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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 :
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.

giac documentation written by Renée De Graeve and Bernard Parisse