Conservative flux field : vpotential

### 2.50.7 Conservative flux field : `vpotential`

`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 :

`vpotential([2*x*y+3,x```^```2-4*z,-2*y*z],[x,y,z])`

Output :

`[0,(-(2*y))*z*x,-x```^```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.