g=applyVectorField(M,f)
g=applyVectorField(V,f)
L=applyVectorField(M,l)
L=applyVectorField(V,l)
J=applyVectorField(m,f)
J=applyVectorField(m,I)
Apply the vector field(s) represented by M, V, or m, to the second parameter, that is, use the vector field(s) as differential operator(s).
When the first parameter is a Matrix or a Vector, then the return type matches the second parameter. If that is a RingElement, then there must only be 1 column in the matrix. When the second parameter is a List l of RingElements, then the returned List is formed by applying each vector field in turn to the first entry of l, then each vector field to the second entry of l, etc.
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When the first parameter is a Module, then the return type is an Ideal. Applying a Module to a RingElement gives the Ideal generated by applying each generator to the function. Applying a Module to an Ideal I produces the Ideal generated by applying every element of the module to every element of I; this is generated by not only the functions formed by applying each generator of the module to each generator of I (as might be computed by the (Matrix,List) version of this function), but also I times the ideal of coefficients of the generators of the module.
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The object applyVectorField is a method function.