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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 :
Output : 
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.

giac documentation written by Renée De Graeve and Bernard Parisse