Potential : potential

potential takes two arguments : a vector field $\overrightarrow{V}$ in Rⁿ with respect to n real variables and the vector of these variable names.
potential returns, if it is possible, a function U such that $\overrightarrow{\mbox{grad}}(U)=\overrightarrow{V}$. When it is possible we say that $\overrightarrow{V}$ derive of the potential U, and U is defined up to a constant.
potential is the reciprocal function of derive.
Input :

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

Output :

2*y*x^2/ 2+3*x+(x^2-4*z-2*x^2/2)*y

Note that in $\mathbb {R}$³ a vector $\overrightarrow{V}$ is a gradient if and only if it's rotationnal is zero i.e. if curl(V)=0. In time-independant electro-magnetism, $\overrightarrow{V}$= $\overrightarrow{E}$ is the electric field and U is the electric potential.