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Intersection

find a LAVF object whose solution space is the intersection of solution spaces of given LAVF objects.

 

Calling Sequence

Parameters

Description

Examples

Compatibility

Calling Sequence

Intersection( L1, L2, ..., depname = vars )

Parameters

L1, L2, ...

-

a sequence of LAVF objects living on the same space

vars

-

(optional) a list of new dependent variable names

Description

• 

Let L1,L2, ... be a sequence of LAVF objects living on the same space (see AreSameSpace). The Intersection method returns a new LAVF object whose solution space is the intersection of solutions of L1,L2,....

• 

By default, the dependent variable names of the returned object are taken from L1. The dependent variable names will be vars if the optional argument depnames = vars is specified.

• 

This method is front-end to the corresponding method of a LHPDE object. That is, let S1, S2,...  be the determining systems of L1,L2,...  (i.e. Si = GetDeterminingSystem(Li)), then the call Intersection(L1,L2,..) is equivalent to Intersection(S1,S2,..). All remaining input arguments will be passed down to its determining system level. See the method Intersection of a LHPDE object for more detail.

• 

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

Examples

with(LieAlgebrasOfVectorFields):

Typesetting:-Settings(userep=true):

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

X := VectorField(xi(x,y)*D[x] + eta(x,y)*D[y], space = [x,y]);

Xξx+ηy

(1)

The determining system for 2-dim Euclidean

E2:= 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], indep = [x,y], dep = [xi,eta]);

E2ξx=0,ηy=0,ξy+ηx=0,ξy,y=0,ηx,x=0,indep=x,y,dep=ξ,η

(2)

The determining system for 2-dim translations

T2 := LHPDE([diff(xi(x,y),x) = 0, diff(xi(x,y),y)=0, diff(eta(x,y),x) = 0, diff(eta(x,y),y)=0], indep = [x,y], dep = [xi,eta]);

T2ξx=0,ξy=0,ηx=0,ηy=0,indep=x,y,dep=ξ,η

(3)

We first construct LAVFs for E(2) and T(2)

LE2 := LAVF(X,E2);

LE2ξx+ηy&whereξy,y=0,ξx=0,ηx=ξy,ηy=0

(4)

LT2 := LAVF(X,T2);

LT2ξx+ηy&whereξx=0,ηx=0,ξy=0,ηy=0

(5)

Intersection(LE2,LT2);

ξx+ηy&whereξx=0,ηx=0,ξy=0,ηy=0

(6)

Intersection(LE2, LT2, depname = [alpha, beta]);

αx,yx+βx,yy&wherexαx,y=0,xβx,y=0,yαx,y=0,yβx,y=0

(7)

Compatibility

• 

The Intersection 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]

AreSameSpace

Intersection