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GetRanking

get ranking of a rif-reduced LHPDEs system

 

Calling Sequence

Parameters

Description

Examples

Compatibility

Calling Sequence

GetRanking( obj)

Parameters

obj

-

a LHPDE object that is in rif-reduced form.

Description

• 

For a LHPDE object that is in rif-reduced form, the GetRanking method returns the ranking of the LHPDE object as a list (or a list of lists) of dependent variable names, if available.

• 

The method returns FAIL if the ranking is unavailable or a LHPDE object is not recorded as being in rif-reduced form.

• 

The returned output - ranking of a LHPDE object - is consistent with the ranking that is used on the DEtools[rifsimp] command. See ranking for more detail.

• 

Rif reduction refers to the differential reduction and completion algorithm performed by the Maple command DEtools[rifsimp].

• 

To rif-reduce a LHPDE object with specific ranking, see RifReduce for more detail.

• 

The ranking can be set while constructing a LHPDE object. See LieAlgebrasOfVectorFields[LHPDE] for more detail.

• 

This method is associated with the LHPDE object. For more detail, see Overview of the LHPDE object.

Examples

with(LieAlgebrasOfVectorFields):

Typesetting:-Settings(userep=true);

false

(1)

Typesetting:-Suppress([xi(x,y),eta(x,y)]);

S := LHPDE([diff(xi(x,y),x)=0, diff(eta(x,y),y)=0, diff(xi(x,y),y)+diff(eta(x,y),x)=0, diff(xi(x,y),y,y)=0, diff(eta(x,y),x,x)=0]);

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

(2)

GetRanking(S);

FAIL

(3)

Using the RifReduce method to reduce a LHPDE object with given ranking:

Sred := RifReduce(S, [xi,eta]);

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

(4)

GetRanking(Sred);

ξ,η

(5)

Specify ranking while constructing a LHPDE object:

S1 := LHPDE([diff(eta(y),y)=0,diff(xi(x),x)=0], dep=[xi,eta], indep=[x,y], inRifReducedForm=true, ranking=[eta,xi]);

S1ⅆⅆyηy=0,ⅆⅆxξx=0,indep=x,y,dep=ξx,ηy

(6)

GetRanking(S1);

η,ξ

(7)

Compatibility

• 

The GetRanking command was introduced in Maple 2020.

• 

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

See Also

LHPDE (Object overview)

LieAlgebrasOfVectorFields[LHPDE]

RifReduce

DEtools[rifsimp]