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AdjustDependencies

adjust dependencies in a LHPDEs system

 

Calling Sequence

Parameters

Description

Examples

Compatibility

Calling Sequence

AdjustDependencies( obj, dep = vars)

Parameters

obj

-

a LHPDE object that is in rif-reduced form (see RifReduce)

vars

-

(optional) either the strings "least" or "full", or a list of functions or names

Description

• 

The AdjustDependencies method adjusts dependencies in a LHPDE object. It returns a new LHPDE object with specified dependencies.

• 

The call AdjustDependencies(obj, dep = "least") returns a new LHPDE object whose dependent variables have smallest possible dependencies on the independent variables of obj.

• 

The call AdjustDependencies(obj, dep = "full") returns a new LHPDE object whose dependent variables depend on all the independent variables of obj.

• 

If the optional argument dep =  vars is specified with vars being a list of functions or names then it represents new dependencies that are to be adjusted in a LHPDEs system.

• 

The call AdjustDependencies(S) is equivalent to the call AdjustDependencies(S, dep = "least").

• 

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

Examples

withLieAlgebrasOfVectorFields:

Typesetting:-Settingsuserep=true:

SLHPDEdiffξx,y,y,y=0,diffξx,y,x=0,diffξx,y,y=diffηx,x,indep=x,y,dep=ξx,y,ηx

S2y2ξx,y=0,xξx,y=0,yξx,y=ⅆⅆxηx,indep=x,y,dep=ξx,y,ηx

(1)

Adjust the dependent variables to have the smallest possible dependencies on the independent variables (x,y).

S1AdjustDependenciesS

S1ⅆ2ⅆy2ξy=0,ⅆⅆyξy=ⅆⅆxηx,indep=x,y,dep=ξy,ηx

(2)

When dep= is specified as list of functions or names, only those dependent variables with new dependencies are required.

AdjustDependenciesS,dep=ξy

ⅆ2ⅆy2ξy=0,ⅆⅆyξy=ⅆⅆxηx,indep=x,y,dep=ξy,ηx

(3)

Adjust the dependent variables to depend on all independent variables.

S2AdjustDependenciesS,dep=full

S22y2ξx,y=0,xξx,y=0,yξx,y=xηx,y,yηx,y=0,indep=x,y,dep=ξx,y,ηx,y

(4)

S3AdjustDependenciesS,dep=ξy,ηx,y

S3ⅆ2ⅆy2ξy=0,ⅆⅆyξy=xηx,y,yηx,y=0,indep=x,y,dep=ξy,ηx,y

(5)

Any invalid adjustment to the dependencies will trigger an error. For example, xi has to depend at least on y.

AdjustDependenciesS,dep=ξ

Error, (in LieAlgebrasOfVectorFields:-LHPDE:-AdjustDependencies) invalid input: dependencies must be at least xi(y)

Note: the second argument dep = [xi] specifies the dependent variable xi to have no dependencies (i.e. to be a constant). These four LHPDEs should be essentially the same (i.e. they have same LHPDOs).

AreSameS,S1

true

(6)

AreSameS1,S2

true

(7)

AreSameS2,S3

true

(8)

Compatibility

• 

The AdjustDependencies 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]

AreSame