### 2.50.6 Potential : `potential`

`potential` takes two arguments : a vector field
*V* in *R*^{n} 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* 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 ℝ^{3}
a vector *V* is a gradient if and only if it’s
rotationnal is zero i.e. if `curl(V)=0`.
In time-independant electro-magnetism,
*V*=*E* is the
electric field and *U* is the electric potential.