Potential : potential

### 4.51.6 Potential : potential

potential takes two arguments : a vector field 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 grad(U)=V. When it is possible, we say that V derives 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 ℝ3 a vector V is a gradient if and only if its rotational is zero i.e. if curl(V)=0. In time-independent electro-magnetism, V=E is the electric field and U is the electric potential.