Vector potential of a three-dimensional vector field
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[x1, x2, x3], <Test>)
vectorPotential(j, x) returns the vector
potential of the vector field
This is a vector field
The vector potential of a vector function
if and only if the divergence of
j is zero. It
is uniquely determined.
If the vector potential of
j does not exist,
j is a vector then the component ring
j must be a field (i.e., a domain of category
Cat::Field) for which definite
integration can be performed.
j is given as a list of three arithmetical
vectorPotential returns a vector
of the domain
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 3-dimensional
vector (i.e., a 3×1 or 1
×3 matrix of a domain of category
Check whether the vector field
Vector with three components, i.e., an 3
×1 or 1×n matrix
of a domain of category
or a boolean value.