Vector potential of a threedimensional vector field
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vectorPotential(j
, [x_{1}, x_{2}, x_{3}]
, <Test>)
vectorPotential(j, x)
returns the vector
potential of the vector field
with
respect to
.
This is a vector field
with
.
The vector potential of a vector function j
exists
if and only if the divergence of j
is zero. It
is uniquely determined.
If the vector potential of j
does not exist,
then vectorPotential
returns FALSE
.
If j
is a vector then the component ring
of j
must be a field (i.e., a domain of category Cat::Field
) for which definite
integration can be performed.
If j
is given as a list of three arithmetical
expressions, then vectorPotential
returns a vector
of the domain Dom::Matrix
()
.
We check if the vector function has a vector potential:
delete x, y, z: vectorPotential( [x^2*y, 1/2*y^2*x, x*y*z], [x, y, z], Test )
The answer is yes, so let us compute the vector potential of :
vectorPotential( [x^2*y, 1/2*y^2*x, x*y*z], [x, y, z] )
We check the result:
curl(%, [x, y, z])
The vector function does not have a vector potential:
vectorPotential([x^2, 2*y, z], [x, y, z])

A list of three arithmetical expressions, or a 3dimensional
vector (i.e., a 3×1 or 1
×3 matrix of a domain of category 

(indexed) identifiers 

Check whether the vector field 
Vector with three components, i.e., an 3
×1 or 1×n matrix
of a domain of category Cat::Matrix
,
or a boolean value.