Conservative flux field : vpotential

vpotential takes two arguments : a vector field $\overrightarrow{V}$ in Rⁿ with respect to n real variables and the vector of these variable names.
vpotential returns, if it is possible, a vector $\overrightarrow{U}$ such that $\overrightarrow{\mbox{curl}}(\overrightarrow{U})=\overrightarrow{V}$. When it is possible we say that $\overrightarrow{V}$ 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 $\mathbb {R}$³, a vector field $\overrightarrow{V}$ is a rotationnal if and only if it's divergence is zero
(divergence(V,[x,y,z])=0). In time-independant electro-magnetism, $\overrightarrow{V}$= $\overrightarrow{B}$ is the magnetic field and $\overrightarrow{U}$= $\overrightarrow{A}$ is the potential vector.