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## Conservative flux field : vpotential

vpotential takes two arguments : a vector field in Rn with respect to n real variables and the vector of these variable names.
vpotential returns, if it is possible, a vector such that . When it is possible we say that 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 :
vpotential([2*x*y+3,x^2-4*z,-2*y*z],[x,y,z])
Output :
[0,(-(2*y))*z*x,-x^3/3-(-(4*z))*x+3*y]
In 3, a vector field is a rotationnal if and only if it's divergence is zero
(divergence(V,[x,y,z])=0). In time-independant electro-magnetism, = is the magnetic field and = is the potential vector.

giac documentation written by Renée De Graeve and Bernard Parisse