### 2.50.7 Conservative flux field : `vpotential`

`vpotential` takes two arguments : a vector field
*V*
in *R*^{n} 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 ℝ^{3}, 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.