VectorCalculus
eval
evaluation for Vectors
Calling Sequence
Parameters
Description
Examples
eval(v, t=a)
eval(v, eqns)
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
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.
with⁡VectorCalculus:
Evaluating free Vectors
1,t,t2t=1|1,t,t2t=1
v1 ≔ Vector⁡x,y2,z3,coords=cartesianx,y,z
eval⁡v1,x=1,y=2,z=3
Evaluating rooted Vectors: both the root point and the components are evaluated.
v2 ≔ RootedVector⁡point=u,Pi,u,v,polarr,t
v2≔uv
v2u=1,v=2|v2u=1,v=2
12
GetRootPoint⁡eval⁡v2,u=1,v=2
If the components have no variables then the root point is evaluated.
v3 ≔ RootedVector⁡point=s,t,1,2,parabolicu,v
v3≔12
v3s=1,t=Pi|v3s=1,t=Pi
GetRootPoint⁡eval⁡v3
If the root point has no variables then the components are evaluated.
v4 ≔ RootedVector⁡point=1,Pi4,Pi4,u,v,w,sphericalr,p,t
v4≔uvw
v4u=1,v=−1,w=1|v4u=1,v=−1,w=1
1−11
GetRootPoint⁡v4
Evaluating position Vectors
pv1 ≔ PositionVector⁡t,t,polar
pv1≔t⁢cos⁡tt⁢sin⁡t
pv1t=3|pv1t=3
pv2 ≔ PositionVector⁡t,v1+t2,v⁢t1+t2,cartesianx,y,z
pv2≔tvt2+1v⁢tt2+1
pv2t=3,v=4|pv2t=3,v=4
Evaluating VectorFields: eval evaluates the components and returns a VectorField.
vf ≔ VectorField⁡1r2,0,0,sphericalr,p,t
vfr=1|vfr=1
attributes⁡vfr=1|vfr=1
vectorfield,coords=sphericalr,p,t
See Also
VectorCalculus[evalVF]
VectorCalculus[PositionVector]
VectorCalculus[RootedVector]
VectorCalculus[Vector]
VectorCalculus[VectorField]
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