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6.21.6  Potential: potential

Recall that a vector field F is conservative if there is a scalar-valued function f such that grad f=F. In this case, f is called a potential of F, and is only determined up to a constant.

The potential command computes the potential of a vector field, or signals an error if the vector field is not conservative.

Note that potential is the reciprocal function of derive.


Example.
Input:

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

Output:

x2 y+3 x−4 y z


Note that in ℝ3, a vector field F is conservative if and only if its curl is zero; i.e., if curlF=0. In time-independent electro-magnetism, F=E is the electric field and f is the electric potential.


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