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AreSame

check if two LAVF objects are the same

 

Calling Sequence

Parameters

Description

Examples

Compatibility

Calling Sequence

AreSame( obj1, obj2, criteria = crit)

Parameters

obj1,obj2, ...

-

LAVF objects

crit

-

(optional) a string: "sameOperator", "sameSystem", or "sameSolutions"

Description

• 

The AreSame method checks if the two LAVF objects obj1 and obj2 are the same.

• 

This method is front-end to the AreSame method of a LHPDE object. That is, let S1, S2 be the determining systems of LAVF objects L1, L2 respectively, then AreSame(L1, L2) equals AreSame(S1,S2).

• 

All optional arguments in this method will pass down to the AreSame method of a LHPDE object. See AreSame of a LHPDE object for how to apply optional arguments.

• 

In the second calling sequence, the word criterion is provided as alias for criteria.

• 

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

Examples

withLieAlgebrasOfVectorFields:

VVectorFieldξx,yDx+ηx,yDy,space=x,y

Vξx,yx+ηx,yy

(1)

VpVectorFieldαx,yDx+βxDy,space=x,y

Vpαx,yx+βxy

(2)

E2LHPDEdiffξx,y,y,y=0,diffηx,y,x=diffξx,y,y,diffηx,y,y=0,diffξx,y,x=0,indep=x,y,dep=ξ,η

E22y2ξx,y=0,xηx,y=yξx,y,yηx,y=0,xξx,y=0,indep=x,y,dep=ξx,y,ηx,y

(3)

E2pLHPDEdiffαx,y,y,y=0,diffβx,x=diffαx,y,y,diffαx,y,x=0,indep=x,y,dep=α,β

E2p2y2αx,y=0,ⅆⅆxβx=yαx,y,xαx,y=0,indep=x,y,dep=αx,y,βx

(4)

Constructing two LAVFs that are essentially E(2) but their systems are different looking..

LE2LAVFV,E2

LE2ξx,yx+ηx,yy&where2y2ξx,y=0,xξx,y=0,xηx,y=yξx,y,yηx,y=0

(5)

LE2pLAVFVp,E2p

LE2pαx,yx+βxy&where2y2αx,y=0,xαx,y=0,ⅆⅆxβx=yαx,y

(6)

The two LAVFs are the same as operators:

AreSameLE2,LE2p

true

(7)

Clearly they have different dependent variables, so the systems are not identical.

AreSameLE2,LE2p,criterion=sameSystem

false

(8)

Since they are same as operator, they definitely have the same solutions.

AreSameLE2,LE2p,criteria=sameSolutions

true

(9)

Compatibility

• 

The AreSame command was introduced in Maple 2020.

• 

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

See Also

LieAlgebrasOfVectorFields (Package overview)

LAVF (Object overview)

LieAlgebrasOfVectorFields[VectorField]

LieAlgebrasOfVectorFields[LHPDE]

LieAlgebrasOfVectorFields[LAVF]

AreSame