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VectorCalculus

  

eval

  

evaluation for Vectors

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

eval(v, t=a)

eval(v, eqns)

Parameters

v

-

Vector(algebraic); Vector or algebraic expression

t

-

name; usually a name but may be a general expression

a

-

expression

eqns

-

list or set; list or set of equations

Description

• 

The eval(v, eqns) command is an extension of the top-level eval command which correctly evaluates free Vectors , rooted Vectors, position Vectors, and VectorFields for the VectorCalculus package.  If v is not a Vector, the arguments are passed to the top level eval command.

• 

If v is a rooted Vector then both the root point or origin and the components, corresponding to the coefficients of the basis vectors, are evaluated.

• 

If v is a VectorField, then the components are evaluated and a VectorField is returned. To properly evaluate a VectorField at a point use evalVF.

• 

If v is a free Vector or a position Vector, then the components are evaluated. The type of the Vector does not change.

Examples

withVectorCalculus:

Evaluating free Vectors

eval1,t,t2,t=1

1ex+1ey+1ez

(1)

v1Vectorx,y2,z3,coords=cartesianx,y,z

v1xex+y2ey+z3ez

(2)

evalv1,x=1,y=2,z=3

1ex+4ey+27ez

(3)

Evaluating rooted Vectors: both the root point and the components are evaluated.

v2RootedVectorpoint=u,π,u,v,polarr,t

v2uv

(4)

evalv2,u=1,v=2

12

(5)

GetRootPointevalv2,u=1,v=2

1er+πet

(6)

If the components have no variables then the root point is evaluated.

v3RootedVectorpoint=s,t,1,2,parabolicu,v

v312

(7)

evalv3,s=1,t=π

12

(8)

GetRootPointevalv3

seu+tev

(9)

If the root point has no variables then the components are evaluated.

v4RootedVectorpoint=1,π4,π4,u,v,w,sphericalr,p,t

v4uvw

(10)

evalv4,u=1,v=1,w=1

1−11

(11)

GetRootPointv4

1er+π4ep+π4et

(12)

Evaluating position Vectors

pv1PositionVectort,t,polar

pv1tcosttsint

(13)

evalpv1,t=3

3cos33sin3

(14)

pv2PositionVectort,vsqrt1+t2,vtsqrt1+t2,cartesianx,y,z

pv2tvt2+1vtt2+1

(15)

evalpv2,t=3,v=4

321056105

(16)

Evaluating VectorFields: eval evaluates the components and returns a VectorField.

vfVectorField1r2,0,0,sphericalr,p,t

vf1r2e_r+0e_p+0e_t

(17)

evalvf,r=1

1e_r+0e_p+0e_t

(18)

attributesevalvf,r=1

vectorfield,coords=sphericalr,p,t

(19)

See Also

eval

VectorCalculus

VectorCalculus[evalVF]

VectorCalculus[PositionVector]

VectorCalculus[RootedVector]

VectorCalculus[Vector]

VectorCalculus[VectorField]