vpotential takes two arguments : a vector field
V
in Rn with respect to n real variables
and the vector of these variable names.
vpotential returns, if it is possible, a vector U such
that curl(U)=V.
When it is possible we say that V is a conservative flux
field or a solenoidal field.
The general solution is the sum of a particular solution and of the
gradient of an arbitrary function, Xcas returns a particular
solution with zero as first component.
vpotential is the reciprocal function of curl.
Input :
^
2-4*z,-2*y*z],[x,y,z]) Output :
^
3/3-(-(4*z))*x+3*y]
In ℝ3, a vector field V is a rotationnal
if and only if it’s
divergence is zero
(divergence(V,[x,y,z])=0).
In time-independant electro-magnetism,
V= B is the magnetic field and
U= A is the potential vector.