ηx=−ξy,ηy=0,indep=x,y,dep=ξ,η
IsRifReducedS
true
IsTotalDegreeRankingS
The status of S1 for being a rif-reduced form is not known:
S1≔LHPDEdiffξx,y,x=0,ηx,y=0,indep=x,y,dep=ξ,η
S1≔ξx=0,η=0,indep=x,y,dep=ξ,η
Therefore, information will not be available..
IsRifReducedS1
FAIL
IsTotalDegreeRankingS1
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
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