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detools::hasPotential -- check for gradient vector field

Introduction

detools::hasPotential(vf,x) checks whether the vector field vf in the coordinates x is the gradient of some potential.

Call(s)

detools::hasPotential(vf, x)

Parameters

vf - the vector field: a list of expressions; its length must be the same as that of the list x.
x - the coordinates: a list of (indexed) identifiers.

Returns

a list of expressions; each component represents an integrability condition which must be satisfied for the vector field vf to possess a potential. If the list is empty, vf is unconditionally a gradient.

Related Functions

detools::hasHamiltonian

Details

Example 1

With the following input one can determine the condition on the components of a two-dimensional vector field so that the field is a gradient.

>> detools::hasPotential([F(x, y), G(x, y)], [x, y])
                   [diff(F(x, y), y) - diff(G(x, y), x)]



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