vpotential takes two arguments : a vector field
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.
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.